lst:=[[x^2*(b*x^3+a*x),x,3,1/4*a*x^4+1/6*b*x^6,1],
[x*(b*x^3+a*x),x,3,1/3*a*x^3+1/5*b*x^5,1],
[b*x^3+a*x,x,1,1/2*a*x^2+1/4*b*x^4,1],
[(b*x^3+a*x)/x,x,2,a*x+1/3*b*x^3,1],
[(b*x^3+a*x)/x^2,x,3,1/2*b*x^2+a*ln(x),1],
[(b*x^3+a*x)/x^3,x,3,-a/x+b*x,1],
[(b*x^3+a*x)/x^4,x,3,-1/2*a/x^2+b*ln(x),1],
[(b*x^3+a*x)/x^5,x,3,-1/3*a/x^3-b/x,1],
[x^2*(b*x^3+a*x)^2,x,3,1/5*a^2*x^5+2/7*a*b*x^7+1/9*b^2*x^9,1],
[x*(b*x^3+a*x)^2,x,4,1/4*a^2*x^4+1/3*a*b*x^6+1/8*b^2*x^8,1],
[(b*x^3+a*x)^2,x,3,1/3*a^2*x^3+2/5*a*b*x^5+1/7*b^2*x^7,1],
[(b*x^3+a*x)^2/x,x,2,1/6*(b*x^2+a)^3/b,1],
[(b*x^3+a*x)^2/x^2,x,3,a^2*x+2/3*a*b*x^3+1/5*b^2*x^5,1],
[(b*x^3+a*x)^2/x^3,x,4,a*b*x^2+1/4*b^2*x^4+a^2*ln(x),1],
[(b*x^3+a*x)^2/x^4,x,3,-a^2/x+2*a*b*x+1/3*b^2*x^3,1],
[(b*x^3+a*x)^2/x^5,x,4,-1/2*a^2/x^2+1/2*b^2*x^2+2*a*b*ln(x),1],
[(b*x^3+a*x)^2/x^6,x,3,-1/3*a^2/x^3-2*a*b/x+b^2*x,1],
[(3*x^3-4*x)^6,x,3,4096/7*x^7-2048*x^9+34560/11*x^11-34560/13*x^13+1296*x^15-5832/17*x^17+729/19*x^19,1],
[x^4/(b*x^3+a*x),x,4,1/2*x^2/b-1/2*a*ln(b*x^2+a)/b^2,1],
[x^3/(b*x^3+a*x),x,3,x/b-sqrt(a)*arctan(sqrt(b)*x/sqrt(a))/b^(3/2),1],
[x^2/(b*x^3+a*x),x,2,1/2*ln(b*x^2+a)/b,1],
[x/(b*x^3+a*x),x,2,arctan(sqrt(b)*x/sqrt(a))/sqrt(a)/sqrt(b),1],
[1/(b*x^3+a*x),x,4,ln(x)/a-1/2*ln(b*x^2+a)/a,1],
[1/x/(b*x^3+a*x),x,3,-1/a/x-sqrt(b)*arctan(sqrt(b)*x/sqrt(a))/a^(3/2),1],
[1/x^2/(b*x^3+a*x),x,4,-1/2/a/x^2-b*ln(x)/a^2+1/2*b*ln(b*x^2+a)/a^2,1],
[1/x^3/(b*x^3+a*x),x,4,-1/3/a/x^3+b/a^2/x+b^(3/2)*arctan(sqrt(b)*x/sqrt(a))/a^(5/2),1],
[1/x^4/(b*x^3+a*x),x,4,-1/4/a/x^4+1/2*b/a^2/x^2+b^2*ln(x)/a^3-1/2*b^2*ln(b*x^2+a)/a^3,1],
[x^2/(b*x^3+a*x)^2,x,3,1/2*x/a/(b*x^2+a)+1/2*arctan(sqrt(b)*x/sqrt(a))/a^(3/2)/sqrt(b),1],
[x/(b*x^3+a*x)^2,x,4,1/2/a/(b*x^2+a)+ln(x)/a^2-1/2*ln(b*x^2+a)/a^2,1],
[1/(b*x^3+a*x)^2,x,4,-1/a^2/x-1/2*b*x/a^2/(b*x^2+a)-3/2*sqrt(b)*arctan(sqrt(b)*x/sqrt(a))/a^(5/2),1],
[1/x/(b*x^3+a*x)^2,x,4,-1/2/a^2/x^2-1/2*b/a^2/(b*x^2+a)-2*b*ln(x)/a^3+b*ln(b*x^2+a)/a^3,1],
[1/x^2/(b*x^3+a*x)^2,x,5,-1/3/a^2/x^3+2*b/a^3/x+1/2*b^2*x/a^3/(b*x^2+a)+5/2*b^(3/2)*arctan(sqrt(b)*x/sqrt(a))/a^(7/2),1],
[x^5/(-x^3+x),x,4,-x-1/3*x^3+arctanh(x),1],
[x^4/(-x^3+x),x,4,-1/2*x^2-1/2*ln(-x^2+1),1],
[x^3/(-x^3+x),x,3,-x+arctanh(x),1],
[x^2/(-x^3+x),x,2,-1/2*ln(-x^2+1),1],
[x/(-x^3+x),x,2,arctanh(x),1],
[1/(-x^3+x),x,4,ln(x)-1/2*ln(-x^2+1),1],
[1/x/(-x^3+x),x,3,-1/x+arctanh(x),1],
[1/x^2/(-x^3+x),x,4,-1/2/x^2+ln(x)-1/2*ln(-x^2+1),1],
[1/x^3/(-x^3+x),x,4,-1/3/x^3-1/x+arctanh(x),1],
[1/x^4/(-x^3+x),x,4,-1/4/x^4-1/2/x^2+ln(x)-1/2*ln(-x^2+1),1],
[1/(b*x^3+x),x,4,ln(x)-1/2*ln(b*x^2+1),1],
[1/(b*x^3-x),x,4,-ln(x)+1/2*ln(-b*x^2+1),1],
[x^3*sqrt(b*x^3+a*x),x,6,-20/231*a^2*sqrt(b*x^3+a*x)/b^2+4/77*a*x^2*sqrt(b*x^3+a*x)/b+2/11*x^4*sqrt(b*x^3+a*x)+10/231*a^(11/4)*sqrt(x)*(sqrt(a)+sqrt(b)*x)*sqrt((b*x^2+a)/(sqrt(a)+sqrt(b)*x)^2)*InverseJacobiAM(2*arctan(b^(1/4)*sqrt(x)/a^(1/4)),sqrt(1/2))/b^(9/4)/sqrt(b*x^3+a*x),1],
[x^2*sqrt(b*x^3+a*x),x,8,-4/15*a^2*x*(b*x^2+a)/b^(3/2)/(sqrt(a)+sqrt(b)*x)/sqrt(b*x^3+a*x)+4/45*a*x*sqrt(b*x^3+a*x)/b+2/9*x^3*sqrt(b*x^3+a*x)+4/15*a^(9/4)*sqrt(x)*(sqrt(a)+sqrt(b)*x)*sqrt((b*x^2+a)/(sqrt(a)+sqrt(b)*x)^2)*EllipticE(sin(2*arctan(b^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))/b^(7/4)/sqrt(b*x^3+a*x)-2/15*a^(9/4)*sqrt(x)*(sqrt(a)+sqrt(b)*x)*sqrt((b*x^2+a)/(sqrt(a)+sqrt(b)*x)^2)*InverseJacobiAM(2*arctan(b^(1/4)*sqrt(x)/a^(1/4)),sqrt(1/2))/b^(7/4)/sqrt(b*x^3+a*x),1],
[x*sqrt(b*x^3+a*x),x,5,4/21*a*sqrt(b*x^3+a*x)/b+2/7*x^2*sqrt(b*x^3+a*x)-2/21*a^(7/4)*sqrt(x)*(sqrt(a)+sqrt(b)*x)*sqrt((b*x^2+a)/(sqrt(a)+sqrt(b)*x)^2)*InverseJacobiAM(2*arctan(b^(1/4)*sqrt(x)/a^(1/4)),sqrt(1/2))/b^(5/4)/sqrt(b*x^3+a*x),1],
[sqrt(b*x^3+a*x),x,7,4/5*a*x*(b*x^2+a)/sqrt(b)/(sqrt(a)+sqrt(b)*x)/sqrt(b*x^3+a*x)+2/5*x*sqrt(b*x^3+a*x)-4/5*a^(5/4)*sqrt(x)*(sqrt(a)+sqrt(b)*x)*sqrt((b*x^2+a)/(sqrt(a)+sqrt(b)*x)^2)*EllipticE(sin(2*arctan(b^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))/b^(3/4)/sqrt(b*x^3+a*x)+2/5*a^(5/4)*sqrt(x)*(sqrt(a)+sqrt(b)*x)*sqrt((b*x^2+a)/(sqrt(a)+sqrt(b)*x)^2)*InverseJacobiAM(2*arctan(b^(1/4)*sqrt(x)/a^(1/4)),sqrt(1/2))/b^(3/4)/sqrt(b*x^3+a*x),1],
[sqrt(b*x^3+a*x)/x,x,4,2/3*sqrt(b*x^3+a*x)+2/3*a^(3/4)*sqrt(x)*(sqrt(a)+sqrt(b)*x)*sqrt((b*x^2+a)/(sqrt(a)+sqrt(b)*x)^2)*InverseJacobiAM(2*arctan(b^(1/4)*sqrt(x)/a^(1/4)),sqrt(1/2))/b^(1/4)/sqrt(b*x^3+a*x),1],
[sqrt(b*x^3+a*x)/x^2,x,7,4*sqrt(b)*x*(b*x^2+a)/(sqrt(a)+sqrt(b)*x)/sqrt(b*x^3+a*x)-2*sqrt(b*x^3+a*x)/x-4*a^(1/4)*b^(1/4)*sqrt(x)*(sqrt(a)+sqrt(b)*x)*sqrt((b*x^2+a)/(sqrt(a)+sqrt(b)*x)^2)*EllipticE(sin(2*arctan(b^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))/sqrt(b*x^3+a*x)+2*a^(1/4)*b^(1/4)*sqrt(x)*(sqrt(a)+sqrt(b)*x)*sqrt((b*x^2+a)/(sqrt(a)+sqrt(b)*x)^2)*InverseJacobiAM(2*arctan(b^(1/4)*sqrt(x)/a^(1/4)),sqrt(1/2))/sqrt(b*x^3+a*x),1],
[sqrt(b*x^3+a*x)/x^3,x,4,-2/3*sqrt(b*x^3+a*x)/x^2+2/3*b^(3/4)*sqrt(x)*(sqrt(a)+sqrt(b)*x)*sqrt((b*x^2+a)/(sqrt(a)+sqrt(b)*x)^2)*InverseJacobiAM(2*arctan(b^(1/4)*sqrt(x)/a^(1/4)),sqrt(1/2))/a^(1/4)/sqrt(b*x^3+a*x),1],
[sqrt(b*x^3+a*x)/x^4,x,8,4/5*b^(3/2)*x*(b*x^2+a)/a/(sqrt(a)+sqrt(b)*x)/sqrt(b*x^3+a*x)-2/5*sqrt(b*x^3+a*x)/x^3-4/5*b*sqrt(b*x^3+a*x)/a/x-4/5*b^(5/4)*sqrt(x)*(sqrt(a)+sqrt(b)*x)*sqrt((b*x^2+a)/(sqrt(a)+sqrt(b)*x)^2)*EllipticE(sin(2*arctan(b^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))/a^(3/4)/sqrt(b*x^3+a*x)+2/5*b^(5/4)*sqrt(x)*(sqrt(a)+sqrt(b)*x)*sqrt((b*x^2+a)/(sqrt(a)+sqrt(b)*x)^2)*InverseJacobiAM(2*arctan(b^(1/4)*sqrt(x)/a^(1/4)),sqrt(1/2))/a^(3/4)/sqrt(b*x^3+a*x),1],
[x^2*(b*x^3+a*x)^(3/2),x,7,-8/231*a^3*sqrt(b*x^3+a*x)/b^2+8/385*a^2*x^2*sqrt(b*x^3+a*x)/b+4/55*a*x^4*sqrt(b*x^3+a*x)+2/15*x^3*(b*x^3+a*x)^(3/2)+4/231*a^(15/4)*sqrt(x)*(sqrt(a)+sqrt(b)*x)*sqrt((b*x^2+a)/(sqrt(a)+sqrt(b)*x)^2)*InverseJacobiAM(2*arctan(b^(1/4)*sqrt(x)/a^(1/4)),sqrt(1/2))/b^(9/4)/sqrt(b*x^3+a*x),1],
[x*(b*x^3+a*x)^(3/2),x,9,-8/65*a^3*x*(b*x^2+a)/b^(3/2)/(sqrt(a)+sqrt(b)*x)/sqrt(b*x^3+a*x)+8/195*a^2*x*sqrt(b*x^3+a*x)/b+4/39*a*x^3*sqrt(b*x^3+a*x)+2/13*x^2*(b*x^3+a*x)^(3/2)+8/65*a^(13/4)*sqrt(x)*(sqrt(a)+sqrt(b)*x)*sqrt((b*x^2+a)/(sqrt(a)+sqrt(b)*x)^2)*EllipticE(sin(2*arctan(b^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))/b^(7/4)/sqrt(b*x^3+a*x)-4/65*a^(13/4)*sqrt(x)*(sqrt(a)+sqrt(b)*x)*sqrt((b*x^2+a)/(sqrt(a)+sqrt(b)*x)^2)*InverseJacobiAM(2*arctan(b^(1/4)*sqrt(x)/a^(1/4)),sqrt(1/2))/b^(7/4)/sqrt(b*x^3+a*x),1],
[(b*x^3+a*x)^(3/2),x,6,8/77*a^2*sqrt(b*x^3+a*x)/b+12/77*a*x^2*sqrt(b*x^3+a*x)+2/11*x*(b*x^3+a*x)^(3/2)-4/77*a^(11/4)*sqrt(x)*(sqrt(a)+sqrt(b)*x)*sqrt((b*x^2+a)/(sqrt(a)+sqrt(b)*x)^2)*InverseJacobiAM(2*arctan(b^(1/4)*sqrt(x)/a^(1/4)),sqrt(1/2))/b^(5/4)/sqrt(b*x^3+a*x),1],
[(b*x^3+a*x)^(3/2)/x,x,8,8/15*a^2*x*(b*x^2+a)/sqrt(b)/(sqrt(a)+sqrt(b)*x)/sqrt(b*x^3+a*x)+4/15*a*x*sqrt(b*x^3+a*x)+2/9*(b*x^3+a*x)^(3/2)-8/15*a^(9/4)*sqrt(x)*(sqrt(a)+sqrt(b)*x)*sqrt((b*x^2+a)/(sqrt(a)+sqrt(b)*x)^2)*EllipticE(sin(2*arctan(b^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))/b^(3/4)/sqrt(b*x^3+a*x)+4/15*a^(9/4)*sqrt(x)*(sqrt(a)+sqrt(b)*x)*sqrt((b*x^2+a)/(sqrt(a)+sqrt(b)*x)^2)*InverseJacobiAM(2*arctan(b^(1/4)*sqrt(x)/a^(1/4)),sqrt(1/2))/b^(3/4)/sqrt(b*x^3+a*x),1],
[(b*x^3+a*x)^(3/2)/x^2,x,5,4/7*a*sqrt(b*x^3+a*x)+2/7*(b*x^3+a*x)^(3/2)/x+4/7*a^(7/4)*sqrt(x)*(sqrt(a)+sqrt(b)*x)*sqrt((b*x^2+a)/(sqrt(a)+sqrt(b)*x)^2)*InverseJacobiAM(2*arctan(b^(1/4)*sqrt(x)/a^(1/4)),sqrt(1/2))/b^(1/4)/sqrt(b*x^3+a*x),1],
[(b*x^3+a*x)^(3/2)/x^3,x,8,24/5*a*sqrt(b)*x*(b*x^2+a)/(sqrt(a)+sqrt(b)*x)/sqrt(b*x^3+a*x)+12/5*b*x*sqrt(b*x^3+a*x)-2*(b*x^3+a*x)^(3/2)/x^2-24/5*a^(5/4)*b^(1/4)*sqrt(x)*(sqrt(a)+sqrt(b)*x)*sqrt((b*x^2+a)/(sqrt(a)+sqrt(b)*x)^2)*EllipticE(sin(2*arctan(b^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))/sqrt(b*x^3+a*x)+12/5*a^(5/4)*b^(1/4)*sqrt(x)*(sqrt(a)+sqrt(b)*x)*sqrt((b*x^2+a)/(sqrt(a)+sqrt(b)*x)^2)*InverseJacobiAM(2*arctan(b^(1/4)*sqrt(x)/a^(1/4)),sqrt(1/2))/sqrt(b*x^3+a*x),1],
[(b*x^3+a*x)^(3/2)/x^4,x,5,4/3*b*sqrt(b*x^3+a*x)-2/3*(b*x^3+a*x)^(3/2)/x^3+4/3*a^(3/4)*b^(3/4)*sqrt(x)*(sqrt(a)+sqrt(b)*x)*sqrt((b*x^2+a)/(sqrt(a)+sqrt(b)*x)^2)*InverseJacobiAM(2*arctan(b^(1/4)*sqrt(x)/a^(1/4)),sqrt(1/2))/sqrt(b*x^3+a*x),1],
[(b*x^3+a*x)^(3/2)/x^5,x,8,24/5*b^(3/2)*x*(b*x^2+a)/(sqrt(a)+sqrt(b)*x)/sqrt(b*x^3+a*x)-12/5*b*sqrt(b*x^3+a*x)/x-2/5*(b*x^3+a*x)^(3/2)/x^4-24/5*a^(1/4)*b^(5/4)*sqrt(x)*(sqrt(a)+sqrt(b)*x)*sqrt((b*x^2+a)/(sqrt(a)+sqrt(b)*x)^2)*EllipticE(sin(2*arctan(b^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))/sqrt(b*x^3+a*x)+12/5*a^(1/4)*b^(5/4)*sqrt(x)*(sqrt(a)+sqrt(b)*x)*sqrt((b*x^2+a)/(sqrt(a)+sqrt(b)*x)^2)*InverseJacobiAM(2*arctan(b^(1/4)*sqrt(x)/a^(1/4)),sqrt(1/2))/sqrt(b*x^3+a*x),1],
[(b*x^3+a*x)^(3/2)/x^6,x,5,-4/7*b*sqrt(b*x^3+a*x)/x^2-2/7*(b*x^3+a*x)^(3/2)/x^5+4/7*b^(7/4)*sqrt(x)*(sqrt(a)+sqrt(b)*x)*sqrt((b*x^2+a)/(sqrt(a)+sqrt(b)*x)^2)*InverseJacobiAM(2*arctan(b^(1/4)*sqrt(x)/a^(1/4)),sqrt(1/2))/a^(1/4)/sqrt(b*x^3+a*x),1],
[(b*x^3+a*x)^(3/2)/x^7,x,9,8/15*b^(5/2)*x*(b*x^2+a)/a/(sqrt(a)+sqrt(b)*x)/sqrt(b*x^3+a*x)-4/15*b*sqrt(b*x^3+a*x)/x^3-8/15*b^2*sqrt(b*x^3+a*x)/a/x-2/9*(b*x^3+a*x)^(3/2)/x^6-8/15*b^(9/4)*sqrt(x)*(sqrt(a)+sqrt(b)*x)*sqrt((b*x^2+a)/(sqrt(a)+sqrt(b)*x)^2)*EllipticE(sin(2*arctan(b^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))/a^(3/4)/sqrt(b*x^3+a*x)+4/15*b^(9/4)*sqrt(x)*(sqrt(a)+sqrt(b)*x)*sqrt((b*x^2+a)/(sqrt(a)+sqrt(b)*x)^2)*InverseJacobiAM(2*arctan(b^(1/4)*sqrt(x)/a^(1/4)),sqrt(1/2))/a^(3/4)/sqrt(b*x^3+a*x),1],
[(b*x^3+a*x)^(3/2)/x^8,x,6,-12/77*b*sqrt(b*x^3+a*x)/x^4-8/77*b^2*sqrt(b*x^3+a*x)/a/x^2-2/11*(b*x^3+a*x)^(3/2)/x^7-4/77*b^(11/4)*sqrt(x)*(sqrt(a)+sqrt(b)*x)*sqrt((b*x^2+a)/(sqrt(a)+sqrt(b)*x)^2)*InverseJacobiAM(2*arctan(b^(1/4)*sqrt(x)/a^(1/4)),sqrt(1/2))/a^(5/4)/sqrt(b*x^3+a*x),1],
[x^4/sqrt(b*x^3+a*x),x,5,-10/21*a*sqrt(b*x^3+a*x)/b^2+2/7*x^2*sqrt(b*x^3+a*x)/b+5/21*a^(7/4)*sqrt(x)*(sqrt(a)+sqrt(b)*x)*sqrt((b*x^2+a)/(sqrt(a)+sqrt(b)*x)^2)*InverseJacobiAM(2*arctan(b^(1/4)*sqrt(x)/a^(1/4)),sqrt(1/2))/b^(9/4)/sqrt(b*x^3+a*x),1],
[x^3/sqrt(b*x^3+a*x),x,7,-6/5*a*x*(b*x^2+a)/b^(3/2)/(sqrt(a)+sqrt(b)*x)/sqrt(b*x^3+a*x)+2/5*x*sqrt(b*x^3+a*x)/b+6/5*a^(5/4)*sqrt(x)*(sqrt(a)+sqrt(b)*x)*sqrt((b*x^2+a)/(sqrt(a)+sqrt(b)*x)^2)*EllipticE(sin(2*arctan(b^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))/b^(7/4)/sqrt(b*x^3+a*x)-3/5*a^(5/4)*sqrt(x)*(sqrt(a)+sqrt(b)*x)*sqrt((b*x^2+a)/(sqrt(a)+sqrt(b)*x)^2)*InverseJacobiAM(2*arctan(b^(1/4)*sqrt(x)/a^(1/4)),sqrt(1/2))/b^(7/4)/sqrt(b*x^3+a*x),1],
[x^2/sqrt(b*x^3+a*x),x,4,2/3*sqrt(b*x^3+a*x)/b-1/3*a^(3/4)*sqrt(x)*(sqrt(a)+sqrt(b)*x)*sqrt((b*x^2+a)/(sqrt(a)+sqrt(b)*x)^2)*InverseJacobiAM(2*arctan(b^(1/4)*sqrt(x)/a^(1/4)),sqrt(1/2))/b^(5/4)/sqrt(b*x^3+a*x),1],
[x/sqrt(b*x^3+a*x),x,6,2*x*(b*x^2+a)/sqrt(b)/(sqrt(a)+sqrt(b)*x)/sqrt(b*x^3+a*x)-2*a^(1/4)*sqrt(x)*(sqrt(a)+sqrt(b)*x)*sqrt((b*x^2+a)/(sqrt(a)+sqrt(b)*x)^2)*EllipticE(sin(2*arctan(b^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))/b^(3/4)/sqrt(b*x^3+a*x)+a^(1/4)*sqrt(x)*(sqrt(a)+sqrt(b)*x)*sqrt((b*x^2+a)/(sqrt(a)+sqrt(b)*x)^2)*InverseJacobiAM(2*arctan(b^(1/4)*sqrt(x)/a^(1/4)),sqrt(1/2))/b^(3/4)/sqrt(b*x^3+a*x),1],
