// Giac integration test file: all independant
// "nock" in position 2 means we do not check the antiderivative, position displayed is line-5
I:=i;
testname:="ind";        
lst:=[ // Apostol
[(1+2*x)^(1/2),x,1,1/3*(1+2*x)^(3/2),1],
[x*(1+3*x)^(1/2),x,2,-2/27*(1+3*x)^(3/2)+2/45*(1+3*x)^(5/2),1],
[x^2*(1+x)^(1/2),x,2,2/3*(1+x)^(3/2)-4/5*(1+x)^(5/2)+2/7*(1+x)^(7/2),1],
[x/(2-3*x)^(1/2),x,2,2/27*(2-3*x)^(3/2)-4/9*(2-3*x)^(1/2),1],
[(1+x)/(x^2+2*x+2)^3,x,1,-1/4/(x^2+2*x+2)^2,1],
[sin(x)^3,x,2,-cos(x)+1/3*cos(x)^3,1],
[(-1+z)^(1/3)*z,z,2,3/4*(-1+z)^(4/3)+3/7*(-1+z)^(7/3),1],
[cos(x)/sin(x)^3,x,2,-1/2*csc(x)^2,1],
[cos(2*x)*(4-sin(2*x))^(1/2),x,2,-1/3*(4-sin(2*x))^(3/2),1],
[sin(x)/(3+cos(x))^2,x,2,1/(3+cos(x)),1],
[sin(x)/(cos(x)^3)^(1/2),x,3,2*cos(x)/(cos(x)^3)^(1/2),1],
[sin((1+x)^(1/2))/(1+x)^(1/2),x,3,-2*cos((1+x)^(1/2)),1],
[x^(-1+n)*sin(x^n),x,2,-cos(x^n)/n,1],
[x^5/(-x^6+1)^(1/2),x,1,-1/3*(-x^6+1)^(1/2),1],
[t*(1+t)^(1/4),t,2,-4/5*(1+t)^(5/4)+4/9*(1+t)^(9/4),1],
[1/(x^2+1)^(3/2),x,1,x/(x^2+1)^(1/2),1],
[x^2*(8*x^3+27)^(2/3),x,1,1/40*(8*x^3+27)^(5/3),1],
[(cos(x)+sin(x))/(-cos(x)+sin(x))^(1/3),x,1,3/2*(-cos(x)+sin(x))^(2/3),1],
[x/(1+x^2+(x^2+1)^(3/2))^(1/2),x,3,2*((x^2+1)*(1+(x^2+1)^(1/2)))^(1/2)/(x^2+1)^(1/2),1],
[x/(x^2+1)^(1/2)/(1+(x^2+1)^(1/2))^(1/2),x,1,2*(1+(x^2+1)^(1/2))^(1/2),1],
[(x^2-2*x+1)^(1/5)/(1-x),x,2,-5/2*(x^2-2*x+1)^(1/5),1],
[x*sin(x),x,2,-x*cos(x)+sin(x),1],
[x^2*sin(x),x,3,2*cos(x)-x^2*cos(x)+2*x*sin(x),1],
[x^3*cos(x),x,4,-6*cos(x)+3*x^2*cos(x)-6*x*sin(x)+x^3*sin(x),1],
[x^3*sin(x),x,4,6*x*cos(x)-x^3*cos(x)-6*sin(x)+3*x^2*sin(x),1],
[cos(x)*sin(x),x,2,1/2*sin(x)^2,1],
[x*cos(x)*sin(x),x,3,-1/4*x+1/4*cos(x)*sin(x)+1/2*x*sin(x)^2,1],
[sin(x)^2,x,2,1/2*x-1/2*cos(x)*sin(x),1],
[sin(x)^3,x,2,-cos(x)+1/3*cos(x)^3,1],
[sin(x)^4,x,3,3/8*x-3/8*cos(x)*sin(x)-1/4*cos(x)*sin(x)^3,1],
[sin(x)^5,x,2,-cos(x)+2/3*cos(x)^3-1/5*cos(x)^5,1],
[sin(x)^6,x,4,5/16*x-5/16*cos(x)*sin(x)-5/24*cos(x)*sin(x)^3-1/6*cos(x)*sin(x)^5,1],
[x*sin(x)^2,x,2,1/4*x^2-1/2*x*cos(x)*sin(x)+1/4*sin(x)^2,1],
[x*sin(x)^3,x,3,-2/3*x*cos(x)+2/3*sin(x)-1/3*x*cos(x)*sin(x)^2+1/9*sin(x)^3,1],
[x^2*sin(x)^2,x,4,-1/4*x+1/6*x^3+1/4*cos(x)*sin(x)-1/2*x^2*cos(x)*sin(x)+1/2*x*sin(x)^2,1],
[cos(x)^2,x,2,1/2*x+1/2*cos(x)*sin(x),1],
[cos(x)^3,x,2,sin(x)-1/3*sin(x)^3,1],
[cos(x)^4,x,3,3/8*x+3/8*cos(x)*sin(x)+1/4*cos(x)^3*sin(x),1],
[(a^2-x^2)^(5/2),x,5,5/24*a^2*x*(a^2-x^2)^(3/2)+1/6*x*(a^2-x^2)^(5/2)+5/16*a^6*arctan(x/(a^2-x^2)^(1/2))+5/16*a^4*x*(a^2-x^2)^(1/2),1],
[x^5/(x^2+5)^(1/2),x,3,-10/3*(x^2+5)^(3/2)+1/5*(x^2+5)^(5/2)+25*(x^2+5)^(1/2),1],
[t^3/(t^3+4)^(1/2),t,2,2/5*t*(t^3+4)^(1/2)-8/15*2^(2/3)*(2^(2/3)+t)*EllipticF((t+2^(2/3)*(1-3^(1/2)))/(t+2^(2/3)*(1+3^(1/2))),I*3^(1/2)+2*I)*(1/2*6^(1/2)+1/2*2^(1/2))*((2*2^(1/3)-2^(2/3)*t+t^2)/(t+2^(2/3)*(1+3^(1/2)))^2)^(1/2)*3^(3/4)/(t^3+4)^(1/2)/((2^(2/3)+t)/(t+2^(2/3)*(1+3^(1/2)))^2)^(1/2),1],
[tan(x)^2,x,2,-x+tan(x),1],
[tan(x)^4,x,3,x-tan(x)+1/3*tan(x)^3,1],
[cot(x)^2,x,2,-x-cot(x),1],
[cot(x)^4,x,3,x+cot(x)-1/3*cot(x)^3,1],
[(2+3*x)*sin(5*x),x,2,-1/5*(2+3*x)*cos(5*x)+3/25*sin(5*x),1],
[x*(x^2+1)^(1/2),x,1,1/3*(x^2+1)^(3/2),1],
[x*(x^2-1)^9,x,1,1/20*(-x^2+1)^10,1],
[(3+2*x)/(7+6*x)^3,x,1,-1/8*(3+2*x)^2/(7+6*x)^2,1],
[x^4*(x^5+1)^5,x,1,1/30*(x^5+1)^6,1],
[(1-x)^20*x^4,x,2,-1/21*(1-x)^21+2/11*(1-x)^22-6/23*(1-x)^23+1/6*(1-x)^24-1/25*(1-x)^25,1],
[sin(1/x)/x^2,x,2,cos(1/x),1],
[sin((-1+x)^(1/4)),x,5,24*(-1+x)^(1/4)*cos((-1+x)^(1/4))-4*(-1+x)^(3/4)*cos((-1+x)^(1/4))-24*sin((-1+x)^(1/4))+12*sin((-1+x)^(1/4))*(-1+x)^(1/2),1],
[x*cos(x^2)*sin(x^2),x,1,1/4*sin(x^2)^2,1],
[sin(2*x)*(1+3*cos(x)^2)^(1/2),x,3,-2/9*(4-3*sin(x)^2)^(3/2),1],
[1/(2+3*x),x,1,1/3*ln(2+3*x),1],
[ln(x)^2,x,2,2*x-2*x*ln(x)+x*ln(x)^2,1],
[x*ln(x),x,1,-1/4*x^2+1/2*x^2*ln(x),1],
[x*ln(x)^2,x,2,1/4*x^2-1/2*x^2*ln(x)+1/2*x^2*ln(x)^2,1],
[1/(1+t),t,1,ln(1+t),1],
[cot(x),x,1,ln(sin(x)),1],
[x^n*ln(a*x),x,1,-x^(1+n)/(1+n)^2+x^(1+n)*ln(a*x)/(1+n),1],
[x^2*ln(x)^2,x,2,2/27*x^3-2/9*x^3*ln(x)+1/3*x^3*ln(x)^2,1],
[1/x/ln(x),x,2,ln(ln(x)),1],
[ln(1-t)/(1-t),t,2,-1/2*ln(1-t)^2,1],
[ln(x)/x/(1+ln(x))^(1/2),x,3,2/3*(1+ln(x))^(3/2)-2*(1+ln(x))^(1/2),1],
[x^3*ln(x)^3,x,3,-3/128*x^4+3/32*x^4*ln(x)-3/16*x^4*ln(x)^2+1/4*x^4*ln(x)^3,1],
[exp(x^3)*x^2,x,1,1/3*exp(x^3),1],
[2^(x^(1/2))/x^(1/2),x,1,2^(1+x^(1/2))/ln(2),1],
[exp(2*sin(x))*cos(x),x,2,1/2*exp(2*sin(x)),1],
[exp(x)*sin(x),x,1,-1/2*exp(x)*cos(x)+1/2*exp(x)*sin(x),1],
[exp(x)*cos(x),x,1,1/2*exp(x)*cos(x)+1/2*exp(x)*sin(x),1],
[1/(1+exp(x)),x,4,x-ln(1+exp(x)),1],
[exp(x)*x,x,2,-exp(x)+exp(x)*x,1],
[x/exp(x),x,2,-1/exp(x)-x/exp(x),1],
[exp(x)*x^2,x,3,2*exp(x)-2*exp(x)*x+exp(x)*x^2,1],
[x^2/exp(2*x),x,3,-1/4/exp(2*x)-1/2*x/exp(2*x)-1/2*x^2/exp(2*x),1],
[exp(x^(1/2)),x,3,-2*exp(x^(1/2))+2*exp(x^(1/2))*x^(1/2),1],
[x^3/exp(x^2),x,2,-1/2/exp(x^2)-1/2*x^2/exp(x^2),1],
[exp(a*x)*cos(b*x),x,1,a*exp(a*x)*cos(b*x)/(a^2+b^2)+b*exp(a*x)*sin(b*x)/(a^2+b^2),1],
[exp(a*x)*sin(b*x),x,1,-b*exp(a*x)*cos(b*x)/(a^2+b^2)+a*exp(a*x)*sin(b*x)/(a^2+b^2),1],
[arccot(x),x,2,x*arccot(x)+1/2*ln(x^2+1),1],
[arcsec(x),x,4,x*arcsec(x)-arctanh((1-1/x^2)^(1/2)),1],
[arccsc(x),x,4,x*arccsc(x)+arctanh((1-1/x^2)^(1/2)),1],
[arcsin(x)^2,x,3,-2*x+x*arcsin(x)^2+2*arcsin(x)*(-x^2+1)^(1/2),1],
[arcsin(x)/x^2,x,4,-arcsin(x)/x-arctanh((-x^2+1)^(1/2)),1],
[1/(a^2-x^2)^(1/2),x,2,arctan(x/(a^2-x^2)^(1/2)),1],
[1/(-x^2-2*x+1)^(1/2),x,2,arcsin(1/2*(1+x)*2^(1/2)),1],
[1/(a^2+x^2),x,1,arctan(x/a)/a,1],
[1/(b*x^2+a),x,1,arctan(x*b^(1/2)/a^(1/2))/a^(1/2)/b^(1/2),1],
[1/(x^2-x+2),x,2,-2/7*arctan(1/7*(1-2*x)*7^(1/2))*7^(1/2),1],
[x*arctan(x),x,3,-1/2*x+1/2*arctan(x)+1/2*x^2*arctan(x),1],
[x^2*arccos(x),x,4,1/9*(-x^2+1)^(3/2)+1/3*x^3*arccos(x)-1/3*(-x^2+1)^(1/2),1],
[x*arctan(x)^2,x,5,-x*arctan(x)+1/2*arctan(x)^2+1/2*x^2*arctan(x)^2+1/2*ln(x^2+1),1],
[arctan(x^(1/2)),x,4,arctan(x^(1/2))+x*arctan(x^(1/2))-x^(1/2),1],
[arctan(x^(1/2))/(1+x)/x^(1/2),x,1,arctan(x^(1/2))^2,1],
[(-x^2+1)^(1/2),x,2,1/2*arcsin(x)+1/2*x*(-x^2+1)^(1/2),1],
[exp(arctan(x))*x/(x^2+1)^(3/2),x,1,-1/2*exp(arctan(x))*(1-x)/(x^2+1)^(1/2),1],
[exp(arctan(x))/(x^2+1)^(3/2),x,1,1/2*exp(arctan(x))*(1+x)/(x^2+1)^(1/2),1],
[x^2/(x^2+1)^2,x,2,-1/2*x/(x^2+1)+1/2*arctan(x),1],
[exp(x)/(1+exp(2*x)),x,2,arctan(exp(x)),1],
[arccot(exp(x))/exp(x),x,5,-x-arccot(exp(x))/exp(x)+1/2*ln(1+exp(2*x)),1],
[((a+x)/(a-x))^(1/2),x,3,2*a*arctan(((a+x)/(a-x))^(1/2))-(a-x)*((a+x)/(a-x))^(1/2),1],
[((b-x)*(-a+x))^(1/2),x,4,-1/8*(a-b)^2*arctan(1/2*(a+b-2*x)/(-a*b+(a+b)*x-x^2)^(1/2))-1/4*(a+b-2*x)*(-a*b+(a+b)*x-x^2)^(1/2),1],
[1/((b-x)*(-a+x))^(1/2),x,3,-arctan(1/2*(a+b-2*x)/(-a*b+(a+b)*x-x^2)^(1/2)),1],
[(3+5*x)/(x^2+2*x-3),x,3,2*ln(1-x)+3*ln(3+x),1],
[(5+2*x)/(x^2+2*x-3),x,3,7/4*ln(1-x)+1/4*ln(3+x),1],
[(x^3+3*x)/(x^2-2*x-3),x,6,2*x+1/2*x^2+9*ln(3-x)+ln(1+x),1],
[(2*x^2+5*x-1)/(x^3+x^2-2*x),x,3,2*ln(1-x)+1/2*ln(x)-1/2*ln(2+x),1],
[(x^2+2*x+3)/(-1+x)/(1+x)^2,x,2,1/(1+x)+3/2*ln(1-x)-1/2*ln(1+x),1],
[(3*x^2+2*x-2)/(x^3-1),x,5,ln(-x^3+1)+4/3*arctan(1/3*(1+2*x)*3^(1/2))*3^(1/2),1],
[(x^4-x^3+2*x^2-x+2)/(-1+x)/(x^2+2)^2,x,6,1/2/(x^2+2)+1/3*ln(1-x)+1/3*ln(x^2+2)-1/6*arctan(1/2*x*2^(1/2))*2^(1/2),1],
[1/(cos(x)+sin(x)),x,2,-1/2*arctanh(1/2*(cos(x)-sin(x))*2^(1/2))*2^(1/2),1],
[x/(4-x^2+(-x^2+4)^(1/2)),x,3,-ln(1+(-x^2+4)^(1/2)),1],
[(3+2*x)/(-2+x)/(5+x),x,2,ln(2-x)+ln(5+x),1],
[x/(1+x)/(2+x)/(3+x),x,2,-1/2*ln(1+x)+2*ln(2+x)-3/2*ln(3+x),1],
[x/(x^3-3*x+2),x,2,1/3/(1-x)+2/9*ln(1-x)-2/9*ln(2+x),1],
[(x^4+2*x-6)/(x^3+x^2-2*x),x,3,-x+1/2*x^2-ln(1-x)+3*ln(x)+ln(2+x),1],
[(8*x^3+7)/(1+x)/(1+2*x)^3,x,2,-3/(1+2*x)^2+3/(1+2*x)+ln(1+x),1],
[(4*x^2+x+1)/(x^3-1),x,3,2*ln(1-x)+ln(x^2+x+1),1],
[x^4/(x^4+5*x^2+4),x,4,x-8/3*arctan(1/2*x)+1/3*arctan(x),1],
[(2+x)/(x^2+x),x,2,2*ln(x)-ln(1+x),1],
[1/x/(x^2+1)^2,x,3,1/2/(x^2+1)+ln(x)-1/2*ln(x^2+1),1],
[1/(1+x)/(2+x)^2/(3+x)^3,x,2,1/(2+x)+1/4/(3+x)^2+5/4/(3+x)+1/8*ln(1+x)+2*ln(2+x)-17/8*ln(3+x),1],
[x/(1+x)^2,x,2,1/(1+x)+ln(1+x),1],
[1/(x^3-x),x,5,-ln(x)+1/2*ln(-x^2+1),1],
[x^2/(x^2+x-6),x,4,x+4/5*ln(2-x)-9/5*ln(3+x),1],
[(2+x)/(x^2-4*x+4),x,3,4/(2-x)+ln(2-x),1],
[1/(x^2-4*x+4)/(x^2-4*x+5),x,4,1/(2-x)-arctan(-2+x),1],
[(-3+x)/(x^3+3*x^2+2*x),x,3,-3/2*ln(x)+4*ln(1+x)-5/2*ln(2+x),1],
[1/(x^2-1)^2,x,2,1/2*x/(-x^2+1)+1/2*arctanh(x),1],
[(1+x)/(x^3-1),x,3,2/3*ln(1-x)-1/3*ln(x^2+x+1),1],
[(x^4+1)/x/(x^2+1)^2,x,3,1/(x^2+1)+ln(x),1],
[1/(x^4-2*x^3),x,3,1/4/x^2+1/4/x+1/8*ln(2-x)-1/8*ln(x),1],
[(-x^3+1)/x/(x^2+1),x,5,-x+arctan(x)+ln(x)-1/2*ln(x^2+1),1],
[1/(x^4-1),x,3,-1/2*arctan(x)-1/2*arctanh(x),1],
[1/(x^4+1),x,9,1/4*arctan(-1+x*2^(1/2))*2^(1/2)+1/4*arctan(1+x*2^(1/2))*2^(1/2)-1/8*ln(1+x^2-x*2^(1/2))*2^(1/2)+1/8*ln(1+x^2+x*2^(1/2))*2^(1/2),1],
[x^2/(x^2+2*x+2)^2,x,3,-1/2*x*(2+x)/(x^2+2*x+2)+arctan(1+x),1],
[(4*x^5-1)/(x^5+x+1)^2,x,1,-x/(x^5+x+1),1],
[1/(5-cos(x)+2*sin(x)),x,3,1/10*x*5^(1/2)+1/5*arctan((2*cos(x)+sin(x))/(5-cos(x)+2*sin(x)+2*5^(1/2)))*5^(1/2),1],
[1/(1+a*cos(x)),x,2,2*arctan((1-a)^(1/2)*tan(1/2*x)/(1+a)^(1/2))/(-a^2+1)^(1/2),1],
[1/(1+2*cos(x)),x,2,-1/3*ln(-sin(1/2*x)+cos(1/2*x)*3^(1/2))*3^(1/2)+1/3*ln(sin(1/2*x)+cos(1/2*x)*3^(1/2))*3^(1/2),1],
[1/(1+1/2*cos(x)),x,1,2/3*x*3^(1/2)-4/3*arctan(sin(x)/(2+cos(x)+3^(1/2)))*3^(1/2),1],
[sin(x)^2/(1+sin(x)^2),x,3,x-1/2*x*2^(1/2)-1/2*arctan(cos(x)*sin(x)/(1+sin(x)^2+2^(1/2)))*2^(1/2),1],
[1/(b^2*cos(x)^2+a^2*sin(x)^2),x,2,arctan(a*tan(x)/b)/a/b,1],
[1/(b*cos(x)+a*sin(x))^2,x,1,sin(x)/b/(b*cos(x)+a*sin(x)),1],
[sin(x)/(1+cos(x)+sin(x)),x,3,1/2*x-1/2*ln(1+cos(x)+sin(x))-1/2*ln(1+tan(1/2*x)),1],
[(-x^2+3)^(1/2),x,2,3/2*arcsin(1/3*x*3^(1/2))+1/2*x*(-x^2+3)^(1/2),1],
[x/(-x^2+3)^(1/2),x,1,-(-x^2+3)^(1/2),1],
[(-x^2+3)^(1/2)/x,x,4,-arctanh(1/3*(-x^2+3)^(1/2)*3^(1/2))*3^(1/2)+(-x^2+3)^(1/2),1],
[(x^2+x)^(1/2)/x,x,3,arctanh(x/(x^2+x)^(1/2))+(x^2+x)^(1/2),1],
[(x^2+5)^(1/2),x,2,5/2*arcsinh(1/5*x*5^(1/2))+1/2*x*(x^2+5)^(1/2),1],
[x/(x^2+x+1)^(1/2),x,3,-1/2*arcsinh(1/3*(1+2*x)*3^(1/2))+(x^2+x+1)^(1/2),1],
[1/(x^2+x)^(1/2),x,2,2*arctanh(x/(x^2+x)^(1/2)),1],
[(-x^2-x+2)^(1/2)/x^2,x,6,-arcsin(1/3+2/3*x)+1/4*arctanh(1/4*(4-x)*2^(1/2)/(-x^2-x+2)^(1/2))*2^(1/2)-(-x^2-x+2)^(1/2)/x,1],
[ln(t)/(1+t),t,2,ln(t)*ln(1+t)+polylog(2,-t),1],
[ln(exp(cos(x))),x,3,-x*cos(x)+x*ln(exp(cos(x)))+sin(x),1],
[exp(t)/t,t,1,Ei(t),1],
[exp(a*t)/t,t,1,Ei(a*t),1],
[exp(t)/t^2,t,2,-exp(t)/t+Ei(t),1],
[exp(1/t),t,2,exp(1/t)*t-Ei(1/t),1],
[1/exp(t)/(-1-a+t),t,1,exp(-1-a)*Ei(1+a-t),1],
[exp(t^2)*t/(t^2+1),t,2,1/2*Ei(t^2+1)/exp(1),1],
[exp(t)/(1+t)^2,t,2,-exp(t)/(1+t)+Ei(1+t)/exp(1),1],
[exp(t)*ln(1+t),t,2,-Ei(1+t)/exp(1)+exp(t)*ln(1+t),1],
[t/exp(t),t,2,-1/exp(t)-t/exp(t),1],
[t^2/exp(t),t,3,-2/exp(t)-2*t/exp(t)-t^2/exp(t),1],
[t^3/exp(t),t,4,-6/exp(t)-6*t/exp(t)-3*t^2/exp(t)-t^3/exp(t),1],
[(b1*cos(x)+a1*sin(x))/(b*cos(x)+a*sin(x)),x,1,(a*a1+b*b1)*x/(a^2+b^2)-(-a*b1+a1*b)*ln(b*cos(x)+a*sin(x))/(a^2+b^2),1],
[1/ln(t),t,1,Li(t),1],
[1/ln(t)^2,t,2,Li(t)-t/ln(t),1],
[ln(t)^(-1-n),t,2,-GAMMA(-n,-ln(t))*(-ln(t))^n/(ln(t)^n),1],
[exp(2*t)/(-1+t),t,1,exp(2)*Ei(-2+2*t),1],
[exp(2*x)/(x^2-3*x+2),x,4,exp(4)*Ei(-4+2*x)-exp(2)*Ei(-2+2*x),1],
[1/(t^3+1)^(1/2),t,1,2/3*(1+t)*EllipticF((1+t-3^(1/2))/(1+t+3^(1/2)),I*3^(1/2)+2*I)*(1/2*6^(1/2)+1/2*2^(1/2))*((t^2-t+1)/(1+t+3^(1/2))^2)^(1/2)*3^(3/4)/(t^3+1)^(1/2)/((1+t)/(1+t+3^(1/2))^2)^(1/2),1], // Bondarenko
[1/(cos(z)+sin(z)+2^(1/2)),z,1,(-1+sin(z)*2^(1/2))/(cos(z)-sin(z)),1],
[1/((1-x)^(1/2)+(1+x)^(1/2))^2,x,4,-1/2/x+1/2*arcsin(x)+1/2*(-x^2+1)^(1/2)/x,1],
[1/(1+cos(x))^2,x,2,1/3*sin(x)/(1+cos(x))^2+1/3*sin(x)/(1+cos(x)),1],
[sin(x)/(1+x)^(1/2),x,5,cos(1)*FresnelS(2^(1/2)/Pi^(1/2)*(1+x)^(1/2))*2^(1/2)*Pi^(1/2)-FresnelC(2^(1/2)/Pi^(1/2)*(1+x)^(1/2))*sin(1)*2^(1/2)*Pi^(1/2),1],
[1/(cos(x)+sin(x))^6,x,3,1/10*(-cos(x)+sin(x))/(cos(x)+sin(x))^5+1/15*(-cos(x)+sin(x))/(cos(x)+sin(x))^3+2/15*sin(x)/(cos(x)+sin(x)),1],
[ln(1/x^4+x^4),x,22,-4*x+x*ln(1/x^4+x^4)-arctan((-2*x+(2+2^(1/2))^(1/2))/(2-2^(1/2))^(1/2))*(2-2^(1/2))^(1/2)+arctan((2*x+(2+2^(1/2))^(1/2))/(2-2^(1/2))^(1/2))*(2-2^(1/2))^(1/2)-1/2*ln(1+x^2-x*(2-2^(1/2))^(1/2))*(2-2^(1/2))^(1/2)+1/2*ln(1+x^2+x*(2-2^(1/2))^(1/2))*(2-2^(1/2))^(1/2)-arctan((-2*x+(2-2^(1/2))^(1/2))/(2+2^(1/2))^(1/2))*(2+2^(1/2))^(1/2)+arctan((2*x+(2-2^(1/2))^(1/2))/(2+2^(1/2))^(1/2))*(2+2^(1/2))^(1/2)-1/2*ln(1+x^2-x*(2+2^(1/2))^(1/2))*(2+2^(1/2))^(1/2)+1/2*ln(1+x^2+x*(2+2^(1/2))^(1/2))*(2+2^(1/2))^(1/2),1],
[ln(1+x)/x/(1+(1+x)^(1/2))^(1/2),x,-1,-8*arctanh((1+(1+x)^(1/2))^(1/2))-arctanh(1/2*(1+(1+x)^(1/2))^(1/2)*2^(1/2))*ln(1+x)*2^(1/2)+2*arctanh(1/2*2^(1/2))*ln(1-(1+(1+x)^(1/2))^(1/2))*2^(1/2)-2*arctanh(1/2*2^(1/2))*ln(1+(1+(1+x)^(1/2))^(1/2))*2^(1/2)+polylog(2,-2^(1/2)*(1-(1+(1+x)^(1/2))^(1/2))/(2-2^(1/2)))*2^(1/2)-polylog(2,2^(1/2)*(1-(1+(1+x)^(1/2))^(1/2))/(2+2^(1/2)))*2^(1/2)-polylog(2,-2^(1/2)*(1+(1+(1+x)^(1/2))^(1/2))/(2-2^(1/2)))*2^(1/2)+polylog(2,2^(1/2)*(1+(1+(1+x)^(1/2))^(1/2))/(2+2^(1/2)))*2^(1/2)-2*ln(1+x)/(1+(1+x)^(1/2))^(1/2),1],
[ln(1+x)*(1+(1+x)^(1/2))^(1/2)/x,x,-1,16*arctanh((1+(1+x)^(1/2))^(1/2))-2*arctanh(1/2*(1+(1+x)^(1/2))^(1/2)*2^(1/2))*ln(1+x)*2^(1/2)+4*arctanh(1/2*2^(1/2))*ln(1-(1+(1+x)^(1/2))^(1/2))*2^(1/2)-4*arctanh(1/2*2^(1/2))*ln(1+(1+(1+x)^(1/2))^(1/2))*2^(1/2)+2*polylog(2,-2^(1/2)*(1-(1+(1+x)^(1/2))^(1/2))/(2-2^(1/2)))*2^(1/2)-2*polylog(2,2^(1/2)*(1-(1+(1+x)^(1/2))^(1/2))/(2+2^(1/2)))*2^(1/2)-2*polylog(2,-2^(1/2)*(1+(1+(1+x)^(1/2))^(1/2))/(2-2^(1/2)))*2^(1/2)+2*polylog(2,2^(1/2)*(1+(1+(1+x)^(1/2))^(1/2))/(2+2^(1/2)))*2^(1/2)-16*(1+(1+x)^(1/2))^(1/2)+4*ln(1+x)*(1+(1+x)^(1/2))^(1/2),1],
[1/(1+(x+(x^2+1)^(1/2))^(1/2)),x,4,1/2*ln(x+(x^2+1)^(1/2))-2*ln(1+(x+(x^2+1)^(1/2))^(1/2))-1/2/(x+(x^2+1)^(1/2))+1/(x+(x^2+1)^(1/2))^(1/2)+(x+(x^2+1)^(1/2))^(1/2),1],
[(1+x)^(1/2)/(x+(1+(1+x)^(1/2))^(1/2)),x,6,8/5*arctanh(1/5*(1+2*(1+(1+x)^(1/2))^(1/2))*5^(1/2))*5^(1/2)+2*(1+x)^(1/2),1],
[1/(x-(1+(1+x)^(1/2))^(1/2)),x,5,2/5*ln(1+5^(1/2)-2*(1+(1+x)^(1/2))^(1/2))*(5-5^(1/2))+2/5*ln(1-5^(1/2)-2*(1+(1+x)^(1/2))^(1/2))*(5+5^(1/2)),1],
[x/(x+(1-(1+x)^(1/2))^(1/2)),x,6,8/5*arctanh(1/5*(1+2*(1-(1+x)^(1/2))^(1/2))*5^(1/2))*5^(1/2)+(1-(1+x)^(1/2))^2+2*(1+x)^(1/2)-4*(1-(1+x)^(1/2))^(1/2),1],
[(x+(1+x)^(1/2))^(1/2)/(x^2+1)/(1+x)^(1/2),x,20,1/2*I*arctanh(1/2*(2-(1-I)^(1/2)-(1+2*(1-I)^(1/2))*(1+x)^(1/2))/(-I+(1-I)^(1/2))^(1/2)/(x+(1+x)^(1/2))^(1/2))/((-1+I)/(I-(1-I)^(1/2)))^(1/2)-1/2*I*arctan(1/2*(2+(1-I)^(1/2)-(1-2*(1-I)^(1/2))*(1+x)^(1/2))/(I+(1-I)^(1/2))^(1/2)/(x+(1+x)^(1/2))^(1/2))/((1-I)/(I+(1-I)^(1/2)))^(1/2)+1/2*I*arctan(1/2*(2+(1+I)^(1/2)-(1-2*(1+I)^(1/2))*(1+x)^(1/2))/(-I+(1+I)^(1/2))^(1/2)/(x+(1+x)^(1/2))^(1/2))/((-1-I)/(I-(1+I)^(1/2)))^(1/2)-1/2*I*arctanh(1/2*(2-(1+I)^(1/2)-(1+2*(1+I)^(1/2))*(1+x)^(1/2))/(I+(1+I)^(1/2))^(1/2)/(x+(1+x)^(1/2))^(1/2))/((1+I)/(I+(1+I)^(1/2)))^(1/2),1],
[(x+(1+x)^(1/2))^(1/2)/(x^2+1),x,22,1/2*I*arctanh(1/2*(2-(1-I)^(1/2)-(1+2*(1-I)^(1/2))*(1+x)^(1/2))/(-I+(1-I)^(1/2))^(1/2)/(x+(1+x)^(1/2))^(1/2))*(-I+(1-I)^(1/2))^(1/2)+1/2*I*arctan(1/2*(2+(1-I)^(1/2)-(1-2*(1-I)^(1/2))*(1+x)^(1/2))/(I+(1-I)^(1/2))^(1/2)/(x+(1+x)^(1/2))^(1/2))*(I+(1-I)^(1/2))^(1/2)-1/2*I*arctan(1/2*(2+(1+I)^(1/2)-(1-2*(1+I)^(1/2))*(1+x)^(1/2))/(-I+(1+I)^(1/2))^(1/2)/(x+(1+x)^(1/2))^(1/2))*(-I+(1+I)^(1/2))^(1/2)-1/2*I*arctanh(1/2*(2-(1+I)^(1/2)-(1+2*(1+I)^(1/2))*(1+x)^(1/2))/(I+(1+I)^(1/2))^(1/2)/(x+(1+x)^(1/2))^(1/2))*(I+(1+I)^(1/2))^(1/2),1],
[(1+x^(1/2)+(1+2*x+2*x^(1/2))^(1/2))^(1/2),x,2,2/15*(2+6*x^(3/2)+x^(1/2)-(2-x^(1/2))*(1+2*x+2*x^(1/2))^(1/2))*(1+x^(1/2)+(1+2*x+2*x^(1/2))^(1/2))^(1/2)/x^(1/2),1],
[(2^(1/2)+x^(1/2)+(2+2*x+2*2^(1/2)*x^(1/2))^(1/2))^(1/2),x,3,2/15*2^(1/2)*(4+3*x^(3/2)*2^(1/2)+2^(1/2)*x^(1/2)-2^(1/2)*(2*2^(1/2)-x^(1/2))*(1+x+2^(1/2)*x^(1/2))^(1/2))*(2^(1/2)+x^(1/2)+2^(1/2)*(1+x+2^(1/2)*x^(1/2))^(1/2))^(1/2)/x^(1/2),1],
[(x+(1+x)^(1/2))^(1/2)/x^2,x,7,-1/4*arctan(1/2*(3+(1+x)^(1/2))/(x+(1+x)^(1/2))^(1/2))+3/4*arctanh(1/2*(1-3*(1+x)^(1/2))/(x+(1+x)^(1/2))^(1/2))-(x+(1+x)^(1/2))^(1/2)/x,1],
[(1/x+(1+1/x)^(1/2))^(1/2),x,7,1/4*arctan(1/2*(3+(1+1/x)^(1/2))/(1/x+(1+1/x)^(1/2))^(1/2))-3/4*arctanh(1/2*(1-3*(1+1/x)^(1/2))/(1/x+(1+1/x)^(1/2))^(1/2))+x*(1/x+(1+1/x)^(1/2))^(1/2),1],
[(1+exp(-x))^(1/2)/(-exp(-x)+exp(x)),x,6,-arctanh(1/2*(1+exp(-x))^(1/2)*2^(1/2))*2^(1/2),1],
[(1+exp(-x))^(1/2)/sinh(x),x,7,-2*arctanh(1/2*(1+exp(-x))^(1/2)*2^(1/2))*2^(1/2),1],
[1/(cos(x)+cos(3*x))^5,x,-45,-523/256*arctanh(sin(x))+1/32*sin(x)/(1-2*sin(x)^2)^4-17/192*sin(x)/(1-2*sin(x)^2)^3+203/768*sin(x)/(1-2*sin(x)^2)^2-437/512*sin(x)/(1-2*sin(x)^2)+1483/1024*arctanh(sin(x)*2^(1/2))*2^(1/2)-43/256*sec(x)*tan(x)-1/128*sec(x)^3*tan(x),1],
[1/(1+cos(x)+sin(x))^2,x,3,-ln(1+tan(1/2*x))+(-cos(x)+sin(x))/(1+cos(x)+sin(x)),1],
[(1+tanh(4*x))^(1/2),x,2,1/4*arctanh(1/2*(1+tanh(4*x))^(1/2)*2^(1/2))*2^(1/2),1],
[tanh(x)/(exp(x)+exp(2*x))^(1/2),x,-11,arctan(1/2*(I+(1+2*I)*exp(x))/(1-I)^(1/2)/(exp(x)+exp(2*x))^(1/2))/(1-I)^(1/2)-arctan(1/2*(I+(-1+2*I)*exp(x))/(1+I)^(1/2)/(exp(x)+exp(2*x))^(1/2))/(1+I)^(1/2)+2*(exp(x)+exp(2*x))^(1/2)/exp(x),1],
[(sinh(2*x)/cosh(x))^(1/2),x,5,2*I*(sin(1/4*Pi+1/2*I*x)^2)^(1/2)/sin(1/4*Pi+1/2*I*x)*EllipticE(cos(1/4*Pi+1/2*I*x),2^(1/2))*2^(1/2)*sinh(x)^(1/2)/(I*sinh(x))^(1/2),1],
[ln(x^2+(-x^2+1)^(1/2)),x,-31,-2*x-arcsin(x)+x*ln(x^2+(-x^2+1)^(1/2))+1/2*arctanh(x*2^(1/2)/(5^(1/2)-1)^(1/2))*(-2+2*5^(1/2))^(1/2)-1/2*arctanh(1/2*x*(-2+2*5^(1/2))^(1/2)/(-x^2+1)^(1/2))*(-2+2*5^(1/2))^(1/2)+1/2*arctan(x*2^(1/2)/(5^(1/2)+1)^(1/2))*(2+2*5^(1/2))^(1/2)+1/2*arctan(1/2*x*(2+2*5^(1/2))^(1/2)/(-x^2+1)^(1/2))*(2+2*5^(1/2))^(1/2),1],
[ln(1+exp(x))/(1+exp(2*x)),x,12,-1/2*ln((1/2-1/2*I)*(I-exp(x)))*ln(1+exp(x))-1/2*ln((-1/2-1/2*I)*(I+exp(x)))*ln(1+exp(x))-polylog(2,-exp(x))-1/2*polylog(2,(1/2-1/2*I)*(1+exp(x)))-1/2*polylog(2,(1/2+1/2*I)*(1+exp(x))),1],
[cosh(x)*ln(1+cosh(x)^2)^2,x,13,8*sinh(x)-4*ln(2+sinh(x)^2)*sinh(x)+ln(2+sinh(x)^2)^2*sinh(x)-8*arctan(1/2*sinh(x)*2^(1/2))*2^(1/2)+4*I*arctan(1/2*sinh(x)*2^(1/2))^2*2^(1/2)+4*arctan(1/2*sinh(x)*2^(1/2))*ln(2+sinh(x)^2)*2^(1/2)+8*arctan(1/2*sinh(x)*2^(1/2))*ln(2*2^(1/2)/(I*sinh(x)+2^(1/2)))*2^(1/2)+4*I*polylog(2,1-2*2^(1/2)/(I*sinh(x)+2^(1/2)))*2^(1/2),1],
[cosh(x)*ln(cosh(x)^2+sinh(x))^2,x,28,-2*ln(1+sinh(x)+sinh(x)^2)+8*sinh(x)-4*ln(1+sinh(x)+sinh(x)^2)*sinh(x)+ln(1+sinh(x)+sinh(x)^2)^2*sinh(x)+ln(1+sinh(x)+sinh(x)^2)*ln(1+2*sinh(x)-I*3^(1/2))*(1-I*3^(1/2))-1/2*ln(1+2*sinh(x)-I*3^(1/2))^2*(1-I*3^(1/2))-ln(1+2*sinh(x)-I*3^(1/2))*ln(-1/6*I*(1+2*sinh(x)+I*3^(1/2))*3^(1/2))*(1-I*3^(1/2))-polylog(2,1/6*(I+2*I*sinh(x)+3^(1/2))*3^(1/2))*(1-I*3^(1/2))+ln(1+sinh(x)+sinh(x)^2)*ln(1+2*sinh(x)+I*3^(1/2))*(1+I*3^(1/2))-1/2*ln(1+2*sinh(x)+I*3^(1/2))^2*(1+I*3^(1/2))-ln(1+2*sinh(x)+I*3^(1/2))*ln(1/6*I*(1+2*sinh(x)-I*3^(1/2))*3^(1/2))*(1+I*3^(1/2))-polylog(2,1/6*(-I-2*I*sinh(x)+3^(1/2))*3^(1/2))*(1+I*3^(1/2))-4*arctan(1/3*(1+2*sinh(x))*3^(1/2))*3^(1/2),1],
[ln(x+(1+x)^(1/2))/(x^2+1),x,44,1/2*I*polylog(2,2*((1+I)^(1/2)-(1+x)^(1/2))/(1+2*(1+I)^(1/2)-5^(1/2)))+1/2*I*ln((1+I)^(1/2)-(1+x)^(1/2))*ln((1-5^(1/2)+2*(1+x)^(1/2))/(1+2*(1+I)^(1/2)-5^(1/2)))+1/2*I*polylog(2,-2*((1+I)^(1/2)+(1+x)^(1/2))/(1-2*(1+I)^(1/2)+5^(1/2)))+1/2*I*ln((1+I)^(1/2)+(1+x)^(1/2))*ln((1-5^(1/2)+2*(1+x)^(1/2))/(1-2*(1+I)^(1/2)-5^(1/2)))+1/2*I*ln(x+(1+x)^(1/2))*ln((1-I)^(1/2)+(1+x)^(1/2))-1/2*I*polylog(2,2*((1-I)^(1/2)-(1+x)^(1/2))/(1+2*(1-I)^(1/2)+5^(1/2)))-1/2*I*ln(x+(1+x)^(1/2))*ln((1+I)^(1/2)+(1+x)^(1/2))-1/2*I*ln((1-I)^(1/2)-(1+x)^(1/2))*ln((1-5^(1/2)+2*(1+x)^(1/2))/(1+2*(1-I)^(1/2)-5^(1/2)))+1/2*I*ln((1+I)^(1/2)-(1+x)^(1/2))*ln((1+5^(1/2)+2*(1+x)^(1/2))/(1+2*(1+I)^(1/2)+5^(1/2)))-1/2*I*polylog(2,-2*((1-I)^(1/2)+(1+x)^(1/2))/(1-2*(1-I)^(1/2)-5^(1/2)))-1/2*I*polylog(2,-2*((1-I)^(1/2)+(1+x)^(1/2))/(1-2*(1-I)^(1/2)+5^(1/2)))+1/2*I*ln((1-I)^(1/2)-(1+x)^(1/2))*ln(x+(1+x)^(1/2))+1/2*I*ln((1+I)^(1/2)+(1+x)^(1/2))*ln((1+5^(1/2)+2*(1+x)^(1/2))/(1-2*(1+I)^(1/2)+5^(1/2)))-1/2*I*ln((1-I)^(1/2)-(1+x)^(1/2))*ln((1+5^(1/2)+2*(1+x)^(1/2))/(1+2*(1-I)^(1/2)+5^(1/2)))-1/2*I*ln((1-I)^(1/2)+(1+x)^(1/2))*ln((1+5^(1/2)+2*(1+x)^(1/2))/(1-2*(1-I)^(1/2)+5^(1/2)))+1/2*I*polylog(2,2*((1+I)^(1/2)-(1+x)^(1/2))/(1+2*(1+I)^(1/2)+5^(1/2)))-1/2*I*polylog(2,2*((1-I)^(1/2)-(1+x)^(1/2))/(1+2*(1-I)^(1/2)-5^(1/2)))-1/2*I*ln((1-I)^(1/2)+(1+x)^(1/2))*ln((1-5^(1/2)+2*(1+x)^(1/2))/(1-2*(1-I)^(1/2)-5^(1/2)))-1/2*I*ln((1+I)^(1/2)-(1+x)^(1/2))*ln(x+(1+x)^(1/2))+1/2*I*polylog(2,-2*((1+I)^(1/2)+(1+x)^(1/2))/(1-2*(1+I)^(1/2)-5^(1/2))),1],
[ln(x+(1+x)^(1/2))^2/(1+x)^2,x,35,ln(1+x)-3*ln(1+x)*ln(x+(1+x)^(1/2))-ln(x+(1+x)^(1/2))^2/(1+x)+6*ln(1/2*5^(1/2)-1/2)*ln(1-5^(1/2)+2*(1+x)^(1/2))+3*ln(1+x)*ln(1+2*(1+x)^(1/2)/(5^(1/2)+1))+6*polylog(2,-2*(1+x)^(1/2)/(5^(1/2)+1))-6*polylog(2,1+2*(1+x)^(1/2)/(-5^(1/2)+1))-ln(1+5^(1/2)+2*(1+x)^(1/2))*(-5^(1/2)+1)+ln(x+(1+x)^(1/2))*ln(1+5^(1/2)+2*(1+x)^(1/2))*(3-5^(1/2))-ln(1/10*(-1+5^(1/2)-2*(1+x)^(1/2))*5^(1/2))*ln(1+5^(1/2)+2*(1+x)^(1/2))*(3-5^(1/2))-1/2*ln(1+5^(1/2)+2*(1+x)^(1/2))^2*(3-5^(1/2))-polylog(2,1/10*(1+5^(1/2)+2*(1+x)^(1/2))*5^(1/2))*(3-5^(1/2))-ln(1-5^(1/2)+2*(1+x)^(1/2))*(5^(1/2)+1)+ln(x+(1+x)^(1/2))*ln(1-5^(1/2)+2*(1+x)^(1/2))*(3+5^(1/2))-1/2*ln(1-5^(1/2)+2*(1+x)^(1/2))^2*(3+5^(1/2))-ln(1-5^(1/2)+2*(1+x)^(1/2))*ln(1/10*(1+5^(1/2)+2*(1+x)^(1/2))*5^(1/2))*(3+5^(1/2))-polylog(2,1/10*(-1+5^(1/2)-2*(1+x)^(1/2))*5^(1/2))*(3+5^(1/2))+2*ln(x+(1+x)^(1/2))/(1+x)^(1/2),1],
[ln(x+(1+x)^(1/2))/x,x,21,ln(-1+(1+x)^(1/2))*ln(x+(1+x)^(1/2))+ln(1+(1+x)^(1/2))*ln(x+(1+x)^(1/2))-ln(-1+(1+x)^(1/2))*ln((1-5^(1/2)+2*(1+x)^(1/2))/(3-5^(1/2)))-ln(1+(1+x)^(1/2))*ln((-1+5^(1/2)-2*(1+x)^(1/2))/(5^(1/2)+1))-ln(1+(1+x)^(1/2))*ln((-1-5^(1/2)-2*(1+x)^(1/2))/(-5^(1/2)+1))-ln(-1+(1+x)^(1/2))*ln((1+5^(1/2)+2*(1+x)^(1/2))/(3+5^(1/2)))-polylog(2,2*(1-(1+x)^(1/2))/(3-5^(1/2)))-polylog(2,2*(1-(1+x)^(1/2))/(3+5^(1/2)))-polylog(2,2*(1+(1+x)^(1/2))/(-5^(1/2)+1))-polylog(2,2*(1+(1+x)^(1/2))/(5^(1/2)+1)),1],
[arctan(2*tan(x)),x,7,x*arctan(2*tan(x))+1/2*I*x*ln(1-3*exp(2*I*x))-1/2*I*x*ln(1-1/3*exp(2*I*x))-1/4*polylog(2,1/3*exp(2*I*x))+1/4*polylog(2,3*exp(2*I*x)),1],
[arctan(x)*ln(x)/x,x,5,1/2*I*ln(x)*polylog(2,-I*x)-1/2*I*ln(x)*polylog(2,I*x)-1/2*I*polylog(3,-I*x)+1/2*I*polylog(3,I*x),1],
[arctan(x)^2*(x^2+1)^(1/2),x,10,arcsinh(x)-I*arctan((1+I*x)/(x^2+1)^(1/2))*arctan(x)^2+I*arctan(x)*polylog(2,-I*(1+I*x)/(x^2+1)^(1/2))-I*arctan(x)*polylog(2,I*(1+I*x)/(x^2+1)^(1/2))-polylog(3,-I*(1+I*x)/(x^2+1)^(1/2))+polylog(3,I*(1+I*x)/(x^2+1)^(1/2))-arctan(x)*(x^2+1)^(1/2)+1/2*x*arctan(x)^2*(x^2+1)^(1/2),1], // Bronstein
[(2*x^8+1)*(x^8+1)^(1/2)/(x^17+2*x^9+x),x,6,-1/4*arctanh((x^8+1)^(1/2))-1/4/(x^8+1)^(1/2),1],
[1/(x^2+1),x,1,arctan(x),1],
[1/(x^8+1)^(1/2)/x,x,3,-1/4*arctanh((x^8+1)^(1/2)),1],
[x/(-x^3+1)^(1/2),x,3,2*(-x^3+1)^(1/2)/(1-x+3^(1/2))+2/3*(1-x)*EllipticF((1-x-3^(1/2))/(1-x+3^(1/2)),I*3^(1/2)+2*I)*2^(1/2)*((x^2+x+1)/(1-x+3^(1/2))^2)^(1/2)*3^(3/4)/(-x^3+1)^(1/2)/((1-x)/(1-x+3^(1/2))^2)^(1/2)-3^(1/4)*(1-x)*EllipticE((1-x-3^(1/2))/(1-x+3^(1/2)),I*3^(1/2)+2*I)*(1/2*6^(1/2)-1/2*2^(1/2))*((x^2+x+1)/(1-x+3^(1/2))^2)^(1/2)/(-x^3+1)^(1/2)/((1-x)/(1-x+3^(1/2))^2)^(1/2),1],
[1/x/(-x^3+1)^(1/2),x,3,-2/3*arctanh((-x^3+1)^(1/2)),1],
[x/(x^4+10*x^2-96*x-71)^(1/2),x,1,1/8*ln(10001+3124*x^2-1408*x^3+54*x^4-128*x^5+20*x^6+x^8+(x^6+15*x^4-80*x^3+27*x^2-528*x+781)*(x^4+10*x^2-96*x-71)^(1/2)),1],
[(x-tan(x))/tan(x)^2,x,6,-1/2*x^2-x*cot(x),1],
[1+x*tan(x)+tan(x)^2,x,7,1/2*I*x^2-x*ln(1+exp(2*I*x))+1/2*I*polylog(2,-exp(2*I*x))+tan(x),1],
[sin(x)/x,x,1,Si(x),1],
[(5*x^2+3*(exp(x)+x)^(1/3)+exp(x)*(2*x^2+3*x))/x/(exp(x)+x)^(1/3),x,8,3*x*(exp(x)+x)^(2/3)+3*ln(x),1],
[1/x+(1+1/x)/(x+ln(x))^(3/2),x,2,ln(x)-2/(x+ln(x))^(1/2),1],
[(x^2+2*x*ln(x)+ln(x)^2+(1+x)*(x+ln(x))^(1/2))/(x^3+2*x^2*ln(x)+x*ln(x)^2),x,-3,ln(x)-2/(x+ln(x))^(1/2),1],
[(-x^2-ln(x)+2*ln(x)^2)/(-x^2*ln(x)+ln(x)^3),x,6,Li(x)-1/2*ln(x-ln(x))+1/2*ln(x+ln(x)),1],
[(x^4-3*x^2+6)/(x^6-5*x^4+5*x^2+4),x,1,arctan(1/2*x*(x^4-3*x^2+1))+arctan(2*x-3^(1/2))+arctan(2*x+3^(1/2)),1], // Calculus
[(-3*x^4+1)/(-2+x)/(x^2+1)^2,x,6,-(1-2*x)/(5*x^2+5)-46/25*arctan(x)-47/25*ln(2-x)-14/25*ln(x^2+1),1],
[(2*x^2-9*x-9)/(x^3-9*x),x,3,-ln(3-x)+ln(x)+2*ln(3+x),1],
[(x^5+2*x^2+1)/(x^3-x),x,6,x+1/3*x^3+2*ln(1-x)-ln(x)+ln(1+x),1],
[(2*x^2+3)/(-1+x)^2/x,x,2,5/(1-x)-ln(1-x)+3*ln(x),1],
[(2*x^2-1)/(-1+4*x)/(x^2+1),x,5,3/17*arctan(x)-7/34*ln(1-4*x)+6/17*ln(x^2+1),1],
[(x^3-3*x^2+2*x-3)/(x^2+1),x,3,-3*x+1/2*x^2+1/2*ln(x^2+1),1],
[(x^4+6*x^3+10*x^2+x)/(x^2+6*x+10),x,7,1/3*x^3-3*arctan(3+x)+1/2*ln(x^2+6*x+10),1],
[1/(x^4-3*x^3-7*x^2+27*x-18),x,3,1/8*ln(1-x)-1/5*ln(2-x)+1/12*ln(3-x)-1/120*ln(3+x),1],
[(x^3+1)/(-2+x),x,2,4*x+x^2+1/3*x^3+9*ln(2-x),1],
[(3*x^3-4*x^2+3*x)/(x^2+1),x,4,-4*x+3/2*x^2+4*arctan(x),1],
[(5+3*x)/(x^3-x^2-x+1),x,4,4/(1-x)+arctanh(x),1],
[(x^4-x^3-x-1)/(x^3-x^2),x,3,-1/x+1/2*x^2-2*ln(1-x)+2*ln(x),1],
[(x^3+x^2+x+2)/(x^4+3*x^2+2),x,6,arctan(x)+1/2*ln(x^2+2),1],
[(x^5-x^4+4*x^3-4*x^2+8*x-4)/(x^2+2)^3,x,7,-1/(x^2+2)^2-arctan(x/sqrt(2))/sqrt(2)+1/2*ln(x^2+2),1],
[(x^2-3*x-1)/(x^3+x^2-2*x),x,3,-ln(1-x)+1/2*ln(x)+3/2*ln(2+x),1],
[(x^4-2*x^3+3*x^2-x+3)/(x^3-2*x^2+3*x),x,4,1/2*x^2+ln(x)-1/2*ln(x^2-2*x+3),1],
[(x^3+x-1)/(x^2+1)^2,x,4,-x/(2*x^2+2)-1/2*arctan(x)+1/2*ln(x^2+1),1],
[(x^4+8*x^3-x^2+2*x+1)/(x^2+x)/(x^3+1),x,8,-3/(1+x)-2*arctan((1-2*x)/sqrt(3))/sqrt(3)+ln(x)-2*ln(1+x)+ln(x^2-x+1),1],
[(x^3+x^2-5*x+15)/(x^2+5)/(x^2+2*x+3),x,7,-sqrt(5)*arctan(x/sqrt(5))+5*arctan((1+x)/sqrt(2))/sqrt(2)+1/2*ln(x^2+2*x+3),1],
[(x^6+7*x^5+15*x^4+32*x^3+23*x^2+25*x-3)/(x^2+1)^2/(x^2+x+2)^2,x,6,-3/(x^2+1)+1/(x^2+x+2)+ln(x^2+1)-ln(x^2+x+2),1],
[1/(x^2+1)/(x^2+4),x,3,-1/6*arctan(1/2*x)+1/3*arctan(x),1],
[(b*x^3+a)/(x^2+1),x,5,1/2*b*x^2+a*arctan(x)-1/2*b*ln(x^2+1),1],
[(x^2+x)/(4+x)/(x^2-4),x,3,-1/2*arctanh(1/2*x)+ln(4+x),1],
[(x^2+4)/(x^2+1)/(x^2+2),x,3,3*arctan(x)-sqrt(2)*arctan(x/sqrt(2)),1],
[(x^4+3*x^2-4*x+5)/(-1+x)^2/(x^2+1),x,5,5/(2-2*x)+x+2*arctan(x)+1/2*ln(1-x)+3/4*ln(x^2+1),1],
[(x^4+1)/(x^2+2),x,3,-2*x+1/3*x^3+5*arctan(x/sqrt(2))/sqrt(2),1],
[(x^4+2*x+2)/(x^5+x^4),x,3,-2/3/x^3+ln(1+x),1],
[(2*x^2-5*x-1)/(x^3-2*x^2-x+2),x,3,2*ln(1-x)-ln(2-x)+ln(1+x),1],
[(x^3+x+2)/(x^4+2*x^2+1),x,5,x/(x^2+1)+arctan(x)+1/2*ln(x^2+1),1],
[(x^3+x^2+2*x+1)/(x^4+2*x^2+1),x,6,-1/(2*x^2+2)+arctan(x)+1/2*ln(x^2+1),1],
[(3+4*x)/(x^2+1)/(x^2+2),x,8,3*arctan(x)-3*arctan(x/sqrt(2))/sqrt(2)+2*ln(x^2+1)-2*ln(x^2+2),1],
[(2+x)/(x^2+1)/(x^2+4),x,8,-1/3*arctan(1/2*x)+2/3*arctan(x)+1/6*ln(x^2+1)-1/6*ln(x^2+4),1],
[(x^3-x+2)/(x^2-6*x-7),x,4,6*x+1/2*x^2+169/4*ln(7-x)-1/4*ln(1+x),1],
[(x^5-1)/(x^2-1),x,3,1/2*x^2+1/4*x^4+ln(1+x),1],
[(x^3-x^2+2*x+5)/(x^2+x+1),x,6,-2*x+1/2*x^2+11*arctan((1+2*x)/sqrt(3))/sqrt(3)+3/2*ln(x^2+x+1),1],
[(x^4-2*x^3+x-3)/(2*x^2-8*x+10),x,6,3/2*x+1/2*x^2+1/6*x^3+6*arctan(2-x)+3/4*ln(x^2-4*x+5),1],
[(x^3+3*x^2+2*x+1)/(-3+x)/(-2+x)/(-1+x),x,2,x+7/2*ln(1-x)-25*ln(2-x)+61/2*ln(3-x),1],
[(x^4-x^3+x^2-7*x+2)/(x^3+x^2-14*x-24),x,2,-2*x+1/2*x^2+13/3*ln(4-x)-22/3*ln(2+x)+20*ln(3+x),1],
[(x^2+2)/(-1+x)^2/x/(1+x),x,4,3/(2-2*x)-5/4*ln(1-x)+2*ln(x)-3/4*ln(1+x),1],
[(x^3+x^2+3)/(x^2+2)^2,x,4,(1-2*x)*x/(4*x^2+8)+5/4*arctan(x/sqrt(2))/sqrt(2)+1/2*ln(x^2+2),1],
[(2*x^3-4*x^2+70*x-35)/(x^2-10*x+26)/(x^2-2*x+17),x,10,-15033/1025*arctan(5-x)-4607/4100*arctan(-1/4+1/4*x)+1003/1025*ln(x^2-10*x+26)+22/1025*ln(x^2-2*x+17),1],
[(x^2+2)/(-5+x)/(-3+x)/(4+x),x,6,-11/14*ln(3-x)+3/2*ln(5-x)+2/7*ln(4+x),1],
[x^4/(-1+x)/(x^2+2),x,5,x+1/2*x^2-2/3*sqrt(2)*arctan(x/sqrt(2))+1/3*ln(1-x)-2/3*ln(x^2+2),1],
[(2*x^2+7*x-1)/(x^3+x^2-x-1),x,3,-3/(1+x)+2*ln(1-x),1],