[1/sqrt(b*x^3+a*x),x,3,sqrt(x)*(sqrt(a)+sqrt(b)*x)*sqrt((b*x^2+a)/(sqrt(a)+sqrt(b)*x)^2)*InverseJacobiAM(2*arctan(b^(1/4)*sqrt(x)/a^(1/4)),sqrt(1/2))/a^(1/4)/b^(1/4)/sqrt(b*x^3+a*x),1],
[1/x/sqrt(b*x^3+a*x),x,7,2*sqrt(b)*x*(b*x^2+a)/a/(sqrt(a)+sqrt(b)*x)/sqrt(b*x^3+a*x)-2*sqrt(b*x^3+a*x)/a/x-2*b^(1/4)*sqrt(x)*(sqrt(a)+sqrt(b)*x)*sqrt((b*x^2+a)/(sqrt(a)+sqrt(b)*x)^2)*EllipticE(sin(2*arctan(b^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))/a^(3/4)/sqrt(b*x^3+a*x)+b^(1/4)*sqrt(x)*(sqrt(a)+sqrt(b)*x)*sqrt((b*x^2+a)/(sqrt(a)+sqrt(b)*x)^2)*InverseJacobiAM(2*arctan(b^(1/4)*sqrt(x)/a^(1/4)),sqrt(1/2))/a^(3/4)/sqrt(b*x^3+a*x),1],
[1/x^2/sqrt(b*x^3+a*x),x,4,-2/3*sqrt(b*x^3+a*x)/a/x^2-1/3*b^(3/4)*sqrt(x)*(sqrt(a)+sqrt(b)*x)*sqrt((b*x^2+a)/(sqrt(a)+sqrt(b)*x)^2)*InverseJacobiAM(2*arctan(b^(1/4)*sqrt(x)/a^(1/4)),sqrt(1/2))/a^(5/4)/sqrt(b*x^3+a*x),1],
[1/x^3/sqrt(b*x^3+a*x),x,8,-6/5*b^(3/2)*x*(b*x^2+a)/a^2/(sqrt(a)+sqrt(b)*x)/sqrt(b*x^3+a*x)-2/5*sqrt(b*x^3+a*x)/a/x^3+6/5*b*sqrt(b*x^3+a*x)/a^2/x+6/5*b^(5/4)*sqrt(x)*(sqrt(a)+sqrt(b)*x)*sqrt((b*x^2+a)/(sqrt(a)+sqrt(b)*x)^2)*EllipticE(sin(2*arctan(b^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))/a^(7/4)/sqrt(b*x^3+a*x)-3/5*b^(5/4)*sqrt(x)*(sqrt(a)+sqrt(b)*x)*sqrt((b*x^2+a)/(sqrt(a)+sqrt(b)*x)^2)*InverseJacobiAM(2*arctan(b^(1/4)*sqrt(x)/a^(1/4)),sqrt(1/2))/a^(7/4)/sqrt(b*x^3+a*x),1],
[x^7/(b*x^3+a*x)^(3/2),x,6,-x^5/b/sqrt(b*x^3+a*x)-15/7*a*sqrt(b*x^3+a*x)/b^3+9/7*x^2*sqrt(b*x^3+a*x)/b^2+15/14*a^(7/4)*sqrt(x)*(sqrt(a)+sqrt(b)*x)*sqrt((b*x^2+a)/(sqrt(a)+sqrt(b)*x)^2)*InverseJacobiAM(2*arctan(b^(1/4)*sqrt(x)/a^(1/4)),sqrt(1/2))/b^(13/4)/sqrt(b*x^3+a*x),1],
[x^6/(b*x^3+a*x)^(3/2),x,8,-x^4/b/sqrt(b*x^3+a*x)-21/5*a*x*(b*x^2+a)/b^(5/2)/(sqrt(a)+sqrt(b)*x)/sqrt(b*x^3+a*x)+7/5*x*sqrt(b*x^3+a*x)/b^2+21/5*a^(5/4)*sqrt(x)*(sqrt(a)+sqrt(b)*x)*sqrt((b*x^2+a)/(sqrt(a)+sqrt(b)*x)^2)*EllipticE(sin(2*arctan(b^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))/b^(11/4)/sqrt(b*x^3+a*x)-21/10*a^(5/4)*sqrt(x)*(sqrt(a)+sqrt(b)*x)*sqrt((b*x^2+a)/(sqrt(a)+sqrt(b)*x)^2)*InverseJacobiAM(2*arctan(b^(1/4)*sqrt(x)/a^(1/4)),sqrt(1/2))/b^(11/4)/sqrt(b*x^3+a*x),1],
[x^5/(b*x^3+a*x)^(3/2),x,5,-x^3/b/sqrt(b*x^3+a*x)+5/3*sqrt(b*x^3+a*x)/b^2-5/6*a^(3/4)*sqrt(x)*(sqrt(a)+sqrt(b)*x)*sqrt((b*x^2+a)/(sqrt(a)+sqrt(b)*x)^2)*InverseJacobiAM(2*arctan(b^(1/4)*sqrt(x)/a^(1/4)),sqrt(1/2))/b^(9/4)/sqrt(b*x^3+a*x),1],
[x^4/(b*x^3+a*x)^(3/2),x,7,-x^2/b/sqrt(b*x^3+a*x)+3*x*(b*x^2+a)/b^(3/2)/(sqrt(a)+sqrt(b)*x)/sqrt(b*x^3+a*x)-3*a^(1/4)*sqrt(x)*(sqrt(a)+sqrt(b)*x)*sqrt((b*x^2+a)/(sqrt(a)+sqrt(b)*x)^2)*EllipticE(sin(2*arctan(b^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))/b^(7/4)/sqrt(b*x^3+a*x)+3/2*a^(1/4)*sqrt(x)*(sqrt(a)+sqrt(b)*x)*sqrt((b*x^2+a)/(sqrt(a)+sqrt(b)*x)^2)*InverseJacobiAM(2*arctan(b^(1/4)*sqrt(x)/a^(1/4)),sqrt(1/2))/b^(7/4)/sqrt(b*x^3+a*x),1],
[x^3/(b*x^3+a*x)^(3/2),x,4,-x/b/sqrt(b*x^3+a*x)+1/2*sqrt(x)*(sqrt(a)+sqrt(b)*x)*sqrt((b*x^2+a)/(sqrt(a)+sqrt(b)*x)^2)*InverseJacobiAM(2*arctan(b^(1/4)*sqrt(x)/a^(1/4)),sqrt(1/2))/a^(1/4)/b^(5/4)/sqrt(b*x^3+a*x),1],
[x^2/(b*x^3+a*x)^(3/2),x,7,x^2/a/sqrt(b*x^3+a*x)-x*(b*x^2+a)/a/sqrt(b)/(sqrt(a)+sqrt(b)*x)/sqrt(b*x^3+a*x)+sqrt(x)*(sqrt(a)+sqrt(b)*x)*sqrt((b*x^2+a)/(sqrt(a)+sqrt(b)*x)^2)*EllipticE(sin(2*arctan(b^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))/a^(3/4)/b^(3/4)/sqrt(b*x^3+a*x)-1/2*sqrt(x)*(sqrt(a)+sqrt(b)*x)*sqrt((b*x^2+a)/(sqrt(a)+sqrt(b)*x)^2)*InverseJacobiAM(2*arctan(b^(1/4)*sqrt(x)/a^(1/4)),sqrt(1/2))/a^(3/4)/b^(3/4)/sqrt(b*x^3+a*x),1],
[x/(b*x^3+a*x)^(3/2),x,4,x/a/sqrt(b*x^3+a*x)+1/2*sqrt(x)*(sqrt(a)+sqrt(b)*x)*sqrt((b*x^2+a)/(sqrt(a)+sqrt(b)*x)^2)*InverseJacobiAM(2*arctan(b^(1/4)*sqrt(x)/a^(1/4)),sqrt(1/2))/a^(5/4)/b^(1/4)/sqrt(b*x^3+a*x),1],
[1/(b*x^3+a*x)^(3/2),x,8,1/a/sqrt(b*x^3+a*x)+3*sqrt(b)*x*(b*x^2+a)/a^2/(sqrt(a)+sqrt(b)*x)/sqrt(b*x^3+a*x)-3*sqrt(b*x^3+a*x)/a^2/x-3*b^(1/4)*sqrt(x)*(sqrt(a)+sqrt(b)*x)*sqrt((b*x^2+a)/(sqrt(a)+sqrt(b)*x)^2)*EllipticE(sin(2*arctan(b^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))/a^(7/4)/sqrt(b*x^3+a*x)+3/2*b^(1/4)*sqrt(x)*(sqrt(a)+sqrt(b)*x)*sqrt((b*x^2+a)/(sqrt(a)+sqrt(b)*x)^2)*InverseJacobiAM(2*arctan(b^(1/4)*sqrt(x)/a^(1/4)),sqrt(1/2))/a^(7/4)/sqrt(b*x^3+a*x),1],
[1/x/(b*x^3+a*x)^(3/2),x,5,1/a/x/sqrt(b*x^3+a*x)-5/3*sqrt(b*x^3+a*x)/a^2/x^2-5/6*b^(3/4)*sqrt(x)*(sqrt(a)+sqrt(b)*x)*sqrt((b*x^2+a)/(sqrt(a)+sqrt(b)*x)^2)*InverseJacobiAM(2*arctan(b^(1/4)*sqrt(x)/a^(1/4)),sqrt(1/2))/a^(9/4)/sqrt(b*x^3+a*x),1],
[1/x^2/(b*x^3+a*x)^(3/2),x,9,1/a/x^2/sqrt(b*x^3+a*x)-21/5*b^(3/2)*x*(b*x^2+a)/a^3/(sqrt(a)+sqrt(b)*x)/sqrt(b*x^3+a*x)-7/5*sqrt(b*x^3+a*x)/a^2/x^3+21/5*b*sqrt(b*x^3+a*x)/a^3/x+21/5*b^(5/4)*sqrt(x)*(sqrt(a)+sqrt(b)*x)*sqrt((b*x^2+a)/(sqrt(a)+sqrt(b)*x)^2)*EllipticE(sin(2*arctan(b^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))/a^(11/4)/sqrt(b*x^3+a*x)-21/10*b^(5/4)*sqrt(x)*(sqrt(a)+sqrt(b)*x)*sqrt((b*x^2+a)/(sqrt(a)+sqrt(b)*x)^2)*InverseJacobiAM(2*arctan(b^(1/4)*sqrt(x)/a^(1/4)),sqrt(1/2))/a^(11/4)/sqrt(b*x^3+a*x),1],
[x^(29/2)/(b*x^3+a*x)^(9/2),x,7,-1/7*x^(25/2)/b/(b*x^3+a*x)^(7/2)-9/35*x^(19/2)/b^2/(b*x^3+a*x)^(5/2)-3/5*x^(13/2)/b^3/(b*x^3+a*x)^(3/2)-3*x^(7/2)/b^4/sqrt(b*x^3+a*x)+9/2*sqrt(x)*sqrt(b*x^3+a*x)/b^5-9/2*a*arctanh(sqrt(b)*x^(3/2)/sqrt(b*x^3+a*x))/b^(11/2),1],
[x^(27/2)/(b*x^3+a*x)^(9/2),x,5,-1/7*x^(23/2)/b/(b*x^3+a*x)^(7/2)-8/35*x^(17/2)/b^2/(b*x^3+a*x)^(5/2)-16/35*x^(11/2)/b^3/(b*x^3+a*x)^(3/2)-64/35*x^(5/2)/b^4/sqrt(b*x^3+a*x)+128/35*sqrt(b*x^3+a*x)/b^5/sqrt(x),1],
[x^(25/2)/(b*x^3+a*x)^(9/2),x,6,-1/7*x^(21/2)/b/(b*x^3+a*x)^(7/2)-1/5*x^(15/2)/b^2/(b*x^3+a*x)^(5/2)-1/3*x^(9/2)/b^3/(b*x^3+a*x)^(3/2)-x^(3/2)/b^4/sqrt(b*x^3+a*x)+arctanh(sqrt(b)*x^(3/2)/sqrt(b*x^3+a*x))/b^(9/2),1],
[x^(23/2)/(b*x^3+a*x)^(9/2),x,4,-1/7*x^(19/2)/b/(b*x^3+a*x)^(7/2)-6/35*x^(13/2)/b^2/(b*x^3+a*x)^(5/2)-8/35*x^(7/2)/b^3/(b*x^3+a*x)^(3/2)-16/35*sqrt(x)/b^4/sqrt(b*x^3+a*x),1],
[x^(21/2)/(b*x^3+a*x)^(9/2),x,1,1/7*x^(21/2)/a/(b*x^3+a*x)^(7/2),1],
[x^(19/2)/(b*x^3+a*x)^(9/2),x,3,-1/7*x^(15/2)/b/(b*x^3+a*x)^(7/2)-4/35*x^(9/2)/b^2/(b*x^3+a*x)^(5/2)-8/105*x^(3/2)/b^3/(b*x^3+a*x)^(3/2),1],
[x^(17/2)/(b*x^3+a*x)^(9/2),x,2,1/7*x^(17/2)/a/(b*x^3+a*x)^(7/2)+2/35*x^(15/2)/a^2/(b*x^3+a*x)^(5/2),1],
[x^(15/2)/(b*x^3+a*x)^(9/2),x,2,-1/7*x^(11/2)/b/(b*x^3+a*x)^(7/2)-2/35*x^(5/2)/b^2/(b*x^3+a*x)^(5/2),1],
[x^(13/2)/(b*x^3+a*x)^(9/2),x,3,1/7*x^(13/2)/a/(b*x^3+a*x)^(7/2)+4/35*x^(11/2)/a^2/(b*x^3+a*x)^(5/2)+8/105*x^(9/2)/a^3/(b*x^3+a*x)^(3/2),1],
[x^(11/2)/(b*x^3+a*x)^(9/2),x,1,-1/7*x^(7/2)/b/(b*x^3+a*x)^(7/2),1],
[x^(9/2)/(b*x^3+a*x)^(9/2),x,4,1/7*x^(9/2)/a/(b*x^3+a*x)^(7/2)+6/35*x^(7/2)/a^2/(b*x^3+a*x)^(5/2)+8/35*x^(5/2)/a^3/(b*x^3+a*x)^(3/2)+16/35*x^(3/2)/a^4/sqrt(b*x^3+a*x),1],
[x^(7/2)/(b*x^3+a*x)^(9/2),x,6,1/7*x^(7/2)/a/(b*x^3+a*x)^(7/2)+1/5*x^(5/2)/a^2/(b*x^3+a*x)^(5/2)+1/3*x^(3/2)/a^3/(b*x^3+a*x)^(3/2)+sqrt(x)/a^4/sqrt(b*x^3+a*x)-arctanh(sqrt(a)*sqrt(x)/sqrt(b*x^3+a*x))/a^(9/2),1],
[x^(5/2)/(b*x^3+a*x)^(9/2),x,5,1/7*x^(5/2)/a/(b*x^3+a*x)^(7/2)+8/35*x^(3/2)/a^2/(b*x^3+a*x)^(5/2)+16/35*sqrt(x)/a^3/(b*x^3+a*x)^(3/2)+64/35/a^4/sqrt(x)/sqrt(b*x^3+a*x)-128/35*sqrt(b*x^3+a*x)/a^5/x^(3/2),1],
[x^(3/2)/(b*x^3+a*x)^(9/2),x,7,1/7*x^(3/2)/a/(b*x^3+a*x)^(7/2)+9/35*sqrt(x)/a^2/(b*x^3+a*x)^(5/2)+3/5/a^3/sqrt(x)/(b*x^3+a*x)^(3/2)+3/a^4/x^(3/2)/sqrt(b*x^3+a*x)-9/2*sqrt(b*x^3+a*x)/a^5/x^(5/2)+9/2*b*arctanh(sqrt(a)*sqrt(x)/sqrt(b*x^3+a*x))/a^(11/2),1],
[sqrt(x)/(b*x^3+a*x)^(9/2),x,6,1/7*sqrt(x)/a/(b*x^3+a*x)^(7/2)+2/7/a^2/sqrt(x)/(b*x^3+a*x)^(5/2)+16/21/a^3/x^(3/2)/(b*x^3+a*x)^(3/2)+32/7/a^4/x^(5/2)/sqrt(b*x^3+a*x)-128/21*sqrt(b*x^3+a*x)/a^5/x^(7/2)+256/21*b*sqrt(b*x^3+a*x)/a^6/x^(3/2),1],
[1/sqrt(x)/(b*x^3+a*x)^(9/2),x,8,1/7/a/sqrt(x)/(b*x^3+a*x)^(7/2)+11/35/a^2/x^(3/2)/(b*x^3+a*x)^(5/2)+33/35/a^3/x^(5/2)/(b*x^3+a*x)^(3/2)+33/5/a^4/x^(7/2)/sqrt(b*x^3+a*x)-33/4*sqrt(b*x^3+a*x)/a^5/x^(9/2)+99/8*b*sqrt(b*x^3+a*x)/a^6/x^(5/2)-99/8*b^2*arctanh(sqrt(a)*sqrt(x)/sqrt(b*x^3+a*x))/a^(13/2),1],
[1/x^(3/2)/(b*x^3+a*x)^(9/2),x,7,1/7/a/x^(3/2)/(b*x^3+a*x)^(7/2)+12/35/a^2/x^(5/2)/(b*x^3+a*x)^(5/2)+8/7/a^3/x^(7/2)/(b*x^3+a*x)^(3/2)+64/7/a^4/x^(9/2)/sqrt(b*x^3+a*x)-384/35*sqrt(b*x^3+a*x)/a^5/x^(11/2)+512/35*b*sqrt(b*x^3+a*x)/a^6/x^(7/2)-1024/35*b^2*sqrt(b*x^3+a*x)/a^7/x^(3/2),1],
[x^4/sqrt(b*x^4+a*x),x,3,1/3*x*sqrt(b*x^4+a*x)/b-1/3*a*arctanh(sqrt(b)*x^2/sqrt(b*x^4+a*x))/b^(3/2),1],
[x/sqrt(b*x^4+a*x),x,2,2/3*arctanh(sqrt(b)*x^2/sqrt(b*x^4+a*x))/sqrt(b),1],
[1/x^2/sqrt(b*x^4+a*x),x,1,-2/3*sqrt(b*x^4+a*x)/a/x^2,1],
[1/x^5/sqrt(b*x^4+a*x),x,2,-2/9*sqrt(b*x^4+a*x)/a/x^5+4/9*b*sqrt(b*x^4+a*x)/a^2/x^2,1],
[1/x^8/sqrt(b*x^4+a*x),x,3,-2/15*sqrt(b*x^4+a*x)/a/x^8+8/45*b*sqrt(b*x^4+a*x)/a^2/x^5-16/45*b^2*sqrt(b*x^4+a*x)/a^3/x^2,1],
[x^3/sqrt(b*x^4+a*x),x,4,1/2*sqrt(b*x^4+a*x)/b-1/12*a^(2/3)*x*(a^(1/3)+b^(1/3)*x)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(1/3)+(1+sqrt(3))*b^(1/3)*x)^2)*InverseJacobiAM(arccos((a^(1/3)+(1-sqrt(3))*b^(1/3)*x)/(a^(1/3)+(1+sqrt(3))*b^(1/3)*x)),sqrt(1/2+1/4*sqrt(3)))*3^(3/4)/b/sqrt(b^(1/3)*x*(a^(1/3)+b^(1/3)*x)/(a^(1/3)+(1+sqrt(3))*b^(1/3)*x)^2)/sqrt(b*x^4+a*x),1],
[1/sqrt(b*x^4+a*x),x,3,1/3*x*(a^(1/3)+b^(1/3)*x)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(1/3)+(1+sqrt(3))*b^(1/3)*x)^2)*InverseJacobiAM(arccos((a^(1/3)+(1-sqrt(3))*b^(1/3)*x)/(a^(1/3)+(1+sqrt(3))*b^(1/3)*x)),sqrt(1/2+1/4*sqrt(3)))*3^(3/4)/a^(1/3)/sqrt(b^(1/3)*x*(a^(1/3)+b^(1/3)*x)/(a^(1/3)+(1+sqrt(3))*b^(1/3)*x)^2)/sqrt(b*x^4+a*x),1],
[1/x^3/sqrt(b*x^4+a*x),x,4,-2/5*sqrt(b*x^4+a*x)/a/x^3-2/15*b*x*(a^(1/3)+b^(1/3)*x)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(1/3)+(1+sqrt(3))*b^(1/3)*x)^2)*InverseJacobiAM(arccos((a^(1/3)+(1-sqrt(3))*b^(1/3)*x)/(a^(1/3)+(1+sqrt(3))*b^(1/3)*x)),sqrt(1/2+1/4*sqrt(3)))*3^(3/4)/a^(4/3)/sqrt(b^(1/3)*x*(a^(1/3)+b^(1/3)*x)/(a^(1/3)+(1+sqrt(3))*b^(1/3)*x)^2)/sqrt(b*x^4+a*x),1],
[x^5/sqrt(b*x^4+a*x),x,6,-5/8*(1+sqrt(3))*a*x*(b*x^3+a)/b^(5/3)/(a^(1/3)+(1+sqrt(3))*b^(1/3)*x)/sqrt(b*x^4+a*x)+1/4*x^2*sqrt(b*x^4+a*x)/b+5/8*3^(1/4)*a^(4/3)*x*(a^(1/3)+b^(1/3)*x)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(1/3)+(1+sqrt(3))*b^(1/3)*x)^2)*EllipticE(sin(arccos((a^(1/3)+(1-sqrt(3))*b^(1/3)*x)/(a^(1/3)+(1+sqrt(3))*b^(1/3)*x))),sqrt(1/2+1/4*sqrt(3)))/b^(5/3)/sqrt(b^(1/3)*x*(a^(1/3)+b^(1/3)*x)/(a^(1/3)+(1+sqrt(3))*b^(1/3)*x)^2)/sqrt(b*x^4+a*x)+5/48*(1-sqrt(3))*a^(4/3)*x*(a^(1/3)+b^(1/3)*x)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(1/3)+(1+sqrt(3))*b^(1/3)*x)^2)*InverseJacobiAM(arccos((a^(1/3)+(1-sqrt(3))*b^(1/3)*x)/(a^(1/3)+(1+sqrt(3))*b^(1/3)*x)),sqrt(1/2+1/4*sqrt(3)))*3^(3/4)/b^(5/3)/sqrt(b^(1/3)*x*(a^(1/3)+b^(1/3)*x)/(a^(1/3)+(1+sqrt(3))*b^(1/3)*x)^2)/sqrt(b*x^4+a*x),1],
[x^2/sqrt(b*x^4+a*x),x,5,(1+sqrt(3))*x*(b*x^3+a)/b^(2/3)/(a^(1/3)+(1+sqrt(3))*b^(1/3)*x)/sqrt(b*x^4+a*x)-3^(1/4)*a^(1/3)*x*(a^(1/3)+b^(1/3)*x)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(1/3)+(1+sqrt(3))*b^(1/3)*x)^2)*EllipticE(sin(arccos((a^(1/3)+(1-sqrt(3))*b^(1/3)*x)/(a^(1/3)+(1+sqrt(3))*b^(1/3)*x))),sqrt(1/2+1/4*sqrt(3)))/b^(2/3)/sqrt(b^(1/3)*x*(a^(1/3)+b^(1/3)*x)/(a^(1/3)+(1+sqrt(3))*b^(1/3)*x)^2)/sqrt(b*x^4+a*x)-1/6*(1-sqrt(3))*a^(1/3)*x*(a^(1/3)+b^(1/3)*x)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(1/3)+(1+sqrt(3))*b^(1/3)*x)^2)*InverseJacobiAM(arccos((a^(1/3)+(1-sqrt(3))*b^(1/3)*x)/(a^(1/3)+(1+sqrt(3))*b^(1/3)*x)),sqrt(1/2+1/4*sqrt(3)))*3^(3/4)/b^(2/3)/sqrt(b^(1/3)*x*(a^(1/3)+b^(1/3)*x)/(a^(1/3)+(1+sqrt(3))*b^(1/3)*x)^2)/sqrt(b*x^4+a*x),1],
[1/x/sqrt(b*x^4+a*x),x,6,2*(1+sqrt(3))*b^(1/3)*x*(b*x^3+a)/a/(a^(1/3)+(1+sqrt(3))*b^(1/3)*x)/sqrt(b*x^4+a*x)-2*sqrt(b*x^4+a*x)/a/x-2*3^(1/4)*b^(1/3)*x*(a^(1/3)+b^(1/3)*x)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(1/3)+(1+sqrt(3))*b^(1/3)*x)^2)*EllipticE(sin(arccos((a^(1/3)+(1-sqrt(3))*b^(1/3)*x)/(a^(1/3)+(1+sqrt(3))*b^(1/3)*x))),sqrt(1/2+1/4*sqrt(3)))/a^(2/3)/sqrt(b^(1/3)*x*(a^(1/3)+b^(1/3)*x)/(a^(1/3)+(1+sqrt(3))*b^(1/3)*x)^2)/sqrt(b*x^4+a*x)-1/3*(1-sqrt(3))*b^(1/3)*x*(a^(1/3)+b^(1/3)*x)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(1/3)+(1+sqrt(3))*b^(1/3)*x)^2)*InverseJacobiAM(arccos((a^(1/3)+(1-sqrt(3))*b^(1/3)*x)/(a^(1/3)+(1+sqrt(3))*b^(1/3)*x)),sqrt(1/2+1/4*sqrt(3)))*3^(3/4)/a^(2/3)/sqrt(b^(1/3)*x*(a^(1/3)+b^(1/3)*x)/(a^(1/3)+(1+sqrt(3))*b^(1/3)*x)^2)/sqrt(b*x^4+a*x),1],
[x^3*sqrt(b*x^(1/3)+a*x),x,11,-884/14421*b^6*sqrt(b*x^(1/3)+a*x)/a^6+884/24035*b^5*x^(2/3)*sqrt(b*x^(1/3)+a*x)/a^5-6188/216315*b^4*x^(4/3)*sqrt(b*x^(1/3)+a*x)/a^4+476/19665*b^3*x^2*sqrt(b*x^(1/3)+a*x)/a^3-28/1311*b^2*x^(8/3)*sqrt(b*x^(1/3)+a*x)/a^2+4/207*b*x^(10/3)*sqrt(b*x^(1/3)+a*x)/a+2/9*x^4*sqrt(b*x^(1/3)+a*x)+442/14421*b^(27/4)*(sqrt(b)+sqrt(a)*x^(1/3))*sqrt((b+a*x^(2/3))/(sqrt(b)+sqrt(a)*x^(1/3))^2)*x^(1/6)*InverseJacobiAM(2*arctan(a^(1/4)*x^(1/6)/b^(1/4)),sqrt(1/2))/a^(25/4)/sqrt(b*x^(1/3)+a*x),1],
[x^2*sqrt(b*x^(1/3)+a*x),x,12,44/221*b^5*(b+a*x^(2/3))*x^(1/3)/a^(9/2)/(sqrt(b)+sqrt(a)*x^(1/3))/sqrt(b*x^(1/3)+a*x)-44/663*b^4*x^(1/3)*sqrt(b*x^(1/3)+a*x)/a^4+220/4641*b^3*x*sqrt(b*x^(1/3)+a*x)/a^3-60/1547*b^2*x^(5/3)*sqrt(b*x^(1/3)+a*x)/a^2+4/119*b*x^(7/3)*sqrt(b*x^(1/3)+a*x)/a+2/7*x^3*sqrt(b*x^(1/3)+a*x)-44/221*b^(21/4)*(sqrt(b)+sqrt(a)*x^(1/3))*sqrt((b+a*x^(2/3))/(sqrt(b)+sqrt(a)*x^(1/3))^2)*x^(1/6)*EllipticE(sin(2*arctan(a^(1/4)*x^(1/6)/b^(1/4))),sqrt(1/2))/a^(19/4)/sqrt(b*x^(1/3)+a*x)+22/221*b^(21/4)*(sqrt(b)+sqrt(a)*x^(1/3))*sqrt((b+a*x^(2/3))/(sqrt(b)+sqrt(a)*x^(1/3))^2)*x^(1/6)*InverseJacobiAM(2*arctan(a^(1/4)*x^(1/6)/b^(1/4)),sqrt(1/2))/a^(19/4)/sqrt(b*x^(1/3)+a*x),1],
[x*sqrt(b*x^(1/3)+a*x),x,8,12/77*b^3*sqrt(b*x^(1/3)+a*x)/a^3-36/385*b^2*x^(2/3)*sqrt(b*x^(1/3)+a*x)/a^2+4/55*b*x^(4/3)*sqrt(b*x^(1/3)+a*x)/a+2/5*x^2*sqrt(b*x^(1/3)+a*x)-6/77*b^(15/4)*(sqrt(b)+sqrt(a)*x^(1/3))*sqrt((b+a*x^(2/3))/(sqrt(b)+sqrt(a)*x^(1/3))^2)*x^(1/6)*InverseJacobiAM(2*arctan(a^(1/4)*x^(1/6)/b^(1/4)),sqrt(1/2))/a^(13/4)/sqrt(b*x^(1/3)+a*x),1],
[sqrt(b*x^(1/3)+a*x),x,9,-4/5*b^2*(b+a*x^(2/3))*x^(1/3)/a^(3/2)/(sqrt(b)+sqrt(a)*x^(1/3))/sqrt(b*x^(1/3)+a*x)+4/15*b*x^(1/3)*sqrt(b*x^(1/3)+a*x)/a+2/3*x*sqrt(b*x^(1/3)+a*x)+4/5*b^(9/4)*(sqrt(b)+sqrt(a)*x^(1/3))*sqrt((b+a*x^(2/3))/(sqrt(b)+sqrt(a)*x^(1/3))^2)*x^(1/6)*EllipticE(sin(2*arctan(a^(1/4)*x^(1/6)/b^(1/4))),sqrt(1/2))/a^(7/4)/sqrt(b*x^(1/3)+a*x)-2/5*b^(9/4)*(sqrt(b)+sqrt(a)*x^(1/3))*sqrt((b+a*x^(2/3))/(sqrt(b)+sqrt(a)*x^(1/3))^2)*x^(1/6)*InverseJacobiAM(2*arctan(a^(1/4)*x^(1/6)/b^(1/4)),sqrt(1/2))/a^(7/4)/sqrt(b*x^(1/3)+a*x),1],
[sqrt(b*x^(1/3)+a*x)/x,x,5,2*sqrt(b*x^(1/3)+a*x)+2*b^(3/4)*(sqrt(b)+sqrt(a)*x^(1/3))*sqrt((b+a*x^(2/3))/(sqrt(b)+sqrt(a)*x^(1/3))^2)*x^(1/6)*InverseJacobiAM(2*arctan(a^(1/4)*x^(1/6)/b^(1/4)),sqrt(1/2))/a^(1/4)/sqrt(b*x^(1/3)+a*x),1],
[sqrt(b*x^(1/3)+a*x)/x^2,x,9,12/5*a^(3/2)*(b+a*x^(2/3))*x^(1/3)/b/(sqrt(b)+sqrt(a)*x^(1/3))/sqrt(b*x^(1/3)+a*x)-6/5*sqrt(b*x^(1/3)+a*x)/x-12/5*a*sqrt(b*x^(1/3)+a*x)/b/x^(1/3)-12/5*a^(5/4)*(sqrt(b)+sqrt(a)*x^(1/3))*sqrt((b+a*x^(2/3))/(sqrt(b)+sqrt(a)*x^(1/3))^2)*x^(1/6)*EllipticE(sin(2*arctan(a^(1/4)*x^(1/6)/b^(1/4))),sqrt(1/2))/b^(3/4)/sqrt(b*x^(1/3)+a*x)+6/5*a^(5/4)*(sqrt(b)+sqrt(a)*x^(1/3))*sqrt((b+a*x^(2/3))/(sqrt(b)+sqrt(a)*x^(1/3))^2)*x^(1/6)*InverseJacobiAM(2*arctan(a^(1/4)*x^(1/6)/b^(1/4)),sqrt(1/2))/b^(3/4)/sqrt(b*x^(1/3)+a*x),1],
[sqrt(b*x^(1/3)+a*x)/x^3,x,7,-6/11*sqrt(b*x^(1/3)+a*x)/x^2-12/77*a*sqrt(b*x^(1/3)+a*x)/b/x^(4/3)+20/77*a^2*sqrt(b*x^(1/3)+a*x)/b^2/x^(2/3)+10/77*a^(11/4)*(sqrt(b)+sqrt(a)*x^(1/3))*sqrt((b+a*x^(2/3))/(sqrt(b)+sqrt(a)*x^(1/3))^2)*x^(1/6)*InverseJacobiAM(2*arctan(a^(1/4)*x^(1/6)/b^(1/4)),sqrt(1/2))/b^(9/4)/sqrt(b*x^(1/3)+a*x),1],
[sqrt(b*x^(1/3)+a*x)/x^4,x,12,-308/1105*a^(9/2)*(b+a*x^(2/3))*x^(1/3)/b^4/(sqrt(b)+sqrt(a)*x^(1/3))/sqrt(b*x^(1/3)+a*x)-6/17*sqrt(b*x^(1/3)+a*x)/x^3-12/221*a*sqrt(b*x^(1/3)+a*x)/b/x^(7/3)+44/663*a^2*sqrt(b*x^(1/3)+a*x)/b^2/x^(5/3)-308/3315*a^3*sqrt(b*x^(1/3)+a*x)/b^3/x+308/1105*a^4*sqrt(b*x^(1/3)+a*x)/b^4/x^(1/3)+308/1105*a^(17/4)*(sqrt(b)+sqrt(a)*x^(1/3))*sqrt((b+a*x^(2/3))/(sqrt(b)+sqrt(a)*x^(1/3))^2)*x^(1/6)*EllipticE(sin(2*arctan(a^(1/4)*x^(1/6)/b^(1/4))),sqrt(1/2))/b^(15/4)/sqrt(b*x^(1/3)+a*x)-154/1105*a^(17/4)*(sqrt(b)+sqrt(a)*x^(1/3))*sqrt((b+a*x^(2/3))/(sqrt(b)+sqrt(a)*x^(1/3))^2)*x^(1/6)*InverseJacobiAM(2*arctan(a^(1/4)*x^(1/6)/b^(1/4)),sqrt(1/2))/b^(15/4)/sqrt(b*x^(1/3)+a*x),1],
[sqrt(b*x^(1/3)+a*x)/x^5,x,10,-6/23*sqrt(b*x^(1/3)+a*x)/x^4-12/437*a*sqrt(b*x^(1/3)+a*x)/b/x^(10/3)+68/2185*a^2*sqrt(b*x^(1/3)+a*x)/b^2/x^(8/3)-884/24035*a^3*sqrt(b*x^(1/3)+a*x)/b^3/x^2+7956/168245*a^4*sqrt(b*x^(1/3)+a*x)/b^4/x^(4/3)-2652/33649*a^5*sqrt(b*x^(1/3)+a*x)/b^5/x^(2/3)-1326/33649*a^(23/4)*(sqrt(b)+sqrt(a)*x^(1/3))*sqrt((b+a*x^(2/3))/(sqrt(b)+sqrt(a)*x^(1/3))^2)*x^(1/6)*InverseJacobiAM(2*arctan(a^(1/4)*x^(1/6)/b^(1/4)),sqrt(1/2))/b^(21/4)/sqrt(b*x^(1/3)+a*x),1],
[x^2*(b*x^(1/3)+a*x)^(3/2),x,11,1768/100947*b^6*sqrt(b*x^(1/3)+a*x)/a^5-1768/168245*b^5*x^(2/3)*sqrt(b*x^(1/3)+a*x)/a^4+1768/216315*b^4*x^(4/3)*sqrt(b*x^(1/3)+a*x)/a^3-136/19665*b^3*x^2*sqrt(b*x^(1/3)+a*x)/a^2+8/1311*b^2*x^(8/3)*sqrt(b*x^(1/3)+a*x)/a+4/69*b*x^(10/3)*sqrt(b*x^(1/3)+a*x)+2/9*x^3*(b*x^(1/3)+a*x)^(3/2)-884/100947*b^(27/4)*(sqrt(b)+sqrt(a)*x^(1/3))*sqrt((b+a*x^(2/3))/(sqrt(b)+sqrt(a)*x^(1/3))^2)*x^(1/6)*InverseJacobiAM(2*arctan(a^(1/4)*x^(1/6)/b^(1/4)),sqrt(1/2))/a^(21/4)/sqrt(b*x^(1/3)+a*x),1],
[x*(b*x^(1/3)+a*x)^(3/2),x,12,-88/1105*b^5*(b+a*x^(2/3))*x^(1/3)/a^(7/2)/(sqrt(b)+sqrt(a)*x^(1/3))/sqrt(b*x^(1/3)+a*x)+88/3315*b^4*x^(1/3)*sqrt(b*x^(1/3)+a*x)/a^3-88/4641*b^3*x*sqrt(b*x^(1/3)+a*x)/a^2+24/1547*b^2*x^(5/3)*sqrt(b*x^(1/3)+a*x)/a+12/119*b*x^(7/3)*sqrt(b*x^(1/3)+a*x)+2/7*x^2*(b*x^(1/3)+a*x)^(3/2)+88/1105*b^(21/4)*(sqrt(b)+sqrt(a)*x^(1/3))*sqrt((b+a*x^(2/3))/(sqrt(b)+sqrt(a)*x^(1/3))^2)*x^(1/6)*EllipticE(sin(2*arctan(a^(1/4)*x^(1/6)/b^(1/4))),sqrt(1/2))/a^(15/4)/sqrt(b*x^(1/3)+a*x)-44/1105*b^(21/4)*(sqrt(b)+sqrt(a)*x^(1/3))*sqrt((b+a*x^(2/3))/(sqrt(b)+sqrt(a)*x^(1/3))^2)*x^(1/6)*InverseJacobiAM(2*arctan(a^(1/4)*x^(1/6)/b^(1/4)),sqrt(1/2))/a^(15/4)/sqrt(b*x^(1/3)+a*x),1],
[(b*x^(1/3)+a*x)^(3/2),x,8,-8/77*b^3*sqrt(b*x^(1/3)+a*x)/a^2+24/385*b^2*x^(2/3)*sqrt(b*x^(1/3)+a*x)/a+12/55*b*x^(4/3)*sqrt(b*x^(1/3)+a*x)+2/5*x*(b*x^(1/3)+a*x)^(3/2)+4/77*b^(15/4)*(sqrt(b)+sqrt(a)*x^(1/3))*sqrt((b+a*x^(2/3))/(sqrt(b)+sqrt(a)*x^(1/3))^2)*x^(1/6)*InverseJacobiAM(2*arctan(a^(1/4)*x^(1/6)/b^(1/4)),sqrt(1/2))/a^(9/4)/sqrt(b*x^(1/3)+a*x),1],
[(b*x^(1/3)+a*x)^(3/2)/x,x,9,8/5*b^2*(b+a*x^(2/3))*x^(1/3)/sqrt(a)/(sqrt(b)+sqrt(a)*x^(1/3))/sqrt(b*x^(1/3)+a*x)+4/5*b*x^(1/3)*sqrt(b*x^(1/3)+a*x)+2/3*(b*x^(1/3)+a*x)^(3/2)-8/5*b^(9/4)*(sqrt(b)+sqrt(a)*x^(1/3))*sqrt((b+a*x^(2/3))/(sqrt(b)+sqrt(a)*x^(1/3))^2)*x^(1/6)*EllipticE(sin(2*arctan(a^(1/4)*x^(1/6)/b^(1/4))),sqrt(1/2))/a^(3/4)/sqrt(b*x^(1/3)+a*x)+4/5*b^(9/4)*(sqrt(b)+sqrt(a)*x^(1/3))*sqrt((b+a*x^(2/3))/(sqrt(b)+sqrt(a)*x^(1/3))^2)*x^(1/6)*InverseJacobiAM(2*arctan(a^(1/4)*x^(1/6)/b^(1/4)),sqrt(1/2))/a^(3/4)/sqrt(b*x^(1/3)+a*x),1],
[(b*x^(1/3)+a*x)^(3/2)/x^2,x,6,4*a*sqrt(b*x^(1/3)+a*x)-2*(b*x^(1/3)+a*x)^(3/2)/x+4*a^(3/4)*b^(3/4)*(sqrt(b)+sqrt(a)*x^(1/3))*sqrt((b+a*x^(2/3))/(sqrt(b)+sqrt(a)*x^(1/3))^2)*x^(1/6)*InverseJacobiAM(2*arctan(a^(1/4)*x^(1/6)/b^(1/4)),sqrt(1/2))/sqrt(b*x^(1/3)+a*x),1],
[(b*x^(1/3)+a*x)^(3/2)/x^3,x,10,8/5*a^(5/2)*(b+a*x^(2/3))*x^(1/3)/b/(sqrt(b)+sqrt(a)*x^(1/3))/sqrt(b*x^(1/3)+a*x)-4/5*a*sqrt(b*x^(1/3)+a*x)/x-8/5*a^2*sqrt(b*x^(1/3)+a*x)/b/x^(1/3)-2/3*(b*x^(1/3)+a*x)^(3/2)/x^2-8/5*a^(9/4)*(sqrt(b)+sqrt(a)*x^(1/3))*sqrt((b+a*x^(2/3))/(sqrt(b)+sqrt(a)*x^(1/3))^2)*x^(1/6)*EllipticE(sin(2*arctan(a^(1/4)*x^(1/6)/b^(1/4))),sqrt(1/2))/b^(3/4)/sqrt(b*x^(1/3)+a*x)+4/5*a^(9/4)*(sqrt(b)+sqrt(a)*x^(1/3))*sqrt((b+a*x^(2/3))/(sqrt(b)+sqrt(a)*x^(1/3))^2)*x^(1/6)*InverseJacobiAM(2*arctan(a^(1/4)*x^(1/6)/b^(1/4)),sqrt(1/2))/b^(3/4)/sqrt(b*x^(1/3)+a*x),1],
[(b*x^(1/3)+a*x)^(3/2)/x^4,x,8,-12/55*a*sqrt(b*x^(1/3)+a*x)/x^2-24/385*a^2*sqrt(b*x^(1/3)+a*x)/b/x^(4/3)+8/77*a^3*sqrt(b*x^(1/3)+a*x)/b^2/x^(2/3)-2/5*(b*x^(1/3)+a*x)^(3/2)/x^3+4/77*a^(15/4)*(sqrt(b)+sqrt(a)*x^(1/3))*sqrt((b+a*x^(2/3))/(sqrt(b)+sqrt(a)*x^(1/3))^2)*x^(1/6)*InverseJacobiAM(2*arctan(a^(1/4)*x^(1/6)/b^(1/4)),sqrt(1/2))/b^(9/4)/sqrt(b*x^(1/3)+a*x),1],
[(b*x^(1/3)+a*x)^(3/2)/x^5,x,13,-88/1105*a^(11/2)*(b+a*x^(2/3))*x^(1/3)/b^4/(sqrt(b)+sqrt(a)*x^(1/3))/sqrt(b*x^(1/3)+a*x)-12/119*a*sqrt(b*x^(1/3)+a*x)/x^3-24/1547*a^2*sqrt(b*x^(1/3)+a*x)/b/x^(7/3)+88/4641*a^3*sqrt(b*x^(1/3)+a*x)/b^2/x^(5/3)-88/3315*a^4*sqrt(b*x^(1/3)+a*x)/b^3/x+88/1105*a^5*sqrt(b*x^(1/3)+a*x)/b^4/x^(1/3)-2/7*(b*x^(1/3)+a*x)^(3/2)/x^4+88/1105*a^(21/4)*(sqrt(b)+sqrt(a)*x^(1/3))*sqrt((b+a*x^(2/3))/(sqrt(b)+sqrt(a)*x^(1/3))^2)*x^(1/6)*EllipticE(sin(2*arctan(a^(1/4)*x^(1/6)/b^(1/4))),sqrt(1/2))/b^(15/4)/sqrt(b*x^(1/3)+a*x)-44/1105*a^(21/4)*(sqrt(b)+sqrt(a)*x^(1/3))*sqrt((b+a*x^(2/3))/(sqrt(b)+sqrt(a)*x^(1/3))^2)*x^(1/6)*InverseJacobiAM(2*arctan(a^(1/4)*x^(1/6)/b^(1/4)),sqrt(1/2))/b^(15/4)/sqrt(b*x^(1/3)+a*x),1],
[(b*x^(1/3)+a*x)^(3/2)/x^6,x,11,-4/69*a*sqrt(b*x^(1/3)+a*x)/x^4-8/1311*a^2*sqrt(b*x^(1/3)+a*x)/b/x^(10/3)+136/19665*a^3*sqrt(b*x^(1/3)+a*x)/b^2/x^(8/3)-1768/216315*a^4*sqrt(b*x^(1/3)+a*x)/b^3/x^2+1768/168245*a^5*sqrt(b*x^(1/3)+a*x)/b^4/x^(4/3)-1768/100947*a^6*sqrt(b*x^(1/3)+a*x)/b^5/x^(2/3)-2/9*(b*x^(1/3)+a*x)^(3/2)/x^5-884/100947*a^(27/4)*(sqrt(b)+sqrt(a)*x^(1/3))*sqrt((b+a*x^(2/3))/(sqrt(b)+sqrt(a)*x^(1/3))^2)*x^(1/6)*InverseJacobiAM(2*arctan(a^(1/4)*x^(1/6)/b^(1/4)),sqrt(1/2))/b^(21/4)/sqrt(b*x^(1/3)+a*x),1],
[x^4/sqrt(b*x^(1/3)+a*x),x,11,11050/14421*b^6*sqrt(b*x^(1/3)+a*x)/a^7-2210/4807*b^5*x^(2/3)*sqrt(b*x^(1/3)+a*x)/a^6+15470/43263*b^4*x^(4/3)*sqrt(b*x^(1/3)+a*x)/a^5-1190/3933*b^3*x^2*sqrt(b*x^(1/3)+a*x)/a^4+350/1311*b^2*x^(8/3)*sqrt(b*x^(1/3)+a*x)/a^3-50/207*b*x^(10/3)*sqrt(b*x^(1/3)+a*x)/a^2+2/9*x^4*sqrt(b*x^(1/3)+a*x)/a-5525/14421*b^(27/4)*(sqrt(b)+sqrt(a)*x^(1/3))*sqrt((b+a*x^(2/3))/(sqrt(b)+sqrt(a)*x^(1/3))^2)*x^(1/6)*InverseJacobiAM(2*arctan(a^(1/4)*x^(1/6)/b^(1/4)),sqrt(1/2))/a^(29/4)/sqrt(b*x^(1/3)+a*x),1],