[(1+2*x)/(x^3-3*x^2+3*x-1),x,2,-1/6*(1+2*x)^2/(1-x)^2,1],
[(x^3+7*x^2-5*x+5)/(-1+x)^2/(1+x)^3,x,2,1/(1-x)-2/(1+x)^2,1],
[(3*x^2+3*x+1)/(x^3+2*x^2+2*x+1),x,7,-2*arctan((1+2*x)/sqrt(3))/sqrt(3)+ln(1+x)+ln(x^2+x+1),1],
[(x^2+2*x-1)/(2*x^3+3*x^2-2*x),x,3,1/10*ln(1-2*x)+1/2*ln(x)-1/10*ln(2+x),1],
[(x^4-2*x^2+4*x+1)/(x^3-x^2-x+1),x,4,2/(1-x)+x+1/2*x^2-2*arctanh(x),1],
[(2*x^2-x+4)/(x^3+4*x),x,6,-1/2*arctan(1/2*x)+ln(x)+1/2*ln(x^2+4),1],
[(x^3+x^2+1)/(-1+x)/x/(x^2+1)^3/(x^2+x+1),x,14,1/8*(1+x)/(x^2+1)^2-3*(1-x)/(8*x^2+8)+3*x/(16*x^2+16)+7/16*arctan(x)-arctan((1+2*x)/sqrt(3))/sqrt(3)+1/8*ln(1-x)-ln(x)+15/16*ln(x^2+1)-1/2*ln(x^2+x+1),1],
[(-x^3+2*x^2-3*x+1)/(x^2+1)^2,x,4,-x*(1+2*x)/(2*x^2+2)+3/2*arctan(x)-1/2*ln(x^2+1),1],
[(-x^3+2*x^2-3*x+1)/x/(x^2+1)^2,x,6,-1/(2*x^2+2)-x/(x^2+1)-2*arctan(x)+ln(x)-1/2*ln(x^2+1),1],
[(x^4+x^3-x^2-x+1)/(x^3-x),x,4,x+1/2*x^2-ln(x)+1/2*ln(-x^2+1),1],
[(x^3-4*x^2+2)/(x^2+1)/(x^2+2),x,8,6*arctan(x)-5*sqrt(2)*arctan(x/sqrt(2))-1/2*ln(x^2+1)+ln(x^2+2),1],
[(x^4+x^2+1)/(x^2+1)/(x^2+4)^2,x,5,-13*x/(24*x^2+96)+25/144*arctan(1/2*x)+1/9*arctan(x),1],
[(x^3+x^2+1)/(x^4+x^3+2*x^2),x,7,-1/2/x+1/4*arctan((1+2*x)/sqrt(7))/sqrt(7)-1/4*ln(x)+5/8*ln(x^2+x+2),1],
[(x^3+x^2-12*x+1)/(x^2+x-12),x,5,1/2*x^2+1/7*ln(3-x)-1/7*ln(4+x),1],
[(6*x^2+5*x-3)/(x^3+2*x^2-3*x),x,3,2*ln(1-x)+ln(x)+3*ln(3+x),1],
[(5*x^2+3*x-2)/(x^3+2*x^2),x,3,1/x+2*ln(x)+3*ln(2+x),1],
[(-4*x^2-2*x+18)/(x^3+4*x^2+x-6),x,2,ln(1-x)-2*ln(2+x)-3*ln(3+x),1],
[(x^3-2*x^2+x+1)/(x^4+5*x^2+4),x,7,-3/2*arctan(1/2*x)+arctan(x)+1/2*ln(x^2+4),1],
[(4*x^3-27*x^2+5*x-32)/(30*x^5-13*x^4+50*x^3-286*x^2-299*x-70),x,6,3988/13685*arctan((1+2*x)/sqrt(19))/sqrt(19)-3146/80155*ln(7-3*x)-334/323*ln(1+2*x)+4822/4879*ln(2+5*x)+11049/260015*ln(x^2+x+5),1],
[(12*x^5-7*x^3-13*x^2+8)/(100*x^6-80*x^5+116*x^4-80*x^3+41*x^2-20*x+4),x,7,5828/(18150-45375*x)-(313+502*x)/(2904*x^2+1452)-251/726*arctan(sqrt(2)*x)/sqrt(2)+272/1331*sqrt(2)*arctan(sqrt(2)*x)-59096/99825*ln(2-5*x)+2843/7986*ln(2*x^2+1),1],
[(x^4+9)/x^2/(x^2+9),x,3,-1/x+x-10/3*arctan(1/3*x),1],
[(x^4+2*x)/(x^2+1),x,6,-x+1/3*x^3+arctan(x)+ln(x^2+1),1],
[(x^3-x)/(-1+x)^2/(x^2+1),x,5,arctan(x)+ln(1-x),1],
[(2*x^3+3*x^2+5*x+2)/(x^2+x+1),x,3,x+x^2+ln(x^2+x+1),1],
[(3*x^3-5*x^2-4*x+3)/x^3/(x^2+x-1),x,4,3/2/x^2-1/x+3*ln(x)-1/10*(15-sqrt(5))*ln(1-sqrt(5)+2*x)-1/10*(15+sqrt(5))*ln(1+sqrt(5)+2*x),1],
[(2*x^3+5*x^2+8*x+4)/(x^2+2*x+2)^2,x,5,-1/(x^2+2*x+2)-arctan(1+x)+ln(x^2+2*x+2),1],
[(-1+x)^4*x^4/(x^2+1),x,3,4*x-4/3*x^3+x^5-2/3*x^6+1/7*x^7-4*arctan(x),1],
[(4*x^2-20*x)/(x^4-10*x^2+9),x,3,ln(1-x)-1/2*ln(3-x)+3/2*ln(1+x)-2*ln(3+x),1],
[(4*x^3+x-1)/(-1+x)/x^2/(x^2+1),x,7,-1/x+arctan(x)+2*ln(1-x)-ln(x^2+1),1],
[(x^4-4*x^3+2*x^2-3*x+1)/(x^2+1)^3,x,3,1/4*x^2/(x^2+1)^2+7/(4*x^2+4)+arctan(x),1],
[(x^4-4*x^3+2*x^2-3*x+1)/(x^6+3*x^4+3*x^2+1),x,5,-1/4/(x^2+1)^2+2/(x^2+1)+arctan(x),1],
[(2*x^3+2*x^2+x+1)/(x^4+x^3+x^2),x,4,-1/x+ln(x^2+x+1),1], // Charlwood
[arcsin(x)*ln(x),x,8,arctanh((-x^2+1)^(1/2))-x*arcsin(x)*(1-ln(x))-2*(-x^2+1)^(1/2)+ln(x)*(-x^2+1)^(1/2),1],
[x*arcsin(x)/(-x^2+1)^(1/2),x,2,x-arcsin(x)*(-x^2+1)^(1/2),1],
[-arcsin(x^(1/2)-(1+x)^(1/2)),x,-3,-(3/8+x)*arcsin(x^(1/2)-(1+x)^(1/2))+1/8*(x^(1/2)+3*(1+x)^(1/2))*(-x+x^(1/2)*(1+x)^(1/2))^(1/2)*2^(1/2),1],
[ln(1+x*(x^2+1)^(1/2)),x,-32,-2*x+x*ln(1+x*(x^2+1)^(1/2))-arctanh((x+(x^2+1)^(1/2))*(2+5^(1/2))^(1/2))*(-2+2*5^(1/2))^(1/2)+arctan((x+(x^2+1)^(1/2))*(-2+5^(1/2))^(1/2))*(2+2*5^(1/2))^(1/2),1],
[cos(x)^2/(1+cos(x)^2+cos(x)^4)^(1/2),x,-5,1/3*x+1/3*arctan(cos(x)*(1+cos(x)^2)*sin(x)/(1+cos(x)^2*(1+cos(x)^2+cos(x)^4)^(1/2))),1],
[(1+tan(x)^4)^(1/2)*tan(x),x,7,-1/2*arcsinh(tan(x)^2)-1/2*arctanh(1/2*(1-tan(x)^2)*2^(1/2)/(1+tan(x)^4)^(1/2))*2^(1/2)+1/2*(1+tan(x)^4)^(1/2),1],
[tan(x)/(1+sec(x)^3)^(1/2),x,4,-2/3*arctanh((1+sec(x)^3)^(1/2)),1],
[(2+2*tan(x)+tan(x)^2)^(1/2),x,9,arcsinh(1+tan(x))-1/2*arctanh((2*5^(1/2)+(5-5^(1/2))*tan(x))/(-10+10*5^(1/2))^(1/2)/(2+2*tan(x)+tan(x)^2)^(1/2))*(-2+2*5^(1/2))^(1/2)-1/2*arctan((2*5^(1/2)-(5+5^(1/2))*tan(x))/(10+10*5^(1/2))^(1/2)/(2+2*tan(x)+tan(x)^2)^(1/2))*(2+2*5^(1/2))^(1/2),1],
[arctan((-1+sec(x))^(1/2))*sin(x),x,7,1/2*arctan((-1+sec(x))^(1/2))-arctan((-1+sec(x))^(1/2))*cos(x)+1/2*cos(x)*(-1+sec(x))^(1/2),1],
[exp(arcsin(x))*x^3/(-x^2+1)^(1/2),x,5,1/10*exp(arcsin(x))*(3*x+x^3-3*(-x^2+1)^(1/2)-3*x^2*(-x^2+1)^(1/2)),1],
[x*ln(x^2+1)*ln(x+(x^2+1)^(1/2))/(x^2+1)^(1/2),x,7,4*x-2*arctan(x)-x*ln(x^2+1)-2*ln(x+(x^2+1)^(1/2))*(x^2+1)^(1/2)+ln(x^2+1)*ln(x+(x^2+1)^(1/2))*(x^2+1)^(1/2),1],
[arctan(x+(-x^2+1)^(1/2)),x,-40,-1/2*arcsin(x)+x*arctan(x+(-x^2+1)^(1/2))-1/4*arctanh(x*(-x^2+1)^(1/2))-1/8*ln(x^4-x^2+1)-1/4*arctan(1/3*(2*x^2-1)*3^(1/2))*3^(1/2)+1/4*arctan((-1+x*3^(1/2))/(-x^2+1)^(1/2))*3^(1/2)+1/4*arctan((1+x*3^(1/2))/(-x^2+1)^(1/2))*3^(1/2),1],
[x*arctan(x+(-x^2+1)^(1/2))/(-x^2+1)^(1/2),x,-32,-1/2*arcsin(x)+1/4*arctanh(x*(-x^2+1)^(1/2))+1/8*ln(x^4-x^2+1)-1/4*arctan(1/3*(2*x^2-1)*3^(1/2))*3^(1/2)+1/4*arctan((-1+x*3^(1/2))/(-x^2+1)^(1/2))*3^(1/2)+1/4*arctan((1+x*3^(1/2))/(-x^2+1)^(1/2))*3^(1/2)-arctan(x+(-x^2+1)^(1/2))*(-x^2+1)^(1/2),1],
[arcsin(x)/(1+(-x^2+1)^(1/2)),x,9,1/2*arcsin(x)^2-ln(1+(-x^2+1)^(1/2))-x*arcsin(x)/(1+(-x^2+1)^(1/2)),1],
[ln(x+(x^2+1)^(1/2))/(-x^2+1)^(3/2),x,3,-1/2*arcsin(x^2)+x*ln(x+(x^2+1)^(1/2))/(-x^2+1)^(1/2),1],
[arcsin(x)/(x^2+1)^(3/2),x,3,-1/2*arcsin(x^2)+x*arcsin(x)/(x^2+1)^(1/2),1],
[ln(x+(x^2-1)^(1/2))/(x^2+1)^(3/2),x,3,-1/2*arccosh(x^2)+x*ln(x+(x^2-1)^(1/2))/(x^2+1)^(1/2),1],
[ln(x)/x^2/(x^2-1)^(1/2),x,4,-arctanh(x/(x^2-1)^(1/2))+(x^2-1)^(1/2)/x+ln(x)*(x^2-1)^(1/2)/x,1],
[(x^3+1)^(1/2)/x,x,4,-2/3*arctanh((x^3+1)^(1/2))+2/3*(x^3+1)^(1/2),1],
[x*ln(x+(x^2-1)^(1/2))/(x^2-1)^(1/2),x,2,-x+ln(x+(x^2-1)^(1/2))*(x^2-1)^(1/2),1],
[x^3*arcsin(x)/(-x^4+1)^(1/2),x,5,1/4*arcsinh(x)+1/4*x*(x^2+1)^(1/2)-1/2*arcsin(x)*(-x^4+1)^(1/2),1],
[x^3*arcsec(x)/(x^4-1)^(1/2),x,7,1/2*arctanh(x*(1-1/x^2)^(1/2)/(x^4-1)^(1/2))+1/2*arcsec(x)*(x^4-1)^(1/2)-1/2*(x^4-1)^(1/2)/x/(1-1/x^2)^(1/2),1],
[x*arctan(x)*ln(x+(x^2+1)^(1/2))/(x^2+1)^(1/2),x,4,-x*arctan(x)+1/2*ln(x^2+1)-1/2*ln(x+(x^2+1)^(1/2))^2+arctan(x)*ln(x+(x^2+1)^(1/2))*(x^2+1)^(1/2),1],
[x*ln(1+(-x^2+1)^(1/2))/(-x^2+1)^(1/2),x,5,-ln(1+(-x^2+1)^(1/2))+(-x^2+1)^(1/2)-ln(1+(-x^2+1)^(1/2))*(-x^2+1)^(1/2),1],
[x*ln(x+(x^2+1)^(1/2))/(x^2+1)^(1/2),x,2,-x+ln(x+(x^2+1)^(1/2))*(x^2+1)^(1/2),1],
[x*ln(x+(-x^2+1)^(1/2))/(-x^2+1)^(1/2),x,18,1/2*arctanh(x*2^(1/2))*2^(1/2)-1/2*arctanh(2^(1/2)*(-x^2+1)^(1/2))*2^(1/2)+(-x^2+1)^(1/2)-ln(x+(-x^2+1)^(1/2))*(-x^2+1)^(1/2),1],
[ln(x)/x^2/(-x^2+1)^(1/2),x,3,-arcsin(x)-(-x^2+1)^(1/2)/x-ln(x)*(-x^2+1)^(1/2)/x,1],
[x*arctan(x)/(x^2+1)^(1/2),x,2,-arcsinh(x)+arctan(x)*(x^2+1)^(1/2),1],
[arctan(x)/x^2/(-x^2+1)^(1/2),x,7,-arctanh((-x^2+1)^(1/2))+arctanh(1/2*2^(1/2)*(-x^2+1)^(1/2))*2^(1/2)-arctan(x)*(-x^2+1)^(1/2)/x,1],
[x*arctan(x)/(-x^2+1)^(1/2),x,5,-arcsin(x)+arctan(x*2^(1/2)/(-x^2+1)^(1/2))*2^(1/2)-arctan(x)*(-x^2+1)^(1/2),1],
[arctan(x)/x^2/(x^2+1)^(1/2),x,4,-arctanh((x^2+1)^(1/2))-arctan(x)*(x^2+1)^(1/2)/x,1],
[arcsin(x)/x^2/(-x^2+1)^(1/2),x,2,ln(x)-arcsin(x)*(-x^2+1)^(1/2)/x,1],
[x*ln(x)/(x^2-1)^(1/2),x,5,arctan((x^2-1)^(1/2))-(x^2-1)^(1/2)+ln(x)*(x^2-1)^(1/2),1],
[ln(x)/x^2/(x^2+1)^(1/2),x,3,arcsinh(x)-(x^2+1)^(1/2)/x-ln(x)*(x^2+1)^(1/2)/x,1],
[x*arcsec(x)/(x^2-1)^(1/2),x,2,-x*ln(x)/(x^2)^(1/2)+arcsec(x)*(x^2-1)^(1/2),1],
[x*ln(x)/(x^2+1)^(1/2),x,5,arctanh((x^2+1)^(1/2))-(x^2+1)^(1/2)+ln(x)*(x^2+1)^(1/2),1],
[sin(x)/(1+sin(x)^2),x,2,-1/2*arctanh(1/2*cos(x)*2^(1/2))*2^(1/2),1],
[(x^2+1)/(-x^2+1)/(x^4+1)^(1/2),x,2,1/2*arctanh(x*2^(1/2)/(x^4+1)^(1/2))*2^(1/2),1],
[(-x^2+1)/(x^2+1)/(x^4+1)^(1/2),x,2,1/2*arctan(x*2^(1/2)/(x^4+1)^(1/2))*2^(1/2),1],
[ln(sin(x))/(1+sin(x)),x,4,-x-arctanh(cos(x))-cos(x)*ln(sin(x))/(1+sin(x)),1],
[ln(sin(x))*(1+sin(x))^(1/2),x,6,-4*arctanh(cos(x)/(1+sin(x))^(1/2))+4*cos(x)/(1+sin(x))^(1/2)-2*cos(x)*ln(sin(x))/(1+sin(x))^(1/2),1],
[sec(x)/(-1+sec(x)^4)^(1/2),x,-5,-1/2*arctanh(1/2*cos(x)*cot(x)*(-1+sec(x)^4)^(1/2)*2^(1/2))*2^(1/2),1],
[tan(x)/(1+tan(x)^4)^(1/2),x,4,-1/4*arctanh(1/2*(1-tan(x)^2)*2^(1/2)/(1+tan(x)^4)^(1/2))*2^(1/2),1],
[sin(x)/(1-sin(x)^6)^(1/2),x,4,1/6*arctanh(1/2*cos(x)*(1+sin(x)^2)*3^(1/2)/(1-sin(x)^6)^(1/2))*3^(1/2),1],
[fail,x,1,2,fail,1],//[(-(-1+sec(x))^(1/2)+(1+sec(x))^(1/2))^(1/2),x,-1,cot(x)*2^(1/2)*(-1+sec(x))^(1/2)*(1+sec(x))^(1/2)*(arctan(1/2*(-2^(1/2)-(-1+sec(x))^(1/2)+(1+sec(x))^(1/2))*(-2+2*2^(1/2))^(1/2)/(-(-1+sec(x))^(1/2)+(1+sec(x))^(1/2))^(1/2))*(2^(1/2)-1)^(1/2)+arctanh((2+2*2^(1/2))^(1/2)*(-(-1+sec(x))^(1/2)+(1+sec(x))^(1/2))^(1/2)/(2^(1/2)-(-1+sec(x))^(1/2)+(1+sec(x))^(1/2)))*(2^(1/2)-1)^(1/2)-arctan(1/2*(-2^(1/2)-(-1+sec(x))^(1/2)+(1+sec(x))^(1/2))*(2+2*2^(1/2))^(1/2)/(-(-1+sec(x))^(1/2)+(1+sec(x))^(1/2))^(1/2))*(1+2^(1/2))^(1/2)-arctanh((-2+2*2^(1/2))^(1/2)*(-(-1+sec(x))^(1/2)+(1+sec(x))^(1/2))^(1/2)/(2^(1/2)-(-1+sec(x))^(1/2)+(1+sec(x))^(1/2)))*(1+2^(1/2))^(1/2)),1],
[x*arctan(x)^2*ln(x^2+1),x,13,3*x*arctan(x)-3/2*arctan(x)^2-1/2*x^2*arctan(x)^2-3/2*ln(x^2+1)-x*arctan(x)*ln(x^2+1)+1/2*(x^2+1)*arctan(x)^2*ln(x^2+1)+1/4*ln(x^2+1)^2,1],
[arctan(x*(x^2+1)^(1/2)),x,12,-1/2*arctan(-3^(1/2)+2*(x^2+1)^(1/2))+x*arctan(x*(x^2+1)^(1/2))-1/2*arctan(3^(1/2)+2*(x^2+1)^(1/2))-1/4*ln(2+x^2-3^(1/2)*(x^2+1)^(1/2))*3^(1/2)+1/4*ln(2+x^2+3^(1/2)*(x^2+1)^(1/2))*3^(1/2),1],
[-arctan(x^(1/2)-(1+x)^(1/2)),x,6,-(1+x)*arctan(x^(1/2)-(1+x)^(1/2))+1/2*x^(1/2),1],
[arcsin(x/(-x^2+1)^(1/2)),x,4,x*arcsin(x/(-x^2+1)^(1/2))+arctan((-2*x^2+1)^(1/2)),1],
[arctan(x*(-x^2+1)^(1/2)),x,6,x*arctan(x*(-x^2+1)^(1/2))+1/2*arctanh(1/2*(-x^2+1)^(1/2)*(-2+2*5^(1/2))^(1/2))*(-2+2*5^(1/2))^(1/2)-1/2*arctan(1/2*(-x^2+1)^(1/2)*(2+2*5^(1/2))^(1/2))*(2+2*5^(1/2))^(1/2),1], // Hearn
[x^2+x+1,x,1,x+1/2*x^2+1/3*x^3,1],
[x^2*(2*x^2+x)^2,x,3,1/5*x^5+2/3*x^6+4/7*x^7,1],
[x*(x^2+2*x+1),x,2,1/2*x^2+2/3*x^3+1/4*x^4,1],
[1/x,x,1,ln(x),1],
[(1+x)^3/(-1+x)^4,x,2,8/3/(1-x)^3-6/(1-x)^2+6/(1-x)+ln(1-x),1],
[1/(-1+x)/x/(1+x)^2,x,2,-1/2/(1+x)+1/4*ln(1-x)-ln(x)+3/4*ln(1+x),1],
[(a*x+b)/(-p+x)/(-q+x),x,2,(a*p+b)*ln(p-x)/(p-q)-(a*q+b)*ln(q-x)/(p-q),1],
[1/(a*x^2+b*x+c),x,2,-2*arctanh((2*a*x+b)/(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2),1],
[(a*x+b)/(x^2+1),x,3,b*arctan(x)+1/2*a*ln(x^2+1),1],
[1/(x^2-2*x+3),x,2,-1/2*arctan(1/2*(1-x)*2^(1/2))*2^(1/2),1],
[1/(-1+x)^2/(x^2+1)^2,x,6,1/4/(1-x)-1/4/(x^2+1)+1/4*arctan(x)-1/2*ln(1-x)+1/4*ln(x^2+1),1],
[x/(-a+x)/(-b+x)/(-c+x),x,2,a*ln(a-x)/(a-b)/(a-c)-b*ln(b-x)/(a-b)/(b-c)+c*ln(c-x)/(a-c)/(b-c),1],
[x/(a^2+x^2)/(b^2+x^2),x,4,-1/2*ln(a^2+x^2)/(a^2-b^2)+1/2*ln(b^2+x^2)/(a^2-b^2),1],
[x^2/(a^2+x^2)/(b^2+x^2),x,3,a*arctan(x/a)/(a^2-b^2)-b*arctan(x/b)/(a^2-b^2),1],
[x/(-1+x)/(x^2+1),x,5,1/2*arctan(x)+1/2*ln(1-x)-1/4*ln(x^2+1),1],
[x/(x^3+1),x,6,-1/3*ln(1+x)+1/6*ln(x^2-x+1)-1/3*arctan(1/3*(1-2*x)*3^(1/2))*3^(1/2),1],
[x^3/(-1+x)^2/(x^3+1),x,3,1/2/(1-x)+3/4*ln(1-x)-1/12*ln(1+x)-1/3*ln(x^2-x+1),1],
[1/(x^4+1),x,9,1/4*arctan(-1+x*2^(1/2))*2^(1/2)+1/4*arctan(1+x*2^(1/2))*2^(1/2)-1/8*ln(1+x^2-x*2^(1/2))*2^(1/2)+1/8*ln(1+x^2+x*2^(1/2))*2^(1/2),1],
[x^2/(x^4+1),x,9,1/4*arctan(-1+x*2^(1/2))*2^(1/2)+1/4*arctan(1+x*2^(1/2))*2^(1/2)+1/8*ln(1+x^2-x*2^(1/2))*2^(1/2)-1/8*ln(1+x^2+x*2^(1/2))*2^(1/2),1],
[1/(x^4+x^2+1),x,9,-1/4*ln(x^2-x+1)+1/4*ln(x^2+x+1)-1/6*arctan(1/3*(1-2*x)*3^(1/2))*3^(1/2)+1/6*arctan(1/3*(1+2*x)*3^(1/2))*3^(1/2),1],
[(b*x+a)^p,x,1,(b*x+a)^(1+p)/b/(1+p),1],
[x*(b*x+a)^p,x,2,-a*(b*x+a)^(1+p)/b^2/(1+p)+(b*x+a)^(2+p)/b^2/(2+p),1],
[x^2*(b*x+a)^p,x,2,a^2*(b*x+a)^(1+p)/b^3/(1+p)-2*a*(b*x+a)^(2+p)/b^3/(2+p)+(b*x+a)^(3+p)/b^3/(3+p),1],
[1/(b*x+a),x,1,ln(b*x+a)/b,1],
[1/(b*x+a)^2,x,1,-1/b/(b*x+a),1],
[x/(b*x+a),x,2,x/b-a*ln(b*x+a)/b^2,1],
[x^2/(b*x+a),x,2,-a*x/b^2+1/2*x^2/b+a^2*ln(b*x+a)/b^3,1],
[1/x/(b*x+a),x,3,ln(x)/a-ln(b*x+a)/a,1],
[1/x^2/(b*x+a),x,2,-1/a/x-b*ln(x)/a^2+b*ln(b*x+a)/a^2,1],
[1/x^2/(b*x+a)^2,x,2,-1/a^2/x-b/a^2/(b*x+a)-2*b*ln(x)/a^3+2*b*ln(b*x+a)/a^3,1],
[1/(c^2+x^2),x,1,arctan(x/c)/c,1],
[1/(c^2-x^2),x,1,arctanh(x/c)/c,1],
[1/(2*x^3-1),x,6,1/6*ln(1-2^(1/3)*x)*2^(2/3)-1/12*ln(1+2^(1/3)*x+2^(2/3)*x^2)*2^(2/3)-1/6*arctan(1/3*(1+2*2^(1/3)*x)*3^(1/2))*2^(2/3)*3^(1/2),1],
[1/(x^3-2),x,6,1/6*ln(2^(1/3)-x)*2^(1/3)-1/12*ln(2^(2/3)+2^(1/3)*x+x^2)*2^(1/3)-1/6*arctan(1/3*(1+2^(2/3)*x)*3^(1/2))*2^(1/3)*3^(1/2),1],
[1/(a*x^3-b),x,6,1/3*ln(b^(1/3)-a^(1/3)*x)/a^(1/3)/b^(2/3)-1/6*ln(b^(2/3)+a^(1/3)*b^(1/3)*x+a^(2/3)*x^2)/a^(1/3)/b^(2/3)-1/3*arctan(1/3*(b^(1/3)+2*a^(1/3)*x)/b^(1/3)*3^(1/2))/a^(1/3)/b^(2/3)*3^(1/2),1],
[1/(x^4-2),x,3,-1/4*arctan(1/2*x*2^(3/4))*2^(1/4)-1/4*arctanh(1/2*x*2^(3/4))*2^(1/4),1],
[1/(5*x^4-1),x,3,-1/10*arctan(5^(1/4)*x)*5^(3/4)-1/10*arctanh(5^(1/4)*x)*5^(3/4),1],
[1/(3*x^4+7),x,9,1/84*arctan(-1+1/7*3^(1/4)*7^(3/4)*x*2^(1/2))*3^(3/4)*7^(1/4)*2^(1/2)+1/84*arctan(1+1/7*3^(1/4)*7^(3/4)*x*2^(1/2))*3^(3/4)*7^(1/4)*2^(1/2)-1/168*ln(3*x^2-3^(3/4)*7^(1/4)*x*2^(1/2)+21^(1/2))*3^(3/4)*7^(1/4)*2^(1/2)+1/168*ln(3*x^2+3^(3/4)*7^(1/4)*x*2^(1/2)+21^(1/2))*3^(3/4)*7^(1/4)*2^(1/2),1],
[1/(x^4+3*x^2-1),x,3,-1/13*arctan(x*2^(1/2)/(3+13^(1/2))^(1/2))*26^(1/2)/(3+13^(1/2))^(1/2)-1/26*arctanh(x*2^(1/2)/(-3+13^(1/2))^(1/2))*(78+26*13^(1/2))^(1/2),1],
[1/(x^4-3*x^2-1),x,3,-1/13*arctanh(x*2^(1/2)/(3+13^(1/2))^(1/2))*26^(1/2)/(3+13^(1/2))^(1/2)-1/26*arctan(x*2^(1/2)/(-3+13^(1/2))^(1/2))*(78+26*13^(1/2))^(1/2),1],
[1/(x^4-3*x^2+1),x,3,-1/5*arctanh(x*2^(1/2)/(3+5^(1/2))^(1/2))*10^(1/2)/(3+5^(1/2))^(1/2)+arctanh(x*(1/2+1/2*5^(1/2)))*(1/2+1/10*5^(1/2)),1],
[1/(x^4-4*x^2+1),x,3,1/2*arctanh(x/(1/2*6^(1/2)-1/2*2^(1/2)))/(3/2*2^(1/2)-1/2*6^(1/2))-1/2*arctanh(x/(1/2*6^(1/2)+1/2*2^(1/2)))/(3/2*2^(1/2)+1/2*6^(1/2)),1],
[1/(x^4+4*x^2+1),x,3,1/2*arctan(x/(1/2*6^(1/2)-1/2*2^(1/2)))/(3/2*2^(1/2)-1/2*6^(1/2))-1/2*arctan(x/(1/2*6^(1/2)+1/2*2^(1/2)))/(3/2*2^(1/2)+1/2*6^(1/2)),1],
[1/(x^4+x^2+2),x,9,-1/28*arctan((-2*x+(-1+2*2^(1/2))^(1/2))/(1+2*2^(1/2))^(1/2))*(-14+28*2^(1/2))^(1/2)+1/28*arctan((2*x+(-1+2*2^(1/2))^(1/2))/(1+2*2^(1/2))^(1/2))*(-14+28*2^(1/2))^(1/2)-1/4*ln(x^2+2^(1/2)-x*(-1+2*2^(1/2))^(1/2))/(-2+4*2^(1/2))^(1/2)+1/4*ln(x^2+2^(1/2)+x*(-1+2*2^(1/2))^(1/2))/(-2+4*2^(1/2))^(1/2),1],
[1/(x^4-x^2+2),x,9,-1/28*arctan((-2*x+(1+2*2^(1/2))^(1/2))/(-1+2*2^(1/2))^(1/2))*(14+28*2^(1/2))^(1/2)+1/28*arctan((2*x+(1+2*2^(1/2))^(1/2))/(-1+2*2^(1/2))^(1/2))*(14+28*2^(1/2))^(1/2)-1/4*ln(x^2+2^(1/2)-x*(1+2*2^(1/2))^(1/2))/(2+4*2^(1/2))^(1/2)+1/4*ln(x^2+2^(1/2)+x*(1+2*2^(1/2))^(1/2))/(2+4*2^(1/2))^(1/2),1],
[1/(x^6-1),x,10,-1/3*arctanh(x)+1/12*ln(x^2-x+1)-1/12*ln(x^2+x+1)+1/6*arctan(1/3*(1-2*x)*3^(1/2))*3^(1/2)-1/6*arctan(1/3*(1+2*x)*3^(1/2))*3^(1/2),1],
[1/(x^6-2),x,10,-1/6*arctanh(1/2*x*2^(5/6))*2^(1/6)+1/24*ln(2^(1/3)-2^(1/6)*x+x^2)*2^(1/6)-1/24*ln(2^(1/3)+2^(1/6)*x+x^2)*2^(1/6)-1/12*arctan(-1/3*3^(1/2)+1/3*2^(5/6)*x*3^(1/2))*2^(1/6)*3^(1/2)-1/12*arctan(1/3*3^(1/2)+1/3*2^(5/6)*x*3^(1/2))*2^(1/6)*3^(1/2),1],
[1/(x^6+2),x,10,1/6*arctan(1/2*x*2^(5/6))*2^(1/6)+1/12*arctan(x*2^(5/6)-3^(1/2))*2^(1/6)+1/12*arctan(x*2^(5/6)+3^(1/2))*2^(1/6)-1/24*ln(2^(1/3)+x^2-2^(1/6)*x*3^(1/2))*2^(1/6)*3^(1/2)+1/24*ln(2^(1/3)+x^2+2^(1/6)*x*3^(1/2))*2^(1/6)*3^(1/2),1],
[1/(x^8+1),x,19,-1/16*ln(1+x^2-x*(2-2^(1/2))^(1/2))*(2-2^(1/2))^(1/2)+1/16*ln(1+x^2+x*(2-2^(1/2))^(1/2))*(2-2^(1/2))^(1/2)-1/4*arctan((-2*x+(2-2^(1/2))^(1/2))/(2+2^(1/2))^(1/2))/(4-2*2^(1/2))^(1/2)+1/4*arctan((2*x+(2-2^(1/2))^(1/2))/(2+2^(1/2))^(1/2))/(4-2*2^(1/2))^(1/2)-1/16*ln(1+x^2-x*(2+2^(1/2))^(1/2))*(2+2^(1/2))^(1/2)+1/16*ln(1+x^2+x*(2+2^(1/2))^(1/2))*(2+2^(1/2))^(1/2)-1/4*arctan((-2*x+(2+2^(1/2))^(1/2))/(2-2^(1/2))^(1/2))/(4+2*2^(1/2))^(1/2)+1/4*arctan((2*x+(2+2^(1/2))^(1/2))/(2-2^(1/2))^(1/2))/(4+2*2^(1/2))^(1/2),1],
[1/(x^8-1),x,13,-1/4*arctan(x)-1/4*arctanh(x)-1/8*arctan(-1+x*2^(1/2))*2^(1/2)-1/8*arctan(1+x*2^(1/2))*2^(1/2)+1/16*ln(1+x^2-x*2^(1/2))*2^(1/2)-1/16*ln(1+x^2+x*2^(1/2))*2^(1/2),1],
[1/(x^8-x^4+1),x,19,-1/12*arctan((-2*x+1/2*6^(1/2)-1/2*2^(1/2))/(1/2*6^(1/2)+1/2*2^(1/2)))*6^(1/2)+1/12*arctan((2*x+1/2*6^(1/2)-1/2*2^(1/2))/(1/2*6^(1/2)+1/2*2^(1/2)))*6^(1/2)-1/12*arctan((-2*x+1/2*6^(1/2)+1/2*2^(1/2))/(1/2*6^(1/2)-1/2*2^(1/2)))*6^(1/2)+1/12*arctan((2*x+1/2*6^(1/2)+1/2*2^(1/2))/(1/2*6^(1/2)-1/2*2^(1/2)))*6^(1/2)-1/24*ln(1+x^2-x*(1/2*6^(1/2)-1/2*2^(1/2)))*6^(1/2)+1/24*ln(1+x^2+x*(1/2*6^(1/2)-1/2*2^(1/2)))*6^(1/2)-1/24*ln(1+x^2-x*(1/2*6^(1/2)+1/2*2^(1/2)))*6^(1/2)+1/24*ln(1+x^2+x*(1/2*6^(1/2)+1/2*2^(1/2)))*6^(1/2),1],
[x^7/(x^12+1),x,7,-1/12*ln(x^4+1)+1/24*ln(x^8-x^4+1)-1/12*arctan(1/3*(-2*x^4+1)*3^(1/2))*3^(1/2),1],
[ln(x),x,1,-x+x*ln(x),1],
[x*ln(x),x,1,-1/4*x^2+1/2*x^2*ln(x),1],
[x^2*ln(x),x,1,-1/9*x^3+1/3*x^3*ln(x),1],
[x^p*ln(x),x,1,-x^(1+p)/(1+p)^2+x^(1+p)*ln(x)/(1+p),1],
[ln(x)^2,x,2,2*x-2*x*ln(x)+x*ln(x)^2,1],
[x^9*ln(x)^11,x,11,-6237/156250000*x^10+6237/15625000*x^10*ln(x)-6237/3125000*x^10*ln(x)^2+2079/312500*x^10*ln(x)^3-2079/125000*x^10*ln(x)^4+2079/62500*x^10*ln(x)^5-693/12500*x^10*ln(x)^6+99/1250*x^10*ln(x)^7-99/1000*x^10*ln(x)^8+11/100*x^10*ln(x)^9-11/100*x^10*ln(x)^10+1/10*x^10*ln(x)^11,1],
[ln(x)^2/x,x,2,1/3*ln(x)^3,1],
[1/ln(x),x,1,Li(x),1],
[1/ln(1+x),x,2,Li(1+x),1],
[1/x/ln(x),x,2,ln(ln(x)),1],
[1/x^2/ln(x)^2,x,3,-Ei(-ln(x))-1/x/ln(x),1],
[ln(x)^p/x,x,2,ln(x)^(1+p)/(1+p),1],
[(a*x+b)*ln(x),x,2,-b*x-1/4*a*x^2+b*x*ln(x)+1/2*a*x^2*ln(x),1],
[(a*x+b)^2*ln(x),x,4,-b^2*x-1/2*a*b*x^2-1/9*a^2*x^3-1/3*b^3*ln(x)/a+1/3*(a*x+b)^3*ln(x)/a,1],
[ln(x)/(a*x+b)^2,x,2,x*ln(x)/b/(a*x+b)-ln(a*x+b)/a/b,1],
[x*ln(a*x+b),x,3,1/2*b*x/a-1/4*x^2-1/2*b^2*ln(a*x+b)/a^2+1/2*x^2*ln(a*x+b),1],
[x^2*ln(a*x+b),x,3,-1/3*b^2*x/a^2+1/6*b*x^2/a-1/9*x^3+1/3*b^3*ln(a*x+b)/a^3+1/3*x^3*ln(a*x+b),1],
[ln(a^2+x^2),x,3,-2*x+2*a*arctan(x/a)+x*ln(a^2+x^2),1],
[x*ln(a^2+x^2),x,3,-1/2*x^2+1/2*(a^2+x^2)*ln(a^2+x^2),1],
[x^2*ln(a^2+x^2),x,4,2/3*a^2*x-2/9*x^3-2/3*a^3*arctan(x/a)+1/3*x^3*ln(a^2+x^2),1],
[x^4*ln(a^2+x^2),x,4,-2/5*a^4*x+2/15*a^2*x^3-2/25*x^5+2/5*a^5*arctan(x/a)+1/5*x^5*ln(a^2+x^2),1],
[ln(-a^2+x^2),x,3,-2*x+2*a*arctanh(x/a)+x*ln(-a^2+x^2),1],
[ln(ln(ln(ln(x)))),x,0,CannotIntegrate(ln(ln(ln(ln(x)))),x),0],
[sin(x),x,1,-cos(x),1],
[cos(x),x,1,sin(x),1],
[tan(x),x,1,-ln(cos(x)),1],
[1/tan(x),x,1,ln(sin(x)),1],
[1/(1+tan(x))^2,x,2,1/2*ln(cos(x)+sin(x))-1/2/(1+tan(x)),1],
[1/cos(x),x,1,arctanh(sin(x)),1],
[1/sin(x),x,1,-arctanh(cos(x)),1],
[sin(x)^2,x,2,1/2*x-1/2*cos(x)*sin(x),1],
[x^3*sin(x^2),x,3,-1/2*x^2*cos(x^2)+1/2*sin(x^2),1],
[sin(x)^3,x,2,-cos(x)+1/3*cos(x)^3,1],
[sin(x)^p,x,1,cos(x)*hypergeom([1/2, 1/2+1/2*p],[3/2+1/2*p],sin(x)^2)*sin(x)^(1+p)/(1+p)/(cos(x)^2)^(1/2),1],
[cos(x)*(1+sin(x)^2)^2,x,3,sin(x)+2/3*sin(x)^3+1/5*sin(x)^5,1],
[cos(x)^2,x,2,1/2*x+1/2*cos(x)*sin(x),1],
[cos(x)^3,x,2,sin(x)-1/3*sin(x)^3,1],
[1/cos(x)^2,x,2,tan(x),1],
[sin(x)*sin(2*x),x,1,1/2*sin(x)-1/6*sin(3*x),1],
[x*sin(x),x,2,-x*cos(x)+sin(x),1],
[x^2*sin(x),x,3,2*cos(x)-x^2*cos(x)+2*x*sin(x),1],
[x*sin(x)^2,x,2,1/4*x^2-1/2*x*cos(x)*sin(x)+1/4*sin(x)^2,1],
[x^2*sin(x)^2,x,4,-1/4*x+1/6*x^3+1/4*cos(x)*sin(x)-1/2*x^2*cos(x)*sin(x)+1/2*x*sin(x)^2,1],
[x*sin(x)^3,x,3,-2/3*x*cos(x)+2/3*sin(x)-1/3*x*cos(x)*sin(x)^2+1/9*sin(x)^3,1],
[x*cos(x),x,2,cos(x)+x*sin(x),1],
[x^2*cos(x),x,3,2*x*cos(x)-2*sin(x)+x^2*sin(x),1],
[x*cos(x)^2,x,2,1/4*x^2+1/4*cos(x)^2+1/2*x*cos(x)*sin(x),1],
[x^2*cos(x)^2,x,4,-1/4*x+1/6*x^3+1/2*x*cos(x)^2-1/4*cos(x)*sin(x)+1/2*x^2*cos(x)*sin(x),1],
[x*cos(x)^3,x,3,2/3*cos(x)+1/9*cos(x)^3+2/3*x*sin(x)+1/3*x*cos(x)^2*sin(x),1],
[sin(x)/x,x,1,Si(x),1],
[cos(x)/x,x,1,Ci(x),1],
[sin(x)/x^2,x,2,Ci(x)-sin(x)/x,1],
[sin(x)^2/x,x,3,-1/2*Ci(2*x)+1/2*ln(x),1],
[tan(x)^3,x,2,ln(cos(x))+1/2*tan(x)^2,1],
[sin(b*x+a),x,1,-cos(b*x+a)/b,1],
[cos(b*x+a),x,1,sin(b*x+a)/b,1],
[tan(b*x+a),x,1,-ln(cos(b*x+a))/b,1],
[1/tan(b*x+a),x,1,ln(sin(b*x+a))/b,1],
[1/sin(b*x+a),x,1,-arctanh(cos(b*x+a))/b,1],
[1/cos(b*x+a),x,1,arctanh(sin(b*x+a))/b,1],
[sin(b*x+a)^2,x,2,1/2*x-1/2*cos(b*x+a)*sin(b*x+a)/b,1],
[sin(b*x+a)^3,x,2,-cos(b*x+a)/b+1/3*cos(b*x+a)^3/b,1],
[cos(b*x+a)^2,x,2,1/2*x+1/2*cos(b*x+a)*sin(b*x+a)/b,1],
[cos(b*x+a)^3,x,2,sin(b*x+a)/b-1/3*sin(b*x+a)^3/b,1],
[1/cos(b*x+a)^2,x,2,tan(b*x+a)/b,1],
[1/(1+cos(x)),x,1,sin(x)/(1+cos(x)),1],
[1/(1-cos(x)),x,1,-sin(x)/(1-cos(x)),1],
[1/(1+sin(x)),x,1,-cos(x)/(1+sin(x)),1],
[1/(1-sin(x)),x,1,cos(x)/(1-sin(x)),1],
[1/(a+b*sin(x)),x,3,2*arctan((b+a*tan(1/2*x))/(a^2-b^2)^(1/2))/(a^2-b^2)^(1/2),1],
[1/(a+cos(x)+b*sin(x)),x,3,-2*arctanh((b-(1-a)*tan(1/2*x))/(-a^2+b^2+1)^(1/2))/(-a^2+b^2+1)^(1/2),1],
[x^2*sin(b*x+a)^2,x,4,-1/4*x/b^2+1/6*x^3+1/4*cos(b*x+a)*sin(b*x+a)/b^3-1/2*x^2*cos(b*x+a)*sin(b*x+a)/b+1/2*x*sin(b*x+a)^2/b^2,1],
[cos(x)*cos(2*x),x,1,1/2*sin(x)+1/6*sin(3*x),1],
[x^2*cos(b*x+a)^2,x,4,-1/4*x/b^2+1/6*x^3+1/2*x*cos(b*x+a)^2/b^2-1/4*cos(b*x+a)*sin(b*x+a)/b^3+1/2*x^2*cos(b*x+a)*sin(b*x+a)/b,1],
[1/tan(x)^3,x,2,-1/2*cot(x)^2-ln(sin(x)),1],
[x^3*tan(x)^4,x,17,-1/2*x^2+4/3*I*x^3+1/4*x^4-4*x^2*ln(1+exp(2*I*x))+ln(cos(x))+4*I*x*polylog(2,-exp(2*I*x))-2*polylog(3,-exp(2*I*x))+x*tan(x)-x^3*tan(x)-1/2*x^2*tan(x)^2+1/3*x^3*tan(x)^3,1],
[x^3*tan(x)^6,x,34,19/20*x^2-23/15*I*x^3-1/4*x^4+23/5*x^2*ln(1+exp(2*I*x))-2*ln(cos(x))-23/5*I*x*polylog(2,-exp(2*I*x))+23/10*polylog(3,-exp(2*I*x))-19/10*x*tan(x)+x^3*tan(x)-1/20*tan(x)^2+4/5*x^2*tan(x)^2+1/10*x*tan(x)^3-1/3*x^3*tan(x)^3-3/20*x^2*tan(x)^4+1/5*x^3*tan(x)^5,1],
[x*tan(x)^2,x,3,-1/2*x^2+ln(cos(x))+x*tan(x),1],
[cos(3*x)*sin(2*x),x,1,1/2*cos(x)-1/10*cos(5*x),1],
[cos(x)^2*sin(x)^2,x,3,1/8*x+1/8*cos(x)*sin(x)-1/4*cos(x)^3*sin(x),1],
[1/cos(x)^2/sin(x)^2,x,3,-cot(x)+tan(x),1],
[d^x*sin(x),x,1,-d^x*cos(x)/(1+ln(d)^2)+d^x*ln(d)*sin(x)/(1+ln(d)^2),1],
[d^x*cos(x),x,1,d^x*cos(x)*ln(d)/(1+ln(d)^2)+d^x*sin(x)/(1+ln(d)^2),1],
[d^x*x*sin(x),x,"nock",2*d^x*cos(x)*ln(d)/(1+ln(d)^2)^2-d^x*x*cos(x)/(1+ln(d)^2)+d^x*sin(x)/(1+ln(d)^2)^2-d^x*ln(d)^2*sin(x)/(1+ln(d)^2)^2+d^x*x*ln(d)*sin(x)/(1+ln(d)^2),1],
[d^x*x*cos(x),x,"nock",d^x*cos(x)/(1+ln(d)^2)^2-d^x*cos(x)*ln(d)^2/(1+ln(d)^2)^2+d^x*x*cos(x)*ln(d)/(1+ln(d)^2)-2*d^x*ln(d)*sin(x)/(1+ln(d)^2)^2+d^x*x*sin(x)/(1+ln(d)^2),1],
[d^x*x^2*sin(x),x,"nock",2*d^x*cos(x)/(1+ln(d)^2)^3-6*d^x*cos(x)*ln(d)^2/(1+ln(d)^2)^3+4*d^x*x*cos(x)*ln(d)/(1+ln(d)^2)^2-d^x*x^2*cos(x)/(1+ln(d)^2)-6*d^x*ln(d)*sin(x)/(1+ln(d)^2)^3+2*d^x*ln(d)^3*sin(x)/(1+ln(d)^2)^3+2*d^x*x*sin(x)/(1+ln(d)^2)^2-2*d^x*x*ln(d)^2*sin(x)/(1+ln(d)^2)^2+d^x*x^2*ln(d)*sin(x)/(1+ln(d)^2),1],
[d^x*x^2*cos(x),x,"nock",-6*d^x*cos(x)*ln(d)/(1+ln(d)^2)^3+2*d^x*cos(x)*ln(d)^3/(1+ln(d)^2)^3+2*d^x*x*cos(x)/(1+ln(d)^2)^2-2*d^x*x*cos(x)*ln(d)^2/(1+ln(d)^2)^2+d^x*x^2*cos(x)*ln(d)/(1+ln(d)^2)-2*d^x*sin(x)/(1+ln(d)^2)^3+6*d^x*ln(d)^2*sin(x)/(1+ln(d)^2)^3-4*d^x*x*ln(d)*sin(x)/(1+ln(d)^2)^2+d^x*x^2*sin(x)/(1+ln(d)^2),1],
[d^x*x^3*sin(x),x,"nock",-24*d^x*cos(x)*ln(d)/(1+ln(d)^2)^4+24*d^x*cos(x)*ln(d)^3/(1+ln(d)^2)^4+6*d^x*x*cos(x)/(1+ln(d)^2)^3-18*d^x*x*cos(x)*ln(d)^2/(1+ln(d)^2)^3+6*d^x*x^2*cos(x)*ln(d)/(1+ln(d)^2)^2-d^x*x^3*cos(x)/(1+ln(d)^2)-6*d^x*sin(x)/(1+ln(d)^2)^4+36*d^x*ln(d)^2*sin(x)/(1+ln(d)^2)^4-6*d^x*ln(d)^4*sin(x)/(1+ln(d)^2)^4-18*d^x*x*ln(d)*sin(x)/(1+ln(d)^2)^3+6*d^x*x*ln(d)^3*sin(x)/(1+ln(d)^2)^3+3*d^x*x^2*sin(x)/(1+ln(d)^2)^2-3*d^x*x^2*ln(d)^2*sin(x)/(1+ln(d)^2)^2+d^x*x^3*ln(d)*sin(x)/(1+ln(d)^2),1],
[d^x*x^3*cos(x),x,"nock",-6*d^x*cos(x)/(1+ln(d)^2)^4+36*d^x*cos(x)*ln(d)^2/(1+ln(d)^2)^4-6*d^x*cos(x)*ln(d)^4/(1+ln(d)^2)^4-18*d^x*x*cos(x)*ln(d)/(1+ln(d)^2)^3+6*d^x*x*cos(x)*ln(d)^3/(1+ln(d)^2)^3+3*d^x*x^2*cos(x)/(1+ln(d)^2)^2-3*d^x*x^2*cos(x)*ln(d)^2/(1+ln(d)^2)^2+d^x*x^3*cos(x)*ln(d)/(1+ln(d)^2)+24*d^x*ln(d)*sin(x)/(1+ln(d)^2)^4-24*d^x*ln(d)^3*sin(x)/(1+ln(d)^2)^4-6*d^x*x*sin(x)/(1+ln(d)^2)^3+18*d^x*x*ln(d)^2*sin(x)/(1+ln(d)^2)^3-6*d^x*x^2*ln(d)*sin(x)/(1+ln(d)^2)^2+d^x*x^3*sin(x)/(1+ln(d)^2),1],
[sin(x)*sin(2*x)*sin(3*x),x,5,-1/8*cos(2*x)-1/16*cos(4*x)+1/24*cos(6*x),1],
[cos(x)*cos(2*x)*cos(3*x),x,5,1/4*x+1/8*sin(2*x)+1/16*sin(4*x)+1/24*sin(6*x),1],
[x^2*sin(k*x)^3,x,6,14/9*cos(k*x)/k^3-2/3*x^2*cos(k*x)/k-2/27*cos(k*x)^3/k^3+4/3*x*sin(k*x)/k^2-1/3*x^2*cos(k*x)*sin(k*x)^2/k+2/9*x*sin(k*x)^3/k^2,1],
[x*cos(x)*cos(k/sin(x))/sin(x)^2,x,0,CannotIntegrate(x*cos(k*csc(x))*cot(x)*csc(x),x),0],
[cos(x)/sin(x)/tan(1/2*x),x,4,-x-cot(1/2*x),1],
[sin(a*x)/(b+c*sin(a*x))^2,x,5,-2*c*arctan((c+b*tan(1/2*a*x))/(b^2-c^2)^(1/2))/a/(b^2-c^2)^(3/2)-b*cos(a*x)/a/(b^2-c^2)/(b+c*sin(a*x)),1],
[sin(ln(x)),x,1,-1/2*x*cos(ln(x))+1/2*x*sin(ln(x)),1],
[cos(ln(x)),x,1,1/2*x*cos(ln(x))+1/2*x*sin(ln(x)),1],
[exp(x),x,1,exp(x),1],
[a^x,x,1,a^x/ln(a),1],
[exp(a*x),x,1,exp(a*x)/a,1],
[exp(a*x)/x,x,1,Ei(a*x),1],
[1/(a+b*exp(m*x)),x,4,x/a-ln(a+b*exp(m*x))/a/m,1],
[exp(2*x)/(1+exp(x)),x,3,exp(x)-ln(1+exp(x)),1],
[exp(a*x+2*x),x,2,exp((2+a)*x)/(2+a),1],
[1/(b/exp(m*x)+a*exp(m*x)),x,2,arctan(exp(m*x)*a^(1/2)/b^(1/2))/m/a^(1/2)/b^(1/2),1],
[exp(a*x)*x,x,2,-exp(a*x)/a^2+exp(a*x)*x/a,1],
[exp(x)*x^20,x,21,2432902008176640000*exp(x)-2432902008176640000*exp(x)*x+1216451004088320000*exp(x)*x^2-405483668029440000*exp(x)*x^3+101370917007360000*exp(x)*x^4-20274183401472000*exp(x)*x^5+3379030566912000*exp(x)*x^6-482718652416000*exp(x)*x^7+60339831552000*exp(x)*x^8-6704425728000*exp(x)*x^9+670442572800*exp(x)*x^10-60949324800*exp(x)*x^11+5079110400*exp(x)*x^12-390700800*exp(x)*x^13+27907200*exp(x)*x^14-1860480*exp(x)*x^15+116280*exp(x)*x^16-6840*exp(x)*x^17+380*exp(x)*x^18-20*exp(x)*x^19+exp(x)*x^20,1],
[a^x/(b^x),x,2,a^x/(b^x)/(ln(a)-ln(b)),1],
[a^x*b^x,x,2,a^x*b^x/(ln(a)+ln(b)),1],
[a^x/x^2,x,2,-a^x/x+Ei(x*ln(a))*ln(a),1],
[a^x*x/(b*x+1)^2,x,5,a^x/b^2/(b*x+1)+Ei((b*x+1)*ln(a)/b)/(a^(1/b))/b^2-Ei((b*x+1)*ln(a)/b)*ln(a)/(a^(1/b))/b^3,1],
[exp(a*x)*x/(a*x+1)^2,x,1,exp(a*x)/a^2/(a*x+1),1],
[k^(x^2)*x,x,1,1/2*k^(x^2)/ln(k),1],
[exp(x^2),x,1,1/2*erfi(x)*Pi^(1/2),1],
[exp(x^2)*x,x,1,1/2*exp(x^2),1],
[exp(1/x)*(1+x)/x^4,x,7,-exp(1/x)-exp(1/x)/x^2+exp(1/x)/x,1],
[exp(1-exp(x^2)*x+2*x^2)*(2*x^3+x)/(1-exp(x^2)*x)^2,x,-3,-exp(1-exp(x^2)*x)/(-1+exp(x^2)*x),1],
[exp(exp(exp(exp(x)))),x,1,CannotIntegrate(exp(exp(exp(exp(x)))),x),0],
[exp(x)*ln(x),x,2,-Ei(x)+exp(x)*ln(x),1],
[exp(x)*x*ln(x),x,5,-exp(x)+Ei(x)-exp(x)*ln(x)+exp(x)*x*ln(x),1],
[exp(2*x)*ln(exp(x)),x,3,-1/4*exp(2*x)+1/2*exp(2*x)*ln(exp(x)),1],
[2*x+x^2*2^(1/2),x,1,x^2+1/3*x^3*2^(1/2),1],
[ln(x)/(a*x+b)^(1/2),x,4,4*arctanh((a*x+b)^(1/2)/b^(1/2))*b^(1/2)/a-4*(a*x+b)^(1/2)/a+2*ln(x)*(a*x+b)^(1/2)/a,1],
[(b*x+a)^(1/2)*(d*x+c)^(1/2),x,5,-1/4*(-a*d+b*c)^2*arctanh(d^(1/2)*(b*x+a)^(1/2)/b^(1/2)/(d*x+c)^(1/2))/b^(3/2)/d^(3/2)+1/2*(b*x+a)^(3/2)*(d*x+c)^(1/2)/b+1/4*(-a*d+b*c)*(b*x+a)^(1/2)*(d*x+c)^(1/2)/b/d,1],
[(b*x+a)^(1/2),x,1,2/3*(b*x+a)^(3/2)/b,1],
[x*(b*x+a)^(1/2),x,2,-2/3*a*(b*x+a)^(3/2)/b^2+2/5*(b*x+a)^(5/2)/b^2,1],
[x^2*(b*x+a)^(1/2),x,2,2/3*a^2*(b*x+a)^(3/2)/b^3-4/5*a*(b*x+a)^(5/2)/b^3+2/7*(b*x+a)^(7/2)/b^3,1],
[(b*x+a)^(1/2)/x,x,3,-2*arctanh((b*x+a)^(1/2)/a^(1/2))*a^(1/2)+2*(b*x+a)^(1/2),1],
[(b*x+a)^(1/2)/x^2,x,3,-b*arctanh((b*x+a)^(1/2)/a^(1/2))/a^(1/2)-(b*x+a)^(1/2)/x,1],
[1/(b*x+a)^(1/2),x,1,2*(b*x+a)^(1/2)/b,1],
[x/(b*x+a)^(1/2),x,2,2/3*(b*x+a)^(3/2)/b^2-2*a*(b*x+a)^(1/2)/b^2,1],
[x^2/(b*x+a)^(1/2),x,2,-4/3*a*(b*x+a)^(3/2)/b^3+2/5*(b*x+a)^(5/2)/b^3+2*a^2*(b*x+a)^(1/2)/b^3,1],
[1/x/(b*x+a)^(1/2),x,2,-2*arctanh((b*x+a)^(1/2)/a^(1/2))/a^(1/2),1],
[1/x^2/(b*x+a)^(1/2),x,3,b*arctanh((b*x+a)^(1/2)/a^(1/2))/a^(3/2)-(b*x+a)^(1/2)/a/x,1],
[((b*x+a)^(1/2))^p,x,1,2*(b*x+a)^(1+1/2*p)/b/(2+p),1],
[x*((b*x+a)^(1/2))^p,x,2,-2*a*(b*x+a)^(1+1/2*p)/b^2/(2+p)+2*(b*x+a)^(2+1/2*p)/b^2/(4+p),1],