[x^3/sqrt(b*x^(1/3)+a*x),x,12,-418/221*b^5*(b+a*x^(2/3))*x^(1/3)/a^(11/2)/(sqrt(b)+sqrt(a)*x^(1/3))/sqrt(b*x^(1/3)+a*x)+418/663*b^4*x^(1/3)*sqrt(b*x^(1/3)+a*x)/a^5-2090/4641*b^3*x*sqrt(b*x^(1/3)+a*x)/a^4+570/1547*b^2*x^(5/3)*sqrt(b*x^(1/3)+a*x)/a^3-38/119*b*x^(7/3)*sqrt(b*x^(1/3)+a*x)/a^2+2/7*x^3*sqrt(b*x^(1/3)+a*x)/a+418/221*b^(21/4)*(sqrt(b)+sqrt(a)*x^(1/3))*sqrt((b+a*x^(2/3))/(sqrt(b)+sqrt(a)*x^(1/3))^2)*x^(1/6)*EllipticE(sin(2*arctan(a^(1/4)*x^(1/6)/b^(1/4))),sqrt(1/2))/a^(23/4)/sqrt(b*x^(1/3)+a*x)-209/221*b^(21/4)*(sqrt(b)+sqrt(a)*x^(1/3))*sqrt((b+a*x^(2/3))/(sqrt(b)+sqrt(a)*x^(1/3))^2)*x^(1/6)*InverseJacobiAM(2*arctan(a^(1/4)*x^(1/6)/b^(1/4)),sqrt(1/2))/a^(23/4)/sqrt(b*x^(1/3)+a*x),1],
[x^2/sqrt(b*x^(1/3)+a*x),x,8,-78/77*b^3*sqrt(b*x^(1/3)+a*x)/a^4+234/385*b^2*x^(2/3)*sqrt(b*x^(1/3)+a*x)/a^3-26/55*b*x^(4/3)*sqrt(b*x^(1/3)+a*x)/a^2+2/5*x^2*sqrt(b*x^(1/3)+a*x)/a+39/77*b^(15/4)*(sqrt(b)+sqrt(a)*x^(1/3))*sqrt((b+a*x^(2/3))/(sqrt(b)+sqrt(a)*x^(1/3))^2)*x^(1/6)*InverseJacobiAM(2*arctan(a^(1/4)*x^(1/6)/b^(1/4)),sqrt(1/2))/a^(17/4)/sqrt(b*x^(1/3)+a*x),1],
[x/sqrt(b*x^(1/3)+a*x),x,9,14/5*b^2*(b+a*x^(2/3))*x^(1/3)/a^(5/2)/(sqrt(b)+sqrt(a)*x^(1/3))/sqrt(b*x^(1/3)+a*x)-14/15*b*x^(1/3)*sqrt(b*x^(1/3)+a*x)/a^2+2/3*x*sqrt(b*x^(1/3)+a*x)/a-14/5*b^(9/4)*(sqrt(b)+sqrt(a)*x^(1/3))*sqrt((b+a*x^(2/3))/(sqrt(b)+sqrt(a)*x^(1/3))^2)*x^(1/6)*EllipticE(sin(2*arctan(a^(1/4)*x^(1/6)/b^(1/4))),sqrt(1/2))/a^(11/4)/sqrt(b*x^(1/3)+a*x)+7/5*b^(9/4)*(sqrt(b)+sqrt(a)*x^(1/3))*sqrt((b+a*x^(2/3))/(sqrt(b)+sqrt(a)*x^(1/3))^2)*x^(1/6)*InverseJacobiAM(2*arctan(a^(1/4)*x^(1/6)/b^(1/4)),sqrt(1/2))/a^(11/4)/sqrt(b*x^(1/3)+a*x),1],
[1/sqrt(b*x^(1/3)+a*x),x,5,2*sqrt(b*x^(1/3)+a*x)/a-b^(3/4)*(sqrt(b)+sqrt(a)*x^(1/3))*sqrt((b+a*x^(2/3))/(sqrt(b)+sqrt(a)*x^(1/3))^2)*x^(1/6)*InverseJacobiAM(2*arctan(a^(1/4)*x^(1/6)/b^(1/4)),sqrt(1/2))/a^(5/4)/sqrt(b*x^(1/3)+a*x),1],
[1/x/sqrt(b*x^(1/3)+a*x),x,8,6*sqrt(a)*(b+a*x^(2/3))*x^(1/3)/b/(sqrt(b)+sqrt(a)*x^(1/3))/sqrt(b*x^(1/3)+a*x)-6*sqrt(b*x^(1/3)+a*x)/b/x^(1/3)-6*a^(1/4)*(sqrt(b)+sqrt(a)*x^(1/3))*sqrt((b+a*x^(2/3))/(sqrt(b)+sqrt(a)*x^(1/3))^2)*x^(1/6)*EllipticE(sin(2*arctan(a^(1/4)*x^(1/6)/b^(1/4))),sqrt(1/2))/b^(3/4)/sqrt(b*x^(1/3)+a*x)+3*a^(1/4)*(sqrt(b)+sqrt(a)*x^(1/3))*sqrt((b+a*x^(2/3))/(sqrt(b)+sqrt(a)*x^(1/3))^2)*x^(1/6)*InverseJacobiAM(2*arctan(a^(1/4)*x^(1/6)/b^(1/4)),sqrt(1/2))/b^(3/4)/sqrt(b*x^(1/3)+a*x),1],
[1/x^2/sqrt(b*x^(1/3)+a*x),x,6,-6/7*sqrt(b*x^(1/3)+a*x)/b/x^(4/3)+10/7*a*sqrt(b*x^(1/3)+a*x)/b^2/x^(2/3)+5/7*a^(7/4)*(sqrt(b)+sqrt(a)*x^(1/3))*sqrt((b+a*x^(2/3))/(sqrt(b)+sqrt(a)*x^(1/3))^2)*x^(1/6)*InverseJacobiAM(2*arctan(a^(1/4)*x^(1/6)/b^(1/4)),sqrt(1/2))/b^(9/4)/sqrt(b*x^(1/3)+a*x),1],
[1/x^3/sqrt(b*x^(1/3)+a*x),x,11,-154/65*a^(7/2)*(b+a*x^(2/3))*x^(1/3)/b^4/(sqrt(b)+sqrt(a)*x^(1/3))/sqrt(b*x^(1/3)+a*x)-6/13*sqrt(b*x^(1/3)+a*x)/b/x^(7/3)+22/39*a*sqrt(b*x^(1/3)+a*x)/b^2/x^(5/3)-154/195*a^2*sqrt(b*x^(1/3)+a*x)/b^3/x+154/65*a^3*sqrt(b*x^(1/3)+a*x)/b^4/x^(1/3)+154/65*a^(13/4)*(sqrt(b)+sqrt(a)*x^(1/3))*sqrt((b+a*x^(2/3))/(sqrt(b)+sqrt(a)*x^(1/3))^2)*x^(1/6)*EllipticE(sin(2*arctan(a^(1/4)*x^(1/6)/b^(1/4))),sqrt(1/2))/b^(15/4)/sqrt(b*x^(1/3)+a*x)-77/65*a^(13/4)*(sqrt(b)+sqrt(a)*x^(1/3))*sqrt((b+a*x^(2/3))/(sqrt(b)+sqrt(a)*x^(1/3))^2)*x^(1/6)*InverseJacobiAM(2*arctan(a^(1/4)*x^(1/6)/b^(1/4)),sqrt(1/2))/b^(15/4)/sqrt(b*x^(1/3)+a*x),1],
[1/x^4/sqrt(b*x^(1/3)+a*x),x,9,-6/19*sqrt(b*x^(1/3)+a*x)/b/x^(10/3)+34/95*a*sqrt(b*x^(1/3)+a*x)/b^2/x^(8/3)-442/1045*a^2*sqrt(b*x^(1/3)+a*x)/b^3/x^2+3978/7315*a^3*sqrt(b*x^(1/3)+a*x)/b^4/x^(4/3)-1326/1463*a^4*sqrt(b*x^(1/3)+a*x)/b^5/x^(2/3)-663/1463*a^(19/4)*(sqrt(b)+sqrt(a)*x^(1/3))*sqrt((b+a*x^(2/3))/(sqrt(b)+sqrt(a)*x^(1/3))^2)*x^(1/6)*InverseJacobiAM(2*arctan(a^(1/4)*x^(1/6)/b^(1/4)),sqrt(1/2))/b^(21/4)/sqrt(b*x^(1/3)+a*x),1],
[x^4/(b*x^(1/3)+a*x)^(3/2),x,13,-4807/221*b^5*(b+a*x^(2/3))*x^(1/3)/a^(13/2)/(sqrt(b)+sqrt(a)*x^(1/3))/sqrt(b*x^(1/3)+a*x)-3*x^4/a/sqrt(b*x^(1/3)+a*x)+4807/663*b^4*x^(1/3)*sqrt(b*x^(1/3)+a*x)/a^6-24035/4641*b^3*x*sqrt(b*x^(1/3)+a*x)/a^5+6555/1547*b^2*x^(5/3)*sqrt(b*x^(1/3)+a*x)/a^4-437/119*b*x^(7/3)*sqrt(b*x^(1/3)+a*x)/a^3+23/7*x^3*sqrt(b*x^(1/3)+a*x)/a^2+4807/221*b^(21/4)*(sqrt(b)+sqrt(a)*x^(1/3))*sqrt((b+a*x^(2/3))/(sqrt(b)+sqrt(a)*x^(1/3))^2)*x^(1/6)*EllipticE(sin(2*arctan(a^(1/4)*x^(1/6)/b^(1/4))),sqrt(1/2))/a^(27/4)/sqrt(b*x^(1/3)+a*x)-4807/442*b^(21/4)*(sqrt(b)+sqrt(a)*x^(1/3))*sqrt((b+a*x^(2/3))/(sqrt(b)+sqrt(a)*x^(1/3))^2)*x^(1/6)*InverseJacobiAM(2*arctan(a^(1/4)*x^(1/6)/b^(1/4)),sqrt(1/2))/a^(27/4)/sqrt(b*x^(1/3)+a*x),1],
[x^3/(b*x^(1/3)+a*x)^(3/2),x,9,-3*x^3/a/sqrt(b*x^(1/3)+a*x)-663/77*b^3*sqrt(b*x^(1/3)+a*x)/a^5+1989/385*b^2*x^(2/3)*sqrt(b*x^(1/3)+a*x)/a^4-221/55*b*x^(4/3)*sqrt(b*x^(1/3)+a*x)/a^3+17/5*x^2*sqrt(b*x^(1/3)+a*x)/a^2+663/154*b^(15/4)*(sqrt(b)+sqrt(a)*x^(1/3))*sqrt((b+a*x^(2/3))/(sqrt(b)+sqrt(a)*x^(1/3))^2)*x^(1/6)*InverseJacobiAM(2*arctan(a^(1/4)*x^(1/6)/b^(1/4)),sqrt(1/2))/a^(21/4)/sqrt(b*x^(1/3)+a*x),1],
[x^2/(b*x^(1/3)+a*x)^(3/2),x,10,77/5*b^2*(b+a*x^(2/3))*x^(1/3)/a^(7/2)/(sqrt(b)+sqrt(a)*x^(1/3))/sqrt(b*x^(1/3)+a*x)-3*x^2/a/sqrt(b*x^(1/3)+a*x)-77/15*b*x^(1/3)*sqrt(b*x^(1/3)+a*x)/a^3+11/3*x*sqrt(b*x^(1/3)+a*x)/a^2-77/5*b^(9/4)*(sqrt(b)+sqrt(a)*x^(1/3))*sqrt((b+a*x^(2/3))/(sqrt(b)+sqrt(a)*x^(1/3))^2)*x^(1/6)*EllipticE(sin(2*arctan(a^(1/4)*x^(1/6)/b^(1/4))),sqrt(1/2))/a^(15/4)/sqrt(b*x^(1/3)+a*x)+77/10*b^(9/4)*(sqrt(b)+sqrt(a)*x^(1/3))*sqrt((b+a*x^(2/3))/(sqrt(b)+sqrt(a)*x^(1/3))^2)*x^(1/6)*InverseJacobiAM(2*arctan(a^(1/4)*x^(1/6)/b^(1/4)),sqrt(1/2))/a^(15/4)/sqrt(b*x^(1/3)+a*x),1],
[x/(b*x^(1/3)+a*x)^(3/2),x,6,-3*x/a/sqrt(b*x^(1/3)+a*x)+5*sqrt(b*x^(1/3)+a*x)/a^2-5/2*b^(3/4)*(sqrt(b)+sqrt(a)*x^(1/3))*sqrt((b+a*x^(2/3))/(sqrt(b)+sqrt(a)*x^(1/3))^2)*x^(1/6)*InverseJacobiAM(2*arctan(a^(1/4)*x^(1/6)/b^(1/4)),sqrt(1/2))/a^(9/4)/sqrt(b*x^(1/3)+a*x),1],
[1/(b*x^(1/3)+a*x)^(3/2),x,8,-3*(b+a*x^(2/3))*x^(1/3)/sqrt(a)/b/(sqrt(b)+sqrt(a)*x^(1/3))/sqrt(b*x^(1/3)+a*x)+3*x^(2/3)/b/sqrt(b*x^(1/3)+a*x)+3*(sqrt(b)+sqrt(a)*x^(1/3))*sqrt((b+a*x^(2/3))/(sqrt(b)+sqrt(a)*x^(1/3))^2)*x^(1/6)*EllipticE(sin(2*arctan(a^(1/4)*x^(1/6)/b^(1/4))),sqrt(1/2))/a^(3/4)/b^(3/4)/sqrt(b*x^(1/3)+a*x)-3/2*(sqrt(b)+sqrt(a)*x^(1/3))*sqrt((b+a*x^(2/3))/(sqrt(b)+sqrt(a)*x^(1/3))^2)*x^(1/6)*InverseJacobiAM(2*arctan(a^(1/4)*x^(1/6)/b^(1/4)),sqrt(1/2))/a^(3/4)/b^(3/4)/sqrt(b*x^(1/3)+a*x),1],
[1/x/(b*x^(1/3)+a*x)^(3/2),x,6,3/b/x^(1/3)/sqrt(b*x^(1/3)+a*x)-5*sqrt(b*x^(1/3)+a*x)/b^2/x^(2/3)-5/2*a^(3/4)*(sqrt(b)+sqrt(a)*x^(1/3))*sqrt((b+a*x^(2/3))/(sqrt(b)+sqrt(a)*x^(1/3))^2)*x^(1/6)*InverseJacobiAM(2*arctan(a^(1/4)*x^(1/6)/b^(1/4)),sqrt(1/2))/b^(9/4)/sqrt(b*x^(1/3)+a*x),1],
[1/x^2/(b*x^(1/3)+a*x)^(3/2),x,11,3/b/x^(4/3)/sqrt(b*x^(1/3)+a*x)+77/5*a^(5/2)*(b+a*x^(2/3))*x^(1/3)/b^4/(sqrt(b)+sqrt(a)*x^(1/3))/sqrt(b*x^(1/3)+a*x)-11/3*sqrt(b*x^(1/3)+a*x)/b^2/x^(5/3)+77/15*a*sqrt(b*x^(1/3)+a*x)/b^3/x-77/5*a^2*sqrt(b*x^(1/3)+a*x)/b^4/x^(1/3)-77/5*a^(9/4)*(sqrt(b)+sqrt(a)*x^(1/3))*sqrt((b+a*x^(2/3))/(sqrt(b)+sqrt(a)*x^(1/3))^2)*x^(1/6)*EllipticE(sin(2*arctan(a^(1/4)*x^(1/6)/b^(1/4))),sqrt(1/2))/b^(15/4)/sqrt(b*x^(1/3)+a*x)+77/10*a^(9/4)*(sqrt(b)+sqrt(a)*x^(1/3))*sqrt((b+a*x^(2/3))/(sqrt(b)+sqrt(a)*x^(1/3))^2)*x^(1/6)*InverseJacobiAM(2*arctan(a^(1/4)*x^(1/6)/b^(1/4)),sqrt(1/2))/b^(15/4)/sqrt(b*x^(1/3)+a*x),1],
[1/x^3/(b*x^(1/3)+a*x)^(3/2),x,9,3/b/x^(7/3)/sqrt(b*x^(1/3)+a*x)-17/5*sqrt(b*x^(1/3)+a*x)/b^2/x^(8/3)+221/55*a*sqrt(b*x^(1/3)+a*x)/b^3/x^2-1989/385*a^2*sqrt(b*x^(1/3)+a*x)/b^4/x^(4/3)+663/77*a^3*sqrt(b*x^(1/3)+a*x)/b^5/x^(2/3)+663/154*a^(15/4)*(sqrt(b)+sqrt(a)*x^(1/3))*sqrt((b+a*x^(2/3))/(sqrt(b)+sqrt(a)*x^(1/3))^2)*x^(1/6)*InverseJacobiAM(2*arctan(a^(1/4)*x^(1/6)/b^(1/4)),sqrt(1/2))/b^(21/4)/sqrt(b*x^(1/3)+a*x),1],
[1/x^4/(b*x^(1/3)+a*x)^(3/2),x,14,3/b/x^(10/3)/sqrt(b*x^(1/3)+a*x)-4807/221*a^(11/2)*(b+a*x^(2/3))*x^(1/3)/b^7/(sqrt(b)+sqrt(a)*x^(1/3))/sqrt(b*x^(1/3)+a*x)-23/7*sqrt(b*x^(1/3)+a*x)/b^2/x^(11/3)+437/119*a*sqrt(b*x^(1/3)+a*x)/b^3/x^3-6555/1547*a^2*sqrt(b*x^(1/3)+a*x)/b^4/x^(7/3)+24035/4641*a^3*sqrt(b*x^(1/3)+a*x)/b^5/x^(5/3)-4807/663*a^4*sqrt(b*x^(1/3)+a*x)/b^6/x+4807/221*a^5*sqrt(b*x^(1/3)+a*x)/b^7/x^(1/3)+4807/221*a^(21/4)*(sqrt(b)+sqrt(a)*x^(1/3))*sqrt((b+a*x^(2/3))/(sqrt(b)+sqrt(a)*x^(1/3))^2)*x^(1/6)*EllipticE(sin(2*arctan(a^(1/4)*x^(1/6)/b^(1/4))),sqrt(1/2))/b^(27/4)/sqrt(b*x^(1/3)+a*x)-4807/442*a^(21/4)*(sqrt(b)+sqrt(a)*x^(1/3))*sqrt((b+a*x^(2/3))/(sqrt(b)+sqrt(a)*x^(1/3))^2)*x^(1/6)*InverseJacobiAM(2*arctan(a^(1/4)*x^(1/6)/b^(1/4)),sqrt(1/2))/b^(27/4)/sqrt(b*x^(1/3)+a*x),1],
[x^3*sqrt(b*x^(2/3)+a*x),x,13,-524288/4345965*b^9*(b*x^(2/3)+a*x)^(3/2)/a^10+8388608/152108775*b^12*(b*x^(2/3)+a*x)^(3/2)/a^13/x-4194304/50702925*b^11*(b*x^(2/3)+a*x)^(3/2)/a^12/x^(2/3)+1048576/10140585*b^10*(b*x^(2/3)+a*x)^(3/2)/a^11/x^(1/3)+65536/482885*b^8*x^(1/3)*(b*x^(2/3)+a*x)^(3/2)/a^9-360448/2414425*b^7*x^(2/3)*(b*x^(2/3)+a*x)^(3/2)/a^8+90112/557175*b^6*x*(b*x^(2/3)+a*x)^(3/2)/a^7-45056/260015*b^5*x^(4/3)*(b*x^(2/3)+a*x)^(3/2)/a^6+2816/15295*b^4*x^(5/3)*(b*x^(2/3)+a*x)^(3/2)/a^5-1408/7245*b^3*x^2*(b*x^(2/3)+a*x)^(3/2)/a^4+352/1725*b^2*x^(7/3)*(b*x^(2/3)+a*x)^(3/2)/a^3-16/75*b*x^(8/3)*(b*x^(2/3)+a*x)^(3/2)/a^2+2/9*x^3*(b*x^(2/3)+a*x)^(3/2)/a,1],
[x^2*sqrt(b*x^(2/3)+a*x),x,10,8192/46189*b^6*(b*x^(2/3)+a*x)^(3/2)/a^7-131072/1616615*b^9*(b*x^(2/3)+a*x)^(3/2)/a^10/x+196608/1616615*b^8*(b*x^(2/3)+a*x)^(3/2)/a^9/x^(2/3)-49152/323323*b^7*(b*x^(2/3)+a*x)^(3/2)/a^8/x^(1/3)-9216/46189*b^5*x^(1/3)*(b*x^(2/3)+a*x)^(3/2)/a^6+4608/20995*b^4*x^(2/3)*(b*x^(2/3)+a*x)^(3/2)/a^5-384/1615*b^3*x*(b*x^(2/3)+a*x)^(3/2)/a^4+576/2261*b^2*x^(4/3)*(b*x^(2/3)+a*x)^(3/2)/a^3-36/133*b*x^(5/3)*(b*x^(2/3)+a*x)^(3/2)/a^2+2/7*x^2*(b*x^(2/3)+a*x)^(3/2)/a,1],
[x*sqrt(b*x^(2/3)+a*x),x,7,-128/429*b^3*(b*x^(2/3)+a*x)^(3/2)/a^4+2048/15015*b^6*(b*x^(2/3)+a*x)^(3/2)/a^7/x-1024/5005*b^5*(b*x^(2/3)+a*x)^(3/2)/a^6/x^(2/3)+256/1001*b^4*(b*x^(2/3)+a*x)^(3/2)/a^5/x^(1/3)+48/143*b^2*x^(1/3)*(b*x^(2/3)+a*x)^(3/2)/a^3-24/65*b*x^(2/3)*(b*x^(2/3)+a*x)^(3/2)/a^2+2/5*x*(b*x^(2/3)+a*x)^(3/2)/a,1],
[sqrt(b*x^(2/3)+a*x),x,4,2/3*(b*x^(2/3)+a*x)^(3/2)/a-32/105*b^3*(b*x^(2/3)+a*x)^(3/2)/a^4/x+16/35*b^2*(b*x^(2/3)+a*x)^(3/2)/a^3/x^(2/3)-4/7*b*(b*x^(2/3)+a*x)^(3/2)/a^2/x^(1/3),1],
[sqrt(b*x^(2/3)+a*x)/x,x,1,2*(b*x^(2/3)+a*x)^(3/2)/a/x,1],
[sqrt(b*x^(2/3)+a*x)/x^2,x,4,-3/2*sqrt(b*x^(2/3)+a*x)/x-3/4*a*sqrt(b*x^(2/3)+a*x)/b/x^(2/3)+3/4*a^2*arctanh(sqrt(b)*x^(1/3)/sqrt(b*x^(2/3)+a*x))/b^(3/2),1],
[sqrt(b*x^(2/3)+a*x)/x^3,x,7,-3/5*sqrt(b*x^(2/3)+a*x)/x^2-3/40*a*sqrt(b*x^(2/3)+a*x)/b/x^(5/3)+7/80*a^2*sqrt(b*x^(2/3)+a*x)/b^2/x^(4/3)-7/64*a^3*sqrt(b*x^(2/3)+a*x)/b^3/x+21/128*a^4*sqrt(b*x^(2/3)+a*x)/b^4/x^(2/3)-21/128*a^5*arctanh(sqrt(b)*x^(1/3)/sqrt(b*x^(2/3)+a*x))/b^(9/2),1],
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[x^2*(b*x^(2/3)+a*x)^(3/2),x,12,45056/557175*b^6*(b*x^(2/3)+a*x)^(5/2)/a^7-1048576/152108775*b^11*(b*x^(2/3)+a*x)^(5/2)/a^12/x^(5/3)+524288/30421755*b^10*(b*x^(2/3)+a*x)^(5/2)/a^11/x^(4/3)-131072/4345965*b^9*(b*x^(2/3)+a*x)^(5/2)/a^10/x+65536/1448655*b^8*(b*x^(2/3)+a*x)^(5/2)/a^9/x^(2/3)-90112/1448655*b^7*(b*x^(2/3)+a*x)^(5/2)/a^8/x^(1/3)-11264/111435*b^5*x^(1/3)*(b*x^(2/3)+a*x)^(5/2)/a^6+5632/45885*b^4*x^(2/3)*(b*x^(2/3)+a*x)^(5/2)/a^5-352/2415*b^3*x*(b*x^(2/3)+a*x)^(5/2)/a^4+176/1035*b^2*x^(4/3)*(b*x^(2/3)+a*x)^(5/2)/a^3-44/225*b*x^(5/3)*(b*x^(2/3)+a*x)^(5/2)/a^2+2/9*x^2*(b*x^(2/3)+a*x)^(5/2)/a,1],