[arctan(1/2*(2*x-2^(1/2))*2^(1/2)),x,6,x*arctan(-1+x*2^(1/2))-1/2*arctan(-1+x*2^(1/2))*2^(1/2)-1/4*ln(1+x^2-x*2^(1/2))*2^(1/2),1],
[1/(x^2-1)^(1/2),x,2,arctanh(x/(x^2-1)^(1/2)),1],
[x^(1/2)*(1+x)^(1/2),x,4,-1/4*arcsinh(x^(1/2))+1/2*x^(3/2)*(1+x)^(1/2)+1/4*x^(1/2)*(1+x)^(1/2),1],
[sin(x^(1/2)),x,3,2*sin(x^(1/2))-2*cos(x^(1/2))*x^(1/2),1],
[x/(-x^2+1)^(9/8),x,1,4/(-x^2+1)^(1/8),1],
[x/(-x^4+1)^(1/2),x,2,1/2*arcsin(x^2),1],
[1/x/(x^4+1)^(1/2),x,3,-1/2*arctanh((x^4+1)^(1/2)),1],
[x/(x^4+x^2+1)^(1/2),x,3,1/2*arcsinh(1/3*(2*x^2+1)*3^(1/2)),1],
[1/x/(-x^4+x^2-1)^(1/2),x,3,-1/2*arctan(1/2*(-x^2+2)/(-x^4+x^2-1)^(1/2)),1],
[(1+x)/(1-x)^2/(x^2+1)^(1/2),x,1,(x^2+1)^(1/2)/(1-x),1],
[1/(x^2+1)^(1/2),x,1,arcsinh(x),1],
[1/2*(x^(1/2)*(1+x)^(1/2)+x^(1/2)*(2+x)^(1/2)+(1+x)^(1/2)*(2+x)^(1/2))/x^(1/2)/(1+x)^(1/2)/(2+x)^(1/2),x,3,x^(1/2)+(1+x)^(1/2)+(2+x)^(1/2),1],
[1/2*(-2*(x^3+1)^(1/2)+5*x^4*(x^3+1)^(1/2)-3*x^2*(x^5-2*x+1)^(1/2))/(x^3+1)^(1/2)/(x^5-2*x+1)^(1/2),x,5,-(x^3+1)^(1/2)+(x^5-2*x+1)^(1/2),1],
[10/(x^2-4)^(1/2)+1/(x^2-1)^(1/2),x,5,10*arctanh(x/(x^2-4)^(1/2))+arctanh(x/(x^2-1)^(1/2)),1],
[(x+(a^2+x^2)^(1/2))^(1/2)/x,x,6,-2*arctan((x+(a^2+x^2)^(1/2))^(1/2)/a^(1/2))*a^(1/2)-2*arctanh((x+(a^2+x^2)^(1/2))^(1/2)/a^(1/2))*a^(1/2)+2*(x+(a^2+x^2)^(1/2))^(1/2),1],
[3/2*x^2/(1+x^3+(x^3+1)^(1/2)),x,4,ln(1+(x^3+1)^(1/2)),1],
[1/(2*h*r^2-alpha^2)^(1/2),r,2,1/2*arctanh(r*2^(1/2)*h^(1/2)/(2*h*r^2-alpha^2)^(1/2))*2^(1/2)/h^(1/2),1],
[1/r/(2*h*r^2-alpha^2-Epsilon^2)^(1/2),r,3,arctan((2*h*r^2-alpha^2-Epsilon^2)^(1/2)/(alpha^2+Epsilon^2)^(1/2))/(alpha^2+Epsilon^2)^(1/2),1],
[1/r/(2*h*r^2-alpha^2-2*k*r)^(1/2),r,2,-arctan((alpha^2+k*r)/alpha/(2*h*r^2-alpha^2-2*k*r)^(1/2))/alpha,1],
[1/r/(2*h*r^2-alpha^2-Epsilon^2-2*k*r)^(1/2),r,2,-arctan((alpha^2+Epsilon^2+k*r)/(alpha^2+Epsilon^2)^(1/2)/(2*h*r^2-alpha^2-Epsilon^2-2*k*r)^(1/2))/(alpha^2+Epsilon^2)^(1/2),1],
[r/(2*e*r^2-alpha^2)^(1/2),r,1,1/2*(2*e*r^2-alpha^2)^(1/2)/e,1],
[r/(2*e*r^2-alpha^2-Epsilon^2)^(1/2),r,1,1/2*(2*e*r^2-alpha^2-Epsilon^2)^(1/2)/e,1],
[r/(-2*k*r^4+2*e*r^2-alpha^2)^(1/2),r,3,-1/4*arctan(1/2*(-2*k*r^2+e)*2^(1/2)/k^(1/2)/(-2*k*r^4+2*e*r^2-alpha^2)^(1/2))*2^(1/2)/k^(1/2),1],
[r/(2*e*r^2-alpha^2-2*k*r)^(1/2),r,3,-1/4*k*arctanh(1/2*(-2*e*r+k)*2^(1/2)/e^(1/2)/(2*e*r^2-alpha^2-2*k*r)^(1/2))/e^(3/2)*2^(1/2)+1/2*(2*e*r^2-alpha^2-2*k*r)^(1/2)/e,1],
[1/r/(-2*k*r^4+2*h*r^2-alpha^2)^(1/2),r,3,-1/2*arctan((-h*r^2+alpha^2)/alpha/(-2*k*r^4+2*h*r^2-alpha^2)^(1/2))/alpha,1],
[1/r/(-2*k*r^4+2*h*r^2-alpha^2-Epsilon^2)^(1/2),r,3,-1/2*arctan((-h*r^2+alpha^2+Epsilon^2)/(alpha^2+Epsilon^2)^(1/2)/(-2*k*r^4+2*h*r^2-alpha^2-Epsilon^2)^(1/2))/(alpha^2+Epsilon^2)^(1/2),1],
[a*cos(5+3*x)*sin(5+3*x)^2,x,3,1/9*a*sin(5+3*x)^3,1],
[ln(x^2)/x^3,x,1,-1/2/x^2-1/2*ln(x^2)/x^2,1],
[x*sin(a+x),x,2,-x*cos(a+x)+sin(a+x),1],
[(-1+(1-x)*ln(x))/exp(x)/ln(x)^2,x,1,x/exp(x)/ln(x),1],
[x^3/(a*x^2+b),x,3,1/2*x^2/a-1/2*b*ln(a*x^2+b)/a^2,1],
[x^(1/2)/(1+x)^(7/2),x,2,2/5*x^(3/2)/(1+x)^(5/2)+4/15*x^(3/2)/(1+x)^(3/2),1],
[1/x/(1+x),x,3,ln(x)-ln(1+x),1],
[1/x^(1/2)/(-1+2*x),x,2,-arctanh(2^(1/2)*x^(1/2))*2^(1/2),1],
[x^(1/2)*(x^2+1),x,2,2/3*x^(3/2)+2/7*x^(7/2),1],
[(-a+x)^(1/3)/x,x,5,3*(-a+x)^(1/3)+1/2*a^(1/3)*ln(x)-3/2*a^(1/3)*ln(a^(1/3)+(-a+x)^(1/3))+a^(1/3)*arctan(1/3*(a^(1/3)-2*(-a+x)^(1/3))/a^(1/3)*3^(1/2))*3^(1/2),1],
[x*sinh(x),x,2,x*cosh(x)-sinh(x),1],
[x*cosh(x),x,2,-cosh(x)+x*sinh(x),1],
[sinh(2*x)/cosh(2*x),x,1,1/2*ln(cosh(2*x)),1],
[(-1+I*eps*sinh(x))/(I*a-x+I*eps*cosh(x)),x,1,ln(a+I*x+eps*cosh(x)),1],
[cos(x)^2*sin(3+2*x),x,4,-1/4*cos(3+2*x)-1/16*cos(3+4*x)+1/4*x*sin(3),1],
[x*arctan(x),x,3,-1/2*x+1/2*arctan(x)+1/2*x^2*arctan(x),1],
[x*arccot(x),x,3,1/2*x+1/2*x^2*arccot(x)-1/2*arctan(x),1],
[x*ln(x^2+a),x,3,-1/2*x^2+1/2*(x^2+a)*ln(x^2+a),1],
[cos(x)*sin(a+x),x,3,-1/4*cos(a+2*x)+1/2*x*sin(a),1],
[cos(a+x)*sin(x),x,3,-1/4*cos(a+2*x)-1/2*x*sin(a),1],
[(1+sin(x))^(1/2),x,1,-2*cos(x)/(1+sin(x))^(1/2),1],
[(1-sin(x))^(1/2),x,1,2*cos(x)/(1-sin(x))^(1/2),1],
[(1+cos(x))^(1/2),x,1,2*sin(x)/(1+cos(x))^(1/2),1],
[(1-cos(x))^(1/2),x,1,-2*sin(x)/(1-cos(x))^(1/2),1],
[1/(-(-1+x)^(1/2)+x^(1/2)),x,3,2/3*(-1+x)^(3/2)+2/3*x^(3/2),1],
[1/(1-(1+x)^(1/2)),x,4,-2*ln(1-(1+x)^(1/2))-2*(1+x)^(1/2),1],
[x/(x^4+36)^(1/2),x,2,1/2*arcsinh(1/6*x^2),1],
[1/(x^(1/3)+x^(1/2)),x,4,6*x^(1/6)-3*x^(1/3)-6*ln(1+x^(1/6))+2*x^(1/2),1],
[ln(3*x^2+2),x,3,-2*x+x*ln(3*x^2+2)+2/3*arctan(1/2*x*6^(1/2))*6^(1/2),1],
[cot(x),x,1,ln(sin(x)),1],
[cot(x)^4,x,3,x+cot(x)-1/3*cot(x)^3,1],
[tanh(x),x,1,ln(cosh(x)),1],
[coth(x),x,1,ln(sinh(x)),1],
[b^x,x,1,b^x/ln(b),1],
[(2+1/x^4+x^4)^(1/2),x,4,-x*(2+1/x^4+x^4)^(1/2)/(x^4+1)+1/3*x^5*(2+1/x^4+x^4)^(1/2)/(x^4+1),1],
[(1+2*x)/(2+3*x),x,2,2/3*x-1/9*ln(2+3*x),1],
[x*ln(x+(x^2+1)^(1/2)),x,3,1/4*arcsinh(x)+1/2*x^2*ln(x+(x^2+1)^(1/2))-1/4*x*(x^2+1)^(1/2),1],
[x*(1+exp(x)*sin(x))^2,x,14,-3/32*exp(2*x)+1/8*exp(2*x)*x+1/2*x^2+exp(x)*cos(x)-exp(x)*x*cos(x)-1/32*exp(2*x)*cos(2*x)+exp(x)*x*sin(x)+1/16*exp(2*x)*cos(x)*sin(x)-1/4*exp(2*x)*x*cos(x)*sin(x)-1/16*exp(2*x)*sin(x)^2+1/4*exp(2*x)*x*sin(x)^2+1/32*exp(2*x)*sin(2*x),1],
[exp(x)*x*cos(x),x,4,1/2*exp(x)*x*cos(x)-1/2*exp(x)*sin(x)+1/2*exp(x)*x*sin(x),1],
[1/(-3+x)^4,x,1,1/3/(3-x)^3,1],
[x/(x^3-1),x,6,1/3*ln(1-x)-1/6*ln(x^2+x+1)+1/3*arctan(1/3*(1+2*x)*3^(1/2))*3^(1/2),1],
[x/(x^4-1),x,2,-1/2*arctanh(x^2),1],
[(x^3+1)*ln(x)/(x^4+2),x,10,1/8*(2+I*(-2)^(1/4))*ln(x)*ln(1-(1/2+1/2*I)*x*2^(1/4))+1/16*(4+(1-I)*2^(3/4))*ln(x)*ln(1+(1/2+1/2*I)*x*2^(1/4))+1/8*(2+(-2)^(1/4))*ln(x)*ln(1-1/2*(-1)^(3/4)*x*2^(3/4))+1/8*(2-(-2)^(1/4))*ln(x)*ln(1+1/2*(-1)^(3/4)*x*2^(3/4))+1/16*(4+(1-I)*2^(3/4))*polylog(2,(-1/2-1/2*I)*x*2^(1/4))+1/8*(2+I*(-2)^(1/4))*polylog(2,(1/2+1/2*I)*x*2^(1/4))+1/8*(2-(-2)^(1/4))*polylog(2,-1/2*(-1)^(3/4)*x*2^(3/4))+1/8*(2+(-2)^(1/4))*polylog(2,1/2*(-1)^(3/4)*x*2^(3/4)),1],
[ln(x)+ln(1+x)+ln(2+x),x,6,-3*x+x*ln(x)+(1+x)*ln(1+x)+(2+x)*ln(2+x),1],
[1/(x^3+5),x,6,1/15*ln(5^(1/3)+x)*5^(1/3)-1/30*ln(5^(2/3)-5^(1/3)*x+x^2)*5^(1/3)-1/15*arctan(1/15*(5^(1/3)-2*x)*5^(2/3)*3^(1/2))*5^(1/3)*3^(1/2),1],
[1/(x^2+1)^(1/2),x,1,arcsinh(x),1],
[(x^2+3)^(1/2),x,2,3/2*arcsinh(1/3*x*3^(1/2))+1/2*x*(x^2+3)^(1/2),1],
[x/(1+x)^2,x,2,1/(1+x)+ln(1+x),1],
[arcsin(x),x,2,x*arcsin(x)+(-x^2+1)^(1/2),1],
[x^2*arcsin(x),x,4,-1/9*(-x^2+1)^(3/2)+1/3*x^3*arcsin(x)+1/3*(-x^2+1)^(1/2),1],
[sec(x)^2/(1+sec(x)^2-3*tan(x)),x,4,-ln(cos(x)-sin(x))+ln(2*cos(x)-sin(x)),1],
[1/sec(x)^2,x,2,1/2*x+1/2*cos(x)*sin(x),1],
[(5*x^2-3*x-2)/(-2+x)/x^2,x,2,-1/x+3*ln(2-x)+2*ln(x),1],
[1/(4*x^2+9)^(1/2),x,1,1/2*arcsinh(2/3*x),1],
[1/(x^2+4)^(1/2),x,1,arcsinh(1/2*x),1],
[1/(9*x^2-12*x+10),x,2,-1/18*arctan(1/6*(2-3*x)*6^(1/2))*6^(1/2),1],
[1/(x^8-2*x^7+2*x^6-2*x^5+x^4),x,3,1/2/(1-x)-1/3/x^3-1/x^2-2/x-5/2*ln(1-x)+2*ln(x)+1/4*ln(x^2+1),1],
[(a*x^3+b*x^2+c*x+d)/(-3+x)/x/(1+x),x,2,a*x+1/12*(27*a+9*b+3*c+d)*ln(3-x)-1/3*d*ln(x)-1/4*(a-b+c-d)*ln(1+x),1],
[1/(2-ln(x^2+1))^5,x,0,Unintegrable(1/(2-ln(x^2+1))^5,x),0],
[exp(x^2)/x+2*exp(x^2)*x*ln(x)+(-2+ln(x))/(x+ln(x)^2)^2+(1+1/x+2*ln(x)/x)/(x+ln(x)^2),x,9,exp(x^2)*ln(x)-ln(x)/(x+ln(x)^2)+ln(x+ln(x)^2),1],
[x^4*exp(1/2*x+x*z)*sin(Pi*z)^4,z,4,24*exp(1/2*x+x*z)*Pi^4*x^3/(64*Pi^4+20*Pi^2*x^2+x^4)-24*exp(1/2*x+x*z)*Pi^3*x^4*cos(Pi*z)*sin(Pi*z)/(64*Pi^4+20*Pi^2*x^2+x^4)+12*exp(1/2*x+x*z)*Pi^2*x^5*sin(Pi*z)^2/(64*Pi^4+20*Pi^2*x^2+x^4)-4*exp(1/2*x+x*z)*Pi*x^4*cos(Pi*z)*sin(Pi*z)^3/(16*Pi^2+x^2)+exp(1/2*x+x*z)*x^5*sin(Pi*z)^4/(16*Pi^2+x^2),1],
[erf(x),x,1,x*erf(x)+1/exp(x^2)/Pi^(1/2),1],
[erf(a+x),x,1,(a+x)*erf(a+x)+1/exp((a+x)^2)/Pi^(1/2),1],
[(2*x^6+4*x^5+7*x^4-3*x^3-x^2-8*x-8)/(2*x^2-1)^2/(x^4+4*x^3+2*x^2+1)^(1/2),x,-10,-arctanh(x*(2+x)*(33*x^3+27*x^2-x+7)/(31*x^3+37*x^2+2)/(x^4+4*x^3+2*x^2+1)^(1/2))+1/2*(1+2*x)*(x^4+4*x^3+2*x^2+1)^(1/2)/(2*x^2-1),1],
[(1+2*y)*(-5*y^2-5*y+1)^(1/2)/y/(1+y)/(2+y)/(-y^2-y+1)^(1/2),y,-2,-1/4*arctanh((1-3*y)*(-5*y^2-5*y+1)^(1/2)/(1-5*y)/(-y^2-y+1)^(1/2))-1/2*arctanh((4+3*y)*(-5*y^2-5*y+1)^(1/2)/(6+5*y)/(-y^2-y+1)^(1/2))+9/4*arctanh(1/3*(11+7*y)*(-5*y^2-5*y+1)^(1/2)/(7+5*y)/(-y^2-y+1)^(1/2)),1],
[x*(-(x^2-4)^(1/2)+x^2*(x^2-4)^(1/2)-4*(x^2-1)^(1/2)+x^2*(x^2-1)^(1/2))/(x^4-5*x^2+4)/(1+(x^2-4)^(1/2)+(x^2-1)^(1/2)),x,1,ln(1+(x^2-4)^(1/2)+(x^2-1)^(1/2)),1],
[-2^(1/2)*(x^4+2*x^2+4*x+1)^(1/2)+x*(-1+2*2^(1/2)),x,-1,1/2*x^2*(-1+2*2^(1/2))-2^(1/2)*(-1/3*(x^4+2*x^2+4*x+1)^(1/2)+1/3*(1+x)*(x^4+2*x^2+4*x+1)^(1/2)+4*I*(-13+3*33^(1/2))^(1/3)*(x^4+2*x^2+4*x+1)^(1/2)/(4*2^(2/3)*(-I+3^(1/2))-2*I*(-13+3*33^(1/2))^(1/3)+6*I*x*(-13+3*33^(1/2))^(1/3)+2^(1/3)*(3^(1/2)+I)*(-13+3*33^(1/2))^(2/3))-8*2^(2/3)*EllipticE((26-6*33^(1/2)+6*x*(-13+3*33^(1/2))+(-13-13*I*3^(1/2)+9*I*11^(1/2)+3*33^(1/2))*(-26+6*33^(1/2))^(1/3)+4*I*(3^(1/2)+I)*(-26+6*33^(1/2))^(2/3))^(1/2)/((39+13*I*3^(1/2)-9*I*11^(1/2)-9*33^(1/2)+4*(3-I*3^(1/2))*(-26+6*33^(1/2))^(1/3))/(39-13*I*3^(1/2)+9*I*11^(1/2)-9*33^(1/2)+4*(3+I*3^(1/2))*(-26+6*33^(1/2))^(1/3)))^(1/2)/(26-6*33^(1/2)+6*x*(-13+3*33^(1/2))+(-13+13*I*3^(1/2)-9*I*11^(1/2)+3*33^(1/2))*(-26+6*33^(1/2))^(1/3)+(-4-4*I*3^(1/2))*(-26+6*33^(1/2))^(2/3))^(1/2),((84+28*I*3^(1/2)-12*I*11^(1/2)-12*33^(1/2)+(3-I*3^(1/2)-3*I*11^(1/2)+3*33^(1/2))*(-26+6*33^(1/2))^(1/3))/(84-28*I*3^(1/2)+12*I*11^(1/2)-12*33^(1/2)+(3+I*3^(1/2)+3*I*11^(1/2)+3*33^(1/2))*(-26+6*33^(1/2))^(1/3)))^(1/2))*(x^4+2*x^2+4*x+1)^(1/2)*3^(1/2)/(-13+3*33^(1/2)+4*(-26+6*33^(1/2))^(1/3))^(1/2)*(I*(-19899+x*(59697-10335*33^(1/2))+3445*33^(1/2)+(-26+6*33^(1/2))^(2/3)*(-2574+466*33^(1/2))+(-26+6*33^(1/2))^(1/3)*(-19899+3445*33^(1/2)))/(-39-13*I*3^(1/2)+9*I*11^(1/2)+9*33^(1/2)+4*I*(3*I+3^(1/2))*(-26+6*33^(1/2))^(1/3))/(26-6*33^(1/2)+6*x*(-13+3*33^(1/2))+(-13+13*I*3^(1/2)-9*I*11^(1/2)+3*33^(1/2))*(-26+6*33^(1/2))^(1/3)+(-4-4*I*3^(1/2))*(-26+6*33^(1/2))^(2/3)))^(1/2)/(4*2^(2/3)-(-13+3*33^(1/2))^(1/3)+3*x*(-13+3*33^(1/2))^(1/3)-2^(1/3)*(-13+3*33^(1/2))^(2/3))/(26-6*33^(1/2)+6*x*(-13+3*33^(1/2))+(-13+13*I*3^(1/2)-9*I*11^(1/2)+3*33^(1/2))*(-26+6*33^(1/2))^(1/3)+(-4-4*I*3^(1/2))*(-26+6*33^(1/2))^(2/3))^(1/2)/(I*(1+x)/(26-6*33^(1/2)+6*x*(-13+3*33^(1/2))+(-13+13*I*3^(1/2)-9*I*11^(1/2)+3*33^(1/2))*(-26+6*33^(1/2))^(1/3)+(-4-4*I*3^(1/2))*(-26+6*33^(1/2))^(2/3))/(104-24*33^(1/2)+(-13-13*I*3^(1/2)+9*I*11^(1/2)+3*33^(1/2))*(-26+6*33^(1/2))^(1/3)+4*I*(3^(1/2)+I)*(-26+6*33^(1/2))^(2/3)))^(1/2)/(26-6*33^(1/2)+6*x*(-13+3*33^(1/2))+(-13-13*I*3^(1/2)+9*I*11^(1/2)+3*33^(1/2))*(-26+6*33^(1/2))^(1/3)+4*I*(3^(1/2)+I)*(-26+6*33^(1/2))^(2/3))^(1/2)+1/6*EllipticPi(1/6*(13-3*33^(1/2)-2^(1/3)*(-13+3*33^(1/2))^(4/3)+4*(-26+6*33^(1/2))^(2/3)+x*(-39+9*33^(1/2)))^(1/2)*2^(5/6)*3^(1/2)/(-13+3*33^(1/2))^(2/3)/(1+x)^(1/2)/((-39+13*I*3^(1/2)-9*I*11^(1/2)+9*33^(1/2)-4*I*(-3*I+3^(1/2))*(-26+6*33^(1/2))^(1/3))/(104-24*33^(1/2)+(-13+13*I*3^(1/2)-9*I*11^(1/2)+3*33^(1/2))*(-26+6*33^(1/2))^(1/3)+(-4-4*I*3^(1/2))*(-26+6*33^(1/2))^(2/3)))^(1/2),2^(1/3)*(4*2^(1/3)*(-3*I+3^(1/2))+(3*I+3^(1/2))*(-13+3*33^(1/2))^(2/3))/(4*2^(2/3)*(-I+3^(1/2))-8*I*(-13+3*33^(1/2))^(1/3)+2^(1/3)*(3^(1/2)+I)*(-13+3*33^(1/2))^(2/3)),((84-28*I*3^(1/2)+12*I*11^(1/2)-12*33^(1/2)+(3+I*3^(1/2)+3*I*11^(1/2)+3*33^(1/2))*(-26+6*33^(1/2))^(1/3))/(84+28*I*3^(1/2)-12*I*11^(1/2)-12*33^(1/2)+(3-I*3^(1/2)-3*I*11^(1/2)+3*33^(1/2))*(-26+6*33^(1/2))^(1/3)))^(1/2))*(4*2^(2/3)+2*(-13+3*33^(1/2))^(1/3)-2^(1/3)*(-13+3*33^(1/2))^(2/3))*(4*2^(2/3)*(3^(1/2)+I)-4*I*(-13+3*33^(1/2))^(1/3)+2^(1/3)*(-I+3^(1/2))*(-13+3*33^(1/2))^(2/3))*(4*2^(2/3)*(-I+3^(1/2))+4*I*(-13+3*33^(1/2))^(1/3)+2^(1/3)*(3^(1/2)+I)*(-13+3*33^(1/2))^(2/3))*(1+x)^(1/2)*(x^4+2*x^2+4*x+1)^(1/2)*((-39+13*I*3^(1/2)-9*I*11^(1/2)+9*33^(1/2)-4*I*(-3*I+3^(1/2))*(-26+6*33^(1/2))^(1/3))/(104-24*33^(1/2)+(-13+13*I*3^(1/2)-9*I*11^(1/2)+3*33^(1/2))*(-26+6*33^(1/2))^(1/3)+(-4-4*I*3^(1/2))*(-26+6*33^(1/2))^(2/3)))^(1/2)*((104-24*33^(1/2)+2*(1+14*I*3^(1/2)-6*I*11^(1/2)+33^(1/2))*(-26+6*33^(1/2))^(1/3)+(-7-I*3^(1/2)-3*I*11^(1/2)+33^(1/2))*(-26+6*33^(1/2))^(2/3)+2*x*(-52+12*33^(1/2)+2^(1/3)*(-13+3*33^(1/2))^(4/3)-4*(-26+6*33^(1/2))^(2/3)))/(1+x)/(-39+13*I*3^(1/2)-9*I*11^(1/2)+9*33^(1/2)-4*I*(-3*I+3^(1/2))*(-26+6*33^(1/2))^(1/3)))^(1/2)*((104-24*33^(1/2)+2*(1-14*I*3^(1/2)+6*I*11^(1/2)+33^(1/2))*(-26+6*33^(1/2))^(1/3)+(-7+I*3^(1/2)+3*I*11^(1/2)+33^(1/2))*(-26+6*33^(1/2))^(2/3)+2*x*(-52+12*33^(1/2)+2^(1/3)*(-13+3*33^(1/2))^(4/3)-4*(-26+6*33^(1/2))^(2/3)))/(1+x)/(-39-13*I*3^(1/2)+9*I*11^(1/2)+9*33^(1/2)+4*I*(3*I+3^(1/2))*(-26+6*33^(1/2))^(1/3)))^(1/2)*2^(5/6)*3^(1/2)/(4*2^(2/3)*(3^(1/2)+I)+2*I*(-13+3*33^(1/2))^(1/3)-6*I*x*(-13+3*33^(1/2))^(1/3)+2^(1/3)*(-I+3^(1/2))*(-13+3*33^(1/2))^(2/3))/(4*2^(2/3)*(-I+3^(1/2))-2*I*(-13+3*33^(1/2))^(1/3)+6*I*x*(-13+3*33^(1/2))^(1/3)+2^(1/3)*(3^(1/2)+I)*(-13+3*33^(1/2))^(2/3))/(13-3*33^(1/2)-2^(1/3)*(-13+3*33^(1/2))^(4/3)+4*(-26+6*33^(1/2))^(2/3)+x*(-39+9*33^(1/2)))^(1/2)+1/18*I*EllipticF(1/6*I*(-52+12*33^(1/2)+2^(1/3)*(-13+3*33^(1/2))^(4/3)-4*(-26+6*33^(1/2))^(2/3))^(1/2)*(26-6*33^(1/2)+6*x*(-13+3*33^(1/2))+(-13-13*I*3^(1/2)+9*I*11^(1/2)+3*33^(1/2))*(-26+6*33^(1/2))^(1/3)+4*I*(3^(1/2)+I)*(-26+6*33^(1/2))^(2/3))^(1/2)*2^(5/6)*3^(1/2)/(-13+3*33^(1/2))^(2/3)/(1+x)^(1/2)/(39+13*I*3^(1/2)-9*I*11^(1/2)-9*33^(1/2)+4*(3-I*3^(1/2))*(-26+6*33^(1/2))^(1/3))^(1/2),((84*I-28*3^(1/2)+12*11^(1/2)-12*I*33^(1/2)+(3*I+3^(1/2)+3*11^(1/2)+3*I*33^(1/2))*(-26+6*33^(1/2))^(1/3))/(-56*3^(1/2)+24*11^(1/2)+2*(-26+6*33^(1/2))^(1/3)*(3^(1/2)+3*11^(1/2))))^(1/2))*(2^(1/3)*(13-13*I*3^(1/2)+9*I*11^(1/2)-3*33^(1/2))+4*2^(2/3)*(1+I*3^(1/2))*(-13+3*33^(1/2))^(1/3)+20*(-13+3*33^(1/2))^(2/3))*(4*2^(2/3)*(3^(1/2)+I)+8*I*(-13+3*33^(1/2))^(1/3)+2^(1/3)*(-I+3^(1/2))*(-13+3*33^(1/2))^(2/3))*(x^4+2*x^2+4*x+1)^(1/2)*((-52+12*33^(1/2)+2^(1/3)*(-13+3*33^(1/2))^(4/3)-4*(-26+6*33^(1/2))^(2/3))/(-13+3*33^(1/2)+4*(-26+6*33^(1/2))^(1/3)))^(1/2)*((-8*I*(-13+3*33^(1/2))+(-43*I-13*3^(1/2)+9*11^(1/2)+5*I*33^(1/2))*(-26+6*33^(1/2))^(1/3)+(2*I+4*3^(1/2)-2*I*33^(1/2))*(-26+6*33^(1/2))^(2/3)+x*(8*I*(-13+3*33^(1/2))+(13*I-13*3^(1/2)+9*11^(1/2)-3*I*33^(1/2))*(-26+6*33^(1/2))^(1/3)+4*(3^(1/2)+I)*(-26+6*33^(1/2))^(2/3)))/(1+x))^(1/2)*2^(1/3)*3^(1/4)/(-13+3*33^(1/2))^(1/3)/(4*2^(2/3)*(-I+3^(1/2))-2*I*(-13+3*33^(1/2))^(1/3)+6*I*x*(-13+3*33^(1/2))^(1/3)+2^(1/3)*(3^(1/2)+I)*(-13+3*33^(1/2))^(2/3))/(1+x)^(1/2)/(39+13*I*3^(1/2)-9*I*11^(1/2)-9*33^(1/2)+4*(3-I*3^(1/2))*(-26+6*33^(1/2))^(1/3))^(1/2)/(26-6*33^(1/2)+6*x*(-13+3*33^(1/2))+(-13-13*I*3^(1/2)+9*I*11^(1/2)+3*33^(1/2))*(-26+6*33^(1/2))^(1/3)+4*I*(3^(1/2)+I)*(-26+6*33^(1/2))^(2/3))^(1/2)/((-104+24*33^(1/2)-(5-3*I*3^(1/2)+3*I*11^(1/2)+33^(1/2))*(-26+6*33^(1/2))^(2/3)+(-26+6*33^(1/2))^(1/3)*(-41+15*I*3^(1/2)-3*I*11^(1/2)+7*33^(1/2))+x*(104-24*33^(1/2)+(-13-13*I*3^(1/2)+9*I*11^(1/2)+3*33^(1/2))*(-26+6*33^(1/2))^(1/3)+4*I*(3^(1/2)+I)*(-26+6*33^(1/2))^(2/3)))/(1+x)/(-39-13*I*3^(1/2)+9*I*11^(1/2)+9*33^(1/2)+4*I*(3*I+3^(1/2))*(-26+6*33^(1/2))^(1/3)))^(1/2)),1],
[1/384*(Pi^2*(4*mc^9-3*mc^8-48*mc^7*x+24*mc^6*x-144*mc^5*x^2+176*mc^3*x^3-24*mc^2*x^3+12*mc*x^4+3*x^4)+12*mc^3*Pi^2*(-12*mc^2+3*mc-8*x)*x^2*ln(x/mc^2))/exp(x/y)/x^2,x,20,1/384*(3-4*mc)*mc^8*Pi^2/exp(x/y)/x+3/8*mc^5*Pi^2*y/exp(x/y)+1/48*(3-22*mc)*mc^2*Pi^2*x*y/exp(x/y)-1/128*(1+4*mc)*Pi^2*x^2*y/exp(x/y)+1/48*(3-22*mc)*mc^2*Pi^2*y^2/exp(x/y)+1/4*mc^3*Pi^2*y^2/exp(x/y)-1/64*(1+4*mc)*Pi^2*x*y^2/exp(x/y)-1/64*(1+4*mc)*Pi^2*y^3/exp(x/y)+1/16*(1-2*mc)*mc^6*Pi^2*Ei(-x/y)+1/384*(3-4*mc)*mc^8*Pi^2*Ei(-x/y)/y+1/32*mc^3*Pi^2*(-12*mc^2+3*mc-8*y)*y*Ei(-x/y)-1/32*mc^3*Pi^2*(3*(1-4*mc)*mc-8*x)*y*ln(x/mc^2)/exp(x/y)+1/4*mc^3*Pi^2*y^2*ln(x/mc^2)/exp(x/y),1],
[sin(2*x)/cos(x),x,2,-2*cos(x),1],
[(7*x^13+10*x^8+4*x^7-7*x^6-4*x^3-4*x^2+3*x+3)/(x^14-2*x^8-2*x^7-2*x^4-4*x^3-x^2+2*x+1),x,-5,-1/2*ln(-1+x^7+x*(2^(1/2)-1)+x^2*2^(1/2))*(2^(1/2)-1)+1/2*ln(1+x-x^7+x*2^(1/2)+x^2*2^(1/2))*(1+2^(1/2)),1],// Hebisch
[(x^6-x^5+x^4-x^3+1)*exp(x),x,25,871*exp(x)-870*exp(x)*x+435*exp(x)*x^2-145*exp(x)*x^3+36*exp(x)*x^4-7*exp(x)*x^5+exp(x)*x^6,1],
[(-x^2+2)*exp(x/(x^2+2))/(x^3+2*x),x,-5,Ei(x/(x^2+2)),1],
[(2*x^4-x^3+3*x^2+2*x+2)*exp(x/(x^2+2))/(x^3+2*x),x,-5,exp(x/(x^2+2))*(x^2+2)+Ei(x/(x^2+2)),1],
[(1+exp(x))*exp(exp(x)+x)/(exp(x)+x),x,2,Ei(exp(x)+x),1],
[(x^3-x^2-3*x+1)*exp(1/(x^2-1))/(x^3-x^2-x+1),x,-6,exp(1/(x^2-1))*(1+x),1],
[exp(1+1/ln(x))*(-1+ln(x)^2)/ln(x)^2,x,1,exp(1+1/ln(x))*x,1],
[exp(x+1/ln(x))*(-1+(1+x)*ln(x)^2)/ln(x)^2,x,-2,exp(x+1/ln(x))*x,1], // Jeffrey
[3/(5-4*cos(x)),x,2,x+2*arctan(sin(x)/(2-cos(x))),1],
[(1+cos(x)+2*sin(x))/(3+cos(x)^2+2*sin(x)-2*cos(x)*sin(x)),x,-43,-arctan((2*cos(x)-sin(x))/(2+sin(x))),1],
[(2+cos(x)+5*sin(x))/(4*cos(x)-2*sin(x)+cos(x)*sin(x)-2*sin(x)^2),x,-25,-ln(1-3*cos(x)+sin(x))+ln(3+cos(x)+sin(x)),1],
[(3+7*cos(x)+2*sin(x))/(1+4*cos(x)+3*cos(x)^2-5*sin(x)-cos(x)*sin(x)),x,-32,-ln(1+cos(x)-2*sin(x))+ln(3+cos(x)+sin(x)),1],
[(-1+4*cos(x)+5*cos(x)^2)/(-1-4*cos(x)-3*cos(x)^2+4*cos(x)^3),x,-2,x-2*arctan(sin(x)/(3+cos(x)))-2*arctan((3*sin(x)+7*cos(x)*sin(x))/(1+2*cos(x)+5*cos(x)^2)),1],
[(-5+2*cos(x)+7*cos(x)^2)/(-1+2*cos(x)-9*cos(x)^2+4*cos(x)^3),x,-2,x-2*arctan(2*cos(x)*sin(x)/(1-cos(x)+2*cos(x)^2)),1],
[3/(5+4*sin(x)),x,2,x+2*arctan(cos(x)/(2+sin(x))),1],
[2/(1+cos(x)^2),x,3,x*2^(1/2)-arctan(cos(x)*sin(x)/(1+cos(x)^2+2^(1/2)))*2^(1/2),1],
[1/(p+q*cos(x)+r*sin(x)),x,3,2*arctan((r+(p-q)*tan(1/2*x))/(p^2-q^2-r^2)^(1/2))/(p^2-q^2-r^2)^(1/2),1],// Moses
[cot(x)^4,x,3,x+cot(x)-1/3*cot(x)^3,1],
[1/x^4/(x^2+1),x,3,-1/3/x^3+1/x+arctan(x),1],
[(x^2+x)/x^(1/2),x,2,2/3*x^(3/2)+2/5*x^(5/2),1],
[cos(x),x,1,sin(x),1],
[exp(x^2)*x,x,1,1/2*exp(x^2),1],
[sec(x)^2*tan(x),x,2,1/2*sec(x)^2,1],
[x*(x^2+1)^(1/2),x,1,1/3*(x^2+1)^(3/2),1],
[exp(x)*sin(x),x,1,-1/2*exp(x)*cos(x)+1/2*exp(x)*sin(x),1],
[cos(x)*csc(x)^2/sin(x)^2,x,2,-1/3*csc(x)^3,1],
[sin(exp(x)),x,2,Si(exp(x)),1],
[sin(y)/y,y,1,Si(y),1],
[exp(x)+sin(x),x,3,exp(x)-cos(x),1],
[exp(x^2)+2*exp(x^2)*x^2,x,4,exp(x^2)*x,1],
[(exp(x)+x)^2,x,5,-2*exp(x)+1/2*exp(2*x)+2*exp(x)*x+1/3*x^3,1],
[2*exp(x)+exp(2*x)+x^2,x,3,2*exp(x)+1/2*exp(2*x)+1/3*x^3,1],
[cos(x)*sin(x),x,2,1/2*sin(x)^2,1],
[exp(x^2)*x,x,1,1/2*exp(x^2),1],
[x*(x^2+1)^(1/2),x,1,1/3*(x^2+1)^(3/2),1],
[exp(x)/(1+exp(x)),x,2,ln(1+exp(x)),1],
[x^(3/2),x,1,2/5*x^(5/2),1],
[cos(3+2*x),x,1,1/2*sin(3+2*x),1],
[2*exp(2*x)*y*z,x,2,exp(2*x)*y*z,1],
[exp(x)*cos(exp(x))^2*sin(exp(x)),x,3,-1/3*cos(exp(x))^3,1],
[x*(1+x)^(1/2),x,2,-2/3*(1+x)^(3/2)+2/5*(1+x)^(5/2),1],
[1/(x^4-1),x,3,-1/2*arctan(x)-1/2*arctanh(x),1],
[exp(x)/(2+3*exp(2*x)),x,2,1/6*arctan(1/2*exp(x)*6^(1/2))*6^(1/2),1],
[exp(2*x)/(A+B*exp(4*x)),x,2,1/2*arctan(exp(2*x)*B^(1/2)/A^(1/2))/A^(1/2)/B^(1/2),1],
[exp(1+x)/(1+exp(x)),x,3,exp(1)*ln(1+exp(x)),1],
[(10*exp(1))^x,x,1,(10*exp(1))^x/(1+ln(10)),1],
[x^3*sin(x^2),x,3,-1/2*x^2*cos(x^2)+1/2*sin(x^2),1],
[x^7/(x^12+1),x,7,-1/12*ln(x^4+1)+1/24*ln(x^8-x^4+1)-1/12*arctan(1/3*(-2*x^4+1)*3^(1/2))*3^(1/2),1],
[x^(3*a)*sin(x^(2*a)),x,3,1/4*I*x^(1+3*a)*GAMMA(3/2+1/2/a,-I*x^(2*a))/a/((-I*x^(2*a))^(1/2*(1+3*a)/a))-1/4*I*x^(1+3*a)*GAMMA(3/2+1/2/a,I*x^(2*a))/a/((I*x^(2*a))^(1/2*(1+3*a)/a)),1],
[cos(x^(1/2)),x,3,2*cos(x^(1/2))+2*sin(x^(1/2))*x^(1/2),1],
[x*(1+x)^(1/2),x,2,-2/3*(1+x)^(3/2)+2/5*(1+x)^(5/2),1],
[1/(x^(1/3)+x^(1/2)),x,4,6*x^(1/6)-3*x^(1/3)-6*ln(1+x^(1/6))+2*x^(1/2),1],
[((1+x)/(3+2*x))^(1/2),x,4,-1/4*arcsinh(2^(1/2)*(1+x)^(1/2))*2^(1/2)+1/2*(1+x)^(1/2)*(3+2*x)^(1/2),1],
[x^4/(-x^2+1)^(5/2),x,3,1/3*x^3/(-x^2+1)^(3/2)+arcsin(x)-x/(-x^2+1)^(1/2),1],
[x^(1/2)*(1+x)^(5/2),x,6,5/24*x^(3/2)*(1+x)^(3/2)+1/4*x^(3/2)*(1+x)^(5/2)-5/64*arcsinh(x^(1/2))+5/32*x^(3/2)*(1+x)^(1/2)+5/64*x^(1/2)*(1+x)^(1/2),1],
[x^4/(-x^2+1)^(5/2),x,3,1/3*x^3/(-x^2+1)^(3/2)+arcsin(x)-x/(-x^2+1)^(1/2),1],
[(-B^2*y^2+A^2+B^2)^(1/2)/(-y^2+1),y,5,B*arctan(B*y/(-B^2*y^2+A^2+B^2)^(1/2))+A*arctanh(A*y/(-B^2*y^2+A^2+B^2)^(1/2)),1],
[sin(x)^2,x,2,1/2*x-1/2*cos(x)*sin(x),1],
[(A^2+B^2*sin(x)^2)^(1/2)/sin(x),x,6,-B*arctan(B*cos(x)/(A^2+B^2*sin(x)^2)^(1/2))-A*arctanh(A*cos(x)/(A^2+B^2*sin(x)^2)^(1/2)),1],
[1/(1+cos(x)),x,1,sin(x)/(1+cos(x)),1],
[exp(x)*x,x,2,-exp(x)+exp(x)*x,1],
[exp(x)*x/(1+x)^2,x,1,exp(x)/(1+x),1],
[exp(x^2)*(2*x^2+1),x,5,exp(x^2)*x,1],
[exp(x^2),x,1,1/2*erfi(x)*Pi^(1/2),1],
[exp(x)/x,x,1,Ei(x),1],
[x/(x^3+1),x,6,-1/3*ln(1+x)+1/6*ln(x^2-x+1)-1/3*arctan(1/3*(1-2*x)*3^(1/2))*3^(1/2),1],
[1/(x^6-1),x,10,-1/3*arctanh(x)-1/6*arctanh(x/(x^2+1))-1/6*arctan(x*3^(1/2)/(-x^2+1))*3^(1/2),1],
[1/(A^4-A^2*B^2+(-A^2+B^2)*x^2),x,1,arctanh(x/A)/A/(A^2-B^2),1],
[x*ln(x),x,1,-1/4*x^2+1/2*x^2*ln(x),1],
[x^2*arcsin(x),x,4,-1/9*(-x^2+1)^(3/2)+1/3*x^3*arcsin(x)+1/3*(-x^2+1)^(1/2),1],
[1/(x^2+2*x+1),x,2,-1/(1+x),1],
[ln(x)/(1+ln(x))^2,x,7,x/(1+ln(x)),1],
[1/x/(1+ln(x)^2),x,2,arctan(ln(x)),1],
[1/ln(x),x,1,Li(x),1],
[x*(cos(x)+sin(x)),x,6,cos(x)-x*cos(x)+sin(x)+x*sin(x),1],
[(exp(x)+x)/exp(x),x,4,-1/exp(x)+x-x/exp(x),1],
[(1+exp(x))^2*x,x,6,-2*exp(x)-1/4*exp(2*x)+2*exp(x)*x+1/2*exp(2*x)*x+1/2*x^2,1],
[x*cos(x),x,2,cos(x)+x*sin(x),1],
[cos(x^(1/2)),x,3,2*cos(x^(1/2))+2*sin(x^(1/2))*x^(1/2),1],
[x*cos(x),x,2,cos(x)+x*sin(x),1],
[x*ln(x)^2,x,2,1/4*x^2-1/2*x^2*ln(x)+1/2*x^2*ln(x)^2,1],
[cos(x)*(1+sin(x)^3),x,2,sin(x)+1/4*sin(x)^4,1],
[1/x/(1+ln(x)^2),x,2,arctan(ln(x)),1],
[1/(1+arcsin(x)^2)/(-x^2+1)^(1/2),x,2,arctan(arcsin(x)),1],
[sin(x)/(cos(x)+sin(x)),x,2,1/2*x-1/2*ln(cos(x)+sin(x)),1],
[-(A^2+B^2*(-y^2+1))^(1/2)/(-y^2+1),y,6,-B*arctan(B*y/(-B^2*y^2+A^2+B^2)^(1/2))-A*arctanh(A*y/(-B^2*y^2+A^2+B^2)^(1/2)),1],
[(-A^2-B^2)*cos(z)^2/B/(1-(A^2+B^2)*sin(z)^2/B^2),z,5,-B*z-A*arctanh(A*tan(z)/B),1],
[(-A^2-B^2)/B/(w^2+1)^2/(1-(A^2+B^2)*w^2/B^2/(w^2+1)),w,6,-B*arctan(w)-A*arctanh(A*w/B),1],
[-B*(A^2+B^2)/(w^2+1)/(-A^2*w^2+B^2),w,4,-B*arctan(w)-A*arctanh(A*w/B),1],
[x^4/(-x^2+1)^(5/2),x,3,1/3*x^3/(-x^2+1)^(3/2)+arcsin(x)-x/(-x^2+1)^(1/2),1],
[sin(y)^4/cos(y)^4,y,3,y-tan(y)+1/3*tan(y)^3,1],
[z^4/(z^2+1),z,3,-z+1/3*z^3+arctan(z),1],
[exp(x^2)*(2*x^2+1),x,5,exp(x^2)*x,1],
[exp(x^2)*(2*x^6+5*x^4+x^3+4*x^2+1)/(x^2+1)^2,x,10,exp(x^2)*x+1/2*exp(x^2)/(x^2+1),1],
[exp(-1-x),x,1,-exp(-1-x),1],
[(1/x+x)*ln(x),x,5,-1/4*x^2+1/2*x^2*ln(x)+1/2*ln(x)^2,1],
[x/(x^4+1),x,2,1/2*arctan(x^2),1],
[x^5/(x^4+1),x,3,1/2*x^2-1/2*arctan(x^2),1],
[1/(1+tan(x)^2),x,3,1/2*x+1/2*cos(x)*sin(x),1],
[x^4/(-x^2+1)^(5/2),x,3,1/3*x^3/(-x^2+1)^(3/2)+arcsin(x)-x/(-x^2+1)^(1/2),1],
[-x^2/(-x^2+1)^(3/2),x,2,arcsin(x)-x/(-x^2+1)^(1/2),1],
[exp(x)*sin(x),x,1,-1/2*exp(x)*cos(x)+1/2*exp(x)*sin(x),1],
[1/x,x,1,ln(x),1],
[sec(2*t)/(1+sec(t)^2+3*tan(t)),t,4,-1/12*ln(cos(t)-sin(t))-1/4*ln(cos(t)+sin(t))+1/3*ln(2*cos(t)+sin(t))-1/2/(1+tan(t)),1],
[1/sec(x)^2,x,2,1/2*x+1/2*cos(x)*sin(x),1],
[(x^2+1)/x^(1/2),x,2,2/5*x^(5/2)+2*x^(1/2),1],
[x/(x^2+2*x+5)^(1/2),x,3,-arcsinh(1/2+1/2*x)+(x^2+2*x+5)^(1/2),1],
[cos(x)*sin(x)^2,x,2,1/3*sin(x)^3,1],
[exp(x)/(1+exp(x)),x,2,ln(1+exp(x)),1],
[exp(2*x)/(1+exp(x)),x,3,exp(x)-ln(1+exp(x)),1],
[1/(1-cos(x)),x,1,-sin(x)/(1-cos(x)),1],
[sec(x)^2*tan(x),x,2,1/2*sec(x)^2,1],
[x*ln(x),x,1,-1/4*x^2+1/2*x^2*ln(x),1],
[cos(x)*sin(x),x,2,1/2*sin(x)^2,1],
[(1+x)/(-x^2+2*x)^(1/2),x,3,2*arcsin(-1+x)-(-x^2+2*x)^(1/2),1],
[2*exp(x)/(2+3*exp(2*x)),x,3,1/3*arctan(1/2*exp(x)*6^(1/2))*6^(1/2),1],
[x^4/(-x^2+1)^(5/2),x,3,1/3*x^3/(-x^2+1)^(3/2)+arcsin(x)-x/(-x^2+1)^(1/2),1],
[exp(6*x)/(1+exp(4*x)),x,3,1/2*exp(2*x)-1/2*arctan(exp(2*x)),1],
[ln(3*x^2+2),x,3,-2*x+x*ln(3*x^2+2)+2/3*arctan(1/2*x*6^(1/2))*6^(1/2),1],
[1/r/(2*H*r^2-a^2)^(1/2),x,1,x/r/(2*H*r^2-a^2)^(1/2),1],
[1/r/(2*H*r^2-a^2-e^2)^(1/2),x,1,x/r/(2*H*r^2-a^2-e^2)^(1/2),1],
[1/r/(-2*K*r^4+2*H*r^2-a^2)^(1/2),x,1,x/r/(-2*K*r^4+2*H*r^2-a^2)^(1/2),1],
[1/r/(-2*K*r^4+2*H*r^2-a^2-e^2)^(1/2),x,1,x/r/(-2*K*r^4+2*H*r^2-a^2-e^2)^(1/2),1],
[1/r/(2*H*r^2-2*K*r-a^2)^(1/2),x,1,x/r/(-a^2-2*r*(-H*r+K))^(1/2),1],
[1/r/(2*H*r^2-2*K*r-a^2-e^2)^(1/2),x,1,x/r/(2*H*r^2-2*K*r-a^2-e^2)^(1/2),1],
[r/(-a^2+2*exp(1)*r^2)^(1/2),x,1,r*x/(-a^2+2*exp(1)*r^2)^(1/2),1],
[r/(-a^2-e^2+2*exp(1)*r^2)^(1/2),x,1,r*x/(-a^2-e^2+2*exp(1)*r^2)^(1/2),1],
[r/(-a^2+2*exp(1)*r^2-2*K*r^4)^(1/2),x,1,r*x/(-a^2+2*exp(1)*r^2-2*K*r^4)^(1/2),1],
[r/(-a^2-e^2+2*exp(1)*r^2-2*K*r^4)^(1/2),x,1,r*x/(-a^2-e^2+2*exp(1)*r^2-2*K*r^4)^(1/2),1],
[r/(2*H*r^2-2*K*r-a^2-e^2)^(1/2),x,1,r*x/(2*H*r^2-2*K*r-a^2-e^2)^(1/2),1], // Stewart
[x^n,x,1,x^(1+n)/(1+n),1],
[exp(x),x,1,exp(x),1],
[1/x,x,1,ln(x),1],
[a^x,x,1,a^x/ln(a),1],
[sin(x),x,1,-cos(x),1],
[cos(x),x,1,sin(x),1],
[sec(x)^2,x,2,tan(x),1],
[csc(x)^2,x,2,-cot(x),1],
[sec(x)*tan(x),x,2,sec(x),1],
[cot(x)*csc(x),x,2,-csc(x),1],
[sinh(x),x,1,cosh(x),1],
[cosh(x),x,1,sinh(x),1],
[tan(x),x,1,-ln(cos(x)),1],
[cot(x),x,1,ln(sin(x)),1],
[x*sin(x),x,2,-x*cos(x)+sin(x),1],
[ln(x),x,1,-x+x*ln(x),1],
[exp(x)*x^2,x,3,2*exp(x)-2*exp(x)*x+exp(x)*x^2,1],
[exp(x)*sin(x),x,1,-1/2*exp(x)*cos(x)+1/2*exp(x)*sin(x),1],
[arctan(x),x,2,x*arctan(x)-1/2*ln(x^2+1),1],
[exp(2*x)*x,x,2,-1/4*exp(2*x)+1/2*exp(2*x)*x,1],
[x*cos(x),x,2,cos(x)+x*sin(x),1],
[x*sin(4*x),x,2,-1/4*x*cos(4*x)+1/16*sin(4*x),1],
[x*ln(x),x,1,-1/4*x^2+1/2*x^2*ln(x),1],
[x^2*cos(3*x),x,3,2/9*x*cos(3*x)-2/27*sin(3*x)+1/3*x^2*sin(3*x),1],
[x^2*sin(2*x),x,3,1/4*cos(2*x)-1/2*x^2*cos(2*x)+1/2*x*sin(2*x),1],
[ln(x)^2,x,2,2*x-2*x*ln(x)+x*ln(x)^2,1],
[arcsin(x),x,2,x*arcsin(x)+(-x^2+1)^(1/2),1],
[t*cos(t)*sin(t),t,3,-1/4*t+1/4*cos(t)*sin(t)+1/2*t*sin(t)^2,1],
[t*sec(t)^2,t,2,ln(cos(t))+t*tan(t),1],
[t^2*ln(t),t,1,-1/9*t^3+1/3*t^3*ln(t),1],
[exp(t)*t^3,t,4,-6*exp(t)+6*exp(t)*t-3*exp(t)*t^2+exp(t)*t^3,1],
[exp(2*t)*sin(3*t),t,1,-3/13*exp(2*t)*cos(3*t)+2/13*exp(2*t)*sin(3*t),1],
[cos(3*t)/exp(t),t,1,-1/10*cos(3*t)/exp(t)+3/10*sin(3*t)/exp(t),1],
[y*sinh(y),y,2,y*cosh(y)-sinh(y),1],
[y*cosh(a*y),y,2,-cosh(a*y)/a^2+y*sinh(a*y)/a,1],
[t/exp(t),t,2,-1/exp(t)-t/exp(t),1],
[ln(t)*t^(1/2),t,1,-4/9*t^(3/2)+2/3*t^(3/2)*ln(t),1],
[x*cos(2*x),x,2,1/4*cos(2*x)+1/2*x*sin(2*x),1],
[x^2/exp(x),x,3,-2/exp(x)-2*x/exp(x)-x^2/exp(x),1],
[arccos(x),x,2,x*arccos(x)-(-x^2+1)^(1/2),1],
[x*csc(x)^2,x,2,-x*cot(x)+ln(sin(x)),1],
[cos(5*x)*sin(3*x),x,1,1/4*cos(2*x)-1/16*cos(8*x),1],
[sin(2*x)*sin(4*x),x,1,1/4*sin(2*x)-1/12*sin(6*x),1],
[cos(x)*ln(sin(x)),x,2,-sin(x)+ln(sin(x))*sin(x),1],
[exp(x^2)*x^3,x,2,-1/2*exp(x^2)+1/2*exp(x^2)*x^2,1],
[exp(x)*(3+2*x),x,2,-2*exp(x)+exp(x)*(3+2*x),1],
[5^x*x,x,2,-5^x/ln(5)^2+5^x*x/ln(5),1],
[cos(ln(x)),x,1,1/2*x*cos(ln(x))+1/2*x*sin(ln(x)),1],
[exp(x^(1/2)),x,3,-2*exp(x^(1/2))+2*exp(x^(1/2))*x^(1/2),1],
[1/2*ln(x),x,1,-1/2*x+1/2*x*ln(x),1],
[sin(ln(x)),x,1,-1/2*x*cos(ln(x))+1/2*x*sin(ln(x)),1],
[sin(x^(1/2)),x,3,2*sin(x^(1/2))-2*cos(x^(1/2))*x^(1/2),1],
[x^5*cos(x^3),x,3,1/3*cos(x^3)+1/3*x^3*sin(x^3),1],
[exp(x^2)*x^5,x,3,exp(x^2)-exp(x^2)*x^2+1/2*exp(x^2)*x^4,1],
[x*arctan(x),x,3,-1/2*x+1/2*arctan(x)+1/2*x^2*arctan(x),1],
[x*cos(Pi*x),x,2,cos(Pi*x)/Pi^2+x*sin(Pi*x)/Pi,1],
[ln(x)*x^(1/2),x,1,-4/9*x^(3/2)+2/3*x^(3/2)*ln(x),1],
[sin(3*x)^2,x,2,1/2*x-1/6*cos(3*x)*sin(3*x),1],
[cos(x)^2,x,2,1/2*x+1/2*cos(x)*sin(x),1],
[cos(x)^4,x,3,3/8*x+3/8*cos(x)*sin(x)+1/4*cos(x)^3*sin(x),1],
[sin(x)^3,x,2,-cos(x)+1/3*cos(x)^3,1],
[cos(x)^4*sin(x)^3,x,3,-1/5*cos(x)^5+1/7*cos(x)^7,1],
[cos(x)^3*sin(x)^4,x,3,1/5*sin(x)^5-1/7*sin(x)^7,1],
[cos(x)^2*sin(x)^4,x,4,1/16*x+1/16*cos(x)*sin(x)-1/8*cos(x)^3*sin(x)-1/6*cos(x)^3*sin(x)^3,1],
[cos(x)^2*sin(x)^2,x,3,1/8*x+1/8*cos(x)*sin(x)-1/4*cos(x)^3*sin(x),1],
[(1-sin(2*x))^2,x,1,3/2*x+cos(2*x)-1/4*cos(2*x)*sin(2*x),1],
[cos(x)*sin(1/6*Pi+x),x,3,1/4*x-1/4*cos(1/6*Pi+2*x),1],
[cos(x)^5*sin(x)^5,x,4,1/6*sin(x)^6-1/4*sin(x)^8+1/10*sin(x)^10,1],
[sin(x)^6,x,4,5/16*x-5/16*cos(x)*sin(x)-5/24*cos(x)*sin(x)^3-1/6*cos(x)*sin(x)^5,1],
[cos(x)^6,x,4,5/16*x+5/16*cos(x)*sin(x)+5/24*cos(x)^3*sin(x)+1/6*cos(x)^5*sin(x),1],