[x*(b*x^(2/3)+a*x)^(3/2),x,9,-256/1615*b^3*(b*x^(2/3)+a*x)^(5/2)/a^4+65536/4849845*b^8*(b*x^(2/3)+a*x)^(5/2)/a^9/x^(5/3)-32768/969969*b^7*(b*x^(2/3)+a*x)^(5/2)/a^8/x^(4/3)+8192/138567*b^6*(b*x^(2/3)+a*x)^(5/2)/a^7/x-4096/46189*b^5*(b*x^(2/3)+a*x)^(5/2)/a^6/x^(2/3)+512/4199*b^4*(b*x^(2/3)+a*x)^(5/2)/a^5/x^(1/3)+64/323*b^2*x^(1/3)*(b*x^(2/3)+a*x)^(5/2)/a^3-32/133*b*x^(2/3)*(b*x^(2/3)+a*x)^(5/2)/a^2+2/7*x*(b*x^(2/3)+a*x)^(5/2)/a,1],
[(b*x^(2/3)+a*x)^(3/2),x,6,2/5*(b*x^(2/3)+a*x)^(5/2)/a-512/15015*b^5*(b*x^(2/3)+a*x)^(5/2)/a^6/x^(5/3)+256/3003*b^4*(b*x^(2/3)+a*x)^(5/2)/a^5/x^(4/3)-64/429*b^3*(b*x^(2/3)+a*x)^(5/2)/a^4/x+32/143*b^2*(b*x^(2/3)+a*x)^(5/2)/a^3/x^(2/3)-4/13*b*(b*x^(2/3)+a*x)^(5/2)/a^2/x^(1/3),1],
[(b*x^(2/3)+a*x)^(3/2)/x,x,3,16/105*b^2*(b*x^(2/3)+a*x)^(5/2)/a^3/x^(5/3)-8/21*b*(b*x^(2/3)+a*x)^(5/2)/a^2/x^(4/3)+2/3*(b*x^(2/3)+a*x)^(5/2)/a/x,1],
[(b*x^(2/3)+a*x)^(3/2)/x^2,x,4,6*b*sqrt(b*x^(2/3)+a*x)/x^(1/3)+2*(b*x^(2/3)+a*x)^(3/2)/x-6*b^(3/2)*arctanh(sqrt(b)*x^(1/3)/sqrt(b*x^(2/3)+a*x)),1],
[(b*x^(2/3)+a*x)^(3/2)/x^3,x,5,-3/4*a*sqrt(b*x^(2/3)+a*x)/x-3/8*a^2*sqrt(b*x^(2/3)+a*x)/b/x^(2/3)-(b*x^(2/3)+a*x)^(3/2)/x^2+3/8*a^3*arctanh(sqrt(b)*x^(1/3)/sqrt(b*x^(2/3)+a*x))/b^(3/2),1],
[(b*x^(2/3)+a*x)^(3/2)/x^4,x,8,-3/20*a*sqrt(b*x^(2/3)+a*x)/x^2-3/160*a^2*sqrt(b*x^(2/3)+a*x)/b/x^(5/3)+7/320*a^3*sqrt(b*x^(2/3)+a*x)/b^2/x^(4/3)-7/256*a^4*sqrt(b*x^(2/3)+a*x)/b^3/x+21/512*a^5*sqrt(b*x^(2/3)+a*x)/b^4/x^(2/3)-1/2*(b*x^(2/3)+a*x)^(3/2)/x^3-21/512*a^6*arctanh(sqrt(b)*x^(1/3)/sqrt(b*x^(2/3)+a*x))/b^(9/2),1],
[(b*x^(2/3)+a*x)^(3/2)/x^5,x,11,-1/16*a*sqrt(b*x^(2/3)+a*x)/x^3-1/224*a^2*sqrt(b*x^(2/3)+a*x)/b/x^(8/3)+13/2688*a^3*sqrt(b*x^(2/3)+a*x)/b^2/x^(7/3)-143/26880*a^4*sqrt(b*x^(2/3)+a*x)/b^3/x^2+429/71680*a^5*sqrt(b*x^(2/3)+a*x)/b^4/x^(5/3)-143/20480*a^6*sqrt(b*x^(2/3)+a*x)/b^5/x^(4/3)+143/16384*a^7*sqrt(b*x^(2/3)+a*x)/b^6/x-429/32768*a^8*sqrt(b*x^(2/3)+a*x)/b^7/x^(2/3)-1/3*(b*x^(2/3)+a*x)^(3/2)/x^4+429/32768*a^9*arctanh(sqrt(b)*x^(1/3)/sqrt(b*x^(2/3)+a*x))/b^(15/2),1],
[(b*x^(2/3)+a*x)^(3/2)/x^6,x,14,-3/88*a*sqrt(b*x^(2/3)+a*x)/x^4-3/1760*a^2*sqrt(b*x^(2/3)+a*x)/b/x^(11/3)+19/10560*a^3*sqrt(b*x^(2/3)+a*x)/b^2/x^(10/3)-323/168960*a^4*sqrt(b*x^(2/3)+a*x)/b^3/x^3+323/157696*a^5*sqrt(b*x^(2/3)+a*x)/b^4/x^(8/3)-4199/1892352*a^6*sqrt(b*x^(2/3)+a*x)/b^5/x^(7/3)+4199/1720320*a^7*sqrt(b*x^(2/3)+a*x)/b^6/x^2-12597/4587520*a^8*sqrt(b*x^(2/3)+a*x)/b^7/x^(5/3)+4199/1310720*a^9*sqrt(b*x^(2/3)+a*x)/b^8/x^(4/3)-4199/1048576*a^10*sqrt(b*x^(2/3)+a*x)/b^9/x+12597/2097152*a^11*sqrt(b*x^(2/3)+a*x)/b^10/x^(2/3)-1/4*(b*x^(2/3)+a*x)^(3/2)/x^5-12597/2097152*a^12*arctanh(sqrt(b)*x^(1/3)/sqrt(b*x^(2/3)+a*x))/b^(21/2),1],
[x^4/sqrt(b*x^(2/3)+a*x),x,14,8388608/11700675*b^12*sqrt(b*x^(2/3)+a*x)/a^13-16777216/11700675*b^13*sqrt(b*x^(2/3)+a*x)/a^14/x^(1/3)-2097152/3900225*b^11*x^(1/3)*sqrt(b*x^(2/3)+a*x)/a^12+1048576/2340135*b^10*x^(2/3)*sqrt(b*x^(2/3)+a*x)/a^11-131072/334305*b^9*x*sqrt(b*x^(2/3)+a*x)/a^10+65536/185725*b^8*x^(4/3)*sqrt(b*x^(2/3)+a*x)/a^9-180224/557175*b^7*x^(5/3)*sqrt(b*x^(2/3)+a*x)/a^8+1171456/3900225*b^6*x^2*sqrt(b*x^(2/3)+a*x)/a^7-73216/260015*b^5*x^(7/3)*sqrt(b*x^(2/3)+a*x)/a^6+36608/137655*b^4*x^(8/3)*sqrt(b*x^(2/3)+a*x)/a^5-9152/36225*b^3*x^3*sqrt(b*x^(2/3)+a*x)/a^4+416/1725*b^2*x^(10/3)*sqrt(b*x^(2/3)+a*x)/a^3-52/225*b*x^(11/3)*sqrt(b*x^(2/3)+a*x)/a^2+2/9*x^4*sqrt(b*x^(2/3)+a*x)/a,1],
[x^3/sqrt(b*x^(2/3)+a*x),x,11,-262144/323323*b^9*sqrt(b*x^(2/3)+a*x)/a^10+524288/323323*b^10*sqrt(b*x^(2/3)+a*x)/a^11/x^(1/3)+196608/323323*b^8*x^(1/3)*sqrt(b*x^(2/3)+a*x)/a^9-163840/323323*b^7*x^(2/3)*sqrt(b*x^(2/3)+a*x)/a^8+20480/46189*b^6*x*sqrt(b*x^(2/3)+a*x)/a^7-18432/46189*b^5*x^(4/3)*sqrt(b*x^(2/3)+a*x)/a^6+1536/4199*b^4*x^(5/3)*sqrt(b*x^(2/3)+a*x)/a^5-768/2261*b^3*x^2*sqrt(b*x^(2/3)+a*x)/a^4+720/2261*b^2*x^(7/3)*sqrt(b*x^(2/3)+a*x)/a^3-40/133*b*x^(8/3)*sqrt(b*x^(2/3)+a*x)/a^2+2/7*x^3*sqrt(b*x^(2/3)+a*x)/a,1],
[x^2/sqrt(b*x^(2/3)+a*x),x,8,2048/2145*b^6*sqrt(b*x^(2/3)+a*x)/a^7-4096/2145*b^7*sqrt(b*x^(2/3)+a*x)/a^8/x^(1/3)-512/715*b^5*x^(1/3)*sqrt(b*x^(2/3)+a*x)/a^6+256/429*b^4*x^(2/3)*sqrt(b*x^(2/3)+a*x)/a^5-224/429*b^3*x*sqrt(b*x^(2/3)+a*x)/a^4+336/715*b^2*x^(4/3)*sqrt(b*x^(2/3)+a*x)/a^3-28/65*b*x^(5/3)*sqrt(b*x^(2/3)+a*x)/a^2+2/5*x^2*sqrt(b*x^(2/3)+a*x)/a,1],
[x/sqrt(b*x^(2/3)+a*x),x,5,-128/105*b^3*sqrt(b*x^(2/3)+a*x)/a^4+256/105*b^4*sqrt(b*x^(2/3)+a*x)/a^5/x^(1/3)+32/35*b^2*x^(1/3)*sqrt(b*x^(2/3)+a*x)/a^3-16/21*b*x^(2/3)*sqrt(b*x^(2/3)+a*x)/a^2+2/3*x*sqrt(b*x^(2/3)+a*x)/a,1],
[1/sqrt(b*x^(2/3)+a*x),x,2,2*sqrt(b*x^(2/3)+a*x)/a-4*b*sqrt(b*x^(2/3)+a*x)/a^2/x^(1/3),1],
[1/x/sqrt(b*x^(2/3)+a*x),x,3,-3*sqrt(b*x^(2/3)+a*x)/b/x^(2/3)+3*a*arctanh(sqrt(b)*x^(1/3)/sqrt(b*x^(2/3)+a*x))/b^(3/2),1],
[1/x^2/sqrt(b*x^(2/3)+a*x),x,6,-3/4*sqrt(b*x^(2/3)+a*x)/b/x^(5/3)+7/8*a*sqrt(b*x^(2/3)+a*x)/b^2/x^(4/3)-35/32*a^2*sqrt(b*x^(2/3)+a*x)/b^3/x+105/64*a^3*sqrt(b*x^(2/3)+a*x)/b^4/x^(2/3)-105/64*a^4*arctanh(sqrt(b)*x^(1/3)/sqrt(b*x^(2/3)+a*x))/b^(9/2),1],
[1/x^3/sqrt(b*x^(2/3)+a*x),x,9,-3/7*sqrt(b*x^(2/3)+a*x)/b/x^(8/3)+13/28*a*sqrt(b*x^(2/3)+a*x)/b^2/x^(7/3)-143/280*a^2*sqrt(b*x^(2/3)+a*x)/b^3/x^2+1287/2240*a^3*sqrt(b*x^(2/3)+a*x)/b^4/x^(5/3)-429/640*a^4*sqrt(b*x^(2/3)+a*x)/b^5/x^(4/3)+429/512*a^5*sqrt(b*x^(2/3)+a*x)/b^6/x-1287/1024*a^6*sqrt(b*x^(2/3)+a*x)/b^7/x^(2/3)+1287/1024*a^7*arctanh(sqrt(b)*x^(1/3)/sqrt(b*x^(2/3)+a*x))/b^(15/2),1],
[1/x^4/sqrt(b*x^(2/3)+a*x),x,12,-3/10*sqrt(b*x^(2/3)+a*x)/b/x^(11/3)+19/60*a*sqrt(b*x^(2/3)+a*x)/b^2/x^(10/3)-323/960*a^2*sqrt(b*x^(2/3)+a*x)/b^3/x^3+323/896*a^3*sqrt(b*x^(2/3)+a*x)/b^4/x^(8/3)-4199/10752*a^4*sqrt(b*x^(2/3)+a*x)/b^5/x^(7/3)+46189/107520*a^5*sqrt(b*x^(2/3)+a*x)/b^6/x^2-138567/286720*a^6*sqrt(b*x^(2/3)+a*x)/b^7/x^(5/3)+46189/81920*a^7*sqrt(b*x^(2/3)+a*x)/b^8/x^(4/3)-46189/65536*a^8*sqrt(b*x^(2/3)+a*x)/b^9/x+138567/131072*a^9*sqrt(b*x^(2/3)+a*x)/b^10/x^(2/3)-138567/131072*a^10*arctanh(sqrt(b)*x^(1/3)/sqrt(b*x^(2/3)+a*x))/b^(21/2),1],
[x^4/(b*x^(2/3)+a*x)^(3/2),x,12,-6*x^4/a/sqrt(b*x^(2/3)+a*x)-524288/29393*b^9*sqrt(b*x^(2/3)+a*x)/a^11+1048576/29393*b^10*sqrt(b*x^(2/3)+a*x)/a^12/x^(1/3)+393216/29393*b^8*x^(1/3)*sqrt(b*x^(2/3)+a*x)/a^10-327680/29393*b^7*x^(2/3)*sqrt(b*x^(2/3)+a*x)/a^9+40960/4199*b^6*x*sqrt(b*x^(2/3)+a*x)/a^8-36864/4199*b^5*x^(4/3)*sqrt(b*x^(2/3)+a*x)/a^7+33792/4199*b^4*x^(5/3)*sqrt(b*x^(2/3)+a*x)/a^6-16896/2261*b^3*x^2*sqrt(b*x^(2/3)+a*x)/a^5+15840/2261*b^2*x^(7/3)*sqrt(b*x^(2/3)+a*x)/a^4-880/133*b*x^(8/3)*sqrt(b*x^(2/3)+a*x)/a^3+44/7*x^3*sqrt(b*x^(2/3)+a*x)/a^2,1],
[x^3/(b*x^(2/3)+a*x)^(3/2),x,9,-6*x^3/a/sqrt(b*x^(2/3)+a*x)+32768/2145*b^6*sqrt(b*x^(2/3)+a*x)/a^8-65536/2145*b^7*sqrt(b*x^(2/3)+a*x)/a^9/x^(1/3)-8192/715*b^5*x^(1/3)*sqrt(b*x^(2/3)+a*x)/a^7+4096/429*b^4*x^(2/3)*sqrt(b*x^(2/3)+a*x)/a^6-3584/429*b^3*x*sqrt(b*x^(2/3)+a*x)/a^5+5376/715*b^2*x^(4/3)*sqrt(b*x^(2/3)+a*x)/a^4-448/65*b*x^(5/3)*sqrt(b*x^(2/3)+a*x)/a^3+32/5*x^2*sqrt(b*x^(2/3)+a*x)/a^2,1],
[x^2/(b*x^(2/3)+a*x)^(3/2),x,6,-6*x^2/a/sqrt(b*x^(2/3)+a*x)-256/21*b^3*sqrt(b*x^(2/3)+a*x)/a^5+512/21*b^4*sqrt(b*x^(2/3)+a*x)/a^6/x^(1/3)+64/7*b^2*x^(1/3)*sqrt(b*x^(2/3)+a*x)/a^4-160/21*b*x^(2/3)*sqrt(b*x^(2/3)+a*x)/a^3+20/3*x*sqrt(b*x^(2/3)+a*x)/a^2,1],
[x/(b*x^(2/3)+a*x)^(3/2),x,3,-6*x/a/sqrt(b*x^(2/3)+a*x)+8*sqrt(b*x^(2/3)+a*x)/a^2-16*b*sqrt(b*x^(2/3)+a*x)/a^3/x^(1/3),1],
[1/(b*x^(2/3)+a*x)^(3/2),x,3,6*x^(1/3)/b/sqrt(b*x^(2/3)+a*x)-6*arctanh(sqrt(b)*x^(1/3)/sqrt(b*x^(2/3)+a*x))/b^(3/2),1],
[1/x/(b*x^(2/3)+a*x)^(3/2),x,6,6/b/x^(2/3)/sqrt(b*x^(2/3)+a*x)-7*sqrt(b*x^(2/3)+a*x)/b^2/x^(4/3)+35/4*a*sqrt(b*x^(2/3)+a*x)/b^3/x-105/8*a^2*sqrt(b*x^(2/3)+a*x)/b^4/x^(2/3)+105/8*a^3*arctanh(sqrt(b)*x^(1/3)/sqrt(b*x^(2/3)+a*x))/b^(9/2),1],
[1/x^2/(b*x^(2/3)+a*x)^(3/2),x,9,6/b/x^(5/3)/sqrt(b*x^(2/3)+a*x)-13/2*sqrt(b*x^(2/3)+a*x)/b^2/x^(7/3)+143/20*a*sqrt(b*x^(2/3)+a*x)/b^3/x^2-1287/160*a^2*sqrt(b*x^(2/3)+a*x)/b^4/x^(5/3)+3003/320*a^3*sqrt(b*x^(2/3)+a*x)/b^5/x^(4/3)-3003/256*a^4*sqrt(b*x^(2/3)+a*x)/b^6/x+9009/512*a^5*sqrt(b*x^(2/3)+a*x)/b^7/x^(2/3)-9009/512*a^6*arctanh(sqrt(b)*x^(1/3)/sqrt(b*x^(2/3)+a*x))/b^(15/2),1],
[1/x^3/(b*x^(2/3)+a*x)^(3/2),x,12,6/b/x^(8/3)/sqrt(b*x^(2/3)+a*x)-19/3*sqrt(b*x^(2/3)+a*x)/b^2/x^(10/3)+323/48*a*sqrt(b*x^(2/3)+a*x)/b^3/x^3-1615/224*a^2*sqrt(b*x^(2/3)+a*x)/b^4/x^(8/3)+20995/2688*a^3*sqrt(b*x^(2/3)+a*x)/b^5/x^(7/3)-46189/5376*a^4*sqrt(b*x^(2/3)+a*x)/b^6/x^2+138567/14336*a^5*sqrt(b*x^(2/3)+a*x)/b^7/x^(5/3)-46189/4096*a^6*sqrt(b*x^(2/3)+a*x)/b^8/x^(4/3)+230945/16384*a^7*sqrt(b*x^(2/3)+a*x)/b^9/x-692835/32768*a^8*sqrt(b*x^(2/3)+a*x)/b^10/x^(2/3)+692835/32768*a^9*arctanh(sqrt(b)*x^(1/3)/sqrt(b*x^(2/3)+a*x))/b^(21/2),1],
[1/x^4/(b*x^(2/3)+a*x)^(3/2),x,15,6/b/x^(11/3)/sqrt(b*x^(2/3)+a*x)-25/4*sqrt(b*x^(2/3)+a*x)/b^2/x^(13/3)+575/88*a*sqrt(b*x^(2/3)+a*x)/b^3/x^4-2415/352*a^2*sqrt(b*x^(2/3)+a*x)/b^4/x^(11/3)+15295/2112*a^3*sqrt(b*x^(2/3)+a*x)/b^5/x^(10/3)-260015/33792*a^4*sqrt(b*x^(2/3)+a*x)/b^6/x^3+185725/22528*a^5*sqrt(b*x^(2/3)+a*x)/b^7/x^(8/3)-2414425/270336*a^6*sqrt(b*x^(2/3)+a*x)/b^8/x^(7/3)+482885/49152*a^7*sqrt(b*x^(2/3)+a*x)/b^9/x^2-1448655/131072*a^8*sqrt(b*x^(2/3)+a*x)/b^10/x^(5/3)+3380195/262144*a^9*sqrt(b*x^(2/3)+a*x)/b^11/x^(4/3)-16900975/1048576*a^10*sqrt(b*x^(2/3)+a*x)/b^12/x+50702925/2097152*a^11*sqrt(b*x^(2/3)+a*x)/b^13/x^(2/3)-50702925/2097152*a^12*arctanh(sqrt(b)*x^(1/3)/sqrt(b*x^(2/3)+a*x))/b^(27/2),1],
[x^2*(b*x^3+a*x^2),x,3,1/5*a*x^5+1/6*b*x^6,1],
[x*(b*x^3+a*x^2),x,3,1/4*a*x^4+1/5*b*x^5,1],
[b*x^3+a*x^2,x,1,1/3*a*x^3+1/4*b*x^4,1],
[(b*x^3+a*x^2)/x,x,3,1/2*a*x^2+1/3*b*x^3,1],
[(b*x^3+a*x^2)/x^2,x,2,1/2*(b*x+a)^2/b,1],
[x^2*(b*x^3+a*x^2)^2,x,3,1/7*a^2*x^7+1/4*a*b*x^8+1/9*b^2*x^9,1],
[x*(b*x^3+a*x^2)^2,x,3,1/6*a^2*x^6+2/7*a*b*x^7+1/8*b^2*x^8,1],
[(b*x^3+a*x^2)^2,x,3,1/5*a^2*x^5+1/3*a*b*x^6+1/7*b^2*x^7,1],
[(b*x^3+a*x^2)^2/x,x,3,1/4*a^2*x^4+2/5*a*b*x^5+1/6*b^2*x^6,1],
[(b*x^3+a*x^2)^2/x^2,x,3,1/3*a^2*x^3+1/2*a*b*x^4+1/5*b^2*x^5,1],
[x^6/(b*x^3+a*x^2),x,3,-a^3*x/b^4+1/2*a^2*x^2/b^3-1/3*a*x^3/b^2+1/4*x^4/b+a^4*ln(b*x+a)/b^5,1],
[x^5/(b*x^3+a*x^2),x,3,a^2*x/b^3-1/2*a*x^2/b^2+1/3*x^3/b-a^3*ln(b*x+a)/b^4,1],
[x^4/(b*x^3+a*x^2),x,3,-a*x/b^2+1/2*x^2/b+a^2*ln(b*x+a)/b^3,1],
[x^3/(b*x^3+a*x^2),x,3,x/b-a*ln(b*x+a)/b^2,1],
[x^2/(b*x^3+a*x^2),x,2,ln(b*x+a)/b,1],
[x/(b*x^3+a*x^2),x,3,ln(x)/a-ln(b*x+a)/a,1],
[1/(b*x^3+a*x^2),x,3,-1/a/x-b*ln(x)/a^2+b*ln(b*x+a)/a^2,1],
[1/x/(b*x^3+a*x^2),x,3,-1/2/a/x^2+b/a^2/x+b^2*ln(x)/a^3-b^2*ln(b*x+a)/a^3,1],
[1/x^2/(b*x^3+a*x^2),x,3,-1/3/a/x^3+1/2*b/a^2/x^2-b^2/a^3/x-b^3*ln(x)/a^4+b^3*ln(b*x+a)/a^4,1],
[x^8/(b*x^3+a*x^2)^2,x,3,3*a^2*x/b^4-a*x^2/b^3+1/3*x^3/b^2-a^4/b^5/(b*x+a)-4*a^3*ln(b*x+a)/b^5,1],
[x^7/(b*x^3+a*x^2)^2,x,3,-2*a*x/b^3+1/2*x^2/b^2+a^3/b^4/(b*x+a)+3*a^2*ln(b*x+a)/b^4,1],
[x^6/(b*x^3+a*x^2)^2,x,3,x/b^2-a^2/b^3/(b*x+a)-2*a*ln(b*x+a)/b^3,1],
[x^5/(b*x^3+a*x^2)^2,x,3,a/b^2/(b*x+a)+ln(b*x+a)/b^2,1],
[x^4/(b*x^3+a*x^2)^2,x,2,-1/b/(b*x+a),1],
[x^3/(b*x^3+a*x^2)^2,x,3,1/a/(b*x+a)+ln(x)/a^2-ln(b*x+a)/a^2,1],
[x^2/(b*x^3+a*x^2)^2,x,3,-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],
[x/(b*x^3+a*x^2)^2,x,3,-1/2/a^2/x^2+2*b/a^3/x+b^2/a^3/(b*x+a)+3*b^2*ln(x)/a^4-3*b^2*ln(b*x+a)/a^4,1],