[cos(2*x)^4*sin(2*x)^2,x,4,1/16*x+1/32*cos(2*x)*sin(2*x)+1/48*cos(2*x)^3*sin(2*x)-1/12*cos(2*x)^5*sin(2*x),1],
[sin(x)^5,x,2,-cos(x)+2/3*cos(x)^3-1/5*cos(x)^5,1],
[cos(x)^4*sin(x)^4,x,5,3/128*x+3/128*cos(x)*sin(x)+1/64*cos(x)^3*sin(x)-1/16*cos(x)^5*sin(x)-1/8*cos(x)^5*sin(x)^3,1],
[sin(x)^3*cos(x)^(1/2),x,3,-2/3*cos(x)^(3/2)+2/7*cos(x)^(7/2),1],
[cos(x)^3*sin(x)^(1/2),x,3,2/3*sin(x)^(3/2)-2/7*sin(x)^(7/2),1],
[cos(x^(1/2))^2/x^(1/2),x,3,cos(x^(1/2))*sin(x^(1/2))+x^(1/2),1],
[x*sin(x^2)^3,x,3,-1/2*cos(x^2)+1/6*cos(x^2)^3,1],
[cos(x)^2*tan(x)^3,x,3,1/2*cos(x)^2-ln(cos(x)),1],
[cot(x)^5*sin(x)^2,x,4,-1/2*csc(x)^2-2*ln(sin(x))+1/2*sin(x)^2,1],
[(1-sin(x))/cos(x),x,2,ln(1+sin(x)),1],
[1/(1-sin(x)),x,1,cos(x)/(1-sin(x)),1],
[tan(x)^2,x,2,-x+tan(x),1],
[tan(x)^4,x,3,x-tan(x)+1/3*tan(x)^3,1],
[sec(x)^4,x,2,tan(x)+1/3*tan(x)^3,1],
[sec(x)^6,x,2,tan(x)+2/3*tan(x)^3+1/5*tan(x)^5,1],
[sec(x)^2*tan(x)^4,x,2,1/5*tan(x)^5,1],
[sec(x)^4*tan(x)^2,x,3,1/3*tan(x)^3+1/5*tan(x)^5,1],
[sec(x)^3*tan(x),x,2,1/3*sec(x)^3,1],
[sec(x)^3*tan(x)^3,x,3,-1/3*sec(x)^3+1/5*sec(x)^5,1],
[tan(x)^5,x,3,-ln(cos(x))-1/2*tan(x)^2+1/4*tan(x)^4,1],
[tan(x)^6,x,4,-x+tan(x)-1/3*tan(x)^3+1/5*tan(x)^5,1],
[sec(x)*tan(x)^5,x,3,sec(x)-2/3*sec(x)^3+1/5*sec(x)^5,1],
[sec(x)^3*tan(x)^5,x,3,1/3*sec(x)^3-2/5*sec(x)^5+1/7*sec(x)^7,1],
[sec(x)^6*tan(x),x,2,1/6*sec(x)^6,1],
[sec(x)^6*tan(x)^3,x,3,-1/6*sec(x)^6+1/8*sec(x)^8,1],
[sec(x)^2/cot(x),x,2,1/2*sec(x)^2,1],
[sec(x)*tan(x)^2,x,2,-1/2*arctanh(sin(x))+1/2*sec(x)*tan(x),1],
[cot(x)^2,x,2,-x-cot(x),1],
[cot(x)^3,x,2,-1/2*cot(x)^2-ln(sin(x)),1],
[cot(x)^4*csc(x)^4,x,3,-1/5*cot(x)^5-1/7*cot(x)^7,1],
[cot(x)^3*csc(x)^4,x,3,1/4*csc(x)^4-1/6*csc(x)^6,1],
[csc(x),x,1,-arctanh(cos(x)),1],
[csc(x)^3,x,2,-1/2*arctanh(cos(x))-1/2*cot(x)*csc(x),1],
[cos(x)^2/sin(x),x,3,-arctanh(cos(x))+cos(x),1],
[1/sin(x)^4,x,2,-cot(x)-1/3*cot(x)^3,1],
[sin(2*x)*sin(5*x),x,1,1/6*sin(3*x)-1/14*sin(7*x),1],
[cos(x)*sin(3*x),x,1,-1/4*cos(2*x)-1/8*cos(4*x),1],
[cos(3*x)*cos(4*x),x,1,1/2*sin(x)+1/14*sin(7*x),1],
[sin(3*x)*sin(6*x),x,1,1/6*sin(3*x)-1/18*sin(9*x),1],
[cos(x)^5*sin(x),x,2,-1/6*cos(x)^6,1],
[cos(x)*cos(2*x)*cos(3*x),x,5,1/4*x+1/8*sin(2*x)+1/16*sin(4*x)+1/24*sin(6*x),1],
[(1-tan(x)^2)/sec(x)^2,x,2,cos(x)*sin(x),1],
[(cos(x)+sin(x))/sin(2*x),x,6,-1/2*arctanh(cos(x))+1/2*arctanh(sin(x)),1],
[sin(x)^2*tan(x),x,3,1/2*cos(x)^2-ln(cos(x)),1],
[cos(x)^2*cot(x)^3,x,4,-1/2*csc(x)^2-2*ln(sin(x))+1/2*sin(x)^2,1],
[sec(x)^3*tan(x),x,2,1/3*sec(x)^3,1],
[sec(x)^3*tan(x)^3,x,3,-1/3*sec(x)^3+1/5*sec(x)^5,1],
[(-x^2+9)^(1/2)/x^2,x,2,-arcsin(1/3*x)-(-x^2+9)^(1/2)/x,1],
[1/x^2/(x^2+4)^(1/2),x,1,-1/4*(x^2+4)^(1/2)/x,1],
[x/(x^2+4)^(1/2),x,1,(x^2+4)^(1/2),1],
[1/(-a^2+x^2)^(1/2),x,2,arctanh(x/(-a^2+x^2)^(1/2)),1],
[x^3/(4*x^2+9)^(3/2),x,3,9/16/(4*x^2+9)^(1/2)+1/16*(4*x^2+9)^(1/2),1],
[x/(-x^2-2*x+3)^(1/2),x,3,-arcsin(1/2+1/2*x)-(-x^2-2*x+3)^(1/2),1],
[1/x^2/(-x^2+1)^(1/2),x,1,-(-x^2+1)^(1/2)/x,1],
[x^3*(-x^2+4)^(1/2),x,3,-4/3*(-x^2+4)^(3/2)+1/5*(-x^2+4)^(5/2),1],
[x/(-x^2+1)^(1/2),x,1,-(-x^2+1)^(1/2),1],
[x*(-x^2+4)^(1/2),x,1,-1/3*(-x^2+4)^(3/2),1],
[(-4*x^2+1)^(1/2),x,2,1/4*arcsin(2*x)+1/2*x*(-4*x^2+1)^(1/2),1],
[x^3/(x^2+4)^(1/2),x,3,1/3*(x^2+4)^(3/2)-4*(x^2+4)^(1/2),1],
[1/(x^2+9)^(1/2),x,1,arcsinh(1/3*x),1],
[(x^2+1)^(1/2),x,2,1/2*arcsinh(x)+1/2*x*(x^2+1)^(1/2),1],
[1/x^3/(x^2-16)^(1/2),x,4,1/128*arctan(1/4*(x^2-16)^(1/2))+1/32*(x^2-16)^(1/2)/x^2,1],
[(-a^2+x^2)^(1/2)/x^4,x,1,1/3*(-a^2+x^2)^(3/2)/a^2/x^3,1],
[(9*x^2-4)^(1/2)/x,x,4,-2*arctan(1/2*(9*x^2-4)^(1/2))+(9*x^2-4)^(1/2),1],
[1/x^2/(16*x^2-9)^(1/2),x,1,1/9*(16*x^2-9)^(1/2)/x,1],
[x^2/(a^2-x^2)^(3/2),x,3,-arctan(x/(a^2-x^2)^(1/2))+x/(a^2-x^2)^(1/2),1],
[x^2/(-x^2+5)^(1/2),x,2,5/2*arcsin(1/5*x*5^(1/2))-1/2*x*(-x^2+5)^(1/2),1],
[1/x/(x^2+3)^(1/2),x,3,-1/3*arctanh(1/3*(x^2+3)^(1/2)*3^(1/2))*3^(1/2),1],
[x/(x^2+4)^(5/2),x,1,-1/3/(x^2+4)^(3/2),1],
[x^3*(-9*x^2+4)^(1/2),x,3,-4/243*(-9*x^2+4)^(3/2)+1/405*(-9*x^2+4)^(5/2),1],
[x^2*(-x^2+9)^(1/2),x,3,81/8*arcsin(1/3*x)-9/8*x*(-x^2+9)^(1/2)+1/4*x^3*(-x^2+9)^(1/2),1],
[5*x*(x^2+1)^(1/2),x,2,5/3*(x^2+1)^(3/2),1],
[1/(4*x^2-25)^(3/2),x,1,-1/25*x/(4*x^2-25)^(1/2),1],
[(-x^2+2*x)^(1/2),x,3,1/2*arcsin(-1+x)-1/2*(1-x)*(-x^2+2*x)^(1/2),1],
[1/(x^2+4*x+8)^(1/2),x,2,arcsinh(1+1/2*x),1],
[1/(9*x^2+6*x-8)^(1/2),x,2,1/3*arctanh((1+3*x)/(9*x^2+6*x-8)^(1/2)),1],
[x^2/(-x^2+4*x)^(1/2),x,4,6*arcsin(-1+1/2*x)-3*(-x^2+4*x)^(1/2)-1/2*x*(-x^2+4*x)^(1/2),1],
[1/(x^2+2*x+2)^2,x,3,1/2*(1+x)/(x^2+2*x+2)+1/2*arctan(1+x),1],
[1/(-x^2-4*x+5)^(5/2),x,2,1/27*(2+x)/(-x^2-4*x+5)^(3/2)+2/243*(2+x)/(-x^2-4*x+5)^(1/2),1],
[exp(t)*(9-exp(2*t))^(1/2),t,3,9/2*arcsin(1/3*exp(t))+1/2*exp(t)*(9-exp(2*t))^(1/2),1],
[(-9+exp(2*t))^(1/2),t,4,-3*arctan(1/3*(-9+exp(2*t))^(1/2))+(-9+exp(2*t))^(1/2),1],
[1/(a^2+x^2)^(1/2),x,2,arctanh(x/(a^2+x^2)^(1/2)),1],
[(5+x)/(x^2+x-2),x,3,2*ln(1-x)-ln(2+x),1],
[(x^3+x)/(-1+x),x,3,2*x+1/2*x^2+1/3*x^3+2*ln(1-x),1],
[(x^2+2*x-1)/(2*x^3+3*x^2-2*x),x,3,1/10*ln(1-2*x)+1/2*ln(x)-1/10*ln(2+x),1],
[(x^4-2*x^2+4*x+1)/(x^3-x^2-x+1),x,2,2/(1-x)+x+1/2*x^2+ln(1-x)-ln(1+x),1],
[(2*x^2-x+4)/(x^3+4*x),x,6,-1/2*arctan(1/2*x)+ln(x)+1/2*ln(x^2+4),1],
[(4*x^2-3*x+2)/(4*x^2-4*x+3),x,6,x+1/8*ln(4*x^2-4*x+3)+1/8*arctan(1/2*(1-2*x)*2^(1/2))*2^(1/2),1],
[(x^3+x^2+1)/(-1+x)/x/(x^2+1)^3/(x^2+x+1),x,14,1/8*(1+x)/(x^2+1)^2-3/8*(1-x)/(x^2+1)+3/16*x/(x^2+1)+7/16*arctan(x)+1/8*ln(1-x)-ln(x)+15/16*ln(x^2+1)-1/2*ln(x^2+x+1)-1/3*arctan(1/3*(1+2*x)*3^(1/2))*3^(1/2),1],
[(-x^3+2*x^2-3*x+1)/x/(x^2+1)^2,x,6,1/2*(-2*x-1)/(x^2+1)-2*arctan(x)+ln(x)-1/2*ln(x^2+1),1],
[1/(x^2+1)^2,x,2,1/2*x/(x^2+1)+1/2*arctan(x),1],
[1/(-1+x)/(2+x),x,3,1/3*ln(1-x)-1/3*ln(2+x),1],
[7/(2*x^2+5*x-12),x,4,7/11*ln(3-2*x)-7/11*ln(4+x),1],
[(x^2+3*x-4)/(-1+2*x)^2/(3+2*x),x,2,-9/32/(1-2*x)+41/128*ln(1-2*x)-25/128*ln(3+2*x),1],
[(x^3-x^2)/(-6+x)/(3+5*x)^3,x,3,-12/1375/(3+5*x)^2+201/15125/(3+5*x)+20/3993*ln(6-x)+1493/499125*ln(3+5*x),1],
[1/(x^4-x^3),x,3,1/2/x^2+1/x+ln(1-x)-ln(x),1],
[(x^4+x^3-x^2-x+1)/(x^3-x),x,4,x+1/2*x^2-ln(x)+1/2*ln(-x^2+1),1],
[(x^2-2)/x/(x^2+2),x,3,-ln(x)+ln(x^2+2),1],
[(x^3-4*x^2+2)/(x^2+1)/(x^2+2),x,8,6*arctan(x)-1/2*ln(x^2+1)+ln(x^2+2)-5*arctan(1/2*x*2^(1/2))*2^(1/2),1],
[(x^4+x^2+1)/(x^2+1)/(x^2+4)^2,x,6,-13/24*x/(x^2+4)+25/144*arctan(1/2*x)+1/9*arctan(x),1],
[(1+16*x)/(5+x)^2/(-3+2*x)/(x^2+x+1),x,6,-79/273/(5+x)+200/3211*ln(3-2*x)+2731/24843*ln(5+x)-481/5586*ln(x^2+x+1)+451/8379*arctan(1/3*(1+2*x)*3^(1/2))*3^(1/2),1],
[x^4/(x^2+9)^3,x,3,-1/4*x^3/(x^2+9)^2-3/8*x/(x^2+9)+1/8*arctan(1/3*x),1],
[19*x/(-1+x)^3/(4*x^2+5*x+3)^2,x,8,-399/736/(1-x)^2-1843/4416/(1-x)+19/276*(39+44*x)/(1-x)^2/(4*x^2+5*x+3)+209/2304*ln(1-x)-209/4608*ln(4*x^2+5*x+3)+114437/1218816*arctan(1/23*(5+8*x)*23^(1/2))*23^(1/2),1],
[(x^3+x^2+1)/(x^4+x^3+2*x^2),x,7,-1/2/x-1/4*ln(x)+5/8*ln(x^2+x+2)+1/28*arctan(1/7*(1+2*x)*7^(1/2))*7^(1/2),1],
[1/(x^6-x^3),x,8,1/2/x^2+1/3*ln(1-x)-1/6*ln(x^2+x+1)-1/3*arctan(1/3*(1+2*x)*3^(1/2))*3^(1/2),1],
[x^2/(1+x),x,2,-x+1/2*x^2+ln(1+x),1],
[x/(-5+x),x,2,x+5*ln(5-x),1],
[(-1+4*x)/(-1+x)/(2+x),x,2,ln(1-x)+3*ln(2+x),1],
[1/(1+x)/(2+x),x,3,ln(1+x)-ln(2+x),1],
[(-5+6*x)/(3+2*x),x,2,3*x-7*ln(3+2*x),1],
[1/(a+x)/(b+x),x,3,-ln(a+x)/(a-b)+ln(b+x)/(a-b),1],
[(x^2+1)/(x^2-x),x,3,x+2*ln(1-x)-ln(x),1],
[(x^3+x^2-12*x+1)/(x^2+x-12),x,5,1/2*x^2+1/7*ln(3-x)-1/7*ln(4+x),1],
[(3+2*x)/(1+x)^2,x,2,-1/(1+x)+2*ln(1+x),1],
[1/x/(1+x)/(3+2*x),x,2,1/3*ln(x)-ln(1+x)+2/3*ln(3+2*x),1],
[(6*x^2+5*x-3)/(x^3+2*x^2-3*x),x,3,2*ln(1-x)+ln(x)+3*ln(3+x),1],
[x/(x^2+4*x+4),x,3,2/(2+x)+ln(2+x),1],
[1/(-1+x)^2/(4+x),x,2,1/5/(1-x)-1/25*ln(1-x)+1/25*ln(4+x),1],
[x^2/(-3+x)/(2+x)^2,x,2,4/5/(2+x)+9/25*ln(3-x)+16/25*ln(2+x),1],
[(5*x^2+3*x-2)/(x^3+2*x^2),x,3,1/x+2*ln(x)+3*ln(2+x),1],
[(-4*x^2-2*x+18)/(x^3+4*x^2+x-6),x,2,ln(1-x)-2*ln(2+x)-3*ln(3+x),1],
[(x^2+2*x)/(x^3+3*x^2+4),x,1,1/3*ln(x^3+3*x^2+4),1],
[1/(-1+x)^2/x^2,x,2,1/(1-x)-1/x-2*ln(1-x)+2*ln(x),1],
[x^2/(1+x)^3,x,2,-1/2/(1+x)^2+2/(1+x)+ln(1+x),1],
[1/(x^4-x^2),x,3,1/x-arctanh(x),1],
[(2*x^3-x)/(x^4-x^2+1),x,1,1/2*ln(x^4-x^2+1),1],
[x^3/(x^2+1),x,3,1/2*x^2-1/2*ln(x^2+1),1],
[(-1+x)/(x^2+2*x+2),x,4,-2*arctan(1+x)+1/2*ln(x^2+2*x+2),1],
[x/(x^2+x+1),x,4,1/2*ln(x^2+x+1)-1/3*arctan(1/3*(1+2*x)*3^(1/2))*3^(1/2),1],
[(4*x^2+5*x+7)/(4*x^2+4*x+5),x,6,x+3/8*arctan(1/2+x)+1/8*ln(4*x^2+4*x+5),1],
[(3*x^2-4*x+5)/(-1+x)/(x^2+1),x,5,-3*arctan(x)+2*ln(1-x)+1/2*ln(x^2+1),1],
[(3+2*x)/(x^3+3*x),x,6,ln(x)-1/2*ln(x^2+3)+2/3*arctan(1/3*x*3^(1/2))*3^(1/2),1],
[1/(x^3-1),x,6,1/3*ln(1-x)-1/6*ln(x^2+x+1)-1/3*arctan(1/3*(1+2*x)*3^(1/2))*3^(1/2),1],
[x^3/(x^3+1),x,7,x-1/3*ln(1+x)+1/6*ln(x^2-x+1)+1/3*arctan(1/3*(1-2*x)*3^(1/2))*3^(1/2),1],
[(x^2-2*x-1)/(-1+x)^2/(x^2+1),x,5,1/(-1+x)+arctan(x)+ln(1-x)-1/2*ln(x^2+1),1],
[x^4/(x^4-1),x,4,x-1/2*arctan(x)-1/2*arctanh(x),1],
[(3*x^3-x^2+6*x-4)/(x^2+1)/(x^2+2),x,6,-3*arctan(x)+3/2*ln(x^2+1)+arctan(1/2*x*2^(1/2))*2^(1/2),1],
[(x^3-2*x^2+x+1)/(x^4+5*x^2+4),x,7,-3/2*arctan(1/2*x)+arctan(x)+1/2*ln(x^2+4),1],
[(-3+x)/(x^2+2*x+4)^2,x,3,1/6*(-7-4*x)/(x^2+2*x+4)-2/9*arctan(1/3*(1+x)*3^(1/2))*3^(1/2),1],
[(x^4+1)/x/(x^2+1)^2,x,3,1/(x^2+1)+ln(x),1],
[cos(x)*(-3+2*sin(x))/(2-3*sin(x)+sin(x)^2),x,2,ln(2-3*sin(x)+sin(x)^2),1],
[cos(x)^2*sin(x)/(5+cos(x)^2),x,3,-cos(x)+arctan(1/5*cos(x)*5^(1/2))*5^(1/2),1],
[1/(x^2+2*x-3),x,3,1/4*ln(1-x)-1/4*ln(3+x),1],
[1/(x^2-2*x),x,1,1/2*ln(2-x)-1/2*ln(x),1],
[(1+2*x)/(4*x^2+12*x-7),x,3,1/8*ln(1-2*x)+3/8*ln(7+2*x),1],
[x/(x^2+x-1),x,3,1/10*ln(1+2*x-5^(1/2))*(5-5^(1/2))+1/10*ln(1+2*x+5^(1/2))*(5+5^(1/2)),1],
[(4*x^3-27*x^2+5*x-32)/(30*x^5-13*x^4+50*x^3-286*x^2-299*x-70),x,6,-3146/80155*ln(7-3*x)-334/323*ln(1+2*x)+4822/4879*ln(2+5*x)+11049/260015*ln(x^2+x+5)+3988/260015*arctan(1/19*(1+2*x)*19^(1/2))*19^(1/2),1],
[(12*x^5-7*x^3-13*x^2+8)/(100*x^6-80*x^5+116*x^4-80*x^3+41*x^2-20*x+4),x,7,5828/9075/(2-5*x)+1/1452*(-313-502*x)/(2*x^2+1)-59096/99825*ln(2-5*x)+2843/7986*ln(2*x^2+1)+503/15972*arctan(x*2^(1/2))*2^(1/2),1],
[(4+x)^(1/2)/x,x,3,-4*arctanh(1/2*(4+x)^(1/2))+2*(4+x)^(1/2),1],
[1/(-1/x^(1/3)+x^(1/2)),x,9,6/5*ln(1-x^(1/6))-3/10*ln(2+x^(1/6)+2*x^(1/3)+x^(1/6)*5^(1/2))*(-5^(1/2)+1)-3/10*ln(2+x^(1/6)+2*x^(1/3)-x^(1/6)*5^(1/2))*(5^(1/2)+1)+2*x^(1/2)+3/5*arctan((1+4*x^(1/6)-5^(1/2))/(10+2*5^(1/2))^(1/2))*(10-2*5^(1/2))^(1/2)-3/5*arctan(1/20*(1+4*x^(1/6)+5^(1/2))*(50+10*5^(1/2))^(1/2))*(10+2*5^(1/2))^(1/2),1],
[1/(-4*cos(x)+3*sin(x)),x,2,-1/5*arctanh(3/5*cos(x)+4/5*sin(x)),1],
[1/(1+x^(1/2)),x,3,-2*ln(1+x^(1/2))+2*x^(1/2),1],
[1/(1+1/x^(1/3)),x,3,3*x^(1/3)-3/2*x^(2/3)+x-3*ln(1+1/x^(1/3))-ln(x),1],
[x^(1/2)/(1+x),x,3,-2*arctan(x^(1/2))+2*x^(1/2),1],
[1/x/(1+x)^(1/2),x,2,-2*arctanh((1+x)^(1/2)),1],
[1/(-x^(1/3)+x),x,2,3/2*ln(1-x^(2/3)),1],
[1/(x-(2+x)^(1/2)),x,4,4/3*ln(2-(2+x)^(1/2))+2/3*ln(1+(2+x)^(1/2)),1],
[x^2/(-1+x)^(1/2),x,2,4/3*(-1+x)^(3/2)+2/5*(-1+x)^(5/2)+2*(-1+x)^(1/2),1],
[(-1+x)^(1/2)/(1+x),x,3,-2*arctan(1/2*(-1+x)^(1/2)*2^(1/2))*2^(1/2)+2*(-1+x)^(1/2),1],
[1/(1+x^(1/2))^(1/2),x,3,4/3*(1+x^(1/2))^(3/2)-4*(1+x^(1/2))^(1/2),1],
[x^(1/2)/(x^2+x),x,3,2*arctan(x^(1/2)),1],
[(1+x^(1/2))/(-1+x^(1/2)),x,3,x+4*ln(1-x^(1/2))+4*x^(1/2),1],
[(1+1/x^(1/3))/(-1+1/x^(1/3)),x,4,-6*x^(1/3)-3*x^(2/3)-x-6*ln(1-x^(1/3)),1],
[x^3/(x^2+1)^(1/3),x,3,-3/4*(x^2+1)^(2/3)+3/10*(x^2+1)^(5/3),1],
[x^(1/2)/(-1/x^(1/3)+x^(1/2)),x,10,6*x^(1/6)+x+6/5*ln(1-x^(1/6))-3/10*ln(2+x^(1/6)+2*x^(1/3)-x^(1/6)*5^(1/2))*(-5^(1/2)+1)-3/10*ln(2+x^(1/6)+2*x^(1/3)+x^(1/6)*5^(1/2))*(5^(1/2)+1)-3/5*arctan(1/20*(1+4*x^(1/6)+5^(1/2))*(50+10*5^(1/2))^(1/2))*(10-2*5^(1/2))^(1/2)-3/5*arctan((1+4*x^(1/6)-5^(1/2))/(10+2*5^(1/2))^(1/2))*(10+2*5^(1/2))^(1/2),1],
[1/(1/x^(1/4)+x^(1/2)),x,9,4/3*ln(1+x^(1/4))-2/3*ln(1-x^(1/4)+x^(1/2))+4/3*arctan(1/3*(1-2*x^(1/4))*3^(1/2))*3^(1/2)+2*x^(1/2),1],
[1/(1/x^(1/3)+1/x^(1/4)),x,4,12*x^(1/12)-6*x^(1/6)+4*x^(1/4)-3*x^(1/3)+12/5*x^(5/12)+12/7*x^(7/12)-3/2*x^(2/3)+4/3*x^(3/4)-6/5*x^(5/6)+12/11*x^(11/12)-x+12/13*x^(13/12)-6/7*x^(7/6)+4/5*x^(5/4)-12*ln(1+x^(1/12))-2*x^(1/2),1],
[((1-x)/x)^(1/2),x,5,-arctan((-1+1/x)^(1/2))+x*(-1+1/x)^(1/2),1],
[cos(x)/(sin(x)+sin(x)^2),x,2,ln(sin(x))-ln(1+sin(x)),1],
[exp(2*x)/(2+3*exp(x)+exp(2*x)),x,4,-ln(1+exp(x))+2*ln(2+exp(x)),1],
[1/(1+exp(x))^(1/2),x,3,-2*arctanh((1+exp(x))^(1/2)),1],
[(1-exp(x))^(1/2),x,4,-2*arctanh((1-exp(x))^(1/2))+2*(1-exp(x))^(1/2),1],
[1/(3-5*sin(x)),x,4,-1/4*ln(cos(1/2*x)-3*sin(1/2*x))+1/4*ln(3*cos(1/2*x)-sin(1/2*x)),1],
[1/(cos(x)+sin(x)),x,2,-1/2*arctanh(1/2*(cos(x)-sin(x))*2^(1/2))*2^(1/2),1],
[1/(1-cos(x)+sin(x)),x,2,-ln(1+cot(1/2*x)),1],
[1/(4*cos(x)+3*sin(x)),x,2,-1/5*arctanh(3/5*cos(x)-4/5*sin(x)),1],
[1/(sin(x)+tan(x)),x,6,-1/2*arctanh(cos(x))+1/2*cot(x)*csc(x)-1/2*csc(x)^2,1],
[1/(2*sin(x)+sin(2*x)),x,4,1/4*ln(tan(1/2*x))+1/8*tan(1/2*x)^2,1],
[sec(x)/(1+sin(x)),x,4,1/2*arctanh(sin(x))-1/2/(1+sin(x)),1],
[1/(b*cos(x)+a*sin(x)),x,2,-arctanh((a*cos(x)-b*sin(x))/(a^2+b^2)^(1/2))/(a^2+b^2)^(1/2),1],
[1/(b^2*cos(x)^2+a^2*sin(x)^2),x,2,arctan(a*tan(x)/b)/a/b,1],
[x/(x^2-1),x,1,1/2*ln(-x^2+1),1],
[x^(1/2)*(1+x^(1/2)),x,2,2/3*x^(3/2)+1/2*x^2,1],
[1/(1-cos(x)),x,1,-sin(x)/(1-cos(x)),1],
[sec(x)*tan(x)^2,x,2,-1/2*arctanh(sin(x))+1/2*sec(x)*tan(x),1],
[sec(x)^3*tan(x)^3,x,3,-1/3*sec(x)^3+1/5*sec(x)^5,1],
[exp(x^(1/2)),x,3,-2*exp(x^(1/2))+2*exp(x^(1/2))*x^(1/2),1],
[(x^5+1)/(x^3-3*x^2-10*x),x,3,19*x+3/2*x^2+1/3*x^3+3126/35*ln(5-x)-1/10*ln(x)-31/14*ln(2+x),1],
[1/x/ln(x)^(1/2),x,2,2*ln(x)^(1/2),1],
[(5+2*x)/(-3+x),x,2,2*x+11*ln(3-x),1],
[exp(exp(x)+x),x,2,exp(exp(x)),1],
[cos(x)^2*sin(x)^2,x,3,1/8*x+1/8*cos(x)*sin(x)-1/4*cos(x)^3*sin(x),1],
[(-cos(x)+sin(x))/(cos(x)+sin(x)),x,1,-ln(cos(x)+sin(x)),1],
[x/(-x^2+1)^(1/2),x,1,-(-x^2+1)^(1/2),1],
[x^3*ln(x),x,1,-1/16*x^4+1/4*x^4*ln(x),1],
[(-2+x)^(1/2)/(2+x),x,3,-4*arctan(1/2*(-2+x)^(1/2))+2*(-2+x)^(1/2),1],
[x/(2+x)^2,x,2,2/(2+x)+ln(2+x),1],
[ln(x^2+1),x,3,-2*x+2*arctan(x)+x*ln(x^2+1),1],
[(1+ln(x))^(1/2)/x/ln(x),x,"nock",-2*arctanh((1+ln(x))^(1/2))+2*(1+ln(x))^(1/2),1],
[(1+x^(1/2))^8,x,3,-2/9*(1+x^(1/2))^9+1/5*(1+x^(1/2))^10,1],
[sec(x)^4*tan(x)^3,x,3,-1/4*sec(x)^4+1/6*sec(x)^6,1],
[x/(x^2-2*x+2),x,4,arctan(-1+x)+1/2*ln(x^2-2*x+2),1],
[x*arcsin(x),x,3,-1/4*arcsin(x)+1/2*x^2*arcsin(x)+1/4*x*(-x^2+1)^(1/2),1],
[(-x^2+9)^(1/2)/x,x,4,-3*arctanh(1/3*(-x^2+9)^(1/2))+(-x^2+9)^(1/2),1],
[x/(x^2+3*x+2),x,3,-ln(1+x)+2*ln(2+x),1],
[x^2*cosh(x),x,3,-2*x*cosh(x)+2*sinh(x)+x^2*sinh(x),1],
[(x^3+x+1)/(x^4+2*x^2+4*x),x,1,1/4*ln(x^4+2*x^2+4*x),1],
[cos(x)/(1+sin(x)^2),x,2,arctan(sin(x)),1],
[cos(x^(1/2)),x,3,2*cos(x^(1/2))+2*sin(x^(1/2))*x^(1/2),1],
[sin(Pi*x),x,1,-cos(Pi*x)/Pi,1],
[exp(2*x)/(1+exp(x)),x,3,exp(x)-ln(1+exp(x)),1],
[exp(3*x)*cos(5*x),x,1,3/34*exp(3*x)*cos(5*x)+5/34*exp(3*x)*sin(5*x),1],
[cos(3*x)*cos(5*x),x,1,1/4*sin(2*x)+1/16*sin(8*x),1],
[1/(x^3+x^2+x+1),x,5,1/2*arctan(x)+1/2*ln(1+x)-1/4*ln(x^2+1),1],
[x^2*ln(1+x),x,3,-1/3*x+1/6*x^2-1/9*x^3+1/3*ln(1+x)+1/3*x^3*ln(1+x),1],
[x^5/exp(x^3),x,2,-1/3/exp(x^3)-1/3*x^3/exp(x^3),1],
[tan(4*x)^2,x,2,-x+1/4*tan(4*x),1],
[1/(9*x^2+12*x-5)^(1/2),x,2,1/3*arctanh((2+3*x)/(9*x^2+12*x-5)^(1/2)),1],
[x^2*arctan(x),x,4,-1/6*x^2+1/3*x^3*arctan(x)+1/6*ln(x^2+1),1],
[(1-x^(1/2))/x^(1/3),x,2,3/2*x^(2/3)-6/7*x^(7/6),1],
[1/(-1/exp(x)+exp(x)),x,2,-arctanh(exp(x)),1],
[x/(x^4+2*x^2+10),x,3,1/6*arctan(1/3*x^2+1/3),1],
[1/(1/x^(1/3)+x),x,2,3/4*ln(1+x^(4/3)),1],
[cos(x)^4*sin(x)^2,x,4,1/16*x+1/16*cos(x)*sin(x)+1/24*cos(x)^3*sin(x)-1/6*cos(x)^5*sin(x),1],
[1/(-x^2-4*x+5)^(1/2),x,2,arcsin(2/3+1/3*x),1],
[x/(1-x^2+(-x^2+1)^(1/2)),x,3,-ln(1+(-x^2+1)^(1/2)),1],
[(1+cos(x))*csc(x),x,2,ln(1-cos(x)),1],
[exp(x)/(-1+exp(2*x)),x,2,-arctanh(exp(x)),1],
[1/(x^3-8),x,6,1/12*ln(2-x)-1/24*ln(x^2+2*x+4)-1/12*arctan(1/3*(1+x)*3^(1/2))*3^(1/2),1],
[x^5*cosh(x),x,6,-120*cosh(x)-60*x^2*cosh(x)-5*x^4*cosh(x)+120*x*sinh(x)+20*x^3*sinh(x)+x^5*sinh(x),1],
[ln(tan(x))/cos(x)/sin(x),x,1,1/2*ln(tan(x))^2,1],
[x^3+x^2-2*x,x,1,-x^2+1/3*x^3+1/4*x^4,1],
[(1+exp(x))/(1-exp(x)),x,3,x-2*ln(1-exp(x)),1],
[x/(x^2+1)/(x^2+4),x,4,1/6*ln(x^2+1)-1/6*ln(x^2+4),1],
[1/(4-5*sin(x)),x,4,-1/3*ln(cos(1/2*x)-2*sin(1/2*x))+1/3*ln(2*cos(1/2*x)-sin(1/2*x)),1],
[x*(c+x)^(1/3),x,2,-3/4*c*(c+x)^(4/3)+3/7*(c+x)^(7/3),1],
[exp(x^(1/3)),x,4,6*exp(x^(1/3))-6*exp(x^(1/3))*x^(1/3)+3*exp(x^(1/3))*x^(2/3),1],
[1/(4+x+(1+x)^(1/2)),x,5,ln(4+x+(1+x)^(1/2))-2/11*arctan(1/11*(1+2*(1+x)^(1/2))*11^(1/2))*11^(1/2),1],
[(x^3+1)/(x^3-x^2),x,3,1/x+x+2*ln(1-x)-ln(x),1],
[(x^2+4*x-3)*sin(2*x),x,8,7/4*cos(2*x)-2*x*cos(2*x)-1/2*x^2*cos(2*x)+sin(2*x)+1/2*x*sin(2*x),1],
[cos(cos(x))*sin(x),x,2,-sin(cos(x)),1],
[1/(-x^2+16)^(1/2),x,1,arcsin(1/4*x),1],
[x^3/(1+x)^10,x,2,1/9/(1+x)^9-3/8/(1+x)^8+3/7/(1+x)^7-1/6/(1+x)^6,1],
[cot(2*x)^3*csc(2*x)^3,x,3,1/6*csc(2*x)^3-1/10*csc(2*x)^5,1],
[(x+sin(x))^2,x,6,1/2*x+1/3*x^3-2*x*cos(x)+2*sin(x)-1/2*cos(x)*sin(x),1],
[exp(arctan(x))/(x^2+1),x,1,exp(arctan(x)),1],
[1/x/(x^4+1),x,4,ln(x)-1/4*ln(x^4+1),1],
[t^3/exp(2*t),t,4,-3/8/exp(2*t)-3/4*t/exp(2*t)-3/4*t^2/exp(2*t)-1/2*t^3/exp(2*t),1],
[t^(1/2)/(1+t^(1/3)),t,7,-6*t^(1/6)-6/5*t^(5/6)+6/7*t^(7/6)+6*arctan(t^(1/6))+2*t^(1/2),1],
[sin(x)*sin(2*x)*sin(3*x),x,5,-1/8*cos(2*x)-1/16*cos(4*x)+1/24*cos(6*x),1],
[ln(1/2*x),x,1,-x+x*ln(1/2*x),1],
[((1+x)/(1-x))^(1/2),x,3,2*arctan(((1+x)/(1-x))^(1/2))-(1-x)*((1+x)/(1-x))^(1/2),1],
[x*ln(x)/(x^2-1)^(1/2),x,5,arctan((x^2-1)^(1/2))-(x^2-1)^(1/2)+ln(x)*(x^2-1)^(1/2),1],
[(a+x)/(a^2+x^2),x,3,arctan(x/a)+1/2*ln(a^2+x^2),1],
[(-x^2+x+1)^(1/2),x,3,-5/8*arcsin(1/5*(1-2*x)*5^(1/2))-1/4*(1-2*x)*(-x^2+x+1)^(1/2),1],
[x^4/(x^10+16),x,2,1/20*arctan(1/4*x^5),1],
[(2+x)/(x^2+x+2),x,4,1/2*ln(x^2+x+2)+3/7*arctan(1/7*(1+2*x)*7^(1/2))*7^(1/2),1],
[x*sec(x)*tan(x),x,2,-arctanh(sin(x))+x*sec(x),1],
[x/(-a^4+x^4),x,2,-1/2*arctanh(x^2/a^2)/a^2,1],
[1/(x^(1/2)+(1+x)^(1/2)),x,3,-2/3*x^(3/2)+2/3*(1+x)^(3/2),1],
[1/(1-1/exp(x)+2*exp(x)),x,4,1/3*ln(1-2*exp(x))-1/3*ln(1+exp(x)),1],
[arctan(x^(1/2))/x^(1/2),x,2,-ln(1+x)+2*arctan(x^(1/2))*x^(1/2),1],
[ln(1+x)/x^2,x,4,ln(x)-ln(1+x)-ln(1+x)/x,1],
[1/(-exp(x)+exp(3*x)),x,3,exp(-x)-arctanh(exp(x)),1],
[(1+cos(x)^2)/(1-cos(x)^2),x,4,-x-2*cot(x),1],
[1/x/(-25+2*x)^(1/2),x,2,2/5*arctan(1/5*(-25+2*x)^(1/2)),1],
[sin(2*x)/(9-cos(x)^4)^(1/2),x,5,-arcsin(1/3*cos(x)^2),1],
[x^2/(-4*x^2+5)^(1/2),x,2,5/16*arcsin(2/5*x*5^(1/2))-1/8*x*(-4*x^2+5)^(1/2),1],
[x^3*sin(x),x,4,6*x*cos(x)-x^3*cos(x)-6*sin(x)+3*x^2*sin(x),1],
[x*(x^2+2*x+4)^(1/2),x,4,1/3*(x^2+2*x+4)^(3/2)-3/2*arcsinh(1/3*(1+x)*3^(1/2))-1/2*(1+x)*(x^2+2*x+4)^(1/2),1],
[x*(x^2+5)^8,x,1,1/18*(x^2+5)^9,1],
[cos(x)^2*sin(x)^5,x,3,-1/3*cos(x)^3+2/5*cos(x)^5-1/7*cos(x)^7,1],
[cos(4*x)/exp(3*x),x,1,-3/25*cos(4*x)/exp(3*x)+4/25*sin(4*x)/exp(3*x),1],
[csc(1/2*x)^3,x,2,-arctanh(cos(1/2*x))-cot(1/2*x)*csc(1/2*x),1],
[(9*x^2-1)^(1/2)/x^2,x,3,3*arctanh(3*x/(9*x^2-1)^(1/2))-(9*x^2-1)^(1/2)/x,1],
[(-3*x^2+4)^(1/2)/x,x,4,-2*arctanh(1/2*(-3*x^2+4)^(1/2))+(-3*x^2+4)^(1/2),1],
[exp(3*x)*x^2,x,3,2/27*exp(3*x)-2/9*exp(3*x)*x+1/3*exp(3*x)*x^2,1],
[cos(x)*sin(x)/(1+sin(x))^(1/2),x,"nock",2/3*(1+sin(x))^(3/2)-2*(1+sin(x))^(1/2),1],
[x*arcsin(x^2),x,3,1/2*x^2*arcsin(x^2)+1/2*(-x^4+1)^(1/2),1],
[x^3*arcsin(x^2),x,5,-1/8*arcsin(x^2)+1/4*x^4*arcsin(x^2)+1/8*x^2*(-x^4+1)^(1/2),1],
[exp(x)*sech(exp(x)),x,2,arctan(sinh(exp(x))),1],
[x^2*cos(3*x),x,3,2/9*x*cos(3*x)-2/27*sin(3*x)+1/3*x^2*sin(3*x),1],
[(-x^2-4*x+5)^(1/2),x,3,9/2*arcsin(2/3+1/3*x)+1/2*(2+x)*(-x^2-4*x+5)^(1/2),1],
[x^5/(x^2+2^(1/2)),x,3,1/4*x^4+ln(x^2+2^(1/2))-1/2*x^2*2^(1/2),1],
[sec(x)^5,x,3,3/8*arctanh(sin(x))+3/8*sec(x)*tan(x)+1/4*sec(x)^3*tan(x),1],
[sin(2*x)^6,x,4,5/16*x-5/32*cos(2*x)*sin(2*x)-5/48*cos(2*x)*sin(2*x)^3-1/12*cos(2*x)*sin(2*x)^5,1],
[cos(x)*ln(sin(x))*sin(x)^2,x,4,-1/9*sin(x)^3+1/3*ln(sin(x))*sin(x)^3,1],
[1/exp(x)/(1+2*exp(x)),x,3,-1/exp(x)-2*x+2*ln(1+2*exp(x)),1],
[(2+3*cos(x))^(1/2)*tan(x),x,4,2*arctanh(1/2*(2+3*cos(x))^(1/2)*2^(1/2))*2^(1/2)-2*(2+3*cos(x))^(1/2),1],
[x/(x^2-4*x)^(1/2),x,3,4*arctanh(x/(x^2-4*x)^(1/2))+(x^2-4*x)^(1/2),1],
[cos(x)^5,x,2,sin(x)-2/3*sin(x)^3+1/5*sin(x)^5,1],
[x^4/exp(x),x,5,-24/exp(x)-24*x/exp(x)-12*x^2/exp(x)-4*x^3/exp(x)-x^4/exp(x),1],
[x^4/(x^10-2)^(1/2),x,3,1/5*arctanh(x^5/(x^10-2)^(1/2)),1],
[exp(x)*cos(4+3*x),x,1,1/10*exp(x)*cos(4+3*x)+3/10*exp(x)*sin(4+3*x),1],
[exp(x)*ln(1+exp(x)),x,4,-exp(x)+(1+exp(x))*ln(1+exp(x)),1],
[x^2*arctan(x),x,4,-1/6*x^2+1/3*x^3*arctan(x)+1/6*ln(x^2+1),1],
[(-1+exp(2*x))^(1/2),x,4,-arctan((-1+exp(2*x))^(1/2))+(-1+exp(2*x))^(1/2),1],
[exp(sin(x))*sin(2*x),x,4,-2*exp(sin(x))+2*exp(sin(x))*sin(x),1],
[x^2*(-x^2+5)^(1/2),x,3,25/8*arcsin(1/5*x*5^(1/2))-5/8*x*(-x^2+5)^(1/2)+1/4*x^3*(-x^2+5)^(1/2),1],
[x^2*(x^3+1)^4,x,1,1/15*(x^3+1)^5,1],
[cos(x)^3*sin(x)^3,x,3,1/4*sin(x)^4-1/6*sin(x)^6,1],
[sec(x)^4*tan(x)^2,x,3,1/3*tan(x)^3+1/5*tan(x)^5,1],
[x*(1+2*x)^(1/2),x,2,-1/6*(1+2*x)^(3/2)+1/10*(1+2*x)^(5/2),1],
[sin(x)^4,x,3,3/8*x-3/8*cos(x)*sin(x)-1/4*cos(x)*sin(x)^3,1],
[tan(x)^3,x,2,ln(cos(x))+1/2*tan(x)^2,1],
[x^5*(x^2+1)^(1/2),x,3,1/3*(x^2+1)^(3/2)-2/5*(x^2+1)^(5/2)+1/7*(x^2+1)^(7/2),1], // Timofeev
[1/(-b^2*x^2+a^2),x,1,arctanh(b*x/a)/a/b,1],
[1/(b^2*x^2+a^2),x,1,arctan(b*x/a)/a/b,1],
[sec(2*a*x),x,1,1/2*arctanh(sin(2*a*x))/a,1],
[1/4/sin(1/3*x),x,2,-3/4*arctanh(cos(1/3*x)),1],
[-1/cos(1/4*Pi+2*x),x,1,-1/2*arctanh(sin(1/4*Pi+2*x)),1],
[sec(x)*tan(x),x,2,sec(x),1],
[cot(x)*csc(x),x,2,-csc(x),1],
[tan(x)/sin(2*x),x,2,1/2*tan(x),1],
[1/(1+cos(x)),x,1,sin(x)/(1+cos(x)),1],
[1/(1-cos(x)),x,1,-sin(x)/(1-cos(x)),1],
[sin(x)/(a-b*cos(x)),x,2,ln(a-b*cos(x))/b,1],
[cos(x)/(a^2+b^2*sin(x)^2),x,2,arctan(b*sin(x)/a)/a/b,1],
[cos(x)/(a^2-b^2*sin(x)^2),x,2,arctanh(b*sin(x)/a)/a/b,1],
[sin(2*x)/(a^2+b^2*sin(x)^2),x,3,ln(a^2+b^2*sin(x)^2)/b^2,1],
[sin(2*x)/(a^2-b^2*sin(x)^2),x,3,-ln(a^2-b^2*sin(x)^2)/b^2,1],
[sin(2*x)/(a^2+b^2*cos(x)^2),x,3,-ln(a^2+b^2*cos(x)^2)/b^2,1],
[sin(2*x)/(a^2-b^2*cos(x)^2),x,3,ln(a^2-b^2*cos(x)^2)/b^2,1],
[1/(4-cos(x)^2),x,2,1/6*x*3^(1/2)+1/6*arctan(cos(x)*sin(x)/(3+sin(x)^2+2*3^(1/2)))*3^(1/2),1],
[exp(x)/(-1+exp(2*x)),x,2,-arctanh(exp(x)),1],
[1/x/ln(x),x,2,ln(ln(x)),1],
[1/x/(1+ln(x)^2),x,2,arctan(ln(x)),1],
[1/x/(1-ln(x)),x,2,-ln(1-ln(x)),1],
[1/x/(1+ln(x/a)),x,2,ln(1+ln(x/a)),1],
[(1+x-x^(1/2))^2/x^2,x,3,-1/x+x+3*ln(x)+4/x^(1/2)-4*x^(1/2),1],
[(2-x^(2/3))*(x+x^(1/2))/x^(3/2),x,4,-3/2*x^(2/3)-6/7*x^(7/6)+2*ln(x)+4*x^(1/2),1],
[(-1+2*x)/(3+2*x),x,2,x-2*ln(3+2*x),1],
[(-5+2*x)/(3*x^2-2),x,3,1/12*ln(-3*x+6^(1/2))*(4-5*6^(1/2))+1/12*ln(3*x+6^(1/2))*(4+5*6^(1/2)),1],
[(-5+2*x)/(3*x^2+2),x,3,1/3*ln(3*x^2+2)-5/6*arctan(1/2*x*6^(1/2))*6^(1/2),1],
[sin(1/4*x)*sin(x),x,1,2/3*sin(3/4*x)-2/5*sin(5/4*x),1],
[cos(3*x)*cos(4*x),x,1,1/2*sin(x)+1/14*sin(7*x),1],
[-tan(x)*tan(a-x),x,4,-x-cot(a)*ln(cos(x))+cot(a)*ln(cos(a-x)),1],
[sin(x)^2,x,2,1/2*x-1/2*cos(x)*sin(x),1],
[cos(x)^2,x,2,1/2*x+1/2*cos(x)*sin(x),1],
[cos(x)^3*sin(x),x,2,-1/4*cos(x)^4,1],
[cos(x)^3/sin(x)^4,x,2,-1/3/sin(x)^3+1/sin(x),1],
[1/cos(x)^2/sin(x)^2,x,3,-cot(x)+tan(x),1],
[cot(3/4*x)^2,x,2,-x-4/3*cot(3/4*x),1],
[(1+tan(2*x))^2,x,2,-ln(cos(2*x))+1/2*tan(2*x),1],
[(-cot(x)+tan(x))^2,x,4,-4*x-cot(x)+tan(x),1],
[(-sec(x)+tan(x))^2,x,4,-x-2*cos(x)/(1+sin(x)),1],
[sin(x)/(1+sin(x)),x,2,x+cos(x)/(1+sin(x)),1],
[cos(x)/(1-cos(x)),x,2,-x-sin(x)/(1-cos(x)),1],
[(-1+exp(1/2*x))^3/exp(1/2*x),x,3,2/exp(1/2*x)-6*exp(1/2*x)+exp(x)+3*x,1],
[1/(x^2-6*x+5),x,3,-1/4*ln(1-x)+1/4*ln(5-x),1],
[x^2/(x^6-6*x^3+13),x,3,1/6*arctan(1/2*x^3-3/2),1],
[(2+x)/(x^2-4*x-1),x,3,1/10*ln(2-x-5^(1/2))*(5-4*5^(1/2))+1/10*ln(2-x+5^(1/2))*(5+4*5^(1/2)),1],
[1/(1+(1+x)^(1/3)),x,4,-3*(1+x)^(1/3)+3/2*(1+x)^(2/3)+3*ln(1+(1+x)^(1/3)),1],
[1/(a*x+b)/x^(1/2),x,2,2*arctan(a^(1/2)*x^(1/2)/b^(1/2))/a^(1/2)/b^(1/2),1],
[x^3*(x^2+1)^(1/2),x,3,-1/3*(x^2+1)^(3/2)+1/5*(x^2+1)^(5/2),1],
[x/(a^4-x^4)^(1/2),x,3,1/2*arctan(x^2/(a^4-x^4)^(1/2)),1],
[1/x/(-a^2+x^2)^(1/2),x,3,arctan((-a^2+x^2)^(1/2)/a)/a,1],
[1/x/(a^2-x^2)^(1/2),x,3,-arctanh((a^2-x^2)^(1/2)/a)/a,1],
[1/x/(a^2+x^2)^(1/2),x,3,-arctanh((a^2+x^2)^(1/2)/a)/a,1],
[1/(-x^2+x+2)^(1/2),x,2,arcsin(-1/3+2/3*x),1],
[1/(3*x^2-4*x+5)^(1/2),x,2,-1/3*arcsinh(1/11*(2-3*x)*11^(1/2))*3^(1/2),1],
[1/(-x^2+x)^(1/2),x,2,arcsin(-1+2*x),1],
[(1+2*x)/(-x^2+x+2)^(1/2),x,3,2*arcsin(-1/3+2/3*x)-2*(-x^2+x+2)^(1/2),1],
[1/x/(-x^2+x+2)^(1/2),x,2,-1/2*arctanh(1/4*(4+x)*2^(1/2)/(-x^2+x+2)^(1/2))*2^(1/2),1],
[1/(-2+x)/(-x^2+x+2)^(1/2),x,1,2/3*(-x^2+x+2)^(1/2)/(-2+x),1],
[(2+3*sin(x))/(1-cos(x))/sin(x),x,7,-arctanh(cos(x))-1/(1-cos(x))-3*sin(x)/(1-cos(x)),1],
[1/(2+3*cos(x)^2),x,2,1/10*x*10^(1/2)-1/10*arctan(3*cos(x)*sin(x)/(2+3*cos(x)^2+10^(1/2)))*10^(1/2),1],
[(1-tan(x))/sin(2*x),x,3,1/2*ln(tan(x))-1/2*tan(x),1],
[(1+tan(x)^2)/(1-tan(x)^2),x,2,1/2*arctanh(2*cos(x)*sin(x)),1],
[(a^2-4*cos(x)^2)^(3/4)*sin(2*x),x,3,1/7*(a^2-4*cos(x)^2)^(7/4),1],
[sin(2*x)/(a^2-4*sin(x)^2)^(1/3),x,3,-3/8*(a^2-4*sin(x)^2)^(2/3),1],
[1/(-1+a^(2*x))^(1/2),x,3,arctan((-1+a^(2*x))^(1/2))/ln(a),1],
[exp(1/2*x)/(-1+exp(x))^(1/2),x,3,2*arctanh(exp(1/2*x)/(-1+exp(x))^(1/2)),1],
[arctan(x)^n/(x^2+1),x,1,arctan(x)^(1+n)/(1+n),1],
[arcsin(x/a)^(3/2)/(a^2-x^2)^(1/2),x,1,2/5*a*arcsin(x/a)^(5/2)*(1-x^2/a^2)^(1/2)/(a^2-x^2)^(1/2),1],
[1/arccos(x)^3/(-x^2+1)^(1/2),x,1,1/2/arccos(x)^2,1],
[x*ln(x)^2,x,2,1/4*x^2-1/2*x^2*ln(x)+1/2*x^2*ln(x)^2,1],
[ln(x)/x^5,x,1,-1/16/x^4-1/4*ln(x)/x^4,1],
[x^2*ln((-1+x)/x),x,5,-1/3*x-1/6*x^2-1/3*ln(-1+x)+1/3*x^3*ln((-1+x)/x),1],
[cos(x)^5,x,2,sin(x)-2/3*sin(x)^3+1/5*sin(x)^5,1],
[cos(x)^4*sin(x)^2,x,4,1/16*x+1/16*cos(x)*sin(x)+1/24*cos(x)^3*sin(x)-1/6*cos(x)^5*sin(x),1],
[1/sin(x)^5,x,3,-3/8*arctanh(cos(x))-3/8*cot(x)*csc(x)-1/4*cot(x)*csc(x)^3,1],
[sin(x)/exp(x),x,1,-1/2*cos(x)/exp(x)-1/2*sin(x)/exp(x),1],
[exp(2*x)*sin(3*x),x,1,-3/13*exp(2*x)*cos(3*x)+2/13*exp(2*x)*sin(3*x),1],
[a^x*cos(x),x,1,a^x*cos(x)*ln(a)/(1+ln(a)^2)+a^x*sin(x)/(1+ln(a)^2),1],
[cos(ln(x)),x,1,1/2*x*cos(ln(x))+1/2*x*sin(ln(x)),1],
[ln(cos(x))*sec(x)^2,x,3,-x+tan(x)+ln(cos(x))*tan(x),1],
[x*tan(x)^2,x,3,-1/2*x^2+ln(cos(x))+x*tan(x),1],
[arcsin(x)/x^2,x,4,-arcsin(x)/x-arctanh((-x^2+1)^(1/2)),1],
[arcsin(x)^2,x,3,-2*x+x*arcsin(x)^2+2*arcsin(x)*(-x^2+1)^(1/2),1],
[x^2*arctan(x)/(x^2+1),x,4,x*arctan(x)-1/2*arctan(x)^2-1/2*ln(x^2+1),1],
[arccos((x/(1+x))^(1/2)),x,6,(1+x)*(arccos((x/(1+x))^(1/2))+(1/(1+x))^(1/2)*(x/(1+x))^(1/2)),1],
[(3*x^2+2*x)^3,x,2,2*x^4+36/5*x^5+9*x^6+27/7*x^7,1],
[(-1+x)*(3*x^2+2*x-1)^2,x,2,-x+5/2*x^2-2/3*x^3-7/2*x^4+3/5*x^5+3/2*x^6,1],
[x^(-1+k)*(a+b*x^k)^n,x,1,(a+b*x^k)^(1+n)/b/k/(1+n),1],
[x^3/(1+2*x),x,2,1/8*x-1/8*x^2+1/6*x^3-1/16*ln(1+2*x),1],
[x^6/(3*x^2+2),x,3,4/27*x-2/27*x^3+1/15*x^5-4/81*arctan(1/2*x*6^(1/2))*6^(1/2),1],
[1/(3*x^2-7*x+2),x,3,-1/5*ln(1-3*x)+1/5*ln(2-x),1],
[(-1+3*x)/(x^2-x+1),x,4,3/2*ln(x^2-x+1)-1/3*arctan(1/3*(1-2*x)*3^(1/2))*3^(1/2),1],
[x^2/(x^2+2*x+5),x,5,x-3/2*arctan(1/2+1/2*x)-ln(x^2+2*x+5),1],
[(6*x^4-5*x^3+4*x^2)/(2*x^2-x+1),x,7,-1/2*x^2+x^3+1/4*ln(2*x^2-x+1)-1/14*arctan(1/7*(-4*x+1)*7^(1/2))*7^(1/2),1],
[(x^2+x-1)/(x^3+x^2-6*x),x,3,1/2*ln(2-x)+1/6*ln(x)+1/3*ln(3+x),1],
[(11*a^2-7*a*x+5*x^2)/(-6*a^3+11*a^2*x-6*a*x^2+x^3),x,2,9/2*ln(a-x)-17*ln(2*a-x)+35/2*ln(3*a-x),1],
[(x^2-x+2)/(x^4-5*x^2+4),x,12,-1/3*ln(1-x)+1/3*ln(2-x)+2/3*ln(1+x)-2/3*ln(2+x),1],
[(2*x^2-5)/(x^4-5*x^2+6),x,3,-1/2*arctanh(1/2*x*2^(1/2))*2^(1/2)-1/3*arctanh(1/3*x*3^(1/2))*3^(1/2),1],
[1/(-4+x)/(-3+x)/(-2+x)/(-1+x),x,2,-1/6*ln(1-x)+1/2*ln(2-x)-1/2*ln(3-x)+1/6*ln(4-x),1],
[(x^2+1)/(-1+x)^3,x,2,-1/(1-x)^2+2/(1-x)+ln(1-x),1],
[x^5/(3+x)^2,x,2,-108*x+27/2*x^2-2*x^3+1/4*x^4+243/(3+x)+405*ln(3+x),1],
[(5*x^3-2)/(x^4-8*x^3+18*x^2-27),x,2,-133/8/(3-x)^2+407/16/(3-x)+313/64*ln(3-x)+7/64*ln(1+x),1],
[(x^3-6*x^2+3*x-9)/(3+x)^2/(4+x)^2,x,2,99/(3+x)+181/(4+x)+264*ln(3+x)-263*ln(4+x),1],
[(x^3+x^2+2)/x/(x^2-1)^2,x,3,1/2*(3+x)/(-x^2+1)-3/4*ln(1-x)+2*ln(x)-5/4*ln(1+x),1],
[1/(x^6-x^5-x^4+x^3),x,2,1/2/(1-x)-1/2/x^2-1/x-7/4*ln(1-x)+2*ln(x)-1/4*ln(1+x),1],
[(x^4+1)/(x^3-x^2+x-1),x,5,x+1/2*x^2-arctan(x)+ln(1-x)-1/2*ln(x^2+1),1],
[1/x/(1+x)/(x^2+1),x,5,-1/2*arctan(x)+ln(x)-1/2*ln(1+x)-1/4*ln(x^2+1),1],
[x^2/(x^4+x^2-2),x,3,-1/3*arctanh(x)+1/3*arctan(1/2*x*2^(1/2))*2^(1/2),1],
[(x^3+4*x^2+6*x)/(x^4+2*x^3+3*x^2+4*x+2),x,6,1/(1+x)-1/3*ln(1+x)+2/3*ln(x^2+2)+4/3*arctan(1/2*x*2^(1/2))*2^(1/2),1],
[x/(1+x)/(1+2*x)^2/(x^2+1),x,5,2/5/(1+2*x)+1/50*arctan(x)-1/2*ln(1+x)+16/25*ln(1+2*x)-7/100*ln(x^2+1),1],
[(3*x^2+x-2)/(-1+x)^3/(x^2+1),x,5,-1/2/(1-x)^2+5/2/(1-x)-arctan(x)-3/2*ln(1-x)+3/4*ln(x^2+1),1],
[1/(x^4+x^2+1),x,9,-1/4*ln(x^2-x+1)+1/4*ln(x^2+x+1)-1/6*arctan(1/3*(1-2*x)*3^(1/2))*3^(1/2)+1/6*arctan(1/3*(1+2*x)*3^(1/2))*3^(1/2),1],
[(2*x^3+3)/(x^5-9*x),x,10,-1/3*ln(x)+1/12*ln(-x^4+9)+1/3*arctan(1/3*x*3^(1/2))*3^(1/2)-1/3*arctanh(1/3*x*3^(1/2))*3^(1/2),1],
[(5*x^3+8*x-20)/(-4+x)^3/(x^2-4*x+8),x,6,-83/4/(4-x)^2+41/4/(4-x)+3/16*arctan(-1+1/2*x)-45/16*ln(4-x)+45/32*ln(x^2-4*x+8),1],
[1/(x^2+1)/(x^2+2)/(x^2+3)/(x^2+4),x,6,-1/12*arctan(1/2*x)+1/6*arctan(x)-1/4*arctan(1/2*x*2^(1/2))*2^(1/2)+1/6*arctan(1/3*x*3^(1/2))*3^(1/2),1],
[x/(x^2+1)/(x^2+2)/(x^2+3)/(x^2+4),x,3,1/12*ln(x^2+1)-1/4*ln(x^2+2)+1/4*ln(x^2+3)-1/12*ln(x^2+4),1],
[1/(a^3+x^3),x,6,1/3*ln(a+x)/a^2-1/6*ln(a^2-a*x+x^2)/a^2-1/3*arctan(1/3*(a-2*x)/a*3^(1/2))/a^2*3^(1/2),1],
[x/(a^3+x^3),x,6,-1/3*ln(a+x)/a+1/6*ln(a^2-a*x+x^2)/a-1/3*arctan(1/3*(a-2*x)/a*3^(1/2))/a*3^(1/2),1],
[x^2/(a^3+x^3),x,1,1/3*ln(a^3+x^3),1],
[1/x/(a^3+x^3),x,4,ln(x)/a^3-1/3*ln(a^3+x^3)/a^3,1],
[1/x^2/(a^3+x^3),x,7,-1/a^3/x+1/3*ln(a+x)/a^4-1/6*ln(a^2-a*x+x^2)/a^4+1/3*arctan(1/3*(a-2*x)/a*3^(1/2))/a^4*3^(1/2),1],
[1/x^3/(a^3+x^3),x,7,-1/2/a^3/x^2-1/3*ln(a+x)/a^5+1/6*ln(a^2-a*x+x^2)/a^5+1/3*arctan(1/3*(a-2*x)/a*3^(1/2))/a^5*3^(1/2),1],
[1/x^4/(a^3+x^3),x,3,-1/3/a^3/x^3-ln(x)/a^6+1/3*ln(a^3+x^3)/a^6,1],
[1/x^5/(a^3+x^3),x,8,-1/4/a^3/x^4+1/a^6/x-1/3*ln(a+x)/a^7+1/6*ln(a^2-a*x+x^2)/a^7-1/3*arctan(1/3*(a-2*x)/a*3^(1/2))/a^7*3^(1/2),1],
[1/(x^m)/(a^3+x^3),x,1,x^(1-m)*hypergeom([1, 1/3-1/3*m],[4/3-1/3*m],-x^3/a^3)/a^3/(1-m),1],
[1/(a^4-x^4),x,3,1/2*arctan(x/a)/a^3+1/2*arctanh(x/a)/a^3,1],
[x/(a^4-x^4),x,2,1/2*arctanh(x^2/a^2)/a^2,1],
[1/x/(a^4-x^4),x,4,ln(x)/a^4-1/4*ln(a^4-x^4)/a^4,1],
[1/x^2/(a^4-x^4),x,4,-1/a^4/x-1/2*arctan(x/a)/a^5+1/2*arctanh(x/a)/a^5,1],
[1/x^3/(a^4-x^4),x,3,-1/2/a^4/x^2+1/2*arctanh(x^2/a^2)/a^6,1],
[1/x^4/(a^4-x^4),x,4,-1/3/a^4/x^3+1/2*arctan(x/a)/a^7+1/2*arctanh(x/a)/a^7,1],
[1/(x^m)/(a^4-x^4),x,1,x^(1-m)*hypergeom([1, 1/4-1/4*m],[5/4-1/4*m],x^4/a^4)/a^4/(1-m),1],
[x/(a^4+x^4),x,2,1/2*arctan(x^2/a^2)/a^2,1],
[x^2/(a^4+x^4),x,9,-1/4*arctan(1-x*2^(1/2)/a)/a*2^(1/2)+1/4*arctan(1+x*2^(1/2)/a)/a*2^(1/2)+1/8*ln(a^2+x^2-a*x*2^(1/2))/a*2^(1/2)-1/8*ln(a^2+x^2+a*x*2^(1/2))/a*2^(1/2),1],
[1/(a^5+x^5),x,6,1/5*ln(a+x)/a^4-1/20*ln(a^2+x^2-1/2*a*x*(-5^(1/2)+1))*(-5^(1/2)+1)/a^4-1/20*ln(a^2+x^2-1/2*a*x*(5^(1/2)+1))*(5^(1/2)+1)/a^4-1/10*arctan(1/20*(-4*x+a*(5^(1/2)+1))*(50+10*5^(1/2))^(1/2)/a)*(10-2*5^(1/2))^(1/2)/a^4-1/10*arctan((-4*x+a*(-5^(1/2)+1))/a/(10+2*5^(1/2))^(1/2))*(10+2*5^(1/2))^(1/2)/a^4,1],
[x/(a^5+x^5),x,6,-1/5*ln(a+x)/a^3+1/20*ln(a^2+x^2-1/2*a*x*(5^(1/2)+1))*(-5^(1/2)+1)/a^3+1/20*ln(a^2+x^2-1/2*a*x*(-5^(1/2)+1))*(5^(1/2)+1)/a^3+1/10*arctan((-4*x+a*(-5^(1/2)+1))/a/(10+2*5^(1/2))^(1/2))*(10-2*5^(1/2))^(1/2)/a^3-1/10*arctan(1/20*(-4*x+a*(5^(1/2)+1))*(50+10*5^(1/2))^(1/2)/a)*(10+2*5^(1/2))^(1/2)/a^3,1],
[x^2/(a^5+x^5),x,6,1/5*ln(a+x)/a^2-1/20*ln(a^2+x^2-1/2*a*x*(5^(1/2)+1))*(-5^(1/2)+1)/a^2-1/20*ln(a^2+x^2-1/2*a*x*(-5^(1/2)+1))*(5^(1/2)+1)/a^2+1/10*arctan((-4*x+a*(-5^(1/2)+1))/a/(10+2*5^(1/2))^(1/2))*(10-2*5^(1/2))^(1/2)/a^2-1/10*arctan(1/20*(-4*x+a*(5^(1/2)+1))*(50+10*5^(1/2))^(1/2)/a)*(10+2*5^(1/2))^(1/2)/a^2,1],
[x^3/(a^5+x^5),x,6,-1/5*ln(a+x)/a+1/20*ln(a^2+x^2-1/2*a*x*(-5^(1/2)+1))*(-5^(1/2)+1)/a+1/20*ln(a^2+x^2-1/2*a*x*(5^(1/2)+1))*(5^(1/2)+1)/a-1/10*arctan(1/20*(-4*x+a*(5^(1/2)+1))*(50+10*5^(1/2))^(1/2)/a)*(10-2*5^(1/2))^(1/2)/a-1/10*arctan((-4*x+a*(-5^(1/2)+1))/a/(10+2*5^(1/2))^(1/2))*(10+2*5^(1/2))^(1/2)/a,1],
[x^4/(a^5+x^5),x,1,1/5*ln(a^5+x^5),1],
[1/x/(a^5+x^5),x,4,ln(x)/a^5-1/5*ln(a^5+x^5)/a^5,1],
[1/x^2/(a^5+x^5),x,7,-1/a^5/x+1/5*ln(a+x)/a^6-1/20*ln(a^2+x^2-1/2*a*x*(-5^(1/2)+1))*(-5^(1/2)+1)/a^6-1/20*ln(a^2+x^2-1/2*a*x*(5^(1/2)+1))*(5^(1/2)+1)/a^6+1/10*arctan(1/20*(-4*x+a*(5^(1/2)+1))*(50+10*5^(1/2))^(1/2)/a)*(10-2*5^(1/2))^(1/2)/a^6+1/10*arctan((-4*x+a*(-5^(1/2)+1))/a/(10+2*5^(1/2))^(1/2))*(10+2*5^(1/2))^(1/2)/a^6,1],
[1/x^3/(a^5+x^5),x,7,-1/2/a^5/x^2-1/5*ln(a+x)/a^7+1/20*ln(a^2+x^2-1/2*a*x*(5^(1/2)+1))*(-5^(1/2)+1)/a^7+1/20*ln(a^2+x^2-1/2*a*x*(-5^(1/2)+1))*(5^(1/2)+1)/a^7-1/10*arctan((-4*x+a*(-5^(1/2)+1))/a/(10+2*5^(1/2))^(1/2))*(10-2*5^(1/2))^(1/2)/a^7+1/10*arctan(1/20*(-4*x+a*(5^(1/2)+1))*(50+10*5^(1/2))^(1/2)/a)*(10+2*5^(1/2))^(1/2)/a^7,1],
[1/x^4/(a^5+x^5),x,7,-1/3/a^5/x^3+1/5*ln(a+x)/a^8-1/20*ln(a^2+x^2-1/2*a*x*(5^(1/2)+1))*(-5^(1/2)+1)/a^8-1/20*ln(a^2+x^2-1/2*a*x*(-5^(1/2)+1))*(5^(1/2)+1)/a^8-1/10*arctan((-4*x+a*(-5^(1/2)+1))/a/(10+2*5^(1/2))^(1/2))*(10-2*5^(1/2))^(1/2)/a^8+1/10*arctan(1/20*(-4*x+a*(5^(1/2)+1))*(50+10*5^(1/2))^(1/2)/a)*(10+2*5^(1/2))^(1/2)/a^8,1],
[1/(x^m)/(a^5+x^5),x,1,x^(1-m)*hypergeom([1, 1/5-1/5*m],[6/5-1/5*m],-x^5/a^5)/a^5/(1-m),1],
[(x^4+1)/(x^6+1),x,22,2/3*arctan(x)+1/3*arctan(2*x-3^(1/2))+1/3*arctan(2*x+3^(1/2)),1],
[1/(x^2+3*x+5)^3,x,4,1/22*(3+2*x)/(x^2+3*x+5)^2+3/121*(3+2*x)/(x^2+3*x+5)+12/1331*arctan(1/11*(3+2*x)*11^(1/2))*11^(1/2),1],
[(x^4+x^2+1)/(x^2+1)^4,x,4,1/6*x/(x^2+1)^3-1/24*x/(x^2+1)^2+7/16*x/(x^2+1)+7/16*arctan(x),1],
[(A*x+B)/(a*x^2+2*b*x+c)^2,x,3,1/2*(-b*B+A*c+(A*b-B*a)*x)/(-a*c+b^2)/(a*x^2+2*b*x+c)-1/2*(A*b-B*a)*arctanh((a*x+b)/(-a*c+b^2)^(1/2))/(-a*c+b^2)^(3/2),1],
[(5*x^3-27*x^2+55*x-41)/(x^2-4*x+5)^2,x,5,(1-x)/(x^2-4*x+5)+2*arctan(-2+x)+5/2*ln(x^2-4*x+5),1],
[1/(x^3-1)^2,x,7,1/3*x/(-x^3+1)-2/9*ln(1-x)+1/9*ln(x^2+x+1)+2/9*arctan(1/3*(1+2*x)*3^(1/2))*3^(1/2),1],
[(3*x^4+4)/x^2/(x^2+1)^3,x,4,-4/x-7/4*x/(x^2+1)^2-25/8*x/(x^2+1)-57/8*arctan(x),1],
[x/(x^6+1),x,7,1/6*ln(x^2+1)-1/12*ln(x^4-x^2+1)-1/6*arctan(1/3*(-2*x^2+1)*3^(1/2))*3^(1/2),1],
[(-1+x^(-1+n))/(-n*x+x^n),x,5,ln(-n*x+x^n)/n,1],
[x^3/(3*x^4-2*x^2+1),x,5,1/12*ln(3*x^4-2*x^2+1)-1/12*arctan(1/2*(-3*x^2+1)*2^(1/2))*2^(1/2),1],
[x^5/(3*x^4+x^2-4),x,5,1/6*x^2+1/14*ln(-x^2+1)-8/63*ln(3*x^2+4),1],
[x^2/(x^6-10*x^3+9),x,4,-1/24*ln(-x^3+1)+1/24*ln(-x^3+9),1],
[(x^3-4*x^2+1)/(-2+x)^4,x,2,-7/3/(2-x)^3+2/(2-x)^2+2/(2-x)+ln(2-x),1],
[x^3/(-1+x)^12,x,2,1/11/(1-x)^11-3/10/(1-x)^10+1/3/(1-x)^9-1/8/(1-x)^8,1],
[(x^4-3*x)/(1+2*x)^5,x,3,-25/128/(1+2*x)^4+7/24/(1+2*x)^3-3/32/(1+2*x)^2+1/8/(1+2*x)+1/32*ln(1+2*x),1],
[1/(-1+x)^2/(1+x)^3,x,3,1/8/(1-x)-1/8/(1+x)^2-1/4/(1+x)+3/8*arctanh(x),1],
[1/(5-6*x)^2/x^2,x,2,6/25/(5-6*x)-1/25/x-12/125*ln(5-6*x)+12/125*ln(x),1],
[1/(x^2-2*x-3)^3,x,5,1/16*(1-x)/(-x^2+2*x+3)^2+3/128*(1-x)/(-x^2+2*x+3)+3/512*ln(3-x)-3/512*ln(1+x),1],
[1/(x^2-4*x+13)^3,x,4,1/36*(-2+x)/(x^2-4*x+13)^2+1/216*(-2+x)/(x^2-4*x+13)+1/648*arctan(-2/3+1/3*x),1],
[1/(2+x)^3/(3+x)^4,x,2,-1/2/(2+x)^2+4/(2+x)+1/3/(3+x)^3+3/2/(3+x)^2+6/(3+x)+10*ln(2+x)-10*ln(3+x),1],
[x^6/(x^2-2)^2,x,4,4*x+1/3*x^3-2*x/(x^2-2)-5*arctanh(1/2*x*2^(1/2))*2^(1/2),1],
[x^8/(x^2+4)^4,x,5,35/16*x-1/6*x^7/(x^2+4)^3-7/24*x^5/(x^2+4)^2-35/48*x^3/(x^2+4)-35/8*arctan(1/2*x),1],
[(-4+7*x)/(3*x^2+2*x+5)^2,x,3,1/28*(-39-19*x)/(3*x^2+2*x+5)-19/392*arctan(1/14*(1+3*x)*14^(1/2))*14^(1/2),1],
[(5-4*x)/(3*x^2-4*x-2)^2,x,3,1/20*(-18+7*x)/(-3*x^2+4*x+2)-7/200*arctanh(1/10*(2-3*x)*10^(1/2))*10^(1/2),1],
[x^5/(x^4+1)^3,x,4,-1/8*x^2/(x^4+1)^2+1/16*x^2/(x^4+1)+1/16*arctan(x^2),1],
[x*(x^2+1)^3/(x^4+2*x^2+2)^2,x,3,1/4/(x^4+2*x^2+2)+1/4*ln(x^4+2*x^2+2),1],
[x^3/(a^4+x^4)^3,x,1,-1/8/(a^4+x^4)^2,1],
[1/x/(a^4+x^4)^3,x,3,1/8/a^4/(a^4+x^4)^2+1/4/a^8/(a^4+x^4)+ln(x)/a^12-1/4*ln(a^4+x^4)/a^12,1],
[1/x^2/(a^4+x^4)^3,x,12,-45/32/a^12/x+1/8/a^4/x/(a^4+x^4)^2+9/32/a^8/x/(a^4+x^4)+45/128*arctan(1-x*2^(1/2)/a)/a^13*2^(1/2)-45/128*arctan(1+x*2^(1/2)/a)/a^13*2^(1/2)-45/256*ln(a^2+x^2-a*x*2^(1/2))/a^13*2^(1/2)+45/256*ln(a^2+x^2+a*x*2^(1/2))/a^13*2^(1/2),1],
[1/x^3/(a^4+x^4)^3,x,5,-15/16/a^12/x^2+1/8/a^4/x^2/(a^4+x^4)^2+5/16/a^8/x^2/(a^4+x^4)-15/16*arctan(x^2/a^2)/a^14,1],
[x^14/(2*x^5+3)^3,x,3,-9/80/(2*x^5+3)^2+3/20/(2*x^5+3)+1/40*ln(2*x^5+3),1],
[x^6/(2*x^5+3)^3,x,8,-1/20*x^2/(2*x^5+3)^2+1/150*x^2/(2*x^5+3)-1/1500*ln(3^(1/5)+2^(1/5)*x)*2^(3/5)*3^(2/5)+1/6000*ln(2^(3/5)*3^(2/5)+2*x^2-1/2*3^(1/5)*2^(4/5)*x*(5^(1/2)+1))*(-5^(1/2)+1)*2^(3/5)*3^(2/5)+1/6000*ln(2^(3/5)*3^(2/5)+2*x^2-1/2*3^(1/5)*2^(4/5)*x*(-5^(1/2)+1))*(5^(1/2)+1)*2^(3/5)*3^(2/5)-1/1500*arctan(1/5*(25-10*5^(1/2))^(1/2)+2/3*2^(7/10)*x*3^(4/5)/(5+5^(1/2))^(1/2))*(5-5^(1/2))^(1/2)*2^(1/10)*3^(2/5)+1/1500*arctan(2/3*2^(7/10)*x*3^(4/5)/(5-5^(1/2))^(1/2)-1/5*(25+10*5^(1/2))^(1/2))*(5+5^(1/2))^(1/2)*2^(1/10)*3^(2/5),1],
[9/5/x^2/(-2*x^2+3)^3,x,5,-1/8/x+3/20/x/(-2*x^2+3)^2+1/8/x/(-2*x^2+3)+1/24*arctanh(1/3*x*6^(1/2))*6^(1/2),1],
[(3*x^4+4)/x^2/(x^2+1)^3,x,4,-4/x-7/4*x/(x^2+1)^2-25/8*x/(x^2+1)-57/8*arctan(x),1],
[(-x^4+5*x^3+6*x^2-3*x+5)/(x^5-x^4-2*x^3+2*x^2+x-1),x,2,-3/2/(1-x)^2+2/(1-x)+1/(1+x)+ln(1-x)-2*ln(1+x),1],
[(x^2+1)/x/(x^3+1)^2,x,7,1/3*x*(-x^2+x)/(x^3+1)+ln(x)-4/9*ln(1+x)-5/18*ln(x^2-x+1)-1/9*arctan(1/3*(1-2*x)*3^(1/2))*3^(1/2),1],
[(x^2-3*x-2)/(1+x)^2/(x^2+x+1)^2,x,7,-2/(1+x)+1/3*(-7-5*x)/(x^2+x+1)-ln(1+x)+1/2*ln(x^2+x+1)-25/9*arctan(1/3*(1+2*x)*3^(1/2))*3^(1/2),1],
[1/(-4*x+1)^3/(2-3*x),x,2,1/10/(-4*x+1)^2-3/25/(-4*x+1)-9/125*ln(-4*x+1)+9/125*ln(2-3*x),1],
[x^3/(-5*x^2+2)^7,x,3,1/150/(-5*x^2+2)^6-1/250/(-5*x^2+2)^5,1],
[x^7/(-5*x^2+2)^3,x,3,-1/250*x^2+2/625/(-5*x^2+2)^2-6/625/(-5*x^2+2)-3/625*ln(-5*x^2+2),1],
[1/(-2+x)^3/(1+x)^2,x,2,-1/18/(-2+x)^2+2/27/(-2+x)+1/27/(1+x)+1/27*ln(-2+x)-1/27*ln(1+x),1],
[1/(2+x)^3/(3+x)^4,x,2,-1/2/(2+x)^2+4/(2+x)+1/3/(3+x)^3+3/2/(3+x)^2+6/(3+x)+10*ln(2+x)-10*ln(3+x),1],
[x^5/(3+x)^2,x,2,-108*x+27/2*x^2-2*x^3+1/4*x^4+243/(3+x)+405*ln(3+x),1],
[(c1*x+b1)*(c*x^2+2*b*x+a),x,2,a*b1*x+1/2*(a*c1+2*b*b1)*x^2+1/3*(2*b*c1+b1*c)*x^3+1/4*c*c1*x^4,1],
[(c1*x+b1)*(c*x^2+2*b*x+a)^2,x,2,a^2*b1*x+1/2*a*(a*c1+4*b*b1)*x^2+2/3*(2*a*b*c1+a*b1*c+2*b^2*b1)*x^3+1/2*(a*c*c1+2*b^2*c1+2*b*b1*c)*x^4+1/5*c*(4*b*c1+b1*c)*x^5+1/6*c^2*c1*x^6,1],
[(c1*x+b1)*(c*x^2+2*b*x+a)^3,x,2,a^3*b1*x+1/2*a^2*(a*c1+6*b*b1)*x^2+a*(2*a*b*c1+a*b1*c+4*b^2*b1)*x^3+1/4*(3*a^2*c*c1+12*a*b^2*c1+12*a*b*b1*c+8*b^3*b1)*x^4+1/5*(12*a*b*c*c1+3*a*b1*c^2+8*b^3*c1+12*b^2*b1*c)*x^5+1/2*c*(a*c*c1+4*b^2*c1+2*b*b1*c)*x^6+1/7*c^2*(6*b*c1+b1*c)*x^7+1/8*c^3*c1*x^8,1],
[(c1*x+b1)*(c*x^2+2*b*x+a)^4,x,2,a^4*b1*x+1/2*a^3*(a*c1+8*b*b1)*x^2+4/3*a^2*(2*a*b*c1+a*b1*c+6*b^2*b1)*x^3+a*(a^2*c*c1+6*a*b^2*c1+6*a*b*b1*c+8*b^3*b1)*x^4+2/5*(12*a^2*b*c*c1+3*a^2*b1*c^2+16*a*b^3*c1+24*a*b^2*b1*c+8*b^4*b1)*x^5+1/3*(3*a^2*c^2*c1+24*a*b^2*c*c1+12*a*b*b1*c^2+8*b^4*c1+16*b^3*b1*c)*x^6+4/7*c*(6*a*b*c*c1+a*b1*c^2+8*b^3*c1+6*b^2*b1*c)*x^7+1/2*c^2*(a*c*c1+6*b^2*c1+2*b*b1*c)*x^8+1/9*c^3*(8*b*c1+b1*c)*x^9+1/10*c^4*c1*x^10,1],
[(c1*x+b1)*(c*x^2+2*b*x+a)^n,x,2,1/2*c1*(c*x^2+2*b*x+a)^(1+n)/c/(1+n)-2^n*(-b*c1+b1*c)*(c*x^2+2*b*x+a)^(1+n)*hypergeom([-n, 1+n],[2+n],1/2*(b+c*x+(-a*c+b^2)^(1/2))/(-a*c+b^2)^(1/2))*((-b-c*x+(-a*c+b^2)^(1/2))/(-a*c+b^2)^(1/2))^(-1-n)/c/(1+n)/(-a*c+b^2)^(1/2),1],
[(c1*x+b1)/(c*x^2+2*b*x+a),x,4,1/2*c1*ln(c*x^2+2*b*x+a)/c-(-b*c1+b1*c)*arctanh((c*x+b)/(-a*c+b^2)^(1/2))/c/(-a*c+b^2)^(1/2),1],
[(c1*x+b1)/(c*x^2+2*b*x+a)^2,x,3,1/2*(-b*b1+a*c1-(-b*c1+b1*c)*x)/(-a*c+b^2)/(c*x^2+2*b*x+a)+1/2*(-b*c1+b1*c)*arctanh((c*x+b)/(-a*c+b^2)^(1/2))/(-a*c+b^2)^(3/2),1],
[(c1*x+b1)/(c*x^2+2*b*x+a)^3,x,4,1/4*(-b*b1+a*c1-(-b*c1+b1*c)*x)/(-a*c+b^2)/(c*x^2+2*b*x+a)^2+3/8*(-b*c1+b1*c)*(c*x+b)/(-a*c+b^2)^2/(c*x^2+2*b*x+a)-3/8*c*(-b*c1+b1*c)*arctanh((c*x+b)/(-a*c+b^2)^(1/2))/(-a*c+b^2)^(5/2),1],
[(c1*x+b1)/(c*x^2+2*b*x+a)^4,x,5,1/6*(-b*b1+a*c1-(-b*c1+b1*c)*x)/(-a*c+b^2)/(c*x^2+2*b*x+a)^3+5/24*(-b*c1+b1*c)*(c*x+b)/(-a*c+b^2)^2/(c*x^2+2*b*x+a)^2-5/16*c*(-b*c1+b1*c)*(c*x+b)/(-a*c+b^2)^3/(c*x^2+2*b*x+a)+5/16*c^2*(-b*c1+b1*c)*arctanh((c*x+b)/(-a*c+b^2)^(1/2))/(-a*c+b^2)^(7/2),1],
[(c1*x+b1)/((c*x^2+2*b*x+a)^n),x,2,1/2*c1*(c*x^2+2*b*x+a)^(1-n)/c/(1-n)-(-b*c1+b1*c)*(c*x^2+2*b*x+a)^(1-n)*hypergeom([n, 1-n],[2-n],1/2*(b+c*x+(-a*c+b^2)^(1/2))/(-a*c+b^2)^(1/2))*((-b-c*x+(-a*c+b^2)^(1/2))/(-a*c+b^2)^(1/2))^(-1+n)/(2^n)/c/(1-n)/(-a*c+b^2)^(1/2),1],
[x/(2*x^2+6*x+3),x,3,1/4*ln(3+2*x-3^(1/2))*(1-3^(1/2))+1/4*ln(3+2*x+3^(1/2))*(1+3^(1/2)),1],
[(-3+2*x)/(2*x^2+6*x+3)^3,x,4,1/4*(5+4*x)/(2*x^2+6*x+3)^2+1/2*(-3-2*x)/(2*x^2+6*x+3)+1/3*arctanh(1/3*(3+2*x)*3^(1/2))*3^(1/2),1],
[(-1+x)/(x^2+5*x+4)^2,x,4,1/9*(13+7*x)/(x^2+5*x+4)+7/27*ln(1+x)-7/27*ln(4+x),1],
[1/(x^2+3*x+2)^5,x,7,1/4*(-3-2*x)/(x^2+3*x+2)^4+7/6*(3+2*x)/(x^2+3*x+2)^3-35/6*(3+2*x)/(x^2+3*x+2)^2+35*(3+2*x)/(x^2+3*x+2)+70*ln(1+x)-70*ln(2+x),1],
[1/x^3/(2*x^2-6*x+7)^2,x,7,-1/490/x^2-69/1715/x+1/35*(-2+3*x)/x^2/(2*x^2-6*x+7)+80/2401*ln(x)-40/2401*ln(2*x^2-6*x+7)-234/60025*arctan(1/5*(3-2*x)*5^(1/2))*5^(1/2),1],
[x^9/(x^2+3*x+2)^5,x,8,735*x+1/4*x^8*(4+3*x)/(x^2+3*x+2)^4-1/12*x^6*(110+81*x)/(x^2+3*x+2)^3+1/2*x^4*(184+135*x)/(x^2+3*x+2)^2-1/2*x^2*(2206+1593*x)/(x^2+3*x+2)-1471*ln(1+x)+1472*ln(2+x),1],
[(1+2*x)^2/(2*x^2+5*x+3)^5,x,7,1/4*(1+2*x)*(7+6*x)/(2*x^2+5*x+3)^4+1/3*(73+62*x)/(2*x^2+5*x+3)^3-155/3*(5+4*x)/(2*x^2+5*x+3)^2+620*(5+4*x)/(2*x^2+5*x+3)+2480*ln(1+x)-2480*ln(3+2*x),1],
[(-b*x^2+a)^3/x^7,x,3,-1/6*a^3/x^6+3/4*a^2*b/x^4-3/2*a*b^2/x^2-b^3*ln(x),1],
[x^13/(a^4+x^4)^5,x,6,-1/16*x^10/(a^4+x^4)^4-5/96*x^6/(a^4+x^4)^3-5/128*x^2/(a^4+x^4)^2+5/256*x^2/a^4/(a^4+x^4)+5/256*arctan(x^2/a^2)/a^6,1],
[x^(3/2)*(x^2+1)*(-x+2*x^(1/2))^2,x,9,8/7*x^(7/2)-x^4+2/9*x^(9/2)+8/11*x^(11/2)-2/3*x^6+2/13*x^(13/2),1],
[(-3*x^(3/5)+x^(3/2))^2*(-1/3*x^(2/3)+4*x^(3/2)),x,5,-45/43*x^(43/15)+360/37*x^(37/10)+60/113*x^(113/30)-120/23*x^(23/5)-1/14*x^(14/3)+8/11*x^(11/2),1],
[1/(1+(1+x)^(1/2)),x,4,-2*ln(1+(1+x)^(1/2))+2*(1+x)^(1/2),1],
[x/(1+(1+x)^(1/2)),x,2,-x+2/3*(1+x)^(3/2),1],
[(1+(1+x)^(1/2))/(-1+(1+x)^(1/2)),x,4,x+4*ln(1-(1+x)^(1/2))+4*(1+x)^(1/2),1],
[1/((1+x)^(2/3)-(1+x)^(1/2)),x,5,6*(1+x)^(1/6)+3*(1+x)^(1/3)+6*ln(1-(1+x)^(1/6)),1],
[(1+x^(1/4))^(1/3)/x^(1/2),x,3,-3*(1+x^(1/4))^(4/3)+12/7*(1+x^(1/4))^(7/3),1],
[1/x^3/(1+x)^(3/2),x,5,-15/4*arctanh((1+x)^(1/2))+15/4/(1+x)^(1/2)-1/2/x^2/(1+x)^(1/2)+5/4/x/(1+x)^(1/2),1],
[1/(1-x)^(7/2)/x^5,x,9,3003/320/(1-x)^(5/2)+1001/64/(1-x)^(3/2)-1/4/(1-x)^(5/2)/x^4-13/24/(1-x)^(5/2)/x^3-143/96/(1-x)^(5/2)/x^2-429/64/(1-x)^(5/2)/x-3003/64*arctanh((1-x)^(1/2))+3003/64/(1-x)^(1/2),1],
[1/(-1+x)^(2/3)/x^5,x,8,1/4*(-1+x)^(1/3)/x^4+11/36*(-1+x)^(1/3)/x^3+11/27*(-1+x)^(1/3)/x^2+55/81*(-1+x)^(1/3)/x+55/81*ln(1+(-1+x)^(1/3))-55/243*ln(x)-110/243*arctan(1/3*(1-2*(-1+x)^(1/3))*3^(1/2))*3^(1/2),1],
[((1-x)/(1+x))^(1/2),x,3,-2*arctan(((1-x)/(1+x))^(1/2))+(1+x)*((1-x)/(1+x))^(1/2),1],
[x*((-a+x)/(b-x))^(1/2),x,4,-1/4*(a-b)*(a+3*b)*arctan(((-a+x)/(b-x))^(1/2))+1/4*(a-5*b)*(b-x)*((-a+x)/(b-x))^(1/2)+1/2*(b-x)^2*((-a+x)/(b-x))^(1/2),1],
[(-5+x)^(1/2)*(3+x)^(1/2)/(-1+x)/(x^2-25),x,6,1/6*arctan(1/4*(-5+x)^(1/2)*(3+x)^(1/2))+1/15*arctanh(5^(1/2)*(3+x)^(1/2)/(-5+x)^(1/2))*5^(1/2),1],
[x^2*(-x^2+1)^(1/4)*(1+x)^(1/2)/(1-x)^(1/2)/((1-x)^(1/2)-(1+x)^(1/2)),x,33,5/16*(1-x)^(3/4)*(1+x)^(1/4)-1/16*(1-x)^(1/4)*(1+x)^(3/4)+1/24*(1-x)^(5/4)*(1+x)^(3/4)+3/16*arctan(-1+(1-x)^(1/4)*2^(1/2)/(1+x)^(1/4))*2^(1/2)+3/16*arctan(1+(1-x)^(1/4)*2^(1/2)/(1+x)^(1/4))*2^(1/2)+1/16*ln(1-(1-x)^(1/4)*2^(1/2)/(1+x)^(1/4)+(1-x)^(1/2)/(1+x)^(1/2))*2^(1/2)-1/16*ln(1+(1-x)^(1/4)*2^(1/2)/(1+x)^(1/4)+(1-x)^(1/2)/(1+x)^(1/2))*2^(1/2)+7/24*(-x^2+1)^(5/4)/(1-x)^(1/2)+1/6*x*(-x^2+1)^(5/4)/(1-x)^(1/2)+1/6*(-x^2+1)^(5/4)*(1+x)^(1/2),1],
[fail,x,1,2,fail,1],//[x*(1+x)^(2/3)*(1-x)^(1/2)/(-(1-x)^(5/6)*(1+x)^(1/3)+(1-x)^(2/3)*(1+x)^(1/2)),x,-4,-1/12*(1-3*x)*(1-x)^(2/3)*(1+x)^(1/3)-1/4*(1-x)*(3+x)+1/12*(1-x)^(1/3)*(1+x)^(2/3)*(1+3*x)+1/12*(1-x)^(1/6)*(1+x)^(5/6)*(2+3*x)-1/12*(1-x)^(5/6)*(1+x)^(1/6)*(10+3*x)+1/6*arctan((1+x)^(1/6)/(1-x)^(1/6))-5/6*arctan(((1-x)^(1/3)-(1+x)^(1/3))/(1-x)^(1/6)/(1+x)^(1/6))-4/9*arctan(1/3*((1-x)^(1/3)-2*(1+x)^(1/3))/(1-x)^(1/3)*3^(1/2))*3^(1/2)+1/18*arctanh((1-x)^(1/6)*(1+x)^(1/6)*3^(1/2)/((1-x)^(1/3)+(1+x)^(1/3)))*3^(1/2)+1/4*x*(1-x)^(1/2)*(1+x)^(1/2),1],
[1/((-1+x)^4*(1+x)^2)^(1/3),x,2,-3/2*(-1+x)*(1+x)/((-1+x)^4*(1+x)^2)^(1/3),1],
[1/((-1+x)^3*(2+x)^5)^(1/4),x,2,4/3*(-1+x)*(2+x)/((-1+x)^3*(2+x)^5)^(1/4),1],
[1/((-1+x)^7*(1+x)^2)^(1/3),x,3,-3/8*(-1+x)*(1+x)/((-1+x)^7*(1+x)^2)^(1/3)+9/16*(-1+x)^2*(1+x)/((-1+x)^7*(1+x)^2)^(1/3),1],
[1/((-1+x)^2*(1+x))^(1/3),x,-3,-1/2*ln(1+x)-3/2*ln(1+(1-x)/((-1+x)^2*(1+x))^(1/3))+arctan(1/3*(1+2*(-1+x)/((-1+x)^2*(1+x))^(1/3))*3^(1/2))*3^(1/2),1],
[(1/x+x)/((-2+x)*(1+x)^3)^(1/2),x,9,-4/3*(-2+x)*(1+x)/((-2+x)*(1+x)^3)^(1/2)+2*(1+x)^(3/2)*arcsinh(1/3*(-2+x)^(1/2)*3^(1/2))*(-2+x)^(1/2)/((-2+x)*(1+x)^3)^(1/2)-(1+x)^(3/2)*arctan(2^(1/2)*(1+x)^(1/2)/(-2+x)^(1/2))*2^(1/2)*(-2+x)^(1/2)/((-2+x)*(1+x)^3)^(1/2),1],
[((-1+x)^2*(1+x))^(1/3)/x^2,x,-6,-((-1+x)^2*(1+x))^(1/3)/x+1/6*ln(x)-2/3*ln(1+x)-3/2*ln(1+(1-x)/((-1+x)^2*(1+x))^(1/3))-1/2*ln(1+(-1+x)/((-1+x)^2*(1+x))^(1/3))-1/3*arctan(1/3*(1-2*(-1+x)/((-1+x)^2*(1+x))^(1/3))*3^(1/2))*3^(1/2)-arctan(1/3*(1+2*(-1+x)/((-1+x)^2*(1+x))^(1/3))*3^(1/2))*3^(1/2),1],
[1/(x^2-2*x-3)^(5/2),x,2,1/12*(1-x)/(x^2-2*x-3)^(3/2)+1/24*(-1+x)/(x^2-2*x-3)^(1/2),1],
[1/(x^3-5*x^2+3*x+9)^(1/2),x,4,(3-x)*arctanh(1/2*(1+x)^(1/2))*(1+x)^(1/2)/(x^3-5*x^2+3*x+9)^(1/2),1],
[1/(x^3-5*x^2+3*x+9)^(3/2),x,7,1/8*(3-x)*(1+x)/(x^3-5*x^2+3*x+9)^(3/2)+5/64*(3-x)^2*(1+x)/(x^3-5*x^2+3*x+9)^(3/2)-15/256*(3-x)^3*(1+x)/(x^3-5*x^2+3*x+9)^(3/2)+15/512*(3-x)^3*(1+x)^(3/2)*arctanh(1/2*(1+x)^(1/2))/(x^3-5*x^2+3*x+9)^(3/2),1],
[1/(x^3-5*x^2+3*x+9)^(1/3),x,-3,-1/2*ln(1+x)-3/2*ln(1+(3-x)/(x^3-5*x^2+3*x+9)^(1/3))+arctan(1/3*(1+2*(-3+x)/(x^3-5*x^2+3*x+9)^(1/3))*3^(1/2))*3^(1/2),1],
[1/(x^3-5*x^2+3*x+9)^(2/3),x,3,3/4*(3-x)*(1+x)/(x^3-5*x^2+3*x+9)^(2/3),1],
[1/(x^3-5*x^2+3*x+9)^(4/3),x,5,3/20*(3-x)*(1+x)/(x^3-5*x^2+3*x+9)^(4/3)+9/80*(3-x)^2*(1+x)/(x^3-5*x^2+3*x+9)^(4/3)-27/320*(3-x)^3*(1+x)/(x^3-5*x^2+3*x+9)^(4/3),1],
[1/(-2*x^2+3*x+4)^(1/2),x,2,-1/2*arcsin(1/41*(3-4*x)*41^(1/2))*2^(1/2),1],
[1/(-x^2+4*x-3)^(1/2),x,2,arcsin(-2+x),1],
[1/(-3*x^2-5*x-2)^(1/2),x,2,1/3*arcsin(5+6*x)*3^(1/2),1],
[1/(x^2+4)/(-x^2+1)^(1/2),x,2,1/10*arctan(1/2*x*5^(1/2)/(-x^2+1)^(1/2))*5^(1/2),1],
[1/(x^2+4)/(4*x^2+1)^(1/2),x,2,1/30*arctanh(1/2*x*15^(1/2)/(4*x^2+1)^(1/2))*15^(1/2),1],
[x/(-x^2+3)/(-x^2+5)^(1/2),x,3,1/2*arctanh(1/2*(-x^2+5)^(1/2)*2^(1/2))*2^(1/2),1],
[x/(-x^2+5)/(-x^2+3)^(1/2),x,3,-1/2*arctan(1/2*(-x^2+3)^(1/2)*2^(1/2))*2^(1/2),1],
[1/(x^4-1)/(x^2+2)^(1/2),x,5,-1/2*arctan(x/(x^2+2)^(1/2))-1/6*arctanh(x*3^(1/2)/(x^2+2)^(1/2))*3^(1/2),1],
[x/(x^2-1)/(x^2+2*x+4)^(1/2),x,5,-1/6*arctanh(1/3*(x^2+2*x+4)^(1/2)*3^(1/2))*3^(1/2)-1/14*arctanh(1/7*(5+2*x)*7^(1/2)/(x^2+2*x+4)^(1/2))*7^(1/2),1],
[1/(x^3-8)/(x^2+2*x+5)^(1/2),x,9,1/12*arctanh((x^2+2*x+5)^(1/2))-1/12*arctan(1/3*(1+x)*3^(1/2)/(x^2+2*x+5)^(1/2))*3^(1/2)-1/156*arctanh(1/13*(7+3*x)*13^(1/2)/(x^2+2*x+5)^(1/2))*13^(1/2),1],
[x/(x^2+x+4)/(4*x^2+4*x+5)^(1/2),x,5,1/11*arctan(1/11*(4*x^2+4*x+5)^(1/2)*11^(1/2))*11^(1/2)-1/165*arctanh(1/15*(1+2*x)*165^(1/2)/(4*x^2+4*x+5)^(1/2))*165^(1/2),1],
[(3+x)/(x^2+1)/(x^2+x+1)^(1/2),x,5,-2*arctan(1/2*(1-x)*2^(1/2)/(x^2+x+1)^(1/2))*2^(1/2)+arctanh(1/2*(1+x)*2^(1/2)/(x^2+x+1)^(1/2))*2^(1/2),1],
[(1+2*x)/(3*x^2+4*x+4)/(x^2+6*x-1)^(1/2),x,5,-1/21*arctanh((1+x)*7^(1/2)/(x^2+6*x-1)^(1/2))*7^(1/2)-5/84*arctan(1/4*(2-x)*7^(1/2)*2^(1/2)/(x^2+6*x-1)^(1/2))*14^(1/2),1],
[(A*x+B)/(5*x^2-18*x+17)/(10*x^2-22*x+13)^(1/2),x,5,-1/35*(2*A+B)*arctan((2-x)*35^(1/2)/(10*x^2-22*x+13)^(1/2))*35^(1/2)-1/70*(A+B)*arctanh(1/2*(1-x)*35^(1/2)/(10*x^2-22*x+13)^(1/2))*35^(1/2),1],
[(-2+x)/(5*x^2-18*x+17)/(10*x^2-22*x+13)^(1/2),x,2,1/70*arctanh(1/2*(1-x)*35^(1/2)/(10*x^2-22*x+13)^(1/2))*35^(1/2),1],
[x^4*(-x^2+5)^(1/2),x,4,125/16*arcsin(1/5*x*5^(1/2))-25/16*x*(-x^2+5)^(1/2)-5/24*x^3*(-x^2+5)^(1/2)+1/6*x^5*(-x^2+5)^(1/2),1],
[1/x^6/(x^2+2)^(1/2),x,3,-1/10*(x^2+2)^(1/2)/x^5+1/15*(x^2+2)^(1/2)/x^3-1/15*(x^2+2)^(1/2)/x,1],
[1/(2*x^2+3)^(7/2),x,3,1/15*x/(2*x^2+3)^(5/2)+4/135*x/(2*x^2+3)^(3/2)+8/405*x/(2*x^2+3)^(1/2),1],
[x/(1+x^2+a*(x^2+1)^(1/2)),x,3,ln(a+(x^2+1)^(1/2)),1],
[(x^2-x+1)/(x^2+1)^(3/2),x,2,arcsinh(x)+1/(x^2+1)^(1/2),1],
[(x^2+1)^(1/2)/(x^2+2),x,4,arcsinh(x)-1/2*arctanh(1/2*x*2^(1/2)/(x^2+1)^(1/2))*2^(1/2),1],
[1/(x^2+2)^2/(x^2+1)^(1/2),x,3,3/8*arctanh(1/2*x*2^(1/2)/(x^2+1)^(1/2))*2^(1/2)-1/4*x*(x^2+1)^(1/2)/(x^2+2),1],
[x^2/(x^2-6)/(x^2-2)^(1/2),x,5,arctanh(x/(x^2-2)^(1/2))-1/2*arctanh(1/3*x*6^(1/2)/(x^2-2)^(1/2))*6^(1/2),1],
[(x^2+5)/(x^2+1)^2/(-x^2+1)^(1/2),x,4,2*arctan(x*2^(1/2)/(-x^2+1)^(1/2))*2^(1/2)+x*(-x^2+1)^(1/2)/(x^2+1),1],
[(4*x-(-x^2+1)^(1/2))/(5+(-x^2+1)^(1/2)),x,15,-x+5*arcsin(x)+20*ln(5+(-x^2+1)^(1/2))+25/12*arctan(1/12*x*6^(1/2))*6^(1/2)-25/12*arctan(5/12*x*6^(1/2)/(-x^2+1)^(1/2))*6^(1/2)-4*(-x^2+1)^(1/2),1],
[x^2*(2-(x^2+1)^(1/2))/(1-x^3+(x^2+1)^(3/2))/(x^2+1)^(1/2),x,32,8/9*x-1/6*x^2-41/54*arcsinh(x)+7/27*arctanh(1/2*(1-x)/(x^2+1)^(1/2))-7/54*ln(3*x^2+2*x+3)+4/27*arctan(1/4*(1+3*x)*2^(1/2))*2^(1/2)+4/27*arctan(1/2*(1+x)*2^(1/2)/(x^2+1)^(1/2))*2^(1/2)+8/9*(x^2+1)^(1/2)-1/6*x*(x^2+1)^(1/2),1],
[x*(2*r*x-x^2)^(1/2),x,4,-1/3*(2*r*x-x^2)^(3/2)+r^3*arctan(x/(2*r*x-x^2)^(1/2))-1/2*r*(r-x)*(2*r*x-x^2)^(1/2),1],
[x^2*(2*r*x-x^2)^(1/2),x,5,-5/12*r*(2*r*x-x^2)^(3/2)-1/4*x*(2*r*x-x^2)^(3/2)+5/4*r^4*arctan(x/(2*r*x-x^2)^(1/2))-5/8*r^2*(r-x)*(2*r*x-x^2)^(1/2),1],
[x^3*(2*r*x-x^2)^(1/2),x,6,-7/12*r^2*(2*r*x-x^2)^(3/2)-7/20*r*x*(2*r*x-x^2)^(3/2)-1/5*x^2*(2*r*x-x^2)^(3/2)+7/4*r^5*arctan(x/(2*r*x-x^2)^(1/2))-7/8*r^3*(r-x)*(2*r*x-x^2)^(1/2),1],
[1/(x^2-1)/(x^2+2*x)^(1/2),x,5,-1/2*arctan((x^2+2*x)^(1/2))-1/6*arctanh(1/3*(1+2*x)*3^(1/2)/(x^2+2*x)^(1/2))*3^(1/2),1],
[(-2+3*x)/(1+x)^3/(-x^2+2*x)^(1/2),x,4,1/6*arctan(1/3*(1-2*x)*3^(1/2)/(-x^2+2*x)^(1/2))*3^(1/2)-5/6*(-x^2+2*x)^(1/2)/(1+x)^2-2/3*(-x^2+2*x)^(1/2)/(1+x),1],
[1/(x^2+x+1)^(1/2),x,2,arcsinh(1/3*(1+2*x)*3^(1/2)),1],
[x^3/(x^2+x+1)^(1/2),x,4,7/16*arcsinh(1/3*(1+2*x)*3^(1/2))+1/3*x^2*(x^2+x+1)^(1/2)-1/24*(1+10*x)*(x^2+x+1)^(1/2),1],
[1/(x^2+x+1)^(3/2),x,1,2/3*(1+2*x)/(x^2+x+1)^(1/2),1],
[x/(x^2+x+1)^(3/2),x,1,-2/3*(2+x)/(x^2+x+1)^(1/2),1],
[x^3/(x^2+x+1)^(3/2),x,4,-3/2*arcsinh(1/3*(1+2*x)*3^(1/2))-2/3*x^2*(2+x)/(x^2+x+1)^(1/2)+1/3*(5+2*x)*(x^2+x+1)^(1/2),1],
[x^2*(x^2+x+1)^(1/2),x,5,-5/24*(x^2+x+1)^(3/2)+1/4*x*(x^2+x+1)^(3/2)+3/128*arcsinh(1/3*(1+2*x)*3^(1/2))+1/64*(1+2*x)*(x^2+x+1)^(1/2),1],
[(x^2+x+1)^(3/2),x,4,1/8*(1+2*x)*(x^2+x+1)^(3/2)+27/128*arcsinh(1/3*(1+2*x)*3^(1/2))+9/64*(1+2*x)*(x^2+x+1)^(1/2),1],
[(x^2+x+1)^(5/2),x,5,5/64*(1+2*x)*(x^2+x+1)^(3/2)+1/12*(1+2*x)*(x^2+x+1)^(5/2)+135/1024*arcsinh(1/3*(1+2*x)*3^(1/2))+45/512*(1+2*x)*(x^2+x+1)^(1/2),1],
[1/x^2/(x^2+x+1)^(1/2),x,3,1/2*arctanh(1/2*(2+x)/(x^2+x+1)^(1/2))-(x^2+x+1)^(1/2)/x,1],
[1/x^3/(x^2+x+1)^(1/2),x,4,1/8*arctanh(1/2*(2+x)/(x^2+x+1)^(1/2))-1/2*(x^2+x+1)^(1/2)/x^2+3/4*(x^2+x+1)^(1/2)/x,1],
[1/x^2/(x^2+x+1)^(3/2),x,4,3/2*arctanh(1/2*(2+x)/(x^2+x+1)^(1/2))+2/3*(1-x)/x/(x^2+x+1)^(1/2)-5/3*(x^2+x+1)^(1/2)/x,1],
[1/x^3/(x^2+x+1)^(3/2),x,5,-3/8*arctanh(1/2*(2+x)/(x^2+x+1)^(1/2))+2/3*(1-x)/x^2/(x^2+x+1)^(1/2)-7/6*(x^2+x+1)^(1/2)/x^2+37/12*(x^2+x+1)^(1/2)/x,1],
[1/(1+x)/(x^2+x+1)^(1/2),x,2,-arctanh(1/2*(1-x)/(x^2+x+1)^(1/2)),1],
[1/(x^3-x)/(x^2+2*x+4)^(1/2),x,10,1/2*arctanh(1/2*(4+x)/(x^2+2*x+4)^(1/2))-1/6*arctanh(1/3*(x^2+2*x+4)^(1/2)*3^(1/2))*3^(1/2)-1/14*arctanh(1/7*(5+2*x)*7^(1/2)/(x^2+2*x+4)^(1/2))*7^(1/2),1],
[(x^2+2*x+4)^(1/2)/(-1+x)^2,x,6,arcsinh(1/3*(1+x)*3^(1/2))-2/7*arctanh(1/7*(5+2*x)*7^(1/2)/(x^2+2*x+4)^(1/2))*7^(1/2)+(x^2+2*x+4)^(1/2)/(1-x),1],
[(3+2*x)/(x^2+2*x+3)^2/(x^2+2*x+4)^(1/2),x,6,arctanh((x^2+2*x+4)^(1/2))-1/8*arctan(1/2*(1+x)*2^(1/2)/(x^2+2*x+4)^(1/2))*2^(1/2)-1/4*(3-x)*(x^2+2*x+4)^(1/2)/(x^2+2*x+3),1],
[(2*x^3+3*x^2)/(2*x^2+x-3)/(x^2+2*x-3)^(1/2),x,4,(x^2+2*x-3)^(1/2)+1/2*(x^2+2*x-3)^(1/2)/(1-x),1],
[(x^4+1)/(x^2+x+1)/(x^2+x+2)^(1/2),x,14,-1/8*arcsinh(1/7*(1+2*x)*7^(1/2))-arctanh((x^2+x+2)^(1/2))+1/3*arctan(1/3*(1+2*x)*3^(1/2)/(x^2+x+2)^(1/2))*3^(1/2)-7/4*(x^2+x+2)^(1/2)+1/2*x*(x^2+x+2)^(1/2),1],
[1/(x^2+2*x+4)^(7/2),x,3,1/15*(1+x)/(x^2+2*x+4)^(5/2)+4/135*(1+x)/(x^2+2*x+4)^(3/2)+8/405*(1+x)/(x^2+2*x+4)^(1/2),1],
[1/(3*x^2+8*x+1)^(5/2),x,2,1/39*(-4-3*x)/(3*x^2+8*x+1)^(3/2)+2/169*(4+3*x)/(3*x^2+8*x+1)^(1/2),1],
[1/(-3*x^2+4*x+5)^(5/2),x,2,1/57*(-2+3*x)/(-3*x^2+4*x+5)^(3/2)-2/361*(2-3*x)/(-3*x^2+4*x+5)^(1/2),1],
[1/(1+(x^2+2*x+2)^(1/2)),x,5,1/(1+x)+arcsinh(1+x)-(x^2+2*x+2)^(1/2)/(1+x),1],
[1/(x+(x^2+x+1)^(1/2)),x,-3,-x-3/2*arcsinh(1/3*(1+2*x)*3^(1/2))+2*ln(x+(x^2+x+1)^(1/2))+(x^2+x+1)^(1/2),1],
[x^2/(1+2*x+2*(x^2+x+1)^(1/2)),x,7,-1/9*x^3-1/6*x^4-5/36*(x^2+x+1)^(3/2)+1/6*x*(x^2+x+1)^(3/2)+1/64*arcsinh(1/3*(1+2*x)*3^(1/2))+1/96*(1+2*x)*(x^2+x+1)^(1/2),1],
[(-3*x+(x^2+x+1)^(1/2))/(-1+(x^2+x+1)^(1/2)),x,26,x+5/2*arcsinh(1/3*(1+2*x)*3^(1/2))+4*arctanh(1/2*(1-x)/(x^2+x+1)^(1/2))-arctanh(1/2*(2+x)/(x^2+x+1)^(1/2))+ln(x)-4*ln(1+x)-3*(x^2+x+1)^(1/2),1],
[(1+x)/(-(x^2+x+1)^(1/2)+(x^2+2*x+4)^(1/2)),x,36,11/2*arcsinh(1/3*(1+x)*3^(1/2))+43/8*arcsinh(1/3*(1+2*x)*3^(1/2))-2*arctanh(1/14*(1+5*x)*7^(1/2)/(x^2+x+1)^(1/2))*7^(1/2)+2*arctanh(1/7*(1-2*x)*7^(1/2)/(x^2+2*x+4)^(1/2))*7^(1/2)-2*(x^2+x+1)^(1/2)+1/4*(1+2*x)*(x^2+x+1)^(1/2)-2*(x^2+2*x+4)^(1/2)+1/2*(1+x)*(x^2+2*x+4)^(1/2),1],
[1/x^3/(-1+x)^(1/2),x,4,3/4*arctan((-1+x)^(1/2))+1/2*(-1+x)^(1/2)/x^2+3/4*(-1+x)^(1/2)/x,1],
[1/(1-3/x)^(4/3)/x^2,x,1,-1/(1-3/x)^(1/3),1],
[(-1+3*x)^(4/3)/x^2,x,6,12*(-1+3*x)^(1/3)-(-1+3*x)^(4/3)/x+2*ln(x)-6*ln(1+(-1+3*x)^(1/3))+4*arctan(1/3*(1-2*(-1+3*x)^(1/3))*3^(1/2))*3^(1/2),1],
[(4-3*x)^(4/3)*x^2,x,2,-16/63*(4-3*x)^(7/3)+4/45*(4-3*x)^(10/3)-1/117*(4-3*x)^(13/3),1],
[(1-2*x^(1/3))^(3/4)/x,x,6,4*(1-2*x^(1/3))^(3/4)+6*arctan((1-2*x^(1/3))^(1/4))-6*arctanh((1-2*x^(1/3))^(1/4)),1],
[x/(3-2*x^(1/2))^(3/4),x,3,-27/2*(3-2*x^(1/2))^(1/4)+27/10*(3-2*x^(1/2))^(5/4)-1/2*(3-2*x^(1/2))^(9/4)+1/26*(3-2*x^(1/2))^(13/4),1],
[(-1+2*x^(1/2))^(5/4)/x^2,x,13,5/4*arctan(-1+2^(1/2)*(-1+2*x^(1/2))^(1/4))*2^(1/2)+5/4*arctan(1+2^(1/2)*(-1+2*x^(1/2))^(1/4))*2^(1/2)-5/8*ln(1-2^(1/2)*(-1+2*x^(1/2))^(1/4)+(-1+2*x^(1/2))^(1/2))*2^(1/2)+5/8*ln(1+2^(1/2)*(-1+2*x^(1/2))^(1/4)+(-1+2*x^(1/2))^(1/2))*2^(1/2)-5/2*(-1+2*x^(1/2))^(1/4)/x^(1/2)-(-1+2*x^(1/2))^(5/4)/x,1],
[x^6*(x^7+1)^(1/3),x,1,3/28*(x^7+1)^(4/3),1],
[x^6/(x^7+1)^(5/3),x,1,-3/14/(x^7+1)^(2/3),1],
[1/x/(2*x^7-27)^(2/3),x,5,-1/18*ln(x)+1/42*ln(3+(2*x^7-27)^(1/3))-1/63*arctan(1/9*(3-2*(2*x^7-27)^(1/3))*3^(1/2))*3^(1/2),1],
[(x^7+1)^(2/3)/x^8,x,6,-1/7*(x^7+1)^(2/3)/x^7-1/3*ln(x)+1/7*ln(1-(x^7+1)^(1/3))+2/21*arctan(1/3*(1+2*(x^7+1)^(1/3))*3^(1/2))*3^(1/2),1],
[(4*x^4+3)^(1/4)/x^2,x,5,-(4*x^4+3)^(1/4)/x-1/2*arctan(x*2^(1/2)/(4*x^4+3)^(1/4))*2^(1/2)+1/2*arctanh(x*2^(1/2)/(4*x^4+3)^(1/4))*2^(1/2),1],
[x^2*(4*x^4+3)^(5/4),x,6,15/32*x^3*(4*x^4+3)^(1/4)+1/8*x^3*(4*x^4+3)^(5/4)-45/256*arctan(x*2^(1/2)/(4*x^4+3)^(1/4))*2^(1/2)+45/256*arctanh(x*2^(1/2)/(4*x^4+3)^(1/4))*2^(1/2),1],