[1/(b*x^3+a*x^2)^2,x,3,-1/3/a^2/x^3+b/a^3/x^2-3*b^2/a^4/x-b^3/a^4/(b*x+a)-4*b^3*ln(x)/a^5+4*b^3*ln(b*x+a)/a^5,1],
[1/x/(b*x^3+a*x^2)^2,x,3,-1/4/a^2/x^4+2/3*b/a^3/x^3-3/2*b^2/a^4/x^2+4*b^3/a^5/x+b^4/a^5/(b*x+a)+5*b^4*ln(x)/a^6-5*b^4*ln(b*x+a)/a^6,1],
[x^2*sqrt(b*x^3+a*x^2),x,4,2/9*(b*x^3+a*x^2)^(3/2)/b-32/315*a^3*(b*x^3+a*x^2)^(3/2)/b^4/x^3+16/105*a^2*(b*x^3+a*x^2)^(3/2)/b^3/x^2-4/21*a*(b*x^3+a*x^2)^(3/2)/b^2/x,1],
[x*sqrt(b*x^3+a*x^2),x,3,16/105*a^2*(b*x^3+a*x^2)^(3/2)/b^3/x^3-8/35*a*(b*x^3+a*x^2)^(3/2)/b^2/x^2+2/7*(b*x^3+a*x^2)^(3/2)/b/x,1],
[sqrt(b*x^3+a*x^2),x,2,-4/15*a*(b*x^3+a*x^2)^(3/2)/b^2/x^3+2/5*(b*x^3+a*x^2)^(3/2)/b/x^2,1],
[sqrt(b*x^3+a*x^2)/x,x,1,2/3*(b*x^3+a*x^2)^(3/2)/b/x^3,1],
[sqrt(b*x^3+a*x^2)/x^2,x,3,2*sqrt(b*x^3+a*x^2)/x-2*sqrt(a)*arctanh(sqrt(a)*x/sqrt(b*x^3+a*x^2)),1],
[sqrt(b*x^3+a*x^2)/x^3,x,3,-sqrt(b*x^3+a*x^2)/x^2-b*arctanh(sqrt(a)*x/sqrt(b*x^3+a*x^2))/sqrt(a),1],
[sqrt(b*x^3+a*x^2)/x^4,x,4,-1/2*sqrt(b*x^3+a*x^2)/x^3-1/4*b*sqrt(b*x^3+a*x^2)/a/x^2+1/4*b^2*arctanh(sqrt(a)*x/sqrt(b*x^3+a*x^2))/a^(3/2),1],
[sqrt(b*x^3+a*x^2)/x^5,x,5,-1/3*sqrt(b*x^3+a*x^2)/x^4-1/12*b*sqrt(b*x^3+a*x^2)/a/x^3+1/8*b^2*sqrt(b*x^3+a*x^2)/a^2/x^2-1/8*b^3*arctanh(sqrt(a)*x/sqrt(b*x^3+a*x^2))/a^(5/2),1],
[x^2*(b*x^3+a*x^2)^(3/2),x,6,2/15*(b*x^3+a*x^2)^(5/2)/b-512/45045*a^5*(b*x^3+a*x^2)^(5/2)/b^6/x^5+256/9009*a^4*(b*x^3+a*x^2)^(5/2)/b^5/x^4-64/1287*a^3*(b*x^3+a*x^2)^(5/2)/b^4/x^3+32/429*a^2*(b*x^3+a*x^2)^(5/2)/b^3/x^2-4/39*a*(b*x^3+a*x^2)^(5/2)/b^2/x,1],
[x*(b*x^3+a*x^2)^(3/2),x,5,256/15015*a^4*(b*x^3+a*x^2)^(5/2)/b^5/x^5-128/3003*a^3*(b*x^3+a*x^2)^(5/2)/b^4/x^4+32/429*a^2*(b*x^3+a*x^2)^(5/2)/b^3/x^3-16/143*a*(b*x^3+a*x^2)^(5/2)/b^2/x^2+2/13*(b*x^3+a*x^2)^(5/2)/b/x,1],
[(b*x^3+a*x^2)^(3/2),x,4,-32/1155*a^3*(b*x^3+a*x^2)^(5/2)/b^4/x^5+16/231*a^2*(b*x^3+a*x^2)^(5/2)/b^3/x^4-4/33*a*(b*x^3+a*x^2)^(5/2)/b^2/x^3+2/11*(b*x^3+a*x^2)^(5/2)/b/x^2,1],
[(b*x^3+a*x^2)^(3/2)/x,x,3,16/315*a^2*(b*x^3+a*x^2)^(5/2)/b^3/x^5-8/63*a*(b*x^3+a*x^2)^(5/2)/b^2/x^4+2/9*(b*x^3+a*x^2)^(5/2)/b/x^3,1],
[(b*x^3+a*x^2)^(3/2)/x^2,x,2,-4/35*a*(b*x^3+a*x^2)^(5/2)/b^2/x^5+2/7*(b*x^3+a*x^2)^(5/2)/b/x^4,1],
[(b*x^3+a*x^2)^(3/2)/x^3,x,1,2/5*(b*x^3+a*x^2)^(5/2)/b/x^5,1],
[(b*x^3+a*x^2)^(3/2)/x^4,x,4,2*a*sqrt(b*x^3+a*x^2)/x+2/3*(b*x^3+a*x^2)^(3/2)/x^3-2*a^(3/2)*arctanh(sqrt(a)*x/sqrt(b*x^3+a*x^2)),1],
[(b*x^3+a*x^2)^(3/2)/x^5,x,4,3*b*sqrt(b*x^3+a*x^2)/x-(b*x^3+a*x^2)^(3/2)/x^4-3*sqrt(a)*b*arctanh(sqrt(a)*x/sqrt(b*x^3+a*x^2)),1],
[(b*x^3+a*x^2)^(3/2)/x^6,x,4,-3/4*b*sqrt(b*x^3+a*x^2)/x^2-1/2*(b*x^3+a*x^2)^(3/2)/x^5-3/4*b^2*arctanh(sqrt(a)*x/sqrt(b*x^3+a*x^2))/sqrt(a),1],
[(b*x^3+a*x^2)^(3/2)/x^7,x,5,-1/4*b*sqrt(b*x^3+a*x^2)/x^3-1/8*b^2*sqrt(b*x^3+a*x^2)/a/x^2-1/3*(b*x^3+a*x^2)^(3/2)/x^6+1/8*b^3*arctanh(sqrt(a)*x/sqrt(b*x^3+a*x^2))/a^(3/2),1],
[(b*x^3+a*x^2)^(3/2)/x^8,x,6,-1/8*b*sqrt(b*x^3+a*x^2)/x^4-1/32*b^2*sqrt(b*x^3+a*x^2)/a/x^3+3/64*b^3*sqrt(b*x^3+a*x^2)/a^2/x^2-1/4*(b*x^3+a*x^2)^(3/2)/x^7-3/64*b^4*arctanh(sqrt(a)*x/sqrt(b*x^3+a*x^2))/a^(5/2),1],
[(b*x^3+a*x^2)^(3/2)/x^9,x,7,-3/40*b*sqrt(b*x^3+a*x^2)/x^5-1/80*b^2*sqrt(b*x^3+a*x^2)/a/x^4+1/64*b^3*sqrt(b*x^3+a*x^2)/a^2/x^3-3/128*b^4*sqrt(b*x^3+a*x^2)/a^3/x^2-1/5*(b*x^3+a*x^2)^(3/2)/x^8+3/128*b^5*arctanh(sqrt(a)*x/sqrt(b*x^3+a*x^2))/a^(7/2),1],
[x^4/sqrt(b*x^3+a*x^2),x,4,16/35*a^2*sqrt(b*x^3+a*x^2)/b^3-32/35*a^3*sqrt(b*x^3+a*x^2)/b^4/x-12/35*a*x*sqrt(b*x^3+a*x^2)/b^2+2/7*x^2*sqrt(b*x^3+a*x^2)/b,1],
[x^3/sqrt(b*x^3+a*x^2),x,3,-8/15*a*sqrt(b*x^3+a*x^2)/b^2+16/15*a^2*sqrt(b*x^3+a*x^2)/b^3/x+2/5*x*sqrt(b*x^3+a*x^2)/b,1],
[x^2/sqrt(b*x^3+a*x^2),x,2,2/3*sqrt(b*x^3+a*x^2)/b-4/3*a*sqrt(b*x^3+a*x^2)/b^2/x,1],
[x/sqrt(b*x^3+a*x^2),x,1,2*sqrt(b*x^3+a*x^2)/b/x,1],
[1/sqrt(b*x^3+a*x^2),x,2,-2*arctanh(sqrt(a)*x/sqrt(b*x^3+a*x^2))/sqrt(a),1],
[1/x/sqrt(b*x^3+a*x^2),x,3,-sqrt(b*x^3+a*x^2)/a/x^2+b*arctanh(sqrt(a)*x/sqrt(b*x^3+a*x^2))/a^(3/2),1],
[1/x^2/sqrt(b*x^3+a*x^2),x,4,-1/2*sqrt(b*x^3+a*x^2)/a/x^3+3/4*b*sqrt(b*x^3+a*x^2)/a^2/x^2-3/4*b^2*arctanh(sqrt(a)*x/sqrt(b*x^3+a*x^2))/a^(5/2),1],
[1/x^3/sqrt(b*x^3+a*x^2),x,5,-1/3*sqrt(b*x^3+a*x^2)/a/x^4+5/12*b*sqrt(b*x^3+a*x^2)/a^2/x^3-5/8*b^2*sqrt(b*x^3+a*x^2)/a^3/x^2+5/8*b^3*arctanh(sqrt(a)*x/sqrt(b*x^3+a*x^2))/a^(7/2),1],
[x^6/(b*x^3+a*x^2)^(3/2),x,4,-2*x^4/b/sqrt(b*x^3+a*x^2)-16/5*a*sqrt(b*x^3+a*x^2)/b^3+32/5*a^2*sqrt(b*x^3+a*x^2)/b^4/x+12/5*x*sqrt(b*x^3+a*x^2)/b^2,1],
[x^5/(b*x^3+a*x^2)^(3/2),x,3,-2*x^3/b/sqrt(b*x^3+a*x^2)+8/3*sqrt(b*x^3+a*x^2)/b^2-16/3*a*sqrt(b*x^3+a*x^2)/b^3/x,1],
[x^4/(b*x^3+a*x^2)^(3/2),x,2,-2*x^2/b/sqrt(b*x^3+a*x^2)+4*sqrt(b*x^3+a*x^2)/b^2/x,1],
[x^3/(b*x^3+a*x^2)^(3/2),x,1,-2*x/b/sqrt(b*x^3+a*x^2),1],
[x^2/(b*x^3+a*x^2)^(3/2),x,3,2*x/a/sqrt(b*x^3+a*x^2)-2*arctanh(sqrt(a)*x/sqrt(b*x^3+a*x^2))/a^(3/2),1],
[x/(b*x^3+a*x^2)^(3/2),x,4,2/a/sqrt(b*x^3+a*x^2)-3*sqrt(b*x^3+a*x^2)/a^2/x^2+3*b*arctanh(sqrt(a)*x/sqrt(b*x^3+a*x^2))/a^(5/2),1],
[1/(b*x^3+a*x^2)^(3/2),x,5,2/a/x/sqrt(b*x^3+a*x^2)-5/2*sqrt(b*x^3+a*x^2)/a^2/x^3+15/4*b*sqrt(b*x^3+a*x^2)/a^3/x^2-15/4*b^2*arctanh(sqrt(a)*x/sqrt(b*x^3+a*x^2))/a^(7/2),1],
[1/x/(b*x^3+a*x^2)^(3/2),x,6,2/a/x^2/sqrt(b*x^3+a*x^2)-7/3*sqrt(b*x^3+a*x^2)/a^2/x^4+35/12*b*sqrt(b*x^3+a*x^2)/a^3/x^3-35/8*b^2*sqrt(b*x^3+a*x^2)/a^4/x^2+35/8*b^3*arctanh(sqrt(a)*x/sqrt(b*x^3+a*x^2))/a^(9/2),1],
[1/x^2/(b*x^3+a*x^2)^(3/2),x,7,2/a/x^3/sqrt(b*x^3+a*x^2)-9/4*sqrt(b*x^3+a*x^2)/a^2/x^5+21/8*b*sqrt(b*x^3+a*x^2)/a^3/x^4-105/32*b^2*sqrt(b*x^3+a*x^2)/a^4/x^3+315/64*b^3*sqrt(b*x^3+a*x^2)/a^5/x^2-315/64*b^4*arctanh(sqrt(a)*x/sqrt(b*x^3+a*x^2))/a^(11/2),1],
[x^(7/2)/sqrt(b*x^3+a*x^2),x,5,5/8*a^2*sqrt(b*x^3+a*x^2)/b^3/sqrt(x)-5/12*a*sqrt(x)*sqrt(b*x^3+a*x^2)/b^2+1/3*x^(3/2)*sqrt(b*x^3+a*x^2)/b-5/8*a^3*arctanh(sqrt(b)*x^(3/2)/sqrt(b*x^3+a*x^2))/b^(7/2),1],
[x^(5/2)/sqrt(b*x^3+a*x^2),x,4,-3/4*a*sqrt(b*x^3+a*x^2)/b^2/sqrt(x)+1/2*sqrt(x)*sqrt(b*x^3+a*x^2)/b+3/4*a^2*arctanh(sqrt(b)*x^(3/2)/sqrt(b*x^3+a*x^2))/b^(5/2),1],
[x^(3/2)/sqrt(b*x^3+a*x^2),x,3,sqrt(b*x^3+a*x^2)/b/sqrt(x)-a*arctanh(sqrt(b)*x^(3/2)/sqrt(b*x^3+a*x^2))/b^(3/2),1],
[sqrt(x)/sqrt(b*x^3+a*x^2),x,2,2*arctanh(sqrt(b)*x^(3/2)/sqrt(b*x^3+a*x^2))/sqrt(b),1],
[1/sqrt(x)/sqrt(b*x^3+a*x^2),x,1,-2*sqrt(b*x^3+a*x^2)/a/x^(3/2),1],
[1/x^(3/2)/sqrt(b*x^3+a*x^2),x,2,-2/3*sqrt(b*x^3+a*x^2)/a/x^(5/2)+4/3*b*sqrt(b*x^3+a*x^2)/a^2/x^(3/2),1],
[1/x^(5/2)/sqrt(b*x^3+a*x^2),x,3,-2/5*sqrt(b*x^3+a*x^2)/a/x^(7/2)+8/15*b*sqrt(b*x^3+a*x^2)/a^2/x^(5/2)-16/15*b^2*sqrt(b*x^3+a*x^2)/a^3/x^(3/2),1],
[1/x^(7/2)/sqrt(b*x^3+a*x^2),x,4,-2/7*sqrt(b*x^3+a*x^2)/a/x^(9/2)+12/35*b*sqrt(b*x^3+a*x^2)/a^2/x^(7/2)-16/35*b^2*sqrt(b*x^3+a*x^2)/a^3/x^(5/2)+32/35*b^3*sqrt(b*x^3+a*x^2)/a^4/x^(3/2),1],
[x^(1-3*p)*(b*x^3+a*x^2)^p,x,3,x^(2-3*p)*(b*x^3+a*x^2)^p*hypergeom([2-p, -p],[3-p],-b*x/a)/(2-p)/((1+b*x/a)^p),1],
[(b*x^3+a*x^2)^p/(x^(3*p)),x,3,x^(-1-3*p)*(b*x^3+a*x^2)^(p+1)*hypergeom([1, 2],[2-p],-b*x/a)/a/(1-p),1],
[x^(-1-3*p)*(b*x^3+a*x^2)^p,x,3,-(b*x^3+a*x^2)^p*hypergeom([-p, -p],[1-p],-b*x/a)/p/(x^(3*p))/((1+b*x/a)^p),1],
[x^(-2-3*p)*(b*x^3+a*x^2)^p,x,1,-(b*x^3+a*x^2)^(p+1)/a/(p+1)/(x^(3*p+3)),1],
[x^(-3-3*p)*(b*x^3+a*x^2)^p,x,2,-x^(-4-3*p)*(b*x^3+a*x^2)^(p+1)/a/(2+p)+b*(b*x^3+a*x^2)^(p+1)/a^2/(p+1)/(2+p)/(x^(3*p+3)),1],
[x^(-4-3*p)*(b*x^3+a*x^2)^p,x,3,-x^(-5-3*p)*(b*x^3+a*x^2)^(p+1)/a/(3+p)+2*b*x^(-4-3*p)*(b*x^3+a*x^2)^(p+1)/a^2/(2+p)/(3+p)-2*b^2*(b*x^3+a*x^2)^(p+1)/a^3/(p+1)/(2+p)/(3+p)/(x^(3*p+3)),1],
[x^11/(b*x^5+a*x^2)^3,x,2,1/6*x^6/a/(b*x^3+a)^2,1],
[x^9/sqrt(b*x^5+a*x^2),x,3,16/45*a^2*sqrt(b*x^5+a*x^2)/b^3/x-8/45*a*x^2*sqrt(b*x^5+a*x^2)/b^2+2/15*x^5*sqrt(b*x^5+a*x^2)/b,1],
[x^6/sqrt(b*x^5+a*x^2),x,2,-4/9*a*sqrt(b*x^5+a*x^2)/b^2/x+2/9*x^2*sqrt(b*x^5+a*x^2)/b,1],
[x^3/sqrt(b*x^5+a*x^2),x,1,2/3*sqrt(b*x^5+a*x^2)/b/x,1],
[1/sqrt(b*x^5+a*x^2),x,2,-2/3*arctanh(sqrt(a)*x/sqrt(b*x^5+a*x^2))/sqrt(a),1],
[1/x^3/sqrt(b*x^5+a*x^2),x,3,-1/3*sqrt(b*x^5+a*x^2)/a/x^4+1/3*b*arctanh(sqrt(a)*x/sqrt(b*x^5+a*x^2))/a^(3/2),1],
[x^4/sqrt(b*x^5+a*x^2),x,3,2/5*sqrt(b*x^5+a*x^2)/b-4/15*sqrt(2+sqrt(3))*a*x*(a^(1/3)+b^(1/3)*x)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/((1+sqrt(3))*a^(1/3)+b^(1/3)*x)^2)*InverseJacobiAM(arcsin(((1-sqrt(3))*a^(1/3)+b^(1/3)*x)/((1+sqrt(3))*a^(1/3)+b^(1/3)*x)),sqrt(-7-4*sqrt(3)))*3^(3/4)/b^(4/3)/sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/((1+sqrt(3))*a^(1/3)+b^(1/3)*x)^2)/sqrt(b*x^5+a*x^2),1],
[x/sqrt(b*x^5+a*x^2),x,2,2/3*sqrt(2+sqrt(3))*x*(a^(1/3)+b^(1/3)*x)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/((1+sqrt(3))*a^(1/3)+b^(1/3)*x)^2)*InverseJacobiAM(arcsin(((1-sqrt(3))*a^(1/3)+b^(1/3)*x)/((1+sqrt(3))*a^(1/3)+b^(1/3)*x)),sqrt(-7-4*sqrt(3)))*3^(3/4)/b^(1/3)/sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/((1+sqrt(3))*a^(1/3)+b^(1/3)*x)^2)/sqrt(b*x^5+a*x^2),1],
[1/x^2/sqrt(b*x^5+a*x^2),x,3,-1/2*sqrt(b*x^5+a*x^2)/a/x^3-1/6*sqrt(2+sqrt(3))*b^(2/3)*x*(a^(1/3)+b^(1/3)*x)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/((1+sqrt(3))*a^(1/3)+b^(1/3)*x)^2)*InverseJacobiAM(arcsin(((1-sqrt(3))*a^(1/3)+b^(1/3)*x)/((1+sqrt(3))*a^(1/3)+b^(1/3)*x)),sqrt(-7-4*sqrt(3)))*3^(3/4)/a/sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/((1+sqrt(3))*a^(1/3)+b^(1/3)*x)^2)/sqrt(b*x^5+a*x^2),1],
[x^5/sqrt(b*x^5+a*x^2),x,5,-8/7*a*x*(b*x^3+a)/b^(5/3)/((1+sqrt(3))*a^(1/3)+b^(1/3)*x)/sqrt(b*x^5+a*x^2)+2/7*x*sqrt(b*x^5+a*x^2)/b+4/7*3^(1/4)*sqrt(2-sqrt(3))*a^(4/3)*x*(a^(1/3)+b^(1/3)*x)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/((1+sqrt(3))*a^(1/3)+b^(1/3)*x)^2)*EllipticE(sin(arcsin(((1-sqrt(3))*a^(1/3)+b^(1/3)*x)/((1+sqrt(3))*a^(1/3)+b^(1/3)*x))),sqrt(-7-4*sqrt(3)))/b^(5/3)/sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/((1+sqrt(3))*a^(1/3)+b^(1/3)*x)^2)/sqrt(b*x^5+a*x^2)-8/21*sqrt(2)*a^(4/3)*x*(a^(1/3)+b^(1/3)*x)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/((1+sqrt(3))*a^(1/3)+b^(1/3)*x)^2)*InverseJacobiAM(arcsin(((1-sqrt(3))*a^(1/3)+b^(1/3)*x)/((1+sqrt(3))*a^(1/3)+b^(1/3)*x)),sqrt(-7-4*sqrt(3)))*3^(3/4)/b^(5/3)/sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/((1+sqrt(3))*a^(1/3)+b^(1/3)*x)^2)/sqrt(b*x^5+a*x^2),1],
[x^2/sqrt(b*x^5+a*x^2),x,4,2*x*(b*x^3+a)/b^(2/3)/((1+sqrt(3))*a^(1/3)+b^(1/3)*x)/sqrt(b*x^5+a*x^2)-3^(1/4)*sqrt(2-sqrt(3))*a^(1/3)*x*(a^(1/3)+b^(1/3)*x)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/((1+sqrt(3))*a^(1/3)+b^(1/3)*x)^2)*EllipticE(sin(arcsin(((1-sqrt(3))*a^(1/3)+b^(1/3)*x)/((1+sqrt(3))*a^(1/3)+b^(1/3)*x))),sqrt(-7-4*sqrt(3)))/b^(2/3)/sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/((1+sqrt(3))*a^(1/3)+b^(1/3)*x)^2)/sqrt(b*x^5+a*x^2)+2/3*sqrt(2)*a^(1/3)*x*(a^(1/3)+b^(1/3)*x)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/((1+sqrt(3))*a^(1/3)+b^(1/3)*x)^2)*InverseJacobiAM(arcsin(((1-sqrt(3))*a^(1/3)+b^(1/3)*x)/((1+sqrt(3))*a^(1/3)+b^(1/3)*x)),sqrt(-7-4*sqrt(3)))*3^(3/4)/b^(2/3)/sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/((1+sqrt(3))*a^(1/3)+b^(1/3)*x)^2)/sqrt(b*x^5+a*x^2),1],