[x^6*(4*x^4+3)^(1/4),x,6,3/128*x^3*(4*x^4+3)^(1/4)+1/8*x^7*(4*x^4+3)^(1/4)+27/1024*arctan(x*2^(1/2)/(4*x^4+3)^(1/4))*2^(1/2)-27/1024*arctanh(x*2^(1/2)/(4*x^4+3)^(1/4))*2^(1/2),1],
[(x*(-x^2+1))^(1/3),x,6,1/2*x*(x*(-x^2+1))^(1/3)+1/12*ln(x)-1/4*ln(x+(x*(-x^2+1))^(1/3))+1/6*arctan(1/3*(2*x-(x*(-x^2+1))^(1/3))/(x*(-x^2+1))^(1/3)*3^(1/2))*3^(1/2),1],
[((1+x^(1/3))*x)^(1/2),x,8,21/128*arctanh(x^(2/3)/((1+x^(1/3))*x)^(1/2))+7/64*((1+x^(1/3))*x)^(1/2)-21/128*((1+x^(1/3))*x)^(1/2)/x^(1/3)-7/80*x^(1/3)*((1+x^(1/3))*x)^(1/2)+3/40*x^(2/3)*((1+x^(1/3))*x)^(1/2)+3/5*x*((1+x^(1/3))*x)^(1/2),1],
[x^3/(x^4-1)/(2*x^8+1)^(1/2),x,3,-1/12*arctanh(1/3*(2*x^4+1)*3^(1/2)/(2*x^8+1)^(1/2))*3^(1/2),1],
[x^9*(x^10+x^5+1)^(1/2),x,5,1/15*(x^10+x^5+1)^(3/2)-3/80*arcsinh(1/3*(2*x^5+1)*3^(1/2))-1/40*(2*x^5+1)*(x^10+x^5+1)^(1/2),1],
[1/x^5/(x^4+2*x^2+4)^(1/2),x,5,1/128*arctanh(1/2*(x^2+4)/(x^4+2*x^2+4)^(1/2))-1/16*(x^4+2*x^2+4)^(1/2)/x^4+3/64*(x^4+2*x^2+4)^(1/2)/x^2,1],
[(x^2-1)/x/(x^4+3*x^2+1)^(1/2),x,3,arctanh((x^2+1)/(x^4+3*x^2+1)^(1/2)),1],
[(2*x^3-3*x)*(x^4-3*x^2)^(3/5),x,1,5/16*(x^4-3*x^2)^(8/5),1],
[(-2*x^5+3*x^8-x^2*(3*x^3-1)^(2/3))/(3*x^3-1)^(3/4),x,9,-4/27*(3*x^3-1)^(1/4)-4/33*(3*x^3-1)^(11/12)+4/243*(3*x^3-1)^(9/4),1],
[1/(x^3-1)/(x^3+2)^(1/3),x,1,-1/3*arctan(1/3*(1+2*3^(1/3)*x/(x^3+2)^(1/3))*3^(1/2))*3^(1/6)-1/18*ln(x^3-1)*3^(2/3)+1/6*ln(3^(1/3)*x-(x^3+2)^(1/3))*3^(2/3),1],
[1/(x^4+1)/(x^4+2)^(1/4),x,10,1/4*arctan(-1+x*2^(1/2)/(x^4+2)^(1/4))*2^(1/2)+1/4*arctan(1+x*2^(1/2)/(x^4+2)^(1/4))*2^(1/2)-1/8*ln(1-x*2^(1/2)/(x^4+2)^(1/4)+x^2/(x^4+2)^(1/2))*2^(1/2)+1/8*ln(1+x*2^(1/2)/(x^4+2)^(1/4)+x^2/(x^4+2)^(1/2))*2^(1/2),1],
[(x^3-1)/(x^3+2)^(1/3),x,2,1/3*x*(x^3+2)^(2/3)+5/6*ln(-x+(x^3+2)^(1/3))-5/9*arctan(1/3*(1+2*x/(x^3+2)^(1/3))*3^(1/2))*3^(1/2),1],
[(x^4+1)^(3/4)/(x^4+2)^2,x,5,1/8*x*(x^4+1)^(3/4)/(x^4+2)+3/32*arctan(1/2*x*2^(3/4)/(x^4+1)^(1/4))*2^(1/4)+3/32*arctanh(1/2*x*2^(3/4)/(x^4+1)^(1/4))*2^(1/4),1],
[(x^5-2)^2/(x^5+3)^(16/5),x,3,-5/33*x*(x^5-2)/(x^5+3)^(11/5)+5/297*x/(x^5+3)^(6/5)+97/891*x/(x^5+3)^(1/5),1],
[1/(x^3+3*x^2+3*x)/(x^3+3*x^2+3*x+3)^(1/3),x,3,-1/3*arctan(1/3*(1+2*3^(1/3)*(1+x)/(2+(1+x)^3)^(1/3))*3^(1/2))*3^(1/6)-1/18*ln(1-(1+x)^3)*3^(2/3)+1/6*ln(3^(1/3)*(1+x)-(2+(1+x)^3)^(1/3))*3^(2/3),1],
[(-x^2+1)/(x^2+1)/(x^4+1)^(1/2),x,2,1/2*arctan(x*2^(1/2)/(x^4+1)^(1/2))*2^(1/2),1],
[(x^2+1)/(-x^2+1)/(x^4+1)^(1/2),x,2,1/2*arctanh(x*2^(1/2)/(x^4+1)^(1/2))*2^(1/2),1],
[(x^2+1)/x/(x^4+1)^(1/2),x,6,arctanh((x^2-1)/(x^4+1)^(1/2)),1],
[(x^2-1)/x/(x^4+1)^(1/2),x,6,arctanh((x^2+1)/(x^4+1)^(1/2)),1],
[(x^2+1)/(-x^2+1)/(x^4+x^2+1)^(1/2),x,2,1/3*arctanh(x*3^(1/2)/(x^4+x^2+1)^(1/2))*3^(1/2),1],
[(-x^2+1)/(x^2+1)/(x^4+x^2+1)^(1/2),x,2,arctan(x/(x^4+x^2+1)^(1/2)),1],
[(x^4-1)/x^2/(x^4+x^2+1)^(1/2),x,1,1/x*(x^4+x^2+1)^(1/2),1],
[(-x^2+1)/(2*a*x+x^2+1)/(2*a*x^3+x^4+2*b*x^2+2*a*x+1)^(1/2),x,1,1/2*arctan(1/2*(a+2*(a^2-b+1)*x+a*x^2)*2^(1/2)/(1-b)^(1/2)/(2*a*x^3+x^4+2*b*x^2+2*a*x+1)^(1/2))*2^(1/2)/(1-b)^(1/2),1],
[1/(x^4+1)/(-x^2+(x^4+1)^(1/2))^(1/2),x,2,arctan(x/(-x^2+(x^4+1)^(1/2))^(1/2)),1],
[1/(1+x^(2*n))/(-x^2+(1+x^(2*n))^(1/n))^(1/2),x,2,arctan(x/(-x^2+(1+x^(2*n))^(1/n))^(1/2)),1],
[cos(x)^2,x,2,1/2*x+1/2*cos(x)*sin(x),1],
[cos(x)^3,x,2,sin(x)-1/3*sin(x)^3,1],
[sin(x)^4,x,3,3/8*x-3/8*cos(x)*sin(x)-1/4*cos(x)*sin(x)^3,1],
[cos(x)^6,x,4,5/16*x+5/16*cos(x)*sin(x)+5/24*cos(x)^3*sin(x)+1/6*cos(x)^5*sin(x),1],
[sin(x)^8,x,5,35/128*x-35/128*cos(x)*sin(x)-35/192*cos(x)*sin(x)^3-7/48*cos(x)*sin(x)^5-1/8*cos(x)*sin(x)^7,1],
[cos(1/4*Pi+1/2*x)^4,x,3,3/8*x+1/2*cos(x)-1/8*cos(x)*sin(x),1],
[-cos(5/12*Pi+3*x)^3,x,2,-1/3*sin(5/12*Pi+3*x)+1/9*sin(5/12*Pi+3*x)^3,1],
[1/sin(x)^6,x,2,-cot(x)-2/3*cot(x)^3-1/5*cot(x)^5,1],
[csc(x)^7,x,4,-5/16*arctanh(cos(x))-5/16*cot(x)*csc(x)-5/24*cot(x)*csc(x)^3-1/6*cot(x)*csc(x)^5,1],
[1/cos(x)^12,x,2,tan(x)+5/3*tan(x)^3+2*tan(x)^5+10/7*tan(x)^7+5/9*tan(x)^9+1/11*tan(x)^11,1],
[1/cos(1/4*Pi+3*x)^3,x,2,1/6*arctanh(sin(1/4*Pi+3*x))+1/6*sec(1/4*Pi+3*x)*tan(1/4*Pi+3*x),1],
[tan(x)^6,x,4,-x+tan(x)-1/3*tan(x)^3+1/5*tan(x)^5,1],
[1/tan(x)^5,x,3,1/2*cot(x)^2-1/4*cot(x)^4+ln(sin(x)),1],
[cot(1/4*Pi+1/3*x)^4,x,3,x+3*cot(1/4*Pi+1/3*x)-cot(1/4*Pi+1/3*x)^3,1],
[cos(x)^6*sin(x)^4,x,6,3/256*x+3/256*cos(x)*sin(x)+1/128*cos(x)^3*sin(x)+1/160*cos(x)^5*sin(x)-3/80*cos(x)^7*sin(x)-1/10*cos(x)^7*sin(x)^3,1],
[cos(x)^6*sin(x)^7,x,3,-1/7*cos(x)^7+1/3*cos(x)^9-3/11*cos(x)^11+1/13*cos(x)^13,1],
[sin(x)^11/cos(x),x,4,5/2*cos(x)^2-5/2*cos(x)^4+5/3*cos(x)^6-5/8*cos(x)^8+1/10*cos(x)^10-ln(cos(x)),1],
[1/cos(x)^6/sin(x)^6,x,3,-10*cot(x)-5/3*cot(x)^3-1/5*cot(x)^5+10*tan(x)+5/3*tan(x)^3+1/5*tan(x)^5,1],
[cos(x)^2*sin(x)^2,x,3,1/8*x+1/8*cos(x)*sin(x)-1/4*cos(x)^3*sin(x),1],
[cos(x)^4*sin(x)^4,x,5,3/128*x+3/128*cos(x)*sin(x)+1/64*cos(x)^3*sin(x)-1/16*cos(x)^5*sin(x)-1/8*cos(x)^5*sin(x)^3,1],
[cos(x)^6*sin(x)^6,x,7,5/1024*x+5/1024*cos(x)*sin(x)+5/1536*cos(x)^3*sin(x)+1/384*cos(x)^5*sin(x)-1/64*cos(x)^7*sin(x)-1/24*cos(x)^7*sin(x)^3-1/12*cos(x)^7*sin(x)^5,1],
[cos(x)^8*sin(x)^8,x,9,35/32768*x+35/32768*cos(x)*sin(x)+35/49152*cos(x)^3*sin(x)+7/12288*cos(x)^5*sin(x)+1/2048*cos(x)^7*sin(x)-1/256*cos(x)^9*sin(x)-5/384*cos(x)^9*sin(x)^3-1/32*cos(x)^9*sin(x)^5-1/16*cos(x)^9*sin(x)^7,1],
[cos(x)^(2*m)*sin(x)^(2*m),x,1,cos(x)^(-1+2*m)*(cos(x)^2)^(1/2-m)*hypergeom([1/2-m, 1/2+m],[3/2+m],sin(x)^2)*sin(x)^(1+2*m)/(1+2*m),1],
[1/cos(1/4*Pi+2*x)/sin(1/4*Pi+2*x)^3,x,3,-1/4*cot(1/4*Pi+2*x)^2+1/2*ln(tan(1/4*Pi+2*x)),1],
[sec(x)^2*tan(x)^2,x,2,1/3*tan(x)^3,1],
[cot(x)^3*csc(x),x,2,csc(x)-1/3*csc(x)^3,1],
[sec(x)^3*tan(x),x,2,1/3*sec(x)^3,1],
[cot(x)^2*csc(x)^3,x,3,1/8*arctanh(cos(x))+1/8*cot(x)*csc(x)-1/4*cot(x)*csc(x)^3,1],
[cos(x)^3/sin(x)^7,x,3,1/4*csc(x)^4-1/6*csc(x)^6,1],
[sec(x)^(3/2)*tan(x)^5,x,3,2/3*sec(x)^(3/2)-4/7*sec(x)^(7/2)+2/11*sec(x)^(11/2),1],
[sec(x)^4*tan(x)^(3/2),x,3,2/5*tan(x)^(5/2)+2/9*tan(x)^(9/2),1],
[cot(x)^4*csc(x)^3,x,4,-1/16*arctanh(cos(x))-1/16*cot(x)*csc(x)+1/8*cot(x)*csc(x)^3-1/6*cot(x)^3*csc(x)^3,1],
[sec(1/4*Pi+1/2*x)^3*tan(1/4*Pi+1/2*x)^2,x,3,-1/4*arctanh(sin(1/4*Pi+1/2*x))-1/4*sec(1/4*Pi+1/2*x)*tan(1/4*Pi+1/2*x)+1/2*sec(1/4*Pi+1/2*x)^3*tan(1/4*Pi+1/2*x),1],
[(1+cot(x)^3)*(a*sec(x)^2-sin(2*x))^2,x,8,1/2*x+4*a*x+2*cos(x)^2+cos(x)^4+4*a*cot(x)-1/2*a^2*cot(x)^2+(4-a)*a*ln(cos(x))+(a^2+4)*ln(sin(x))+1/2*cos(x)*sin(x)-cos(x)^3*sin(x)+a^2*tan(x)+1/3*a^2*tan(x)^3,1],
[(4-3*cos(x))*(1-1/2*sin(x))^4,x,15,227/32*x+10*cos(x)-3*cos(x)^2-2/3*cos(x)^3-3*sin(x)-99/32*cos(x)*sin(x)-3/2*sin(x)^3-1/16*cos(x)*sin(x)^3+3/8*sin(x)^4-3/80*sin(x)^5,1],
[(1/2-3*cot(x))*(3-2*cot(x))^3,x,4,-285/2*x+5*(3-2*cot(x))^2+(3-2*cot(x))^3-42*cot(x)+4*ln(sin(x)),1],
[cos(5*x)/cos(x)^5,x,4,16*x-15*tan(x)+5/3*tan(x)^3,1],
[cos(4*x)/cos(x),x,4,arctanh(sin(x))-8/3*sin(x)^3,1],
[cos(x)*cos(4*x),x,1,1/6*sin(3*x)+1/10*sin(5*x),1],
[cos(4*x)/cos(x)^5,x,4,35/8*arctanh(sin(x))-29/8*sec(x)*tan(x)+1/4*sec(x)^3*tan(x),1],
[cos(x)^4*cos(4*x),x,6,1/16*x+1/8*sin(2*x)+3/32*sin(4*x)+1/24*sin(6*x)+1/128*sin(8*x),1],
[cos(5*x)/sin(x)^5,x,4,6*csc(x)^2-1/4*csc(x)^4+16*ln(sin(x)),1],
[sin(4*x)/sin(x)^4,x,3,-2*csc(x)^2-8*ln(sin(x)),1],
[cos(x)/sin(x)/(2+sin(2*x)),x,7,1/2*ln(sin(x))-1/4*ln(1+cos(x)*sin(x))-1/6*x*3^(1/2)+1/6*arctan((1-2*cos(x)^2)/(2+2*cos(x)*sin(x)+3^(1/2)))*3^(1/2),1],
[cos(x)^2/cos(3*x)/sin(x),x,5,-1/2*ln(-4+csc(x)^2),1],
[sin(2*x)/(cos(x)^4+sin(x)^4),x,5,-arctan(cos(2*x)),1],
[1/(4+sin(x)+cos(x)*3^(1/2)),x,3,1/6*x*3^(1/2)+1/3*arctan((cos(x)-sin(x)*3^(1/2))/(sin(x)+cos(x)*3^(1/2)+4+2*3^(1/2)))*3^(1/2),1],
[1/(3+4*cos(x)+4*sin(x)),x,3,-1/23*arctanh((cos(x)-sin(x))*23^(1/2)/(8+3*cos(x)+3*sin(x)))*23^(1/2),1],
[1/(4-3*cos(x)^2+5*sin(x)^2),x,2,1/3*x+1/3*arctan(2*cos(x)*sin(x)/(1+2*sin(x)^2)),1],
[1/(4+4*cot(x)+tan(x)),x,6,4/25*x-3/25*ln(2*cos(x)+sin(x))+2/5/(2+tan(x)),1],
[1/(2*sec(x)+sin(x))^2,x,4,8/225*x*15^(1/2)-8/225*arctan((1-2*cos(x)^2)/(4+2*cos(x)*sin(x)+15^(1/2)))*15^(1/2)+1/15*(1+4*tan(x))/(2+tan(x)+2*tan(x)^2),1],
[1/(cos(x)+2*sec(x))^2,x,3,1/36*x*6^(1/2)-1/36*arctan(cos(x)*sin(x)/(2+cos(x)^2+6^(1/2)))*6^(1/2)+1/6*tan(x)/(3+2*tan(x)^2),1],
[(5-tan(x)-6*tan(x)^2)/(1+3*tan(x))^3,x,4,-67/250*x-28/125*ln(cos(x)+3*sin(x))-7/10/(1+3*tan(x))^2-29/50/(1+3*tan(x)),1],
[cos(x)^2/cos(3*x),x,2,1/2*arctanh(2*sin(x)),1],
[sin(x)/cos(2*x),x,2,1/2*arctanh(cos(x)*2^(1/2))*2^(1/2),1],
[sin(x)^2/cos(2*x),x,4,-1/2*x+1/4*arctanh(2*cos(x)*sin(x)),1],
[sin(x)^3/cos(3*x),x,4,1/3*ln(cos(x))-1/24*ln(3-4*cos(x)^2),1],
[cos(x)/sin(3*x),x,5,1/3*ln(sin(x))-1/6*ln(3-4*sin(x)^2),1],
[sin(x)/sin(4*x),x,4,-1/4*arctanh(sin(x))+1/4*arctanh(sin(x)*2^(1/2))*2^(1/2),1],
[sin(x)^3/sin(4*x),x,4,-1/4*arctanh(sin(x))+1/8*arctanh(sin(x)*2^(1/2))*2^(1/2),1],
[(1+sin(2*x))^(1/2),x,1,-cos(2*x)/(1+sin(2*x))^(1/2),1],
[(1-sin(2*x))^(1/2),x,1,cos(2*x)/(1-sin(2*x))^(1/2),1],
[1/(1+cos(2*x))^(1/2),x,2,1/2*arctanh(1/2*sin(2*x)*2^(1/2)/(1+cos(2*x))^(1/2))*2^(1/2),1],
[1/(1-cos(2*x))^(1/2),x,2,-1/2*arctanh(1/2*sin(2*x)*2^(1/2)/(1-cos(2*x))^(1/2))*2^(1/2),1],
[1/(1-cos(3*x))^(3/2),x,3,-1/6*sin(3*x)/(1-cos(3*x))^(3/2)-1/12*arctanh(1/2*sin(3*x)*2^(1/2)/(1-cos(3*x))^(1/2))*2^(1/2),1],
[(1-sin(2/3*x))^(5/2),x,3,3/5*cos(2/3*x)*(1-sin(2/3*x))^(3/2)+32/5*cos(2/3*x)/(1-sin(2/3*x))^(1/2)+8/5*cos(2/3*x)*(1-sin(2/3*x))^(1/2),1],
[cos(x)*(-cos(x)^2+2*(1+2*sin(x))^(1/4))/(1+2*sin(x))^(3/2),x,4,-4/(1+2*sin(x))^(1/4)+1/12*(1+2*sin(x))^(3/2)+3/4/(1+2*sin(x))^(1/2)-1/2*(1+2*sin(x))^(1/2),1],
[tan(x)^(1/2),x,11,1/2*arctan(-1+2^(1/2)*tan(x)^(1/2))*2^(1/2)+1/2*arctan(1+2^(1/2)*tan(x)^(1/2))*2^(1/2)+1/4*ln(1-2^(1/2)*tan(x)^(1/2)+tan(x))*2^(1/2)-1/4*ln(1+2^(1/2)*tan(x)^(1/2)+tan(x))*2^(1/2),1],
[1/tan(5*x)^(1/3),x,9,3/20*ln(1+tan(5*x)^(2/3))-1/20*ln(1+tan(5*x)^2)-1/10*arctan(1/3*(1-2*tan(5*x)^(2/3))*3^(1/2))*3^(1/2),1],
[1/(4+3*tan(2*x))^(3/2),x,6,-9/500*arctan(1/2*(1-3*tan(2*x))*2^(1/2)/(4+3*tan(2*x))^(1/2))*2^(1/2)+13/500*arctanh(1/2*(3+tan(2*x))*2^(1/2)/(4+3*tan(2*x))^(1/2))*2^(1/2)-3/25/(4+3*tan(2*x))^(1/2),1],
[(-(4-3*tan(x))^(1/2)+3*tan(x))/cos(x)^2/(4-3*tan(x))^(3/2),x,4,1/3*ln(4-3*tan(x))+8/3/(4-3*tan(x))^(1/2)+2/3*(4-3*tan(x))^(1/2),1],
[tan(x)/(-1+tan(x)^(1/2))^2,x,-19,-1/2*x+1/2*ln(cos(x))+ln(1-tan(x)^(1/2))+1/2*arctan(1/2*(1-tan(x))*2^(1/2)/tan(x)^(1/2))*2^(1/2)+1/2*arctanh(1/2*(1+tan(x))*2^(1/2)/tan(x)^(1/2))*2^(1/2)+1/(1-tan(x)^(1/2)),1],
[sin(x)/sin(2*x)^(1/2),x,1,-1/2*arcsin(cos(x)-sin(x))-1/2*ln(cos(x)+sin(x)+sin(2*x)^(1/2)),1],
[cos(x)/sin(2*x)^(1/2),x,1,-1/2*arcsin(cos(x)-sin(x))+1/2*ln(cos(x)+sin(x)+sin(2*x)^(1/2)),1],
[sin(x)*sin(2*x)^(1/2),x,2,-1/4*arcsin(cos(x)-sin(x))+1/4*ln(cos(x)+sin(x)+sin(2*x)^(1/2))-1/2*cos(x)*sin(2*x)^(1/2),1],
[(cos(x)-sin(x))*sin(2*x)^(1/2),x,6,-1/2*ln(cos(x)+sin(x)+sin(2*x)^(1/2))+1/2*cos(x)*sin(2*x)^(1/2)+1/2*sin(x)*sin(2*x)^(1/2),1],
[sin(x)^7/sin(2*x)^(7/2),x,4,-1/16*arcsin(cos(x)-sin(x))+1/16*ln(cos(x)+sin(x)+sin(2*x)^(1/2))+1/5*sin(x)^5/sin(2*x)^(5/2)-1/4*sin(x)/sin(2*x)^(1/2),1],
[cos(x)^7/sin(2*x)^(7/2),x,4,-1/16*arcsin(cos(x)-sin(x))-1/16*ln(cos(x)+sin(x)+sin(2*x)^(1/2))-1/5*cos(x)^5/sin(2*x)^(5/2)+1/4*cos(x)/sin(2*x)^(1/2),1],
[sin(2*x)^(3/2)/sin(x)^5,x,1,-1/5*csc(x)^5*sin(2*x)^(5/2),1],
[1/cos(x)^3/sin(2*x)^(1/2),x,2,4/5*sec(x)*sin(2*x)^(1/2)+1/5*sec(x)^3*sin(2*x)^(1/2),1],
[1/sin(x)/sin(2*x)^(3/2),x,3,-2/3*cos(x)/sin(2*x)^(3/2)+4/3*sin(x)/sin(2*x)^(1/2),1],
[cos(x)^3*(cos(2*x)-3*tan(x))/(sin(x)^2-sin(2*x))/sin(2*x)^(5/2),x,6,33/32*arctanh(1/2*sin(2*x)^(1/2)/cos(x))-9/16*cos(x)/sin(2*x)^(1/2)-5/24*cos(x)*cot(x)/sin(2*x)^(1/2)+1/20*cos(x)*cot(x)^2/sin(2*x)^(1/2),1],
[(sin(x)/cos(x)^5)^(1/2),x,5,2/3*cos(x)*sin(x)*(sec(x)^4*tan(x))^(1/2),1],
[(sin(x)^5/cos(x))^(1/2),x,13,3/8*arctan(1/2*(1-cot(x))*csc(x)^2*(sin(x)^4*tan(x))^(1/2)*2^(1/2))*2^(1/2)+3/8*ln(cos(x)+sin(x)-cot(x)*csc(x)*2^(1/2)*(sin(x)^4*tan(x))^(1/2))*2^(1/2)-1/2*cot(x)*(sin(x)^4*tan(x))^(1/2),1],
[(sin(x)^2/cos(x)^14)^(1/3),x,5,3/5*cos(x)^3*sin(x)*(sec(x)^12*tan(x)^2)^(1/3)+3/11*cos(x)*sin(x)^3*(sec(x)^12*tan(x)^2)^(1/3),1],
[1/(cos(x)^11*sin(x)^13)^(1/4),x,4,-4/9*cos(x)^5*sin(x)/(cos(x)^11*sin(x)^13)^(1/4)-8*cos(x)^3*sin(x)^3/(cos(x)^11*sin(x)^13)^(1/4)+4/7*cos(x)*sin(x)^5/(cos(x)^11*sin(x)^13)^(1/4),1],
[(cos(2*x)-sin(2*x)^(1/2))/(cos(x)^3*sin(x))^(1/2),x,-28,-ln(cos(x)+sin(x)-sec(x)*2^(1/2)*(cos(x)^3*sin(x))^(1/2))*2^(1/2)-sin(2*x)/(cos(x)^3*sin(x))^(1/2)-arcsin(cos(x)-sin(x))*cos(x)*sin(2*x)^(1/2)/(cos(x)^3*sin(x))^(1/2)-arctanh(sin(x))*cos(x)*sin(2*x)^(1/2)/(cos(x)^3*sin(x))^(1/2),1],
[(-2*sin(2*x)+(cos(x)*sin(x)^3)^(1/2))/(-(cos(x)^3*sin(x))^(1/2)+tan(x)^(1/2)),x,66,2^(1/4)*arccoth(1/2*cos(x)*(sin(x)+cos(x)*2^(1/2))*2^(1/4)/(cos(x)^3*sin(x))^(1/2))-2^(1/4)*arccoth(1/2*(2^(1/2)+tan(x))*2^(1/4)/tan(x)^(1/2))+2^(1/4)*arctan(1/2*cos(x)*(-sin(x)+cos(x)*2^(1/2))*2^(1/4)/(cos(x)^3*sin(x))^(1/2))-2^(1/4)*arctan(1/2*(2^(1/2)-tan(x))*2^(1/4)/tan(x)^(1/2))-2*arccoth(1/2*cos(x)*(cos(x)+sin(x))*2^(1/2)/(cos(x)^3*sin(x))^(1/2))*2^(1/2)-2*arctan(1/2*cos(x)*(cos(x)-sin(x))*2^(1/2)/(cos(x)^3*sin(x))^(1/2))*2^(1/2)+4*csc(x)*sec(x)*(cos(x)^3*sin(x))^(1/2)+1/4*csc(x)^2*ln(1+cos(x)^2)*sec(x)^2*(cos(x)^3*sin(x))^(1/2)*(cos(x)*sin(x)^3)^(1/2)+1/2*csc(x)^2*ln(sin(x))*sec(x)^2*(cos(x)^3*sin(x))^(1/2)*(cos(x)*sin(x)^3)^(1/2)+4/tan(x)^(1/2)-1/4*csc(x)^2*ln(1+cos(x)^2)*(cos(x)*sin(x)^3)^(1/2)*tan(x)^(1/2)+1/2*csc(x)^2*ln(sin(x))*(cos(x)*sin(x)^3)^(1/2)*tan(x)^(1/2),1],
[((sin(x)/cos(x)^7)^(1/3)-3*tan(x))/(cos(x)^5*sin(x))^(2/3),x,"nock",-9/10*sin(x)^4/(cos(x)^5*sin(x))^(2/3)-9/4*sec(x)^8*(cos(x)^5*sin(x))^(4/3)+3/2*(cos(x)^5*sin(x))^(1/3)*(sec(x)^6*tan(x))^(1/3)+3/4*(cos(x)^5*sin(x))^(1/3)*tan(x)^2*(sec(x)^6*tan(x))^(1/3)+3/14*(cos(x)^5*sin(x))^(1/3)*tan(x)^4*(sec(x)^6*tan(x))^(1/3),1],
[(1+2*cos(x)^2)^(5/2)*sin(x),x,"nock",-5/24*cos(x)*(1+2*cos(x)^2)^(3/2)-1/6*cos(x)*(1+2*cos(x)^2)^(5/2)-5/32*arcsinh(cos(x)*2^(1/2))*2^(1/2)-5/16*cos(x)*(1+2*cos(x)^2)^(1/2),1],
[cos(x)*(5*cos(x)^2+sin(x)^2)^(5/2),x,5,625/32*arcsin(2/5*sin(x)*5^(1/2))+25/24*sin(x)*(5-4*sin(x)^2)^(3/2)+1/6*sin(x)*(5-4*sin(x)^2)^(5/2)+125/16*sin(x)*(5-4*sin(x)^2)^(1/2),1],
[cos(x)*(-cos(x)^2-5*sin(x)^2)^(3/2),x,5,3/16*arctan(2*sin(x)/(-1-4*sin(x)^2)^(1/2))+1/4*sin(x)*(-1-4*sin(x)^2)^(3/2)-3/8*sin(x)*(-1-4*sin(x)^2)^(1/2),1],
[sin(x)/(5*cos(x)^2-2*sin(x)^2)^(7/2),x,4,1/10*cos(x)/(-2+7*cos(x)^2)^(5/2)-1/15*cos(x)/(-2+7*cos(x)^2)^(3/2)+1/15*cos(x)/(-2+7*cos(x)^2)^(1/2),1],
[cos(x)*cos(2*x)/(2-5*sin(x)^2)^(3/2),x,"nock",2/25*arcsin(1/2*sin(x)*10^(1/2))*5^(1/2)+1/10*sin(x)/(2-5*sin(x)^2)^(1/2),1],
[sin(5*x)/(5*cos(x)^2+9*sin(x)^2)^(5/2),x,"nock",-1/2*arcsin(2/3*cos(x))-55/27*cos(x)/(9-4*cos(x)^2)^(3/2)+295/243*cos(x)/(9-4*cos(x)^2)^(1/2),1],
[cos(x)*cos(2*x)*sin(3*x)/(-5+4*sin(x)^2)^(5/2),x,"nock",-1/4/(-5+4*sin(x)^2)^(3/2)-5/8/(-5+4*sin(x)^2)^(1/2)+1/8*(-5+4*sin(x)^2)^(1/2),1],
[(-2*cos(x)^3*(-1+sin(x))+cos(2*x)*sin(x))/sin(x)^2/(-5+sin(x)^2)^(1/2),x,"nock",2*arctan(cos(x)/(-5+sin(x)^2)^(1/2))-2*arctanh(sin(x)/(-5+sin(x)^2)^(1/2))-1/5*arctan(cos(x)*5^(1/2)/(-5+sin(x)^2)^(1/2))*5^(1/2)-2/5*arctan(1/5*(-5+sin(x)^2)^(1/2)*5^(1/2))*5^(1/2)+2*(-5+sin(x)^2)^(1/2)+2/5*(-5+sin(x)^2)^(1/2)/sin(x),1],
[cos(3*x)/(-(-1+8*cos(x)^2)^(1/2)+(3*cos(x)^2-sin(x)^2)^(1/2)),x,27,3/4*arcsin(2/3*sin(x)*3^(1/2))-3/4*arctan(sin(x)/(-1+4*cos(x)^2)^(1/2))-3/4*arctan(sin(x)/(-1+8*cos(x)^2)^(1/2))+5/8*arcsin(2/7*sin(x)*14^(1/2))*2^(1/2)-1/2*sin(x)*(-1+4*cos(x)^2)^(1/2)-1/2*sin(x)*(-1+8*cos(x)^2)^(1/2),1],
[(2-3*sin(x)^2)^(3/5)*sin(4*x),x,5,5/36*(2-3*sin(x)^2)^(8/5)-20/117*(2-3*sin(x)^2)^(13/5),1],
[cos(x)*cos(2*x)^(1/2),x,3,1/4*arcsin(sin(x)*2^(1/2))*2^(1/2)+1/2*sin(x)*cos(2*x)^(1/2),1],
[cos(2*x)^(3/2)*sin(x),x,5,-1/4*cos(x)*cos(2*x)^(3/2)-3/16*arctanh(cos(x)*2^(1/2)/cos(2*x)^(1/2))*2^(1/2)+3/8*cos(x)*cos(2*x)^(1/2),1],
[sin(x)/cos(2*x)^(5/2),x,1,-1/3*cos(3*x)/cos(2*x)^(3/2),1],
[cos(2*x)^(3/2)/cos(x)^3,x,6,-5/2*arctan(sin(x)/cos(2*x)^(1/2))+2*arcsin(sin(x)*2^(1/2))*2^(1/2)-1/2*sec(x)*cos(2*x)^(1/2)*tan(x),1],
[(3*sin(x)^3-cos(x)*sin(4*x))/cos(2*x)^(7/2)/csc(x)^2,x,11,-11/20*cos(x)/cos(2*x)^(3/2)-2/3*cos(x)^3/cos(2*x)^(3/2)+3/10*cos(x)*sin(x)^2/cos(2*x)^(5/2)-1/2*arctanh(cos(x)*2^(1/2)/cos(2*x)^(1/2))*2^(1/2)+63/20*cos(x)/cos(2*x)^(1/2),1],
[(4-5*sec(x)^2)^(3/2),x,7,8*arctan(2*tan(x)/(-1-5*tan(x)^2)^(1/2))-7/2*arctan(5^(1/2)*tan(x)/(-1-5*tan(x)^2)^(1/2))*5^(1/2)-5/2*(-1-5*tan(x)^2)^(1/2)*tan(x),1],
[1/(4-5*sec(x)^2)^(3/2),x,4,1/8*arctan(2*tan(x)/(-1-5*tan(x)^2)^(1/2))-5/4*tan(x)/(-1-5*tan(x)^2)^(1/2),1],
[(-2*cot(x)^2+sin(x))/(1+5*tan(x)^2)^(3/2),x,10,-1/4*arctanh(2*tan(x)/(1+5*tan(x)^2)^(1/2))-1/4*cos(x)/(1+5*tan(x)^2)^(1/2)-5/2*cot(x)/(1+5*tan(x)^2)^(1/2)-1/8*cos(x)*(1+5*tan(x)^2)^(1/2)+9/2*cot(x)*(1+5*tan(x)^2)^(1/2),1],
[(-3+cos(2*x))/cos(x)^4/(4-cot(x)^2)^(1/2),x,5,-2/3*(4-cot(x)^2)^(1/2)*tan(x)-1/3*(4-cot(x)^2)^(1/2)*tan(x)^3,1],
[(3+sin(x)^2)*tan(x)^3/(-2+cos(x)^2)/(5-4*sec(x)^2)^(3/2),x,16,-1/18*arctanh(1/3*(5-4*sec(x)^2)^(1/2)*3^(1/2))*3^(1/2)-1/25*arctanh(1/5*(5-4*sec(x)^2)^(1/2)*5^(1/2))*5^(1/2)-2/15/(5-4*sec(x)^2)^(1/2),1],
[(sec(x)^2-3*(4*sec(x)^2+5*tan(x)^2)^(1/2)*tan(x))/sin(x)^2/(4*sec(x)^2+5*tan(x)^2)^(3/2),x,10,-3/4*ln(tan(x))+3/8*ln(4+9*tan(x)^2)-1/4*cot(x)/(4+9*tan(x)^2)^(1/2)-7/8*tan(x)/(4+9*tan(x)^2)^(1/2),1],
[tan(x)*(1+5*tan(x)^2)^(5/2),x,7,-32*arctan(1/2*(1+5*tan(x)^2)^(1/2))+16*(1+5*tan(x)^2)^(1/2)-4/3*(1+5*tan(x)^2)^(3/2)+1/5*(1+5*tan(x)^2)^(5/2),1],
[tan(x)/(1+5*tan(x)^2)^(5/2),x,6,1/32*arctan(1/2*(1+5*tan(x)^2)^(1/2))+1/16/(1+5*tan(x)^2)^(1/2)-1/12/(1+5*tan(x)^2)^(3/2),1],
[tan(x)/(a^3+b^3*tan(x)^2)^(1/3),x,6,1/2*ln(cos(x))/(a^3-b^3)^(1/3)+3/4*ln((a^3-b^3)^(1/3)-(a^3+b^3*tan(x)^2)^(1/3))/(a^3-b^3)^(1/3)+1/2*arctan(1/3*(1+2*(a^3+b^3*tan(x)^2)^(1/3)/(a^3-b^3)^(1/3))*3^(1/2))*3^(1/2)/(a^3-b^3)^(1/3),1],
[tan(x)*(1-7*tan(x)^2)^(2/3),x,7,2*ln(cos(x))+3*ln(2-(1-7*tan(x)^2)^(1/3))+2*arctan(1/3*(1+(1-7*tan(x)^2)^(1/3))*3^(1/2))*3^(1/2)+3/4*(1-7*tan(x)^2)^(2/3),1],
[cot(x)/(a^4+b^4*csc(x)^2)^(1/4),x,6,-arctan((a^4+b^4*csc(x)^2)^(1/4)/a)/a+arctanh((a^4+b^4*csc(x)^2)^(1/4)/a)/a,1],
[cot(x)/(a^4-b^4*csc(x)^2)^(1/4),x,6,-arctan((a^4-b^4*csc(x)^2)^(1/4)/a)/a+arctanh((a^4-b^4*csc(x)^2)^(1/4)/a)/a,1],
[tan(x)*((1-3*sec(x)^2)^(1/3)*sin(x)^2+3*tan(x)^2)/cos(x)^2/(1-3*sec(x)^2)^(5/6)/(1-(1-3*sec(x)^2)^(1/2)),x,29,1/4*ln(sec(x)^2)-3/2*ln(1-(1-3*sec(x)^2)^(1/6))+1/3*ln(1-(1-3*sec(x)^2)^(1/2))-(1-3*sec(x)^2)^(1/6)-1/4*(1-3*sec(x)^2)^(2/3)+arctan(1/3*(1+2*(1-3*sec(x)^2)^(1/6))*3^(1/2))*3^(1/2)+1/2/(1-(1-3*sec(x)^2)^(1/2)),1],
[(-cos(2*x)+2*tan(x)^2)/cos(x)^2/(tan(x)*tan(2*x))^(3/2),x,-22,2*arctanh(tan(x)/(tan(x)*tan(2*x))^(1/2))-11/8*arctanh(2^(1/2)*tan(x)/(tan(x)*tan(2*x))^(1/2))*2^(1/2)+3/4*tan(x)/(tan(x)*tan(2*x))^(1/2)+1/2*tan(x)/(tan(x)*tan(2*x))^(3/2)+2/3*tan(x)^3/(tan(x)*tan(2*x))^(3/2),1],
[tan(x)/(a^3-b^3*cos(x)^n)^(4/3),x,7,-3/a^3/n/(a^3-b^3*cos(x)^n)^(1/3)+1/2*ln(cos(x))/a^4-3/2*ln(a-(a^3-b^3*cos(x)^n)^(1/3))/a^4/n-arctan(1/3*(a+2*(a^3-b^3*cos(x)^n)^(1/3))/a*3^(1/2))*3^(1/2)/a^4/n,1],
[(1+2*cos(x)^9)^(5/6)*tan(x),x,"nock",1/3*arctanh((1+2*cos(x)^9)^(1/6))-1/9*arctanh((1+2*cos(x)^9)^(1/2))-2/15*(1+2*cos(x)^9)^(5/6)+1/9*arctan(1/3*(1-(1+2*cos(x)^9)^(1/3))/(1+2*cos(x)^9)^(1/6)*3^(1/2))*3^(1/2),1],
[cot(x)*sin(x)^9/(2-5*sin(x)^3)^(4/3),x,4,4/125/(2-5*sin(x)^3)^(1/3)+2/125*(2-5*sin(x)^3)^(2/3)-1/625*(2-5*sin(x)^3)^(5/3),1],
[tan(x)*(1+(1-8*tan(x)^2)^(1/3))/cos(x)^2/(1-8*tan(x)^2)^(2/3),x,2,-3/32*(1+(1-8*tan(x)^2)^(1/3))^2,1],
[cot(x)*(1+(1-8*tan(x)^2)^(1/3))/cos(x)^2/(1-8*tan(x)^2)^(2/3),x,15,-ln(tan(x))+3/2*ln(1-(1-8*tan(x)^2)^(1/3)),1],
[(5*cos(x)^2-(-1+5*sin(x)^2)^(1/2))*tan(x)/(-1+5*sin(x)^2)^(1/4)/(2+(-1+5*sin(x)^2)^(1/2)),x,14,2*(-1+5*sin(x)^2)^(1/4)-3/2*arctan(1/2*(-1+5*sin(x)^2)^(1/4)*2^(1/2))*2^(1/2)-1/4*arctanh(1/2*(-1+5*sin(x)^2)^(1/4)*2^(1/2))*2^(1/2)-1/2*(-1+5*sin(x)^2)^(1/4)/(2+(-1+5*sin(x)^2)^(1/2)),1],
[cos(x)^4*cos(2*x)^(2/3)*tan(x),x,4,-3/40*cos(2*x)^(5/3)-3/64*cos(2*x)^(8/3),1],
[sin(x)^6*tan(x)/cos(2*x)^(3/4),x,-14,7/4*cos(2*x)^(1/4)-1/5*cos(2*x)^(5/4)+1/36*cos(2*x)^(9/4)+1/2*arctan(1/2*(1-cos(2*x)^(1/2))/cos(2*x)^(1/4)*2^(1/2))*2^(1/2)-1/2*arctanh(1/2*(1+cos(2*x)^(1/2))/cos(2*x)^(1/4)*2^(1/2))*2^(1/2),1],
[(tan(x)*tan(2*x))^(1/2),x,3,-arctanh(tan(x)/(tan(x)*tan(2*x))^(1/2)),1],
[(cot(2*x)/cot(x))^(1/2),x,"nock",arctan(2^(1/2)*tan(x)/(1-tan(x)^2)^(1/2))-1/2*arcsin(tan(x))*2^(1/2),1],
[1/x^5/(x^2+5),x,3,-1/20/x^4+1/50/x^2+1/125*ln(x)-1/250*ln(x^2+5),1],
[1/x^6/(x^2+5),x,4,-1/25/x^5+1/75/x^3-1/125/x-1/625*arctan(1/5*x*5^(1/2))*5^(1/2),1],
[1/x/(x^2-4)^4,x,3,1/24/(-x^2+4)^3+1/64/(-x^2+4)^2+1/128/(-x^2+4)+1/256*ln(x)-1/512*ln(-x^2+4),1],
[1/x/(x^2-2)^(5/2),x,5,-1/6/(x^2-2)^(3/2)+1/8*arctan(1/2*(x^2-2)^(1/2)*2^(1/2))*2^(1/2)+1/4/(x^2-2)^(1/2),1],
[(x^2-10)^(5/2)/x,x,6,-10/3*(x^2-10)^(3/2)+1/5*(x^2-10)^(5/2)-100*arctan(1/10*(x^2-10)^(1/2)*10^(1/2))*10^(1/2)+100*(x^2-10)^(1/2),1],
[x^(1+2*n),x,1,1/2*x^(2+2*n)/(1+n),1],
[x^7/(x^2-5)^3,x,3,1/2*x^2-125/4/(-x^2+5)^2+75/2/(-x^2+5)+15/2*ln(-x^2+5),1],
[(3*x^5-4*x^3)/(x^2-1)^5,x,4,1/8/(-x^2+1)^4+1/3/(-x^2+1)^3-3/4/(-x^2+1)^2,1],
[x^3*(x^2+1)^(9/14),x,3,-7/23*(x^2+1)^(23/14)+7/37*(x^2+1)^(37/14),1],
[x^5/(x^2-4)^(13/6),x,3,-48/7/(x^2-4)^(7/6)-24/(x^2-4)^(1/6)+3/5*(x^2-4)^(5/6),1],
[1/(2*x^2+1)^(5/2),x,2,1/3*x/(2*x^2+1)^(3/2)+2/3*x/(2*x^2+1)^(1/2),1],
[1/(x^2-2*x-1)^(5/2),x,2,1/6*(1-x)/(x^2-2*x-1)^(3/2)+1/6*(-1+x)/(x^2-2*x-1)^(1/2),1],
[1/x^4/(x^2-8)^(3/2),x,3,1/24/x^3/(x^2-8)^(1/2)+1/48/x/(x^2-8)^(1/2)-1/192*x/(x^2-8)^(1/2),1],
[(x^2+5)^2/x^(13/3),x,2,-15/2/x^(10/3)-15/2/x^(4/3)+3/2*x^(2/3),1],
[1/x^7/(x^2+1)^3,x,3,-1/6/x^6+3/4/x^4-3/x^2-1/4/(x^2+1)^2-2/(x^2+1)-10*ln(x)+5*ln(x^2+1),1],
[((x^2+2)/x^2)^(7/9)/(x^2+2)^(3/2),x,3,-9/10*(1+2/x^2)^(7/9)*x/(x^2+2)^(1/2),1],
[x^4/(-x^2+10^(1/2))^(9/2),x,2,1/70*x^5*10^(1/2)/(-x^2+10^(1/2))^(7/2)+1/175*x^5/(-x^2+10^(1/2))^(5/2),1],
[x^2/(-x^2+3)^(3/2),x,2,-arcsin(1/3*x*3^(1/2))+x/(-x^2+3)^(1/2),1],
[(-x^2+25)^(3/2)/x^4,x,3,-1/3*(-x^2+25)^(3/2)/x^3+arcsin(1/5*x)+(-x^2+25)^(1/2)/x,1],
[1/(-2*x^2+1)^(7/2),x,3,1/5*x/(-2*x^2+1)^(5/2)+4/15*x/(-2*x^2+1)^(3/2)+8/15*x/(-2*x^2+1)^(1/2),1],
[1/(-x^2+6*x-7)^(5/2),x,2,1/6*(-3+x)/(-x^2+6*x-7)^(3/2)+1/6*(-3+x)/(-x^2+6*x-7)^(1/2),1],
[(-2*x^2-2*x+1)^3,x,2,x-3*x^2+2*x^3+4*x^4-12/5*x^5-4*x^6-8/7*x^7,1],
[(-1+5*x)*(x^2-x-1)^2,x,2,-x+3/2*x^2+11/3*x^3-3/4*x^4-11/5*x^5+5/6*x^6,1],
[(1+3*x)/(2*x^2-8*x+1)^(5/2),x,2,1/6*(1-2*x)/(2*x^2-8*x+1)^(3/2)-2/21*(2-x)/(2*x^2-8*x+1)^(1/2),1],
[(8*x^3-8*x-1)/(-4*x^2+2*x+1)^(5/2),x,2,-4/15*(1+x)/(-4*x^2+2*x+1)^(3/2)+1/75*(-7-122*x)/(-4*x^2+2*x+1)^(1/2),1],
[x^2*cos(x)^5,x,9,16/15*x*cos(x)+8/45*x*cos(x)^3+2/25*x*cos(x)^5-298/225*sin(x)+8/15*x^2*sin(x)+4/15*x^2*cos(x)^2*sin(x)+1/5*x^2*cos(x)^4*sin(x)+76/675*sin(x)^3-2/125*sin(x)^5,1],
[x^3*sin(x)^3,x,8,40/9*x*cos(x)-2/3*x^3*cos(x)-40/9*sin(x)+2*x^2*sin(x)+2/9*x*cos(x)*sin(x)^2-1/3*x^3*cos(x)*sin(x)^2-2/27*sin(x)^3+1/3*x^2*sin(x)^3,1],
[x^2*sin(x)^6,x,13,-245/1152*x+5/48*x^3+245/1152*cos(x)*sin(x)-5/16*x^2*cos(x)*sin(x)+5/16*x*sin(x)^2+65/1728*cos(x)*sin(x)^3-5/24*x^2*cos(x)*sin(x)^3+5/48*x*sin(x)^4+1/108*cos(x)*sin(x)^5-1/6*x^2*cos(x)*sin(x)^5+1/18*x*sin(x)^6,1],
[x^2*cos(x)*sin(x)^2,x,4,4/9*x*cos(x)-4/9*sin(x)+2/9*x*cos(x)*sin(x)^2-2/27*sin(x)^3+1/3*x^2*sin(x)^3,1],
[x*cos(x)^4/sin(x)^2,x,6,-3/4*x^2-1/4*cos(x)^2-x*cot(x)+ln(sin(x))-1/2*x*cos(x)*sin(x),1],
[x*sin(x)^3/cos(x)^4,x,5,5/6*arctanh(sin(x))-x*sec(x)+1/3*x*sec(x)^3-1/6*sec(x)*tan(x),1],
[x*sin(x)/cos(x)^3,x,3,1/2*x*sec(x)^2-1/2*tan(x),1],
[x*sin(x)^3/cos(x),x,8,1/4*x+1/2*I*x^2-x*ln(1+exp(2*I*x))+1/2*I*polylog(2,-exp(2*I*x))-1/4*cos(x)*sin(x)-1/2*x*sin(x)^2,1],
[x*sin(x)^3/cos(x)^3,x,7,1/2*x-1/2*I*x^2+x*ln(1+exp(2*I*x))-1/2*I*polylog(2,-exp(2*I*x))-1/2*tan(x)+1/2*x*tan(x)^2,1],
[(2*x+sin(2*x))/(cos(x)+x*sin(x))^2,x,2,2/(1+cot(x)/x),1],
[x^2/(x*cos(x)-sin(x))^2,x,3,-cot(x)+x*csc(x)/(x*cos(x)-sin(x)),1],
[a^(m*x)*b^(n*x),x,2,a^(m*x)*b^(n*x)/(m*ln(a)+n*ln(b)),1],
[(a^x-b^x)^2/(a^x)/(b^x),x,9,-2*x+(a^x/(b^x)-b^x/(a^x))/(ln(a)-ln(b)),1],
[-1/exp(x)+exp(x),x,3,exp(-x)+exp(x),1],
[(-1/exp(x)+exp(x))^2,x,4,-1/2/exp(2*x)+1/2*exp(2*x)-2*x,1],
[(-1/exp(x)+exp(x))^3,x,3,1/3/exp(3*x)-3/exp(x)-3*exp(x)+1/3*exp(3*x),1],
[(-1/exp(x)+exp(x))^4,x,4,-1/4/exp(4*x)+2/exp(2*x)-2*exp(2*x)+1/4*exp(4*x)+6*x,1],
[(-1/exp(x)+exp(x))^n,x,4,-(-1/exp(x)+exp(x))^n*(1-exp(2*x))*hypergeom([1, 1+1/2*n],[1-1/2*n],exp(2*x))/n,1],
[(1/(a^(4*x))-a^(2*x))^3,x,4,3*x-1/12/(a^(12*x))/ln(a)+1/2/(a^(6*x))/ln(a)-1/6*a^(6*x)/ln(a),1],
[a^(k*x)+a^(l*x),x,3,a^(k*x)/k/ln(a)+a^(l*x)/l/ln(a),1],
[(a^(k*x)+a^(l*x))^2,x,6,1/2*a^(2*k*x)/k/ln(a)+1/2*a^(2*l*x)/l/ln(a)+2*a^((k+l)*x)/(k+l)/ln(a),1],
[(a^(k*x)+a^(l*x))^3,x,7,1/3*a^(3*k*x)/k/ln(a)+1/3*a^(3*l*x)/l/ln(a)+3*a^((2*k+l)*x)/(2*k+l)/ln(a)+3*a^((k+2*l)*x)/(k+2*l)/ln(a),1],
[(a^(k*x)+a^(l*x))^4,x,8,1/4*a^(4*k*x)/k/ln(a)+1/4*a^(4*l*x)/l/ln(a)+3*a^(2*(k+l)*x)/(k+l)/ln(a)+4*a^((3*k+l)*x)/(3*k+l)/ln(a)+4*a^((k+3*l)*x)/(k+3*l)/ln(a),1],
[(a^(k*x)+a^(l*x))^n,x,2,(1+a^((k-l)*x))*(a^(k*x)+a^(l*x))^n*hypergeom([1, 1+k*n/(k-l)],[1+l*n/(k-l)],-a^((k-l)*x))/l/n/ln(a),1],
[a^(k*x)-a^(l*x),x,3,a^(k*x)/k/ln(a)-a^(l*x)/l/ln(a),1],
[(a^(k*x)-a^(l*x))^2,x,6,1/2*a^(2*k*x)/k/ln(a)+1/2*a^(2*l*x)/l/ln(a)-2*a^((k+l)*x)/(k+l)/ln(a),1],
[(a^(k*x)-a^(l*x))^3,x,7,1/3*a^(3*k*x)/k/ln(a)-1/3*a^(3*l*x)/l/ln(a)-3*a^((2*k+l)*x)/(2*k+l)/ln(a)+3*a^((k+2*l)*x)/(k+2*l)/ln(a),1],
[(a^(k*x)-a^(l*x))^4,x,8,1/4*a^(4*k*x)/k/ln(a)+1/4*a^(4*l*x)/l/ln(a)+3*a^(2*(k+l)*x)/(k+l)/ln(a)-4*a^((3*k+l)*x)/(3*k+l)/ln(a)-4*a^((k+3*l)*x)/(k+3*l)/ln(a),1],
[(a^(k*x)-a^(l*x))^n,x,2,(1-a^((k-l)*x))*(a^(k*x)-a^(l*x))^n*hypergeom([1, 1+k*n/(k-l)],[1+l*n/(k-l)],a^((k-l)*x))/l/n/ln(a),1],
[1+a^(m*x),x,2,x+a^(m*x)/m/ln(a),1],
[(1+a^(m*x))^2,x,3,x+2*a^(m*x)/m/ln(a)+1/2*a^(2*m*x)/m/ln(a),1],
[(1+a^(m*x))^3,x,3,x+3*a^(m*x)/m/ln(a)+3/2*a^(2*m*x)/m/ln(a)+1/3*a^(3*m*x)/m/ln(a),1],
[(1+a^(m*x))^4,x,3,x+4*a^(m*x)/m/ln(a)+3*a^(2*m*x)/m/ln(a)+4/3*a^(3*m*x)/m/ln(a)+1/4*a^(4*m*x)/m/ln(a),1],
[(1+a^(m*x))^n,x,2,-(1+a^(m*x))^(1+n)*hypergeom([1, 1+n],[2+n],1+a^(m*x))/m/(1+n)/ln(a),1],
[1-a^(m*x),x,2,x-a^(m*x)/m/ln(a),1],
[(1-a^(m*x))^2,x,3,x-2*a^(m*x)/m/ln(a)+1/2*a^(2*m*x)/m/ln(a),1],
[(1-a^(m*x))^3,x,3,x-3*a^(m*x)/m/ln(a)+3/2*a^(2*m*x)/m/ln(a)-1/3*a^(3*m*x)/m/ln(a),1],
[(1-a^(m*x))^4,x,3,x-4*a^(m*x)/m/ln(a)+3*a^(2*m*x)/m/ln(a)-4/3*a^(3*m*x)/m/ln(a)+1/4*a^(4*m*x)/m/ln(a),1],
[(1-a^(m*x))^n,x,2,-(1-a^(m*x))^(1+n)*hypergeom([1, 1+n],[2+n],1-a^(m*x))/m/(1+n)/ln(a),1],
[1/(b+a*exp(n*x)),x,4,x/b-ln(b+a*exp(n*x))/b/n,1],
[exp(x)/(b+a*exp(3*x)),x,7,1/2*ln(b^(1/3)+a^(1/3)*exp(x))/a^(1/3)/b^(2/3)-1/6*ln(b+a*exp(3*x))/a^(1/3)/b^(2/3)-1/3*arctan(1/3*(b^(1/3)-2*a^(1/3)*exp(x))/b^(1/3)*3^(1/2))/a^(1/3)/b^(2/3)*3^(1/2),1],
[(-1+exp(x))/(1+exp(x)),x,3,-x+2*ln(1+exp(x)),1],
[exp(4*x)/(1-2*exp(2*x)+3*exp(4*x)),x,5,1/12*ln(1-2*exp(2*x)+3*exp(4*x))-1/12*arctan(1/2*(1-3*exp(2*x))*2^(1/2))*2^(1/2),1],
[(exp(x)+exp(5*x))/(-1+exp(x)-exp(2*x)+exp(3*x)),x,6,exp(x)+1/2*exp(2*x)-arctan(exp(x))+ln(1-exp(x))-1/2*ln(1+exp(2*x)),1],
[fail,x,1,2,fail,1],//[exp(n*x)*(a+b*exp(n*x))^(r/s),x,2,(a+b*exp(n*x))^((r+s)/s)*s/b/n/(r+s),1],
[(1-2*exp(1/3*x))^(1/4),x,6,12*(1-2*exp(1/3*x))^(1/4)-6*arctan((1-2*exp(1/3*x))^(1/4))-6*arctanh((1-2*exp(1/3*x))^(1/4)),1],
[fail,x,1,2,fail,1],//[(a+b*exp(n*x))^(r/s),x,2,-(a+b*exp(n*x))^((r+s)/s)*s*hypergeom([1, (r+s)/s],[2+r/s],1+b*exp(n*x)/a)/a/n/(r+s),1],
[exp(x)/(a^2+exp(2*x))^(1/2),x,3,arctanh(exp(x)/(a^2+exp(2*x))^(1/2)),1],
[exp(x)/(-a^2+exp(2*x))^(1/2),x,3,arctanh(exp(x)/(-a^2+exp(2*x))^(1/2)),1],
[exp(3/4*x)/(-2+exp(3/4*x))/(-2+exp(3/4*x)+exp(3/2*x))^(1/2),x,3,2/3*arctanh(1/4*(2-5*exp(3/4*x))/(-2+exp(3/4*x)+exp(3/2*x))^(1/2)),1],
[(-3+exp(7*x))^(2/3)/exp(2*x),x,4,1/6*(-3+exp(7*x))^(5/3)*hypergeom([1, 29/21],[5/7],1/3*exp(7*x))/exp(2*x),1],
[exp(2*x)/(3-exp(1/2*x))^(3/4),x,3,-216*(3-exp(1/2*x))^(1/4)+216/5*(3-exp(1/2*x))^(5/4)-8*(3-exp(1/2*x))^(9/4)+8/13*(3-exp(1/2*x))^(13/4),1],
[x^3/exp(1/2*x),x,4,-96/exp(1/2*x)-48*x/exp(1/2*x)-12*x^2/exp(1/2*x)-2*x^3/exp(1/2*x),1],
[1/exp(1/2*x)/x^3,x,3,-1/2/exp(1/2*x)/x^2+1/4/exp(1/2*x)/x+1/8*Ei(-1/2*x),1],
[a^(3*x)*x^2,x,3,2/27*a^(3*x)/ln(a)^3-2/9*a^(3*x)*x/ln(a)^2+1/3*a^(3*x)*x^2/ln(a),1],
[exp(x^2)*x*(x^2+1),x,5,1/2*exp(x^2)*x^2,1],
[x/(exp(-x)+exp(x))^2,x,6,1/2*x-1/2*x/(1+exp(2*x))-1/4*ln(1+exp(2*x)),1],
[exp(x)*(-x^2-x+1)/(-x^2+1)^(1/2),x,1,exp(x)*(-x^2+1)^(1/2),1],
[cos(2*x)/exp(3*x),x,1,-3/13*cos(2*x)/exp(3*x)+2/13*sin(2*x)/exp(3*x),1],
[(cos(1/2*x)+sin(1/2*x))/exp(x)^(1/3),x,6,-30/13*cos(1/2*x)/exp(x)^(1/3)+6/13*sin(1/2*x)/exp(x)^(1/3),1],
[cos(3/2*x)/(3^(3*x))^(1/4),x,2,-4/3*cos(3/2*x)*ln(3)/(3^(3*x))^(1/4)/(4+ln(3)^2)+8/3*sin(3/2*x)/(3^(3*x))^(1/4)/(4+ln(3)^2),1],
[exp(m*x)*cos(x)^2,x,2,2*exp(m*x)/m/(m^2+4)+exp(m*x)*m*cos(x)^2/(m^2+4)+2*exp(m*x)*cos(x)*sin(x)/(m^2+4),1],
[exp(m*x)*sin(x)^3,x,2,-6*exp(m*x)*cos(x)/(m^4+10*m^2+9)+6*exp(m*x)*m*sin(x)/(m^4+10*m^2+9)-3*exp(m*x)*cos(x)*sin(x)^2/(m^2+9)+exp(m*x)*m*sin(x)^3/(m^2+9),1],
[cos(1/3*x)^3/exp(x)^(1/2),x,3,-48/65*cos(1/3*x)/exp(x)^(1/2)-2/5*cos(1/3*x)^3/exp(x)^(1/2)+32/65*sin(1/3*x)/exp(x)^(1/2)+4/5*cos(1/3*x)^2*sin(1/3*x)/exp(x)^(1/2),1],
[exp(2*x)*cos(x)^2*sin(x)^2,x,4,1/16*exp(2*x)-1/80*exp(2*x)*cos(4*x)-1/40*exp(2*x)*sin(4*x),1],
[exp(3*x)*cos(3/2*x)^2*sin(3/2*x)^2,x,4,1/24*exp(3*x)-1/120*exp(3*x)*cos(6*x)-1/60*exp(3*x)*sin(6*x),1],
[exp(m*x)*tan(x)^2,x,5,-exp(m*x)/m+4*exp((2*I+m)*x)*hypergeom([2, 1-1/2*I*m],[2-1/2*I*m],-exp(2*I*x))/(2*I+m),1],
[exp(m*x)/sin(x)^2,x,1,-4*exp((2*I+m)*x)*hypergeom([2, 1-1/2*I*m],[2-1/2*I*m],exp(2*I*x))/(2*I+m),1],
[exp(m*x)/cos(x)^3,x,2,8*exp((3*I+m)*x)*hypergeom([3, 3/2-1/2*I*m],[5/2-1/2*I*m],-exp(2*I*x))/(3*I+m),1],
[exp(x)/(1+cos(x)),x,2,(1-I)*exp((1+I)*x)*hypergeom([2, 1-I],[2-I],-exp(I*x)),1],
[exp(x)/(1-cos(x)),x,2,(-1+I)*exp((1+I)*x)*hypergeom([2, 1-I],[2-I],exp(I*x)),1],
[exp(x)/(1+sin(x)),x,2,(-1+I)*exp((1-I)*x)*hypergeom([2, 1+I],[2+I],-I/exp(I*x)),1],
[exp(x)/(1-sin(x)),x,2,(1+I)*exp((1+I)*x)*hypergeom([2, 1-I],[2-I],-I*exp(I*x)),1],
[exp(x)*(1-sin(x))/(1-cos(x)),x,1,-exp(x)*sin(x)/(1-cos(x)),1],
[exp(x)*(1+sin(x))/(1-cos(x)),x,7,(-2+2*I)*exp((1+I)*x)*hypergeom([2, 1-I],[2-I],exp(I*x))+exp(x)*sin(x)/(1-cos(x)),1],
[exp(x)*(1+sin(x))/(1+cos(x)),x,1,exp(x)*sin(x)/(1+cos(x)),1],
[exp(x)*(1-sin(x))/(1+cos(x)),x,7,(2-2*I)*exp((1+I)*x)*hypergeom([2, 1-I],[2-I],-exp(I*x))-exp(x)*sin(x)/(1+cos(x)),1],
[exp(x)*(1-cos(x))/(1-sin(x)),x,7,(2+2*I)*exp((1+I)*x)*hypergeom([2, 1-I],[2-I],-I*exp(I*x))-exp(x)*cos(x)/(1-sin(x)),1],
[exp(x)*(1+cos(x))/(1-sin(x)),x,1,exp(x)*cos(x)/(1-sin(x)),1],
[exp(x)*(1+cos(x))/(1+sin(x)),x,7,(-2-2*I)*exp((1+I)*x)*hypergeom([2, 1-I],[2-I],I*exp(I*x))+exp(x)*cos(x)/(1+sin(x)),1],
[exp(x)*(1-cos(x))/(1+sin(x)),x,1,-exp(x)*cos(x)/(1+sin(x)),1],
[exp(x)*x*cos(x),x,4,1/2*exp(x)*x*cos(x)-1/2*exp(x)*sin(x)+1/2*exp(x)*x*sin(x),1],
[exp(x)*x^2*sin(x),x,11,-1/2*exp(x)*cos(x)+exp(x)*x*cos(x)-1/2*exp(x)*x^2*cos(x)-1/2*exp(x)*sin(x)+1/2*exp(x)*x^2*sin(x),1],
[x^2*sin(x)/exp(3*x),x,11,-13/250*cos(x)/exp(3*x)-3/25*x*cos(x)/exp(3*x)-1/10*x^2*cos(x)/exp(3*x)-9/250*sin(x)/exp(3*x)-4/25*x*sin(x)/exp(3*x)-3/10*x^2*sin(x)/exp(3*x),1],
[exp(1/2*x)*x^2*cos(x)^3,x,-31,-132/125*exp(1/2*x)*cos(x)+18/25*exp(1/2*x)*x*cos(x)+48/185*exp(1/2*x)*x^2*cos(x)+2/37*exp(1/2*x)*x^2*cos(x)^3-428/50653*exp(1/2*x)*cos(3*x)+70/1369*exp(1/2*x)*x*cos(3*x)-24/125*exp(1/2*x)*sin(x)-24/25*exp(1/2*x)*x*sin(x)+96/185*exp(1/2*x)*x^2*sin(x)+12/37*exp(1/2*x)*x^2*cos(x)^2*sin(x)-792/50653*exp(1/2*x)*sin(3*x)-24/1369*exp(1/2*x)*x*sin(3*x),1],
[exp(2*x)*x^2*sin(4*x),x,11,1/250*exp(2*x)*cos(4*x)+2/25*exp(2*x)*x*cos(4*x)-1/5*exp(2*x)*x^2*cos(4*x)-11/500*exp(2*x)*sin(4*x)+3/50*exp(2*x)*x*sin(4*x)+1/10*exp(2*x)*x^2*sin(4*x),1],
[exp(1/2*x)*x^2*cos(x)*sin(x)^2,x,24,-44/125*exp(1/2*x)*cos(x)+6/25*exp(1/2*x)*x*cos(x)+1/10*exp(1/2*x)*x^2*cos(x)+428/50653*exp(1/2*x)*cos(3*x)-70/1369*exp(1/2*x)*x*cos(3*x)-1/74*exp(1/2*x)*x^2*cos(3*x)-8/125*exp(1/2*x)*sin(x)-8/25*exp(1/2*x)*x*sin(x)+1/5*exp(1/2*x)*x^2*sin(x)+792/50653*exp(1/2*x)*sin(3*x)+24/1369*exp(1/2*x)*x*sin(3*x)-3/37*exp(1/2*x)*x^2*sin(3*x),1],
[cosh(x),x,1,sinh(x),1],
[sinh(x),x,1,cosh(x),1],
[tanh(x),x,1,ln(cosh(x)),1],
[coth(x),x,1,ln(sinh(x)),1],
[sech(x),x,1,arctan(sinh(x)),1],
[csch(x),x,1,-arctanh(cosh(x)),1],
[cosh(x)^2,x,2,1/2*x+1/2*cosh(x)*sinh(x),1],
[sinh(x)^5,x,2,cosh(x)-2/3*cosh(x)^3+1/5*cosh(x)^5,1],
[tanh(x)^4,x,3,x-tanh(x)-1/3*tanh(x)^3,1],
[csch(x)^3,x,2,1/2*arctanh(cosh(x))-1/2*coth(x)*csch(x),1],
[1/cosh(x)^5,x,3,3/8*arctan(sinh(x))+3/8*sech(x)*tanh(x)+1/4*sech(x)^3*tanh(x),1],
[tanh(x)^5/sech(x)^4,x,4,-cosh(x)^2+1/4*cosh(x)^4+ln(cosh(x)),1],
[sech(x)^(3/4)*tanh(x)^5,x,3,-4/3*sech(x)^(3/4)+8/11*sech(x)^(11/4)-4/19*sech(x)^(19/4),1],
[1/(a+b*cosh(x)),x,2,2*arctanh((a-b)*tanh(1/2*x)/(a^2-b^2)^(1/2))/(a^2-b^2)^(1/2),1],
[1/(1+cosh(x))^2,x,2,1/3*sinh(x)/(1+cosh(x))^2+1/3*sinh(x)/(1+cosh(x)),1],
[1/(a+b*tanh(x)),x,2,a*x/(a^2-b^2)-b*ln(a*cosh(x)+b*sinh(x))/(a^2-b^2),1],
[1/(a^2+b^2*cosh(x)^2),x,2,arctanh(a*tanh(x)/(a^2+b^2)^(1/2))/a/(a^2+b^2)^(1/2),1],
[1/(a^2-b^2*cosh(x)^2),x,2,arctanh(a*tanh(x)/(a^2-b^2)^(1/2))/a/(a^2-b^2)^(1/2),1],
[1/(1-sinh(x)^4),x,3,1/4*arctanh(2^(1/2)*tanh(x))*2^(1/2)+1/2*tanh(x),1],
[(cosh(x)^3-sinh(x)^3)/(cosh(x)^3+sinh(x)^3),x,5,-4/9*arctan(1/3*(1-2*tanh(x))*3^(1/2))*3^(1/2)-1/3/(1+tanh(x)),1],
[cosh(x)*cosh(2*x)*cosh(3*x),x,5,1/4*x+1/8*sinh(2*x)+1/16*sinh(4*x)+1/24*sinh(6*x),1],
[cosh(3/2*x)*sinh(x)*sinh(5/2*x),x,5,-1/4*x+1/8*sinh(2*x)-1/12*sinh(3*x)+1/20*sinh(5*x),1],
[cosh(x)*(-cosh(2*x)+tanh(x))/(sinh(x)^2+sinh(2*x))/sinh(2*x)^(1/2),x,8,1/6*arctan(sinh(x)/sinh(2*x)^(1/2))+arctan(sech(x)*(cosh(x)*sinh(x))^(1/2))*2^(1/2)-1/3*arctanh(sech(x)*(cosh(x)*sinh(x))^(1/2))*2^(1/2)+cosh(x)/sinh(2*x)^(1/2),1],
[sinh(x)/(-9+4*cosh(x)^2)^(5/2),x,3,-1/27*cosh(x)/(-9+4*cosh(x)^2)^(3/2)+2/243*cosh(x)/(-9+4*cosh(x)^2)^(1/2),1],
[sinh(x)^2*sinh(2*x)/(1-sinh(x)^2)^(3/2),x,5,2/(1-sinh(x)^2)^(1/2)+2*(1-sinh(x)^2)^(1/2),1],
[cosh(x)/cosh(2*x)^(1/2),x,2,1/2*arcsinh(sinh(x)*2^(1/2))*2^(1/2),1],
[x*tanh(x)^2,x,3,1/2*x^2+ln(cosh(x))-x*tanh(x),1],
[x*coth(x)^2,x,3,1/2*x^2-x*coth(x)+ln(sinh(x)),1],
[(x+cosh(x)+sinh(x))/(cosh(x)-sinh(x)),x,13,-exp(x)+1/2*exp(2*x)+exp(x)*x,1],
[(x+cosh(x)+sinh(x))/(1+cosh(x)),x,8,x-(1-x)*tanh(1/2*x),1],
[exp(2*x)/sinh(x)^4,x,3,8/3*exp(6*x)/(1-exp(2*x))^3,1],
[1/exp(2*x)/cosh(x)^4,x,3,-8/3/(1+exp(2*x))^3,1],
[exp(x)/(cosh(x)-sinh(x)),x,2,1/2*exp(2*x),1],
[exp(m*x)/(cosh(x)+sinh(x)),x,3,exp((-1+m)*x)/(-1+m),1],
[exp(x)/(cosh(x)+sinh(x)),x,2,x,1],
[exp(x)/(1-cosh(x)),x,4,-2/(1-exp(x))-2*ln(1-exp(x)),1],
[exp(x)*(1+sinh(x))/(1+cosh(x)),x,3,exp(x)+2/(1+exp(x)),1],
[exp(x)*(1-sinh(x))/(1-cosh(x)),x,3,exp(x)-2/(1-exp(x)),1],
[x^m*ln(x),x,1,-x^(1+m)/(1+m)^2+x^(1+m)*ln(x)/(1+m),1],
[x^m*ln(x)^2,x,2,2*x^(1+m)/(1+m)^3-2*x^(1+m)*ln(x)/(1+m)^2+x^(1+m)*ln(x)^2/(1+m),1],
[ln(x)^2/x^(5/2),x,2,-16/27/x^(3/2)-8/9*ln(x)/x^(3/2)-2/3*ln(x)^2/x^(3/2),1],
[(b*x+a)*ln(x),x,2,-a*x-1/4*b*x^2+a*x*ln(x)+1/2*b*x^2*ln(x),1],
[(b*x+a)^3*ln(x),x,4,-a^3*x-3/4*a^2*b*x^2-1/3*a*b^2*x^3-1/16*b^3*x^4-1/4*a^4*ln(x)/b+1/4*(b*x+a)^4*ln(x)/b,1],
[-1-8*ln(x)^2+3*ln(x)^3,x,6,-35*x+34*x*ln(x)-17*x*ln(x)^2+3*x*ln(x)^3,1],
[(x^4+1)*(1-2*ln(x)+ln(x)^3),x,13,-3*x+169/625*x^5+4*x*ln(x)-44/125*x^5*ln(x)-3*x*ln(x)^2-3/25*x^5*ln(x)^2+x*ln(x)^3+1/5*x^5*ln(x)^3,1],
[1/x^3/ln(x)^4,x,5,-4/3*Ei(-2*ln(x))-1/3/x^2/ln(x)^3+1/3/x^2/ln(x)^2-2/3/x^2/ln(x),1],
[ln(x)/(b*x+a),x,2,ln(x)*ln(1+b*x/a)/b+polylog(2,-b*x/a)/b,1],
[ln(x)/(b*x+a)^2,x,2,x*ln(x)/a/(b*x+a)-ln(b*x+a)/a/b,1],
[ln(x)^n/x,x,2,ln(x)^(1+n)/(1+n),1],
[(a+b*ln(x))^n/x,x,2,(a+b*ln(x))^(1+n)/b/(1+n),1],
[1/x/(a+b*ln(x)),x,2,ln(a+b*ln(x))/b,1],
[1/x/((a+b*ln(x))^n),x,2,(a+b*ln(x))^(1-n)/b/(1-n),1],
[1/x/(a^2+ln(x)^2)^(1/2),x,3,arctanh(ln(x)/(a^2+ln(x)^2)^(1/2)),1],
[fail,x,1,2,fail,1],//[1/x/(-a^2+ln(x)^2)^(1/2),x,3,arctanh(ln(x)/(-a^2+ln(x)^2)^(1/2)),1],
[1/x/(a^2-ln(x)^2)^(1/2),x,3,arctan(ln(x)/(a^2-ln(x)^2)^(1/2)),1],
[1/x/ln(x)/(a^2+ln(x)^2)^(1/2),x,4,-arctanh((a^2+ln(x)^2)^(1/2)/a)/a,1],
[fail,x,1,2,fail,1],//[1/x/ln(x)/(a^2-ln(x)^2)^(1/2),x,4,-arctanh((a^2-ln(x)^2)^(1/2)/a)/a,1],
[1/x/ln(x)/(-a^2+ln(x)^2)^(1/2),x,4,arctan((-a^2+ln(x)^2)^(1/2)/a)/a,1],
[ln(ln(x))/x,x,1,-ln(x)+ln(x)*ln(ln(x)),1],
[ln(ln(x))^2/x,x,3,2*ln(x)-2*ln(x)*ln(ln(x))+ln(x)*ln(ln(x))^2,1],
[ln(ln(x))^3/x,x,4,-6*ln(x)+6*ln(x)*ln(ln(x))-3*ln(x)*ln(ln(x))^2+ln(x)*ln(ln(x))^3,1],
[ln(ln(x))^4/x,x,5,24*ln(x)-24*ln(x)*ln(ln(x))+12*ln(x)*ln(ln(x))^2-4*ln(x)*ln(ln(x))^3+ln(x)*ln(ln(x))^4,1],
[ln(ln(x))^n/x,x,3,GAMMA(1+n,-ln(ln(x)))*ln(ln(x))^n/((-ln(ln(x)))^n),1],
[cot(x)/ln(sin(x)),x,3,ln(ln(sin(x))),1],
[(1/cos(x)+cos(x))*tan(x),x,3,-cos(x)+sec(x),1],
[ln(cosh(x))*sinh(x),x,2,-cosh(x)+cosh(x)*ln(cosh(x)),1],
[ln(cosh(x))*tanh(x),x,2,1/2*ln(cosh(x))^2,1],
[ln(x-(x^2+1)^(1/2)),x,2,x*ln(x-(x^2+1)^(1/2))+(x^2+1)^(1/2),1],
[ln(-1+x)/x^3,x,3,1/2/x+1/2*ln(1-x)-1/2*ln(-1+x)/x^2-1/2*ln(x),1],
[(-1/exp(x)+exp(x))*ln(1+exp(2*x)),x,8,-2*exp(x)+ln(1+exp(2*x))/exp(x)+exp(x)*ln(1+exp(2*x)),1],
[exp(3/2*x)*ln(-1+exp(x)),x,6,-4/3*exp(1/2*x)-4/9*exp(3/2*x)+4/3*arctanh(exp(1/2*x))+2/3*exp(3/2*x)*ln(-1+exp(x)),1],
[cos(x)^3*ln(sin(x)),x,4,-sin(x)+ln(sin(x))*sin(x)+1/9*sin(x)^3-1/3*ln(sin(x))*sin(x)^3,1],
[ln(tan(x))/cos(x)^4,x,4,-tan(x)+ln(tan(x))*tan(x)-1/9*tan(x)^3+1/3*ln(tan(x))*tan(x)^3,1],
[ln(cos(1/2*x))/(1+cos(x)),x,4,-1/2*x+ln(cos(1/2*x))*sin(x)/(1+cos(x))+tan(1/2*x),1],
[cos(x)*ln(sin(x))/(1+cos(x))^2,x,6,-2/3*x-1/9*sin(x)/(1+cos(x))^2+8/9*sin(x)/(1+cos(x))-1/3*ln(sin(x))*sin(x)/(1+cos(x))^2+2/3*ln(sin(x))*sin(x)/(1+cos(x)),1],
[arccos(x)^2/x^5,x,5,-1/12/x^2-1/4*arccos(x)^2/x^4+1/3*ln(x)+1/6*arccos(x)*(-x^2+1)^(1/2)/x^3+1/3*arccos(x)*(-x^2+1)^(1/2)/x,1],
[x^2*arcsin(x)^2,x,5,-4/9*x-2/27*x^3+1/3*x^3*arcsin(x)^2+4/9*arcsin(x)*(-x^2+1)^(1/2)+2/9*x^2*arcsin(x)*(-x^2+1)^(1/2),1],
[x^3*arctan(x)^2,x,10,1/12*x^2+1/2*x*arctan(x)-1/6*x^3*arctan(x)-1/4*arctan(x)^2+1/4*x^4*arctan(x)^2-1/3*ln(x^2+1),1],
[arctan(x)^2/x^5,x,13,-1/12/x^2-1/6*arctan(x)/x^3+1/2*arctan(x)/x+1/4*arctan(x)^2-1/4*arctan(x)^2/x^4-2/3*ln(x)+1/3*ln(x^2+1),1],
[x^3*arccsc(x)^2,x,5,1/12*x^2+1/4*x^4*arccsc(x)^2+1/3*ln(x)+1/3*x*arccsc(x)*(1-1/x^2)^(1/2)+1/6*x^3*arccsc(x)*(1-1/x^2)^(1/2),1],
[arcsec(x)^4/x^5,x,10,-3/128/x^4-45/128/x^2-45/128*arcsec(x)^2+3/16*arcsec(x)^2/x^4+9/16*arcsec(x)^2/x^2+3/32*arcsec(x)^4-1/4*arcsec(x)^4/x^4-3/32*arcsec(x)*(1-1/x^2)^(1/2)/x^3-45/64*arcsec(x)*(1-1/x^2)^(1/2)/x+1/4*arcsec(x)^3*(1-1/x^2)^(1/2)/x^3+3/8*arcsec(x)^3*(1-1/x^2)^(1/2)/x,1],
[arcsin(x)*(-x^2+1)^(1/2),x,3,-1/4*x^2+1/4*arcsin(x)^2+1/2*x*arcsin(x)*(-x^2+1)^(1/2),1],
[arccos(x)*(-x^2+1)^(1/2),x,3,1/4*x^2-1/4*arccos(x)^2+1/2*x*arccos(x)*(-x^2+1)^(1/2),1],
[x*arccos(x)*(-x^2+1)^(1/2),x,2,-1/3*x+1/9*x^3-1/3*(-x^2+1)^(3/2)*arccos(x),1],
[(-x^2+1)^(3/2)*arcsin(x),x,6,-5/16*x^2+1/16*x^4+1/4*x*(-x^2+1)^(3/2)*arcsin(x)+3/16*arcsin(x)^2+3/8*x*arcsin(x)*(-x^2+1)^(1/2),1],
[x*(-x^2+1)^(3/2)*arcsin(x),x,3,1/5*x-2/15*x^3+1/25*x^5-1/5*(-x^2+1)^(5/2)*arcsin(x),1],
[x^3*(-x^2+1)^(3/2)*arccos(x),x,4,-2/35*x-1/105*x^3+8/175*x^5-1/49*x^7-1/5*(-x^2+1)^(5/2)*arccos(x)+1/7*(-x^2+1)^(7/2)*arccos(x),1],
[(-x^2+1)^(3/2)*arccos(x)/x,x,10,4/3*x-1/9*x^3+1/3*(-x^2+1)^(3/2)*arccos(x)+2*I*arccos(x)*arctan(x+I*(-x^2+1)^(1/2))-I*polylog(2,-I*(x+I*(-x^2+1)^(1/2)))+I*polylog(2,I*(x+I*(-x^2+1)^(1/2)))+arccos(x)*(-x^2+1)^(1/2),1],
[(-x^2+1)^(3/2)*arcsin(x)/x^6,x,4,-1/20/x^4+1/5/x^2-1/5*(-x^2+1)^(5/2)*arcsin(x)/x^5+1/5*ln(x),1],
[x^2*arcsin(x)/(-x^2+1)^(1/2),x,3,1/4*x^2+1/4*arcsin(x)^2-1/2*x*arcsin(x)*(-x^2+1)^(1/2),1],
[x^4*arcsin(x)/(-x^2+1)^(1/2),x,5,3/16*x^2+1/16*x^4+3/16*arcsin(x)^2-3/8*x*arcsin(x)*(-x^2+1)^(1/2)-1/4*x^3*arcsin(x)*(-x^2+1)^(1/2),1],
[x*arcsin(x)/(-x^2+1)^(3/2),x,2,-arctanh(x)+arcsin(x)/(-x^2+1)^(1/2),1],
[x*arccos(x)/(-x^2+1)^(3/2),x,2,arctanh(x)+arccos(x)/(-x^2+1)^(1/2),1],
[arcsin(x)/(-x^2+1)^(5/2),x,4,-1/6/(-x^2+1)+1/3*x*arcsin(x)/(-x^2+1)^(3/2)+1/3*ln(-x^2+1)+2/3*x*arcsin(x)/(-x^2+1)^(1/2),1],
[x^3*arcsin(x)/(-x^2+1)^(3/2),x,3,-x-arctanh(x)+arcsin(x)/(-x^2+1)^(1/2)+arcsin(x)*(-x^2+1)^(1/2),1],
[arcsin(x)/x/(-x^2+1)^(3/2),x,8,-2*arcsin(x)*arctanh(I*x+(-x^2+1)^(1/2))-arctanh(x)+I*polylog(2,-I*x-(-x^2+1)^(1/2))-I*polylog(2,I*x+(-x^2+1)^(1/2))+arcsin(x)/(-x^2+1)^(1/2),1],
[arccos(x)/x^4/(-x^2+1)^(1/2),x,4,1/6/x^2-2/3*ln(x)-1/3*arccos(x)*(-x^2+1)^(1/2)/x^3-2/3*arccos(x)*(-x^2+1)^(1/2)/x,1],
[x*arccos(x)^2*(-x^2+1)^(1/2),x,5,2/27*(-x^2+1)^(3/2)-2/3*x*arccos(x)+2/9*x^3*arccos(x)-1/3*(-x^2+1)^(3/2)*arccos(x)^2+4/9*(-x^2+1)^(1/2),1],
[x^2*arcsin(x)^3/(-x^2+1)^(1/2),x,6,-3/8*x^2-3/8*arcsin(x)^2+3/4*x^2*arcsin(x)^2+1/8*arcsin(x)^4+3/4*x*arcsin(x)*(-x^2+1)^(1/2)-1/2*x*arcsin(x)^3*(-x^2+1)^(1/2),1],
[x*arctan(x)/(x^2+1)^2,x,3,1/4*x/(x^2+1)+1/4*arctan(x)-1/2*arctan(x)/(x^2+1),1],
[x*arctan(x)/(x^2+1)^3,x,4,1/16*x/(x^2+1)^2+3/32*x/(x^2+1)+3/32*arctan(x)-1/4*arctan(x)/(x^2+1)^2,1],
[x^2*arctan(x)/(x^2+1),x,4,x*arctan(x)-1/2*arctan(x)^2-1/2*ln(x^2+1),1],
[x^3*arctan(x)/(x^2+1),x,8,-1/2*x+1/2*arctan(x)+1/2*x^2*arctan(x)+1/2*I*arctan(x)^2+arctan(x)*ln(2/(1+I*x))+1/2*I*polylog(2,1-2/(1+I*x)),1],
[x^2*arctan(x)/(x^2+1)^2,x,2,-1/4/(x^2+1)-1/2*x*arctan(x)/(x^2+1)+1/4*arctan(x)^2,1],
[x^3*arctan(x)/(x^2+1)^2,x,8,-1/4*x/(x^2+1)-1/4*arctan(x)+1/2*arctan(x)/(x^2+1)-1/2*I*arctan(x)^2-arctan(x)*ln(2/(1+I*x))-1/2*I*polylog(2,1-2/(1+I*x)),1],
[x^5*arctan(x)/(x^2+1)^2,x,17,-1/2*x+1/4*x/(x^2+1)+3/4*arctan(x)+1/2*x^2*arctan(x)-1/2*arctan(x)/(x^2+1)+I*arctan(x)^2+2*arctan(x)*ln(2/(1+I*x))+I*polylog(2,1-2/(1+I*x)),1],
[(x^2+1)*arctan(x)/x^2,x,8,-arctan(x)/x+x*arctan(x)+ln(x)-ln(x^2+1),1],
[(x^2+1)*arctan(x)/x^5,x,3,-1/12/x^3-1/4/x-1/4*(x^2+1)^2*arctan(x)/x^4,1],
[(x^2+1)^2*arctan(x)/x^5,x,12,-1/12/x^3-3/4/x-3/4*arctan(x)-1/4*arctan(x)/x^4-arctan(x)/x^2+1/2*I*polylog(2,-I*x)-1/2*I*polylog(2,I*x),1],
[arctan(x)/x^2/(x^2+1),x,7,-arctan(x)/x-1/2*arctan(x)^2+ln(x)-1/2*ln(x^2+1),1],
[arctan(x)^2/x^3,x,8,-arctan(x)/x-1/2*arctan(x)^2-1/2*arctan(x)^2/x^2+ln(x)-1/2*ln(x^2+1),1],
[(x^2+1)*arctan(x)^2/x^5,x,11,-1/12/x^2-1/6*arctan(x)/x^3-1/2*arctan(x)/x-1/4*(x^2+1)^2*arctan(x)^2/x^4+1/3*ln(x)-1/6*ln(x^2+1),1],
[x^3*arctan(x)^2/(x^2+1)^3,x,4,-1/32/(x^2+1)^2+5/32/(x^2+1)+1/8*x^3*arctan(x)/(x^2+1)^2+3/16*x*arctan(x)/(x^2+1)-3/32*arctan(x)^2+1/4*x^4*arctan(x)^2/(x^2+1)^2,1],
[arcsec(x)*(x^2-1)^(1/2)/x^2,x,9,-(x^2)^(1/2)/x^2-2*I*arcsec(x)*arctan(1/x+I*(1-1/x^2)^(1/2))*(x^2)^(1/2)/x+I*polylog(2,-I*(1/x+I*(1-1/x^2)^(1/2)))*(x^2)^(1/2)/x-I*polylog(2,I*(1/x+I*(1-1/x^2)^(1/2)))*(x^2)^(1/2)/x-arcsec(x)*(x^2-1)^(1/2)/x,1],
[(x^2-1)^(5/2)*arccsc(x)/x^3,x,11,-5/3*(x^2-1)^(3/2)*arccsc(x)/x^2+1/3*(x^2-1)^(5/2)*arccsc(x)/x^2+1/12*(2*x^4+3)/x/(x^2)^(1/2)-5/4*x*arccsc(x)^2/(x^2)^(1/2)-7/3*x*ln(x)/(x^2)^(1/2)-5/2*arccsc(x)*(x^2-1)^(1/2)/x^2,1],
[arcsec(x)*(x^2-1)^(1/2)/x^4,x,4,1/3*(x^2-1)^(3/2)*arcsec(x)/x^3+1/3/(x^2)^(1/2)-1/9/x^2/(x^2)^(1/2),1],
[arcsec(x)/(x^2-1)^(5/2),x,4,5/6*arccoth((x^2)^(1/2))-1/3*x*arcsec(x)/(x^2-1)^(3/2)+1/6*(x^2)^(1/2)/(-x^2+1)+2/3*x*arcsec(x)/(x^2-1)^(1/2),1],
[x^2*arcsec(x)/(x^2-1)^(5/2),x,4,-1/6*arccoth((x^2)^(1/2))-1/3*x^3*arcsec(x)/(x^2-1)^(3/2)+1/6*(x^2)^(1/2)/(-x^2+1),1],
[x^3*arcsec(x)/(x^2-1)^(5/2),x,5,-1/3*arcsec(x)/(x^2-1)^(3/2)+1/6*x/(-x^2+1)/(x^2)^(1/2)-2/3*x*ln(x)/(x^2)^(1/2)+1/3*x*ln(x^2-1)/(x^2)^(1/2)-arcsec(x)/(x^2-1)^(1/2),1],
[x^6*arcsec(x)/(x^2-1)^(5/2),x,16,-13/6*arccoth((x^2)^(1/2))-5/6*x^3*arcsec(x)/(x^2-1)^(3/2)+1/2*x^5*arcsec(x)/(x^2-1)^(3/2)+1/6*(-3*x^2+2)*(x^2)^(1/2)/(x^2-1)-5*I*arcsec(x)*arctan(1/x+I*(1-1/x^2)^(1/2))*(x^2)^(1/2)/x+5/2*I*polylog(2,-I*(1/x+I*(1-1/x^2)^(1/2)))*(x^2)^(1/2)/x-5/2*I*polylog(2,I*(1/x+I*(1-1/x^2)^(1/2)))*(x^2)^(1/2)/x-5/2*x*arcsec(x)/(x^2-1)^(1/2),1],
[arcsec(x)/x^2/(x^2-1)^(1/2),x,2,1/(x^2)^(1/2)+arcsec(x)*(x^2-1)^(1/2)/x,1],
[arccsc(x)/x^2/(x^2-1)^(5/2),x,5,-11/6*arccoth((x^2)^(1/2))+1/3*(8*x^4-12*x^2+3)*arccsc(x)/x/(x^2-1)^(3/2)-1/(x^2)^(1/2)+1/6*(x^2)^(1/2)/(x^2-1),1],
[arccsc(x)^4/x^2/(x^2-1)^(1/2),x,6,24*arccsc(x)/(x^2)^(1/2)-4*arccsc(x)^3/(x^2)^(1/2)+24*(x^2-1)^(1/2)/x-12*arccsc(x)^2*(x^2-1)^(1/2)/x+arccsc(x)^4*(x^2-1)^(1/2)/x,1],
[(x^2-1)^(3/2)*arcsec(x)^2/x^5,x,11,-1/4*(x^2-1)^(3/2)*arcsec(x)^2/x^4-3/8*arcsec(x)/x/(x^2)^(1/2)+9/64*x*arcsec(x)/(x^2)^(1/2)+1/8*(x^2-1)^2*arcsec(x)/x^3/(x^2)^(1/2)+1/8*x*arcsec(x)^3/(x^2)^(1/2)+1/64*(17*x^2-2)*(x^2-1)^(1/2)/x^4-3/8*arcsec(x)^2*(x^2-1)^(1/2)/x^2,1],
[arcsec(x)^3*(x^2-1)^(1/2)/x^4,x,8,-2/9*(x^2-1)^(3/2)*arcsec(x)/x^3+1/3*(x^2-1)^(3/2)*arcsec(x)^3/x^3+2/27*(-21*x^2+1)/x^2/(x^2)^(1/2)+2/3*arcsec(x)^2/(x^2)^(1/2)+1/3*(x^2-1)*arcsec(x)^2/x^2/(x^2)^(1/2)-4/3*arcsec(x)*(x^2-1)^(1/2)/x,1],
[arcsin(((-a+x)/(a+x))^(1/2)),x,-8,(a+x)*arcsin(((-a+x)/(a+x))^(1/2))-a*2^(1/2)*((-a+x)/(a+x))^(1/2)/(a/(a+x))^(1/2),1],
[arctan(((-a+x)/(a+x))^(1/2)),x,4,x*arctan(((-a+x)/(a+x))^(1/2))-a*arctanh(((-a+x)/(a+x))^(1/2)),1],
[arctan(x)/(1+x)^3,x,5,-1/4/(1+x)-1/2*arctan(x)/(1+x)^2+1/4*ln(1+x)-1/8*ln(x^2+1),1],
[-arctan(a-x)/(a+x),x,5,arctan(a-x)*ln(2/(1-I*(a-x)))-arctan(a-x)*ln(-2*(a+x)/(I-2*a)/(1-I*(a-x)))-1/2*I*polylog(2,1-2/(1-I*(a-x)))+1/2*I*polylog(2,1+2*(a+x)/(I-2*a)/(1-I*(a-x))),1],
[arcsin((-x^2+1)^(1/2))/(-x^2+1)^(1/2),x,2,-1/2*arcsin((-x^2+1)^(1/2))^2*(x^2)^(1/2)/x,1],
[x*arctan((x^2+1)^(1/2))/(x^2+1)^(1/2),x,2,-1/2*ln(x^2+2)+arctan((x^2+1)^(1/2))*(x^2+1)^(1/2),1],
[arcsin(x)/(1-x)^(5/2),x,5,2/3*arcsin(x)/(1-x)^(3/2)-1/6*arctanh(1/2*2^(1/2)*(1+x)^(1/2))*2^(1/2)-1/3*(1+x)^(1/2)/(1-x),1],
[(-1+x)^(5/2)*arccsc(x),x,7,2/7*(-1+x)^(7/2)*arccsc(x)+4/7*x*arctanh((x^2-1)^(1/2)/(-1+x)^(1/2))/(x^2)^(1/2)+4/105*x*(3*x^2-19*x+83)*(x^2-1)^(1/2)/(-1+x)^(1/2)/(x^2)^(1/2),1],
[arcsin(sinh(x))*sech(x)^4,x,5,-2/3*arcsin(1/2*cosh(x)*2^(1/2))+1/6*sech(x)*(1-sinh(x)^2)^(1/2)+arcsin(sinh(x))*tanh(x)-1/3*arcsin(sinh(x))*tanh(x)^3,1],
[arccot(cosh(x))*cosh(x)/sinh(x)^4,x,6,1/6*coth(x)-1/3*arccot(cosh(x))*csch(x)^3+1/12*arctanh(1/2*2^(1/2)*tanh(x))*2^(1/2),1],
[exp(x)*arcsin(tanh(x)),x,5,exp(x)*arcsin(tanh(x))-cosh(x)*ln(1+exp(2*x))*(sech(x)^2)^(1/2),1],// Welz
[1/(-a*x+1)^(1/2),x,1,-2*(-a*x+1)^(1/2)/a,1],
[1/2*(ln(a*x-1)-2*ln(-(a*x-1)^(1/2)))/Pi/(a*x-1)^(1/2),x,5,-2*(-a*x+1)^(1/2)/a,1],
[1/(2*x+(x^2+1)^(1/2))^2,x,9,4/3*x/(-3*x^2+1)-1/9*arctanh(x*3^(1/2))*3^(1/2)+1/9*arctanh(1/2*3^(1/2)*(x^2+1)^(1/2))*3^(1/2)-2/3*(x^2+1)^(1/2)/(-3*x^2+1),1],
[1/(3*x^2-4)^2/(x^2-1)^(1/2),x,3,5/16*arctanh(1/2*x/(x^2-1)^(1/2))+3/8*x*(x^2-1)^(1/2)/(-3*x^2+4),1],
[1/(2*x^(1/2)+(1+x)^(1/2))^2,x,8,8/9/(1-3*x)-8/9*arcsinh(x^(1/2))+10/9*arctanh(2*x^(1/2)/(1+x)^(1/2))+5/9*ln(1-3*x)-4/3*x^(1/2)*(1+x)^(1/2)/(1-3*x),1],
[(x^2-1)^(1/2)/(-I+x)^2,x,6,arctanh(x/(x^2-1)^(1/2))-1/2*I*arctan(1/2*(1-I*x)*2^(1/2)/(x^2-1)^(1/2))*2^(1/2)+(x^2-1)^(1/2)/(I-x),1],
[1/(x^2+1)^2/(x^2-1)^(1/2),x,3,3/8*arctanh(x*2^(1/2)/(x^2-1)^(1/2))*2^(1/2)-1/4*x*(x^2-1)^(1/2)/(x^2+1),1],
[1/(-1+x)^(1/2)/((-1+x)^(1/2)+x^(1/2))^2,x,4,4/3*(-1+x)^(3/2)-4/3*x^(3/2)+2*(-1+x)^(1/2),1],
[1/(x^2-1)^(1/2)/(x^(1/2)+(x^2-1)^(1/2))^2,x,-18,1/5*(2-4*x)/(x^(1/2)+(x^2-1)^(1/2))-1/50*arctan((x^2-1)^(1/2)*(-2+2*5^(1/2))^(1/2)/(2-x*(-5^(1/2)+1)))*(-110+50*5^(1/2))^(1/2)+1/25*arctan(1/2*x^(1/2)*(2+2*5^(1/2))^(1/2))*(-110+50*5^(1/2))^(1/2)-1/25*arctanh(1/2*x^(1/2)*(-2+2*5^(1/2))^(1/2))*(110+50*5^(1/2))^(1/2)-1/50*arctanh((x^2-1)^(1/2)*(2+2*5^(1/2))^(1/2)/(2-x-x*5^(1/2)))*(110+50*5^(1/2))^(1/2),1],
[(x^(1/2)-(x^2-1)^(1/2))^2/(-x^2+x+1)^2/(x^2-1)^(1/2),x,-25,1/5*(2-4*x)/(x^(1/2)+(x^2-1)^(1/2))-1/50*arctan((x^2-1)^(1/2)*(-2+2*5^(1/2))^(1/2)/(2-x*(-5^(1/2)+1)))*(-110+50*5^(1/2))^(1/2)+1/25*arctan(1/2*x^(1/2)*(2+2*5^(1/2))^(1/2))*(-110+50*5^(1/2))^(1/2)-1/25*arctanh(1/2*x^(1/2)*(-2+2*5^(1/2))^(1/2))*(110+50*5^(1/2))^(1/2)-1/50*arctanh((x^2-1)^(1/2)*(2+2*5^(1/2))^(1/2)/(2-x-x*5^(1/2)))*(110+50*5^(1/2))^(1/2),1],
[1/2/(1+x)^2*2^(1/2)/(-I+x^2)^(1/2)+1/2/(1+x)^2*2^(1/2)/(I+x^2)^(1/2),x,7,1/2*arctanh((I+x)/(1-I)^(1/2)/(-I+x^2)^(1/2))/(1-I)^(3/2)*2^(1/2)-1/2*arctanh((I-x)/(1+I)^(1/2)/(I+x^2)^(1/2))/(1+I)^(3/2)*2^(1/2)-(1/4+1/4*I)*(-I+x^2)^(1/2)/(1+x)*2^(1/2)+(-1/4+1/4*I)*(I+x^2)^(1/2)/(1+x)*2^(1/2),1],
[(x^2+(x^4+1)^(1/2))^(1/2)/(1+x)^2/(x^4+1)^(1/2),x,7,-1/4*(1-I)^(3/2)*arctanh((1+I*x)/(1-I)^(1/2)/(1-I*x^2)^(1/2))-1/4*(1+I)^(3/2)*arctanh((1-I*x)/(1+I)^(1/2)/(1+I*x^2)^(1/2))-1/2*(1-I*x^2)^(1/2)/(1+x)-1/2*(1+I*x^2)^(1/2)/(1+x),1],
[(x^2+(x^4+1)^(1/2))^(1/2)/(1+x)/(x^4+1)^(1/2),x,5,-1/2*arctanh((1+I*x)/(1-I)^(1/2)/(1-I*x^2)^(1/2))*(1-I)^(1/2)-1/2*arctanh((1-I*x)/(1+I)^(1/2)/(1+I*x^2)^(1/2))*(1+I)^(1/2),1],
[(x^2+(x^4+1)^(1/2))^(1/2)/(x^4+1)^(1/2),x,2,1/2*arctanh(x*2^(1/2)/(x^2+(x^4+1)^(1/2))^(1/2))*2^(1/2),1],
[(-x^2+(x^4+1)^(1/2))^(1/2)/(x^4+1)^(1/2),x,2,1/2*arctan(x*2^(1/2)/(-x^2+(x^4+1)^(1/2))^(1/2))*2^(1/2),1],
[((-1+x)^(3/2)+(1+x)^(3/2))/(-1+x)^(3/2)/(1+x)^(3/2),x,2,-2/(-1+x)^(1/2)-2/(1+x)^(1/2),1],
[(x+(x^2+a)^(1/2))^b,x,3,-1/2*a*(x+(x^2+a)^(1/2))^(-1+b)/(1-b)+1/2*(x+(x^2+a)^(1/2))^(1+b)/(1+b),1],
[(x-(x^2+a)^(1/2))^b,x,3,-1/2*a*(x-(x^2+a)^(1/2))^(-1+b)/(1-b)+1/2*(x-(x^2+a)^(1/2))^(1+b)/(1+b),1],
[(x+(x^2+a)^(1/2))^b/(x^2+a)^(1/2),x,2,(x+(x^2+a)^(1/2))^b/b,1],
[(x-(x^2+a)^(1/2))^b/(x^2+a)^(1/2),x,2,-(x-(x^2+a)^(1/2))^b/b,1],
[1/(a+b*exp(p*x))^2,x,3,1/a/(a+b*exp(p*x))/p+x/a^2-ln(a+b*exp(p*x))/a^2/p,1],
[1/(b/exp(p*x)+a*exp(p*x))^2,x,2,-1/2/a/(b+a*exp(2*p*x))/p,1],
[x/(b/exp(p*x)+a*exp(p*x))^2,x,6,1/2*x/a/b/p-1/2*x/a/(b+a*exp(2*p*x))/p-1/4*ln(b+a*exp(2*p*x))/a/b/p^2,1],
[(3*x^2-x+1)/(x^2+x+1)^2/(x^2-x+1)^(1/2),x,6,arctan((1+x)*2^(1/2)/(x^2-x+1)^(1/2))*2^(1/2)-1/6*arctanh(1/3*(1-x)*6^(1/2)/(x^2-x+1)^(1/2))*6^(1/2)+(1+x)*(x^2-x+1)^(1/2)/(x^2+x+1),1],
[(x+(a^2+x^2)^(1/2))^(1/2)/(a^2+x^2)^(1/2),x,2,2*(x+(a^2+x^2)^(1/2))^(1/2),1],
[(b*x+(b^2*x^2+a)^(1/2))^(1/2)/(b^2*x^2+a)^(1/2),x,2,2*(b*x+(b^2*x^2+a)^(1/2))^(1/2)/b,1],
[1/x/(a^2+x^2)^(1/2)/(x+(a^2+x^2)^(1/2))^(1/2),x,5,-2*arctan((x+(a^2+x^2)^(1/2))^(1/2)/a^(1/2))/a^(3/2)-2*arctanh((x+(a^2+x^2)^(1/2))^(1/2)/a^(1/2))/a^(3/2),1],
[(x+(a^2+x^2)^(1/2))^(1/2)/x,x,6,-2*arctan((x+(a^2+x^2)^(1/2))^(1/2)/a^(1/2))*a^(1/2)-2*arctanh((x+(a^2+x^2)^(1/2))^(1/2)/a^(1/2))*a^(1/2)+2*(x+(a^2+x^2)^(1/2))^(1/2),1],
[x^3*ln(2+x)^3*ln(3+x),x,359,-302177/1152*x-43/12*ln(2+x)^2+3891/128*ln(3+x)+2069/144*ln(2+x)-5609/96*polylog(2,-2-x)-563/8*polylog(3,-2-x)-195/2*polylog(4,-2-x)+377/64*(2+x)^2-71/216*(2+x)^3+3/256*(2+x)^4-25*x*ln(2+x)*ln(3+x)+13/4*x^2*ln(2+x)*ln(3+x)-7/12*x^3*ln(2+x)*ln(3+x)+3/32*x^4*ln(2+x)*ln(3+x)+6*x*ln(2+x)^2*ln(3+x)-3/2*x^2*ln(2+x)^2*ln(3+x)+1/2*x^3*ln(2+x)^2*ln(3+x)-3/16*x^4*ln(2+x)^2*ln(3+x)+1/4*x^4*ln(2+x)^3*ln(3+x)+963/16*ln(2+x)^2*ln(3+x)-81/4*ln(2+x)^3*ln(3+x)+563/8*ln(2+x)*polylog(2,-2-x)-195/4*ln(2+x)^2*polylog(2,-2-x)+195/2*ln(2+x)*polylog(3,-2-x)-187/64*x^2*ln(2+x)+83/288*x^3*ln(2+x)-3/128*x^4*ln(2+x)+6733/32*(2+x)*ln(2+x)-377/32*(2+x)^2*ln(2+x)+71/72*(2+x)^3*ln(2+x)-3/64*(2+x)^4*ln(2+x)-17/48*x^3*ln(2+x)^2+3/64*x^4*ln(2+x)^2-1251/16*(2+x)*ln(2+x)^2+273/32*(2+x)^2*ln(2+x)^2-3/4*(2+x)^3*ln(2+x)^2+3/64*(2+x)^4*ln(2+x)^2+65/4*(2+x)*ln(2+x)^3-33/8*(2+x)^2*ln(2+x)^3+3/4*(2+x)^3*ln(2+x)^3-1/16*(2+x)^4*ln(2+x)^3-115/48*x^2*ln(3+x)+37/144*x^3*ln(3+x)-3/128*x^4*ln(3+x)+415/12*(3+x)*ln(3+x)-4083/32*ln(2+x)*ln(3+x)+3/256*x^4+8029/2304*x^2-763/3456*x^3,1],
[(x+(x^2+b)^(1/2))^a/(x^2+b)^(1/2),x,2,(x+(x^2+b)^(1/2))^a/a,1],
[(x+(x^2+b)^(1/2))^a,x,3,-1/2*b*(x+(x^2+b)^(1/2))^(-1+a)/(1-a)+1/2*(x+(x^2+b)^(1/2))^(1+a)/(1+a),1],
[(6+3*x^a+2*x^(2*a))^(1/a)*(x^a+x^(2*a)+x^(3*a)),x,2,1/6*x^(1+a)*(6+3*x^a+2*x^(2*a))^(1+1/a)/(1+a),1],
[1/x/(-x^2+1)^(1/3),x,5,-1/2*ln(x)+3/4*ln(1-(-x^2+1)^(1/3))+1/2*arctan(1/3*(1+2*(-x^2+1)^(1/3))*3^(1/2))*3^(1/2),1],
[1/x/(-x^2+1)^(2/3),x,5,-1/2*ln(x)+3/4*ln(1-(-x^2+1)^(1/3))-1/2*arctan(1/3*(1+2*(-x^2+1)^(1/3))*3^(1/2))*3^(1/2),1],
[1/(-x^3+1)^(1/3),x,1,1/2*ln(x+(-x^3+1)^(1/3))-1/3*arctan(1/3*(1-2*x/(-x^3+1)^(1/3))*3^(1/2))*3^(1/2),1],
[1/x/(-x^3+1)^(1/3),x,5,-1/2*ln(x)+1/2*ln(1-(-x^3+1)^(1/3))+1/3*arctan(1/3*(1+2*(-x^3+1)^(1/3))*3^(1/2))*3^(1/2),1],
[1/(1+x)/(-x^3+1)^(1/3),x,1,-1/8*ln((1-x)*(1+x)^2)*2^(2/3)+3/8*ln(-1+x+2^(2/3)*(-x^3+1)^(1/3))*2^(2/3)-1/4*arctan(1/3*(1+2^(1/3)*(1-x)/(-x^3+1)^(1/3))*3^(1/2))*3^(1/2)*2^(2/3),1],
[x/(1+x)/(-x^3+1)^(1/3),x,3,1/8*ln((1-x)*(1+x)^2)*2^(2/3)+1/2*ln(x+(-x^3+1)^(1/3))-3/8*ln(-1+x+2^(2/3)*(-x^3+1)^(1/3))*2^(2/3)-1/3*arctan(1/3*(1-2*x/(-x^3+1)^(1/3))*3^(1/2))*3^(1/2)+1/4*arctan(1/3*(1+2^(1/3)*(1-x)/(-x^3+1)^(1/3))*3^(1/2))*3^(1/2)*2^(2/3),1],
[1/x/(x^2-3*x+2)^(1/3),x,-2,-1/8*ln(2-x)*2^(2/3)-1/4*ln(x)*2^(2/3)+3/8*ln(2-x-2^(2/3)*(x^2-3*x+2)^(1/3))*2^(2/3)+1/4*arctan(-1/3*3^(1/2)-1/3*2^(1/3)*(2-x)/(x^2-3*x+2)^(1/3)*3^(1/2))*3^(1/2)*2^(2/3),1],
[1/(x^3-3*x^2+7*x-5)^(1/3),x,-5,1/4*ln(1-x)-3/4*ln(1-x+(x^3-3*x^2+7*x-5)^(1/3))+1/2*arctan(1/3*3^(1/2)+2/3*(-1+x)/(x^3-3*x^2+7*x-5)^(1/3)*3^(1/2))*3^(1/2),1],
[1/(x*(x^2-q))^(1/3),x,-5,1/4*ln(x)-3/4*ln(-x+(x*(x^2-q))^(1/3))+1/2*arctan(1/3*3^(1/2)+2/3*x/(x*(x^2-q))^(1/3)*3^(1/2))*3^(1/2),1],
[1/((-1+x)*(x^2+q-2*x))^(1/3),x,-5,1/4*ln(1-x)-3/4*ln(1-x+((-1+x)*(x^2+q-2*x))^(1/3))+1/2*arctan(1/3*3^(1/2)+2/3*(-1+x)/((-1+x)*(x^2+q-2*x))^(1/3)*3^(1/2))*3^(1/2),1],
[1/x/((-1+x)*(-2*q*x+x^2+q))^(1/3),x,-2,1/4*ln(1-x)/q^(1/3)+1/2*ln(x)/q^(1/3)-3/4*ln(-q^(1/3)*(-1+x)+((-1+x)*(-2*q*x+x^2+q))^(1/3))/q^(1/3)+1/2*arctan(1/3*3^(1/2)+2/3*q^(1/3)*(-1+x)/((-1+x)*(-2*q*x+x^2+q))^(1/3)*3^(1/2))*3^(1/2)/q^(1/3),1],
[(2-(1+k)*x)/((1-x)*x*(-k*x+1))^(1/3)/(1-(1+k)*x),x,-3,1/2*ln(x)/k^(1/3)+1/2*ln(1-(1+k)*x)/k^(1/3)-3/2*ln(-k^(1/3)*x+((1-x)*x*(-k*x+1))^(1/3))/k^(1/3)+arctan(1/3*(1+2*k^(1/3)*x/((1-x)*x*(-k*x+1))^(1/3))*3^(1/2))*3^(1/2)/k^(1/3),1],
[(-k*x+1)/(1+(-2+k)*x)/((1-x)*x*(-k*x+1))^(2/3),x,-1,1/2*ln(1-(2-k)*x)*2^(1/3)/(1-k)^(1/3)+1/4*ln(-k*x+1)*2^(1/3)/(1-k)^(1/3)-3/4*ln(-1+k*x+2^(2/3)*(1-k)^(1/3)*((1-x)*x*(-k*x+1))^(1/3))*2^(1/3)/(1-k)^(1/3)-1/2*arctan(1/3*(1+2^(1/3)*(-k*x+1)/(1-k)^(1/3)/((1-x)*x*(-k*x+1))^(1/3))*3^(1/2))*3^(1/2)*2^(1/3)/(1-k)^(1/3),1],
[(c*x^2+b*x+a)/(x^2-x+1)/(-x^3+1)^(1/3),x,19,1/24*(a+b)*ln((1-x)*(1+x)^2)*2^(2/3)-1/12*(a-c)*ln(x^3+1)*2^(2/3)-1/12*(b+c)*ln(x^3+1)*2^(2/3)+1/12*(a+b)*ln(1+2^(2/3)*(1-x)^2/(-x^3+1)^(2/3)-2^(1/3)*(1-x)/(-x^3+1)^(1/3))*2^(2/3)-1/6*(a+b)*ln(1+2^(1/3)*(1-x)/(-x^3+1)^(1/3))*2^(2/3)+1/4*(b+c)*ln(2^(1/3)-(-x^3+1)^(1/3))*2^(2/3)+1/4*(a-c)*ln(-2^(1/3)*x-(-x^3+1)^(1/3))*2^(2/3)+1/2*c*ln(x+(-x^3+1)^(1/3))-1/8*(a+b)*ln(-1+x+2^(2/3)*(-x^3+1)^(1/3))*2^(2/3)+1/6*(a+b)*arctan(1/3*(1-2*2^(1/3)*(1-x)/(-x^3+1)^(1/3))*3^(1/2))*2^(2/3)*3^(1/2)+1/12*(a+b)*arctan(1/3*(1+2^(1/3)*(1-x)/(-x^3+1)^(1/3))*3^(1/2))*2^(2/3)*3^(1/2)-1/3*c*arctan(1/3*(1-2*x/(-x^3+1)^(1/3))*3^(1/2))*3^(1/2)-1/6*(a-c)*arctan(1/3*(1-2*2^(1/3)*x/(-x^3+1)^(1/3))*3^(1/2))*2^(2/3)*3^(1/2)+1/6*(b+c)*arctan(1/3*(1+2^(2/3)*(-x^3+1)^(1/3))*3^(1/2))*2^(2/3)*3^(1/2),1],