[1/x/sqrt(b*x^5+a*x^2),x,5,b^(1/3)*x*(b*x^3+a)/a/((1+sqrt(3))*a^(1/3)+b^(1/3)*x)/sqrt(b*x^5+a*x^2)-sqrt(b*x^5+a*x^2)/a/x^2-1/2*3^(1/4)*sqrt(2-sqrt(3))*b^(1/3)*x*(a^(1/3)+b^(1/3)*x)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/((1+sqrt(3))*a^(1/3)+b^(1/3)*x)^2)*EllipticE(sin(arcsin(((1-sqrt(3))*a^(1/3)+b^(1/3)*x)/((1+sqrt(3))*a^(1/3)+b^(1/3)*x))),sqrt(-7-4*sqrt(3)))/a^(2/3)/sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/((1+sqrt(3))*a^(1/3)+b^(1/3)*x)^2)/sqrt(b*x^5+a*x^2)+1/3*sqrt(2)*b^(1/3)*x*(a^(1/3)+b^(1/3)*x)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/((1+sqrt(3))*a^(1/3)+b^(1/3)*x)^2)*InverseJacobiAM(arcsin(((1-sqrt(3))*a^(1/3)+b^(1/3)*x)/((1+sqrt(3))*a^(1/3)+b^(1/3)*x)),sqrt(-7-4*sqrt(3)))*3^(3/4)/a^(2/3)/sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/((1+sqrt(3))*a^(1/3)+b^(1/3)*x)^2)/sqrt(b*x^5+a*x^2),1],
[x^(13/2)/sqrt(b*x^5+a*x^2),x,5,-7/20*a*sqrt(b*x^5+a*x^2)/b^2/sqrt(x)+1/5*x^(5/2)*sqrt(b*x^5+a*x^2)/b+7/120*a^(5/3)*x^(3/2)*(a^(1/3)+b^(1/3)*x)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(1/3)+(1+sqrt(3))*b^(1/3)*x)^2)*InverseJacobiAM(arccos((a^(1/3)+(1-sqrt(3))*b^(1/3)*x)/(a^(1/3)+(1+sqrt(3))*b^(1/3)*x)),sqrt(1/2+1/4*sqrt(3)))*3^(3/4)/b^2/sqrt(b^(1/3)*x*(a^(1/3)+b^(1/3)*x)/(a^(1/3)+(1+sqrt(3))*b^(1/3)*x)^2)/sqrt(b*x^5+a*x^2),1],
[x^(11/2)/sqrt(b*x^5+a*x^2),x,6,-5/8*(1+sqrt(3))*a*x^(3/2)*(b*x^3+a)/b^(5/3)/(a^(1/3)+(1+sqrt(3))*b^(1/3)*x)/sqrt(b*x^5+a*x^2)+1/4*x^(3/2)*sqrt(b*x^5+a*x^2)/b+5/8*3^(1/4)*a^(4/3)*x^(3/2)*(a^(1/3)+b^(1/3)*x)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(1/3)+(1+sqrt(3))*b^(1/3)*x)^2)*EllipticE(sin(arccos((a^(1/3)+(1-sqrt(3))*b^(1/3)*x)/(a^(1/3)+(1+sqrt(3))*b^(1/3)*x))),sqrt(1/2+1/4*sqrt(3)))/b^(5/3)/sqrt(b^(1/3)*x*(a^(1/3)+b^(1/3)*x)/(a^(1/3)+(1+sqrt(3))*b^(1/3)*x)^2)/sqrt(b*x^5+a*x^2)+5/48*(1-sqrt(3))*a^(4/3)*x^(3/2)*(a^(1/3)+b^(1/3)*x)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(1/3)+(1+sqrt(3))*b^(1/3)*x)^2)*InverseJacobiAM(arccos((a^(1/3)+(1-sqrt(3))*b^(1/3)*x)/(a^(1/3)+(1+sqrt(3))*b^(1/3)*x)),sqrt(1/2+1/4*sqrt(3)))*3^(3/4)/b^(5/3)/sqrt(b^(1/3)*x*(a^(1/3)+b^(1/3)*x)/(a^(1/3)+(1+sqrt(3))*b^(1/3)*x)^2)/sqrt(b*x^5+a*x^2),1],
[x^(9/2)/sqrt(b*x^5+a*x^2),x,3,1/3*sqrt(x)*sqrt(b*x^5+a*x^2)/b-1/3*a*arctanh(sqrt(b)*x^(5/2)/sqrt(b*x^5+a*x^2))/b^(3/2),1],
[x^(7/2)/sqrt(b*x^5+a*x^2),x,4,1/2*sqrt(b*x^5+a*x^2)/b/sqrt(x)-1/12*a^(2/3)*x^(3/2)*(a^(1/3)+b^(1/3)*x)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(1/3)+(1+sqrt(3))*b^(1/3)*x)^2)*InverseJacobiAM(arccos((a^(1/3)+(1-sqrt(3))*b^(1/3)*x)/(a^(1/3)+(1+sqrt(3))*b^(1/3)*x)),sqrt(1/2+1/4*sqrt(3)))*3^(3/4)/b/sqrt(b^(1/3)*x*(a^(1/3)+b^(1/3)*x)/(a^(1/3)+(1+sqrt(3))*b^(1/3)*x)^2)/sqrt(b*x^5+a*x^2),1],
[x^(5/2)/sqrt(b*x^5+a*x^2),x,5,(1+sqrt(3))*x^(3/2)*(b*x^3+a)/b^(2/3)/(a^(1/3)+(1+sqrt(3))*b^(1/3)*x)/sqrt(b*x^5+a*x^2)-3^(1/4)*a^(1/3)*x^(3/2)*(a^(1/3)+b^(1/3)*x)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(1/3)+(1+sqrt(3))*b^(1/3)*x)^2)*EllipticE(sin(arccos((a^(1/3)+(1-sqrt(3))*b^(1/3)*x)/(a^(1/3)+(1+sqrt(3))*b^(1/3)*x))),sqrt(1/2+1/4*sqrt(3)))/b^(2/3)/sqrt(b^(1/3)*x*(a^(1/3)+b^(1/3)*x)/(a^(1/3)+(1+sqrt(3))*b^(1/3)*x)^2)/sqrt(b*x^5+a*x^2)-1/6*(1-sqrt(3))*a^(1/3)*x^(3/2)*(a^(1/3)+b^(1/3)*x)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(1/3)+(1+sqrt(3))*b^(1/3)*x)^2)*InverseJacobiAM(arccos((a^(1/3)+(1-sqrt(3))*b^(1/3)*x)/(a^(1/3)+(1+sqrt(3))*b^(1/3)*x)),sqrt(1/2+1/4*sqrt(3)))*3^(3/4)/b^(2/3)/sqrt(b^(1/3)*x*(a^(1/3)+b^(1/3)*x)/(a^(1/3)+(1+sqrt(3))*b^(1/3)*x)^2)/sqrt(b*x^5+a*x^2),1],
[x^(3/2)/sqrt(b*x^5+a*x^2),x,2,2/3*arctanh(sqrt(b)*x^(5/2)/sqrt(b*x^5+a*x^2))/sqrt(b),1],
[sqrt(x)/sqrt(b*x^5+a*x^2),x,3,1/3*x^(3/2)*(a^(1/3)+b^(1/3)*x)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(1/3)+(1+sqrt(3))*b^(1/3)*x)^2)*InverseJacobiAM(arccos((a^(1/3)+(1-sqrt(3))*b^(1/3)*x)/(a^(1/3)+(1+sqrt(3))*b^(1/3)*x)),sqrt(1/2+1/4*sqrt(3)))*3^(3/4)/a^(1/3)/sqrt(b^(1/3)*x*(a^(1/3)+b^(1/3)*x)/(a^(1/3)+(1+sqrt(3))*b^(1/3)*x)^2)/sqrt(b*x^5+a*x^2),1],
[1/sqrt(x)/sqrt(b*x^5+a*x^2),x,6,2*(1+sqrt(3))*b^(1/3)*x^(3/2)*(b*x^3+a)/a/(a^(1/3)+(1+sqrt(3))*b^(1/3)*x)/sqrt(b*x^5+a*x^2)-2*sqrt(b*x^5+a*x^2)/a/x^(3/2)-2*3^(1/4)*b^(1/3)*x^(3/2)*(a^(1/3)+b^(1/3)*x)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(1/3)+(1+sqrt(3))*b^(1/3)*x)^2)*EllipticE(sin(arccos((a^(1/3)+(1-sqrt(3))*b^(1/3)*x)/(a^(1/3)+(1+sqrt(3))*b^(1/3)*x))),sqrt(1/2+1/4*sqrt(3)))/a^(2/3)/sqrt(b^(1/3)*x*(a^(1/3)+b^(1/3)*x)/(a^(1/3)+(1+sqrt(3))*b^(1/3)*x)^2)/sqrt(b*x^5+a*x^2)-1/3*(1-sqrt(3))*b^(1/3)*x^(3/2)*(a^(1/3)+b^(1/3)*x)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(1/3)+(1+sqrt(3))*b^(1/3)*x)^2)*InverseJacobiAM(arccos((a^(1/3)+(1-sqrt(3))*b^(1/3)*x)/(a^(1/3)+(1+sqrt(3))*b^(1/3)*x)),sqrt(1/2+1/4*sqrt(3)))*3^(3/4)/a^(2/3)/sqrt(b^(1/3)*x*(a^(1/3)+b^(1/3)*x)/(a^(1/3)+(1+sqrt(3))*b^(1/3)*x)^2)/sqrt(b*x^5+a*x^2),1],
[1/x^(3/2)/sqrt(b*x^5+a*x^2),x,1,-2/3*sqrt(b*x^5+a*x^2)/a/x^(5/2),1],
[1/x^(5/2)/sqrt(b*x^5+a*x^2),x,4,-2/5*sqrt(b*x^5+a*x^2)/a/x^(7/2)-2/15*b*x^(3/2)*(a^(1/3)+b^(1/3)*x)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(1/3)+(1+sqrt(3))*b^(1/3)*x)^2)*InverseJacobiAM(arccos((a^(1/3)+(1-sqrt(3))*b^(1/3)*x)/(a^(1/3)+(1+sqrt(3))*b^(1/3)*x)),sqrt(1/2+1/4*sqrt(3)))*3^(3/4)/a^(4/3)/sqrt(b^(1/3)*x*(a^(1/3)+b^(1/3)*x)/(a^(1/3)+(1+sqrt(3))*b^(1/3)*x)^2)/sqrt(b*x^5+a*x^2),1],
[1/x^(7/2)/sqrt(b*x^5+a*x^2),x,7,-8/7*(1+sqrt(3))*b^(4/3)*x^(3/2)*(b*x^3+a)/a^2/(a^(1/3)+(1+sqrt(3))*b^(1/3)*x)/sqrt(b*x^5+a*x^2)-2/7*sqrt(b*x^5+a*x^2)/a/x^(9/2)+8/7*b*sqrt(b*x^5+a*x^2)/a^2/x^(3/2)+8/7*3^(1/4)*b^(4/3)*x^(3/2)*(a^(1/3)+b^(1/3)*x)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(1/3)+(1+sqrt(3))*b^(1/3)*x)^2)*EllipticE(sin(arccos((a^(1/3)+(1-sqrt(3))*b^(1/3)*x)/(a^(1/3)+(1+sqrt(3))*b^(1/3)*x))),sqrt(1/2+1/4*sqrt(3)))/a^(5/3)/sqrt(b^(1/3)*x*(a^(1/3)+b^(1/3)*x)/(a^(1/3)+(1+sqrt(3))*b^(1/3)*x)^2)/sqrt(b*x^5+a*x^2)+4/21*(1-sqrt(3))*b^(4/3)*x^(3/2)*(a^(1/3)+b^(1/3)*x)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(1/3)+(1+sqrt(3))*b^(1/3)*x)^2)*InverseJacobiAM(arccos((a^(1/3)+(1-sqrt(3))*b^(1/3)*x)/(a^(1/3)+(1+sqrt(3))*b^(1/3)*x)),sqrt(1/2+1/4*sqrt(3)))*3^(3/4)/a^(5/3)/sqrt(b^(1/3)*x*(a^(1/3)+b^(1/3)*x)/(a^(1/3)+(1+sqrt(3))*b^(1/3)*x)^2)/sqrt(b*x^5+a*x^2),1],
[1/x^(9/2)/sqrt(b*x^5+a*x^2),x,2,-2/9*sqrt(b*x^5+a*x^2)/a/x^(11/2)+4/9*b*sqrt(b*x^5+a*x^2)/a^2/x^(5/2),1],
[1/x^(11/2)/sqrt(b*x^5+a*x^2),x,5,-2/11*sqrt(b*x^5+a*x^2)/a/x^(13/2)+16/55*b*sqrt(b*x^5+a*x^2)/a^2/x^(7/2)+16/165*b^2*x^(3/2)*(a^(1/3)+b^(1/3)*x)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(1/3)+(1+sqrt(3))*b^(1/3)*x)^2)*InverseJacobiAM(arccos((a^(1/3)+(1-sqrt(3))*b^(1/3)*x)/(a^(1/3)+(1+sqrt(3))*b^(1/3)*x)),sqrt(1/2+1/4*sqrt(3)))*3^(3/4)/a^(7/3)/sqrt(b^(1/3)*x*(a^(1/3)+b^(1/3)*x)/(a^(1/3)+(1+sqrt(3))*b^(1/3)*x)^2)/sqrt(b*x^5+a*x^2),1],
[x/(b*x^4+a*x^3),x,3,-1/a/x-b*ln(x)/a^2+b*ln(b*x+a)/a^2,1],
[1/(b*x^4+a*x^3),x,3,-1/2/a/x^2+b/a^2/x+b^2*ln(x)/a^3-b^2*ln(b*x+a)/a^3,1],
[x^4/sqrt(b*x^4+a*x^3),x,5,-5/12*a*sqrt(b*x^4+a*x^3)/b^2+5/8*a^2*sqrt(b*x^4+a*x^3)/b^3/x+1/3*x*sqrt(b*x^4+a*x^3)/b-5/8*a^3*arctanh(sqrt(b)*x^2/sqrt(b*x^4+a*x^3))/b^(7/2),1],
[x^3/sqrt(b*x^4+a*x^3),x,4,1/2*sqrt(b*x^4+a*x^3)/b-3/4*a*sqrt(b*x^4+a*x^3)/b^2/x+3/4*a^2*arctanh(sqrt(b)*x^2/sqrt(b*x^4+a*x^3))/b^(5/2),1],
[x^2/sqrt(b*x^4+a*x^3),x,3,sqrt(b*x^4+a*x^3)/b/x-a*arctanh(sqrt(b)*x^2/sqrt(b*x^4+a*x^3))/b^(3/2),1],
[x/sqrt(b*x^4+a*x^3),x,2,2*arctanh(sqrt(b)*x^2/sqrt(b*x^4+a*x^3))/sqrt(b),1],
[1/sqrt(b*x^4+a*x^3),x,1,-2*sqrt(b*x^4+a*x^3)/a/x^2,1],
[1/x/sqrt(b*x^4+a*x^3),x,2,-2/3*sqrt(b*x^4+a*x^3)/a/x^3+4/3*b*sqrt(b*x^4+a*x^3)/a^2/x^2,1],
[1/x^2/sqrt(b*x^4+a*x^3),x,3,-2/5*sqrt(b*x^4+a*x^3)/a/x^4+8/15*b*sqrt(b*x^4+a*x^3)/a^2/x^3-16/15*b^2*sqrt(b*x^4+a*x^3)/a^3/x^2,1],
[1/x^3/sqrt(b*x^4+a*x^3),x,4,-2/7*sqrt(b*x^4+a*x^3)/a/x^5+12/35*b*sqrt(b*x^4+a*x^3)/a^2/x^4-16/35*b^2*sqrt(b*x^4+a*x^3)/a^3/x^3+32/35*b^3*sqrt(b*x^4+a*x^3)/a^4/x^2,1],
[1/(b*x^5+x^3),x,4,-1/2/x^2-b*ln(x)+1/2*b*ln(b*x^2+1),1],
[1/(b*x^5-x^3),x,4,1/2/x^2-b*ln(x)+1/2*b*ln(-b*x^2+1),1],
[1/(a*x+b*x),x,2,ln(x)/(a+b),1],
[1/(a*x+b*x)^2,x,2,-1/(a+b)^2/x,1],
[1/(a*x+b*x)^3,x,2,-1/2/(a+b)^3/x^2,1],
[1/(a*x^2+b*x^2),x,2,-1/(a+b)/x,1],
[1/(a*x^n+b*x^n),x,2,x^(1-n)/(a+b)/(1-n),1],
[1/(a*x^n+b*x^n)^2,x,2,x^(1-2*n)/(a+b)^2/(1-2*n),1],
[1/(a*x^n+b*x^n)^3,x,2,x^(1-3*n)/(a+b)^3/(1-3*n),1],
[(b*x^14+a*x)^12,x,2,1/169*(b*x^13+a)^13/b,1],
[x^12*(b*x^26+a*x)^12,x,2,1/325*(b*x^25+a)^13/b,1],
[x^24*(b*x^38+a*x)^12,x,2,1/481*(b*x^37+a)^13/b,1],
[x^(-12+12*m)*(a*x+b*x^(2+12*m))^12,x,2,1/13*(a+b*x^(1+12*m))^13/b/(1+12*m),1],
[(b*x^14+a*x)^12,x,2,1/169*(b*x^13+a)^13/b,1],
[(b*x^27+a*x^2)^12,x,2,1/325*(b*x^25+a)^13/b,1],
[(b*x^40+a*x^3)^12,x,2,1/481*(b*x^37+a)^13/b,1],
[(a*x^m+b*x^(1+13*m))^12,x,2,1/13*(a+b*x^(1+12*m))^13/b/(1+12*m),1],
[(a*x^m+b*x^(1+6*m))^5,x,2,1/6*(a+b*x^(1+5*m))^6/b/(1+5*m),1],
[1/(b*x^(1-2*m)+a*x^m)^3,x,2,-1/2/b/(1-3*m)/(a+b*x^(1-3*m))^2,1],
[1/(b/x+a*x),x,2,1/2*ln(a*x^2+b)/a,1],
[1/(b/x^2+a*x),x,2,1/3*ln(a*x^3+b)/a,1],
[1/(b/x^3+a*x),x,2,1/4*ln(a*x^4+b)/a,1],
[1/(b/x+a*x)^3,x,2,1/4*x^4/b/(a*x^2+b)^2,1],
[1/(b/x^3+a*x^2)^3,x,2,1/10*x^10/b/(a*x^5+b)^2,1],
[1/(b/x^5+a*x^3)^3,x,2,1/16*x^16/b/(a*x^8+b)^2,1],
[(a/x+b*x)^2,x,3,-a^2/x+2*a*b*x+1/3*b^2*x^3,1],
[(a/x+b*x)^3,x,4,-1/2*a^3/x^2+3/2*a*b^2*x^2+1/4*b^3*x^4+3*a^2*b*ln(x),1],
[(a/x+b*x)^4,x,3,-1/3*a^4/x^3-4*a^3*b/x+6*a^2*b^2*x+4/3*a*b^3*x^3+1/5*b^4*x^5,1],
[x/(1/x+x),x,3,x-arctan(x),1],
[1/(1/x^2+x^3),x,7,1/5*sqrt(5/2-1/2*sqrt(5))*arctan((1-sqrt(5)-4*x)/sqrt(10+2*sqrt(5)))-1/5*sqrt(5/2+1/2*sqrt(5))*arctan(1/2*sqrt(1/2+1/10*sqrt(5))*(1+sqrt(5)-4*x))+1/5*ln(1+x)-1/20*(1+sqrt(5))*ln(1-1/2*(1-sqrt(5))*x+x^2)-1/20*(1-sqrt(5))*ln(1-1/2*(1+sqrt(5))*x+x^2),1],
[x^p*(a*x^n+b*x^(1+13*n+p))^12,x,2,1/13*(a+b*x^(1+12*n+p))^13/b/(1+12*n+p),1],
[x^12*(b*x^13+a)^12,x,1,1/169*(b*x^13+a)^13/b,1],
[x^12*(b*x^26+a*x)^12,x,2,1/325*(b*x^25+a)^13/b,1],
[x^12*(b*x^39+a*x^2)^12,x,2,1/481*(b*x^37+a)^13/b,1],
[x^24*(b*x^25+a)^12,x,1,1/325*(b*x^25+a)^13/b,1],
[x^24*(b*x^38+a*x)^12,x,2,1/481*(b*x^37+a)^13/b,1],
[x^36*(b*x^37+a)^12,x,1,1/481*(b*x^37+a)^13/b,1],
[1/(a*x+b*x^n),x,2,ln(b+a*x^(1-n))/a/(1-n),1],
[1/(a*x+b*x^(1+n)),x,5,ln(x)/a-ln(a+b*x^n)/a/n,1],
[1/(a*x+b*x^(1-n)),x,2,ln(b+a*x^n)/a/n,1],
[1/(2*x+3*x^(1+n)),x,5,1/2*ln(x)-1/2*ln(2+3*x^n)/n,1],
[1/(2*x+3*x^(1-n)),x,2,1/2*ln(3+2*x^n)/n,1],
[1/(-sqrt(x)+x),x,3,2*ln(1-sqrt(x)),1],
[1/(-x^(3/5)+x),x,2,5/2*ln(1-x^(2/5)),1],
[1/(1/x^(1/3)+x),x,2,3/4*ln(1+x^(4/3)),1],
[1/(x+x^sqrt(2)),x,5,ln(x)-(1+sqrt(2))*ln(1+x^(-1+sqrt(2))),1],
[x^(-1-1/2*j)*sqrt(a*x^j+b*x^n),x,3,-2*sqrt(a*x^j+b*x^n)/(j-n)/(x^(1/2*j))+2*sqrt(a)*arctanh(sqrt(a)*x^(1/2*j)/sqrt(a*x^j+b*x^n))/(j-n),1],
[(c*x)^(-1-1/2*j)*sqrt(a*x^j+b*x^n),x,4,-2*sqrt(a*x^j+b*x^n)/c/(j-n)/((c*x)^(1/2*j))+2*sqrt(a)*x^(1/2*j)*arctanh(sqrt(a)*x^(1/2*j)/sqrt(a*x^j+b*x^n))/c/(j-n)/((c*x)^(1/2*j)),1],
[sqrt(a*x^3+b*x^n)/(c*x)^(5/2),x,4,-2*sqrt(a*x^3+b*x^n)/c/(3-n)/(c*x)^(3/2)+2*sqrt(a)*sqrt(c*x)*arctanh(sqrt(a)*x^(3/2)/sqrt(a*x^3+b*x^n))/c^3/(3-n)/sqrt(x),1],
[sqrt(a*x^2+b*x^n)/c^2/x^2,x,4,-2*sqrt(a*x^2+b*x^n)/c^2/(2-n)/x+2*sqrt(a)*arctanh(sqrt(a)*x/sqrt(a*x^2+b*x^n))/c^2/(2-n),1],
[sqrt(a*x+b*x^n)/(c*x)^(3/2),x,4,-2*sqrt(a*x+b*x^n)/c/(1-n)/sqrt(c*x)+2*sqrt(a)*sqrt(x)*arctanh(sqrt(a)*sqrt(x)/sqrt(a*x+b*x^n))/c/(1-n)/sqrt(c*x),1],