[1/(3-2*x)^(11/2)/(2*x^2+x+1)^5,x,19,-19255/395136/(3-2*x)^(9/2)-462025/30118144/(3-2*x)^(7/2)-38491/8605184/(3-2*x)^(5/2)-141045/120472576/(3-2*x)^(3/2)+1/28*x/(3-2*x)^(9/2)/(2*x^2+x+1)^4+1/1176*(23+73*x)/(3-2*x)^(9/2)/(2*x^2+x+1)^3+1/32928*(1387+3049*x)/(3-2*x)^(9/2)/(2*x^2+x+1)^2+5/153664*(3049+4377*x)/(3-2*x)^(9/2)/(2*x^2+x+1)-38225/240945152/(3-2*x)^(1/2)+5/13492928512*ln(3-2*x+14^(1/2)-(3-2*x)^(1/2)*(7+2*14^(1/2))^(1/2))*(-298093007954+81630132224*14^(1/2))^(1/2)-5/13492928512*ln(3-2*x+14^(1/2)+(3-2*x)^(1/2)*(7+2*14^(1/2))^(1/2))*(-298093007954+81630132224*14^(1/2))^(1/2)+5/6746464256*arctan((-2*(3-2*x)^(1/2)+(7+2*14^(1/2))^(1/2))/(-7+2*14^(1/2))^(1/2))*(298093007954+81630132224*14^(1/2))^(1/2)-5/6746464256*arctan((2*(3-2*x)^(1/2)+(7+2*14^(1/2))^(1/2))/(-7+2*14^(1/2))^(1/2))*(298093007954+81630132224*14^(1/2))^(1/2),1],
[1/(3-2*x)^(21/2)/(2*x^2+x+1)^10,x,29,4718120139975/351733660450816/(3-2*x)^(19/2)-815900548375/629418129227776/(3-2*x)^(17/2)-3029508823715/1555033025150976/(3-2*x)^(15/2)-13515743021825/13476952884641792/(3-2*x)^(13/2)-5846828446875/14513641568075776/(3-2*x)^(11/2)-37283626871975/261245548225363968/(3-2*x)^(9/2)-132355162272575/2844673747342852096/(3-2*x)^(7/2)-11557581705725/812763927812243456/(3-2*x)^(5/2)-46601678385075/11378694989371408384/(3-2*x)^(3/2)+1/63*x/(3-2*x)^(19/2)/(2*x^2+x+1)^9+1/7056*(53+173*x)/(3-2*x)^(19/2)/(2*x^2+x+1)^8+1/691488*(8477+21409*x)/(3-2*x)^(19/2)/(2*x^2+x+1)^7+5/6453888*(21409+47471*x)/(3-2*x)^(19/2)/(2*x^2+x+1)^6+41/90354432*(47471+92875*x)/(3-2*x)^(19/2)/(2*x^2+x+1)^5+41/5059848192*(3436375+5677637*x)/(3-2*x)^(19/2)/(2*x^2+x+1)^4+451/10119696384*(811091+998691*x)/(3-2*x)^(19/2)/(2*x^2+x+1)^3+451/283351498752*(28962039+14627273*x)/(3-2*x)^(19/2)/(2*x^2+x+1)^2+11275/3966920982528*(14627273-35058731*x)/(3-2*x)^(19/2)/(2*x^2+x+1)-24229218097975/22757389978742816768/(3-2*x)^(1/2)+11275/1274413838809597739008*ln(3-2*x+14^(1/2)-(3-2*x)^(1/2)*(7+2*14^(1/2))^(1/2))*(9756589235-2148932869*14^(1/2))*(-14+4*14^(1/2))^(1/2)-11275/1274413838809597739008*ln(3-2*x+14^(1/2)+(3-2*x)^(1/2)*(7+2*14^(1/2))^(1/2))*(9756589235-2148932869*14^(1/2))*(-14+4*14^(1/2))^(1/2)+11275/637206919404798869504*arctan((-2*(3-2*x)^(1/2)+(7+2*14^(1/2))^(1/2))/(-7+2*14^(1/2))^(1/2))*(9756589235+2148932869*14^(1/2))*(14+4*14^(1/2))^(1/2)-11275/637206919404798869504*arctan((2*(3-2*x)^(1/2)+(7+2*14^(1/2))^(1/2))/(-7+2*14^(1/2))^(1/2))*(9756589235+2148932869*14^(1/2))*(14+4*14^(1/2))^(1/2),1],
[1/(3-2*x)^(41/2)/(2*x^2+x+1)^20,x,49,-927027754781476746208047620505/58004665448193406009502274443388060172288/(3-2*x)^(1/2)-3948194343291401740321996415/202881463139404195937734623232/(3-2*x)^(37/2)-304688229262620222736480811/537361713180043545997243056128/(3-2*x)^(35/2)+2124315846756567455653862925/1688851098565851144562763890688/(3-2*x)^(33/2)+47657515074514118796095929535/66632852434325399703658138959872/(3-2*x)^(31/2)+34911619993974714062172751985/124667917457770102671360389021696/(3-2*x)^(29/2)+149066309808794760843017404825/1624981820656451683095663001731072/(3-2*x)^(27/2)+15848613964169066543734380171/601845118761648771516912222863360/(3-2*x)^(25/2)+11155168222970774232376891145/1685166332532616560247354224017408/(3-2*x)^(23/2)+14011818498091020272474956375/10110997995195699361484125344104448/(3-2*x)^(21/2)-13056959628363355534285785425/106924014357253562723941220352/(3-2*x)^(39/2)+173441368149804378661935869705/896508488907352010051592447177261056/(3-2*x)^(19/2)-22724090823469905152713519545/1604278348571050965355481221264572416/(3-2*x)^(17/2)-101190274412779618678573275245/3963511214116714149701777134888943616/(3-2*x)^(15/2)-460503190416958283087439337135/34350430522344855964082068502370844672/(3-2*x)^(13/2)-2211619588790911794826342607495/406920484649315986036049119181931544576/(3-2*x)^(11/2)-143401467550777247627940437025/73985542663511997461099839851260280832/(3-2*x)^(9/2)-4611053278117143010907562317585/7250583181024175751187784305423507521536/(3-2*x)^(7/2)-405965372440630510720926890227/2071595194578335928910795515835287863296/(3-2*x)^(5/2)-4986681479187781853417316522775/87006998172290109014253411665082090258432/(3-2*x)^(3/2)+115/3248261265098830736532127368829731369648128*ln(3-2*x+14^(1/2)-(3-2*x)^(1/2)*(7+2*14^(1/2))^(1/2))*(30297118912219360725028693061-8061110911143276053983022787*14^(1/2))*(-14+4*14^(1/2))^(1/2)-115/3248261265098830736532127368829731369648128*ln(3-2*x+14^(1/2)+(3-2*x)^(1/2)*(7+2*14^(1/2))^(1/2))*(30297118912219360725028693061-8061110911143276053983022787*14^(1/2))*(-14+4*14^(1/2))^(1/2)+115/1624130632549415368266063684414865684824064*arctan((-2*(3-2*x)^(1/2)+(7+2*14^(1/2))^(1/2))/(-7+2*14^(1/2))^(1/2))*(30297118912219360725028693061+8061110911143276053983022787*14^(1/2))*(14+4*14^(1/2))^(1/2)-115/1624130632549415368266063684414865684824064*arctan((2*(3-2*x)^(1/2)+(7+2*14^(1/2))^(1/2))/(-7+2*14^(1/2))^(1/2))*(30297118912219360725028693061+8061110911143276053983022787*14^(1/2))*(14+4*14^(1/2))^(1/2)+23/1576711628592227945545728*(919498192874055581221+908287136092467468517*x)/(3-2*x)^(39/2)/(2*x^2+x+1)^7+115/10187982830903626725064704*(908287136092467468517+298281884944522225747*x)/(3-2*x)^(39/2)/(2*x^2+x+1)^6+23/20375965661807253450129408*(2599313568802265110081-10426142448623187379187*x)/(3-2*x)^(39/2)/(2*x^2+x+1)^5-23/20018492580021161284337664*(10426142448623187379187+27513723463194262383705*x)/(3-2*x)^(39/2)/(2*x^2+x+1)^4-115/76434244396444433994743808*(26513224428169016478843+30673415406553789342019*x)/(3-2*x)^(39/2)/(2*x^2+x+1)^3-115/125891696652967303050166272*(88411609113007981044643-5712269536245152162963*x)/(3-2*x)^(39/2)/(2*x^2+x+1)^2+115/195831528126838026966925312*(28561347681225760814815+965934812839019490346107*x)/(3-2*x)^(39/2)/(2*x^2+x+1)+1/133*x/(3-2*x)^(39/2)/(2*x^2+x+1)^19+1/33516*(113+373*x)/(3-2*x)^(39/2)/(2*x^2+x+1)^18+1/7976808*(40657+107329*x)/(3-2*x)^(39/2)/(2*x^2+x+1)^17+5/595601664*(751303+1831285*x)/(3-2*x)^(39/2)/(2*x^2+x+1)^16+1/25015269888*(184959785+429411497*x)/(3-2*x)^(39/2)/(2*x^2+x+1)^15+1/4902992898048*(41652915209+92630823167*x)/(3-2*x)^(39/2)/(2*x^2+x+1)^14+1/297448235814912*(2871555518177+6100156355517*x)/(3-2*x)^(39/2)/(2*x^2+x+1)^13+1/7138757659557888*(77559130805859+156274047129113*x)/(3-2*x)^(39/2)/(2*x^2+x+1)^12+5/1099368679571914752*(2656658801194921+5020880176134289*x)/(3-2*x)^(39/2)/(2*x^2+x+1)^11+1/3420258114223734784*(45187921585208601+78752911037377255*x)/(3-2*x)^(39/2)/(2*x^2+x+1)^10+1/430952522392190582784*(6063974149878048635+9477172618423641847*x)/(3-2*x)^(39/2)/(2*x^2+x+1)^9+1/48266682507925345271808*(691833601144925854831+919498192874055581221*x)/(3-2*x)^(39/2)/(2*x^2+x+1)^8,1],
[fail,x,1,2,fail,1],//[1/(x^2-2*x+3)^(11/2)/(2*x^2+x+1)^5,x,14,1/123480000*(-3450497+2004270*x)/(x^2-2*x+3)^(9/2)+1/411600000*(-4878869+2578034*x)/(x^2-2*x+3)^(7/2)+1/6860000000*(-30316369+15043110*x)/(x^2-2*x+3)^(5/2)+1/41160000000*(-63043297+29625922*x)/(x^2-2*x+3)^(3/2)+1/280*(-1+10*x)/(x^2-2*x+3)^(9/2)/(2*x^2+x+1)^4+1/1050*(28+67*x)/(x^2-2*x+3)^(9/2)/(2*x^2+x+1)^3+1/117600*(5485+8878*x)/(x^2-2*x+3)^(9/2)/(2*x^2+x+1)^2+3/343000*(8822+8233*x)/(x^2-2*x+3)^(9/2)/(2*x^2+x+1)-31/411600000000*(7434109-3088870*x)/(x^2-2*x+3)^(1/2)-1/9604000000000*arctanh(1/7*(308108167+x*(932587773-620347970*2^(1/2))-312239803*2^(1/2))*35^(1/2)/(-151363871237318045+110320475741093888*2^(1/2))^(1/2)/(x^2-2*x+3)^(1/2))*(-10595470986612263150+7722433301876572160*2^(1/2))^(1/2)+1/9604000000000*arctan(1/7*(308108167+312239803*2^(1/2)+x*(932587773+620347970*2^(1/2)))*35^(1/2)/(151363871237318045+110320475741093888*2^(1/2))^(1/2)/(x^2-2*x+3)^(1/2))*(10595470986612263150+7722433301876572160*2^(1/2))^(1/2),1],
[fail,x,1,2,fail,1],//[1/(x^2-2*x+3)^(21/2)/(2*x^2+x+1)^10,x,24,1/1840124479200000000*(37358055634422583-14024622879097678*x)/(x^2-2*x+3)^(19/2)+1/104273720488000000000*(476849951294984711-125181871472148210*x)/(x^2-2*x+3)^(17/2)+1/15641058073200000000000*(7851758375483333511+1942164996204584234*x)/(x^2-2*x+3)^(15/2)-11/406667509903200000000000*(7502325106308201089-7813986379726516886*x)/(x^2-2*x+3)^(13/2)-3/1147010925368000000000000*(69053268515296359011-44840736195018286006*x)/(x^2-2*x+3)^(11/2)+1/9384634843920000000000000*(-838519439380295335657+466189390555853643870*x)/(x^2-2*x+3)^(9/2)+1/31282116146400000000000000*(-1117646664729238460189+568839749685437871554*x)/(x^2-2*x+3)^(7/2)+1/521368602440000000000000000*(-6551405511565449301689+3127298559983309301910*x)/(x^2-2*x+3)^(5/2)+1/1042737204880000000000000000*(-4179039782398459850819+1886993445589652402694*x)/(x^2-2*x+3)^(3/2)+1/630*(-1+10*x)/(x^2-2*x+3)^(19/2)/(2*x^2+x+1)^9+1/88200*(887+2218*x)/(x^2-2*x+3)^(19/2)/(2*x^2+x+1)^8+1/1080450*(14453+29371*x)/(x^2-2*x+3)^(19/2)/(2*x^2+x+1)^7+1/605052000*(8837931+17459234*x)/(x^2-2*x+3)^(19/2)/(2*x^2+x+1)^6+1/26471025000*(447940041+813432205*x)/(x^2-2*x+3)^(19/2)/(2*x^2+x+1)^5+1/29647548000000*(592729157441+911061463974*x)/(x^2-2*x+3)^(19/2)/(2*x^2+x+1)^4+1/12353145000000*(277010166219+310705340015*x)/(x^2-2*x+3)^(19/2)/(2*x^2+x+1)^3+1/276710448000000*(5488221294349+1384103301166*x)/(x^2-2*x+3)^(19/2)/(2*x^2+x+1)^2+1/2421216420000000*(-37857197792117-146548895467025*x)/(x^2-2*x+3)^(19/2)/(2*x^2+x+1)+1/10427372048800000000000000000*(-12105495874518671061833+5117656435043679338190*x)/(x^2-2*x+3)^(1/2)-1/2259801992000000000000000000*arctanh(1/7*(272944589523248381749+x*(656826642296538601431-464885615909893491590*2^(1/2))-191941026386645109841*2^(1/2))*35^(1/2)/(-81042225921274689605478944797800854846405+57305922523001707126026363878666500308992*2^(1/2))^(1/2)/(x^2-2*x+3)^(1/2))*(-5672955814489228272383526135846059839248350+4011414576610119498821845471506655021629440*2^(1/2))^(1/2)+1/2259801992000000000000000000*arctan(1/7*(272944589523248381749+191941026386645109841*2^(1/2)+x*(656826642296538601431+464885615909893491590*2^(1/2)))*35^(1/2)/(81042225921274689605478944797800854846405+57305922523001707126026363878666500308992*2^(1/2))^(1/2)/(x^2-2*x+3)^(1/2))*(5672955814489228272383526135846059839248350+4011414576610119498821845471506655021629440*2^(1/2))^(1/2),1],
[(-a+x-(a^2+1)^(1/2))/(-a+x+(a^2+1)^(1/2))/((-a+x)*(x^2+1))^(1/2),x,-9,-arctan((-a+x)*2^(1/2)*(-a+(a^2+1)^(1/2))^(1/2)/((-a+x)*(x^2+1))^(1/2))*2^(1/2)*(a+(a^2+1)^(1/2))^(1/2),1],
[(b*x+a)/(-x^2+1)^(1/3)/(x^2+3),x,7,-1/12*a*arctanh(x)*2^(1/3)+1/4*a*arctanh(x/(1+2^(1/3)*(-x^2+1)^(1/3)))*2^(1/3)-1/8*b*ln(x^2+3)*2^(1/3)+3/8*b*ln(2^(2/3)-(-x^2+1)^(1/3))*2^(1/3)+1/12*a*arctan(3^(1/2)/x)*2^(1/3)*3^(1/2)+1/12*a*arctan((1-2^(1/3)*(-x^2+1)^(1/3))*3^(1/2)/x)*2^(1/3)*3^(1/2)+1/4*b*arctan(1/3*(1+(-2*x^2+2)^(1/3))*3^(1/2))*3^(1/2)*2^(1/3),1],
[(b*x+a)/(-x^2+3)/(x^2+1)^(1/3),x,7,-1/12*a*arctan(x)*2^(1/3)+1/4*a*arctan(x/(1+2^(1/3)*(x^2+1)^(1/3)))*2^(1/3)+1/8*b*ln(-x^2+3)*2^(1/3)-3/8*b*ln(2^(2/3)-(x^2+1)^(1/3))*2^(1/3)-1/12*a*arctanh(3^(1/2)/x)*2^(1/3)*3^(1/2)-1/12*a*arctanh((1-2^(1/3)*(x^2+1)^(1/3))*3^(1/2)/x)*2^(1/3)*3^(1/2)-1/4*b*arctan(1/3*(1+2^(1/3)*(x^2+1)^(1/3))*3^(1/2))*3^(1/2)*2^(1/3),1],
[1/x/(3*x^2-6*x+4)^(1/3),x,1,-1/4*ln(x)*2^(1/3)+1/4*ln(6-3*x-3*2^(1/3)*(3*x^2-6*x+4)^(1/3))*2^(1/3)+1/6*arctan(-1/3*3^(1/2)-1/3*2^(2/3)*(2-x)/(3*x^2-6*x+4)^(1/3)*3^(1/2))*2^(1/3)*3^(1/2),1],
[x*(-x^3+1)^(1/3),x,2,1/3*x^2*(-x^3+1)^(1/3)-1/6*ln(-x-(-x^3+1)^(1/3))-1/9*arctan(1/3*(1-2*x/(-x^3+1)^(1/3))*3^(1/2))*3^(1/2),1],
[(-x^3+1)^(1/3)/x,x,6,(-x^3+1)^(1/3)-1/2*ln(x)+1/2*ln(1-(-x^3+1)^(1/3))-1/3*arctan(1/3*(1+2*(-x^3+1)^(1/3))*3^(1/2))*3^(1/2),1],
[(-x^3+1)^(1/3)/(1+x),x,25,(-x^3+1)^(1/3)-1/3*2^(1/3)*ln(x^3+1)+1/6*ln(2^(2/3)+(-1+x)/(-x^3+1)^(1/3))*2^(1/3)-1/6*ln(1+2^(2/3)*(1-x)^2/(-x^3+1)^(2/3)-2^(1/3)*(1-x)/(-x^3+1)^(1/3))*2^(1/3)+1/3*2^(1/3)*ln(1+2^(1/3)*(1-x)/(-x^3+1)^(1/3))-1/12*ln(2*2^(1/3)+(1-x)^2/(-x^3+1)^(2/3)+2^(2/3)*(1-x)/(-x^3+1)^(1/3))*2^(1/3)+1/2*ln(2^(1/3)-(-x^3+1)^(1/3))*2^(1/3)-1/2*ln(-x-(-x^3+1)^(1/3))+1/2*ln(-2^(1/3)*x-(-x^3+1)^(1/3))*2^(1/3)+1/3*2^(1/3)*arctan(1/3*(1-2*2^(1/3)*(1-x)/(-x^3+1)^(1/3))*3^(1/2))*3^(1/2)+1/6*arctan(1/3*(1+2^(1/3)*(1-x)/(-x^3+1)^(1/3))*3^(1/2))*2^(1/3)*3^(1/2)-1/3*arctan(1/3*(1-2*x/(-x^3+1)^(1/3))*3^(1/2))*3^(1/2)+1/3*2^(1/3)*arctan(1/3*(1-2*2^(1/3)*x/(-x^3+1)^(1/3))*3^(1/2))*3^(1/2)-1/3*2^(1/3)*arctan(1/3*(1+2^(2/3)*(-x^3+1)^(1/3))*3^(1/2))*3^(1/2),1],
[(-x^3+1)^(1/3)/(x^2-x+1),x,19,-1/4*ln(-3*(-1+x)*(x^2-x+1))*2^(1/3)+1/4*ln(2^(1/3)-(-x^3+1)^(1/3))*2^(1/3)+3/4*ln(-2^(1/3)*(-1+x)+(-x^3+1)^(1/3))*2^(1/3)+1/2*ln(x+(-x^3+1)^(1/3))-1/4*ln(2^(1/3)*x+(-x^3+1)^(1/3))*2^(1/3)+1/3*arctan(1/3*(1-2*x/(-x^3+1)^(1/3))*3^(1/2))*3^(1/2)-1/6*2^(1/3)*arctan(1/3*(1-2*2^(1/3)*x/(-x^3+1)^(1/3))*3^(1/2))*3^(1/2)-1/6*2^(1/3)*arctan(1/3*(1+2^(2/3)*(-x^3+1)^(1/3))*3^(1/2))*3^(1/2)+1/2*arctan(1/3*(1+2*2^(1/3)*(-1+x)/(-x^3+1)^(1/3))*3^(1/2))*3^(1/2)*2^(1/3),1],
[(-x^3+1)^(1/3)/(2+x),x,12,(-x^3+1)^(1/3)+1/2*x*AppellF1(1/3,-1/3,1,4/3,x^3,-1/8*x^3)-3^(1/6)*arctan(2/9*(-x^3+1)^(1/3)*3^(5/6)+1/3*3^(1/2))+3^(1/6)*arctan(1/3*(1-3^(2/3)*x/(-x^3+1)^(1/3))*3^(1/2))-1/3*ln(x^3+8)*3^(2/3)+1/2*3^(2/3)*ln(3^(2/3)-(-x^3+1)^(1/3))-ln(-x-(-x^3+1)^(1/3))+1/2*3^(2/3)*ln(-1/2*3^(2/3)*x-(-x^3+1)^(1/3))-2/3*arctan(1/3*(1-2*x/(-x^3+1)^(1/3))*3^(1/2))*3^(1/2),1],
[(2+x)/(x^2+x+1)/(x^3+2)^(1/3),x,9,-1/4*x^2*AppellF1(2/3,1,1/3,5/3,x^3,-1/2*x^3)*2^(2/3)+1/3*arctan(1/3*(3^(1/3)+2*(x^3+2)^(1/3))*3^(1/6))*3^(1/6)+2/3*arctan(1/3*(1+2*3^(1/3)*x/(x^3+2)^(1/3))*3^(1/2))*3^(1/6)+1/18*ln(-x^3+1)*3^(2/3)+1/6*ln(3^(1/3)-(x^3+2)^(1/3))*3^(2/3)-1/3*ln(3^(1/3)*x-(x^3+2)^(1/3))*3^(2/3),1],
[(160*x^3+30*x^2-3*x+3)/(320*x^4+80*x^3-12*x^2+24*x+9),x,1,1/8*ln(320*x^4+80*x^3-12*x^2+24*x+9),1],
[(20*x^2+12*x+3)/(320*x^4+80*x^3-12*x^2+24*x+9),x,1,-1/22*arctan(1/55*(7-40*x)*11^(1/2))*11^(1/2)+1/22*arctan(1/66*(800*x^3-40*x^2+30*x+57)*11^(1/2))*11^(1/2),1],
[(2560*x^3-400*x^2-576*x-84)/(320*x^4+80*x^3-12*x^2+24*x+9),x,2,2*ln(320*x^4+80*x^3-12*x^2+24*x+9)+2*arctan(1/55*(7-40*x)*11^(1/2))*11^(1/2)-2*arctan(1/66*(800*x^3-40*x^2+30*x+57)*11^(1/2))*11^(1/2),1],
[(-x^4+1)^(1/2)/(x^4+1),x,1,1/2*arctan(x*(x^2+1)/(-x^4+1)^(1/2))+1/2*arctanh(x*(-x^2+1)/(-x^4+1)^(1/2)),1],
[(x^4+1)^(1/2)/(-x^4+1),x,4,1/4*arctan(x*2^(1/2)/(x^4+1)^(1/2))*2^(1/2)+1/4*arctanh(x*2^(1/2)/(x^4+1)^(1/2))*2^(1/2),1],
[(x^4+p*x^2+1)^(1/2)/(-x^4+1),x,4,1/4*arctan(x*(2-p)^(1/2)/(x^4+p*x^2+1)^(1/2))*(2-p)^(1/2)+1/4*arctanh(x*(2+p)^(1/2)/(x^4+p*x^2+1)^(1/2))*(2+p)^(1/2),1],
[(-x^4+p*x^2+1)^(1/2)/(x^4+1),x,1,1/4*arctanh(1/4*x*(p-2*x^2+(p^2+4)^(1/2))*(-p+(p^2+4)^(1/2))^(1/2)*2^(1/2)/(-x^4+p*x^2+1)^(1/2))*(-p+(p^2+4)^(1/2))^(1/2)*2^(1/2)-1/4*arctan(1/4*x*(p-2*x^2-(p^2+4)^(1/2))*(p+(p^2+4)^(1/2))^(1/2)*2^(1/2)/(-x^4+p*x^2+1)^(1/2))*(p+(p^2+4)^(1/2))^(1/2)*2^(1/2),1],
[(b*x+a)/(-x^2+2)/(x^2-1)^(1/4),x,7,-b*arctan((x^2-1)^(1/4))+b*arctanh((x^2-1)^(1/4))+1/4*a*arctan(1/2*x/(x^2-1)^(1/4)*2^(1/2))*2^(1/2)+1/4*a*arctanh(1/2*x/(x^2-1)^(1/4)*2^(1/2))*2^(1/2),1],
[(b*x+a)/(-x^2-1)^(1/4)/(x^2+2),x,7,b*arctan((-x^2-1)^(1/4))-b*arctanh((-x^2-1)^(1/4))+1/4*a*arctan(1/2*x/(-x^2-1)^(1/4)*2^(1/2))*2^(1/2)+1/4*a*arctanh(1/2*x/(-x^2-1)^(1/4)*2^(1/2))*2^(1/2),1],
[(b*x+a)/(-x^2+1)^(1/4)/(-x^2+2),x,3,1/2*a*arctan((1-(-x^2+1)^(1/2))/x/(-x^2+1)^(1/4))+1/2*a*arctanh((1+(-x^2+1)^(1/2))/x/(-x^2+1)^(1/4))+1/2*b*arctan(1/2*(1-(-x^2+1)^(1/2))/(-x^2+1)^(1/4)*2^(1/2))*2^(1/2)+1/2*b*arctanh(1/2*(1+(-x^2+1)^(1/2))/(-x^2+1)^(1/4)*2^(1/2))*2^(1/2),1],
[(b*x+a)/(x^2+1)^(1/4)/(x^2+2),x,3,-1/2*a*arctan((1+(x^2+1)^(1/2))/x/(x^2+1)^(1/4))-1/2*a*arctanh((1-(x^2+1)^(1/2))/x/(x^2+1)^(1/4))-1/2*b*arctan(1/2*(1-(x^2+1)^(1/2))/(x^2+1)^(1/4)*2^(1/2))*2^(1/2)-1/2*b*arctanh(1/2*(1+(x^2+1)^(1/2))/(x^2+1)^(1/4)*2^(1/2))*2^(1/2),1],
[x/(-x^3+4)/(-x^3+1)^(1/2),x,1,-1/6*arctanh((1+2^(1/3)*x)/(-x^3+1)^(1/2))*2^(1/3)+1/18*arctanh((-x^3+1)^(1/2))*2^(1/3)-1/18*arctan((1-2^(1/3)*x)*3^(1/2)/(-x^3+1)^(1/2))*2^(1/3)*3^(1/2)+1/18*arctan(1/3*(-x^3+1)^(1/2)*3^(1/2))*2^(1/3)*3^(1/2),1],
[x/(-d*x^3+4)/(d*x^3-1)^(1/2),x,1,-1/6*arctan((1+2^(1/3)*d^(1/3)*x)/(d*x^3-1)^(1/2))*2^(1/3)/d^(2/3)-1/18*arctan((d*x^3-1)^(1/2))*2^(1/3)/d^(2/3)-1/18*arctanh((1-2^(1/3)*d^(1/3)*x)*3^(1/2)/(d*x^3-1)^(1/2))*2^(1/3)/d^(2/3)*3^(1/2)-1/18*arctanh(1/3*(d*x^3-1)^(1/2)*3^(1/2))*2^(1/3)/d^(2/3)*3^(1/2),1],
[x/(x^3+8)/(x^3-1)^(1/2),x,8,1/18*arctan(1/3*(1-x)^2/(x^3-1)^(1/2))+1/18*arctan(1/3*(x^3-1)^(1/2))-1/18*arctanh((1-x)*3^(1/2)/(x^3-1)^(1/2))*3^(1/2),1],
[x/(-d*x^3+8)/(d*x^3+1)^(1/2),x,8,1/18*arctanh(1/3*(1+d^(1/3)*x)^2/(d*x^3+1)^(1/2))/d^(2/3)-1/18*arctanh(1/3*(d*x^3+1)^(1/2))/d^(2/3)-1/18*arctan((1+d^(1/3)*x)*3^(1/2)/(d*x^3+1)^(1/2))/d^(2/3)*3^(1/2),1],
[1/(-3*x^2+1)^(1/3)/(-x^2+3),x,1,1/4*arctan((1-(-3*x^2+1)^(1/3))/x)+1/12*arctanh(1/3*x*3^(1/2))*3^(1/2)-1/12*arctanh(1/9*(1-(-3*x^2+1)^(1/3))^2/x*3^(1/2))*3^(1/2),1],
[1/(x^2+3)/(3*x^2+1)^(1/3),x,1,-1/4*arctanh((1-(3*x^2+1)^(1/3))/x)+1/12*arctan(1/3*x*3^(1/2))*3^(1/2)+1/12*arctan(1/9*(1-(3*x^2+1)^(1/3))^2/x*3^(1/2))*3^(1/2),1],
[1/(-x^2+1)^(1/3)/(x^2+3),x,1,-1/12*arctanh(x)*2^(1/3)+1/4*arctanh(x/(1+2^(1/3)*(-x^2+1)^(1/3)))*2^(1/3)+1/12*arctan(3^(1/2)/x)*2^(1/3)*3^(1/2)+1/12*arctan((1-2^(1/3)*(-x^2+1)^(1/3))*3^(1/2)/x)*2^(1/3)*3^(1/2),1],
[1/(-x^2+3)/(x^2+1)^(1/3),x,1,-1/12*arctan(x)*2^(1/3)+1/4*arctan(x/(1+2^(1/3)*(x^2+1)^(1/3)))*2^(1/3)-1/12*arctanh(3^(1/2)/x)*2^(1/3)*3^(1/2)-1/12*arctanh((1-2^(1/3)*(x^2+1)^(1/3))*3^(1/2)/x)*2^(1/3)*3^(1/2),1],
[(a+x)/(-a+x)/(a^2*x-(a^2+1)*x^2+x^3)^(1/2),x,4,-2*arctan((1-a)*x^(1/2)/(a^2-(a^2+1)*x+x^2)^(1/2))*x^(1/2)*(a^2-(a^2+1)*x+x^2)^(1/2)/(1-a)/(a^2*x-(a^2+1)*x^2+x^3)^(1/2),1],
[(-2+a+x)/(-a+x)/((2-a)*a*x+(a^2-2*a-1)*x^2+x^3)^(1/2),x,-5,0,1],
[(-a+(-1+2*a)*x)/(-a+x)/(a^2*x-(a^2+2*a-1)*x^2+(-1+2*a)*x^3)^(1/2),x,-7,ln((-a^2+2*a*x+x^2-2*x-2*((1-x)*x*(a^2-2*a*x+x))^(1/2))/(a-x)^2),1],
[(1-2^(1/3)*x)/(2^(2/3)+x)/(x^3+1)^(1/2),x,2,2/3*arctan((1+2^(1/3)*x)*3^(1/2)/(x^3+1)^(1/2))*3^(1/2),1],
[(1+x)/(-2+x)/(x^3+1)^(1/2),x,2,-2/3*arctanh(1/3*(1+x)^2/(x^3+1)^(1/2)),1],
[x/(10+x^3+6*3^(1/2))/(x^3+1)^(1/2),x,1,-1/12*arctan(1/2*3^(1/4)*(1+x)*(1+3^(1/2))*2^(1/2)/(x^3+1)^(1/2))*(2-3^(1/2))*3^(1/4)*2^(1/2)-1/18*arctan(1/6*(1-3^(1/2))*(x^3+1)^(1/2)*3^(1/4)*2^(1/2))*(2-3^(1/2))*3^(1/4)*2^(1/2)-1/36*arctanh(1/2*3^(1/4)*(1+x)*(1-3^(1/2))*2^(1/2)/(x^3+1)^(1/2))*(2-3^(1/2))*3^(3/4)*2^(1/2)-1/18*arctanh(1/2*3^(1/4)*(1-2*x+3^(1/2))*2^(1/2)/(x^3+1)^(1/2))*(2-3^(1/2))*3^(3/4)*2^(1/2),1],
[x/(10+x^3-6*3^(1/2))/(x^3+1)^(1/2),x,1,-1/18*arctan(1/2*3^(1/4)*(1-2*x-3^(1/2))*2^(1/2)/(x^3+1)^(1/2))*(2+3^(1/2))*3^(3/4)*2^(1/2)-1/36*arctan(1/2*3^(1/4)*(1+x)*(1+3^(1/2))*2^(1/2)/(x^3+1)^(1/2))*(2+3^(1/2))*3^(3/4)*2^(1/2)+1/12*arctanh(1/2*3^(1/4)*(1+x)*(1-3^(1/2))*2^(1/2)/(x^3+1)^(1/2))*(2+3^(1/2))*3^(1/4)*2^(1/2)+1/18*arctanh(1/6*(1+3^(1/2))*(x^3+1)^(1/2)*3^(1/4)*2^(1/2))*(2+3^(1/2))*3^(1/4)*2^(1/2),1],
[x/(-10+x^3-6*3^(1/2))/(x^3-1)^(1/2),x,1,1/36*arctan(1/2*3^(1/4)*(1-x)*(1-3^(1/2))*2^(1/2)/(x^3-1)^(1/2))*(2-3^(1/2))*3^(3/4)*2^(1/2)+1/18*arctan(1/2*3^(1/4)*(1+2*x+3^(1/2))*2^(1/2)/(x^3-1)^(1/2))*(2-3^(1/2))*3^(3/4)*2^(1/2)+1/12*arctanh(1/2*3^(1/4)*(1-x)*(1+3^(1/2))*2^(1/2)/(x^3-1)^(1/2))*(2-3^(1/2))*3^(1/4)*2^(1/2)-1/18*arctanh(1/6*(1-3^(1/2))*(x^3-1)^(1/2)*3^(1/4)*2^(1/2))*(2-3^(1/2))*3^(1/4)*2^(1/2),1],
[x/(-10+x^3+6*3^(1/2))/(x^3-1)^(1/2),x,1,-1/12*arctan(1/2*3^(1/4)*(1-x)*(1-3^(1/2))*2^(1/2)/(x^3-1)^(1/2))*(2+3^(1/2))*3^(1/4)*2^(1/2)+1/18*arctan(1/6*(1+3^(1/2))*(x^3-1)^(1/2)*3^(1/4)*2^(1/2))*(2+3^(1/2))*3^(1/4)*2^(1/2)+1/18*arctanh(1/2*3^(1/4)*(1+2*x-3^(1/2))*2^(1/2)/(x^3-1)^(1/2))*(2+3^(1/2))*3^(3/4)*2^(1/2)+1/36*arctanh(1/2*3^(1/4)*(1-x)*(1+3^(1/2))*2^(1/2)/(x^3-1)^(1/2))*(2+3^(1/2))*3^(3/4)*2^(1/2),1],
[(1+x-3^(1/2))/(1+x+3^(1/2))/(-4+x^4+4*3^(1/2)*x^2)^(1/2),x,2,1/3*arctanh((1+x-3^(1/2))^2/(-9+6*3^(1/2))^(1/2)/(-4+x^4+4*3^(1/2)*x^2)^(1/2))*(-3+2*3^(1/2))^(1/2),1],
[(1+x+3^(1/2))/(1+x-3^(1/2))/(-4+x^4-4*3^(1/2)*x^2)^(1/2),x,2,-1/3*arctan((1+x+3^(1/2))^2/(9+6*3^(1/2))^(1/2)/(-4+x^4-4*3^(1/2)*x^2)^(1/2))*(3+2*3^(1/2))^(1/2),1],
[(-1+x)/(1+x)/(x^3+2)^(1/3),x,1,ln(1+x)-3/2*ln(2+x-(x^3+2)^(1/3))+arctan(1/3*(1+2*(2+x)/(x^3+2)^(1/3))*3^(1/2))*3^(1/2),1],
[1/(1+x)/(x^3+2)^(1/3),x,3,-1/2*ln(1+x)+3/4*ln(2+x-(x^3+2)^(1/3))-1/4*ln(-x+(x^3+2)^(1/3))+1/6*arctan(1/3*(1+2*x/(x^3+2)^(1/3))*3^(1/2))*3^(1/2)-1/2*arctan(1/3*(1+2*(2+x)/(x^3+2)^(1/3))*3^(1/2))*3^(1/2),1],
[1/(-x^3+1)/(b*x^3+a)^(1/3),x,1,1/6*ln(-x^3+1)/(a+b)^(1/3)-1/2*ln((a+b)^(1/3)*x-(b*x^3+a)^(1/3))/(a+b)^(1/3)+1/3*arctan(1/3*(1+2*(a+b)^(1/3)*x/(b*x^3+a)^(1/3))*3^(1/2))/(a+b)^(1/3)*3^(1/2),1],
[(1+x)/(x^2+x+1)/(b*x^3+a)^(1/3),x,8,1/2*ln((a+b)^(1/3)-(b*x^3+a)^(1/3))/(a+b)^(1/3)-1/2*ln((a+b)^(1/3)*x-(b*x^3+a)^(1/3))/(a+b)^(1/3)+1/3*arctan(1/3*(1+2*(a+b)^(1/3)*x/(b*x^3+a)^(1/3))*3^(1/2))/(a+b)^(1/3)*3^(1/2)+1/3*arctan(1/3*(1+2*(b*x^3+a)^(1/3)/(a+b)^(1/3))*3^(1/2))/(a+b)^(1/3)*3^(1/2),1],
[x^2/(-x^3+1)/(b*x^3+a)^(1/3),x,5,1/6*ln(-x^3+1)/(a+b)^(1/3)-1/2*ln((a+b)^(1/3)-(b*x^3+a)^(1/3))/(a+b)^(1/3)-1/3*arctan(1/3*(1+2*(b*x^3+a)^(1/3)/(a+b)^(1/3))*3^(1/2))/(a+b)^(1/3)*3^(1/2),1],
[1/(-x^3+1)^(1/3)/(x^3+1),x,1,-1/12*ln(x^3+1)*2^(2/3)+1/4*ln(-2^(1/3)*x-(-x^3+1)^(1/3))*2^(2/3)-1/6*arctan(1/3*(1-2*2^(1/3)*x/(-x^3+1)^(1/3))*3^(1/2))*2^(2/3)*3^(1/2),1],
[x/(-x^3+1)^(1/3)/(x^3+1),x,8,1/24*ln((1-x)*(1+x)^2)*2^(2/3)+1/12*ln(1+2^(2/3)*(1-x)^2/(-x^3+1)^(2/3)-2^(1/3)*(1-x)/(-x^3+1)^(1/3))*2^(2/3)-1/6*ln(1+2^(1/3)*(1-x)/(-x^3+1)^(1/3))*2^(2/3)-1/8*ln(-1+x+2^(2/3)*(-x^3+1)^(1/3))*2^(2/3)+1/6*arctan(1/3*(1-2*2^(1/3)*(1-x)/(-x^3+1)^(1/3))*3^(1/2))*2^(2/3)*3^(1/2)+1/12*arctan(1/3*(1+2^(1/3)*(1-x)/(-x^3+1)^(1/3))*3^(1/2))*3^(1/2)*2^(2/3),1],
[x^2/(-x^3+1)^(1/3)/(x^3+1),x,5,-1/12*ln(x^3+1)*2^(2/3)+1/4*ln(2^(1/3)-(-x^3+1)^(1/3))*2^(2/3)+1/6*arctan(1/3*(1+2^(2/3)*(-x^3+1)^(1/3))*3^(1/2))*2^(2/3)*3^(1/2),1],
[(1+x)/(x^2-x+1)/(-x^3+1)^(1/3),x,-16,1/4*ln(1+2^(2/3)*(1-x)^2/(-x^3+1)^(2/3)-2^(1/3)*(1-x)/(-x^3+1)^(1/3))*2^(2/3)-1/2*ln(1+2^(1/3)*(1-x)/(-x^3+1)^(1/3))*2^(2/3)+1/2*arctan(1/3*(1-2*2^(1/3)*(1-x)/(-x^3+1)^(1/3))*3^(1/2))*2^(2/3)*3^(1/2),1],
[(1+x)^2/(-x^3+1)^(1/3)/(x^3+1),x,-17,1/4*ln(1+2^(2/3)*(1-x)^2/(-x^3+1)^(2/3)-2^(1/3)*(1-x)/(-x^3+1)^(1/3))*2^(2/3)-1/2*ln(1+2^(1/3)*(1-x)/(-x^3+1)^(1/3))*2^(2/3)+1/2*arctan(1/3*(1-2*2^(1/3)*(1-x)/(-x^3+1)^(1/3))*3^(1/2))*2^(2/3)*3^(1/2),1],
[(1-x)/(x^2+x+1)/(x^3+1)^(1/3),x,-16,-1/4*ln(1+2^(2/3)*(1+x)^2/(x^3+1)^(2/3)-2^(1/3)*(1+x)/(x^3+1)^(1/3))*2^(2/3)+1/2*ln(1+2^(1/3)*(1+x)/(x^3+1)^(1/3))*2^(2/3)-1/2*arctan(1/3*(1-2*2^(1/3)*(1+x)/(x^3+1)^(1/3))*3^(1/2))*3^(1/2)*2^(2/3),1],
[(-x^3+1)^(2/3)/(x^2+x+1)^2,x,5,1/(-x^3+1)^(1/3)+x/(-x^3+1)^(1/3)-x^2*hypergeom([2/3, 4/3],[5/3],x^3),1],
[(1-x)/(x^2+x+1)/(-x^3+1)^(1/3),x,5,1/(-x^3+1)^(1/3)+x/(-x^3+1)^(1/3)-x^2*hypergeom([2/3, 4/3],[5/3],x^3),1],
[(1-x)^2/(-x^3+1)^(4/3),x,3,(1+(1-2*x)*x)/(-x^3+1)^(1/3)+x^2*hypergeom([1/3, 2/3],[5/3],x^3),1],
[(-x^3+1)^(2/3),x,2,1/3*x*(-x^3+1)^(2/3)+1/3*ln(x+(-x^3+1)^(1/3))-2/9*arctan(1/3*(1-2*x/(-x^3+1)^(1/3))*3^(1/2))*3^(1/2),1],
[(-x^3+1)^(2/3)/x,x,6,1/2*(-x^3+1)^(2/3)-1/2*ln(x)+1/2*ln(1-(-x^3+1)^(1/3))+1/3*arctan(1/3*(1+2*(-x^3+1)^(1/3))*3^(1/2))*3^(1/2),1],
[(-x^3+1)^(2/3)/(b*x+a),x,13,1/2*(-x^3+1)^(2/3)/b-1/2*(a^3+b^3)*x^2*AppellF1(2/3,1/3,1,5/3,x^3,-b^3*x^3/a^3)/a^2/b^2+1/2*a*x^2*hypergeom([1/3, 2/3],[5/3],x^3)/b^2-1/3*(a^3+b^3)^(2/3)*ln(b^3*x^3+a^3)/b^3+1/2*(a^3+b^3)^(2/3)*ln(-(a^3+b^3)^(1/3)*x/a-(-x^3+1)^(1/3))/b^3-1/2*a^2*ln(x+(-x^3+1)^(1/3))/b^3+1/2*(a^3+b^3)^(2/3)*ln((a^3+b^3)^(1/3)-b*(-x^3+1)^(1/3))/b^3+1/3*a^2*arctan(1/3*(1-2*x/(-x^3+1)^(1/3))*3^(1/2))/b^3*3^(1/2)-1/3*(a^3+b^3)^(2/3)*arctan(1/3*(1-2*(a^3+b^3)^(1/3)*x/a/(-x^3+1)^(1/3))*3^(1/2))/b^3*3^(1/2)+1/3*(a^3+b^3)^(2/3)*arctan(1/3*(1+2*b*(-x^3+1)^(1/3)/(a^3+b^3)^(1/3))*3^(1/2))/b^3*3^(1/2),1],
[(-x^3+1)^(2/3)/(x^2-x+1)^2,x,13,-1/3*(-x^3+1)^(2/3)/(x^3+1)+1/3*x*(-x^3+1)^(2/3)/(x^3+1)+2/3*x^2*(-x^3+1)^(2/3)/(x^3+1)+1/3*x^2*hypergeom([1/3, 2/3],[5/3],x^3)-1/6*ln(2^(1/3)-(-x^3+1)^(1/3))*2^(2/3)+1/6*ln(-2^(1/3)*x-(-x^3+1)^(1/3))*2^(2/3)-1/9*arctan(1/3*(1-2*2^(1/3)*x/(-x^3+1)^(1/3))*3^(1/2))*2^(2/3)*3^(1/2)-1/9*arctan(1/3*(1+2^(2/3)*(-x^3+1)^(1/3))*3^(1/2))*2^(2/3)*3^(1/2),1],
[(1-2*x)*(-x^3+1)^(2/3)/(x^2-x+1)^2,x,14,(-x^3+1)^(2/3)/(x^2-x+1)+1/2*ln(2^(1/3)-(-x^3+1)^(1/3))*2^(2/3)-1/2*ln(-2^(1/3)*x-(-x^3+1)^(1/3))*2^(2/3)+ln(x+(-x^3+1)^(1/3))-2/3*arctan(1/3*(1-2*x/(-x^3+1)^(1/3))*3^(1/2))*3^(1/2)+1/3*arctan(1/3*(1-2*2^(1/3)*x/(-x^3+1)^(1/3))*3^(1/2))*2^(2/3)*3^(1/2)+1/3*arctan(1/3*(1+2^(2/3)*(-x^3+1)^(1/3))*3^(1/2))*2^(2/3)*3^(1/2),1],
[(-x^3+1)^(2/3)/(1+x),x,5,1/2*(-x^3+1)^(2/3)+1/2*x^2*hypergeom([1/3, 2/3],[5/3],x^3)-1/4*ln((1-x)*(1+x)^2)*2^(2/3)-1/2*ln(x+(-x^3+1)^(1/3))+3/4*ln(-1+x+2^(2/3)*(-x^3+1)^(1/3))*2^(2/3)+1/3*arctan(1/3*(1-2*x/(-x^3+1)^(1/3))*3^(1/2))*3^(1/2)-1/2*arctan(1/3*(1+2^(1/3)*(1-x)/(-x^3+1)^(1/3))*3^(1/2))*3^(1/2)*2^(2/3),1],
[(x^2-x+1)*(-x^3+1)^(2/3)/(x^3+1),x,6,1/2*(-x^3+1)^(2/3)+1/2*x^2*hypergeom([1/3, 2/3],[5/3],x^3)-1/4*ln((1-x)*(1+x)^2)*2^(2/3)-1/2*ln(x+(-x^3+1)^(1/3))+3/4*ln(-1+x+2^(2/3)*(-x^3+1)^(1/3))*2^(2/3)+1/3*arctan(1/3*(1-2*x/(-x^3+1)^(1/3))*3^(1/2))*3^(1/2)-1/2*arctan(1/3*(1+2^(1/3)*(1-x)/(-x^3+1)^(1/3))*3^(1/2))*3^(1/2)*2^(2/3),1],
[(-x^3+1)^(2/3)/(x^3+1),x,3,-1/6*ln(x^3+1)*2^(2/3)+1/2*ln(-2^(1/3)*x-(-x^3+1)^(1/3))*2^(2/3)-1/2*ln(x+(-x^3+1)^(1/3))+1/3*arctan(1/3*(1-2*x/(-x^3+1)^(1/3))*3^(1/2))*3^(1/2)-1/3*arctan(1/3*(1-2*2^(1/3)*x/(-x^3+1)^(1/3))*3^(1/2))*2^(2/3)*3^(1/2),1],
[x*(-x^3+1)^(2/3)/(x^3+1),x,10,-1/2*x^2*hypergeom([1/3, 2/3],[5/3],x^3)+1/12*ln((1-x)*(1+x)^2)*2^(2/3)+1/6*ln(1+2^(2/3)*(1-x)^2/(-x^3+1)^(2/3)-2^(1/3)*(1-x)/(-x^3+1)^(1/3))*2^(2/3)-1/3*ln(1+2^(1/3)*(1-x)/(-x^3+1)^(1/3))*2^(2/3)-1/4*ln(-1+x+2^(2/3)*(-x^3+1)^(1/3))*2^(2/3)+1/3*arctan(1/3*(1-2*2^(1/3)*(1-x)/(-x^3+1)^(1/3))*3^(1/2))*2^(2/3)*3^(1/2)+1/6*arctan(1/3*(1+2^(1/3)*(1-x)/(-x^3+1)^(1/3))*3^(1/2))*3^(1/2)*2^(2/3),1],
[(1-x)*(-x^3+1)^(2/3)/(x^3+1),x,-17,1/2*x^2*hypergeom([1/3, 2/3],[5/3],x^3)-1/12*ln((1-x)*(1+x)^2)*2^(2/3)-1/6*ln(x^3+1)*2^(2/3)-1/6*ln(1+2^(2/3)*(1-x)^2/(-x^3+1)^(2/3)-2^(1/3)*(1-x)/(-x^3+1)^(1/3))*2^(2/3)+1/3*ln(1+2^(1/3)*(1-x)/(-x^3+1)^(1/3))*2^(2/3)+1/2*ln(-2^(1/3)*x-(-x^3+1)^(1/3))*2^(2/3)-1/2*ln(x+(-x^3+1)^(1/3))+1/4*ln(-1+x+2^(2/3)*(-x^3+1)^(1/3))*2^(2/3)-1/3*arctan(1/3*(1-2*2^(1/3)*(1-x)/(-x^3+1)^(1/3))*3^(1/2))*2^(2/3)*3^(1/2)-1/6*arctan(1/3*(1+2^(1/3)*(1-x)/(-x^3+1)^(1/3))*3^(1/2))*3^(1/2)*2^(2/3)+1/3*arctan(1/3*(1-2*x/(-x^3+1)^(1/3))*3^(1/2))*3^(1/2)-1/3*arctan(1/3*(1-2*2^(1/3)*x/(-x^3+1)^(1/3))*3^(1/2))*2^(2/3)*3^(1/2),1],
[(-x^3+1)^(1/3)/(x^3+1),x,14,1/6*ln(2^(2/3)+(-1+x)/(-x^3+1)^(1/3))*2^(1/3)-1/6*ln(1+2^(2/3)*(1-x)^2/(-x^3+1)^(2/3)-2^(1/3)*(1-x)/(-x^3+1)^(1/3))*2^(1/3)+1/3*2^(1/3)*ln(1+2^(1/3)*(1-x)/(-x^3+1)^(1/3))-1/12*ln(2*2^(1/3)+(1-x)^2/(-x^3+1)^(2/3)+2^(2/3)*(1-x)/(-x^3+1)^(1/3))*2^(1/3)+1/3*2^(1/3)*arctan(1/3*(1-2*2^(1/3)*(1-x)/(-x^3+1)^(1/3))*3^(1/2))*3^(1/2)+1/6*arctan(1/3*(1+2^(1/3)*(1-x)/(-x^3+1)^(1/3))*3^(1/2))*2^(1/3)*3^(1/2),1], // Wester
[(-5+3*x)^2/(-1+2*x)^(7/2),x,2,-49/20/(-1+2*x)^(5/2)+7/2/(-1+2*x)^(3/2)-9/4/sqrt(-1+2*x),1],
[1/(-5/exp(m*x)+2*exp(m*x)),x,2,-arctanh(sqrt(2/5)*exp(m*x))/sqrt(10)/m,1],
[1/(a+b*cos(x)),x,2,2*arctan(sqrt(a-b)*tan(1/2*x)/sqrt(a+b))/sqrt(a-b)/sqrt(a+b),1],
[1/(3+3*cos(x)+4*sin(x)),x,2,1/4*ln(3+4*tan(1/2*x)),1],
[1/(4+3*cos(x)+4*sin(x)),x,2,-1/3*ln(4+3*cot(1/4*Pi+1/2*x)),1],
[1/(5+3*cos(x)+4*sin(x)),x,1,-1/(2+tan(1/2*x)),1],
[1/(6+3*cos(x)+4*sin(x)),x,3,x/sqrt(11)+2*arctan((4*cos(x)-3*sin(x))/(6+sqrt(11)+3*cos(x)+4*sin(x)))/sqrt(11),1],
[1/2*ln((-a^2+x^2)^2),x,4,-2*x+2*a*arctanh(x/a)+1/2*x*ln((-a^2+x^2)^2),1]
]:;        

read("chkint"):;        