[sqrt(a+b*x^n)/c/x,x,5,2*sqrt(a+b*x^n)/c/n-2*sqrt(a)*arctanh(sqrt(a+b*x^n)/sqrt(a))/c/n,1],
[sqrt(a/x+b*x^n)/sqrt(c*x),x,4,2*sqrt(c*x)*sqrt(a/x+b*x^n)/c/(1+n)-2*sqrt(a)*sqrt(x)*arctanh(sqrt(a)/sqrt(x)/sqrt(a/x+b*x^n))/(1+n)/sqrt(c*x),1],
[sqrt(a/x^2+b*x^n),x,3,2*x*sqrt(a/x^2+b*x^n)/(2+n)-2*sqrt(a)*arctanh(sqrt(a)/x/sqrt(a/x^2+b*x^n))/(2+n),1],
[sqrt(c*x)*sqrt(a/x^3+b*x^n),x,4,2*(c*x)^(3/2)*sqrt(a/x^3+b*x^n)/c/(3+n)-2*sqrt(a)*c*sqrt(x)*arctanh(sqrt(a)/x^(3/2)/sqrt(a/x^3+b*x^n))/(3+n)/sqrt(c*x),1],
[(c*x)^(-1-3/2*j)*(a*x^j+b*x^n)^(3/2),x,5,-2*a*x^j*sqrt(a*x^j+b*x^n)/c/(j-n)/((c*x)^(3/2*j))-2/3*(a*x^j+b*x^n)^(3/2)/c/(j-n)/((c*x)^(3/2*j))+2*a^(3/2)*x^(3/2*j)*arctanh(sqrt(a)*x^(1/2*j)/sqrt(a*x^j+b*x^n))/c/(j-n)/((c*x)^(3/2*j)),1],
[(a*x^3+b*x^n)^(3/2)/(c*x)^(11/2),x,5,-2*a*sqrt(a*x^3+b*x^n)/c^4/(3-n)/(c*x)^(3/2)-2/3*(a*x^3+b*x^n)^(3/2)/c/(3-n)/(c*x)^(9/2)+2*a^(3/2)*sqrt(c*x)*arctanh(sqrt(a)*x^(3/2)/sqrt(a*x^3+b*x^n))/c^6/(3-n)/sqrt(x),1],
[(a*x^2+b*x^n)^(3/2)/c^4/x^4,x,5,-2*a*sqrt(a*x^2+b*x^n)/c^4/(2-n)/x-2/3*(a*x^2+b*x^n)^(3/2)/c^4/(2-n)/x^3+2*a^(3/2)*arctanh(sqrt(a)*x/sqrt(a*x^2+b*x^n))/c^4/(2-n),1],
[(a*x+b*x^n)^(3/2)/(c*x)^(5/2),x,5,-2*a*sqrt(a*x+b*x^n)/c^2/(1-n)/sqrt(c*x)-2/3*(a*x+b*x^n)^(3/2)/c/(1-n)/(c*x)^(3/2)+2*a^(3/2)*sqrt(x)*arctanh(sqrt(a)*sqrt(x)/sqrt(a*x+b*x^n))/c^2/(1-n)/sqrt(c*x),1],
[(a+b*x^n)^(3/2)/c/x,x,6,2*a*sqrt(a+b*x^n)/c/n+2/3*(a+b*x^n)^(3/2)/c/n-2*a^(3/2)*arctanh(sqrt(a+b*x^n)/sqrt(a))/c/n,1],
[sqrt(c*x)*(a/x+b*x^n)^(3/2),x,5,2*a*sqrt(c*x)*sqrt(a/x+b*x^n)/(1+n)+2/3*(c*x)^(3/2)*(a/x+b*x^n)^(3/2)/c/(1+n)-2*a^(3/2)*c*sqrt(x)*arctanh(sqrt(a)/sqrt(x)/sqrt(a/x+b*x^n))/(1+n)/sqrt(c*x),1],
[c^2*x^2*(a/x^2+b*x^n)^(3/2),x,5,2*a*c^2*x*sqrt(a/x^2+b*x^n)/(2+n)+2*c^2*x^3*(a/x^2+b*x^n)^(3/2)/(6+3*n)-2*a^(3/2)*c^2*arctanh(sqrt(a)/x/sqrt(a/x^2+b*x^n))/(2+n),1],
[(c*x)^(7/2)*(a/x^3+b*x^n)^(3/2),x,5,2*a*c^2*(c*x)^(3/2)*sqrt(a/x^3+b*x^n)/(3+n)+2/3*(c*x)^(9/2)*(a/x^3+b*x^n)^(3/2)/c/(3+n)-2*a^(3/2)*c^4*sqrt(x)*arctanh(sqrt(a)/x^(3/2)/sqrt(a/x^3+b*x^n))/(3+n)/sqrt(c*x),1],
[c^5*x^5*(a/x^4+b*x^n)^(3/2),x,5,2*a*c^5*x^2*sqrt(a/x^4+b*x^n)/(4+n)+2*c^5*x^6*(a/x^4+b*x^n)^(3/2)/(12+3*n)-2*a^(3/2)*c^5*arctanh(sqrt(a)/x^2/sqrt(a/x^4+b*x^n))/(4+n),1],
[sqrt((b*x+a)/x^2),x,6,2*x*sqrt((b*x+a)/x^2)-2*sqrt(a)*arctanh(x*sqrt((b*x+a)/x^2)/sqrt(a)),1],
[sqrt((b*x^2+a)/x^2),x,5,sqrt(b+a/x^2)*x-sqrt(a)*arctanh(sqrt(a)/sqrt(b+a/x^2)/x),1],
[sqrt((b*x^3+a)/x^2),x,4,2/3*x*sqrt(a/x^2+b*x)-2/3*sqrt(a)*arctanh(sqrt(a)/x/sqrt(a/x^2+b*x)),1],
[sqrt((a+b*x^n)/x^2),x,4,2*x*sqrt(a/x^2+b*x^(-2+n))/n-2*sqrt(a)*arctanh(sqrt(a)/x/sqrt(a/x^2+b*x^(-2+n)))/n,1],
[sqrt((b*x-a)/x^2),x,6,2*x*sqrt((b*x-a)/x^2)-2*sqrt(a)*arctan(x*sqrt((b*x-a)/x^2)/sqrt(a)),1],
[sqrt((b*x^2-a)/x^2),x,5,sqrt(b-a/x^2)*x+sqrt(a)*arctan(sqrt(a)/sqrt(b-a/x^2)/x),1],
[sqrt((b*x^3-a)/x^2),x,4,2/3*x*sqrt(-a/x^2+b*x)+2/3*sqrt(a)*arctan(sqrt(a)/x/sqrt(-a/x^2+b*x)),1],
[sqrt((-a+b*x^n)/x^2),x,4,2*x*sqrt(-a/x^2+b*x^(-2+n))/n+2*sqrt(a)*arctan(sqrt(a)/x/sqrt(-a/x^2+b*x^(-2+n)))/n,1],
[(c*x)^(-1+1/2*j)/sqrt(a*x^j+b*x^n),x,3,2*(c*x)^(1/2*j)*arctanh(sqrt(a)*x^(1/2*j)/sqrt(a*x^j+b*x^n))/sqrt(a)/c/(j-n)/(x^(1/2*j)),1],
[sqrt(c*x)/sqrt(a*x^3+b*x^n),x,3,2*sqrt(c*x)*arctanh(sqrt(a)*x^(3/2)/sqrt(a*x^3+b*x^n))/sqrt(a)/(3-n)/sqrt(x),1],
[1/sqrt(a*x^2+b*x^n),x,2,2*arctanh(sqrt(a)*x/sqrt(a*x^2+b*x^n))/sqrt(a)/(2-n),1],
[1/sqrt(c*x)/sqrt(a*x+b*x^n),x,3,2*sqrt(x)*arctanh(sqrt(a)*sqrt(x)/sqrt(a*x+b*x^n))/sqrt(a)/(1-n)/sqrt(c*x),1],
[1/c/x/sqrt(a+b*x^n),x,4,-2*arctanh(sqrt(a+b*x^n)/sqrt(a))/sqrt(a)/c/n,1],
[1/(c*x)^(3/2)/sqrt(a/x+b*x^n),x,3,-2*sqrt(x)*arctanh(sqrt(a)/sqrt(x)/sqrt(a/x+b*x^n))/sqrt(a)/c/(1+n)/sqrt(c*x),1],
[1/c^2/x^2/sqrt(a/x^2+b*x^n),x,3,-2*arctanh(sqrt(a)/x/sqrt(a/x^2+b*x^n))/sqrt(a)/c^2/(2+n),1],
[1/(c*x)^(5/2)/sqrt(a/x^3+b*x^n),x,3,-2*sqrt(x)*arctanh(sqrt(a)/x^(3/2)/sqrt(a/x^3+b*x^n))/sqrt(a)/c^2/(3+n)/sqrt(c*x),1],
[(c*x)^(-1+3/2*j)/(a*x^j+b*x^n)^(3/2),x,4,-2*(c*x)^(3/2*j)/a/c/(j-n)/(x^j)/sqrt(a*x^j+b*x^n)+2*(c*x)^(3/2*j)*arctanh(sqrt(a)*x^(1/2*j)/sqrt(a*x^j+b*x^n))/a^(3/2)/c/(j-n)/(x^(3/2*j)),1],
[(c*x)^(7/2)/(a*x^3+b*x^n)^(3/2),x,4,-2*c^2*(c*x)^(3/2)/a/(3-n)/sqrt(a*x^3+b*x^n)+2*c^3*sqrt(c*x)*arctanh(sqrt(a)*x^(3/2)/sqrt(a*x^3+b*x^n))/a^(3/2)/(3-n)/sqrt(x),1],
[c^2*x^2/(a*x^2+b*x^n)^(3/2),x,4,-2*c^2*x/a/(2-n)/sqrt(a*x^2+b*x^n)+2*c^2*arctanh(sqrt(a)*x/sqrt(a*x^2+b*x^n))/a^(3/2)/(2-n),1],
[sqrt(c*x)/(a*x+b*x^n)^(3/2),x,4,-2*sqrt(c*x)/a/(1-n)/sqrt(a*x+b*x^n)+2*c*sqrt(x)*arctanh(sqrt(a)*sqrt(x)/sqrt(a*x+b*x^n))/a^(3/2)/(1-n)/sqrt(c*x),1],
[1/c/x/(a+b*x^n)^(3/2),x,5,2/a/c/n/sqrt(a+b*x^n)-2*arctanh(sqrt(a+b*x^n)/sqrt(a))/a^(3/2)/c/n,1],
[1/(c*x)^(5/2)/(a/x+b*x^n)^(3/2),x,4,2/a/c^2/(1+n)/sqrt(c*x)/sqrt(a/x+b*x^n)-2*sqrt(x)*arctanh(sqrt(a)/sqrt(x)/sqrt(a/x+b*x^n))/a^(3/2)/c^2/(1+n)/sqrt(c*x),1],
[1/c^4/x^4/(a/x^2+b*x^n)^(3/2),x,4,2/a/c^4/(2+n)/x/sqrt(a/x^2+b*x^n)-2*arctanh(sqrt(a)/x/sqrt(a/x^2+b*x^n))/a^(3/2)/c^4/(2+n),1],
[1/(c*x)^(11/2)/(a/x^3+b*x^n)^(3/2),x,4,2/a/c^4/(3+n)/(c*x)^(3/2)/sqrt(a/x^3+b*x^n)-2*sqrt(x)*arctanh(sqrt(a)/x^(3/2)/sqrt(a/x^3+b*x^n))/a^(3/2)/c^5/(3+n)/sqrt(c*x),1],
[1/c^7/x^7/(a/x^4+b*x^n)^(3/2),x,4,2/a/c^7/(4+n)/x^2/sqrt(a/x^4+b*x^n)-2*arctanh(sqrt(a)/x^2/sqrt(a/x^4+b*x^n))/a^(3/2)/c^7/(4+n),1],
[1/sqrt((b*x^3+a)/x),x,3,2/3*arctanh(sqrt(b)*x/sqrt(a/x+b*x^2))/sqrt(b),1],
[1/sqrt((b*x^4+a)/x^2),x,3,1/2*arctanh(sqrt(b)*x/sqrt(a/x^2+b*x^2))/sqrt(b),1],
[1/sqrt((b*x^5+a)/x^3),x,3,2/5*arctanh(sqrt(b)*x/sqrt(a/x^3+b*x^2))/sqrt(b),1],
[1/sqrt(x^(2-n)*(a+b*x^n)),x,3,2*arctanh(sqrt(b)*x/sqrt(b*x^2+a*x^(2-n)))/sqrt(b)/n,1],
[1/sqrt((-b*x^3+a)/x),x,3,2/3*arctan(sqrt(b)*x/sqrt(a/x-b*x^2))/sqrt(b),1],
[1/sqrt((-b*x^4+a)/x^2),x,3,1/2*arctan(sqrt(b)*x/sqrt(a/x^2-b*x^2))/sqrt(b),1],
[1/sqrt((-b*x^5+a)/x^3),x,3,2/5*arctan(sqrt(b)*x/sqrt(a/x^3-b*x^2))/sqrt(b),1],
[1/sqrt(x^(2-n)*(a-b*x^n)),x,3,2*arctan(sqrt(b)*x/sqrt(-b*x^2+a*x^(2-n)))/sqrt(b)/n,1],
[1/sqrt(x^n*(a+b*x^(2-n))),x,3,2*arctanh(sqrt(b)*x/sqrt(b*x^2+a*x^n))/sqrt(b)/(2-n),1],
[1/sqrt(x^2*(b+a*x^(-2+n))),x,3,2*arctanh(sqrt(b)*x/sqrt(b*x^2+a*x^n))/sqrt(b)/(2-n),1],
[1/sqrt(x*(b*x+a*x^(-1+n))),x,3,2*arctanh(sqrt(b)*x/sqrt(b*x^2+a*x^n))/sqrt(b)/(2-n),1],
[1/sqrt(x^n*(a-b*x^(2-n))),x,3,2*arctan(sqrt(b)*x/sqrt(-b*x^2+a*x^n))/sqrt(b)/(2-n),1],
[1/sqrt(x^2*(-b+a*x^(-2+n))),x,3,2*arctan(sqrt(b)*x/sqrt(-b*x^2+a*x^n))/sqrt(b)/(2-n),1],
[1/sqrt(x*(-b*x+a*x^(-1+n))),x,3,2*arctan(sqrt(b)*x/sqrt(-b*x^2+a*x^n))/sqrt(b)/(2-n),1],
[(c*x)^m*(a*x^j+b*x^n)^(3/2),x,3,2*b*x^(1+n)*(c*x)^m*sqrt(a*x^j+b*x^n)*hypergeom([-3/2, (1+m+3/2*n)/(j-n)],[1+(1+m+3/2*n)/(j-n)],-a*x^(j-n)/b)/(2+2*m+3*n)/sqrt(1+a*x^(j-n)/b),1],
[(c*x)^m*sqrt(a*x^j+b*x^n),x,3,2*x*(c*x)^m*sqrt(a*x^j+b*x^n)*hypergeom([-1/2, (1+m+1/2*n)/(j-n)],[1+(2+2*m+n)/(2*j-2*n)],-a*x^(j-n)/b)/(2+2*m+n)/sqrt(1+a*x^(j-n)/b),1],
[(c*x)^m/sqrt(a*x^j+b*x^n),x,3,2*x*(c*x)^m*sqrt(1+a*x^(j-n)/b)*hypergeom([1/2, (1+m-1/2*n)/(j-n)],[1+(1+m-1/2*n)/(j-n)],-a*x^(j-n)/b)/(2+2*m-n)/sqrt(a*x^j+b*x^n),1],
[(c*x)^m/(a*x^j+b*x^n)^(3/2),x,3,2*x^(1-n)*(c*x)^m*sqrt(1+a*x^(j-n)/b)*hypergeom([3/2, (1+m-3/2*n)/(j-n)],[1+(1+m-3/2*n)/(j-n)],-a*x^(j-n)/b)/b/(2+2*m-3*n)/sqrt(a*x^j+b*x^n),1],
[(c*x)^m/(a*x^j+b*x^n)^(5/2),x,3,2*x^(1-2*n)*(c*x)^m*sqrt(1+a*x^(j-n)/b)*hypergeom([5/2, (1+m-5/2*n)/(j-n)],[1+(1+m-5/2*n)/(j-n)],-a*x^(j-n)/b)/b^2/(2+2*m-5*n)/sqrt(a*x^j+b*x^n),1],
[(a*x^j+b*x^n)^(3/2),x,3,2*b*x^(1+n)*sqrt(a*x^j+b*x^n)*hypergeom([-3/2, (1+3/2*n)/(j-n)],[(2+2*j+n)/(2*j-2*n)],-a*x^(j-n)/b)/(2+3*n)/sqrt(1+a*x^(j-n)/b),1],
[sqrt(a*x^j+b*x^n),x,3,2*x*sqrt(a*x^j+b*x^n)*hypergeom([-1/2, (2+n)/(2*j-2*n)],[1+(2+n)/(2*j-2*n)],-a*x^(j-n)/b)/(2+n)/sqrt(1+a*x^(j-n)/b),1],
[1/sqrt(a*x^j+b*x^n),x,3,2*x*sqrt(1+a*x^(j-n)/b)*hypergeom([1/2, (2-n)/(2*j-2*n)],[1+(1-1/2*n)/(j-n)],-a*x^(j-n)/b)/(2-n)/sqrt(a*x^j+b*x^n),1],
[1/(a*x^j+b*x^n)^(3/2),x,3,2*x^(1-n)*sqrt(1+a*x^(j-n)/b)*hypergeom([3/2, (1-3/2*n)/(j-n)],[1+(1-3/2*n)/(j-n)],-a*x^(j-n)/b)/b/(2-3*n)/sqrt(a*x^j+b*x^n),1],
[1/(a*x^j+b*x^n)^(5/2),x,3,2*x^(1-2*n)*sqrt(1+a*x^(j-n)/b)*hypergeom([5/2, (1-5/2*n)/(j-n)],[1+(1-5/2*n)/(j-n)],-a*x^(j-n)/b)/b^2/(2-5*n)/sqrt(a*x^j+b*x^n),1],
[sqrt((1+x)/x^5),x,2,-2/3*x^6*((1+x)/x^5)^(3/2),1],
[sqrt(x+x^(5/2)),x,1,4/9*(x+x^(5/2))^(3/2)/x^(3/2),1],
[1/(sqrt(x)+x^(3/2)),x,3,2*arctan(sqrt(x)),1],
[x*sqrt(x^2*(b*x^3+a)),x,2,2/9*(b*x^5+a*x^2)^(3/2)/b/x^3,1],
[x*sqrt(b*x^5+a*x^2),x,1,2/9*(b*x^5+a*x^2)^(3/2)/b/x^3,1],
[sqrt(x^4*(b*x^3+a)),x,2,2/9*(b*x^7+a*x^4)^(3/2)/b/x^6,1],
[(c*x)^m*(a*x^q+b*x^r)^3,x,3,a^3*x^(1+3*q)*(c*x)^m/(1+m+3*q)+3*a^2*b*x^(1+2*q+r)*(c*x)^m/(1+m+2*q+r)+3*a*b^2*x^(1+q+2*r)*(c*x)^m/(1+m+q+2*r)+b^3*x^(1+3*r)*(c*x)^m/(1+m+3*r),1],
[(c*x)^m*(a*x^q+b*x^r)^2,x,3,a^2*x^(1+2*q)*(c*x)^m/(1+m+2*q)+2*a*b*x^(1+q+r)*(c*x)^m/(1+m+q+r)+b^2*x^(1+2*r)*(c*x)^m/(1+m+2*r),1],
[(c*x)^m*(a*x^q+b*x^r),x,3,a*x^(1+q)*(c*x)^m/(1+m+q)+b*x^(1+r)*(c*x)^m/(1+m+r),1],
[(c*x)^m/(a*x^q+b*x^r),x,2,x^(1-r)*(c*x)^m*hypergeom([1, (1+m-r)/(q-r)],[(1+m+q-2*r)/(q-r)],-a*x^(q-r)/b)/b/(1+m-r),1],
[(c*x)^m/(a*x^q+b*x^r)^2,x,2,x^(1-2*r)*(c*x)^m*hypergeom([2, (1+m-2*r)/(q-r)],[(1+m+q-3*r)/(q-r)],-a*x^(q-r)/b)/b^2/(1+m-2*r),1],
[(c*x)^m/(a*x^q+b*x^r)^3,x,2,x^(1-3*r)*(c*x)^m*hypergeom([3, (1+m-3*r)/(q-r)],[(1+m+q-4*r)/(q-r)],-a*x^(q-r)/b)/b^3/(1+m-3*r),1],
[x^m*(a*x^j+b*x^n)^p,x,3,x^(1+m)*(a*x^j+b*x^n)^p*hypergeom([-p, (n*p+m+1)/(j-n)],[1+(n*p+m+1)/(j-n)],-a*x^(j-n)/b)/(n*p+m+1)/((1+a*x^(j-n)/b)^p),1],
[x^(-p*q-1)*(b*x^n+a*x^q)^p,x,3,-(a+b*x^(n-q))*(b*x^n+a*x^q)^p*hypergeom([1, p+1],[2+p],1+b*x^(n-q)/a)/a/(p+1)/(n-q)/(x^(p*q)),1],
[x^(-n*p-1)*(b*x^n+a*x^q)^p,x,3,-(b*x^n+a*x^q)^p*hypergeom([-p, -p],[1-p],-b*x^(n-q)/a)/p/(n-q)/(x^(n*p))/((1+b*x^(n-q)/a)^p),1],
[x^(-1-n-(-1+p)*q)*(b*x^n+a*x^q)^p,x,3,b*(a+b*x^(n-q))*(b*x^n+a*x^q)^p*hypergeom([2, p+1],[2+p],1+b*x^(n-q)/a)/a^2/(p+1)/(n-q)/(x^(p*q)),1],
[x^(-1-n*(-1+p)-q)*(b*x^n+a*x^q)^p,x,3,x^(-n*p+n-q)*(b*x^n+a*x^q)^p*hypergeom([1-p, -p],[2-p],-b*x^(n-q)/a)/(1-p)/(n-q)/((1+b*x^(n-q)/a)^p),1],
[(-1/x+x)^p/x,x,3,-(-1/x+x)^p*hypergeom([-p, -1/2*p],[1-1/2*p],x^2)/p/((-x^2+1)^p),1],
[(a*x^m+b*x^(m*p+m+1))^p,x,1,(a*x^m+b*x^(m*p+m+1))^(p+1)/b/(p+1)/(m*p+1)/(x^(m*(p+1))),1],
[(x^m*(a+b*x^(m*p+1)))^p,x,2,(a*x^m+b*x^(m*p+m+1))^(p+1)/b/(p+1)/(m*p+1)/(x^(m*(p+1))),1],
[x^n*(x^m*(a+b*x^(m*p+n+1)))^p,x,2,(a*x^m+b*x^(m*p+m+n+1))^(p+1)/b/(p+1)/(m*p+n+1)/(x^(m*(p+1))),1],
[x^n*(a*x^m+b*x^(m*p+m+n+1))^p,x,1,(a*x^m+b*x^(m*p+m+n+1))^(p+1)/b/(p+1)/(m*p+n+1)/(x^(m*(p+1))),1],
[sqrt(x^(-2+2*n)*(a+b*x^n)),x,2,2/3*x^(3-3*n)*(a/(x^(2-2*n))+b*x^(-2+3*n))^(3/2)/b/n,1],
[(x^(-3+3*n)*(a+b*x^n))^(1/3),x,2,3/4*x^(4-4*n)*(a/(x^(3-3*n))+b*x^(-3+4*n))^(4/3)/b/n,1],
[(x^(-4+4*n)*(a+b*x^n))^(1/4),x,2,4/5*x^(5-5*n)*(a/(x^(4-4*n))+b*x^(-4+5*n))^(5/4)/b/n,1],
[(x^((-1+n)*p)*(a+b*x^n))^(1/p),x,2,p*x^((1-n)*(p+1))*(a/(x^((1-n)*p))+b*x^(n-(1-n)*p))^(1+1/p)/b/n/(p+1),1],
[(x^((-1+n)/p)*(a+b*x^n))^p,x,2,x^((1-n)*(p+1)/p)*(b*x^(n-(1-n)/p)+a/(x^((1-n)/p)))^(p+1)/b/n/(p+1),1],
[x^(-1+n-p*(1+q))*(a*x^n+b*x^p)^q,x,1,(a*x^n+b*x^p)^(1+q)/a/(n-p)/(1+q)/(x^(p*(1+q))),1],
[x^(-1-n*q-p*(1+q))*(x^n*(a+b*x^p))^q,x,2,-(a*x^n+b*x^(n+p))^(1+q)/a/p/(1+q)/(x^((n+p)*(1+q))),1]]: