# Maple integration test file: "1 Algebraic functions\1.1 Binomial products\1.1.3 General\1.1.3.4 (e x)^m (a+b x^n)^p (c+d x^n)^q.txt"

lst:=[

# Integrands of the form (e x)^m (a+b x^3)^p (c+d x^3)^q

# Integrands of the form (e x)^m (a+b x^3)^p (c+d x^3)^q

# Integrands of the form x^m (a+b x^3)^p (c+d x^3)

# p>0
[x^2*(a+b*x^3)*(A+B*x^3),x,3,1/3*a*A*x^3+1/6*(A*b+a*B)*x^6+1/9*b*B*x^9],
[x*(a+b*x^3)*(A+B*x^3),x,2,1/2*a*A*x^2+1/5*(A*b+a*B)*x^5+1/8*b*B*x^8],
[(a+b*x^3)*(A+B*x^3),x,2,a*A*x+1/4*(A*b+a*B)*x^4+1/7*b*B*x^7],
[(a+b*x^3)*(A+B*x^3)/x,x,3,1/3*(A*b+a*B)*x^3+1/6*b*B*x^6+a*A*log(x)],
[(a+b*x^3)*(A+B*x^3)/x^2,x,2,-a*A/x+1/2*(A*b+a*B)*x^2+1/5*b*B*x^5],
[(a+b*x^3)*(A+B*x^3)/x^3,x,2,-1/2*a*A/x^2+(A*b+a*B)*x+1/4*b*B*x^4],
[(a+b*x^3)*(A+B*x^3)/x^4,x,3,-1/3*a*A/x^3+1/3*b*B*x^3+(A*b+a*B)*log(x)],
[(a+b*x^3)*(A+B*x^3)/x^5,x,2,-1/4*a*A/x^4+(-A*b-a*B)/x+1/2*b*B*x^2],
[(a+b*x^3)*(A+B*x^3)/x^6,x,2,-1/5*a*A/x^5+1/2*(-A*b-a*B)/x^2+b*B*x],
[(a+b*x^3)*(A+B*x^3)/x^7,x,3,-1/6*a*A/x^6+1/3*(-A*b-a*B)/x^3+b*B*log(x)],
[x^2*(a+b*x^3)^2*(A+B*x^3),x,3,1/9*(A*b-a*B)*(a+b*x^3)^3/b^2+1/12*B*(a+b*x^3)^4/b^2],
[x*(a+b*x^3)^2*(A+B*x^3),x,2,1/2*a^2*A*x^2+1/5*a*(2*A*b+a*B)*x^5+1/8*b*(A*b+2*a*B)*x^8+1/11*b^2*B*x^11],
[(a+b*x^3)^2*(A+B*x^3),x,2,a^2*A*x+1/4*a*(2*A*b+a*B)*x^4+1/7*b*(A*b+2*a*B)*x^7+1/10*b^2*B*x^10],
[(a+b*x^3)^2*(A+B*x^3)/x,x,4,2/3*a*A*b*x^3+1/6*A*b^2*x^6+1/9*B*(a+b*x^3)^3/b+a^2*A*log(x)],
[(a+b*x^3)^2*(A+B*x^3)/x^2,x,2,-a^2*A/x+1/2*a*(2*A*b+a*B)*x^2+1/5*b*(A*b+2*a*B)*x^5+1/8*b^2*B*x^8],
[(a+b*x^3)^2*(A+B*x^3)/x^3,x,2,-1/2*a^2*A/x^2+a*(2*A*b+a*B)*x+1/4*b*(A*b+2*a*B)*x^4+1/7*b^2*B*x^7],
[(a+b*x^3)^2*(A+B*x^3)/x^4,x,3,-1/3*a^2*A/x^3+1/3*b*(A*b+2*a*B)*x^3+1/6*b^2*B*x^6+a*(2*A*b+a*B)*log(x)],
[(a+b*x^3)^2*(A+B*x^3)/x^5,x,2,-1/4*a^2*A/x^4-a*(2*A*b+a*B)/x+1/2*b*(A*b+2*a*B)*x^2+1/5*b^2*B*x^5],
[(a+b*x^3)^2*(A+B*x^3)/x^6,x,2,-1/5*a^2*A/x^5-1/2*a*(2*A*b+a*B)/x^2+b*(A*b+2*a*B)*x+1/4*b^2*B*x^4],
[(a+b*x^3)^2*(A+B*x^3)/x^7,x,3,-1/6*a^2*A/x^6-1/3*a*(2*A*b+a*B)/x^3+1/3*b^2*B*x^3+b*(A*b+2*a*B)*log(x)],
[(a+b*x^3)^2*(A+B*x^3)/x^8,x,2,-1/7*a^2*A/x^7-1/4*a*(2*A*b+a*B)/x^4-b*(A*b+2*a*B)/x+1/2*b^2*B*x^2],
[(a+b*x^3)^2*(A+B*x^3)/x^9,x,2,-1/8*a^2*A/x^8-1/5*a*(2*A*b+a*B)/x^5-1/2*b*(A*b+2*a*B)/x^2+b^2*B*x],
[x^9*(a+b*x^3)^5*(A+B*x^3),x,2,1/10*a^5*A*x^10+1/13*a^4*(5*A*b+a*B)*x^13+5/16*a^3*b*(2*A*b+a*B)*x^16+10/19*a^2*b^2*(A*b+a*B)*x^19+5/22*a*b^3*(A*b+2*a*B)*x^22+1/25*b^4*(A*b+5*a*B)*x^25+1/28*b^5*B*x^28],
[x^8*(a+b*x^3)^5*(A+B*x^3),x,3,1/18*a^2*(A*b-a*B)*(a+b*x^3)^6/b^4-1/21*a*(2*A*b-3*a*B)*(a+b*x^3)^7/b^4+1/24*(A*b-3*a*B)*(a+b*x^3)^8/b^4+1/27*B*(a+b*x^3)^9/b^4],
[x^7*(a+b*x^3)^5*(A+B*x^3),x,2,1/8*a^5*A*x^8+1/11*a^4*(5*A*b+a*B)*x^11+5/14*a^3*b*(2*A*b+a*B)*x^14+10/17*a^2*b^2*(A*b+a*B)*x^17+1/4*a*b^3*(A*b+2*a*B)*x^20+1/23*b^4*(A*b+5*a*B)*x^23+1/26*b^5*B*x^26],
[x^6*(a+b*x^3)^5*(A+B*x^3),x,2,1/7*a^5*A*x^7+1/10*a^4*(5*A*b+a*B)*x^10+5/13*a^3*b*(2*A*b+a*B)*x^13+5/8*a^2*b^2*(A*b+a*B)*x^16+5/19*a*b^3*(A*b+2*a*B)*x^19+1/22*b^4*(A*b+5*a*B)*x^22+1/25*b^5*B*x^25],
[x^5*(a+b*x^3)^5*(A+B*x^3),x,3,-1/18*a*(A*b-a*B)*(a+b*x^3)^6/b^3+1/21*(A*b-2*a*B)*(a+b*x^3)^7/b^3+1/24*B*(a+b*x^3)^8/b^3],
[x^4*(a+b*x^3)^5*(A+B*x^3),x,2,1/5*a^5*A*x^5+1/8*a^4*(5*A*b+a*B)*x^8+5/11*a^3*b*(2*A*b+a*B)*x^11+5/7*a^2*b^2*(A*b+a*B)*x^14+5/17*a*b^3*(A*b+2*a*B)*x^17+1/20*b^4*(A*b+5*a*B)*x^20+1/23*b^5*B*x^23],
[x^3*(a+b*x^3)^5*(A+B*x^3),x,2,1/4*a^5*A*x^4+1/7*a^4*(5*A*b+a*B)*x^7+1/2*a^3*b*(2*A*b+a*B)*x^10+10/13*a^2*b^2*(A*b+a*B)*x^13+5/16*a*b^3*(A*b+2*a*B)*x^16+1/19*b^4*(A*b+5*a*B)*x^19+1/22*b^5*B*x^22],
[x^2*(a+b*x^3)^5*(A+B*x^3),x,3,1/18*(A*b-a*B)*(a+b*x^3)^6/b^2+1/21*B*(a+b*x^3)^7/b^2],
[x*(a+b*x^3)^5*(A+B*x^3),x,2,1/2*a^5*A*x^2+1/5*a^4*(5*A*b+a*B)*x^5+5/8*a^3*b*(2*A*b+a*B)*x^8+10/11*a^2*b^2*(A*b+a*B)*x^11+5/14*a*b^3*(A*b+2*a*B)*x^14+1/17*b^4*(A*b+5*a*B)*x^17+1/20*b^5*B*x^20],
[(a+b*x^3)^5*(A+B*x^3),x,2,a^5*A*x+1/4*a^4*(5*A*b+a*B)*x^4+5/7*a^3*b*(2*A*b+a*B)*x^7+a^2*b^2*(A*b+a*B)*x^10+5/13*a*b^3*(A*b+2*a*B)*x^13+1/16*b^4*(A*b+5*a*B)*x^16+1/19*b^5*B*x^19],
[(a+b*x^3)^5*(A+B*x^3)/x,x,4,5/3*a^4*A*b*x^3+5/3*a^3*A*b^2*x^6+10/9*a^2*A*b^3*x^9+5/12*a*A*b^4*x^12+1/15*A*b^5*x^15+1/18*B*(a+b*x^3)^6/b+a^5*A*log(x)],
[(a+b*x^3)^5*(A+B*x^3)/x^2,x,2,-a^5*A/x+1/2*a^4*(5*A*b+a*B)*x^2+a^3*b*(2*A*b+a*B)*x^5+5/4*a^2*b^2*(A*b+a*B)*x^8+5/11*a*b^3*(A*b+2*a*B)*x^11+1/14*b^4*(A*b+5*a*B)*x^14+1/17*b^5*B*x^17],
[(a+b*x^3)^5*(A+B*x^3)/x^3,x,2,-1/2*a^5*A/x^2+a^4*(5*A*b+a*B)*x+5/4*a^3*b*(2*A*b+a*B)*x^4+10/7*a^2*b^2*(A*b+a*B)*x^7+1/2*a*b^3*(A*b+2*a*B)*x^10+1/13*b^4*(A*b+5*a*B)*x^13+1/16*b^5*B*x^16],
[(a+b*x^3)^5*(A+B*x^3)/x^4,x,3,-1/3*a^5*A/x^3+5/3*a^3*b*(2*A*b+a*B)*x^3+5/3*a^2*b^2*(A*b+a*B)*x^6+5/9*a*b^3*(A*b+2*a*B)*x^9+1/12*b^4*(A*b+5*a*B)*x^12+1/15*b^5*B*x^15+a^4*(5*A*b+a*B)*log(x)],
[(a+b*x^3)^5*(A+B*x^3)/x^5,x,2,-1/4*a^5*A/x^4-a^4*(5*A*b+a*B)/x+5/2*a^3*b*(2*A*b+a*B)*x^2+2*a^2*b^2*(A*b+a*B)*x^5+5/8*a*b^3*(A*b+2*a*B)*x^8+1/11*b^4*(A*b+5*a*B)*x^11+1/14*b^5*B*x^14],
[(a+b*x^3)^5*(A+B*x^3)/x^6,x,2,-1/5*a^5*A/x^5-1/2*a^4*(5*A*b+a*B)/x^2+5*a^3*b*(2*A*b+a*B)*x+5/2*a^2*b^2*(A*b+a*B)*x^4+5/7*a*b^3*(A*b+2*a*B)*x^7+1/10*b^4*(A*b+5*a*B)*x^10+1/13*b^5*B*x^13],
[(a+b*x^3)^5*(A+B*x^3)/x^7,x,3,-1/6*a^5*A/x^6-1/3*a^4*(5*A*b+a*B)/x^3+10/3*a^2*b^2*(A*b+a*B)*x^3+5/6*a*b^3*(A*b+2*a*B)*x^6+1/9*b^4*(A*b+5*a*B)*x^9+1/12*b^5*B*x^12+5*a^3*b*(2*A*b+a*B)*log(x)],
[(a+b*x^3)^5*(A+B*x^3)/x^8,x,2,-1/7*a^5*A/x^7-1/4*a^4*(5*A*b+a*B)/x^4-5*a^3*b*(2*A*b+a*B)/x+5*a^2*b^2*(A*b+a*B)*x^2+a*b^3*(A*b+2*a*B)*x^5+1/8*b^4*(A*b+5*a*B)*x^8+1/11*b^5*B*x^11],
[(a+b*x^3)^5*(A+B*x^3)/x^9,x,2,-1/8*a^5*A/x^8-1/5*a^4*(5*A*b+a*B)/x^5-5/2*a^3*b*(2*A*b+a*B)/x^2+10*a^2*b^2*(A*b+a*B)*x+5/4*a*b^3*(A*b+2*a*B)*x^4+1/7*b^4*(A*b+5*a*B)*x^7+1/10*b^5*B*x^10],
[(a+b*x^3)^5*(A+B*x^3)/x^10,x,3,-1/9*a^5*A/x^9-1/6*a^4*(5*A*b+a*B)/x^6-5/3*a^3*b*(2*A*b+a*B)/x^3+5/3*a*b^3*(A*b+2*a*B)*x^3+1/6*b^4*(A*b+5*a*B)*x^6+1/9*b^5*B*x^9+10*a^2*b^2*(A*b+a*B)*log(x)],
[(a+b*x^3)^5*(A+B*x^3)/x^11,x,2,-1/10*a^5*A/x^10-1/7*a^4*(5*A*b+a*B)/x^7-5/4*a^3*b*(2*A*b+a*B)/x^4-10*a^2*b^2*(A*b+a*B)/x+5/2*a*b^3*(A*b+2*a*B)*x^2+1/5*b^4*(A*b+5*a*B)*x^5+1/8*b^5*B*x^8],
[(a+b*x^3)^5*(A+B*x^3)/x^12,x,2,-1/11*a^5*A/x^11-1/8*a^4*(5*A*b+a*B)/x^8-a^3*b*(2*A*b+a*B)/x^5-5*a^2*b^2*(A*b+a*B)/x^2+5*a*b^3*(A*b+2*a*B)*x+1/4*b^4*(A*b+5*a*B)*x^4+1/7*b^5*B*x^7],
[(a+b*x^3)^5*(A+B*x^3)/x^13,x,3,-1/12*a^5*A/x^12-1/9*a^4*(5*A*b+a*B)/x^9-5/6*a^3*b*(2*A*b+a*B)/x^6-10/3*a^2*b^2*(A*b+a*B)/x^3+1/3*b^4*(A*b+5*a*B)*x^3+1/6*b^5*B*x^6+5*a*b^3*(A*b+2*a*B)*log(x)],
[(a+b*x^3)^5*(A+B*x^3)/x^14,x,2,-1/13*a^5*A/x^13-1/10*a^4*(5*A*b+a*B)/x^10-5/7*a^3*b*(2*A*b+a*B)/x^7-5/2*a^2*b^2*(A*b+a*B)/x^4-5*a*b^3*(A*b+2*a*B)/x+1/2*b^4*(A*b+5*a*B)*x^2+1/5*b^5*B*x^5],
[(a+b*x^3)^5*(A+B*x^3)/x^15,x,2,-1/14*a^5*A/x^14-1/11*a^4*(5*A*b+a*B)/x^11-5/8*a^3*b*(2*A*b+a*B)/x^8-2*a^2*b^2*(A*b+a*B)/x^5-5/2*a*b^3*(A*b+2*a*B)/x^2+b^4*(A*b+5*a*B)*x+1/4*b^5*B*x^4],
[(a+b*x^3)^5*(A+B*x^3)/x^16,x,3,-1/15*a^5*A/x^15-1/12*a^4*(5*A*b+a*B)/x^12-5/9*a^3*b*(2*A*b+a*B)/x^9-5/3*a^2*b^2*(A*b+a*B)/x^6-5/3*a*b^3*(A*b+2*a*B)/x^3+1/3*b^5*B*x^3+b^4*(A*b+5*a*B)*log(x)],
[(a+b*x^3)^5*(A+B*x^3)/x^17,x,2,-1/16*a^5*A/x^16-1/13*a^4*(5*A*b+a*B)/x^13-1/2*a^3*b*(2*A*b+a*B)/x^10-10/7*a^2*b^2*(A*b+a*B)/x^7-5/4*a*b^3*(A*b+2*a*B)/x^4-b^4*(A*b+5*a*B)/x+1/2*b^5*B*x^2],
[(a+b*x^3)^5*(A+B*x^3)/x^18,x,2,-1/17*a^5*A/x^17-1/14*a^4*(5*A*b+a*B)/x^14-5/11*a^3*b*(2*A*b+a*B)/x^11-5/4*a^2*b^2*(A*b+a*B)/x^8-a*b^3*(A*b+2*a*B)/x^5-1/2*b^4*(A*b+5*a*B)/x^2+b^5*B*x],
[(a+b*x^3)^5*(A+B*x^3)/x^19,x,4,-1/15*a^5*B/x^15-5/12*a^4*b*B/x^12-10/9*a^3*b^2*B/x^9-5/3*a^2*b^3*B/x^6-5/3*a*b^4*B/x^3-1/18*A*(a+b*x^3)^6/(a*x^18)+b^5*B*log(x)],
[(a+b*x^3)^5*(A+B*x^3)/x^20,x,2,-1/19*a^5*A/x^19-1/16*a^4*(5*A*b+a*B)/x^16-5/13*a^3*b*(2*A*b+a*B)/x^13-a^2*b^2*(A*b+a*B)/x^10-5/7*a*b^3*(A*b+2*a*B)/x^7-1/4*b^4*(A*b+5*a*B)/x^4-b^5*B/x],
[(a+b*x^3)^5*(A+B*x^3)/x^21,x,2,-1/20*a^5*A/x^20-1/17*a^4*(5*A*b+a*B)/x^17-5/14*a^3*b*(2*A*b+a*B)/x^14-10/11*a^2*b^2*(A*b+a*B)/x^11-5/8*a*b^3*(A*b+2*a*B)/x^8-1/5*b^4*(A*b+5*a*B)/x^5-1/2*b^5*B/x^2],
[(a+b*x^3)^5*(A+B*x^3)/x^22,x,3,-1/21*A*(a+b*x^3)^6/(a*x^21)+1/126*(A*b-7*a*B)*(a+b*x^3)^6/(a^2*x^18)],
[(a+b*x^3)^5*(A+B*x^3)/x^23,x,2,-1/22*a^5*A/x^22-1/19*a^4*(5*A*b+a*B)/x^19-5/16*a^3*b*(2*A*b+a*B)/x^16-10/13*a^2*b^2*(A*b+a*B)/x^13-1/2*a*b^3*(A*b+2*a*B)/x^10-1/7*b^4*(A*b+5*a*B)/x^7-1/4*b^5*B/x^4],

# p<0
[x^6*(A+B*x^3)/(a+b*x^3),x,9,-a*(A*b-a*B)*x/b^3+1/4*(A*b-a*B)*x^4/b^2+1/7*B*x^7/b+1/3*a^(4/3)*(A*b-a*B)*log(a^(1/3)+b^(1/3)*x)/b^(10/3)-1/6*a^(4/3)*(A*b-a*B)*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/b^(10/3)-a^(4/3)*(A*b-a*B)*arctan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(b^(10/3)*sqrt(3))],
[x^5*(A+B*x^3)/(a+b*x^3),x,3,1/3*(A*b-a*B)*x^3/b^2+1/6*B*x^6/b-1/3*a*(A*b-a*B)*log(a+b*x^3)/b^3],
[x^4*(A+B*x^3)/(a+b*x^3),x,8,1/2*(A*b-a*B)*x^2/b^2+1/5*B*x^5/b+1/3*a^(2/3)*(A*b-a*B)*log(a^(1/3)+b^(1/3)*x)/b^(8/3)-1/6*a^(2/3)*(A*b-a*B)*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/b^(8/3)+a^(2/3)*(A*b-a*B)*arctan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(b^(8/3)*sqrt(3))],
[x^3*(A+B*x^3)/(a+b*x^3),x,8,(A*b-a*B)*x/b^2+1/4*B*x^4/b-1/3*a^(1/3)*(A*b-a*B)*log(a^(1/3)+b^(1/3)*x)/b^(7/3)+1/6*a^(1/3)*(A*b-a*B)*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/b^(7/3)+a^(1/3)*(A*b-a*B)*arctan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(b^(7/3)*sqrt(3))],
[x^2*(A+B*x^3)/(a+b*x^3),x,3,1/3*B*x^3/b+1/3*(A*b-a*B)*log(a+b*x^3)/b^2],
[x*(A+B*x^3)/(a+b*x^3),x,7,1/2*B*x^2/b-1/3*(A*b-a*B)*log(a^(1/3)+b^(1/3)*x)/(a^(1/3)*b^(5/3))+1/6*(A*b-a*B)*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(1/3)*b^(5/3))-(A*b-a*B)*arctan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(a^(1/3)*b^(5/3)*sqrt(3))],
[(A+B*x^3)/(a+b*x^3),x,7,B*x/b+1/3*(A*b-a*B)*log(a^(1/3)+b^(1/3)*x)/(a^(2/3)*b^(4/3))-1/6*(A*b-a*B)*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(2/3)*b^(4/3))-(A*b-a*B)*arctan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(a^(2/3)*b^(4/3)*sqrt(3))],
[(A+B*x^3)/(x*(a+b*x^3)),x,3,A*log(x)/a-1/3*(A*b-a*B)*log(a+b*x^3)/(a*b)],
[(A+B*x^3)/(x^2*(a+b*x^3)),x,7,-A/(a*x)+1/3*(A*b-a*B)*log(a^(1/3)+b^(1/3)*x)/(a^(4/3)*b^(2/3))-1/6*(A*b-a*B)*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(4/3)*b^(2/3))+(A*b-a*B)*arctan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(a^(4/3)*b^(2/3)*sqrt(3))],
[(A+B*x^3)/(x^3*(a+b*x^3)),x,7,-1/2*A/(a*x^2)-1/3*(A*b-a*B)*log(a^(1/3)+b^(1/3)*x)/(a^(5/3)*b^(1/3))+1/6*(A*b-a*B)*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(5/3)*b^(1/3))+(A*b-a*B)*arctan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(a^(5/3)*b^(1/3)*sqrt(3))],
[(A+B*x^3)/(x^4*(a+b*x^3)),x,3,-1/3*A/(a*x^3)-(A*b-a*B)*log(x)/a^2+1/3*(A*b-a*B)*log(a+b*x^3)/a^2],
[(A+B*x^3)/(x^5*(a+b*x^3)),x,8,-1/4*A/(a*x^4)+(A*b-a*B)/(a^2*x)-1/3*b^(1/3)*(A*b-a*B)*log(a^(1/3)+b^(1/3)*x)/a^(7/3)+1/6*b^(1/3)*(A*b-a*B)*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/a^(7/3)-b^(1/3)*(A*b-a*B)*arctan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(a^(7/3)*sqrt(3))],
[(A+B*x^3)/(x^6*(a+b*x^3)),x,8,-1/5*A/(a*x^5)+1/2*(A*b-a*B)/(a^2*x^2)+1/3*b^(2/3)*(A*b-a*B)*log(a^(1/3)+b^(1/3)*x)/a^(8/3)-1/6*b^(2/3)*(A*b-a*B)*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/a^(8/3)-b^(2/3)*(A*b-a*B)*arctan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(a^(8/3)*sqrt(3))],
[(A+B*x^3)/(x^7*(a+b*x^3)),x,3,-1/6*A/(a*x^6)+1/3*(A*b-a*B)/(a^2*x^3)+b*(A*b-a*B)*log(x)/a^3-1/3*b*(A*b-a*B)*log(a+b*x^3)/a^3],
[(A+B*x^3)/(x^8*(a+b*x^3)),x,9,-1/7*A/(a*x^7)+1/4*(A*b-a*B)/(a^2*x^4)-b*(A*b-a*B)/(a^3*x)+1/3*b^(4/3)*(A*b-a*B)*log(a^(1/3)+b^(1/3)*x)/a^(10/3)-1/6*b^(4/3)*(A*b-a*B)*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/a^(10/3)+b^(4/3)*(A*b-a*B)*arctan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(a^(10/3)*sqrt(3))],
[x^9*(A+B*x^3)/(a+b*x^3)^2,x,9,-1/3*a*(7*A*b-10*a*B)*x/b^4+1/12*(7*A*b-10*a*B)*x^4/b^3-1/21*(7*A*b-10*a*B)*x^7/(a*b^2)+1/3*(A*b-a*B)*x^10/(a*b*(a+b*x^3))+1/9*a^(4/3)*(7*A*b-10*a*B)*log(a^(1/3)+b^(1/3)*x)/b^(13/3)-1/18*a^(4/3)*(7*A*b-10*a*B)*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/b^(13/3)-1/3*a^(4/3)*(7*A*b-10*a*B)*arctan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(b^(13/3)*sqrt(3))],
[x^8*(A+B*x^3)/(a+b*x^3)^2,x,3,1/3*(A*b-2*a*B)*x^3/b^3+1/6*B*x^6/b^2-1/3*a^2*(A*b-a*B)/(b^4*(a+b*x^3))-1/3*a*(2*A*b-3*a*B)*log(a+b*x^3)/b^4],
[x^7*(A+B*x^3)/(a+b*x^3)^2,x,9,1/6*(5*A*b-8*a*B)*x^2/b^3-1/15*(5*A*b-8*a*B)*x^5/(a*b^2)+1/3*(A*b-a*B)*x^8/(a*b*(a+b*x^3))+1/9*a^(2/3)*(5*A*b-8*a*B)*log(a^(1/3)+b^(1/3)*x)/b^(11/3)-1/18*a^(2/3)*(5*A*b-8*a*B)*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/b^(11/3)+1/3*a^(2/3)*(5*A*b-8*a*B)*arctan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(b^(11/3)*sqrt(3))],
[x^6*(A+B*x^3)/(a+b*x^3)^2,x,9,1/3*(4*A*b-7*a*B)*x/b^3-1/12*(4*A*b-7*a*B)*x^4/(a*b^2)+1/3*(A*b-a*B)*x^7/(a*b*(a+b*x^3))-1/9*a^(1/3)*(4*A*b-7*a*B)*log(a^(1/3)+b^(1/3)*x)/b^(10/3)+1/18*a^(1/3)*(4*A*b-7*a*B)*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/b^(10/3)+1/3*a^(1/3)*(4*A*b-7*a*B)*arctan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(b^(10/3)*sqrt(3))],
[x^5*(A+B*x^3)/(a+b*x^3)^2,x,3,1/3*B*x^3/b^2+1/3*a*(A*b-a*B)/(b^3*(a+b*x^3))+1/3*(A*b-2*a*B)*log(a+b*x^3)/b^3],
[x^4*(A+B*x^3)/(a+b*x^3)^2,x,8,-1/6*(2*A*b-5*a*B)*x^2/(a*b^2)+1/3*(A*b-a*B)*x^5/(a*b*(a+b*x^3))-1/9*(2*A*b-5*a*B)*log(a^(1/3)+b^(1/3)*x)/(a^(1/3)*b^(8/3))+1/18*(2*A*b-5*a*B)*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(1/3)*b^(8/3))-1/3*(2*A*b-5*a*B)*arctan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(a^(1/3)*b^(8/3)*sqrt(3))],
[x^3*(A+B*x^3)/(a+b*x^3)^2,x,8,-1/3*(A*b-4*a*B)*x/(a*b^2)+1/3*(A*b-a*B)*x^4/(a*b*(a+b*x^3))+1/9*(A*b-4*a*B)*log(a^(1/3)+b^(1/3)*x)/(a^(2/3)*b^(7/3))-1/18*(A*b-4*a*B)*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(2/3)*b^(7/3))-1/3*(A*b-4*a*B)*arctan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(a^(2/3)*b^(7/3)*sqrt(3))],
[x^2*(A+B*x^3)/(a+b*x^3)^2,x,3,1/3*(-A*b+a*B)/(b^2*(a+b*x^3))+1/3*B*log(a+b*x^3)/b^2],
[x*(A+B*x^3)/(a+b*x^3)^2,x,7,1/3*(A*b-a*B)*x^2/(a*b*(a+b*x^3))-1/9*(A*b+2*a*B)*log(a^(1/3)+b^(1/3)*x)/(a^(4/3)*b^(5/3))+1/18*(A*b+2*a*B)*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(4/3)*b^(5/3))-1/3*(A*b+2*a*B)*arctan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(a^(4/3)*b^(5/3)*sqrt(3))],
[(A+B*x^3)/(a+b*x^3)^2,x,7,1/3*(A*b-a*B)*x/(a*b*(a+b*x^3))+1/9*(2*A*b+a*B)*log(a^(1/3)+b^(1/3)*x)/(a^(5/3)*b^(4/3))-1/18*(2*A*b+a*B)*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(5/3)*b^(4/3))-1/3*(2*A*b+a*B)*arctan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(a^(5/3)*b^(4/3)*sqrt(3))],
[(A+B*x^3)/(x*(a+b*x^3)^2),x,3,1/3*(A*b-a*B)/(a*b*(a+b*x^3))+A*log(x)/a^2-1/3*A*log(a+b*x^3)/a^2],
[(A+B*x^3)/(x^2*(a+b*x^3)^2),x,8,1/3*(-4*A*b+a*B)/(a^2*b*x)+1/3*(A*b-a*B)/(a*b*x*(a+b*x^3))+1/9*(4*A*b-a*B)*log(a^(1/3)+b^(1/3)*x)/(a^(7/3)*b^(2/3))-1/18*(4*A*b-a*B)*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(7/3)*b^(2/3))+1/3*(4*A*b-a*B)*arctan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(a^(7/3)*b^(2/3)*sqrt(3))],
[(A+B*x^3)/(x^3*(a+b*x^3)^2),x,8,1/6*(-5*A*b+2*a*B)/(a^2*b*x^2)+1/3*(A*b-a*B)/(a*b*x^2*(a+b*x^3))-1/9*(5*A*b-2*a*B)*log(a^(1/3)+b^(1/3)*x)/(a^(8/3)*b^(1/3))+1/18*(5*A*b-2*a*B)*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(8/3)*b^(1/3))+1/3*(5*A*b-2*a*B)*arctan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(a^(8/3)*b^(1/3)*sqrt(3))],
[(A+B*x^3)/(x^4*(a+b*x^3)^2),x,3,-1/3*A/(a^2*x^3)+1/3*(-A*b+a*B)/(a^2*(a+b*x^3))-(2*A*b-a*B)*log(x)/a^3+1/3*(2*A*b-a*B)*log(a+b*x^3)/a^3],
[(A+B*x^3)/(x^5*(a+b*x^3)^2),x,9,1/12*(-7*A*b+4*a*B)/(a^2*b*x^4)+1/3*(7*A*b-4*a*B)/(a^3*x)+1/3*(A*b-a*B)/(a*b*x^4*(a+b*x^3))-1/9*b^(1/3)*(7*A*b-4*a*B)*log(a^(1/3)+b^(1/3)*x)/a^(10/3)+1/18*b^(1/3)*(7*A*b-4*a*B)*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/a^(10/3)-1/3*b^(1/3)*(7*A*b-4*a*B)*arctan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(a^(10/3)*sqrt(3))],
[(A+B*x^3)/(x^6*(a+b*x^3)^2),x,9,1/15*(-8*A*b+5*a*B)/(a^2*b*x^5)+1/6*(8*A*b-5*a*B)/(a^3*x^2)+1/3*(A*b-a*B)/(a*b*x^5*(a+b*x^3))+1/9*b^(2/3)*(8*A*b-5*a*B)*log(a^(1/3)+b^(1/3)*x)/a^(11/3)-1/18*b^(2/3)*(8*A*b-5*a*B)*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/a^(11/3)-1/3*b^(2/3)*(8*A*b-5*a*B)*arctan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(a^(11/3)*sqrt(3))],
[(A+B*x^3)/(x^7*(a+b*x^3)^2),x,3,-1/6*A/(a^2*x^6)+1/3*(2*A*b-a*B)/(a^3*x^3)+1/3*b*(A*b-a*B)/(a^3*(a+b*x^3))+b*(3*A*b-2*a*B)*log(x)/a^4-1/3*b*(3*A*b-2*a*B)*log(a+b*x^3)/a^4],
[x^11*(A+B*x^3)/(a+b*x^3)^3,x,3,1/3*(A*b-3*a*B)*x^3/b^4+1/6*B*x^6/b^3+1/6*a^3*(A*b-a*B)/(b^5*(a+b*x^3)^2)-1/3*a^2*(3*A*b-4*a*B)/(b^5*(a+b*x^3))-a*(A*b-2*a*B)*log(a+b*x^3)/b^5],
[x^8*(A+B*x^3)/(a+b*x^3)^3,x,3,1/3*B*x^3/b^3-1/6*a^2*(A*b-a*B)/(b^4*(a+b*x^3)^2)+1/3*a*(2*A*b-3*a*B)/(b^4*(a+b*x^3))+1/3*(A*b-3*a*B)*log(a+b*x^3)/b^4],
[x^5*(A+B*x^3)/(a+b*x^3)^3,x,3,1/6*a*(A*b-a*B)/(b^3*(a+b*x^3)^2)+1/3*(-A*b+2*a*B)/(b^3*(a+b*x^3))+1/3*B*log(a+b*x^3)/b^3],
[x^2*(A+B*x^3)/(a+b*x^3)^3,x,2,-1/6*(A+B*x^3)^2/((A*b-a*B)*(a+b*x^3)^2)],
[(A+B*x^3)/(x*(a+b*x^3)^3),x,3,1/6*(A*b-a*B)/(a*b*(a+b*x^3)^2)+1/3*A/(a^2*(a+b*x^3))+A*log(x)/a^3-1/3*A*log(a+b*x^3)/a^3],
[(A+B*x^3)/(x^4*(a+b*x^3)^3),x,3,-1/3*A/(a^3*x^3)+1/6*(-A*b+a*B)/(a^2*(a+b*x^3)^2)+1/3*(-2*A*b+a*B)/(a^3*(a+b*x^3))-(3*A*b-a*B)*log(x)/a^4+1/3*(3*A*b-a*B)*log(a+b*x^3)/a^4],
[(A+B*x^3)/(x^7*(a+b*x^3)^3),x,3,-1/6*A/(a^3*x^6)+1/3*(3*A*b-a*B)/(a^4*x^3)+1/6*b*(A*b-a*B)/(a^3*(a+b*x^3)^2)+1/3*b*(3*A*b-2*a*B)/(a^4*(a+b*x^3))+3*b*(2*A*b-a*B)*log(x)/a^5-b*(2*A*b-a*B)*log(a+b*x^3)/a^5],
[x^10*(A+B*x^3)/(a+b*x^3)^3,x,10,2/9*(5*A*b-11*a*B)*x^2/b^4-4/45*(5*A*b-11*a*B)*x^5/(a*b^3)+1/6*(A*b-a*B)*x^11/(a*b*(a+b*x^3)^2)+1/18*(5*A*b-11*a*B)*x^8/(a*b^2*(a+b*x^3))+4/27*a^(2/3)*(5*A*b-11*a*B)*log(a^(1/3)+b^(1/3)*x)/b^(14/3)-2/27*a^(2/3)*(5*A*b-11*a*B)*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/b^(14/3)+4/9*a^(2/3)*(5*A*b-11*a*B)*arctan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(b^(14/3)*sqrt(3))],
[x^9*(A+B*x^3)/(a+b*x^3)^3,x,10,7/9*(2*A*b-5*a*B)*x/b^4-7/36*(2*A*b-5*a*B)*x^4/(a*b^3)+1/6*(A*b-a*B)*x^10/(a*b*(a+b*x^3)^2)+1/9*(2*A*b-5*a*B)*x^7/(a*b^2*(a+b*x^3))-7/27*a^(1/3)*(2*A*b-5*a*B)*log(a^(1/3)+b^(1/3)*x)/b^(13/3)+7/54*a^(1/3)*(2*A*b-5*a*B)*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/b^(13/3)+7/9*a^(1/3)*(2*A*b-5*a*B)*arctan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(b^(13/3)*sqrt(3))],
[x^7*(A+B*x^3)/(a+b*x^3)^3,x,9,-5/18*(A*b-4*a*B)*x^2/(a*b^3)+1/6*(A*b-a*B)*x^8/(a*b*(a+b*x^3)^2)+1/9*(A*b-4*a*B)*x^5/(a*b^2*(a+b*x^3))-5/27*(A*b-4*a*B)*log(a^(1/3)+b^(1/3)*x)/(a^(1/3)*b^(11/3))+5/54*(A*b-4*a*B)*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(1/3)*b^(11/3))-5/9*(A*b-4*a*B)*arctan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(a^(1/3)*b^(11/3)*sqrt(3))],
[x^6*(A+B*x^3)/(a+b*x^3)^3,x,9,-2/9*(A*b-7*a*B)*x/(a*b^3)+1/6*(A*b-a*B)*x^7/(a*b*(a+b*x^3)^2)+1/18*(A*b-7*a*B)*x^4/(a*b^2*(a+b*x^3))+2/27*(A*b-7*a*B)*log(a^(1/3)+b^(1/3)*x)/(a^(2/3)*b^(10/3))-1/27*(A*b-7*a*B)*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(2/3)*b^(10/3))-2/9*(A*b-7*a*B)*arctan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(a^(2/3)*b^(10/3)*sqrt(3))],
[x^4*(A+B*x^3)/(a+b*x^3)^3,x,8,1/6*(A*b-a*B)*x^5/(a*b*(a+b*x^3)^2)-1/18*(A*b+5*a*B)*x^2/(a*b^2*(a+b*x^3))-1/27*(A*b+5*a*B)*log(a^(1/3)+b^(1/3)*x)/(a^(4/3)*b^(8/3))+1/54*(A*b+5*a*B)*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(4/3)*b^(8/3))-1/9*(A*b+5*a*B)*arctan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(a^(4/3)*b^(8/3)*sqrt(3))],
[x^3*(A+B*x^3)/(a+b*x^3)^3,x,8,1/6*(A*b-a*B)*x^4/(a*b*(a+b*x^3)^2)-1/9*(A*b+2*a*B)*x/(a*b^2*(a+b*x^3))+1/27*(A*b+2*a*B)*log(a^(1/3)+b^(1/3)*x)/(a^(5/3)*b^(7/3))-1/54*(A*b+2*a*B)*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(5/3)*b^(7/3))-1/9*(A*b+2*a*B)*arctan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(a^(5/3)*b^(7/3)*sqrt(3))],
[x*(A+B*x^3)/(a+b*x^3)^3,x,8,1/6*(A*b-a*B)*x^2/(a*b*(a+b*x^3)^2)+1/9*(2*A*b+a*B)*x^2/(a^2*b*(a+b*x^3))-1/27*(2*A*b+a*B)*log(a^(1/3)+b^(1/3)*x)/(a^(7/3)*b^(5/3))+1/54*(2*A*b+a*B)*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(7/3)*b^(5/3))-1/9*(2*A*b+a*B)*arctan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(a^(7/3)*b^(5/3)*sqrt(3))],
[(A+B*x^3)/(a+b*x^3)^3,x,8,1/6*(A*b-a*B)*x/(a*b*(a+b*x^3)^2)+1/18*(5*A*b+a*B)*x/(a^2*b*(a+b*x^3))+1/27*(5*A*b+a*B)*log(a^(1/3)+b^(1/3)*x)/(a^(8/3)*b^(4/3))-1/54*(5*A*b+a*B)*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(8/3)*b^(4/3))-1/9*(5*A*b+a*B)*arctan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(a^(8/3)*b^(4/3)*sqrt(3))],
[(A+B*x^3)/(x^2*(a+b*x^3)^3),x,9,-2/9*(7*A*b-a*B)/(a^3*b*x)+1/6*(A*b-a*B)/(a*b*x*(a+b*x^3)^2)+1/18*(7*A*b-a*B)/(a^2*b*x*(a+b*x^3))+2/27*(7*A*b-a*B)*log(a^(1/3)+b^(1/3)*x)/(a^(10/3)*b^(2/3))-1/27*(7*A*b-a*B)*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(10/3)*b^(2/3))+2/9*(7*A*b-a*B)*arctan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(a^(10/3)*b^(2/3)*sqrt(3))],
[(A+B*x^3)/(x^3*(a+b*x^3)^3),x,9,-5/18*(4*A*b-a*B)/(a^3*b*x^2)+1/6*(A*b-a*B)/(a*b*x^2*(a+b*x^3)^2)+1/9*(4*A*b-a*B)/(a^2*b*x^2*(a+b*x^3))-5/27*(4*A*b-a*B)*log(a^(1/3)+b^(1/3)*x)/(a^(11/3)*b^(1/3))+5/54*(4*A*b-a*B)*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(11/3)*b^(1/3))+5/9*(4*A*b-a*B)*arctan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(a^(11/3)*b^(1/3)*sqrt(3))],
[(A+B*x^3)/(x^5*(a+b*x^3)^3),x,10,-7/36*(5*A*b-2*a*B)/(a^3*b*x^4)+7/9*(5*A*b-2*a*B)/(a^4*x)+1/6*(A*b-a*B)/(a*b*x^4*(a+b*x^3)^2)+1/9*(5*A*b-2*a*B)/(a^2*b*x^4*(a+b*x^3))-7/27*b^(1/3)*(5*A*b-2*a*B)*log(a^(1/3)+b^(1/3)*x)/a^(13/3)+7/54*b^(1/3)*(5*A*b-2*a*B)*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/a^(13/3)-7/9*b^(1/3)*(5*A*b-2*a*B)*arctan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(a^(13/3)*sqrt(3))],
[(A+B*x^3)/(x^6*(a+b*x^3)^3),x,10,-4/45*(11*A*b-5*a*B)/(a^3*b*x^5)+2/9*(11*A*b-5*a*B)/(a^4*x^2)+1/6*(A*b-a*B)/(a*b*x^5*(a+b*x^3)^2)+1/18*(11*A*b-5*a*B)/(a^2*b*x^5*(a+b*x^3))+4/27*b^(2/3)*(11*A*b-5*a*B)*log(a^(1/3)+b^(1/3)*x)/a^(14/3)-2/27*b^(2/3)*(11*A*b-5*a*B)*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/a^(14/3)-4/9*b^(2/3)*(11*A*b-5*a*B)*arctan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(a^(14/3)*sqrt(3))],

# Integrands of the form x^m (a+b x^3)^p / (c+d x^3)

# p>0

# p<0
[x^8/((a+b*x^3)*(c+d*x^3)),x,3,1/3*x^3/(b*d)+1/3*a^2*log(a+b*x^3)/(b^2*(b*c-a*d))-1/3*c^2*log(c+d*x^3)/(d^2*(b*c-a*d))],
[x^7/((a+b*x^3)*(c+d*x^3)),x,15,1/2*x^2/(b*d)-1/3*a^(5/3)*log(a^(1/3)+b^(1/3)*x)/(b^(5/3)*(b*c-a*d))+1/3*c^(5/3)*log(c^(1/3)+d^(1/3)*x)/(d^(5/3)*(b*c-a*d))+1/6*a^(5/3)*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(5/3)*(b*c-a*d))-1/6*c^(5/3)*log(c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(5/3)*(b*c-a*d))-a^(5/3)*arctan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(b^(5/3)*(b*c-a*d)*sqrt(3))+c^(5/3)*arctan((c^(1/3)-2*d^(1/3)*x)/(c^(1/3)*sqrt(3)))/(d^(5/3)*(b*c-a*d)*sqrt(3))],
[x^6/((a+b*x^3)*(c+d*x^3)),x,14,x/(b*d)+1/3*a^(4/3)*log(a^(1/3)+b^(1/3)*x)/(b^(4/3)*(b*c-a*d))-1/3*c^(4/3)*log(c^(1/3)+d^(1/3)*x)/(d^(4/3)*(b*c-a*d))-1/6*a^(4/3)*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(4/3)*(b*c-a*d))+1/6*c^(4/3)*log(c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(4/3)*(b*c-a*d))-a^(4/3)*arctan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(b^(4/3)*(b*c-a*d)*sqrt(3))+c^(4/3)*arctan((c^(1/3)-2*d^(1/3)*x)/(c^(1/3)*sqrt(3)))/(d^(4/3)*(b*c-a*d)*sqrt(3))],
[x^5/((a+b*x^3)*(c+d*x^3)),x,3,-1/3*a*log(a+b*x^3)/(b*(b*c-a*d))+1/3*c*log(c+d*x^3)/(d*(b*c-a*d))],
[x^4/((a+b*x^3)*(c+d*x^3)),x,13,1/3*a^(2/3)*log(a^(1/3)+b^(1/3)*x)/(b^(2/3)*(b*c-a*d))-1/3*c^(2/3)*log(c^(1/3)+d^(1/3)*x)/(d^(2/3)*(b*c-a*d))-1/6*a^(2/3)*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(2/3)*(b*c-a*d))+1/6*c^(2/3)*log(c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(2/3)*(b*c-a*d))+a^(2/3)*arctan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(b^(2/3)*(b*c-a*d)*sqrt(3))-c^(2/3)*arctan((c^(1/3)-2*d^(1/3)*x)/(c^(1/3)*sqrt(3)))/(d^(2/3)*(b*c-a*d)*sqrt(3))],
[x^3/((a+b*x^3)*(c+d*x^3)),x,13,-1/3*a^(1/3)*log(a^(1/3)+b^(1/3)*x)/(b^(1/3)*(b*c-a*d))+1/3*c^(1/3)*log(c^(1/3)+d^(1/3)*x)/(d^(1/3)*(b*c-a*d))+1/6*a^(1/3)*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(1/3)*(b*c-a*d))-1/6*c^(1/3)*log(c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*(b*c-a*d))+a^(1/3)*arctan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(b^(1/3)*(b*c-a*d)*sqrt(3))-c^(1/3)*arctan((c^(1/3)-2*d^(1/3)*x)/(c^(1/3)*sqrt(3)))/(d^(1/3)*(b*c-a*d)*sqrt(3))],
[x^2/((a+b*x^3)*(c+d*x^3)),x,4,1/3*log(a+b*x^3)/(b*c-a*d)-1/3*log(c+d*x^3)/(b*c-a*d)],
[x/((a+b*x^3)*(c+d*x^3)),x,13,-1/3*b^(1/3)*log(a^(1/3)+b^(1/3)*x)/(a^(1/3)*(b*c-a*d))+1/3*d^(1/3)*log(c^(1/3)+d^(1/3)*x)/(c^(1/3)*(b*c-a*d))+1/6*b^(1/3)*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(1/3)*(b*c-a*d))-1/6*d^(1/3)*log(c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(c^(1/3)*(b*c-a*d))-b^(1/3)*arctan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(a^(1/3)*(b*c-a*d)*sqrt(3))+d^(1/3)*arctan((c^(1/3)-2*d^(1/3)*x)/(c^(1/3)*sqrt(3)))/(c^(1/3)*(b*c-a*d)*sqrt(3))],
[1/((a+b*x^3)*(c+d*x^3)),x,13,1/3*b^(2/3)*log(a^(1/3)+b^(1/3)*x)/(a^(2/3)*(b*c-a*d))-1/3*d^(2/3)*log(c^(1/3)+d^(1/3)*x)/(c^(2/3)*(b*c-a*d))-1/6*b^(2/3)*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(2/3)*(b*c-a*d))+1/6*d^(2/3)*log(c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(c^(2/3)*(b*c-a*d))-b^(2/3)*arctan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(a^(2/3)*(b*c-a*d)*sqrt(3))+d^(2/3)*arctan((c^(1/3)-2*d^(1/3)*x)/(c^(1/3)*sqrt(3)))/(c^(2/3)*(b*c-a*d)*sqrt(3))],
[1/(x*(a+b*x^3)*(c+d*x^3)),x,3,log(x)/(a*c)-1/3*b*log(a+b*x^3)/(a*(b*c-a*d))+1/3*d*log(c+d*x^3)/(c*(b*c-a*d))],
[1/(x^2*(a+b*x^3)*(c+d*x^3)),x,15,(-1)/(a*c*x)+1/3*b^(4/3)*log(a^(1/3)+b^(1/3)*x)/(a^(4/3)*(b*c-a*d))-1/3*d^(4/3)*log(c^(1/3)+d^(1/3)*x)/(c^(4/3)*(b*c-a*d))-1/6*b^(4/3)*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(4/3)*(b*c-a*d))+1/6*d^(4/3)*log(c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(c^(4/3)*(b*c-a*d))+b^(4/3)*arctan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(a^(4/3)*(b*c-a*d)*sqrt(3))-d^(4/3)*arctan((c^(1/3)-2*d^(1/3)*x)/(c^(1/3)*sqrt(3)))/(c^(4/3)*(b*c-a*d)*sqrt(3))],
[1/(x^3*(a+b*x^3)*(c+d*x^3)),x,14,(-1/2)/(a*c*x^2)-1/3*b^(5/3)*log(a^(1/3)+b^(1/3)*x)/(a^(5/3)*(b*c-a*d))+1/3*d^(5/3)*log(c^(1/3)+d^(1/3)*x)/(c^(5/3)*(b*c-a*d))+1/6*b^(5/3)*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(5/3)*(b*c-a*d))-1/6*d^(5/3)*log(c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(c^(5/3)*(b*c-a*d))+b^(5/3)*arctan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(a^(5/3)*(b*c-a*d)*sqrt(3))-d^(5/3)*arctan((c^(1/3)-2*d^(1/3)*x)/(c^(1/3)*sqrt(3)))/(c^(5/3)*(b*c-a*d)*sqrt(3))],
[1/(x^4*(a+b*x^3)*(c+d*x^3)),x,3,(-1/3)/(a*c*x^3)-(b*c+a*d)*log(x)/(a^2*c^2)+1/3*b^2*log(a+b*x^3)/(a^2*(b*c-a*d))-1/3*d^2*log(c+d*x^3)/(c^2*(b*c-a*d))],
[1/(x^5*(a+b*x^3)*(c+d*x^3)),x,16,(-1/4)/(a*c*x^4)+(b*c+a*d)/(a^2*c^2*x)-1/3*b^(7/3)*log(a^(1/3)+b^(1/3)*x)/(a^(7/3)*(b*c-a*d))+1/3*d^(7/3)*log(c^(1/3)+d^(1/3)*x)/(c^(7/3)*(b*c-a*d))+1/6*b^(7/3)*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(7/3)*(b*c-a*d))-1/6*d^(7/3)*log(c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(c^(7/3)*(b*c-a*d))-b^(7/3)*arctan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(a^(7/3)*(b*c-a*d)*sqrt(3))+d^(7/3)*arctan((c^(1/3)-2*d^(1/3)*x)/(c^(1/3)*sqrt(3)))/(c^(7/3)*(b*c-a*d)*sqrt(3))],
[1/(x^6*(a+b*x^3)*(c+d*x^3)),x,15,(-1/5)/(a*c*x^5)+1/2*(b*c+a*d)/(a^2*c^2*x^2)+1/3*b^(8/3)*log(a^(1/3)+b^(1/3)*x)/(a^(8/3)*(b*c-a*d))-1/3*d^(8/3)*log(c^(1/3)+d^(1/3)*x)/(c^(8/3)*(b*c-a*d))-1/6*b^(8/3)*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(8/3)*(b*c-a*d))+1/6*d^(8/3)*log(c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(c^(8/3)*(b*c-a*d))-b^(8/3)*arctan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(a^(8/3)*(b*c-a*d)*sqrt(3))+d^(8/3)*arctan((c^(1/3)-2*d^(1/3)*x)/(c^(1/3)*sqrt(3)))/(c^(8/3)*(b*c-a*d)*sqrt(3))],
[1/(x^7*(a+b*x^3)*(c+d*x^3)),x,3,(-1/6)/(a*c*x^6)+1/3*(b*c+a*d)/(a^2*c^2*x^3)+(b^2*c^2+a*b*c*d+a^2*d^2)*log(x)/(a^3*c^3)-1/3*b^3*log(a+b*x^3)/(a^3*(b*c-a*d))+1/3*d^3*log(c+d*x^3)/(c^3*(b*c-a*d))],
[1/(x^8*(a+b*x^3)*(c+d*x^3)),x,17,(-1/7)/(a*c*x^7)+1/4*(b*c+a*d)/(a^2*c^2*x^4)+(-b^2*c^2-a*b*c*d-a^2*d^2)/(a^3*c^3*x)+1/3*b^(10/3)*log(a^(1/3)+b^(1/3)*x)/(a^(10/3)*(b*c-a*d))-1/3*d^(10/3)*log(c^(1/3)+d^(1/3)*x)/(c^(10/3)*(b*c-a*d))-1/6*b^(10/3)*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(10/3)*(b*c-a*d))+1/6*d^(10/3)*log(c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(c^(10/3)*(b*c-a*d))+b^(10/3)*arctan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(a^(10/3)*(b*c-a*d)*sqrt(3))-d^(10/3)*arctan((c^(1/3)-2*d^(1/3)*x)/(c^(1/3)*sqrt(3)))/(c^(10/3)*(b*c-a*d)*sqrt(3))],

# Integrands of the form (e x)^m (a+b x^3)^p (c+d x^3)^q with m symbolic
[x^m*(a+b*x^3)^5*(A+B*x^3),x,2,a^5*A*x^(1+m)/(1+m)+a^4*(5*A*b+a*B)*x^(4+m)/(4+m)+5*a^3*b*(2*A*b+a*B)*x^(7+m)/(7+m)+10*a^2*b^2*(A*b+a*B)*x^(10+m)/(10+m)+5*a*b^3*(A*b+2*a*B)*x^(13+m)/(13+m)+b^4*(A*b+5*a*B)*x^(16+m)/(16+m)+b^5*B*x^(19+m)/(19+m)],
[x^m*(a+b*x^3)^2*(A+B*x^3),x,2,a^2*A*x^(1+m)/(1+m)+a*(2*A*b+a*B)*x^(4+m)/(4+m)+b*(A*b+2*a*B)*x^(7+m)/(7+m)+b^2*B*x^(10+m)/(10+m)],
[x^m*(a+b*x^3)*(A+B*x^3),x,2,a*A*x^(1+m)/(1+m)+(A*b+a*B)*x^(4+m)/(4+m)+b*B*x^(7+m)/(7+m)],
[x^m*(A+B*x^3)/(a+b*x^3),x,2,B*x^(1+m)/(b*(1+m))+(A*b-a*B)*x^(1+m)*hypergeom([1,1/3*(1+m)],[1/3*(4+m)],-b*x^3/a)/(a*b*(1+m))],
[x^m*(A+B*x^3)/(a+b*x^3)^2,x,2,1/3*(A*b-a*B)*x^(1+m)/(a*b*(a+b*x^3))+1/3*(A*b*(2-m)+a*B*(1+m))*x^(1+m)*hypergeom([1,1/3*(1+m)],[1/3*(4+m)],-b*x^3/a)/(a^2*b*(1+m))],
[x^m*(A+B*x^3)/(a+b*x^3)^3,x,2,1/6*(A*b-a*B)*x^(1+m)/(a*b*(a+b*x^3)^2)+1/6*(A*b*(5-m)+a*B*(1+m))*x^(1+m)*hypergeom([2,1/3*(1+m)],[1/3*(4+m)],-b*x^3/a)/(a^3*b*(1+m))],
[(e*x)^m/((a+b*x^3)*(c+d*x^3)),x,3,b*(e*x)^(1+m)*hypergeom([1,1/3*(1+m)],[1/3*(4+m)],-b*x^3/a)/(a*(b*c-a*d)*e*(1+m))-d*(e*x)^(1+m)*hypergeom([1,1/3*(1+m)],[1/3*(4+m)],-d*x^3/c)/(c*(b*c-a*d)*e*(1+m))],

# Integrands of the form (e x)^(m/2) (a+b x^3)^p (c+d x^3)^q

# Integrands of the form x^(m/2) (a+b x^3)^p (c+d x^3)^1

# p>0
[x^(7/2)*(a+b*x^3)*(A+B*x^3),x,2,2/9*a*A*x^(9/2)+2/15*(A*b+a*B)*x^(15/2)+2/21*b*B*x^(21/2)],
[x^(5/2)*(a+b*x^3)*(A+B*x^3),x,2,2/7*a*A*x^(7/2)+2/13*(A*b+a*B)*x^(13/2)+2/19*b*B*x^(19/2)],
[x^(3/2)*(a+b*x^3)*(A+B*x^3),x,2,2/5*a*A*x^(5/2)+2/11*(A*b+a*B)*x^(11/2)+2/17*b*B*x^(17/2)],
[(a+b*x^3)*(A+B*x^3)*sqrt(x),x,2,2/3*a*A*x^(3/2)+2/9*(A*b+a*B)*x^(9/2)+2/15*b*B*x^(15/2)],
[(a+b*x^3)*(A+B*x^3)/sqrt(x),x,2,2/7*(A*b+a*B)*x^(7/2)+2/13*b*B*x^(13/2)+2*a*A*sqrt(x)],
[(a+b*x^3)*(A+B*x^3)/x^(3/2),x,2,2/5*(A*b+a*B)*x^(5/2)+2/11*b*B*x^(11/2)-2*a*A/sqrt(x)],
[(a+b*x^3)*(A+B*x^3)/x^(5/2),x,2,-2/3*a*A/x^(3/2)+2/3*(A*b+a*B)*x^(3/2)+2/9*b*B*x^(9/2)],
[(a+b*x^3)*(A+B*x^3)/x^(7/2),x,2,-2/5*a*A/x^(5/2)+2/7*b*B*x^(7/2)+2*(A*b+a*B)*sqrt(x)],
[x^(7/2)*(a+b*x^3)^2*(A+B*x^3),x,2,2/9*a^2*A*x^(9/2)+2/15*a*(2*A*b+a*B)*x^(15/2)+2/21*b*(A*b+2*a*B)*x^(21/2)+2/27*b^2*B*x^(27/2)],
[x^(5/2)*(a+b*x^3)^2*(A+B*x^3),x,2,2/7*a^2*A*x^(7/2)+2/13*a*(2*A*b+a*B)*x^(13/2)+2/19*b*(A*b+2*a*B)*x^(19/2)+2/25*b^2*B*x^(25/2)],
[x^(3/2)*(a+b*x^3)^2*(A+B*x^3),x,2,2/5*a^2*A*x^(5/2)+2/11*a*(2*A*b+a*B)*x^(11/2)+2/17*b*(A*b+2*a*B)*x^(17/2)+2/23*b^2*B*x^(23/2)],
[(a+b*x^3)^2*(A+B*x^3)*sqrt(x),x,2,2/3*a^2*A*x^(3/2)+2/9*a*(2*A*b+a*B)*x^(9/2)+2/15*b*(A*b+2*a*B)*x^(15/2)+2/21*b^2*B*x^(21/2)],
[(a+b*x^3)^2*(A+B*x^3)/sqrt(x),x,2,2/7*a*(2*A*b+a*B)*x^(7/2)+2/13*b*(A*b+2*a*B)*x^(13/2)+2/19*b^2*B*x^(19/2)+2*a^2*A*sqrt(x)],
[(a+b*x^3)^2*(A+B*x^3)/x^(3/2),x,2,2/5*a*(2*A*b+a*B)*x^(5/2)+2/11*b*(A*b+2*a*B)*x^(11/2)+2/17*b^2*B*x^(17/2)-2*a^2*A/sqrt(x)],
[(a+b*x^3)^2*(A+B*x^3)/x^(5/2),x,2,-2/3*a^2*A/x^(3/2)+2/3*a*(2*A*b+a*B)*x^(3/2)+2/9*b*(A*b+2*a*B)*x^(9/2)+2/15*b^2*B*x^(15/2)],
[(a+b*x^3)^2*(A+B*x^3)/x^(7/2),x,2,-2/5*a^2*A/x^(5/2)+2/7*b*(A*b+2*a*B)*x^(7/2)+2/13*b^2*B*x^(13/2)+2*a*(2*A*b+a*B)*sqrt(x)],
[x^(7/2)*(a+b*x^3)^3*(A+B*x^3),x,2,2/9*a^3*A*x^(9/2)+2/15*a^2*(3*A*b+a*B)*x^(15/2)+2/7*a*b*(A*b+a*B)*x^(21/2)+2/27*b^2*(A*b+3*a*B)*x^(27/2)+2/33*b^3*B*x^(33/2)],
[x^(5/2)*(a+b*x^3)^3*(A+B*x^3),x,2,2/7*a^3*A*x^(7/2)+2/13*a^2*(3*A*b+a*B)*x^(13/2)+6/19*a*b*(A*b+a*B)*x^(19/2)+2/25*b^2*(A*b+3*a*B)*x^(25/2)+2/31*b^3*B*x^(31/2)],
[x^(3/2)*(a+b*x^3)^3*(A+B*x^3),x,2,2/5*a^3*A*x^(5/2)+2/11*a^2*(3*A*b+a*B)*x^(11/2)+6/17*a*b*(A*b+a*B)*x^(17/2)+2/23*b^2*(A*b+3*a*B)*x^(23/2)+2/29*b^3*B*x^(29/2)],
[(a+b*x^3)^3*(A+B*x^3)*sqrt(x),x,2,2/3*a^3*A*x^(3/2)+2/9*a^2*(3*A*b+a*B)*x^(9/2)+2/5*a*b*(A*b+a*B)*x^(15/2)+2/21*b^2*(A*b+3*a*B)*x^(21/2)+2/27*b^3*B*x^(27/2)],
[(a+b*x^3)^3*(A+B*x^3)/sqrt(x),x,2,2/7*a^2*(3*A*b+a*B)*x^(7/2)+6/13*a*b*(A*b+a*B)*x^(13/2)+2/19*b^2*(A*b+3*a*B)*x^(19/2)+2/25*b^3*B*x^(25/2)+2*a^3*A*sqrt(x)],
[(a+b*x^3)^3*(A+B*x^3)/x^(3/2),x,2,2/5*a^2*(3*A*b+a*B)*x^(5/2)+6/11*a*b*(A*b+a*B)*x^(11/2)+2/17*b^2*(A*b+3*a*B)*x^(17/2)+2/23*b^3*B*x^(23/2)-2*a^3*A/sqrt(x)],
[(a+b*x^3)^3*(A+B*x^3)/x^(5/2),x,2,-2/3*a^3*A/x^(3/2)+2/3*a^2*(3*A*b+a*B)*x^(3/2)+2/3*a*b*(A*b+a*B)*x^(9/2)+2/15*b^2*(A*b+3*a*B)*x^(15/2)+2/21*b^3*B*x^(21/2)],
[(a+b*x^3)^3*(A+B*x^3)/x^(7/2),x,2,-2/5*a^3*A/x^(5/2)+6/7*a*b*(A*b+a*B)*x^(7/2)+2/13*b^2*(A*b+3*a*B)*x^(13/2)+2/19*b^3*B*x^(19/2)+2*a^2*(3*A*b+a*B)*sqrt(x)],

# p<0
[x^(7/2)*(A+B*x^3)/(a+b*x^3),x,5,2/3*(A*b-a*B)*x^(3/2)/b^2+2/9*B*x^(9/2)/b-2/3*(A*b-a*B)*arctan(x^(3/2)*sqrt(b)/sqrt(a))*sqrt(a)/b^(5/2)],
[x^(5/2)*(A+B*x^3)/(a+b*x^3),x,13,2/7*B*x^(7/2)/b-2/3*a^(1/6)*(A*b-a*B)*arctan(b^(1/6)*sqrt(x)/a^(1/6))/b^(13/6)+1/3*a^(1/6)*(A*b-a*B)*arctan(sqrt(3)-2*b^(1/6)*sqrt(x)/a^(1/6))/b^(13/6)-1/3*a^(1/6)*(A*b-a*B)*arctan(sqrt(3)+2*b^(1/6)*sqrt(x)/a^(1/6))/b^(13/6)+1/2*a^(1/6)*(A*b-a*B)*log(a^(1/3)+b^(1/3)*x-a^(1/6)*b^(1/6)*sqrt(3)*sqrt(x))/(b^(13/6)*sqrt(3))-1/2*a^(1/6)*(A*b-a*B)*log(a^(1/3)+b^(1/3)*x+a^(1/6)*b^(1/6)*sqrt(3)*sqrt(x))/(b^(13/6)*sqrt(3))+2*(A*b-a*B)*sqrt(x)/b^2],
[x^(3/2)*(A+B*x^3)/(a+b*x^3),x,12,2/5*B*x^(5/2)/b+2/3*(A*b-a*B)*arctan(b^(1/6)*sqrt(x)/a^(1/6))/(a^(1/6)*b^(11/6))-1/3*(A*b-a*B)*arctan(sqrt(3)-2*b^(1/6)*sqrt(x)/a^(1/6))/(a^(1/6)*b^(11/6))+1/3*(A*b-a*B)*arctan(sqrt(3)+2*b^(1/6)*sqrt(x)/a^(1/6))/(a^(1/6)*b^(11/6))+1/2*(A*b-a*B)*log(a^(1/3)+b^(1/3)*x-a^(1/6)*b^(1/6)*sqrt(3)*sqrt(x))/(a^(1/6)*b^(11/6)*sqrt(3))-1/2*(A*b-a*B)*log(a^(1/3)+b^(1/3)*x+a^(1/6)*b^(1/6)*sqrt(3)*sqrt(x))/(a^(1/6)*b^(11/6)*sqrt(3))],
[(A+B*x^3)*sqrt(x)/(a+b*x^3),x,4,2/3*B*x^(3/2)/b+2/3*(A*b-a*B)*arctan(x^(3/2)*sqrt(b)/sqrt(a))/(b^(3/2)*sqrt(a))],
[(A+B*x^3)/((a+b*x^3)*sqrt(x)),x,12,2/3*(A*b-a*B)*arctan(b^(1/6)*sqrt(x)/a^(1/6))/(a^(5/6)*b^(7/6))-1/3*(A*b-a*B)*arctan(sqrt(3)-2*b^(1/6)*sqrt(x)/a^(1/6))/(a^(5/6)*b^(7/6))+1/3*(A*b-a*B)*arctan(sqrt(3)+2*b^(1/6)*sqrt(x)/a^(1/6))/(a^(5/6)*b^(7/6))-1/2*(A*b-a*B)*log(a^(1/3)+b^(1/3)*x-a^(1/6)*b^(1/6)*sqrt(3)*sqrt(x))/(a^(5/6)*b^(7/6)*sqrt(3))+1/2*(A*b-a*B)*log(a^(1/3)+b^(1/3)*x+a^(1/6)*b^(1/6)*sqrt(3)*sqrt(x))/(a^(5/6)*b^(7/6)*sqrt(3))+2*B*sqrt(x)/b],
[(A+B*x^3)/(x^(3/2)*(a+b*x^3)),x,12,-2/3*(A*b-a*B)*arctan(b^(1/6)*sqrt(x)/a^(1/6))/(a^(7/6)*b^(5/6))+1/3*(A*b-a*B)*arctan(sqrt(3)-2*b^(1/6)*sqrt(x)/a^(1/6))/(a^(7/6)*b^(5/6))-1/3*(A*b-a*B)*arctan(sqrt(3)+2*b^(1/6)*sqrt(x)/a^(1/6))/(a^(7/6)*b^(5/6))-1/2*(A*b-a*B)*log(a^(1/3)+b^(1/3)*x-a^(1/6)*b^(1/6)*sqrt(3)*sqrt(x))/(a^(7/6)*b^(5/6)*sqrt(3))+1/2*(A*b-a*B)*log(a^(1/3)+b^(1/3)*x+a^(1/6)*b^(1/6)*sqrt(3)*sqrt(x))/(a^(7/6)*b^(5/6)*sqrt(3))-2*A/(a*sqrt(x))],
[(A+B*x^3)/(x^(5/2)*(a+b*x^3)),x,4,-2/3*A/(a*x^(3/2))-2/3*(A*b-a*B)*arctan(x^(3/2)*sqrt(b)/sqrt(a))/(a^(3/2)*sqrt(b))],
[(A+B*x^3)/(x^(7/2)*(a+b*x^3)),x,12,-2/5*A/(a*x^(5/2))-2/3*(A*b-a*B)*arctan(b^(1/6)*sqrt(x)/a^(1/6))/(a^(11/6)*b^(1/6))+1/3*(A*b-a*B)*arctan(sqrt(3)-2*b^(1/6)*sqrt(x)/a^(1/6))/(a^(11/6)*b^(1/6))-1/3*(A*b-a*B)*arctan(sqrt(3)+2*b^(1/6)*sqrt(x)/a^(1/6))/(a^(11/6)*b^(1/6))+1/2*(A*b-a*B)*log(a^(1/3)+b^(1/3)*x-a^(1/6)*b^(1/6)*sqrt(3)*sqrt(x))/(a^(11/6)*b^(1/6)*sqrt(3))-1/2*(A*b-a*B)*log(a^(1/3)+b^(1/3)*x+a^(1/6)*b^(1/6)*sqrt(3)*sqrt(x))/(a^(11/6)*b^(1/6)*sqrt(3))],
[x^(7/2)*(A+B*x^3)/(a+b*x^3)^2,x,5,-1/3*(A*b-3*a*B)*x^(3/2)/(a*b^2)+1/3*(A*b-a*B)*x^(9/2)/(a*b*(a+b*x^3))+1/3*(A*b-3*a*B)*arctan(x^(3/2)*sqrt(b)/sqrt(a))/(b^(5/2)*sqrt(a))],
[x^(5/2)*(A+B*x^3)/(a+b*x^3)^2,x,13,1/3*(A*b-a*B)*x^(7/2)/(a*b*(a+b*x^3))+1/9*(A*b-7*a*B)*arctan(b^(1/6)*sqrt(x)/a^(1/6))/(a^(5/6)*b^(13/6))-1/18*(A*b-7*a*B)*arctan(sqrt(3)-2*b^(1/6)*sqrt(x)/a^(1/6))/(a^(5/6)*b^(13/6))+1/18*(A*b-7*a*B)*arctan(sqrt(3)+2*b^(1/6)*sqrt(x)/a^(1/6))/(a^(5/6)*b^(13/6))-1/12*(A*b-7*a*B)*log(a^(1/3)+b^(1/3)*x-a^(1/6)*b^(1/6)*sqrt(3)*sqrt(x))/(a^(5/6)*b^(13/6)*sqrt(3))+1/12*(A*b-7*a*B)*log(a^(1/3)+b^(1/3)*x+a^(1/6)*b^(1/6)*sqrt(3)*sqrt(x))/(a^(5/6)*b^(13/6)*sqrt(3))-1/3*(A*b-7*a*B)*sqrt(x)/(a*b^2)],
[x^(3/2)*(A+B*x^3)/(a+b*x^3)^2,x,12,1/3*(A*b-a*B)*x^(5/2)/(a*b*(a+b*x^3))+1/9*(A*b+5*a*B)*arctan(b^(1/6)*sqrt(x)/a^(1/6))/(a^(7/6)*b^(11/6))-1/18*(A*b+5*a*B)*arctan(sqrt(3)-2*b^(1/6)*sqrt(x)/a^(1/6))/(a^(7/6)*b^(11/6))+1/18*(A*b+5*a*B)*arctan(sqrt(3)+2*b^(1/6)*sqrt(x)/a^(1/6))/(a^(7/6)*b^(11/6))+1/12*(A*b+5*a*B)*log(a^(1/3)+b^(1/3)*x-a^(1/6)*b^(1/6)*sqrt(3)*sqrt(x))/(a^(7/6)*b^(11/6)*sqrt(3))-1/12*(A*b+5*a*B)*log(a^(1/3)+b^(1/3)*x+a^(1/6)*b^(1/6)*sqrt(3)*sqrt(x))/(a^(7/6)*b^(11/6)*sqrt(3))],
[(A+B*x^3)*sqrt(x)/(a+b*x^3)^2,x,4,1/3*(A*b-a*B)*x^(3/2)/(a*b*(a+b*x^3))+1/3*(A*b+a*B)*arctan(x^(3/2)*sqrt(b)/sqrt(a))/(a^(3/2)*b^(3/2))],
[(A+B*x^3)/((a+b*x^3)^2*sqrt(x)),x,12,1/9*(5*A*b+a*B)*arctan(b^(1/6)*sqrt(x)/a^(1/6))/(a^(11/6)*b^(7/6))-1/18*(5*A*b+a*B)*arctan(sqrt(3)-2*b^(1/6)*sqrt(x)/a^(1/6))/(a^(11/6)*b^(7/6))+1/18*(5*A*b+a*B)*arctan(sqrt(3)+2*b^(1/6)*sqrt(x)/a^(1/6))/(a^(11/6)*b^(7/6))-1/12*(5*A*b+a*B)*log(a^(1/3)+b^(1/3)*x-a^(1/6)*b^(1/6)*sqrt(3)*sqrt(x))/(a^(11/6)*b^(7/6)*sqrt(3))+1/12*(5*A*b+a*B)*log(a^(1/3)+b^(1/3)*x+a^(1/6)*b^(1/6)*sqrt(3)*sqrt(x))/(a^(11/6)*b^(7/6)*sqrt(3))+1/3*(A*b-a*B)*sqrt(x)/(a*b*(a+b*x^3))],
[(A+B*x^3)/(x^(3/2)*(a+b*x^3)^2),x,13,-1/9*(7*A*b-a*B)*arctan(b^(1/6)*sqrt(x)/a^(1/6))/(a^(13/6)*b^(5/6))+1/18*(7*A*b-a*B)*arctan(sqrt(3)-2*b^(1/6)*sqrt(x)/a^(1/6))/(a^(13/6)*b^(5/6))-1/18*(7*A*b-a*B)*arctan(sqrt(3)+2*b^(1/6)*sqrt(x)/a^(1/6))/(a^(13/6)*b^(5/6))-1/12*(7*A*b-a*B)*log(a^(1/3)+b^(1/3)*x-a^(1/6)*b^(1/6)*sqrt(3)*sqrt(x))/(a^(13/6)*b^(5/6)*sqrt(3))+1/12*(7*A*b-a*B)*log(a^(1/3)+b^(1/3)*x+a^(1/6)*b^(1/6)*sqrt(3)*sqrt(x))/(a^(13/6)*b^(5/6)*sqrt(3))+1/3*(-7*A*b+a*B)/(a^2*b*sqrt(x))+1/3*(A*b-a*B)/(a*b*(a+b*x^3)*sqrt(x))],
[(A+B*x^3)/(x^(5/2)*(a+b*x^3)^2),x,5,1/3*(-3*A*b+a*B)/(a^2*b*x^(3/2))+1/3*(A*b-a*B)/(a*b*x^(3/2)*(a+b*x^3))-1/3*(3*A*b-a*B)*arctan(x^(3/2)*sqrt(b)/sqrt(a))/(a^(5/2)*sqrt(b))],
[(A+B*x^3)/(x^(7/2)*(a+b*x^3)^2),x,13,1/15*(-11*A*b+5*a*B)/(a^2*b*x^(5/2))+1/3*(A*b-a*B)/(a*b*x^(5/2)*(a+b*x^3))-1/9*(11*A*b-5*a*B)*arctan(b^(1/6)*sqrt(x)/a^(1/6))/(a^(17/6)*b^(1/6))+1/18*(11*A*b-5*a*B)*arctan(sqrt(3)-2*b^(1/6)*sqrt(x)/a^(1/6))/(a^(17/6)*b^(1/6))-1/18*(11*A*b-5*a*B)*arctan(sqrt(3)+2*b^(1/6)*sqrt(x)/a^(1/6))/(a^(17/6)*b^(1/6))+1/12*(11*A*b-5*a*B)*log(a^(1/3)+b^(1/3)*x-a^(1/6)*b^(1/6)*sqrt(3)*sqrt(x))/(a^(17/6)*b^(1/6)*sqrt(3))-1/12*(11*A*b-5*a*B)*log(a^(1/3)+b^(1/3)*x+a^(1/6)*b^(1/6)*sqrt(3)*sqrt(x))/(a^(17/6)*b^(1/6)*sqrt(3))],
[x^(7/2)*(A+B*x^3)/(a+b*x^3)^3,x,5,1/6*(A*b-a*B)*x^(9/2)/(a*b*(a+b*x^3)^2)-1/12*(A*b+3*a*B)*x^(3/2)/(a*b^2*(a+b*x^3))+1/12*(A*b+3*a*B)*arctan(x^(3/2)*sqrt(b)/sqrt(a))/(a^(3/2)*b^(5/2))],
[x^(5/2)*(A+B*x^3)/(a+b*x^3)^3,x,13,1/6*(A*b-a*B)*x^(7/2)/(a*b*(a+b*x^3)^2)+1/108*(5*A*b+7*a*B)*arctan(b^(1/6)*sqrt(x)/a^(1/6))/(a^(11/6)*b^(13/6))-1/216*(5*A*b+7*a*B)*arctan(sqrt(3)-2*b^(1/6)*sqrt(x)/a^(1/6))/(a^(11/6)*b^(13/6))+1/216*(5*A*b+7*a*B)*arctan(sqrt(3)+2*b^(1/6)*sqrt(x)/a^(1/6))/(a^(11/6)*b^(13/6))-1/144*(5*A*b+7*a*B)*log(a^(1/3)+b^(1/3)*x-a^(1/6)*b^(1/6)*sqrt(3)*sqrt(x))/(a^(11/6)*b^(13/6)*sqrt(3))+1/144*(5*A*b+7*a*B)*log(a^(1/3)+b^(1/3)*x+a^(1/6)*b^(1/6)*sqrt(3)*sqrt(x))/(a^(11/6)*b^(13/6)*sqrt(3))-1/36*(5*A*b+7*a*B)*sqrt(x)/(a*b^2*(a+b*x^3))],
[x^(3/2)*(A+B*x^3)/(a+b*x^3)^3,x,13,1/6*(A*b-a*B)*x^(5/2)/(a*b*(a+b*x^3)^2)+1/36*(7*A*b+5*a*B)*x^(5/2)/(a^2*b*(a+b*x^3))+1/108*(7*A*b+5*a*B)*arctan(b^(1/6)*sqrt(x)/a^(1/6))/(a^(13/6)*b^(11/6))-1/216*(7*A*b+5*a*B)*arctan(sqrt(3)-2*b^(1/6)*sqrt(x)/a^(1/6))/(a^(13/6)*b^(11/6))+1/216*(7*A*b+5*a*B)*arctan(sqrt(3)+2*b^(1/6)*sqrt(x)/a^(1/6))/(a^(13/6)*b^(11/6))+1/144*(7*A*b+5*a*B)*log(a^(1/3)+b^(1/3)*x-a^(1/6)*b^(1/6)*sqrt(3)*sqrt(x))/(a^(13/6)*b^(11/6)*sqrt(3))-1/144*(7*A*b+5*a*B)*log(a^(1/3)+b^(1/3)*x+a^(1/6)*b^(1/6)*sqrt(3)*sqrt(x))/(a^(13/6)*b^(11/6)*sqrt(3))],
[(A+B*x^3)*sqrt(x)/(a+b*x^3)^3,x,5,1/6*(A*b-a*B)*x^(3/2)/(a*b*(a+b*x^3)^2)+1/12*(3*A*b+a*B)*x^(3/2)/(a^2*b*(a+b*x^3))+1/12*(3*A*b+a*B)*arctan(x^(3/2)*sqrt(b)/sqrt(a))/(a^(5/2)*b^(3/2))],
[(A+B*x^3)/((a+b*x^3)^3*sqrt(x)),x,13,5/108*(11*A*b+a*B)*arctan(b^(1/6)*sqrt(x)/a^(1/6))/(a^(17/6)*b^(7/6))-5/216*(11*A*b+a*B)*arctan(sqrt(3)-2*b^(1/6)*sqrt(x)/a^(1/6))/(a^(17/6)*b^(7/6))+5/216*(11*A*b+a*B)*arctan(sqrt(3)+2*b^(1/6)*sqrt(x)/a^(1/6))/(a^(17/6)*b^(7/6))-5/144*(11*A*b+a*B)*log(a^(1/3)+b^(1/3)*x-a^(1/6)*b^(1/6)*sqrt(3)*sqrt(x))/(a^(17/6)*b^(7/6)*sqrt(3))+5/144*(11*A*b+a*B)*log(a^(1/3)+b^(1/3)*x+a^(1/6)*b^(1/6)*sqrt(3)*sqrt(x))/(a^(17/6)*b^(7/6)*sqrt(3))+1/6*(A*b-a*B)*sqrt(x)/(a*b*(a+b*x^3)^2)+1/36*(11*A*b+a*B)*sqrt(x)/(a^2*b*(a+b*x^3))],
[(A+B*x^3)/(x^(3/2)*(a+b*x^3)^3),x,14,-7/108*(13*A*b-a*B)*arctan(b^(1/6)*sqrt(x)/a^(1/6))/(a^(19/6)*b^(5/6))+7/216*(13*A*b-a*B)*arctan(sqrt(3)-2*b^(1/6)*sqrt(x)/a^(1/6))/(a^(19/6)*b^(5/6))-7/216*(13*A*b-a*B)*arctan(sqrt(3)+2*b^(1/6)*sqrt(x)/a^(1/6))/(a^(19/6)*b^(5/6))-7/144*(13*A*b-a*B)*log(a^(1/3)+b^(1/3)*x-a^(1/6)*b^(1/6)*sqrt(3)*sqrt(x))/(a^(19/6)*b^(5/6)*sqrt(3))+7/144*(13*A*b-a*B)*log(a^(1/3)+b^(1/3)*x+a^(1/6)*b^(1/6)*sqrt(3)*sqrt(x))/(a^(19/6)*b^(5/6)*sqrt(3))-7/36*(13*A*b-a*B)/(a^3*b*sqrt(x))+1/6*(A*b-a*B)/(a*b*(a+b*x^3)^2*sqrt(x))+1/36*(13*A*b-a*B)/(a^2*b*(a+b*x^3)*sqrt(x))],
[(A+B*x^3)/(x^(5/2)*(a+b*x^3)^3),x,6,1/4*(-5*A*b+a*B)/(a^3*b*x^(3/2))+1/6*(A*b-a*B)/(a*b*x^(3/2)*(a+b*x^3)^2)+1/12*(5*A*b-a*B)/(a^2*b*x^(3/2)*(a+b*x^3))-1/4*(5*A*b-a*B)*arctan(x^(3/2)*sqrt(b)/sqrt(a))/(a^(7/2)*sqrt(b))],
[(A+B*x^3)/(x^(7/2)*(a+b*x^3)^3),x,14,-11/180*(17*A*b-5*a*B)/(a^3*b*x^(5/2))+1/6*(A*b-a*B)/(a*b*x^(5/2)*(a+b*x^3)^2)+1/36*(17*A*b-5*a*B)/(a^2*b*x^(5/2)*(a+b*x^3))-11/108*(17*A*b-5*a*B)*arctan(b^(1/6)*sqrt(x)/a^(1/6))/(a^(23/6)*b^(1/6))+11/216*(17*A*b-5*a*B)*arctan(sqrt(3)-2*b^(1/6)*sqrt(x)/a^(1/6))/(a^(23/6)*b^(1/6))-11/216*(17*A*b-5*a*B)*arctan(sqrt(3)+2*b^(1/6)*sqrt(x)/a^(1/6))/(a^(23/6)*b^(1/6))+11/144*(17*A*b-5*a*B)*log(a^(1/3)+b^(1/3)*x-a^(1/6)*b^(1/6)*sqrt(3)*sqrt(x))/(a^(23/6)*b^(1/6)*sqrt(3))-11/144*(17*A*b-5*a*B)*log(a^(1/3)+b^(1/3)*x+a^(1/6)*b^(1/6)*sqrt(3)*sqrt(x))/(a^(23/6)*b^(1/6)*sqrt(3))],

# Integrands of the form (e x)^m (a+b x^3)^p (c+d x^3)^(q/2)

# Integrands of the form x^m (a+b x^3) (c+d x^3)^(q/2)

# q>0
[x^8*(A+B*x^3)*sqrt(a+b*x^3),x,3,2/9*a^2*(A*b-a*B)*(a+b*x^3)^(3/2)/b^4-2/15*a*(2*A*b-3*a*B)*(a+b*x^3)^(5/2)/b^4+2/21*(A*b-3*a*B)*(a+b*x^3)^(7/2)/b^4+2/27*B*(a+b*x^3)^(9/2)/b^4],
[x^5*(A+B*x^3)*sqrt(a+b*x^3),x,3,-2/9*a*(A*b-a*B)*(a+b*x^3)^(3/2)/b^3+2/15*(A*b-2*a*B)*(a+b*x^3)^(5/2)/b^3+2/21*B*(a+b*x^3)^(7/2)/b^3],
[x^2*(A+B*x^3)*sqrt(a+b*x^3),x,3,2/9*(A*b-a*B)*(a+b*x^3)^(3/2)/b^2+2/15*B*(a+b*x^3)^(5/2)/b^2],
[(A+B*x^3)*sqrt(a+b*x^3)/x,x,5,2/9*B*(a+b*x^3)^(3/2)/b-2/3*A*arctanh(sqrt(a+b*x^3)/sqrt(a))*sqrt(a)+2/3*A*sqrt(a+b*x^3)],
[(A+B*x^3)*sqrt(a+b*x^3)/x^4,x,5,-1/3*A*(a+b*x^3)^(3/2)/(a*x^3)-1/3*(A*b+2*a*B)*arctanh(sqrt(a+b*x^3)/sqrt(a))/sqrt(a)+1/3*(A*b+2*a*B)*sqrt(a+b*x^3)/a],
[(A+B*x^3)*sqrt(a+b*x^3)/x^7,x,5,-1/6*A*(a+b*x^3)^(3/2)/(a*x^6)+1/12*b*(A*b-4*a*B)*arctanh(sqrt(a+b*x^3)/sqrt(a))/a^(3/2)+1/12*(A*b-4*a*B)*sqrt(a+b*x^3)/(a*x^3)],
[x^3*(A+B*x^3)*sqrt(a+b*x^3),x,4,2/17*B*x^4*(a+b*x^3)^(3/2)/b+6/935*a*(17*A*b-8*a*B)*x*sqrt(a+b*x^3)/b^2+2/187*(17*A*b-8*a*B)*x^4*sqrt(a+b*x^3)/b-4/935*3^(3/4)*a^2*(17*A*b-8*a*B)*(a^(1/3)+b^(1/3)*x)*EllipticF((b^(1/3)*x+a^(1/3)*(1-sqrt(3)))/(b^(1/3)*x+a^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2+sqrt(3))*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2)/(b^(7/3)*sqrt(a+b*x^3)*sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2))],
[(A+B*x^3)*sqrt(a+b*x^3),x,3,2/11*B*x*(a+b*x^3)^(3/2)/b+2/55*(11*A*b-2*a*B)*x*sqrt(a+b*x^3)/b+2/55*3^(3/4)*a*(11*A*b-2*a*B)*(a^(1/3)+b^(1/3)*x)*EllipticF((b^(1/3)*x+a^(1/3)*(1-sqrt(3)))/(b^(1/3)*x+a^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2+sqrt(3))*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2)/(b^(4/3)*sqrt(a+b*x^3)*sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2))],
[(A+B*x^3)*sqrt(a+b*x^3)/x^3,x,3,-1/2*A*(a+b*x^3)^(3/2)/(a*x^2)+1/10*(5*A*b+4*a*B)*x*sqrt(a+b*x^3)/a+1/10*3^(3/4)*(5*A*b+4*a*B)*(a^(1/3)+b^(1/3)*x)*EllipticF((b^(1/3)*x+a^(1/3)*(1-sqrt(3)))/(b^(1/3)*x+a^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2+sqrt(3))*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2)/(b^(1/3)*sqrt(a+b*x^3)*sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2))],
[(A+B*x^3)*sqrt(a+b*x^3)/x^6,x,3,-1/5*A*(a+b*x^3)^(3/2)/(a*x^5)+1/20*(A*b-10*a*B)*sqrt(a+b*x^3)/(a*x^2)-1/20*3^(3/4)*b^(2/3)*(A*b-10*a*B)*(a^(1/3)+b^(1/3)*x)*EllipticF((b^(1/3)*x+a^(1/3)*(1-sqrt(3)))/(b^(1/3)*x+a^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2+sqrt(3))*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2)/(a*sqrt(a+b*x^3)*sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2))],
[(A+B*x^3)*sqrt(a+b*x^3)/x^9,x,4,-1/8*A*(a+b*x^3)^(3/2)/(a*x^8)+1/80*(7*A*b-16*a*B)*sqrt(a+b*x^3)/(a*x^5)+3/320*b*(7*A*b-16*a*B)*sqrt(a+b*x^3)/(a^2*x^2)+1/320*3^(3/4)*b^(5/3)*(7*A*b-16*a*B)*(a^(1/3)+b^(1/3)*x)*EllipticF((b^(1/3)*x+a^(1/3)*(1-sqrt(3)))/(b^(1/3)*x+a^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2+sqrt(3))*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2)/(a^2*sqrt(a+b*x^3)*sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2))],
[x^4*(A+B*x^3)*sqrt(a+b*x^3),x,6,2/19*B*x^5*(a+b*x^3)^(3/2)/b+6/1729*a*(19*A*b-10*a*B)*x^2*sqrt(a+b*x^3)/b^2+2/247*(19*A*b-10*a*B)*x^5*sqrt(a+b*x^3)/b-24/1729*a^2*(19*A*b-10*a*B)*sqrt(a+b*x^3)/(b^(8/3)*(b^(1/3)*x+a^(1/3)*(1+sqrt(3))))-8/1729*3^(3/4)*a^(7/3)*(19*A*b-10*a*B)*(a^(1/3)+b^(1/3)*x)*EllipticF((b^(1/3)*x+a^(1/3)*(1-sqrt(3)))/(b^(1/3)*x+a^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2)/(b^(8/3)*sqrt(a+b*x^3)*sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2))+12/1729*3^(1/4)*a^(7/3)*(19*A*b-10*a*B)*(a^(1/3)+b^(1/3)*x)*EllipticE((b^(1/3)*x+a^(1/3)*(1-sqrt(3)))/(b^(1/3)*x+a^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2)/(b^(8/3)*sqrt(a+b*x^3)*sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2))],
[x*(A+B*x^3)*sqrt(a+b*x^3),x,5,2/13*B*x^2*(a+b*x^3)^(3/2)/b+2/91*(13*A*b-4*a*B)*x^2*sqrt(a+b*x^3)/b+6/91*a*(13*A*b-4*a*B)*sqrt(a+b*x^3)/(b^(5/3)*(b^(1/3)*x+a^(1/3)*(1+sqrt(3))))+2/91*3^(3/4)*a^(4/3)*(13*A*b-4*a*B)*(a^(1/3)+b^(1/3)*x)*EllipticF((b^(1/3)*x+a^(1/3)*(1-sqrt(3)))/(b^(1/3)*x+a^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2)/(b^(5/3)*sqrt(a+b*x^3)*sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2))-3/91*3^(1/4)*a^(4/3)*(13*A*b-4*a*B)*(a^(1/3)+b^(1/3)*x)*EllipticE((b^(1/3)*x+a^(1/3)*(1-sqrt(3)))/(b^(1/3)*x+a^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2)/(b^(5/3)*sqrt(a+b*x^3)*sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2))],
[(A+B*x^3)*sqrt(a+b*x^3)/x^2,x,5,-A*(a+b*x^3)^(3/2)/(a*x)+1/7*(7*A*b+2*a*B)*x^2*sqrt(a+b*x^3)/a+3/7*(7*A*b+2*a*B)*sqrt(a+b*x^3)/(b^(2/3)*(b^(1/3)*x+a^(1/3)*(1+sqrt(3))))+1/7*3^(3/4)*a^(1/3)*(7*A*b+2*a*B)*(a^(1/3)+b^(1/3)*x)*EllipticF((b^(1/3)*x+a^(1/3)*(1-sqrt(3)))/(b^(1/3)*x+a^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2)/(b^(2/3)*sqrt(a+b*x^3)*sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2))-3/14*3^(1/4)*a^(1/3)*(7*A*b+2*a*B)*(a^(1/3)+b^(1/3)*x)*EllipticE((b^(1/3)*x+a^(1/3)*(1-sqrt(3)))/(b^(1/3)*x+a^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2)/(b^(2/3)*sqrt(a+b*x^3)*sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2))],
[(A+B*x^3)*sqrt(a+b*x^3)/x^5,x,5,-1/4*A*(a+b*x^3)^(3/2)/(a*x^4)-1/8*(A*b+8*a*B)*sqrt(a+b*x^3)/(a*x)+3/8*b^(1/3)*(A*b+8*a*B)*sqrt(a+b*x^3)/(a*(b^(1/3)*x+a^(1/3)*(1+sqrt(3))))+1/4*3^(3/4)*b^(1/3)*(A*b+8*a*B)*(a^(1/3)+b^(1/3)*x)*EllipticF((b^(1/3)*x+a^(1/3)*(1-sqrt(3)))/(b^(1/3)*x+a^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2)/(a^(2/3)*sqrt(2)*sqrt(a+b*x^3)*sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2))-3/16*3^(1/4)*b^(1/3)*(A*b+8*a*B)*(a^(1/3)+b^(1/3)*x)*EllipticE((b^(1/3)*x+a^(1/3)*(1-sqrt(3)))/(b^(1/3)*x+a^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2)/(a^(2/3)*sqrt(a+b*x^3)*sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2))],
[(A+B*x^3)*sqrt(a+b*x^3)/x^8,x,6,-1/7*A*(a+b*x^3)^(3/2)/(a*x^7)+1/56*(5*A*b-14*a*B)*sqrt(a+b*x^3)/(a*x^4)+3/112*b*(5*A*b-14*a*B)*sqrt(a+b*x^3)/(a^2*x)-3/112*b^(4/3)*(5*A*b-14*a*B)*sqrt(a+b*x^3)/(a^2*(b^(1/3)*x+a^(1/3)*(1+sqrt(3))))-1/56*3^(3/4)*b^(4/3)*(5*A*b-14*a*B)*(a^(1/3)+b^(1/3)*x)*EllipticF((b^(1/3)*x+a^(1/3)*(1-sqrt(3)))/(b^(1/3)*x+a^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2)/(a^(5/3)*sqrt(2)*sqrt(a+b*x^3)*sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2))+3/224*3^(1/4)*b^(4/3)*(5*A*b-14*a*B)*(a^(1/3)+b^(1/3)*x)*EllipticE((b^(1/3)*x+a^(1/3)*(1-sqrt(3)))/(b^(1/3)*x+a^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2)/(a^(5/3)*sqrt(a+b*x^3)*sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2))],
[(A+B*x^3)*sqrt(a+b*x^3)/x^11,x,7,-1/10*A*(a+b*x^3)^(3/2)/(a*x^10)+1/140*(11*A*b-20*a*B)*sqrt(a+b*x^3)/(a*x^7)+3/1120*b*(11*A*b-20*a*B)*sqrt(a+b*x^3)/(a^2*x^4)-3/448*b^2*(11*A*b-20*a*B)*sqrt(a+b*x^3)/(a^3*x)+3/448*b^(7/3)*(11*A*b-20*a*B)*sqrt(a+b*x^3)/(a^3*(b^(1/3)*x+a^(1/3)*(1+sqrt(3))))+1/224*3^(3/4)*b^(7/3)*(11*A*b-20*a*B)*(a^(1/3)+b^(1/3)*x)*EllipticF((b^(1/3)*x+a^(1/3)*(1-sqrt(3)))/(b^(1/3)*x+a^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2)/(a^(8/3)*sqrt(2)*sqrt(a+b*x^3)*sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2))-3/896*3^(1/4)*b^(7/3)*(11*A*b-20*a*B)*(a^(1/3)+b^(1/3)*x)*EllipticE((b^(1/3)*x+a^(1/3)*(1-sqrt(3)))/(b^(1/3)*x+a^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2)/(a^(8/3)*sqrt(a+b*x^3)*sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2))],
[x^8*(a+b*x^3)^(3/2)*(A+B*x^3),x,3,2/15*a^2*(A*b-a*B)*(a+b*x^3)^(5/2)/b^4-2/21*a*(2*A*b-3*a*B)*(a+b*x^3)^(7/2)/b^4+2/27*(A*b-3*a*B)*(a+b*x^3)^(9/2)/b^4+2/33*B*(a+b*x^3)^(11/2)/b^4],
[x^5*(a+b*x^3)^(3/2)*(A+B*x^3),x,3,-2/15*a*(A*b-a*B)*(a+b*x^3)^(5/2)/b^3+2/21*(A*b-2*a*B)*(a+b*x^3)^(7/2)/b^3+2/27*B*(a+b*x^3)^(9/2)/b^3],
[x^2*(a+b*x^3)^(3/2)*(A+B*x^3),x,3,2/15*(A*b-a*B)*(a+b*x^3)^(5/2)/b^2+2/21*B*(a+b*x^3)^(7/2)/b^2],
[(a+b*x^3)^(3/2)*(A+B*x^3)/x,x,6,2/9*A*(a+b*x^3)^(3/2)+2/15*B*(a+b*x^3)^(5/2)/b-2/3*a^(3/2)*A*arctanh(sqrt(a+b*x^3)/sqrt(a))+2/3*a*A*sqrt(a+b*x^3)],
[(a+b*x^3)^(3/2)*(A+B*x^3)/x^4,x,6,1/9*(3*A*b+2*a*B)*(a+b*x^3)^(3/2)/a-1/3*A*(a+b*x^3)^(5/2)/(a*x^3)-1/3*(3*A*b+2*a*B)*arctanh(sqrt(a+b*x^3)/sqrt(a))*sqrt(a)+1/3*(3*A*b+2*a*B)*sqrt(a+b*x^3)],
[(a+b*x^3)^(3/2)*(A+B*x^3)/x^7,x,6,-1/12*(A*b+4*a*B)*(a+b*x^3)^(3/2)/(a*x^3)-1/6*A*(a+b*x^3)^(5/2)/(a*x^6)-1/4*b*(A*b+4*a*B)*arctanh(sqrt(a+b*x^3)/sqrt(a))/sqrt(a)+1/4*b*(A*b+4*a*B)*sqrt(a+b*x^3)/a],
[x^3*(a+b*x^3)^(3/2)*(A+B*x^3),x,5,2/391*(23*A*b-8*a*B)*x^4*(a+b*x^3)^(3/2)/b+2/23*B*x^4*(a+b*x^3)^(5/2)/b+54/21505*a^2*(23*A*b-8*a*B)*x*sqrt(a+b*x^3)/b^2+18/4301*a*(23*A*b-8*a*B)*x^4*sqrt(a+b*x^3)/b-36/21505*3^(3/4)*a^3*(23*A*b-8*a*B)*(a^(1/3)+b^(1/3)*x)*EllipticF((b^(1/3)*x+a^(1/3)*(1-sqrt(3)))/(b^(1/3)*x+a^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2+sqrt(3))*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2)/(b^(7/3)*sqrt(a+b*x^3)*sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2))],
[(a+b*x^3)^(3/2)*(A+B*x^3),x,4,2/187*(17*A*b-2*a*B)*x*(a+b*x^3)^(3/2)/b+2/17*B*x*(a+b*x^3)^(5/2)/b+18/935*a*(17*A*b-2*a*B)*x*sqrt(a+b*x^3)/b+18/935*3^(3/4)*a^2*(17*A*b-2*a*B)*(a^(1/3)+b^(1/3)*x)*EllipticF((b^(1/3)*x+a^(1/3)*(1-sqrt(3)))/(b^(1/3)*x+a^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2+sqrt(3))*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2)/(b^(4/3)*sqrt(a+b*x^3)*sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2))],
[(a+b*x^3)^(3/2)*(A+B*x^3)/x^3,x,4,1/22*(11*A*b+4*a*B)*x*(a+b*x^3)^(3/2)/a-1/2*A*(a+b*x^3)^(5/2)/(a*x^2)+9/110*(11*A*b+4*a*B)*x*sqrt(a+b*x^3)+9/110*3^(3/4)*a*(11*A*b+4*a*B)*(a^(1/3)+b^(1/3)*x)*EllipticF((b^(1/3)*x+a^(1/3)*(1-sqrt(3)))/(b^(1/3)*x+a^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2+sqrt(3))*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2)/(b^(1/3)*sqrt(a+b*x^3)*sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2))],
[(a+b*x^3)^(3/2)*(A+B*x^3)/x^6,x,4,-1/4*(A*b+2*a*B)*(a+b*x^3)^(3/2)/(a*x^2)-1/5*A*(a+b*x^3)^(5/2)/(a*x^5)+9/20*b*(A*b+2*a*B)*x*sqrt(a+b*x^3)/a+9/20*3^(3/4)*b^(2/3)*(A*b+2*a*B)*(a^(1/3)+b^(1/3)*x)*EllipticF((b^(1/3)*x+a^(1/3)*(1-sqrt(3)))/(b^(1/3)*x+a^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2+sqrt(3))*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2)/(sqrt(a+b*x^3)*sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2))],
[(a+b*x^3)^(3/2)*(A+B*x^3)/x^9,x,4,1/80*(A*b-16*a*B)*(a+b*x^3)^(3/2)/(a*x^5)-1/8*A*(a+b*x^3)^(5/2)/(a*x^8)+9/320*b*(A*b-16*a*B)*sqrt(a+b*x^3)/(a*x^2)-9/320*3^(3/4)*b^(5/3)*(A*b-16*a*B)*(a^(1/3)+b^(1/3)*x)*EllipticF((b^(1/3)*x+a^(1/3)*(1-sqrt(3)))/(b^(1/3)*x+a^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2+sqrt(3))*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2)/(a*sqrt(a+b*x^3)*sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2))],
[x^4*(a+b*x^3)^(3/2)*(A+B*x^3),x,7,2/95*(5*A*b-2*a*B)*x^5*(a+b*x^3)^(3/2)/b+2/25*B*x^5*(a+b*x^3)^(5/2)/b+54/8645*a^2*(5*A*b-2*a*B)*x^2*sqrt(a+b*x^3)/b^2+18/1235*a*(5*A*b-2*a*B)*x^5*sqrt(a+b*x^3)/b-216/8645*a^3*(5*A*b-2*a*B)*sqrt(a+b*x^3)/(b^(8/3)*(b^(1/3)*x+a^(1/3)*(1+sqrt(3))))-72/8645*3^(3/4)*a^(10/3)*(5*A*b-2*a*B)*(a^(1/3)+b^(1/3)*x)*EllipticF((b^(1/3)*x+a^(1/3)*(1-sqrt(3)))/(b^(1/3)*x+a^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2)/(b^(8/3)*sqrt(a+b*x^3)*sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2))+108/8645*3^(1/4)*a^(10/3)*(5*A*b-2*a*B)*(a^(1/3)+b^(1/3)*x)*EllipticE((b^(1/3)*x+a^(1/3)*(1-sqrt(3)))/(b^(1/3)*x+a^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2)/(b^(8/3)*sqrt(a+b*x^3)*sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2))],
[x*(a+b*x^3)^(3/2)*(A+B*x^3),x,6,2/247*(19*A*b-4*a*B)*x^2*(a+b*x^3)^(3/2)/b+2/19*B*x^2*(a+b*x^3)^(5/2)/b+18/1729*a*(19*A*b-4*a*B)*x^2*sqrt(a+b*x^3)/b+54/1729*a^2*(19*A*b-4*a*B)*sqrt(a+b*x^3)/(b^(5/3)*(b^(1/3)*x+a^(1/3)*(1+sqrt(3))))+18/1729*3^(3/4)*a^(7/3)*(19*A*b-4*a*B)*(a^(1/3)+b^(1/3)*x)*EllipticF((b^(1/3)*x+a^(1/3)*(1-sqrt(3)))/(b^(1/3)*x+a^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2)/(b^(5/3)*sqrt(a+b*x^3)*sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2))-27/1729*3^(1/4)*a^(7/3)*(19*A*b-4*a*B)*(a^(1/3)+b^(1/3)*x)*EllipticE((b^(1/3)*x+a^(1/3)*(1-sqrt(3)))/(b^(1/3)*x+a^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2)/(b^(5/3)*sqrt(a+b*x^3)*sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2))],
[(a+b*x^3)^(3/2)*(A+B*x^3)/x^2,x,6,1/13*(13*A*b+2*a*B)*x^2*(a+b*x^3)^(3/2)/a-A*(a+b*x^3)^(5/2)/(a*x)+9/91*(13*A*b+2*a*B)*x^2*sqrt(a+b*x^3)+27/91*a*(13*A*b+2*a*B)*sqrt(a+b*x^3)/(b^(2/3)*(b^(1/3)*x+a^(1/3)*(1+sqrt(3))))+9/91*3^(3/4)*a^(4/3)*(13*A*b+2*a*B)*(a^(1/3)+b^(1/3)*x)*EllipticF((b^(1/3)*x+a^(1/3)*(1-sqrt(3)))/(b^(1/3)*x+a^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2)/(b^(2/3)*sqrt(a+b*x^3)*sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2))-27/182*3^(1/4)*a^(4/3)*(13*A*b+2*a*B)*(a^(1/3)+b^(1/3)*x)*EllipticE((b^(1/3)*x+a^(1/3)*(1-sqrt(3)))/(b^(1/3)*x+a^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2)/(b^(2/3)*sqrt(a+b*x^3)*sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2))],
[(a+b*x^3)^(3/2)*(A+B*x^3)/x^5,x,6,-1/8*(7*A*b+8*a*B)*(a+b*x^3)^(3/2)/(a*x)-1/4*A*(a+b*x^3)^(5/2)/(a*x^4)+9/56*b*(7*A*b+8*a*B)*x^2*sqrt(a+b*x^3)/a+27/56*b^(1/3)*(7*A*b+8*a*B)*sqrt(a+b*x^3)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))+9/28*3^(3/4)*a^(1/3)*b^(1/3)*(7*A*b+8*a*B)*(a^(1/3)+b^(1/3)*x)*EllipticF((b^(1/3)*x+a^(1/3)*(1-sqrt(3)))/(b^(1/3)*x+a^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2)/(sqrt(2)*sqrt(a+b*x^3)*sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2))-27/112*3^(1/4)*a^(1/3)*b^(1/3)*(7*A*b+8*a*B)*(a^(1/3)+b^(1/3)*x)*EllipticE((b^(1/3)*x+a^(1/3)*(1-sqrt(3)))/(b^(1/3)*x+a^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2)/(sqrt(a+b*x^3)*sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2))],
[(a+b*x^3)^(3/2)*(A+B*x^3)/x^8,x,6,-1/56*(A*b+14*a*B)*(a+b*x^3)^(3/2)/(a*x^4)-1/7*A*(a+b*x^3)^(5/2)/(a*x^7)-9/112*b*(A*b+14*a*B)*sqrt(a+b*x^3)/(a*x)+27/112*b^(4/3)*(A*b+14*a*B)*sqrt(a+b*x^3)/(a*(b^(1/3)*x+a^(1/3)*(1+sqrt(3))))+9/56*3^(3/4)*b^(4/3)*(A*b+14*a*B)*(a^(1/3)+b^(1/3)*x)*EllipticF((b^(1/3)*x+a^(1/3)*(1-sqrt(3)))/(b^(1/3)*x+a^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2)/(a^(2/3)*sqrt(2)*sqrt(a+b*x^3)*sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2))-27/224*3^(1/4)*b^(4/3)*(A*b+14*a*B)*(a^(1/3)+b^(1/3)*x)*EllipticE((b^(1/3)*x+a^(1/3)*(1-sqrt(3)))/(b^(1/3)*x+a^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2)/(a^(2/3)*sqrt(a+b*x^3)*sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2))],
[(a+b*x^3)^(3/2)*(A+B*x^3)/x^11,x,7,1/28*(A*b-4*a*B)*(a+b*x^3)^(3/2)/(a*x^7)-1/10*A*(a+b*x^3)^(5/2)/(a*x^10)+9/224*b*(A*b-4*a*B)*sqrt(a+b*x^3)/(a*x^4)+27/448*b^2*(A*b-4*a*B)*sqrt(a+b*x^3)/(a^2*x)-27/448*b^(7/3)*(A*b-4*a*B)*sqrt(a+b*x^3)/(a^2*(b^(1/3)*x+a^(1/3)*(1+sqrt(3))))-9/224*3^(3/4)*b^(7/3)*(A*b-4*a*B)*(a^(1/3)+b^(1/3)*x)*EllipticF((b^(1/3)*x+a^(1/3)*(1-sqrt(3)))/(b^(1/3)*x+a^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2)/(a^(5/3)*sqrt(2)*sqrt(a+b*x^3)*sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2))+27/896*3^(1/4)*b^(7/3)*(A*b-4*a*B)*(a^(1/3)+b^(1/3)*x)*EllipticE((b^(1/3)*x+a^(1/3)*(1-sqrt(3)))/(b^(1/3)*x+a^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2)/(a^(5/3)*sqrt(a+b*x^3)*sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2))],

# q<0
[x^8*(A+B*x^3)/sqrt(a+b*x^3),x,3,-2/9*a*(2*A*b-3*a*B)*(a+b*x^3)^(3/2)/b^4+2/15*(A*b-3*a*B)*(a+b*x^3)^(5/2)/b^4+2/21*B*(a+b*x^3)^(7/2)/b^4+2/3*a^2*(A*b-a*B)*sqrt(a+b*x^3)/b^4],
[x^5*(A+B*x^3)/sqrt(a+b*x^3),x,3,2/9*(A*b-2*a*B)*(a+b*x^3)^(3/2)/b^3+2/15*B*(a+b*x^3)^(5/2)/b^3-2/3*a*(A*b-a*B)*sqrt(a+b*x^3)/b^3],
[x^2*(A+B*x^3)/sqrt(a+b*x^3),x,3,2/9*B*(a+b*x^3)^(3/2)/b^2+2/3*(A*b-a*B)*sqrt(a+b*x^3)/b^2],
[(A+B*x^3)/(x*sqrt(a+b*x^3)),x,4,-2/3*A*arctanh(sqrt(a+b*x^3)/sqrt(a))/sqrt(a)+2/3*B*sqrt(a+b*x^3)/b],
[(A+B*x^3)/(x^4*sqrt(a+b*x^3)),x,4,1/3*(A*b-2*a*B)*arctanh(sqrt(a+b*x^3)/sqrt(a))/a^(3/2)-1/3*A*sqrt(a+b*x^3)/(a*x^3)],
[(A+B*x^3)/(x^7*sqrt(a+b*x^3)),x,5,-1/12*b*(3*A*b-4*a*B)*arctanh(sqrt(a+b*x^3)/sqrt(a))/a^(5/2)-1/6*A*sqrt(a+b*x^3)/(a*x^6)+1/12*(3*A*b-4*a*B)*sqrt(a+b*x^3)/(a^2*x^3)],
[x^3*(A+B*x^3)/sqrt(a+b*x^3),x,3,2/55*(11*A*b-8*a*B)*x*sqrt(a+b*x^3)/b^2+2/11*B*x^4*sqrt(a+b*x^3)/b-4/55*a*(11*A*b-8*a*B)*(a^(1/3)+b^(1/3)*x)*EllipticF((b^(1/3)*x+a^(1/3)*(1-sqrt(3)))/(b^(1/3)*x+a^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2+sqrt(3))*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2)/(3^(1/4)*b^(7/3)*sqrt(a+b*x^3)*sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2))],
[(A+B*x^3)/sqrt(a+b*x^3),x,2,2/5*B*x*sqrt(a+b*x^3)/b+2/5*(5*A*b-2*a*B)*(a^(1/3)+b^(1/3)*x)*EllipticF((b^(1/3)*x+a^(1/3)*(1-sqrt(3)))/(b^(1/3)*x+a^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2+sqrt(3))*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2)/(3^(1/4)*b^(4/3)*sqrt(a+b*x^3)*sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2))],
[(A+B*x^3)/(x^3*sqrt(a+b*x^3)),x,2,-1/2*A*sqrt(a+b*x^3)/(a*x^2)-1/2*(A*b-4*a*B)*(a^(1/3)+b^(1/3)*x)*EllipticF((b^(1/3)*x+a^(1/3)*(1-sqrt(3)))/(b^(1/3)*x+a^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2+sqrt(3))*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2)/(3^(1/4)*a*b^(1/3)*sqrt(a+b*x^3)*sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2))],
[(A+B*x^3)/(x^6*sqrt(a+b*x^3)),x,3,-1/5*A*sqrt(a+b*x^3)/(a*x^5)+1/20*(7*A*b-10*a*B)*sqrt(a+b*x^3)/(a^2*x^2)+1/20*b^(2/3)*(7*A*b-10*a*B)*(a^(1/3)+b^(1/3)*x)*EllipticF((b^(1/3)*x+a^(1/3)*(1-sqrt(3)))/(b^(1/3)*x+a^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2+sqrt(3))*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2)/(3^(1/4)*a^2*sqrt(a+b*x^3)*sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2))],
[x^4*(A+B*x^3)/sqrt(a+b*x^3),x,5,2/91*(13*A*b-10*a*B)*x^2*sqrt(a+b*x^3)/b^2+2/13*B*x^5*sqrt(a+b*x^3)/b-8/91*a*(13*A*b-10*a*B)*sqrt(a+b*x^3)/(b^(8/3)*(b^(1/3)*x+a^(1/3)*(1+sqrt(3))))-8/91*a^(4/3)*(13*A*b-10*a*B)*(a^(1/3)+b^(1/3)*x)*EllipticF((b^(1/3)*x+a^(1/3)*(1-sqrt(3)))/(b^(1/3)*x+a^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2)/(3^(1/4)*b^(8/3)*sqrt(a+b*x^3)*sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2))+4/91*3^(1/4)*a^(4/3)*(13*A*b-10*a*B)*(a^(1/3)+b^(1/3)*x)*EllipticE((b^(1/3)*x+a^(1/3)*(1-sqrt(3)))/(b^(1/3)*x+a^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2)/(b^(8/3)*sqrt(a+b*x^3)*sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2))],
[x*(A+B*x^3)/sqrt(a+b*x^3),x,4,2/7*B*x^2*sqrt(a+b*x^3)/b+2/7*(7*A*b-4*a*B)*sqrt(a+b*x^3)/(b^(5/3)*(b^(1/3)*x+a^(1/3)*(1+sqrt(3))))+2/7*a^(1/3)*(7*A*b-4*a*B)*(a^(1/3)+b^(1/3)*x)*EllipticF((b^(1/3)*x+a^(1/3)*(1-sqrt(3)))/(b^(1/3)*x+a^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2)/(3^(1/4)*b^(5/3)*sqrt(a+b*x^3)*sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2))-1/7*3^(1/4)*a^(1/3)*(7*A*b-4*a*B)*(a^(1/3)+b^(1/3)*x)*EllipticE((b^(1/3)*x+a^(1/3)*(1-sqrt(3)))/(b^(1/3)*x+a^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2)/(b^(5/3)*sqrt(a+b*x^3)*sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2))],
[(A+B*x^3)/(x^2*sqrt(a+b*x^3)),x,4,-A*sqrt(a+b*x^3)/(a*x)+(A*b+2*a*B)*sqrt(a+b*x^3)/(a*b^(2/3)*(b^(1/3)*x+a^(1/3)*(1+sqrt(3))))+(A*b+2*a*B)*(a^(1/3)+b^(1/3)*x)*EllipticF((b^(1/3)*x+a^(1/3)*(1-sqrt(3)))/(b^(1/3)*x+a^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2)/(3^(1/4)*a^(2/3)*b^(2/3)*sqrt(a+b*x^3)*sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2))-1/2*3^(1/4)*(A*b+2*a*B)*(a^(1/3)+b^(1/3)*x)*EllipticE((b^(1/3)*x+a^(1/3)*(1-sqrt(3)))/(b^(1/3)*x+a^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2)/(a^(2/3)*b^(2/3)*sqrt(a+b*x^3)*sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2))],
[(A+B*x^3)/(x^5*sqrt(a+b*x^3)),x,5,-1/4*A*sqrt(a+b*x^3)/(a*x^4)+1/8*(5*A*b-8*a*B)*sqrt(a+b*x^3)/(a^2*x)-1/8*b^(1/3)*(5*A*b-8*a*B)*sqrt(a+b*x^3)/(a^2*(b^(1/3)*x+a^(1/3)*(1+sqrt(3))))-1/4*b^(1/3)*(5*A*b-8*a*B)*(a^(1/3)+b^(1/3)*x)*EllipticF((b^(1/3)*x+a^(1/3)*(1-sqrt(3)))/(b^(1/3)*x+a^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2)/(3^(1/4)*a^(5/3)*sqrt(2)*sqrt(a+b*x^3)*sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2))+1/16*3^(1/4)*b^(1/3)*(5*A*b-8*a*B)*(a^(1/3)+b^(1/3)*x)*EllipticE((b^(1/3)*x+a^(1/3)*(1-sqrt(3)))/(b^(1/3)*x+a^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2)/(a^(5/3)*sqrt(a+b*x^3)*sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2))],
[(A+B*x^3)/(x^8*sqrt(a+b*x^3)),x,6,-1/7*A*sqrt(a+b*x^3)/(a*x^7)+1/56*(11*A*b-14*a*B)*sqrt(a+b*x^3)/(a^2*x^4)-5/112*b*(11*A*b-14*a*B)*sqrt(a+b*x^3)/(a^3*x)+5/112*b^(4/3)*(11*A*b-14*a*B)*sqrt(a+b*x^3)/(a^3*(b^(1/3)*x+a^(1/3)*(1+sqrt(3))))+5/56*b^(4/3)*(11*A*b-14*a*B)*(a^(1/3)+b^(1/3)*x)*EllipticF((b^(1/3)*x+a^(1/3)*(1-sqrt(3)))/(b^(1/3)*x+a^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2)/(3^(1/4)*a^(8/3)*sqrt(2)*sqrt(a+b*x^3)*sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2))-5/224*3^(1/4)*b^(4/3)*(11*A*b-14*a*B)*(a^(1/3)+b^(1/3)*x)*EllipticE((b^(1/3)*x+a^(1/3)*(1-sqrt(3)))/(b^(1/3)*x+a^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2)/(a^(8/3)*sqrt(a+b*x^3)*sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2))],
[x^8*(A+B*x^3)/(a+b*x^3)^(3/2),x,3,2/9*(A*b-3*a*B)*(a+b*x^3)^(3/2)/b^4+2/15*B*(a+b*x^3)^(5/2)/b^4-2/3*a^2*(A*b-a*B)/(b^4*sqrt(a+b*x^3))-2/3*a*(2*A*b-3*a*B)*sqrt(a+b*x^3)/b^4],
[x^5*(A+B*x^3)/(a+b*x^3)^(3/2),x,3,2/9*B*(a+b*x^3)^(3/2)/b^3+2/3*a*(A*b-a*B)/(b^3*sqrt(a+b*x^3))+2/3*(A*b-2*a*B)*sqrt(a+b*x^3)/b^3],
[x^2*(A+B*x^3)/(a+b*x^3)^(3/2),x,3,-2/3*(A*b-a*B)/(b^2*sqrt(a+b*x^3))+2/3*B*sqrt(a+b*x^3)/b^2],
[(A+B*x^3)/(x*(a+b*x^3)^(3/2)),x,4,-2/3*A*arctanh(sqrt(a+b*x^3)/sqrt(a))/a^(3/2)+2/3*(A*b-a*B)/(a*b*sqrt(a+b*x^3))],
[(A+B*x^3)/(x^4*(a+b*x^3)^(3/2)),x,5,1/3*(3*A*b-2*a*B)*arctanh(sqrt(a+b*x^3)/sqrt(a))/a^(5/2)+1/3*(-3*A*b+2*a*B)/(a^2*sqrt(a+b*x^3))-1/3*A/(a*x^3*sqrt(a+b*x^3))],
[(A+B*x^3)/(x^7*(a+b*x^3)^(3/2)),x,6,-1/4*b*(5*A*b-4*a*B)*arctanh(sqrt(a+b*x^3)/sqrt(a))/a^(7/2)+1/4*b*(5*A*b-4*a*B)/(a^3*sqrt(a+b*x^3))-1/6*A/(a*x^6*sqrt(a+b*x^3))+1/12*(5*A*b-4*a*B)/(a^2*x^3*sqrt(a+b*x^3))],
[x^6*(A+B*x^3)/(a+b*x^3)^(3/2),x,4,-2/33*(11*A*b-14*a*B)*x^4/(b^2*sqrt(a+b*x^3))+2/11*B*x^7/(b*sqrt(a+b*x^3))+16/165*(11*A*b-14*a*B)*x*sqrt(a+b*x^3)/b^3-32/165*a*(11*A*b-14*a*B)*(a^(1/3)+b^(1/3)*x)*EllipticF((b^(1/3)*x+a^(1/3)*(1-sqrt(3)))/(b^(1/3)*x+a^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2+sqrt(3))*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2)/(3^(1/4)*b^(10/3)*sqrt(a+b*x^3)*sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2))],
[x^3*(A+B*x^3)/(a+b*x^3)^(3/2),x,3,-2/15*(5*A*b-8*a*B)*x/(b^2*sqrt(a+b*x^3))+2/5*B*x^4/(b*sqrt(a+b*x^3))+4/15*(5*A*b-8*a*B)*(a^(1/3)+b^(1/3)*x)*EllipticF((b^(1/3)*x+a^(1/3)*(1-sqrt(3)))/(b^(1/3)*x+a^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2+sqrt(3))*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2)/(3^(1/4)*b^(7/3)*sqrt(a+b*x^3)*sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2))],
[(A+B*x^3)/(a+b*x^3)^(3/2),x,2,2/3*(A*b-a*B)*x/(a*b*sqrt(a+b*x^3))+2/3*(A*b+2*a*B)*(a^(1/3)+b^(1/3)*x)*EllipticF((b^(1/3)*x+a^(1/3)*(1-sqrt(3)))/(b^(1/3)*x+a^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2+sqrt(3))*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2)/(3^(1/4)*a*b^(4/3)*sqrt(a+b*x^3)*sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2))],
[(A+B*x^3)/(x^3*(a+b*x^3)^(3/2)),x,3,-1/2*A/(a*x^2*sqrt(a+b*x^3))-1/6*(7*A*b-4*a*B)*x/(a^2*sqrt(a+b*x^3))-1/6*(7*A*b-4*a*B)*(a^(1/3)+b^(1/3)*x)*EllipticF((b^(1/3)*x+a^(1/3)*(1-sqrt(3)))/(b^(1/3)*x+a^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2+sqrt(3))*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2)/(3^(1/4)*a^2*b^(1/3)*sqrt(a+b*x^3)*sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2))],
[(A+B*x^3)/(x^6*(a+b*x^3)^(3/2)),x,4,-1/5*A/(a*x^5*sqrt(a+b*x^3))+1/15*(-13*A*b+10*a*B)/(a^2*x^2*sqrt(a+b*x^3))+7/60*(13*A*b-10*a*B)*sqrt(a+b*x^3)/(a^3*x^2)+7/60*b^(2/3)*(13*A*b-10*a*B)*(a^(1/3)+b^(1/3)*x)*EllipticF((b^(1/3)*x+a^(1/3)*(1-sqrt(3)))/(b^(1/3)*x+a^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2+sqrt(3))*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2)/(3^(1/4)*a^3*sqrt(a+b*x^3)*sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2))],
[x^4*(A+B*x^3)/(a+b*x^3)^(3/2),x,5,-2/21*(7*A*b-10*a*B)*x^2/(b^2*sqrt(a+b*x^3))+2/7*B*x^5/(b*sqrt(a+b*x^3))+8/21*(7*A*b-10*a*B)*sqrt(a+b*x^3)/(b^(8/3)*(b^(1/3)*x+a^(1/3)*(1+sqrt(3))))+8/21*a^(1/3)*(7*A*b-10*a*B)*(a^(1/3)+b^(1/3)*x)*EllipticF((b^(1/3)*x+a^(1/3)*(1-sqrt(3)))/(b^(1/3)*x+a^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2)/(3^(1/4)*b^(8/3)*sqrt(a+b*x^3)*sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2))-4/7*a^(1/3)*(7*A*b-10*a*B)*(a^(1/3)+b^(1/3)*x)*EllipticE((b^(1/3)*x+a^(1/3)*(1-sqrt(3)))/(b^(1/3)*x+a^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2)/(3^(3/4)*b^(8/3)*sqrt(a+b*x^3)*sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2))],
[x*(A+B*x^3)/(a+b*x^3)^(3/2),x,4,2/3*(A*b-a*B)*x^2/(a*b*sqrt(a+b*x^3))-2/3*(A*b-4*a*B)*sqrt(a+b*x^3)/(a*b^(5/3)*(b^(1/3)*x+a^(1/3)*(1+sqrt(3))))-2/3*(A*b-4*a*B)*(a^(1/3)+b^(1/3)*x)*EllipticF((b^(1/3)*x+a^(1/3)*(1-sqrt(3)))/(b^(1/3)*x+a^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2)/(3^(1/4)*a^(2/3)*b^(5/3)*sqrt(a+b*x^3)*sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2))+(A*b-4*a*B)*(a^(1/3)+b^(1/3)*x)*EllipticE((b^(1/3)*x+a^(1/3)*(1-sqrt(3)))/(b^(1/3)*x+a^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2)/(3^(3/4)*a^(2/3)*b^(5/3)*sqrt(a+b*x^3)*sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2))],
[(A+B*x^3)/(x^2*(a+b*x^3)^(3/2)),x,5,-A/(a*x*sqrt(a+b*x^3))-1/3*(5*A*b-2*a*B)*x^2/(a^2*sqrt(a+b*x^3))+1/3*(5*A*b-2*a*B)*sqrt(a+b*x^3)/(a^2*b^(2/3)*(b^(1/3)*x+a^(1/3)*(1+sqrt(3))))+1/3*(5*A*b-2*a*B)*(a^(1/3)+b^(1/3)*x)*EllipticF((b^(1/3)*x+a^(1/3)*(1-sqrt(3)))/(b^(1/3)*x+a^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2)/(3^(1/4)*a^(5/3)*b^(2/3)*sqrt(a+b*x^3)*sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2))-1/2*(5*A*b-2*a*B)*(a^(1/3)+b^(1/3)*x)*EllipticE((b^(1/3)*x+a^(1/3)*(1-sqrt(3)))/(b^(1/3)*x+a^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2)/(3^(3/4)*a^(5/3)*b^(2/3)*sqrt(a+b*x^3)*sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2))],
[(A+B*x^3)/(x^5*(a+b*x^3)^(3/2)),x,6,-1/4*A/(a*x^4*sqrt(a+b*x^3))+1/12*(-11*A*b+8*a*B)/(a^2*x*sqrt(a+b*x^3))+5/24*(11*A*b-8*a*B)*sqrt(a+b*x^3)/(a^3*x)-5/24*b^(1/3)*(11*A*b-8*a*B)*sqrt(a+b*x^3)/(a^3*(b^(1/3)*x+a^(1/3)*(1+sqrt(3))))-5/12*b^(1/3)*(11*A*b-8*a*B)*(a^(1/3)+b^(1/3)*x)*EllipticF((b^(1/3)*x+a^(1/3)*(1-sqrt(3)))/(b^(1/3)*x+a^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2)/(3^(1/4)*a^(8/3)*sqrt(2)*sqrt(a+b*x^3)*sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2))+5/16*b^(1/3)*(11*A*b-8*a*B)*(a^(1/3)+b^(1/3)*x)*EllipticE((b^(1/3)*x+a^(1/3)*(1-sqrt(3)))/(b^(1/3)*x+a^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2)/(3^(3/4)*a^(8/3)*sqrt(a+b*x^3)*sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2))],
[(A+B*x^3)/(x^8*(a+b*x^3)^(3/2)),x,7,-1/7*A/(a*x^7*sqrt(a+b*x^3))+1/21*(-17*A*b+14*a*B)/(a^2*x^4*sqrt(a+b*x^3))+11/168*(17*A*b-14*a*B)*sqrt(a+b*x^3)/(a^3*x^4)-55/336*b*(17*A*b-14*a*B)*sqrt(a+b*x^3)/(a^4*x)+55/336*b^(4/3)*(17*A*b-14*a*B)*sqrt(a+b*x^3)/(a^4*(b^(1/3)*x+a^(1/3)*(1+sqrt(3))))+55/168*b^(4/3)*(17*A*b-14*a*B)*(a^(1/3)+b^(1/3)*x)*EllipticF((b^(1/3)*x+a^(1/3)*(1-sqrt(3)))/(b^(1/3)*x+a^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2)/(3^(1/4)*a^(11/3)*sqrt(2)*sqrt(a+b*x^3)*sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2))-55/224*b^(4/3)*(17*A*b-14*a*B)*(a^(1/3)+b^(1/3)*x)*EllipticE((b^(1/3)*x+a^(1/3)*(1-sqrt(3)))/(b^(1/3)*x+a^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2)/(3^(3/4)*a^(11/3)*sqrt(a+b*x^3)*sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2))],
[x^8*(A+B*x^3)/(a+b*x^3)^(5/2),x,3,-2/9*a^2*(A*b-a*B)/(b^4*(a+b*x^3)^(3/2))+2/9*B*(a+b*x^3)^(3/2)/b^4+2/3*a*(2*A*b-3*a*B)/(b^4*sqrt(a+b*x^3))+2/3*(A*b-3*a*B)*sqrt(a+b*x^3)/b^4],
[x^5*(A+B*x^3)/(a+b*x^3)^(5/2),x,3,2/9*a*(A*b-a*B)/(b^3*(a+b*x^3)^(3/2))-2/3*(A*b-2*a*B)/(b^3*sqrt(a+b*x^3))+2/3*B*sqrt(a+b*x^3)/b^3],
[x^2*(A+B*x^3)/(a+b*x^3)^(5/2),x,3,-2/9*(A*b-a*B)/(b^2*(a+b*x^3)^(3/2))-2/3*B/(b^2*sqrt(a+b*x^3))],
[(A+B*x^3)/(x*(a+b*x^3)^(5/2)),x,5,2/9*(A*b-a*B)/(a*b*(a+b*x^3)^(3/2))-2/3*A*arctanh(sqrt(a+b*x^3)/sqrt(a))/a^(5/2)+2/3*A/(a^2*sqrt(a+b*x^3))],
[(A+B*x^3)/(x^4*(a+b*x^3)^(5/2)),x,6,1/9*(-5*A*b+2*a*B)/(a^2*(a+b*x^3)^(3/2))-1/3*A/(a*x^3*(a+b*x^3)^(3/2))+1/3*(5*A*b-2*a*B)*arctanh(sqrt(a+b*x^3)/sqrt(a))/a^(7/2)+1/3*(-5*A*b+2*a*B)/(a^3*sqrt(a+b*x^3))],
[x^6*(A+B*x^3)/(a+b*x^3)^(5/2),x,4,-2/45*(5*A*b-14*a*B)*x^4/(b^2*(a+b*x^3)^(3/2))+2/5*B*x^7/(b*(a+b*x^3)^(3/2))-16/135*(5*A*b-14*a*B)*x/(b^3*sqrt(a+b*x^3))+32/135*(5*A*b-14*a*B)*(a^(1/3)+b^(1/3)*x)*EllipticF((b^(1/3)*x+a^(1/3)*(1-sqrt(3)))/(b^(1/3)*x+a^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2+sqrt(3))*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2)/(3^(1/4)*b^(10/3)*sqrt(a+b*x^3)*sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2))],
[x^3*(A+B*x^3)/(a+b*x^3)^(5/2),x,3,2/9*(A*b-a*B)*x^4/(a*b*(a+b*x^3)^(3/2))-2/27*(A*b+8*a*B)*x/(a*b^2*sqrt(a+b*x^3))+4/27*(A*b+8*a*B)*(a^(1/3)+b^(1/3)*x)*EllipticF((b^(1/3)*x+a^(1/3)*(1-sqrt(3)))/(b^(1/3)*x+a^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2+sqrt(3))*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2)/(3^(1/4)*a*b^(7/3)*sqrt(a+b*x^3)*sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2))],
[(A+B*x^3)/(a+b*x^3)^(5/2),x,3,2/9*(A*b-a*B)*x/(a*b*(a+b*x^3)^(3/2))+2/27*(7*A*b+2*a*B)*x/(a^2*b*sqrt(a+b*x^3))+2/27*(7*A*b+2*a*B)*(a^(1/3)+b^(1/3)*x)*EllipticF((b^(1/3)*x+a^(1/3)*(1-sqrt(3)))/(b^(1/3)*x+a^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2+sqrt(3))*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2)/(3^(1/4)*a^2*b^(4/3)*sqrt(a+b*x^3)*sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2))],
[(A+B*x^3)/(x^3*(a+b*x^3)^(5/2)),x,4,-1/2*A/(a*x^2*(a+b*x^3)^(3/2))-1/18*(13*A*b-4*a*B)*x/(a^2*(a+b*x^3)^(3/2))-7/54*(13*A*b-4*a*B)*x/(a^3*sqrt(a+b*x^3))-7/54*(13*A*b-4*a*B)*(a^(1/3)+b^(1/3)*x)*EllipticF((b^(1/3)*x+a^(1/3)*(1-sqrt(3)))/(b^(1/3)*x+a^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2+sqrt(3))*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2)/(3^(1/4)*a^3*b^(1/3)*sqrt(a+b*x^3)*sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2))],
[(A+B*x^3)/(x^6*(a+b*x^3)^(5/2)),x,5,-1/5*A/(a*x^5*(a+b*x^3)^(3/2))+1/45*(-19*A*b+10*a*B)/(a^2*x^2*(a+b*x^3)^(3/2))-13/135*(19*A*b-10*a*B)/(a^3*x^2*sqrt(a+b*x^3))+91/540*(19*A*b-10*a*B)*sqrt(a+b*x^3)/(a^4*x^2)+91/540*b^(2/3)*(19*A*b-10*a*B)*(a^(1/3)+b^(1/3)*x)*EllipticF((b^(1/3)*x+a^(1/3)*(1-sqrt(3)))/(b^(1/3)*x+a^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2+sqrt(3))*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2)/(3^(1/4)*a^4*sqrt(a+b*x^3)*sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2))],
[x^7*(A+B*x^3)/(a+b*x^3)^(5/2),x,6,-2/63*(7*A*b-16*a*B)*x^5/(b^2*(a+b*x^3)^(3/2))+2/7*B*x^8/(b*(a+b*x^3)^(3/2))-20/189*(7*A*b-16*a*B)*x^2/(b^3*sqrt(a+b*x^3))+80/189*(7*A*b-16*a*B)*sqrt(a+b*x^3)/(b^(11/3)*(b^(1/3)*x+a^(1/3)*(1+sqrt(3))))+80/189*a^(1/3)*(7*A*b-16*a*B)*(a^(1/3)+b^(1/3)*x)*EllipticF((b^(1/3)*x+a^(1/3)*(1-sqrt(3)))/(b^(1/3)*x+a^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2)/(3^(1/4)*b^(11/3)*sqrt(a+b*x^3)*sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2))-40/63*a^(1/3)*(7*A*b-16*a*B)*(a^(1/3)+b^(1/3)*x)*EllipticE((b^(1/3)*x+a^(1/3)*(1-sqrt(3)))/(b^(1/3)*x+a^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2)/(3^(3/4)*b^(11/3)*sqrt(a+b*x^3)*sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2))],
[x^4*(A+B*x^3)/(a+b*x^3)^(5/2),x,5,2/9*(A*b-a*B)*x^5/(a*b*(a+b*x^3)^(3/2))+2/27*(A*b-10*a*B)*x^2/(a*b^2*sqrt(a+b*x^3))-8/27*(A*b-10*a*B)*sqrt(a+b*x^3)/(a*b^(8/3)*(b^(1/3)*x+a^(1/3)*(1+sqrt(3))))-8/27*(A*b-10*a*B)*(a^(1/3)+b^(1/3)*x)*EllipticF((b^(1/3)*x+a^(1/3)*(1-sqrt(3)))/(b^(1/3)*x+a^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2)/(3^(1/4)*a^(2/3)*b^(8/3)*sqrt(a+b*x^3)*sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2))+4/9*(A*b-10*a*B)*(a^(1/3)+b^(1/3)*x)*EllipticE((b^(1/3)*x+a^(1/3)*(1-sqrt(3)))/(b^(1/3)*x+a^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2)/(3^(3/4)*a^(2/3)*b^(8/3)*sqrt(a+b*x^3)*sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2))],
[x*(A+B*x^3)/(a+b*x^3)^(5/2),x,5,2/9*(A*b-a*B)*x^2/(a*b*(a+b*x^3)^(3/2))+2/27*(5*A*b+4*a*B)*x^2/(a^2*b*sqrt(a+b*x^3))-2/27*(5*A*b+4*a*B)*sqrt(a+b*x^3)/(a^2*b^(5/3)*(b^(1/3)*x+a^(1/3)*(1+sqrt(3))))-2/27*(5*A*b+4*a*B)*(a^(1/3)+b^(1/3)*x)*EllipticF((b^(1/3)*x+a^(1/3)*(1-sqrt(3)))/(b^(1/3)*x+a^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2)/(3^(1/4)*a^(5/3)*b^(5/3)*sqrt(a+b*x^3)*sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2))+1/9*(5*A*b+4*a*B)*(a^(1/3)+b^(1/3)*x)*EllipticE((b^(1/3)*x+a^(1/3)*(1-sqrt(3)))/(b^(1/3)*x+a^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2)/(3^(3/4)*a^(5/3)*b^(5/3)*sqrt(a+b*x^3)*sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2))],
[(A+B*x^3)/(x^2*(a+b*x^3)^(5/2)),x,6,-A/(a*x*(a+b*x^3)^(3/2))-1/9*(11*A*b-2*a*B)*x^2/(a^2*(a+b*x^3)^(3/2))-5/27*(11*A*b-2*a*B)*x^2/(a^3*sqrt(a+b*x^3))+5/27*(11*A*b-2*a*B)*sqrt(a+b*x^3)/(a^3*b^(2/3)*(b^(1/3)*x+a^(1/3)*(1+sqrt(3))))+5/27*(11*A*b-2*a*B)*(a^(1/3)+b^(1/3)*x)*EllipticF((b^(1/3)*x+a^(1/3)*(1-sqrt(3)))/(b^(1/3)*x+a^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2)/(3^(1/4)*a^(8/3)*b^(2/3)*sqrt(a+b*x^3)*sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2))-5/18*(11*A*b-2*a*B)*(a^(1/3)+b^(1/3)*x)*EllipticE((b^(1/3)*x+a^(1/3)*(1-sqrt(3)))/(b^(1/3)*x+a^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2)/(3^(3/4)*a^(8/3)*b^(2/3)*sqrt(a+b*x^3)*sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2))],
[(A+B*x^3)/(x^5*(a+b*x^3)^(5/2)),x,7,-1/4*A/(a*x^4*(a+b*x^3)^(3/2))+1/36*(-17*A*b+8*a*B)/(a^2*x*(a+b*x^3)^(3/2))-11/108*(17*A*b-8*a*B)/(a^3*x*sqrt(a+b*x^3))+55/216*(17*A*b-8*a*B)*sqrt(a+b*x^3)/(a^4*x)-55/216*b^(1/3)*(17*A*b-8*a*B)*sqrt(a+b*x^3)/(a^4*(b^(1/3)*x+a^(1/3)*(1+sqrt(3))))-55/108*b^(1/3)*(17*A*b-8*a*B)*(a^(1/3)+b^(1/3)*x)*EllipticF((b^(1/3)*x+a^(1/3)*(1-sqrt(3)))/(b^(1/3)*x+a^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2)/(3^(1/4)*a^(11/3)*sqrt(2)*sqrt(a+b*x^3)*sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2))+55/144*b^(1/3)*(17*A*b-8*a*B)*(a^(1/3)+b^(1/3)*x)*EllipticE((b^(1/3)*x+a^(1/3)*(1-sqrt(3)))/(b^(1/3)*x+a^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2)/(3^(3/4)*a^(11/3)*sqrt(a+b*x^3)*sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2))],

# Integrands of the form x^m (c+d x^3)^(q/2) / (a+b x^3)

# q>0 when 4 b c-a d=0
[x^8*sqrt(c+d*x^3)/(4*c+d*x^3),x,6,-10/9*c*(c+d*x^3)^(3/2)/d^3+2/15*(c+d*x^3)^(5/2)/d^3-32*c^(5/2)*arctan(sqrt(c+d*x^3)/(sqrt(3)*sqrt(c)))/(d^3*sqrt(3))+32/3*c^2*sqrt(c+d*x^3)/d^3],
[x^5*sqrt(c+d*x^3)/(4*c+d*x^3),x,5,2/9*(c+d*x^3)^(3/2)/d^2+8*c^(3/2)*arctan(sqrt(c+d*x^3)/(sqrt(3)*sqrt(c)))/(d^2*sqrt(3))-8/3*c*sqrt(c+d*x^3)/d^2],
[x^2*sqrt(c+d*x^3)/(4*c+d*x^3),x,4,-2*arctan(sqrt(c+d*x^3)/(sqrt(3)*sqrt(c)))*sqrt(c)/(d*sqrt(3))+2/3*sqrt(c+d*x^3)/d],
[sqrt(c+d*x^3)/(x*(4*c+d*x^3)),x,6,-1/6*arctanh(sqrt(c+d*x^3)/sqrt(c))/sqrt(c)+1/2*arctan(sqrt(c+d*x^3)/(sqrt(3)*sqrt(c)))/(sqrt(3)*sqrt(c))],
[sqrt(c+d*x^3)/(x^4*(4*c+d*x^3)),x,7,-1/24*d*arctanh(sqrt(c+d*x^3)/sqrt(c))/c^(3/2)-1/8*d*arctan(sqrt(c+d*x^3)/(sqrt(3)*sqrt(c)))/(c^(3/2)*sqrt(3))-1/12*sqrt(c+d*x^3)/(c*x^3)],
[x^4*sqrt(c+d*x^3)/(4*c+d*x^3),x,7,-2*2^(1/3)*c^(7/6)*arctanh(c^(1/6)*(c^(1/3)-2^(1/3)*d^(1/3)*x)/sqrt(c+d*x^3))/d^(5/3)+2/3*2^(1/3)*c^(7/6)*arctanh(sqrt(c+d*x^3)/sqrt(c))/d^(5/3)-2*2^(1/3)*c^(7/6)*arctan(c^(1/6)*(c^(1/3)+2^(1/3)*d^(1/3)*x)*sqrt(3)/sqrt(c+d*x^3))/(d^(5/3)*sqrt(3))+2*2^(1/3)*c^(7/6)*arctan(sqrt(c+d*x^3)/(sqrt(3)*sqrt(c)))/(d^(5/3)*sqrt(3))+2/7*x^2*sqrt(c+d*x^3)/d-50/7*c*sqrt(c+d*x^3)/(d^(5/3)*(d^(1/3)*x+c^(1/3)*(1+sqrt(3))))-50/7*c^(4/3)*(c^(1/3)+d^(1/3)*x)*EllipticF((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2)*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(3^(1/4)*d^(5/3)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))+25/7*3^(1/4)*c^(4/3)*(c^(1/3)+d^(1/3)*x)*EllipticE((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(d^(5/3)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))],
[x*sqrt(c+d*x^3)/(4*c+d*x^3),x,5,c^(1/6)*arctanh(c^(1/6)*(c^(1/3)-2^(1/3)*d^(1/3)*x)/sqrt(c+d*x^3))/(2^(2/3)*d^(2/3))-1/3*c^(1/6)*arctanh(sqrt(c+d*x^3)/sqrt(c))/(2^(2/3)*d^(2/3))+c^(1/6)*arctan(c^(1/6)*(c^(1/3)+2^(1/3)*d^(1/3)*x)*sqrt(3)/sqrt(c+d*x^3))/(2^(2/3)*d^(2/3)*sqrt(3))-c^(1/6)*arctan(sqrt(c+d*x^3)/(sqrt(3)*sqrt(c)))/(2^(2/3)*d^(2/3)*sqrt(3))+2*sqrt(c+d*x^3)/(d^(2/3)*(d^(1/3)*x+c^(1/3)*(1+sqrt(3))))+2*c^(1/3)*(c^(1/3)+d^(1/3)*x)*EllipticF((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2)*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(3^(1/4)*d^(2/3)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))-3^(1/4)*c^(1/3)*(c^(1/3)+d^(1/3)*x)*EllipticE((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(d^(2/3)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))],
[sqrt(c+d*x^3)/(x^2*(4*c+d*x^3)),x,7,-1/4*d^(1/3)*arctanh(c^(1/6)*(c^(1/3)-2^(1/3)*d^(1/3)*x)/sqrt(c+d*x^3))/(2^(2/3)*c^(5/6))+1/12*d^(1/3)*arctanh(sqrt(c+d*x^3)/sqrt(c))/(2^(2/3)*c^(5/6))-1/4*d^(1/3)*arctan(c^(1/6)*(c^(1/3)+2^(1/3)*d^(1/3)*x)*sqrt(3)/sqrt(c+d*x^3))/(2^(2/3)*c^(5/6)*sqrt(3))+1/4*d^(1/3)*arctan(sqrt(c+d*x^3)/(sqrt(3)*sqrt(c)))/(2^(2/3)*c^(5/6)*sqrt(3))-1/4*sqrt(c+d*x^3)/(c*x)+1/4*d^(1/3)*sqrt(c+d*x^3)/(c*(d^(1/3)*x+c^(1/3)*(1+sqrt(3))))+1/2*d^(1/3)*(c^(1/3)+d^(1/3)*x)*EllipticF((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(3^(1/4)*c^(2/3)*sqrt(2)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))-1/8*3^(1/4)*d^(1/3)*(c^(1/3)+d^(1/3)*x)*EllipticE((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(c^(2/3)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))],
[x^3*sqrt(c+d*x^3)/(4*c+d*x^3),x,2,1/16*x^4*AppellF1(4/3,1,-1/2,7/3,-1/4*d*x^3/c,-d*x^3/c)*sqrt(c+d*x^3)/(c*sqrt(1+d*x^3/c))],
[sqrt(c+d*x^3)/(4*c+d*x^3),x,2,1/4*x*AppellF1(1/3,1,-1/2,4/3,-1/4*d*x^3/c,-d*x^3/c)*sqrt(c+d*x^3)/(c*sqrt(1+d*x^3/c))],
[sqrt(c+d*x^3)/(x^3*(4*c+d*x^3)),x,2,-1/8*AppellF1(-2/3,1,-1/2,1/3,-1/4*d*x^3/c,-d*x^3/c)*sqrt(c+d*x^3)/(c*x^2*sqrt(1+d*x^3/c))],

# q<0 when 4 b c-a d=0
[x^8/((4*c+d*x^3)*sqrt(c+d*x^3)),x,5,2/9*(c+d*x^3)^(3/2)/d^3+32/3*c^(3/2)*arctan(sqrt(c+d*x^3)/(sqrt(3)*sqrt(c)))/(d^3*sqrt(3))-10/3*c*sqrt(c+d*x^3)/d^3],
[x^5/((4*c+d*x^3)*sqrt(c+d*x^3)),x,4,-8/3*arctan(sqrt(c+d*x^3)/(sqrt(3)*sqrt(c)))*sqrt(c)/(d^2*sqrt(3))+2/3*sqrt(c+d*x^3)/d^2],
[x^2/((4*c+d*x^3)*sqrt(c+d*x^3)),x,3,2/3*arctan(sqrt(c+d*x^3)/(sqrt(3)*sqrt(c)))/(d*sqrt(3)*sqrt(c))],
[1/(x*(4*c+d*x^3)*sqrt(c+d*x^3)),x,6,-1/6*arctanh(sqrt(c+d*x^3)/sqrt(c))/c^(3/2)-1/6*arctan(sqrt(c+d*x^3)/(sqrt(3)*sqrt(c)))/(c^(3/2)*sqrt(3))],
[1/(x^4*(4*c+d*x^3)*sqrt(c+d*x^3)),x,7,1/8*d*arctanh(sqrt(c+d*x^3)/sqrt(c))/c^(5/2)+1/24*d*arctan(sqrt(c+d*x^3)/(sqrt(3)*sqrt(c)))/(c^(5/2)*sqrt(3))-1/12*sqrt(c+d*x^3)/(c^2*x^3)],
[x^4/((4*c+d*x^3)*sqrt(c+d*x^3)),x,5,2/3*2^(1/3)*c^(1/6)*arctanh(c^(1/6)*(c^(1/3)-2^(1/3)*d^(1/3)*x)/sqrt(c+d*x^3))/d^(5/3)-2/9*2^(1/3)*c^(1/6)*arctanh(sqrt(c+d*x^3)/sqrt(c))/d^(5/3)+2/3*2^(1/3)*c^(1/6)*arctan(c^(1/6)*(c^(1/3)+2^(1/3)*d^(1/3)*x)*sqrt(3)/sqrt(c+d*x^3))/(d^(5/3)*sqrt(3))-2/3*2^(1/3)*c^(1/6)*arctan(sqrt(c+d*x^3)/(sqrt(3)*sqrt(c)))/(d^(5/3)*sqrt(3))+2*sqrt(c+d*x^3)/(d^(5/3)*(d^(1/3)*x+c^(1/3)*(1+sqrt(3))))+2*c^(1/3)*(c^(1/3)+d^(1/3)*x)*EllipticF((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2)*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(3^(1/4)*d^(5/3)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))-3^(1/4)*c^(1/3)*(c^(1/3)+d^(1/3)*x)*EllipticE((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(d^(5/3)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))],
[x/((4*c+d*x^3)*sqrt(c+d*x^3)),x,1,-1/3*arctanh(c^(1/6)*(c^(1/3)-2^(1/3)*d^(1/3)*x)/sqrt(c+d*x^3))/(2^(2/3)*c^(5/6)*d^(2/3))+1/9*arctanh(sqrt(c+d*x^3)/sqrt(c))/(2^(2/3)*c^(5/6)*d^(2/3))-1/3*arctan(c^(1/6)*(c^(1/3)+2^(1/3)*d^(1/3)*x)*sqrt(3)/sqrt(c+d*x^3))/(2^(2/3)*c^(5/6)*d^(2/3)*sqrt(3))+1/3*arctan(sqrt(c+d*x^3)/(sqrt(3)*sqrt(c)))/(2^(2/3)*c^(5/6)*d^(2/3)*sqrt(3))],
[1/(x^2*(4*c+d*x^3)*sqrt(c+d*x^3)),x,7,1/12*d^(1/3)*arctanh(c^(1/6)*(c^(1/3)-2^(1/3)*d^(1/3)*x)/sqrt(c+d*x^3))/(2^(2/3)*c^(11/6))-1/36*d^(1/3)*arctanh(sqrt(c+d*x^3)/sqrt(c))/(2^(2/3)*c^(11/6))+1/12*d^(1/3)*arctan(c^(1/6)*(c^(1/3)+2^(1/3)*d^(1/3)*x)*sqrt(3)/sqrt(c+d*x^3))/(2^(2/3)*c^(11/6)*sqrt(3))-1/12*d^(1/3)*arctan(sqrt(c+d*x^3)/(sqrt(3)*sqrt(c)))/(2^(2/3)*c^(11/6)*sqrt(3))-1/4*sqrt(c+d*x^3)/(c^2*x)+1/4*d^(1/3)*sqrt(c+d*x^3)/(c^2*(d^(1/3)*x+c^(1/3)*(1+sqrt(3))))+1/2*d^(1/3)*(c^(1/3)+d^(1/3)*x)*EllipticF((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(3^(1/4)*c^(5/3)*sqrt(2)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))-1/8*3^(1/4)*d^(1/3)*(c^(1/3)+d^(1/3)*x)*EllipticE((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(c^(5/3)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))],
[x^3/((4*c+d*x^3)*sqrt(c+d*x^3)),x,2,1/16*x^4*AppellF1(4/3,1,1/2,7/3,-1/4*d*x^3/c,-d*x^3/c)*sqrt(1+d*x^3/c)/(c*sqrt(c+d*x^3))],
[1/((4*c+d*x^3)*sqrt(c+d*x^3)),x,2,1/4*x*AppellF1(1/3,1,1/2,4/3,-1/4*d*x^3/c,-d*x^3/c)*sqrt(1+d*x^3/c)/(c*sqrt(c+d*x^3))],
[1/(x^3*(4*c+d*x^3)*sqrt(c+d*x^3)),x,2,-1/8*AppellF1(-2/3,1,1/2,1/3,-1/4*d*x^3/c,-d*x^3/c)*sqrt(1+d*x^3/c)/(c*x^2*sqrt(c+d*x^3))],
[x/((4-x^3)*sqrt(1-x^3)),x,1,-1/3*arctanh((1+2^(1/3)*x)/sqrt(1-x^3))/2^(2/3)+1/9*arctanh(sqrt(1-x^3))/2^(2/3)-1/3*arctan((1-2^(1/3)*x)*sqrt(3)/sqrt(1-x^3))/(2^(2/3)*sqrt(3))+1/3*arctan(sqrt(1-x^3)/sqrt(3))/(2^(2/3)*sqrt(3))],

# q>0 when 8 b c+a d=0
[x^11*sqrt(c+d*x^3)/(8*c-d*x^3),x,6,-38/3*c^2*(c+d*x^3)^(3/2)/d^4-4/5*c*(c+d*x^3)^(5/2)/d^4-2/21*(c+d*x^3)^(7/2)/d^4+1024*c^(7/2)*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))/d^4-1024/3*c^3*sqrt(c+d*x^3)/d^4],
[x^8*sqrt(c+d*x^3)/(8*c-d*x^3),x,6,-14/9*c*(c+d*x^3)^(3/2)/d^3-2/15*(c+d*x^3)^(5/2)/d^3+128*c^(5/2)*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))/d^3-128/3*c^2*sqrt(c+d*x^3)/d^3],
[x^5*sqrt(c+d*x^3)/(8*c-d*x^3),x,5,-2/9*(c+d*x^3)^(3/2)/d^2+16*c^(3/2)*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))/d^2-16/3*c*sqrt(c+d*x^3)/d^2],
[x^2*sqrt(c+d*x^3)/(8*c-d*x^3),x,4,2*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))*sqrt(c)/d-2/3*sqrt(c+d*x^3)/d],
[sqrt(c+d*x^3)/(x*(8*c-d*x^3)),x,6,1/4*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))/sqrt(c)-1/12*arctanh(sqrt(c+d*x^3)/sqrt(c))/sqrt(c)],
[sqrt(c+d*x^3)/(x^4*(8*c-d*x^3)),x,7,1/32*d*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))/c^(3/2)-5/96*d*arctanh(sqrt(c+d*x^3)/sqrt(c))/c^(3/2)-1/24*sqrt(c+d*x^3)/(c*x^3)],
[sqrt(c+d*x^3)/(x^7*(8*c-d*x^3)),x,8,1/256*d^2*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))/c^(5/2)+1/256*d^2*arctanh(sqrt(c+d*x^3)/sqrt(c))/c^(5/2)-1/48*sqrt(c+d*x^3)/(c*x^6)-1/64*d*sqrt(c+d*x^3)/(c^2*x^3)],
[x^7*sqrt(c+d*x^3)/(8*c-d*x^3),x,15,32*c^(13/6)*arctanh(1/3*(c^(1/3)+d^(1/3)*x)^2/(c^(1/6)*sqrt(c+d*x^3)))/d^(8/3)-32*c^(13/6)*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))/d^(8/3)-32*c^(13/6)*arctan(c^(1/6)*(c^(1/3)+d^(1/3)*x)*sqrt(3)/sqrt(c+d*x^3))*sqrt(3)/d^(8/3)-214/91*c*x^2*sqrt(c+d*x^3)/d^2-2/13*x^5*sqrt(c+d*x^3)/d-12248/91*c^2*sqrt(c+d*x^3)/(d^(8/3)*(d^(1/3)*x+c^(1/3)*(1+sqrt(3))))-12248/91*c^(7/3)*(c^(1/3)+d^(1/3)*x)*EllipticF((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2)*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(3^(1/4)*d^(8/3)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))+6124/91*3^(1/4)*c^(7/3)*(c^(1/3)+d^(1/3)*x)*EllipticE((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(d^(8/3)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))],
[x^4*sqrt(c+d*x^3)/(8*c-d*x^3),x,14,4*c^(7/6)*arctanh(1/3*(c^(1/3)+d^(1/3)*x)^2/(c^(1/6)*sqrt(c+d*x^3)))/d^(5/3)-4*c^(7/6)*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))/d^(5/3)-4*c^(7/6)*arctan(c^(1/6)*(c^(1/3)+d^(1/3)*x)*sqrt(3)/sqrt(c+d*x^3))*sqrt(3)/d^(5/3)-2/7*x^2*sqrt(c+d*x^3)/d-118/7*c*sqrt(c+d*x^3)/(d^(5/3)*(d^(1/3)*x+c^(1/3)*(1+sqrt(3))))-118/7*c^(4/3)*(c^(1/3)+d^(1/3)*x)*EllipticF((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2)*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(3^(1/4)*d^(5/3)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))+59/7*3^(1/4)*c^(4/3)*(c^(1/3)+d^(1/3)*x)*EllipticE((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(d^(5/3)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))],
[x*sqrt(c+d*x^3)/(8*c-d*x^3),x,12,1/2*c^(1/6)*arctanh(1/3*(c^(1/3)+d^(1/3)*x)^2/(c^(1/6)*sqrt(c+d*x^3)))/d^(2/3)-1/2*c^(1/6)*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))/d^(2/3)-1/2*c^(1/6)*arctan(c^(1/6)*(c^(1/3)+d^(1/3)*x)*sqrt(3)/sqrt(c+d*x^3))*sqrt(3)/d^(2/3)-2*sqrt(c+d*x^3)/(d^(2/3)*(d^(1/3)*x+c^(1/3)*(1+sqrt(3))))-2*c^(1/3)*(c^(1/3)+d^(1/3)*x)*EllipticF((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2)*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(3^(1/4)*d^(2/3)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))+3^(1/4)*c^(1/3)*(c^(1/3)+d^(1/3)*x)*EllipticE((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(d^(2/3)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))],
[sqrt(c+d*x^3)/(x^2*(8*c-d*x^3)),x,14,1/16*d^(1/3)*arctanh(1/3*(c^(1/3)+d^(1/3)*x)^2/(c^(1/6)*sqrt(c+d*x^3)))/c^(5/6)-1/16*d^(1/3)*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))/c^(5/6)-1/16*d^(1/3)*arctan(c^(1/6)*(c^(1/3)+d^(1/3)*x)*sqrt(3)/sqrt(c+d*x^3))*sqrt(3)/c^(5/6)-1/8*sqrt(c+d*x^3)/(c*x)+1/8*d^(1/3)*sqrt(c+d*x^3)/(c*(d^(1/3)*x+c^(1/3)*(1+sqrt(3))))+1/4*d^(1/3)*(c^(1/3)+d^(1/3)*x)*EllipticF((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(3^(1/4)*c^(2/3)*sqrt(2)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))-1/16*3^(1/4)*d^(1/3)*(c^(1/3)+d^(1/3)*x)*EllipticE((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(c^(2/3)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))],
[sqrt(c+d*x^3)/(x^5*(8*c-d*x^3)),x,15,1/128*d^(4/3)*arctanh(1/3*(c^(1/3)+d^(1/3)*x)^2/(c^(1/6)*sqrt(c+d*x^3)))/c^(11/6)-1/128*d^(4/3)*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))/c^(11/6)-1/128*d^(4/3)*arctan(c^(1/6)*(c^(1/3)+d^(1/3)*x)*sqrt(3)/sqrt(c+d*x^3))*sqrt(3)/c^(11/6)-1/32*sqrt(c+d*x^3)/(c*x^4)-1/16*d*sqrt(c+d*x^3)/(c^2*x)+1/16*d^(4/3)*sqrt(c+d*x^3)/(c^2*(d^(1/3)*x+c^(1/3)*(1+sqrt(3))))+1/8*d^(4/3)*(c^(1/3)+d^(1/3)*x)*EllipticF((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(3^(1/4)*c^(5/3)*sqrt(2)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))-1/32*3^(1/4)*d^(4/3)*(c^(1/3)+d^(1/3)*x)*EllipticE((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(c^(5/3)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))],
[sqrt(c+d*x^3)/(x^8*(8*c-d*x^3)),x,16,1/1024*d^(7/3)*arctanh(1/3*(c^(1/3)+d^(1/3)*x)^2/(c^(1/6)*sqrt(c+d*x^3)))/c^(17/6)-1/1024*d^(7/3)*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))/c^(17/6)-1/1024*d^(7/3)*arctan(c^(1/6)*(c^(1/3)+d^(1/3)*x)*sqrt(3)/sqrt(c+d*x^3))*sqrt(3)/c^(17/6)-1/56*sqrt(c+d*x^3)/(c*x^7)-19/1792*d*sqrt(c+d*x^3)/(c^2*x^4)+1/112*d^2*sqrt(c+d*x^3)/(c^3*x)-1/112*d^(7/3)*sqrt(c+d*x^3)/(c^3*(d^(1/3)*x+c^(1/3)*(1+sqrt(3))))-1/56*d^(7/3)*(c^(1/3)+d^(1/3)*x)*EllipticF((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(3^(1/4)*c^(8/3)*sqrt(2)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))+1/224*3^(1/4)*d^(7/3)*(c^(1/3)+d^(1/3)*x)*EllipticE((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(c^(8/3)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))],
[x^11*(c+d*x^3)^(3/2)/(8*c-d*x^3),x,7,-1024/9*c^3*(c+d*x^3)^(3/2)/d^4-38/5*c^2*(c+d*x^3)^(5/2)/d^4-4/7*c*(c+d*x^3)^(7/2)/d^4-2/27*(c+d*x^3)^(9/2)/d^4+9216*c^(9/2)*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))/d^4-3072*c^4*sqrt(c+d*x^3)/d^4],
[x^8*(c+d*x^3)^(3/2)/(8*c-d*x^3),x,7,-128/9*c^2*(c+d*x^3)^(3/2)/d^3-14/15*c*(c+d*x^3)^(5/2)/d^3-2/21*(c+d*x^3)^(7/2)/d^3+1152*c^(7/2)*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))/d^3-384*c^3*sqrt(c+d*x^3)/d^3],
[x^5*(c+d*x^3)^(3/2)/(8*c-d*x^3),x,6,-16/9*c*(c+d*x^3)^(3/2)/d^2-2/15*(c+d*x^3)^(5/2)/d^2+144*c^(5/2)*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))/d^2-48*c^2*sqrt(c+d*x^3)/d^2],
[x^2*(c+d*x^3)^(3/2)/(8*c-d*x^3),x,5,-2/9*(c+d*x^3)^(3/2)/d+18*c^(3/2)*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))/d-6*c*sqrt(c+d*x^3)/d],
[(c+d*x^3)^(3/2)/(x*(8*c-d*x^3)),x,7,9/4*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))*sqrt(c)-1/12*arctanh(sqrt(c+d*x^3)/sqrt(c))*sqrt(c)-2/3*sqrt(c+d*x^3)],
[(c+d*x^3)^(3/2)/(x^4*(8*c-d*x^3)),x,7,9/32*d*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))/sqrt(c)-13/96*d*arctanh(sqrt(c+d*x^3)/sqrt(c))/sqrt(c)-1/24*sqrt(c+d*x^3)/x^3],
[(c+d*x^3)^(3/2)/(x^7*(8*c-d*x^3)),x,8,9/256*d^2*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))/c^(3/2)-37/768*d^2*arctanh(sqrt(c+d*x^3)/sqrt(c))/c^(3/2)-1/48*sqrt(c+d*x^3)/x^6-11/192*d*sqrt(c+d*x^3)/(c*x^3)],
[x^7*(c+d*x^3)^(3/2)/(8*c-d*x^3),x,16,288*c^(19/6)*arctanh(1/3*(c^(1/3)+d^(1/3)*x)^2/(c^(1/6)*sqrt(c+d*x^3)))/d^(8/3)-288*c^(19/6)*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))/d^(8/3)-288*c^(19/6)*arctan(c^(1/6)*(c^(1/3)+d^(1/3)*x)*sqrt(3)/sqrt(c+d*x^3))*sqrt(3)/d^(8/3)-36534/1729*c^2*x^2*sqrt(c+d*x^3)/d^2-348/247*c*x^5*sqrt(c+d*x^3)/d-2/19*x^8*sqrt(c+d*x^3)-2094648/1729*c^3*sqrt(c+d*x^3)/(d^(8/3)*(d^(1/3)*x+c^(1/3)*(1+sqrt(3))))-698216/1729*3^(3/4)*c^(10/3)*(c^(1/3)+d^(1/3)*x)*EllipticF((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2)*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(d^(8/3)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))+1047324/1729*3^(1/4)*c^(10/3)*(c^(1/3)+d^(1/3)*x)*EllipticE((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(d^(8/3)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))],
[x^4*(c+d*x^3)^(3/2)/(8*c-d*x^3),x,15,36*c^(13/6)*arctanh(1/3*(c^(1/3)+d^(1/3)*x)^2/(c^(1/6)*sqrt(c+d*x^3)))/d^(5/3)-36*c^(13/6)*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))/d^(5/3)-36*c^(13/6)*arctan(c^(1/6)*(c^(1/3)+d^(1/3)*x)*sqrt(3)/sqrt(c+d*x^3))*sqrt(3)/d^(5/3)-240/91*c*x^2*sqrt(c+d*x^3)/d-2/13*x^5*sqrt(c+d*x^3)-13782/91*c^2*sqrt(c+d*x^3)/(d^(5/3)*(d^(1/3)*x+c^(1/3)*(1+sqrt(3))))-4594/91*3^(3/4)*c^(7/3)*(c^(1/3)+d^(1/3)*x)*EllipticF((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2)*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(d^(5/3)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))+6891/91*3^(1/4)*c^(7/3)*(c^(1/3)+d^(1/3)*x)*EllipticE((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(d^(5/3)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))],
[x*(c+d*x^3)^(3/2)/(8*c-d*x^3),x,14,9/2*c^(7/6)*arctanh(1/3*(c^(1/3)+d^(1/3)*x)^2/(c^(1/6)*sqrt(c+d*x^3)))/d^(2/3)-9/2*c^(7/6)*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))/d^(2/3)-9/2*c^(7/6)*arctan(c^(1/6)*(c^(1/3)+d^(1/3)*x)*sqrt(3)/sqrt(c+d*x^3))*sqrt(3)/d^(2/3)-2/7*x^2*sqrt(c+d*x^3)-132/7*c*sqrt(c+d*x^3)/(d^(2/3)*(d^(1/3)*x+c^(1/3)*(1+sqrt(3))))-44/7*3^(3/4)*c^(4/3)*(c^(1/3)+d^(1/3)*x)*EllipticF((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2)*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(d^(2/3)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))+66/7*3^(1/4)*c^(4/3)*(c^(1/3)+d^(1/3)*x)*EllipticE((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(d^(2/3)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))],
[(c+d*x^3)^(3/2)/(x^2*(8*c-d*x^3)),x,14,9/16*c^(1/6)*d^(1/3)*arctanh(1/3*(c^(1/3)+d^(1/3)*x)^2/(c^(1/6)*sqrt(c+d*x^3)))-9/16*c^(1/6)*d^(1/3)*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))-9/16*c^(1/6)*d^(1/3)*arctan(c^(1/6)*(c^(1/3)+d^(1/3)*x)*sqrt(3)/sqrt(c+d*x^3))*sqrt(3)-1/8*sqrt(c+d*x^3)/x-15/8*d^(1/3)*sqrt(c+d*x^3)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))-5/4*3^(3/4)*c^(1/3)*d^(1/3)*(c^(1/3)+d^(1/3)*x)*EllipticF((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(sqrt(2)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))+15/16*3^(1/4)*c^(1/3)*d^(1/3)*(c^(1/3)+d^(1/3)*x)*EllipticE((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))],
[(c+d*x^3)^(3/2)/(x^5*(8*c-d*x^3)),x,15,9/128*d^(4/3)*arctanh(1/3*(c^(1/3)+d^(1/3)*x)^2/(c^(1/6)*sqrt(c+d*x^3)))/c^(5/6)-9/128*d^(4/3)*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))/c^(5/6)-9/128*d^(4/3)*arctan(c^(1/6)*(c^(1/3)+d^(1/3)*x)*sqrt(3)/sqrt(c+d*x^3))*sqrt(3)/c^(5/6)-1/32*sqrt(c+d*x^3)/x^4-3/16*d*sqrt(c+d*x^3)/(c*x)+3/16*d^(4/3)*sqrt(c+d*x^3)/(c*(d^(1/3)*x+c^(1/3)*(1+sqrt(3))))+1/8*3^(3/4)*d^(4/3)*(c^(1/3)+d^(1/3)*x)*EllipticF((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(c^(2/3)*sqrt(2)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))-3/32*3^(1/4)*d^(4/3)*(c^(1/3)+d^(1/3)*x)*EllipticE((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(c^(2/3)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))],
[(c+d*x^3)^(3/2)/(x^8*(8*c-d*x^3)),x,16,9/1024*d^(7/3)*arctanh(1/3*(c^(1/3)+d^(1/3)*x)^2/(c^(1/6)*sqrt(c+d*x^3)))/c^(11/6)-9/1024*d^(7/3)*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))/c^(11/6)-9/1024*d^(7/3)*arctan(c^(1/6)*(c^(1/3)+d^(1/3)*x)*sqrt(3)/sqrt(c+d*x^3))*sqrt(3)/c^(11/6)-1/56*sqrt(c+d*x^3)/x^7-75/1792*d*sqrt(c+d*x^3)/(c*x^4)-3/56*d^2*sqrt(c+d*x^3)/(c^2*x)+3/56*d^(7/3)*sqrt(c+d*x^3)/(c^2*(d^(1/3)*x+c^(1/3)*(1+sqrt(3))))+1/28*3^(3/4)*d^(7/3)*(c^(1/3)+d^(1/3)*x)*EllipticF((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(c^(5/3)*sqrt(2)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))-3/112*3^(1/4)*d^(7/3)*(c^(1/3)+d^(1/3)*x)*EllipticE((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(c^(5/3)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))],

# q<0 when 8 b c+a d=0
[x^11/((8*c-d*x^3)*sqrt(c+d*x^3)),x,5,-4/3*c*(c+d*x^3)^(3/2)/d^4-2/15*(c+d*x^3)^(5/2)/d^4+1024/9*c^(5/2)*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))/d^4-38*c^2*sqrt(c+d*x^3)/d^4],
[x^8/((8*c-d*x^3)*sqrt(c+d*x^3)),x,5,-2/9*(c+d*x^3)^(3/2)/d^3+128/9*c^(3/2)*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))/d^3-14/3*c*sqrt(c+d*x^3)/d^3],
[x^5/((8*c-d*x^3)*sqrt(c+d*x^3)),x,4,16/9*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))*sqrt(c)/d^2-2/3*sqrt(c+d*x^3)/d^2],
[x^2/((8*c-d*x^3)*sqrt(c+d*x^3)),x,3,2/9*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))/(d*sqrt(c))],
[1/(x*(8*c-d*x^3)*sqrt(c+d*x^3)),x,6,1/36*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))/c^(3/2)-1/12*arctanh(sqrt(c+d*x^3)/sqrt(c))/c^(3/2)],
[1/(x^4*(8*c-d*x^3)*sqrt(c+d*x^3)),x,7,1/288*d*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))/c^(5/2)+1/32*d*arctanh(sqrt(c+d*x^3)/sqrt(c))/c^(5/2)-1/24*sqrt(c+d*x^3)/(c^2*x^3)],
[1/(x^7*(8*c-d*x^3)*sqrt(c+d*x^3)),x,8,1/2304*d^2*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))/c^(7/2)-7/256*d^2*arctanh(sqrt(c+d*x^3)/sqrt(c))/c^(7/2)-1/48*sqrt(c+d*x^3)/(c^2*x^6)+5/192*d*sqrt(c+d*x^3)/(c^3*x^3)],
[x^7/((8*c-d*x^3)*sqrt(c+d*x^3)),x,14,32/9*c^(7/6)*arctanh(1/3*(c^(1/3)+d^(1/3)*x)^2/(c^(1/6)*sqrt(c+d*x^3)))/d^(8/3)-32/9*c^(7/6)*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))/d^(8/3)-32/3*c^(7/6)*arctan(c^(1/6)*(c^(1/3)+d^(1/3)*x)*sqrt(3)/sqrt(c+d*x^3))/(d^(8/3)*sqrt(3))-2/7*x^2*sqrt(c+d*x^3)/d^2-104/7*c*sqrt(c+d*x^3)/(d^(8/3)*(d^(1/3)*x+c^(1/3)*(1+sqrt(3))))-104/7*c^(4/3)*(c^(1/3)+d^(1/3)*x)*EllipticF((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2)*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(3^(1/4)*d^(8/3)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))+52/7*3^(1/4)*c^(4/3)*(c^(1/3)+d^(1/3)*x)*EllipticE((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(d^(8/3)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))],
[x^4/((8*c-d*x^3)*sqrt(c+d*x^3)),x,12,4/9*c^(1/6)*arctanh(1/3*(c^(1/3)+d^(1/3)*x)^2/(c^(1/6)*sqrt(c+d*x^3)))/d^(5/3)-4/9*c^(1/6)*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))/d^(5/3)-4/3*c^(1/6)*arctan(c^(1/6)*(c^(1/3)+d^(1/3)*x)*sqrt(3)/sqrt(c+d*x^3))/(d^(5/3)*sqrt(3))-2*sqrt(c+d*x^3)/(d^(5/3)*(d^(1/3)*x+c^(1/3)*(1+sqrt(3))))-2*c^(1/3)*(c^(1/3)+d^(1/3)*x)*EllipticF((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2)*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(3^(1/4)*d^(5/3)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))+3^(1/4)*c^(1/3)*(c^(1/3)+d^(1/3)*x)*EllipticE((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(d^(5/3)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))],
[x/((8*c-d*x^3)*sqrt(c+d*x^3)),x,8,1/18*arctanh(1/3*(c^(1/3)+d^(1/3)*x)^2/(c^(1/6)*sqrt(c+d*x^3)))/(c^(5/6)*d^(2/3))-1/18*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))/(c^(5/6)*d^(2/3))-1/6*arctan(c^(1/6)*(c^(1/3)+d^(1/3)*x)*sqrt(3)/sqrt(c+d*x^3))/(c^(5/6)*d^(2/3)*sqrt(3))],
[1/(x^2*(8*c-d*x^3)*sqrt(c+d*x^3)),x,14,1/144*d^(1/3)*arctanh(1/3*(c^(1/3)+d^(1/3)*x)^2/(c^(1/6)*sqrt(c+d*x^3)))/c^(11/6)-1/144*d^(1/3)*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))/c^(11/6)-1/48*d^(1/3)*arctan(c^(1/6)*(c^(1/3)+d^(1/3)*x)*sqrt(3)/sqrt(c+d*x^3))/(c^(11/6)*sqrt(3))-1/8*sqrt(c+d*x^3)/(c^2*x)+1/8*d^(1/3)*sqrt(c+d*x^3)/(c^2*(d^(1/3)*x+c^(1/3)*(1+sqrt(3))))+1/4*d^(1/3)*(c^(1/3)+d^(1/3)*x)*EllipticF((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(3^(1/4)*c^(5/3)*sqrt(2)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))-1/16*3^(1/4)*d^(1/3)*(c^(1/3)+d^(1/3)*x)*EllipticE((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(c^(5/3)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))],
[1/(x^5*(8*c-d*x^3)*sqrt(c+d*x^3)),x,15,1/1152*d^(4/3)*arctanh(1/3*(c^(1/3)+d^(1/3)*x)^2/(c^(1/6)*sqrt(c+d*x^3)))/c^(17/6)-1/1152*d^(4/3)*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))/c^(17/6)-1/384*d^(4/3)*arctan(c^(1/6)*(c^(1/3)+d^(1/3)*x)*sqrt(3)/sqrt(c+d*x^3))/(c^(17/6)*sqrt(3))-1/32*sqrt(c+d*x^3)/(c^2*x^4)+1/16*d*sqrt(c+d*x^3)/(c^3*x)-1/16*d^(4/3)*sqrt(c+d*x^3)/(c^3*(d^(1/3)*x+c^(1/3)*(1+sqrt(3))))-1/8*d^(4/3)*(c^(1/3)+d^(1/3)*x)*EllipticF((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(3^(1/4)*c^(8/3)*sqrt(2)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))+1/32*3^(1/4)*d^(4/3)*(c^(1/3)+d^(1/3)*x)*EllipticE((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(c^(8/3)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))],
[1/(x^8*(8*c-d*x^3)*sqrt(c+d*x^3)),x,16,1/9216*d^(7/3)*arctanh(1/3*(c^(1/3)+d^(1/3)*x)^2/(c^(1/6)*sqrt(c+d*x^3)))/c^(23/6)-1/9216*d^(7/3)*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))/c^(23/6)-1/3072*d^(7/3)*arctan(c^(1/6)*(c^(1/3)+d^(1/3)*x)*sqrt(3)/sqrt(c+d*x^3))/(c^(23/6)*sqrt(3))-1/56*sqrt(c+d*x^3)/(c^2*x^7)+37/1792*d*sqrt(c+d*x^3)/(c^3*x^4)-3/56*d^2*sqrt(c+d*x^3)/(c^4*x)+3/56*d^(7/3)*sqrt(c+d*x^3)/(c^4*(d^(1/3)*x+c^(1/3)*(1+sqrt(3))))+1/28*3^(3/4)*d^(7/3)*(c^(1/3)+d^(1/3)*x)*EllipticF((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(c^(11/3)*sqrt(2)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))-3/112*3^(1/4)*d^(7/3)*(c^(1/3)+d^(1/3)*x)*EllipticE((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(c^(11/3)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))],
[x^3/((8*c-d*x^3)*sqrt(c+d*x^3)),x,2,1/32*x^4*AppellF1(4/3,1,1/2,7/3,1/8*d*x^3/c,-d*x^3/c)*sqrt(1+d*x^3/c)/(c*sqrt(c+d*x^3))],
[1/((8*c-d*x^3)*sqrt(c+d*x^3)),x,2,1/8*x*AppellF1(1/3,1,1/2,4/3,1/8*d*x^3/c,-d*x^3/c)*sqrt(1+d*x^3/c)/(c*sqrt(c+d*x^3))],
[1/(x^3*(8*c-d*x^3)*sqrt(c+d*x^3)),x,2,-1/16*AppellF1(-2/3,1,1/2,1/3,1/8*d*x^3/c,-d*x^3/c)*sqrt(1+d*x^3/c)/(c*x^2*sqrt(c+d*x^3))],
[1/(x^6*(8*c-d*x^3)*sqrt(c+d*x^3)),x,2,-1/40*AppellF1(-5/3,1,1/2,-2/3,1/8*d*x^3/c,-d*x^3/c)*sqrt(1+d*x^3/c)/(c*x^5*sqrt(c+d*x^3))],
[x^11/((8*c-d*x^3)*(c+d*x^3)^(3/2)),x,7,-2/9*(c+d*x^3)^(3/2)/d^4+1024/81*c^(3/2)*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))/d^4+2/27*c^2/(d^4*sqrt(c+d*x^3))-4*c*sqrt(c+d*x^3)/d^4],
[x^8/((8*c-d*x^3)*(c+d*x^3)^(3/2)),x,5,128/81*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))*sqrt(c)/d^3-2/27*c/(d^3*sqrt(c+d*x^3))-2/3*sqrt(c+d*x^3)/d^3],
[x^5/((8*c-d*x^3)*(c+d*x^3)^(3/2)),x,4,16/81*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))/(d^2*sqrt(c))+2/27/(d^2*sqrt(c+d*x^3))],
[x^2/((8*c-d*x^3)*(c+d*x^3)^(3/2)),x,4,2/81*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))/(c^(3/2)*d)+(-2/27)/(c*d*sqrt(c+d*x^3))],
[1/(x*(8*c-d*x^3)*(c+d*x^3)^(3/2)),x,7,1/324*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))/c^(5/2)-1/12*arctanh(sqrt(c+d*x^3)/sqrt(c))/c^(5/2)+2/27/(c^2*sqrt(c+d*x^3))],
[1/(x^4*(8*c-d*x^3)*(c+d*x^3)^(3/2)),x,8,1/2592*d*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))/c^(7/2)+11/96*d*arctanh(sqrt(c+d*x^3)/sqrt(c))/c^(7/2)-25/216*d/(c^3*sqrt(c+d*x^3))+(-1/24)/(c^2*x^3*sqrt(c+d*x^3))],
[1/(x^7*(8*c-d*x^3)*(c+d*x^3)^(3/2)),x,9,1/20736*d^2*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))/c^(9/2)-109/768*d^2*arctanh(sqrt(c+d*x^3)/sqrt(c))/c^(9/2)+245/1728*d^2/(c^4*sqrt(c+d*x^3))+(-1/48)/(c^2*x^6*sqrt(c+d*x^3))+3/64*d/(c^3*x^3*sqrt(c+d*x^3))],
[x^7/((8*c-d*x^3)*(c+d*x^3)^(3/2)),x,14,32/81*c^(1/6)*arctanh(1/3*(c^(1/3)+d^(1/3)*x)^2/(c^(1/6)*sqrt(c+d*x^3)))/d^(8/3)-32/81*c^(1/6)*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))/d^(8/3)-32/27*c^(1/6)*arctan(c^(1/6)*(c^(1/3)+d^(1/3)*x)*sqrt(3)/sqrt(c+d*x^3))/(d^(8/3)*sqrt(3))+2/27*x^2/(d^2*sqrt(c+d*x^3))-56/27*sqrt(c+d*x^3)/(d^(8/3)*(d^(1/3)*x+c^(1/3)*(1+sqrt(3))))-56/27*c^(1/3)*(c^(1/3)+d^(1/3)*x)*EllipticF((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2)*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(3^(1/4)*d^(8/3)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))+28/9*c^(1/3)*(c^(1/3)+d^(1/3)*x)*EllipticE((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(3^(3/4)*d^(8/3)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))],
[x^4/((8*c-d*x^3)*(c+d*x^3)^(3/2)),x,14,4/81*arctanh(1/3*(c^(1/3)+d^(1/3)*x)^2/(c^(1/6)*sqrt(c+d*x^3)))/(c^(5/6)*d^(5/3))-4/81*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))/(c^(5/6)*d^(5/3))-4/27*arctan(c^(1/6)*(c^(1/3)+d^(1/3)*x)*sqrt(3)/sqrt(c+d*x^3))/(c^(5/6)*d^(5/3)*sqrt(3))-2/27*x^2/(c*d*sqrt(c+d*x^3))+2/27*sqrt(c+d*x^3)/(c*d^(5/3)*(d^(1/3)*x+c^(1/3)*(1+sqrt(3))))+2/27*(c^(1/3)+d^(1/3)*x)*EllipticF((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2)*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(3^(1/4)*c^(2/3)*d^(5/3)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))-1/9*(c^(1/3)+d^(1/3)*x)*EllipticE((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(3^(3/4)*c^(2/3)*d^(5/3)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))],
[x/((8*c-d*x^3)*(c+d*x^3)^(3/2)),x,14,1/162*arctanh(1/3*(c^(1/3)+d^(1/3)*x)^2/(c^(1/6)*sqrt(c+d*x^3)))/(c^(11/6)*d^(2/3))-1/162*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))/(c^(11/6)*d^(2/3))-1/54*arctan(c^(1/6)*(c^(1/3)+d^(1/3)*x)*sqrt(3)/sqrt(c+d*x^3))/(c^(11/6)*d^(2/3)*sqrt(3))+2/27*x^2/(c^2*sqrt(c+d*x^3))-2/27*sqrt(c+d*x^3)/(c^2*d^(2/3)*(d^(1/3)*x+c^(1/3)*(1+sqrt(3))))-2/27*(c^(1/3)+d^(1/3)*x)*EllipticF((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2)*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(3^(1/4)*c^(5/3)*d^(2/3)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))+1/9*(c^(1/3)+d^(1/3)*x)*EllipticE((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(3^(3/4)*c^(5/3)*d^(2/3)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))],
[1/(x^2*(8*c-d*x^3)*(c+d*x^3)^(3/2)),x,15,1/1296*d^(1/3)*arctanh(1/3*(c^(1/3)+d^(1/3)*x)^2/(c^(1/6)*sqrt(c+d*x^3)))/c^(17/6)-1/1296*d^(1/3)*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))/c^(17/6)-1/432*d^(1/3)*arctan(c^(1/6)*(c^(1/3)+d^(1/3)*x)*sqrt(3)/sqrt(c+d*x^3))/(c^(17/6)*sqrt(3))+2/27/(c^2*x*sqrt(c+d*x^3))-43/216*sqrt(c+d*x^3)/(c^3*x)+43/216*d^(1/3)*sqrt(c+d*x^3)/(c^3*(d^(1/3)*x+c^(1/3)*(1+sqrt(3))))+43/108*d^(1/3)*(c^(1/3)+d^(1/3)*x)*EllipticF((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(3^(1/4)*c^(8/3)*sqrt(2)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))-43/144*d^(1/3)*(c^(1/3)+d^(1/3)*x)*EllipticE((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(3^(3/4)*c^(8/3)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))],
[1/(x^5*(8*c-d*x^3)*(c+d*x^3)^(3/2)),x,16,1/10368*d^(4/3)*arctanh(1/3*(c^(1/3)+d^(1/3)*x)^2/(c^(1/6)*sqrt(c+d*x^3)))/c^(23/6)-1/10368*d^(4/3)*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))/c^(23/6)-1/3456*d^(4/3)*arctan(c^(1/6)*(c^(1/3)+d^(1/3)*x)*sqrt(3)/sqrt(c+d*x^3))/(c^(23/6)*sqrt(3))+2/27/(c^2*x^4*sqrt(c+d*x^3))-91/864*sqrt(c+d*x^3)/(c^3*x^4)+113/432*d*sqrt(c+d*x^3)/(c^4*x)-113/432*d^(4/3)*sqrt(c+d*x^3)/(c^4*(d^(1/3)*x+c^(1/3)*(1+sqrt(3))))-113/216*d^(4/3)*(c^(1/3)+d^(1/3)*x)*EllipticF((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(3^(1/4)*c^(11/3)*sqrt(2)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))+113/288*d^(4/3)*(c^(1/3)+d^(1/3)*x)*EllipticE((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(3^(3/4)*c^(11/3)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))],
[1/(x^8*(8*c-d*x^3)*(c+d*x^3)^(3/2)),x,17,1/82944*d^(7/3)*arctanh(1/3*(c^(1/3)+d^(1/3)*x)^2/(c^(1/6)*sqrt(c+d*x^3)))/c^(29/6)-1/82944*d^(7/3)*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))/c^(29/6)-1/27648*d^(7/3)*arctan(c^(1/6)*(c^(1/3)+d^(1/3)*x)*sqrt(3)/sqrt(c+d*x^3))/(c^(29/6)*sqrt(3))+2/27/(c^2*x^7*sqrt(c+d*x^3))-139/1512*sqrt(c+d*x^3)/(c^3*x^7)+6095/48384*d*sqrt(c+d*x^3)/(c^4*x^4)-953/3024*d^2*sqrt(c+d*x^3)/(c^5*x)+953/3024*d^(7/3)*sqrt(c+d*x^3)/(c^5*(d^(1/3)*x+c^(1/3)*(1+sqrt(3))))+953/1512*d^(7/3)*(c^(1/3)+d^(1/3)*x)*EllipticF((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(3^(1/4)*c^(14/3)*sqrt(2)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))-953/2016*d^(7/3)*(c^(1/3)+d^(1/3)*x)*EllipticE((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(3^(3/4)*c^(14/3)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))],
[x^3/((8*c-d*x^3)*(c+d*x^3)^(3/2)),x,2,1/32*x^4*AppellF1(4/3,1,3/2,7/3,1/8*d*x^3/c,-d*x^3/c)*sqrt(1+d*x^3/c)/(c^2*sqrt(c+d*x^3))],
[1/((8*c-d*x^3)*(c+d*x^3)^(3/2)),x,2,1/8*x*AppellF1(1/3,1,3/2,4/3,1/8*d*x^3/c,-d*x^3/c)*sqrt(1+d*x^3/c)/(c^2*sqrt(c+d*x^3))],
[1/(x^3*(8*c-d*x^3)*(c+d*x^3)^(3/2)),x,2,-1/16*AppellF1(-2/3,1,3/2,1/3,1/8*d*x^3/c,-d*x^3/c)*sqrt(1+d*x^3/c)/(c^2*x^2*sqrt(c+d*x^3))],
[1/(x^6*(8*c-d*x^3)*(c+d*x^3)^(3/2)),x,2,-1/40*AppellF1(-5/3,1,3/2,-2/3,1/8*d*x^3/c,-d*x^3/c)*sqrt(1+d*x^3/c)/(c^2*x^5*sqrt(c+d*x^3))],

# q>0 when b^2 c^2-20 a b c d-8 a^2 d^2=0
[x*sqrt(a+b*x^3)/(b*x^3+2*a*(5+3*sqrt(3))),x,5,1/2*3^(3/4)*a^(1/6)*arctan(3^(1/4)*a^(1/6)*(a^(1/3)+b^(1/3)*x)*(1+sqrt(3))/(sqrt(2)*sqrt(a+b*x^3)))/(b^(2/3)*sqrt(2))+a^(1/6)*arctan((1-sqrt(3))*sqrt(a+b*x^3)/(3^(3/4)*sqrt(2)*sqrt(a)))/(3^(1/4)*b^(2/3)*sqrt(2))+1/2*3^(1/4)*a^(1/6)*arctanh(3^(1/4)*a^(1/6)*(a^(1/3)+b^(1/3)*x)*(1-sqrt(3))/(sqrt(2)*sqrt(a+b*x^3)))/(b^(2/3)*sqrt(2))+3^(1/4)*a^(1/6)*arctanh(3^(1/4)*a^(1/6)*(-2*b^(1/3)*x+a^(1/3)*(1+sqrt(3)))/(sqrt(2)*sqrt(a+b*x^3)))/(b^(2/3)*sqrt(2))+2*sqrt(a+b*x^3)/(b^(2/3)*(b^(1/3)*x+a^(1/3)*(1+sqrt(3))))+2*a^(1/3)*(a^(1/3)+b^(1/3)*x)*EllipticF((b^(1/3)*x+a^(1/3)*(1-sqrt(3)))/(b^(1/3)*x+a^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2)/(3^(1/4)*b^(2/3)*sqrt(a+b*x^3)*sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2))-3^(1/4)*a^(1/3)*(a^(1/3)+b^(1/3)*x)*EllipticE((b^(1/3)*x+a^(1/3)*(1-sqrt(3)))/(b^(1/3)*x+a^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2)/(b^(2/3)*sqrt(a+b*x^3)*sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2))],
[x*sqrt(a-b*x^3)/(-b*x^3+2*a*(5+3*sqrt(3))),x,5,1/2*3^(3/4)*a^(1/6)*arctan(3^(1/4)*a^(1/6)*(a^(1/3)-b^(1/3)*x)*(1+sqrt(3))/(sqrt(2)*sqrt(a-b*x^3)))/(b^(2/3)*sqrt(2))+a^(1/6)*arctan((1-sqrt(3))*sqrt(a-b*x^3)/(3^(3/4)*sqrt(2)*sqrt(a)))/(3^(1/4)*b^(2/3)*sqrt(2))+1/2*3^(1/4)*a^(1/6)*arctanh(3^(1/4)*a^(1/6)*(a^(1/3)-b^(1/3)*x)*(1-sqrt(3))/(sqrt(2)*sqrt(a-b*x^3)))/(b^(2/3)*sqrt(2))+3^(1/4)*a^(1/6)*arctanh(3^(1/4)*a^(1/6)*(2*b^(1/3)*x+a^(1/3)*(1+sqrt(3)))/(sqrt(2)*sqrt(a-b*x^3)))/(b^(2/3)*sqrt(2))+2*sqrt(a-b*x^3)/(b^(2/3)*(-b^(1/3)*x+a^(1/3)*(1+sqrt(3))))+2*a^(1/3)*(a^(1/3)-b^(1/3)*x)*EllipticF((-b^(1/3)*x+a^(1/3)*(1-sqrt(3)))/(-b^(1/3)*x+a^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2)*sqrt((a^(2/3)+a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(-b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2)/(3^(1/4)*b^(2/3)*sqrt(a-b*x^3)*sqrt(a^(1/3)*(a^(1/3)-b^(1/3)*x)/(-b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2))-3^(1/4)*a^(1/3)*(a^(1/3)-b^(1/3)*x)*EllipticE((-b^(1/3)*x+a^(1/3)*(1-sqrt(3)))/(-b^(1/3)*x+a^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((a^(2/3)+a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(-b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2)/(b^(2/3)*sqrt(a-b*x^3)*sqrt(a^(1/3)*(a^(1/3)-b^(1/3)*x)/(-b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2))],
[x*sqrt(-a+b*x^3)/(b*x^3-2*a*(5+3*sqrt(3))),x,5,1/2*3^(1/4)*a^(1/6)*arctan(3^(1/4)*a^(1/6)*(a^(1/3)-b^(1/3)*x)*(1-sqrt(3))/(sqrt(2)*sqrt(-a+b*x^3)))/(b^(2/3)*sqrt(2))+3^(1/4)*a^(1/6)*arctan(3^(1/4)*a^(1/6)*(2*b^(1/3)*x+a^(1/3)*(1+sqrt(3)))/(sqrt(2)*sqrt(-a+b*x^3)))/(b^(2/3)*sqrt(2))+1/2*3^(3/4)*a^(1/6)*arctanh(3^(1/4)*a^(1/6)*(a^(1/3)-b^(1/3)*x)*(1+sqrt(3))/(sqrt(2)*sqrt(-a+b*x^3)))/(b^(2/3)*sqrt(2))-a^(1/6)*arctanh((1-sqrt(3))*sqrt(-a+b*x^3)/(3^(3/4)*sqrt(2)*sqrt(a)))/(3^(1/4)*b^(2/3)*sqrt(2))-2*sqrt(-a+b*x^3)/(b^(2/3)*(-b^(1/3)*x+a^(1/3)*(1-sqrt(3))))-2*a^(1/3)*(a^(1/3)-b^(1/3)*x)*EllipticF((-b^(1/3)*x+a^(1/3)*(1+sqrt(3)))/(-b^(1/3)*x+a^(1/3)*(1-sqrt(3))),sqrt(-7+4*sqrt(3)))*sqrt(2)*sqrt((a^(2/3)+a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(-b^(1/3)*x+a^(1/3)*(1-sqrt(3)))^2)/(3^(1/4)*b^(2/3)*sqrt(-a+b*x^3)*sqrt(-a^(1/3)*(a^(1/3)-b^(1/3)*x)/(-b^(1/3)*x+a^(1/3)*(1-sqrt(3)))^2))+3^(1/4)*a^(1/3)*(a^(1/3)-b^(1/3)*x)*EllipticE((-b^(1/3)*x+a^(1/3)*(1+sqrt(3)))/(-b^(1/3)*x+a^(1/3)*(1-sqrt(3))),sqrt(-7+4*sqrt(3)))*sqrt((a^(2/3)+a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(-b^(1/3)*x+a^(1/3)*(1-sqrt(3)))^2)*sqrt(2+sqrt(3))/(b^(2/3)*sqrt(-a+b*x^3)*sqrt(-a^(1/3)*(a^(1/3)-b^(1/3)*x)/(-b^(1/3)*x+a^(1/3)*(1-sqrt(3)))^2))],
[x*sqrt(-a-b*x^3)/(-b*x^3-2*a*(5+3*sqrt(3))),x,5,1/2*3^(1/4)*a^(1/6)*arctan(3^(1/4)*a^(1/6)*(a^(1/3)+b^(1/3)*x)*(1-sqrt(3))/(sqrt(2)*sqrt(-a-b*x^3)))/(b^(2/3)*sqrt(2))+3^(1/4)*a^(1/6)*arctan(3^(1/4)*a^(1/6)*(-2*b^(1/3)*x+a^(1/3)*(1+sqrt(3)))/(sqrt(2)*sqrt(-a-b*x^3)))/(b^(2/3)*sqrt(2))+1/2*3^(3/4)*a^(1/6)*arctanh(3^(1/4)*a^(1/6)*(a^(1/3)+b^(1/3)*x)*(1+sqrt(3))/(sqrt(2)*sqrt(-a-b*x^3)))/(b^(2/3)*sqrt(2))-a^(1/6)*arctanh((1-sqrt(3))*sqrt(-a-b*x^3)/(3^(3/4)*sqrt(2)*sqrt(a)))/(3^(1/4)*b^(2/3)*sqrt(2))-2*sqrt(-a-b*x^3)/(b^(2/3)*(b^(1/3)*x+a^(1/3)*(1-sqrt(3))))-2*a^(1/3)*(a^(1/3)+b^(1/3)*x)*EllipticF((b^(1/3)*x+a^(1/3)*(1+sqrt(3)))/(b^(1/3)*x+a^(1/3)*(1-sqrt(3))),sqrt(-7+4*sqrt(3)))*sqrt(2)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(1/3)*x+a^(1/3)*(1-sqrt(3)))^2)/(3^(1/4)*b^(2/3)*sqrt(-a-b*x^3)*sqrt(-a^(1/3)*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*x+a^(1/3)*(1-sqrt(3)))^2))+3^(1/4)*a^(1/3)*(a^(1/3)+b^(1/3)*x)*EllipticE((b^(1/3)*x+a^(1/3)*(1+sqrt(3)))/(b^(1/3)*x+a^(1/3)*(1-sqrt(3))),sqrt(-7+4*sqrt(3)))*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(1/3)*x+a^(1/3)*(1-sqrt(3)))^2)*sqrt(2+sqrt(3))/(b^(2/3)*sqrt(-a-b*x^3)*sqrt(-a^(1/3)*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*x+a^(1/3)*(1-sqrt(3)))^2))],
[x*sqrt(a+b*x^3)/(b*x^3+2*a*(5-3*sqrt(3))),x,5,-3^(1/4)*a^(1/6)*arctan(3^(1/4)*a^(1/6)*(-2*b^(1/3)*x+a^(1/3)*(1-sqrt(3)))/(sqrt(2)*sqrt(a+b*x^3)))/(b^(2/3)*sqrt(2))-1/2*3^(1/4)*a^(1/6)*arctan(3^(1/4)*a^(1/6)*(a^(1/3)+b^(1/3)*x)*(1+sqrt(3))/(sqrt(2)*sqrt(a+b*x^3)))/(b^(2/3)*sqrt(2))+1/2*3^(3/4)*a^(1/6)*arctanh(3^(1/4)*a^(1/6)*(a^(1/3)+b^(1/3)*x)*(1-sqrt(3))/(sqrt(2)*sqrt(a+b*x^3)))/(b^(2/3)*sqrt(2))+a^(1/6)*arctanh((1+sqrt(3))*sqrt(a+b*x^3)/(3^(3/4)*sqrt(2)*sqrt(a)))/(3^(1/4)*b^(2/3)*sqrt(2))+2*sqrt(a+b*x^3)/(b^(2/3)*(b^(1/3)*x+a^(1/3)*(1+sqrt(3))))+2*a^(1/3)*(a^(1/3)+b^(1/3)*x)*EllipticF((b^(1/3)*x+a^(1/3)*(1-sqrt(3)))/(b^(1/3)*x+a^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2)/(3^(1/4)*b^(2/3)*sqrt(a+b*x^3)*sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2))-3^(1/4)*a^(1/3)*(a^(1/3)+b^(1/3)*x)*EllipticE((b^(1/3)*x+a^(1/3)*(1-sqrt(3)))/(b^(1/3)*x+a^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2)/(b^(2/3)*sqrt(a+b*x^3)*sqrt(a^(1/3)*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2))],
[x*sqrt(a-b*x^3)/(-b*x^3+2*a*(5-3*sqrt(3))),x,5,-3^(1/4)*a^(1/6)*arctan(3^(1/4)*a^(1/6)*(2*b^(1/3)*x+a^(1/3)*(1-sqrt(3)))/(sqrt(2)*sqrt(a-b*x^3)))/(b^(2/3)*sqrt(2))-1/2*3^(1/4)*a^(1/6)*arctan(3^(1/4)*a^(1/6)*(a^(1/3)-b^(1/3)*x)*(1+sqrt(3))/(sqrt(2)*sqrt(a-b*x^3)))/(b^(2/3)*sqrt(2))+1/2*3^(3/4)*a^(1/6)*arctanh(3^(1/4)*a^(1/6)*(a^(1/3)-b^(1/3)*x)*(1-sqrt(3))/(sqrt(2)*sqrt(a-b*x^3)))/(b^(2/3)*sqrt(2))+a^(1/6)*arctanh((1+sqrt(3))*sqrt(a-b*x^3)/(3^(3/4)*sqrt(2)*sqrt(a)))/(3^(1/4)*b^(2/3)*sqrt(2))+2*sqrt(a-b*x^3)/(b^(2/3)*(-b^(1/3)*x+a^(1/3)*(1+sqrt(3))))+2*a^(1/3)*(a^(1/3)-b^(1/3)*x)*EllipticF((-b^(1/3)*x+a^(1/3)*(1-sqrt(3)))/(-b^(1/3)*x+a^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2)*sqrt((a^(2/3)+a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(-b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2)/(3^(1/4)*b^(2/3)*sqrt(a-b*x^3)*sqrt(a^(1/3)*(a^(1/3)-b^(1/3)*x)/(-b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2))-3^(1/4)*a^(1/3)*(a^(1/3)-b^(1/3)*x)*EllipticE((-b^(1/3)*x+a^(1/3)*(1-sqrt(3)))/(-b^(1/3)*x+a^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((a^(2/3)+a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(-b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2)/(b^(2/3)*sqrt(a-b*x^3)*sqrt(a^(1/3)*(a^(1/3)-b^(1/3)*x)/(-b^(1/3)*x+a^(1/3)*(1+sqrt(3)))^2))],
[x*sqrt(-a+b*x^3)/(-b*x^3+2*a*(5-3*sqrt(3))),x,5,-1/2*3^(3/4)*a^(1/6)*arctan(3^(1/4)*a^(1/6)*(a^(1/3)-b^(1/3)*x)*(1-sqrt(3))/(sqrt(2)*sqrt(-a+b*x^3)))/(b^(2/3)*sqrt(2))+a^(1/6)*arctan((1+sqrt(3))*sqrt(-a+b*x^3)/(3^(3/4)*sqrt(2)*sqrt(a)))/(3^(1/4)*b^(2/3)*sqrt(2))+3^(1/4)*a^(1/6)*arctanh(3^(1/4)*a^(1/6)*(2*b^(1/3)*x+a^(1/3)*(1-sqrt(3)))/(sqrt(2)*sqrt(-a+b*x^3)))/(b^(2/3)*sqrt(2))+1/2*3^(1/4)*a^(1/6)*arctanh(3^(1/4)*a^(1/6)*(a^(1/3)-b^(1/3)*x)*(1+sqrt(3))/(sqrt(2)*sqrt(-a+b*x^3)))/(b^(2/3)*sqrt(2))+2*sqrt(-a+b*x^3)/(b^(2/3)*(-b^(1/3)*x+a^(1/3)*(1-sqrt(3))))+2*a^(1/3)*(a^(1/3)-b^(1/3)*x)*EllipticF((-b^(1/3)*x+a^(1/3)*(1+sqrt(3)))/(-b^(1/3)*x+a^(1/3)*(1-sqrt(3))),sqrt(-7+4*sqrt(3)))*sqrt(2)*sqrt((a^(2/3)+a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(-b^(1/3)*x+a^(1/3)*(1-sqrt(3)))^2)/(3^(1/4)*b^(2/3)*sqrt(-a+b*x^3)*sqrt(-a^(1/3)*(a^(1/3)-b^(1/3)*x)/(-b^(1/3)*x+a^(1/3)*(1-sqrt(3)))^2))-3^(1/4)*a^(1/3)*(a^(1/3)-b^(1/3)*x)*EllipticE((-b^(1/3)*x+a^(1/3)*(1+sqrt(3)))/(-b^(1/3)*x+a^(1/3)*(1-sqrt(3))),sqrt(-7+4*sqrt(3)))*sqrt((a^(2/3)+a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(-b^(1/3)*x+a^(1/3)*(1-sqrt(3)))^2)*sqrt(2+sqrt(3))/(b^(2/3)*sqrt(-a+b*x^3)*sqrt(-a^(1/3)*(a^(1/3)-b^(1/3)*x)/(-b^(1/3)*x+a^(1/3)*(1-sqrt(3)))^2))],
[x*sqrt(-a-b*x^3)/(b*x^3+2*a*(5-3*sqrt(3))),x,5,-1/2*3^(3/4)*a^(1/6)*arctan(3^(1/4)*a^(1/6)*(a^(1/3)+b^(1/3)*x)*(1-sqrt(3))/(sqrt(2)*sqrt(-a-b*x^3)))/(b^(2/3)*sqrt(2))+a^(1/6)*arctan((1+sqrt(3))*sqrt(-a-b*x^3)/(3^(3/4)*sqrt(2)*sqrt(a)))/(3^(1/4)*b^(2/3)*sqrt(2))+3^(1/4)*a^(1/6)*arctanh(3^(1/4)*a^(1/6)*(-2*b^(1/3)*x+a^(1/3)*(1-sqrt(3)))/(sqrt(2)*sqrt(-a-b*x^3)))/(b^(2/3)*sqrt(2))+1/2*3^(1/4)*a^(1/6)*arctanh(3^(1/4)*a^(1/6)*(a^(1/3)+b^(1/3)*x)*(1+sqrt(3))/(sqrt(2)*sqrt(-a-b*x^3)))/(b^(2/3)*sqrt(2))+2*sqrt(-a-b*x^3)/(b^(2/3)*(b^(1/3)*x+a^(1/3)*(1-sqrt(3))))+2*a^(1/3)*(a^(1/3)+b^(1/3)*x)*EllipticF((b^(1/3)*x+a^(1/3)*(1+sqrt(3)))/(b^(1/3)*x+a^(1/3)*(1-sqrt(3))),sqrt(-7+4*sqrt(3)))*sqrt(2)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(1/3)*x+a^(1/3)*(1-sqrt(3)))^2)/(3^(1/4)*b^(2/3)*sqrt(-a-b*x^3)*sqrt(-a^(1/3)*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*x+a^(1/3)*(1-sqrt(3)))^2))-3^(1/4)*a^(1/3)*(a^(1/3)+b^(1/3)*x)*EllipticE((b^(1/3)*x+a^(1/3)*(1+sqrt(3)))/(b^(1/3)*x+a^(1/3)*(1-sqrt(3))),sqrt(-7+4*sqrt(3)))*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(1/3)*x+a^(1/3)*(1-sqrt(3)))^2)*sqrt(2+sqrt(3))/(b^(2/3)*sqrt(-a-b*x^3)*sqrt(-a^(1/3)*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*x+a^(1/3)*(1-sqrt(3)))^2))],

# q<0 when b^2 c^2-20 a b c d-8 a^2 d^2=0
[x/((b*x^3+2*a*(5+3*sqrt(3)))*sqrt(a+b*x^3)),x,1,-1/2*arctan(3^(1/4)*a^(1/6)*(a^(1/3)+b^(1/3)*x)*(1+sqrt(3))/(sqrt(2)*sqrt(a+b*x^3)))*(2-sqrt(3))/(3^(3/4)*a^(5/6)*b^(2/3)*sqrt(2))-1/3*arctan((1-sqrt(3))*sqrt(a+b*x^3)/(3^(3/4)*sqrt(2)*sqrt(a)))*(2-sqrt(3))/(3^(3/4)*a^(5/6)*b^(2/3)*sqrt(2))-1/6*arctanh(3^(1/4)*a^(1/6)*(a^(1/3)+b^(1/3)*x)*(1-sqrt(3))/(sqrt(2)*sqrt(a+b*x^3)))*(2-sqrt(3))/(3^(1/4)*a^(5/6)*b^(2/3)*sqrt(2))-1/3*arctanh(3^(1/4)*a^(1/6)*(-2*b^(1/3)*x+a^(1/3)*(1+sqrt(3)))/(sqrt(2)*sqrt(a+b*x^3)))*(2-sqrt(3))/(3^(1/4)*a^(5/6)*b^(2/3)*sqrt(2))],
[x/((-b*x^3+2*a*(5+3*sqrt(3)))*sqrt(a-b*x^3)),x,1,-1/2*arctan(3^(1/4)*a^(1/6)*(a^(1/3)-b^(1/3)*x)*(1+sqrt(3))/(sqrt(2)*sqrt(a-b*x^3)))*(2-sqrt(3))/(3^(3/4)*a^(5/6)*b^(2/3)*sqrt(2))-1/3*arctan((1-sqrt(3))*sqrt(a-b*x^3)/(3^(3/4)*sqrt(2)*sqrt(a)))*(2-sqrt(3))/(3^(3/4)*a^(5/6)*b^(2/3)*sqrt(2))-1/6*arctanh(3^(1/4)*a^(1/6)*(a^(1/3)-b^(1/3)*x)*(1-sqrt(3))/(sqrt(2)*sqrt(a-b*x^3)))*(2-sqrt(3))/(3^(1/4)*a^(5/6)*b^(2/3)*sqrt(2))-1/3*arctanh(3^(1/4)*a^(1/6)*(2*b^(1/3)*x+a^(1/3)*(1+sqrt(3)))/(sqrt(2)*sqrt(a-b*x^3)))*(2-sqrt(3))/(3^(1/4)*a^(5/6)*b^(2/3)*sqrt(2))],
[x/((b*x^3-2*a*(5+3*sqrt(3)))*sqrt(-a+b*x^3)),x,1,1/6*arctan(3^(1/4)*a^(1/6)*(a^(1/3)-b^(1/3)*x)*(1-sqrt(3))/(sqrt(2)*sqrt(-a+b*x^3)))*(2-sqrt(3))/(3^(1/4)*a^(5/6)*b^(2/3)*sqrt(2))+1/3*arctan(3^(1/4)*a^(1/6)*(2*b^(1/3)*x+a^(1/3)*(1+sqrt(3)))/(sqrt(2)*sqrt(-a+b*x^3)))*(2-sqrt(3))/(3^(1/4)*a^(5/6)*b^(2/3)*sqrt(2))+1/2*arctanh(3^(1/4)*a^(1/6)*(a^(1/3)-b^(1/3)*x)*(1+sqrt(3))/(sqrt(2)*sqrt(-a+b*x^3)))*(2-sqrt(3))/(3^(3/4)*a^(5/6)*b^(2/3)*sqrt(2))-1/3*arctanh((1-sqrt(3))*sqrt(-a+b*x^3)/(3^(3/4)*sqrt(2)*sqrt(a)))*(2-sqrt(3))/(3^(3/4)*a^(5/6)*b^(2/3)*sqrt(2))],
[x/((-b*x^3-2*a*(5+3*sqrt(3)))*sqrt(-a-b*x^3)),x,1,1/6*arctan(3^(1/4)*a^(1/6)*(a^(1/3)+b^(1/3)*x)*(1-sqrt(3))/(sqrt(2)*sqrt(-a-b*x^3)))*(2-sqrt(3))/(3^(1/4)*a^(5/6)*b^(2/3)*sqrt(2))+1/3*arctan(3^(1/4)*a^(1/6)*(-2*b^(1/3)*x+a^(1/3)*(1+sqrt(3)))/(sqrt(2)*sqrt(-a-b*x^3)))*(2-sqrt(3))/(3^(1/4)*a^(5/6)*b^(2/3)*sqrt(2))+1/2*arctanh(3^(1/4)*a^(1/6)*(a^(1/3)+b^(1/3)*x)*(1+sqrt(3))/(sqrt(2)*sqrt(-a-b*x^3)))*(2-sqrt(3))/(3^(3/4)*a^(5/6)*b^(2/3)*sqrt(2))-1/3*arctanh((1-sqrt(3))*sqrt(-a-b*x^3)/(3^(3/4)*sqrt(2)*sqrt(a)))*(2-sqrt(3))/(3^(3/4)*a^(5/6)*b^(2/3)*sqrt(2))],
[x/((b*x^3+2*a*(5-3*sqrt(3)))*sqrt(a+b*x^3)),x,1,-1/3*arctan(3^(1/4)*a^(1/6)*(-2*b^(1/3)*x+a^(1/3)*(1-sqrt(3)))/(sqrt(2)*sqrt(a+b*x^3)))*(2+sqrt(3))/(3^(1/4)*a^(5/6)*b^(2/3)*sqrt(2))-1/6*arctan(3^(1/4)*a^(1/6)*(a^(1/3)+b^(1/3)*x)*(1+sqrt(3))/(sqrt(2)*sqrt(a+b*x^3)))*(2+sqrt(3))/(3^(1/4)*a^(5/6)*b^(2/3)*sqrt(2))+1/2*arctanh(3^(1/4)*a^(1/6)*(a^(1/3)+b^(1/3)*x)*(1-sqrt(3))/(sqrt(2)*sqrt(a+b*x^3)))*(2+sqrt(3))/(3^(3/4)*a^(5/6)*b^(2/3)*sqrt(2))+1/3*arctanh((1+sqrt(3))*sqrt(a+b*x^3)/(3^(3/4)*sqrt(2)*sqrt(a)))*(2+sqrt(3))/(3^(3/4)*a^(5/6)*b^(2/3)*sqrt(2))],
[x/((-b*x^3+2*a*(5-3*sqrt(3)))*sqrt(a-b*x^3)),x,1,-1/3*arctan(3^(1/4)*a^(1/6)*(2*b^(1/3)*x+a^(1/3)*(1-sqrt(3)))/(sqrt(2)*sqrt(a-b*x^3)))*(2+sqrt(3))/(3^(1/4)*a^(5/6)*b^(2/3)*sqrt(2))-1/6*arctan(3^(1/4)*a^(1/6)*(a^(1/3)-b^(1/3)*x)*(1+sqrt(3))/(sqrt(2)*sqrt(a-b*x^3)))*(2+sqrt(3))/(3^(1/4)*a^(5/6)*b^(2/3)*sqrt(2))+1/2*arctanh(3^(1/4)*a^(1/6)*(a^(1/3)-b^(1/3)*x)*(1-sqrt(3))/(sqrt(2)*sqrt(a-b*x^3)))*(2+sqrt(3))/(3^(3/4)*a^(5/6)*b^(2/3)*sqrt(2))+1/3*arctanh((1+sqrt(3))*sqrt(a-b*x^3)/(3^(3/4)*sqrt(2)*sqrt(a)))*(2+sqrt(3))/(3^(3/4)*a^(5/6)*b^(2/3)*sqrt(2))],
[x/((-b*x^3+2*a*(5-3*sqrt(3)))*sqrt(-a+b*x^3)),x,1,1/2*arctan(3^(1/4)*a^(1/6)*(a^(1/3)-b^(1/3)*x)*(1-sqrt(3))/(sqrt(2)*sqrt(-a+b*x^3)))*(2+sqrt(3))/(3^(3/4)*a^(5/6)*b^(2/3)*sqrt(2))-1/3*arctan((1+sqrt(3))*sqrt(-a+b*x^3)/(3^(3/4)*sqrt(2)*sqrt(a)))*(2+sqrt(3))/(3^(3/4)*a^(5/6)*b^(2/3)*sqrt(2))-1/3*arctanh(3^(1/4)*a^(1/6)*(2*b^(1/3)*x+a^(1/3)*(1-sqrt(3)))/(sqrt(2)*sqrt(-a+b*x^3)))*(2+sqrt(3))/(3^(1/4)*a^(5/6)*b^(2/3)*sqrt(2))-1/6*arctanh(3^(1/4)*a^(1/6)*(a^(1/3)-b^(1/3)*x)*(1+sqrt(3))/(sqrt(2)*sqrt(-a+b*x^3)))*(2+sqrt(3))/(3^(1/4)*a^(5/6)*b^(2/3)*sqrt(2))],
[x/((b*x^3+2*a*(5-3*sqrt(3)))*sqrt(-a-b*x^3)),x,1,1/2*arctan(3^(1/4)*a^(1/6)*(a^(1/3)+b^(1/3)*x)*(1-sqrt(3))/(sqrt(2)*sqrt(-a-b*x^3)))*(2+sqrt(3))/(3^(3/4)*a^(5/6)*b^(2/3)*sqrt(2))-1/3*arctan((1+sqrt(3))*sqrt(-a-b*x^3)/(3^(3/4)*sqrt(2)*sqrt(a)))*(2+sqrt(3))/(3^(3/4)*a^(5/6)*b^(2/3)*sqrt(2))-1/3*arctanh(3^(1/4)*a^(1/6)*(-2*b^(1/3)*x+a^(1/3)*(1-sqrt(3)))/(sqrt(2)*sqrt(-a-b*x^3)))*(2+sqrt(3))/(3^(1/4)*a^(5/6)*b^(2/3)*sqrt(2))-1/6*arctanh(3^(1/4)*a^(1/6)*(a^(1/3)+b^(1/3)*x)*(1+sqrt(3))/(sqrt(2)*sqrt(-a-b*x^3)))*(2+sqrt(3))/(3^(1/4)*a^(5/6)*b^(2/3)*sqrt(2))],

# q>0
[x^8*sqrt(c+d*x^3)/(a+b*x^3),x,6,-2/9*(b*c+a*d)*(c+d*x^3)^(3/2)/(b^2*d^2)+2/15*(c+d*x^3)^(5/2)/(b*d^2)-2/3*a^2*arctanh(sqrt(b)*sqrt(c+d*x^3)/sqrt(b*c-a*d))*sqrt(b*c-a*d)/b^(7/2)+2/3*a^2*sqrt(c+d*x^3)/b^3],
[x^5*sqrt(c+d*x^3)/(a+b*x^3),x,5,2/9*(c+d*x^3)^(3/2)/(b*d)+2/3*a*arctanh(sqrt(b)*sqrt(c+d*x^3)/sqrt(b*c-a*d))*sqrt(b*c-a*d)/b^(5/2)-2/3*a*sqrt(c+d*x^3)/b^2],
[x^2*sqrt(c+d*x^3)/(a+b*x^3),x,4,-2/3*arctanh(sqrt(b)*sqrt(c+d*x^3)/sqrt(b*c-a*d))*sqrt(b*c-a*d)/b^(3/2)+2/3*sqrt(c+d*x^3)/b],
[sqrt(c+d*x^3)/(x*(a+b*x^3)),x,6,-2/3*arctanh(sqrt(c+d*x^3)/sqrt(c))*sqrt(c)/a+2/3*arctanh(sqrt(b)*sqrt(c+d*x^3)/sqrt(b*c-a*d))*sqrt(b*c-a*d)/(a*sqrt(b))],
[sqrt(c+d*x^3)/(x^4*(a+b*x^3)),x,7,1/3*(2*b*c-a*d)*arctanh(sqrt(c+d*x^3)/sqrt(c))/(a^2*sqrt(c))-2/3*arctanh(sqrt(b)*sqrt(c+d*x^3)/sqrt(b*c-a*d))*sqrt(b)*sqrt(b*c-a*d)/a^2-1/3*sqrt(c+d*x^3)/(a*x^3)],
[x^3*sqrt(c+d*x^3)/(a+b*x^3),x,2,1/4*x^4*AppellF1(4/3,1,-1/2,7/3,-b*x^3/a,-d*x^3/c)*sqrt(c+d*x^3)/(a*sqrt(1+d*x^3/c))],
[x*sqrt(c+d*x^3)/(a+b*x^3),x,2,1/2*x^2*AppellF1(2/3,1,-1/2,5/3,-b*x^3/a,-d*x^3/c)*sqrt(c+d*x^3)/(a*sqrt(1+d*x^3/c))],
[sqrt(c+d*x^3)/(a+b*x^3),x,2,x*AppellF1(1/3,1,-1/2,4/3,-b*x^3/a,-d*x^3/c)*sqrt(c+d*x^3)/(a*sqrt(1+d*x^3/c))],
[sqrt(c+d*x^3)/(x^2*(a+b*x^3)),x,2,-AppellF1(-1/3,1,-1/2,2/3,-b*x^3/a,-d*x^3/c)*sqrt(c+d*x^3)/(a*x*sqrt(1+d*x^3/c))],
[sqrt(c+d*x^3)/(x^3*(a+b*x^3)),x,2,-1/2*AppellF1(-2/3,1,-1/2,1/3,-b*x^3/a,-d*x^3/c)*sqrt(c+d*x^3)/(a*x^2*sqrt(1+d*x^3/c))],
[x^8*(c+d*x^3)^(3/2)/(a+b*x^3),x,7,2/9*a^2*(c+d*x^3)^(3/2)/b^3-2/15*(b*c+a*d)*(c+d*x^3)^(5/2)/(b^2*d^2)+2/21*(c+d*x^3)^(7/2)/(b*d^2)-2/3*a^2*(b*c-a*d)^(3/2)*arctanh(sqrt(b)*sqrt(c+d*x^3)/sqrt(b*c-a*d))/b^(9/2)+2/3*a^2*(b*c-a*d)*sqrt(c+d*x^3)/b^4],
[x^5*(c+d*x^3)^(3/2)/(a+b*x^3),x,6,-2/9*a*(c+d*x^3)^(3/2)/b^2+2/15*(c+d*x^3)^(5/2)/(b*d)+2/3*a*(b*c-a*d)^(3/2)*arctanh(sqrt(b)*sqrt(c+d*x^3)/sqrt(b*c-a*d))/b^(7/2)-2/3*a*(b*c-a*d)*sqrt(c+d*x^3)/b^3],
[x^2*(c+d*x^3)^(3/2)/(a+b*x^3),x,5,2/9*(c+d*x^3)^(3/2)/b-2/3*(b*c-a*d)^(3/2)*arctanh(sqrt(b)*sqrt(c+d*x^3)/sqrt(b*c-a*d))/b^(5/2)+2/3*(b*c-a*d)*sqrt(c+d*x^3)/b^2],
[(c+d*x^3)^(3/2)/(x*(a+b*x^3)),x,7,-2/3*c^(3/2)*arctanh(sqrt(c+d*x^3)/sqrt(c))/a+2/3*(b*c-a*d)^(3/2)*arctanh(sqrt(b)*sqrt(c+d*x^3)/sqrt(b*c-a*d))/(a*b^(3/2))+2/3*d*sqrt(c+d*x^3)/b],
[(c+d*x^3)^(3/2)/(x^4*(a+b*x^3)),x,7,-2/3*(b*c-a*d)^(3/2)*arctanh(sqrt(b)*sqrt(c+d*x^3)/sqrt(b*c-a*d))/(a^2*sqrt(b))+1/3*(2*b*c-3*a*d)*arctanh(sqrt(c+d*x^3)/sqrt(c))*sqrt(c)/a^2-1/3*c*sqrt(c+d*x^3)/(a*x^3)],
[x^3*(c+d*x^3)^(3/2)/(a+b*x^3),x,2,1/4*c*x^4*AppellF1(4/3,1,-3/2,7/3,-b*x^3/a,-d*x^3/c)*sqrt(c+d*x^3)/(a*sqrt(1+d*x^3/c))],
[x*(c+d*x^3)^(3/2)/(a+b*x^3),x,2,1/2*c*x^2*AppellF1(2/3,1,-3/2,5/3,-b*x^3/a,-d*x^3/c)*sqrt(c+d*x^3)/(a*sqrt(1+d*x^3/c))],
[(c+d*x^3)^(3/2)/(a+b*x^3),x,2,c*x*AppellF1(1/3,1,-3/2,4/3,-b*x^3/a,-d*x^3/c)*sqrt(c+d*x^3)/(a*sqrt(1+d*x^3/c))],
[(c+d*x^3)^(3/2)/(x^2*(a+b*x^3)),x,2,-c*AppellF1(-1/3,1,-3/2,2/3,-b*x^3/a,-d*x^3/c)*sqrt(c+d*x^3)/(a*x*sqrt(1+d*x^3/c))],
[(c+d*x^3)^(3/2)/(x^3*(a+b*x^3)),x,2,-1/2*c*AppellF1(-2/3,1,-3/2,1/3,-b*x^3/a,-d*x^3/c)*sqrt(c+d*x^3)/(a*x^2*sqrt(1+d*x^3/c))],

# q<0
[x^8/((a+b*x^3)*sqrt(c+d*x^3)),x,5,2/9*(c+d*x^3)^(3/2)/(b*d^2)-2/3*a^2*arctanh(sqrt(b)*sqrt(c+d*x^3)/sqrt(b*c-a*d))/(b^(5/2)*sqrt(b*c-a*d))-2/3*(b*c+a*d)*sqrt(c+d*x^3)/(b^2*d^2)],
[x^5/((a+b*x^3)*sqrt(c+d*x^3)),x,4,2/3*a*arctanh(sqrt(b)*sqrt(c+d*x^3)/sqrt(b*c-a*d))/(b^(3/2)*sqrt(b*c-a*d))+2/3*sqrt(c+d*x^3)/(b*d)],
[x^2/((a+b*x^3)*sqrt(c+d*x^3)),x,3,-2/3*arctanh(sqrt(b)*sqrt(c+d*x^3)/sqrt(b*c-a*d))/(sqrt(b)*sqrt(b*c-a*d))],
[1/(x*(a+b*x^3)*sqrt(c+d*x^3)),x,6,-2/3*arctanh(sqrt(c+d*x^3)/sqrt(c))/(a*sqrt(c))+2/3*arctanh(sqrt(b)*sqrt(c+d*x^3)/sqrt(b*c-a*d))*sqrt(b)/(a*sqrt(b*c-a*d))],
[1/(x^4*(a+b*x^3)*sqrt(c+d*x^3)),x,7,1/3*(2*b*c+a*d)*arctanh(sqrt(c+d*x^3)/sqrt(c))/(a^2*c^(3/2))-2/3*b^(3/2)*arctanh(sqrt(b)*sqrt(c+d*x^3)/sqrt(b*c-a*d))/(a^2*sqrt(b*c-a*d))-1/3*sqrt(c+d*x^3)/(a*c*x^3)],
[x^3/((a+b*x^3)*sqrt(c+d*x^3)),x,2,1/4*x^4*AppellF1(4/3,1,1/2,7/3,-b*x^3/a,-d*x^3/c)*sqrt(1+d*x^3/c)/(a*sqrt(c+d*x^3))],
[x/((a+b*x^3)*sqrt(c+d*x^3)),x,2,1/2*x^2*AppellF1(2/3,1,1/2,5/3,-b*x^3/a,-d*x^3/c)*sqrt(1+d*x^3/c)/(a*sqrt(c+d*x^3))],
[1/((a+b*x^3)*sqrt(c+d*x^3)),x,2,x*AppellF1(1/3,1,1/2,4/3,-b*x^3/a,-d*x^3/c)*sqrt(1+d*x^3/c)/(a*sqrt(c+d*x^3))],
[1/(x^2*(a+b*x^3)*sqrt(c+d*x^3)),x,2,-AppellF1(-1/3,1,1/2,2/3,-b*x^3/a,-d*x^3/c)*sqrt(1+d*x^3/c)/(a*x*sqrt(c+d*x^3))],
[1/(x^3*(a+b*x^3)*sqrt(c+d*x^3)),x,2,-1/2*AppellF1(-2/3,1,1/2,1/3,-b*x^3/a,-d*x^3/c)*sqrt(1+d*x^3/c)/(a*x^2*sqrt(c+d*x^3))],
[x^8/((a+b*x^3)*(c+d*x^3)^(3/2)),x,5,-2/3*a^2*arctanh(sqrt(b)*sqrt(c+d*x^3)/sqrt(b*c-a*d))/(b^(3/2)*(b*c-a*d)^(3/2))+2/3*c^2/(d^2*(b*c-a*d)*sqrt(c+d*x^3))+2/3*sqrt(c+d*x^3)/(b*d^2)],
[x^5/((a+b*x^3)*(c+d*x^3)^(3/2)),x,4,2/3*a*arctanh(sqrt(b)*sqrt(c+d*x^3)/sqrt(b*c-a*d))/((b*c-a*d)^(3/2)*sqrt(b))-2/3*c/(d*(b*c-a*d)*sqrt(c+d*x^3))],
[x^2/((a+b*x^3)*(c+d*x^3)^(3/2)),x,4,-2/3*arctanh(sqrt(b)*sqrt(c+d*x^3)/sqrt(b*c-a*d))*sqrt(b)/(b*c-a*d)^(3/2)+2/3/((b*c-a*d)*sqrt(c+d*x^3))],
[1/(x*(a+b*x^3)*(c+d*x^3)^(3/2)),x,7,-2/3*arctanh(sqrt(c+d*x^3)/sqrt(c))/(a*c^(3/2))+2/3*b^(3/2)*arctanh(sqrt(b)*sqrt(c+d*x^3)/sqrt(b*c-a*d))/(a*(b*c-a*d)^(3/2))-2/3*d/(c*(b*c-a*d)*sqrt(c+d*x^3))],
[1/(x^4*(a+b*x^3)*(c+d*x^3)^(3/2)),x,8,1/3*(2*b*c+3*a*d)*arctanh(sqrt(c+d*x^3)/sqrt(c))/(a^2*c^(5/2))-2/3*b^(5/2)*arctanh(sqrt(b)*sqrt(c+d*x^3)/sqrt(b*c-a*d))/(a^2*(b*c-a*d)^(3/2))-1/3*d*(b*c-3*a*d)/(a*c^2*(b*c-a*d)*sqrt(c+d*x^3))+(-1/3)/(a*c*x^3*sqrt(c+d*x^3))],
[x^3/((a+b*x^3)*(c+d*x^3)^(3/2)),x,2,1/4*x^4*AppellF1(4/3,1,3/2,7/3,-b*x^3/a,-d*x^3/c)*sqrt(1+d*x^3/c)/(a*c*sqrt(c+d*x^3))],
[x/((a+b*x^3)*(c+d*x^3)^(3/2)),x,2,1/2*x^2*AppellF1(2/3,1,3/2,5/3,-b*x^3/a,-d*x^3/c)*sqrt(1+d*x^3/c)/(a*c*sqrt(c+d*x^3))],
[1/((a+b*x^3)*(c+d*x^3)^(3/2)),x,2,x*AppellF1(1/3,1,3/2,4/3,-b*x^3/a,-d*x^3/c)*sqrt(1+d*x^3/c)/(a*c*sqrt(c+d*x^3))],
[1/(x^2*(a+b*x^3)*(c+d*x^3)^(3/2)),x,2,-AppellF1(-1/3,1,3/2,2/3,-b*x^3/a,-d*x^3/c)*sqrt(1+d*x^3/c)/(a*c*x*sqrt(c+d*x^3))],
[1/(x^3*(a+b*x^3)*(c+d*x^3)^(3/2)),x,2,-1/2*AppellF1(-2/3,1,3/2,1/3,-b*x^3/a,-d*x^3/c)*sqrt(1+d*x^3/c)/(a*c*x^2*sqrt(c+d*x^3))],

# Integrands of the form x^m (c+d x^3)^(q/2) / (a+b x^3)^2

# q>0 when 8 b c+a d=0
[x^11*sqrt(c+d*x^3)/(8*c-d*x^3)^2,x,6,-3968/9*c^(5/2)*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))/d^4+7/15*x^6*sqrt(c+d*x^3)/d^2+1/3*x^9*sqrt(c+d*x^3)/(d*(8*c-d*x^3))+2/15*c*(1146*c+47*d*x^3)*sqrt(c+d*x^3)/d^4],
[x^8*sqrt(c+d*x^3)/(8*c-d*x^3)^2,x,6,2/9*(c+d*x^3)^(3/2)/d^3+64/27*c*(c+d*x^3)^(3/2)/(d^3*(8*c-d*x^3))-352/9*c^(3/2)*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))/d^3+352/27*c*sqrt(c+d*x^3)/d^3],
[x^5*sqrt(c+d*x^3)/(8*c-d*x^3)^2,x,5,8/27*(c+d*x^3)^(3/2)/(d^2*(8*c-d*x^3))-26/9*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))*sqrt(c)/d^2+26/27*sqrt(c+d*x^3)/d^2],
[x^2*sqrt(c+d*x^3)/(8*c-d*x^3)^2,x,4,-1/9*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))/(d*sqrt(c))+1/3*sqrt(c+d*x^3)/(d*(8*c-d*x^3))],
[sqrt(c+d*x^3)/(x*(8*c-d*x^3)^2),x,7,5/288*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))/c^(3/2)-1/96*arctanh(sqrt(c+d*x^3)/sqrt(c))/c^(3/2)+1/24*sqrt(c+d*x^3)/(c*(8*c-d*x^3))],
[sqrt(c+d*x^3)/(x^4*(8*c-d*x^3)^2),x,8,7/1152*d*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))/c^(5/2)-1/128*d*arctanh(sqrt(c+d*x^3)/sqrt(c))/c^(5/2)+1/96*d*sqrt(c+d*x^3)/(c^2*(8*c-d*x^3))-1/24*sqrt(c+d*x^3)/(c*x^3*(8*c-d*x^3))],
[sqrt(c+d*x^3)/(x^7*(8*c-d*x^3)^2),x,9,23/18432*d^2*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))/c^(7/2)-1/2048*d^2*arctanh(sqrt(c+d*x^3)/sqrt(c))/c^(7/2)+5/1536*d^2*sqrt(c+d*x^3)/(c^3*(8*c-d*x^3))-1/48*sqrt(c+d*x^3)/(c*x^6*(8*c-d*x^3))-7/384*d*sqrt(c+d*x^3)/(c^2*x^3*(8*c-d*x^3))],
[x^7*sqrt(c+d*x^3)/(8*c-d*x^3)^2,x,15,-76/9*c^(7/6)*arctanh(1/3*(c^(1/3)+d^(1/3)*x)^2/(c^(1/6)*sqrt(c+d*x^3)))/d^(8/3)+76/9*c^(7/6)*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))/d^(8/3)+76/3*c^(7/6)*arctan(c^(1/6)*(c^(1/3)+d^(1/3)*x)*sqrt(3)/sqrt(c+d*x^3))/(d^(8/3)*sqrt(3))+13/21*x^2*sqrt(c+d*x^3)/d^2+1/3*x^5*sqrt(c+d*x^3)/(d*(8*c-d*x^3))+746/21*c*sqrt(c+d*x^3)/(d^(8/3)*(d^(1/3)*x+c^(1/3)*(1+sqrt(3))))+746/21*c^(4/3)*(c^(1/3)+d^(1/3)*x)*EllipticF((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2)*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(3^(1/4)*d^(8/3)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))-373/7*c^(4/3)*(c^(1/3)+d^(1/3)*x)*EllipticE((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(3^(3/4)*d^(8/3)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))],
[x^4*sqrt(c+d*x^3)/(8*c-d*x^3)^2,x,14,-5/9*c^(1/6)*arctanh(1/3*(c^(1/3)+d^(1/3)*x)^2/(c^(1/6)*sqrt(c+d*x^3)))/d^(5/3)+5/9*c^(1/6)*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))/d^(5/3)+5/3*c^(1/6)*arctan(c^(1/6)*(c^(1/3)+d^(1/3)*x)*sqrt(3)/sqrt(c+d*x^3))/(d^(5/3)*sqrt(3))+1/3*x^2*sqrt(c+d*x^3)/(d*(8*c-d*x^3))+7/3*sqrt(c+d*x^3)/(d^(5/3)*(d^(1/3)*x+c^(1/3)*(1+sqrt(3))))+7/3*c^(1/3)*(c^(1/3)+d^(1/3)*x)*EllipticF((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2)*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(3^(1/4)*d^(5/3)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))-7/2*c^(1/3)*(c^(1/3)+d^(1/3)*x)*EllipticE((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(3^(3/4)*d^(5/3)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))],
[x*sqrt(c+d*x^3)/(8*c-d*x^3)^2,x,14,-1/144*arctanh(1/3*(c^(1/3)+d^(1/3)*x)^2/(c^(1/6)*sqrt(c+d*x^3)))/(c^(5/6)*d^(2/3))+1/144*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))/(c^(5/6)*d^(2/3))+1/48*arctan(c^(1/6)*(c^(1/3)+d^(1/3)*x)*sqrt(3)/sqrt(c+d*x^3))/(c^(5/6)*d^(2/3)*sqrt(3))+1/24*x^2*sqrt(c+d*x^3)/(c*(8*c-d*x^3))+1/24*sqrt(c+d*x^3)/(c*d^(2/3)*(d^(1/3)*x+c^(1/3)*(1+sqrt(3))))+1/12*(c^(1/3)+d^(1/3)*x)*EllipticF((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(3^(1/4)*c^(2/3)*d^(2/3)*sqrt(2)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))-1/16*(c^(1/3)+d^(1/3)*x)*EllipticE((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(3^(3/4)*c^(2/3)*d^(2/3)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))],
[sqrt(c+d*x^3)/(x^2*(8*c-d*x^3)^2),x,15,1/144*d^(1/3)*arctanh(1/3*(c^(1/3)+d^(1/3)*x)^2/(c^(1/6)*sqrt(c+d*x^3)))/c^(11/6)-1/144*d^(1/3)*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))/c^(11/6)-1/48*d^(1/3)*arctan(c^(1/6)*(c^(1/3)+d^(1/3)*x)*sqrt(3)/sqrt(c+d*x^3))/(c^(11/6)*sqrt(3))-1/48*sqrt(c+d*x^3)/(c^2*x)+1/24*sqrt(c+d*x^3)/(c*x*(8*c-d*x^3))+1/48*d^(1/3)*sqrt(c+d*x^3)/(c^2*(d^(1/3)*x+c^(1/3)*(1+sqrt(3))))+1/24*d^(1/3)*(c^(1/3)+d^(1/3)*x)*EllipticF((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(3^(1/4)*c^(5/3)*sqrt(2)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))-1/32*d^(1/3)*(c^(1/3)+d^(1/3)*x)*EllipticE((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(3^(3/4)*c^(5/3)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))],
[sqrt(c+d*x^3)/(x^5*(8*c-d*x^3)^2),x,16,17/9216*d^(4/3)*arctanh(1/3*(c^(1/3)+d^(1/3)*x)^2/(c^(1/6)*sqrt(c+d*x^3)))/c^(17/6)-17/9216*d^(4/3)*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))/c^(17/6)-17/3072*d^(4/3)*arctan(c^(1/6)*(c^(1/3)+d^(1/3)*x)*sqrt(3)/sqrt(c+d*x^3))/(c^(17/6)*sqrt(3))-7/768*sqrt(c+d*x^3)/(c^2*x^4)-1/96*d*sqrt(c+d*x^3)/(c^3*x)+1/24*sqrt(c+d*x^3)/(c*x^4*(8*c-d*x^3))+1/96*d^(4/3)*sqrt(c+d*x^3)/(c^3*(d^(1/3)*x+c^(1/3)*(1+sqrt(3))))+1/48*d^(4/3)*(c^(1/3)+d^(1/3)*x)*EllipticF((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(3^(1/4)*c^(8/3)*sqrt(2)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))-1/64*d^(4/3)*(c^(1/3)+d^(1/3)*x)*EllipticE((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(3^(3/4)*c^(8/3)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))],
[sqrt(c+d*x^3)/(x^8*(8*c-d*x^3)^2),x,17,13/36864*d^(7/3)*arctanh(1/3*(c^(1/3)+d^(1/3)*x)^2/(c^(1/6)*sqrt(c+d*x^3)))/c^(23/6)-13/36864*d^(7/3)*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))/c^(23/6)-13/12288*d^(7/3)*arctan(c^(1/6)*(c^(1/3)+d^(1/3)*x)*sqrt(3)/sqrt(c+d*x^3))/(c^(23/6)*sqrt(3))-5/672*sqrt(c+d*x^3)/(c^2*x^7)-53/21504*d*sqrt(c+d*x^3)/(c^3*x^4)-1/5376*d^2*sqrt(c+d*x^3)/(c^4*x)+1/24*sqrt(c+d*x^3)/(c*x^7*(8*c-d*x^3))+1/5376*d^(7/3)*sqrt(c+d*x^3)/(c^4*(d^(1/3)*x+c^(1/3)*(1+sqrt(3))))+1/2688*d^(7/3)*(c^(1/3)+d^(1/3)*x)*EllipticF((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(3^(1/4)*c^(11/3)*sqrt(2)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))-1/3584*d^(7/3)*(c^(1/3)+d^(1/3)*x)*EllipticE((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(3^(3/4)*c^(11/3)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))],
[x^11*(c+d*x^3)^(3/2)/(8*c-d*x^3)^2,x,7,3/7*x^6*(c+d*x^3)^(3/2)/d^2+1/3*x^9*(c+d*x^3)^(3/2)/(d*(8*c-d*x^3))+2/21*c*(c+d*x^3)^(3/2)*(694*c+51*d*x^3)/d^4-4992*c^(7/2)*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))/d^4+1664*c^3*sqrt(c+d*x^3)/d^4],
[x^8*(c+d*x^3)^(3/2)/(8*c-d*x^3)^2,x,7,160/27*c*(c+d*x^3)^(3/2)/d^3+2/15*(c+d*x^3)^(5/2)/d^3+64/27*c*(c+d*x^3)^(5/2)/(d^3*(8*c-d*x^3))-480*c^(5/2)*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))/d^3+160*c^2*sqrt(c+d*x^3)/d^3],
[x^5*(c+d*x^3)^(3/2)/(8*c-d*x^3)^2,x,6,14/27*(c+d*x^3)^(3/2)/d^2+8/27*(c+d*x^3)^(5/2)/(d^2*(8*c-d*x^3))-42*c^(3/2)*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))/d^2+14*c*sqrt(c+d*x^3)/d^2],
[x^2*(c+d*x^3)^(3/2)/(8*c-d*x^3)^2,x,5,1/3*(c+d*x^3)^(3/2)/(d*(8*c-d*x^3))-3*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))*sqrt(c)/d+sqrt(c+d*x^3)/d],
[(c+d*x^3)^(3/2)/(x*(8*c-d*x^3)^2),x,7,-3/32*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))/sqrt(c)-1/96*arctanh(sqrt(c+d*x^3)/sqrt(c))/sqrt(c)+3/8*sqrt(c+d*x^3)/(8*c-d*x^3)],
[(c+d*x^3)^(3/2)/(x^4*(8*c-d*x^3)^2),x,8,3/128*d*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))/c^(3/2)-7/384*d*arctanh(sqrt(c+d*x^3)/sqrt(c))/c^(3/2)+5/96*d*sqrt(c+d*x^3)/(c*(8*c-d*x^3))-1/24*sqrt(c+d*x^3)/(x^3*(8*c-d*x^3))],
[(c+d*x^3)^(3/2)/(x^7*(8*c-d*x^3)^2),x,9,15/2048*d^2*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))/c^(5/2)-17/2048*d^2*arctanh(sqrt(c+d*x^3)/sqrt(c))/c^(5/2)+7/512*d^2*sqrt(c+d*x^3)/(c^2*(8*c-d*x^3))-1/48*sqrt(c+d*x^3)/(x^6*(8*c-d*x^3))-23/384*d*sqrt(c+d*x^3)/(c*x^3*(8*c-d*x^3))],
[x^7*(c+d*x^3)^(3/2)/(8*c-d*x^3)^2,x,16,1/3*x^5*(c+d*x^3)^(3/2)/(d*(8*c-d*x^3))-108*c^(13/6)*arctanh(1/3*(c^(1/3)+d^(1/3)*x)^2/(c^(1/6)*sqrt(c+d*x^3)))/d^(8/3)+108*c^(13/6)*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))/d^(8/3)+108*c^(13/6)*arctan(c^(1/6)*(c^(1/3)+d^(1/3)*x)*sqrt(3)/sqrt(c+d*x^3))*sqrt(3)/d^(8/3)+103/13*c*x^2*sqrt(c+d*x^3)/d^2+19/39*x^5*sqrt(c+d*x^3)/d+5906/13*c^2*sqrt(c+d*x^3)/(d^(8/3)*(d^(1/3)*x+c^(1/3)*(1+sqrt(3))))+5906/13*c^(7/3)*(c^(1/3)+d^(1/3)*x)*EllipticF((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2)*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(3^(1/4)*d^(8/3)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))-2953/13*3^(1/4)*c^(7/3)*(c^(1/3)+d^(1/3)*x)*EllipticE((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(d^(8/3)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))],
[x^4*(c+d*x^3)^(3/2)/(8*c-d*x^3)^2,x,15,1/3*x^2*(c+d*x^3)^(3/2)/(d*(8*c-d*x^3))-9*c^(7/6)*arctanh(1/3*(c^(1/3)+d^(1/3)*x)^2/(c^(1/6)*sqrt(c+d*x^3)))/d^(5/3)+9*c^(7/6)*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))/d^(5/3)+9*c^(7/6)*arctan(c^(1/6)*(c^(1/3)+d^(1/3)*x)*sqrt(3)/sqrt(c+d*x^3))*sqrt(3)/d^(5/3)+13/21*x^2*sqrt(c+d*x^3)/d+265/7*c*sqrt(c+d*x^3)/(d^(5/3)*(d^(1/3)*x+c^(1/3)*(1+sqrt(3))))+265/7*c^(4/3)*(c^(1/3)+d^(1/3)*x)*EllipticF((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2)*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(3^(1/4)*d^(5/3)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))-265/14*3^(1/4)*c^(4/3)*(c^(1/3)+d^(1/3)*x)*EllipticE((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(d^(5/3)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))],
[x*(c+d*x^3)^(3/2)/(8*c-d*x^3)^2,x,14,-9/16*c^(1/6)*arctanh(1/3*(c^(1/3)+d^(1/3)*x)^2/(c^(1/6)*sqrt(c+d*x^3)))/d^(2/3)+9/16*c^(1/6)*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))/d^(2/3)+9/16*c^(1/6)*arctan(c^(1/6)*(c^(1/3)+d^(1/3)*x)*sqrt(3)/sqrt(c+d*x^3))*sqrt(3)/d^(2/3)+3/8*x^2*sqrt(c+d*x^3)/(8*c-d*x^3)+19/8*sqrt(c+d*x^3)/(d^(2/3)*(d^(1/3)*x+c^(1/3)*(1+sqrt(3))))+19/4*c^(1/3)*(c^(1/3)+d^(1/3)*x)*EllipticF((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(3^(1/4)*d^(2/3)*sqrt(2)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))-19/16*3^(1/4)*c^(1/3)*(c^(1/3)+d^(1/3)*x)*EllipticE((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(d^(2/3)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))],
[(c+d*x^3)^(3/2)/(x^2*(8*c-d*x^3)^2),x,6,-1/16*sqrt(c+d*x^3)/(c*x)+3/8*sqrt(c+d*x^3)/(x*(8*c-d*x^3))+1/16*d^(1/3)*sqrt(c+d*x^3)/(c*(d^(1/3)*x+c^(1/3)*(1+sqrt(3))))+1/8*d^(1/3)*(c^(1/3)+d^(1/3)*x)*EllipticF((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(3^(1/4)*c^(2/3)*sqrt(2)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))-1/32*3^(1/4)*d^(1/3)*(c^(1/3)+d^(1/3)*x)*EllipticE((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(c^(2/3)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))],
[(c+d*x^3)^(3/2)/(x^5*(8*c-d*x^3)^2),x,16,9/1024*d^(4/3)*arctanh(1/3*(c^(1/3)+d^(1/3)*x)^2/(c^(1/6)*sqrt(c+d*x^3)))/c^(11/6)-9/1024*d^(4/3)*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))/c^(11/6)-9/1024*d^(4/3)*arctan(c^(1/6)*(c^(1/3)+d^(1/3)*x)*sqrt(3)/sqrt(c+d*x^3))*sqrt(3)/c^(11/6)-13/256*sqrt(c+d*x^3)/(c*x^4)-1/32*d*sqrt(c+d*x^3)/(c^2*x)+3/8*sqrt(c+d*x^3)/(x^4*(8*c-d*x^3))+1/32*d^(4/3)*sqrt(c+d*x^3)/(c^2*(d^(1/3)*x+c^(1/3)*(1+sqrt(3))))+1/16*d^(4/3)*(c^(1/3)+d^(1/3)*x)*EllipticF((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(3^(1/4)*c^(5/3)*sqrt(2)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))-1/64*3^(1/4)*d^(4/3)*(c^(1/3)+d^(1/3)*x)*EllipticE((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(c^(5/3)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))],
[(c+d*x^3)^(3/2)/(x^8*(8*c-d*x^3)^2),x,17,9/4096*d^(7/3)*arctanh(1/3*(c^(1/3)+d^(1/3)*x)^2/(c^(1/6)*sqrt(c+d*x^3)))/c^(17/6)-9/4096*d^(7/3)*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))/c^(17/6)-9/4096*d^(7/3)*arctan(c^(1/6)*(c^(1/3)+d^(1/3)*x)*sqrt(3)/sqrt(c+d*x^3))*sqrt(3)/c^(17/6)-11/224*sqrt(c+d*x^3)/(c*x^7)-83/7168*d*sqrt(c+d*x^3)/(c^2*x^4)-19/1792*d^2*sqrt(c+d*x^3)/(c^3*x)+3/8*sqrt(c+d*x^3)/(x^7*(8*c-d*x^3))+19/1792*d^(7/3)*sqrt(c+d*x^3)/(c^3*(d^(1/3)*x+c^(1/3)*(1+sqrt(3))))+19/896*d^(7/3)*(c^(1/3)+d^(1/3)*x)*EllipticF((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(3^(1/4)*c^(8/3)*sqrt(2)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))-19/3584*3^(1/4)*d^(7/3)*(c^(1/3)+d^(1/3)*x)*EllipticE((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(c^(8/3)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))],

# q<0 when 8 b c+a d=0
[x^11/((8*c-d*x^3)^2*sqrt(c+d*x^3)),x,5,-2944/81*c^(3/2)*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))/d^4+8/27*x^6*sqrt(c+d*x^3)/(d^2*(8*c-d*x^3))+2/27*(170*c+7*d*x^3)*sqrt(c+d*x^3)/d^4],
[x^8/((8*c-d*x^3)^2*sqrt(c+d*x^3)),x,5,-224/81*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))*sqrt(c)/d^3+2/3*sqrt(c+d*x^3)/d^3+64/27*c*sqrt(c+d*x^3)/(d^3*(8*c-d*x^3))],
[x^5/((8*c-d*x^3)^2*sqrt(c+d*x^3)),x,4,-10/81*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))/(d^2*sqrt(c))+8/27*sqrt(c+d*x^3)/(d^2*(8*c-d*x^3))],
[x^2/((8*c-d*x^3)^2*sqrt(c+d*x^3)),x,4,1/81*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))/(c^(3/2)*d)+1/27*sqrt(c+d*x^3)/(c*d*(8*c-d*x^3))],
[1/(x*(8*c-d*x^3)^2*sqrt(c+d*x^3)),x,7,13/2592*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))/c^(5/2)-1/96*arctanh(sqrt(c+d*x^3)/sqrt(c))/c^(5/2)+1/216*sqrt(c+d*x^3)/(c^2*(8*c-d*x^3))],
[1/(x^4*(8*c-d*x^3)^2*sqrt(c+d*x^3)),x,8,11/10368*d*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))/c^(7/2)+1/384*d*arctanh(sqrt(c+d*x^3)/sqrt(c))/c^(7/2)+5/864*d*sqrt(c+d*x^3)/(c^3*(8*c-d*x^3))-1/24*sqrt(c+d*x^3)/(c^2*x^3*(8*c-d*x^3))],
[1/(x^7*(8*c-d*x^3)^2*sqrt(c+d*x^3)),x,9,31/165888*d^2*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))/c^(9/2)-19/6144*d^2*arctanh(sqrt(c+d*x^3)/sqrt(c))/c^(9/2)-35/13824*d^2*sqrt(c+d*x^3)/(c^4*(8*c-d*x^3))-1/48*sqrt(c+d*x^3)/(c^2*x^6*(8*c-d*x^3))+3/128*d*sqrt(c+d*x^3)/(c^3*x^3*(8*c-d*x^3))],
[x^7/((8*c-d*x^3)^2*sqrt(c+d*x^3)),x,14,-44/81*c^(1/6)*arctanh(1/3*(c^(1/3)+d^(1/3)*x)^2/(c^(1/6)*sqrt(c+d*x^3)))/d^(8/3)+44/81*c^(1/6)*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))/d^(8/3)+44/27*c^(1/6)*arctan(c^(1/6)*(c^(1/3)+d^(1/3)*x)*sqrt(3)/sqrt(c+d*x^3))/(d^(8/3)*sqrt(3))+8/27*x^2*sqrt(c+d*x^3)/(d^2*(8*c-d*x^3))+62/27*sqrt(c+d*x^3)/(d^(8/3)*(d^(1/3)*x+c^(1/3)*(1+sqrt(3))))+62/27*c^(1/3)*(c^(1/3)+d^(1/3)*x)*EllipticF((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2)*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(3^(1/4)*d^(8/3)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))-31/9*c^(1/3)*(c^(1/3)+d^(1/3)*x)*EllipticE((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(3^(3/4)*d^(8/3)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))],
[x^4/((8*c-d*x^3)^2*sqrt(c+d*x^3)),x,14,-1/81*arctanh(1/3*(c^(1/3)+d^(1/3)*x)^2/(c^(1/6)*sqrt(c+d*x^3)))/(c^(5/6)*d^(5/3))+1/81*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))/(c^(5/6)*d^(5/3))+1/27*arctan(c^(1/6)*(c^(1/3)+d^(1/3)*x)*sqrt(3)/sqrt(c+d*x^3))/(c^(5/6)*d^(5/3)*sqrt(3))+1/27*x^2*sqrt(c+d*x^3)/(c*d*(8*c-d*x^3))+1/27*sqrt(c+d*x^3)/(c*d^(5/3)*(d^(1/3)*x+c^(1/3)*(1+sqrt(3))))+1/27*(c^(1/3)+d^(1/3)*x)*EllipticF((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2)*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(3^(1/4)*c^(2/3)*d^(5/3)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))-1/18*(c^(1/3)+d^(1/3)*x)*EllipticE((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(3^(3/4)*c^(2/3)*d^(5/3)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))],
[x/((8*c-d*x^3)^2*sqrt(c+d*x^3)),x,14,7/1296*arctanh(1/3*(c^(1/3)+d^(1/3)*x)^2/(c^(1/6)*sqrt(c+d*x^3)))/(c^(11/6)*d^(2/3))-7/1296*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))/(c^(11/6)*d^(2/3))-7/432*arctan(c^(1/6)*(c^(1/3)+d^(1/3)*x)*sqrt(3)/sqrt(c+d*x^3))/(c^(11/6)*d^(2/3)*sqrt(3))+1/216*x^2*sqrt(c+d*x^3)/(c^2*(8*c-d*x^3))+1/216*sqrt(c+d*x^3)/(c^2*d^(2/3)*(d^(1/3)*x+c^(1/3)*(1+sqrt(3))))+1/108*(c^(1/3)+d^(1/3)*x)*EllipticF((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(3^(1/4)*c^(5/3)*d^(2/3)*sqrt(2)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))-1/144*(c^(1/3)+d^(1/3)*x)*EllipticE((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(3^(3/4)*c^(5/3)*d^(2/3)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))],
[1/(x^2*(8*c-d*x^3)^2*sqrt(c+d*x^3)),x,15,1/648*d^(1/3)*arctanh(1/3*(c^(1/3)+d^(1/3)*x)^2/(c^(1/6)*sqrt(c+d*x^3)))/c^(17/6)-1/648*d^(1/3)*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))/c^(17/6)-1/216*d^(1/3)*arctan(c^(1/6)*(c^(1/3)+d^(1/3)*x)*sqrt(3)/sqrt(c+d*x^3))/(c^(17/6)*sqrt(3))-7/432*sqrt(c+d*x^3)/(c^3*x)+1/216*sqrt(c+d*x^3)/(c^2*x*(8*c-d*x^3))+7/432*d^(1/3)*sqrt(c+d*x^3)/(c^3*(d^(1/3)*x+c^(1/3)*(1+sqrt(3))))+7/216*d^(1/3)*(c^(1/3)+d^(1/3)*x)*EllipticF((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(3^(1/4)*c^(8/3)*sqrt(2)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))-7/288*d^(1/3)*(c^(1/3)+d^(1/3)*x)*EllipticE((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(3^(3/4)*c^(8/3)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))],
[1/(x^5*(8*c-d*x^3)^2*sqrt(c+d*x^3)),x,16,25/82944*d^(4/3)*arctanh(1/3*(c^(1/3)+d^(1/3)*x)^2/(c^(1/6)*sqrt(c+d*x^3)))/c^(23/6)-25/82944*d^(4/3)*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))/c^(23/6)-25/27648*d^(4/3)*arctan(c^(1/6)*(c^(1/3)+d^(1/3)*x)*sqrt(3)/sqrt(c+d*x^3))/(c^(23/6)*sqrt(3))-31/6912*sqrt(c+d*x^3)/(c^3*x^4)+5/864*d*sqrt(c+d*x^3)/(c^4*x)+1/216*sqrt(c+d*x^3)/(c^2*x^4*(8*c-d*x^3))-5/864*d^(4/3)*sqrt(c+d*x^3)/(c^4*(d^(1/3)*x+c^(1/3)*(1+sqrt(3))))-5/432*d^(4/3)*(c^(1/3)+d^(1/3)*x)*EllipticF((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(3^(1/4)*c^(11/3)*sqrt(2)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))+5/576*d^(4/3)*(c^(1/3)+d^(1/3)*x)*EllipticE((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(3^(3/4)*c^(11/3)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))],
[1/(x^8*(8*c-d*x^3)^2*sqrt(c+d*x^3)),x,17,17/331776*d^(7/3)*arctanh(1/3*(c^(1/3)+d^(1/3)*x)^2/(c^(1/6)*sqrt(c+d*x^3)))/c^(29/6)-17/331776*d^(7/3)*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))/c^(29/6)-17/110592*d^(7/3)*arctan(c^(1/6)*(c^(1/3)+d^(1/3)*x)*sqrt(3)/sqrt(c+d*x^3))/(c^(29/6)*sqrt(3))-17/6048*sqrt(c+d*x^3)/(c^3*x^7)+391/193536*d*sqrt(c+d*x^3)/(c^4*x^4)-289/48384*d^2*sqrt(c+d*x^3)/(c^5*x)+1/216*sqrt(c+d*x^3)/(c^2*x^7*(8*c-d*x^3))+289/48384*d^(7/3)*sqrt(c+d*x^3)/(c^5*(d^(1/3)*x+c^(1/3)*(1+sqrt(3))))+289/24192*d^(7/3)*(c^(1/3)+d^(1/3)*x)*EllipticF((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(3^(1/4)*c^(14/3)*sqrt(2)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))-289/32256*d^(7/3)*(c^(1/3)+d^(1/3)*x)*EllipticE((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(3^(3/4)*c^(14/3)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))],
[x^6/((8*c-d*x^3)^2*sqrt(c+d*x^3)),x,2,1/448*x^7*AppellF1(7/3,2,1/2,10/3,1/8*d*x^3/c,-d*x^3/c)*sqrt(1+d*x^3/c)/(c^2*sqrt(c+d*x^3))],
[x^3/((8*c-d*x^3)^2*sqrt(c+d*x^3)),x,2,1/256*x^4*AppellF1(4/3,2,1/2,7/3,1/8*d*x^3/c,-d*x^3/c)*sqrt(1+d*x^3/c)/(c^2*sqrt(c+d*x^3))],
[1/((8*c-d*x^3)^2*sqrt(c+d*x^3)),x,2,1/64*x*AppellF1(1/3,2,1/2,4/3,1/8*d*x^3/c,-d*x^3/c)*sqrt(1+d*x^3/c)/(c^2*sqrt(c+d*x^3))],
[1/(x^3*(8*c-d*x^3)^2*sqrt(c+d*x^3)),x,2,-1/128*AppellF1(-2/3,2,1/2,1/3,1/8*d*x^3/c,-d*x^3/c)*sqrt(1+d*x^3/c)/(c^2*x^2*sqrt(c+d*x^3))],
[1/(x^6*(8*c-d*x^3)^2*sqrt(c+d*x^3)),x,2,-1/320*AppellF1(-5/3,2,1/2,-2/3,1/8*d*x^3/c,-d*x^3/c)*sqrt(1+d*x^3/c)/(c^2*x^5*sqrt(c+d*x^3))],
[x^11/((8*c-d*x^3)^2*(c+d*x^3)^(3/2)),x,5,-640/243*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))*sqrt(c)/d^4+8/27*x^6/(d^2*(8*c-d*x^3)*sqrt(c+d*x^3))+2/81*(38*c+39*d*x^3)/(d^4*sqrt(c+d*x^3))],
[x^8/((8*c-d*x^3)^2*(c+d*x^3)^(3/2)),x,5,-32/243*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))/(d^3*sqrt(c))+(-22/81)/(d^3*sqrt(c+d*x^3))+64/27*c/(d^3*(8*c-d*x^3)*sqrt(c+d*x^3))],
[x^5/((8*c-d*x^3)^2*(c+d*x^3)^(3/2)),x,5,2/243*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))/(c^(3/2)*d^2)+(-2/81)/(c*d^2*sqrt(c+d*x^3))+8/27/(d^2*(8*c-d*x^3)*sqrt(c+d*x^3))],
[x^2/((8*c-d*x^3)^2*(c+d*x^3)^(3/2)),x,5,1/243*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))/(c^(5/2)*d)+(-1/81)/(c^2*d*sqrt(c+d*x^3))+1/27/(c*d*(8*c-d*x^3)*sqrt(c+d*x^3))],
[1/(x*(8*c-d*x^3)^2*(c+d*x^3)^(3/2)),x,8,7/7776*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))/c^(7/2)-1/96*arctanh(sqrt(c+d*x^3)/sqrt(c))/c^(7/2)+5/648/(c^3*sqrt(c+d*x^3))+1/216/(c^2*(8*c-d*x^3)*sqrt(c+d*x^3))],
[1/(x^4*(8*c-d*x^3)^2*(c+d*x^3)^(3/2)),x,9,5/31104*d*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))/c^(9/2)+5/384*d*arctanh(sqrt(c+d*x^3)/sqrt(c))/c^(9/2)-35/2592*d/(c^4*sqrt(c+d*x^3))+5/864*d/(c^3*(8*c-d*x^3)*sqrt(c+d*x^3))+(-1/24)/(c^2*x^3*(8*c-d*x^3)*sqrt(c+d*x^3))],
[1/(x^7*(8*c-d*x^3)^2*(c+d*x^3)^(3/2)),x,10,13/497664*d^2*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))/c^(11/2)-33/2048*d^2*arctanh(sqrt(c+d*x^3)/sqrt(c))/c^(11/2)+665/41472*d^2/(c^5*sqrt(c+d*x^3))-71/13824*d^2/(c^4*(8*c-d*x^3)*sqrt(c+d*x^3))+(-1/48)/(c^2*x^6*(8*c-d*x^3)*sqrt(c+d*x^3))+17/384*d/(c^3*x^3*(8*c-d*x^3)*sqrt(c+d*x^3))],
[x^7/((8*c-d*x^3)^2*(c+d*x^3)^(3/2)),x,15,-4/243*arctanh(1/3*(c^(1/3)+d^(1/3)*x)^2/(c^(1/6)*sqrt(c+d*x^3)))/(c^(5/6)*d^(8/3))+4/243*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))/(c^(5/6)*d^(8/3))+4/81*arctan(c^(1/6)*(c^(1/3)+d^(1/3)*x)*sqrt(3)/sqrt(c+d*x^3))/(c^(5/6)*d^(8/3)*sqrt(3))-2/81*x^2/(c*d^2*sqrt(c+d*x^3))+8/27*x^2/(d^2*(8*c-d*x^3)*sqrt(c+d*x^3))+2/81*sqrt(c+d*x^3)/(c*d^(8/3)*(d^(1/3)*x+c^(1/3)*(1+sqrt(3))))+2/81*(c^(1/3)+d^(1/3)*x)*EllipticF((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2)*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(3^(1/4)*c^(2/3)*d^(8/3)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))-1/27*(c^(1/3)+d^(1/3)*x)*EllipticE((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(3^(3/4)*c^(2/3)*d^(8/3)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))],
[x^4/((8*c-d*x^3)^2*(c+d*x^3)^(3/2)),x,15,1/243*arctanh(1/3*(c^(1/3)+d^(1/3)*x)^2/(c^(1/6)*sqrt(c+d*x^3)))/(c^(11/6)*d^(5/3))-1/243*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))/(c^(11/6)*d^(5/3))-1/81*arctan(c^(1/6)*(c^(1/3)+d^(1/3)*x)*sqrt(3)/sqrt(c+d*x^3))/(c^(11/6)*d^(5/3)*sqrt(3))-1/81*x^2/(c^2*d*sqrt(c+d*x^3))+1/27*x^2/(c*d*(8*c-d*x^3)*sqrt(c+d*x^3))+1/81*sqrt(c+d*x^3)/(c^2*d^(5/3)*(d^(1/3)*x+c^(1/3)*(1+sqrt(3))))+1/81*(c^(1/3)+d^(1/3)*x)*EllipticF((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2)*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(3^(1/4)*c^(5/3)*d^(5/3)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))-1/54*(c^(1/3)+d^(1/3)*x)*EllipticE((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(3^(3/4)*c^(5/3)*d^(5/3)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))],
[x/((8*c-d*x^3)^2*(c+d*x^3)^(3/2)),x,15,5/3888*arctanh(1/3*(c^(1/3)+d^(1/3)*x)^2/(c^(1/6)*sqrt(c+d*x^3)))/(c^(17/6)*d^(2/3))-5/3888*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))/(c^(17/6)*d^(2/3))-5/1296*arctan(c^(1/6)*(c^(1/3)+d^(1/3)*x)*sqrt(3)/sqrt(c+d*x^3))/(c^(17/6)*d^(2/3)*sqrt(3))+5/648*x^2/(c^3*sqrt(c+d*x^3))+1/216*x^2/(c^2*(8*c-d*x^3)*sqrt(c+d*x^3))-5/648*sqrt(c+d*x^3)/(c^3*d^(2/3)*(d^(1/3)*x+c^(1/3)*(1+sqrt(3))))-5/324*(c^(1/3)+d^(1/3)*x)*EllipticF((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(3^(1/4)*c^(8/3)*d^(2/3)*sqrt(2)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))+5/432*(c^(1/3)+d^(1/3)*x)*EllipticE((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(3^(3/4)*c^(8/3)*d^(2/3)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))],
[1/(x^2*(8*c-d*x^3)^2*(c+d*x^3)^(3/2)),x,16,1/3888*d^(1/3)*arctanh(1/3*(c^(1/3)+d^(1/3)*x)^2/(c^(1/6)*sqrt(c+d*x^3)))/c^(23/6)-1/3888*d^(1/3)*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))/c^(23/6)-1/1296*d^(1/3)*arctan(c^(1/6)*(c^(1/3)+d^(1/3)*x)*sqrt(3)/sqrt(c+d*x^3))/(c^(23/6)*sqrt(3))+5/648/(c^3*x*sqrt(c+d*x^3))+1/216/(c^2*x*(8*c-d*x^3)*sqrt(c+d*x^3))-31/1296*sqrt(c+d*x^3)/(c^4*x)+31/1296*d^(1/3)*sqrt(c+d*x^3)/(c^4*(d^(1/3)*x+c^(1/3)*(1+sqrt(3))))+31/648*d^(1/3)*(c^(1/3)+d^(1/3)*x)*EllipticF((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(3^(1/4)*c^(11/3)*sqrt(2)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))-31/864*d^(1/3)*(c^(1/3)+d^(1/3)*x)*EllipticE((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(3^(3/4)*c^(11/3)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))],
[1/(x^5*(8*c-d*x^3)^2*(c+d*x^3)^(3/2)),x,17,11/248832*d^(4/3)*arctanh(1/3*(c^(1/3)+d^(1/3)*x)^2/(c^(1/6)*sqrt(c+d*x^3)))/c^(29/6)-11/248832*d^(4/3)*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))/c^(29/6)-11/82944*d^(4/3)*arctan(c^(1/6)*(c^(1/3)+d^(1/3)*x)*sqrt(3)/sqrt(c+d*x^3))/(c^(29/6)*sqrt(3))+5/648/(c^3*x^4*sqrt(c+d*x^3))+1/216/(c^2*x^4*(8*c-d*x^3)*sqrt(c+d*x^3))-253/20736*sqrt(c+d*x^3)/(c^4*x^4)+77/2592*d*sqrt(c+d*x^3)/(c^5*x)-77/2592*d^(4/3)*sqrt(c+d*x^3)/(c^5*(d^(1/3)*x+c^(1/3)*(1+sqrt(3))))-77/1296*d^(4/3)*(c^(1/3)+d^(1/3)*x)*EllipticF((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(3^(1/4)*c^(14/3)*sqrt(2)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))+77/1728*d^(4/3)*(c^(1/3)+d^(1/3)*x)*EllipticE((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(3^(3/4)*c^(14/3)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))],
[1/(x^8*(8*c-d*x^3)^2*(c+d*x^3)^(3/2)),x,18,7/995328*d^(7/3)*arctanh(1/3*(c^(1/3)+d^(1/3)*x)^2/(c^(1/6)*sqrt(c+d*x^3)))/c^(35/6)-7/995328*d^(7/3)*arctanh(1/3*sqrt(c+d*x^3)/sqrt(c))/c^(35/6)-7/331776*d^(7/3)*arctan(c^(1/6)*(c^(1/3)+d^(1/3)*x)*sqrt(3)/sqrt(c+d*x^3))/(c^(35/6)*sqrt(3))+5/648/(c^3*x^7*sqrt(c+d*x^3))+1/216/(c^2*x^7*(8*c-d*x^3)*sqrt(c+d*x^3))-191/18144*sqrt(c+d*x^3)/(c^4*x^7)+8257/580608*d*sqrt(c+d*x^3)/(c^5*x^4)-5179/145152*d^2*sqrt(c+d*x^3)/(c^6*x)+5179/145152*d^(7/3)*sqrt(c+d*x^3)/(c^6*(d^(1/3)*x+c^(1/3)*(1+sqrt(3))))+5179/72576*d^(7/3)*(c^(1/3)+d^(1/3)*x)*EllipticF((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(3^(1/4)*c^(17/3)*sqrt(2)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))-5179/96768*d^(7/3)*(c^(1/3)+d^(1/3)*x)*EllipticE((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(3^(3/4)*c^(17/3)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))],
[x^6/((8*c-d*x^3)^2*(c+d*x^3)^(3/2)),x,-2,2/81*x*(4*c+d*x^3)/(c*d^2*(8*c-d*x^3)*sqrt(c+d*x^3))-2/81*(c^(1/3)+d^(1/3)*x)*EllipticF((d^(1/3)*x+c^(1/3)*(1-sqrt(3)))/(d^(1/3)*x+c^(1/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2+sqrt(3))*sqrt((c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2)/(3^(1/4)*c*d^(7/3)*sqrt(c+d*x^3)*sqrt(c^(1/3)*(c^(1/3)+d^(1/3)*x)/(d^(1/3)*x+c^(1/3)*(1+sqrt(3)))^2))],
[x^3/((8*c-d*x^3)^2*(c+d*x^3)^(3/2)),x,2,1/256*x^4*AppellF1(4/3,2,3/2,7/3,1/8*d*x^3/c,-d*x^3/c)*sqrt(1+d*x^3/c)/(c^3*sqrt(c+d*x^3))],
[1/((8*c-d*x^3)^2*(c+d*x^3)^(3/2)),x,2,1/64*x*AppellF1(1/3,2,3/2,4/3,1/8*d*x^3/c,-d*x^3/c)*sqrt(1+d*x^3/c)/(c^3*sqrt(c+d*x^3))],
[1/(x^3*(8*c-d*x^3)^2*(c+d*x^3)^(3/2)),x,2,-1/128*AppellF1(-2/3,2,3/2,1/3,1/8*d*x^3/c,-d*x^3/c)*sqrt(1+d*x^3/c)/(c^3*x^2*sqrt(c+d*x^3))],
[1/(x^6*(8*c-d*x^3)^2*(c+d*x^3)^(3/2)),x,2,-1/320*AppellF1(-5/3,2,3/2,-2/3,1/8*d*x^3/c,-d*x^3/c)*sqrt(1+d*x^3/c)/(c^3*x^5*sqrt(c+d*x^3))],

# q>0
[x^8*sqrt(c+d*x^3)/(a+b*x^3)^2,x,6,2/9*(c+d*x^3)^(3/2)/(b^2*d)-1/3*a^2*(c+d*x^3)^(3/2)/(b^2*(b*c-a*d)*(a+b*x^3))+1/3*a*(4*b*c-5*a*d)*arctanh(sqrt(b)*sqrt(c+d*x^3)/sqrt(b*c-a*d))/(b^(7/2)*sqrt(b*c-a*d))-1/3*a*(4*b*c-5*a*d)*sqrt(c+d*x^3)/(b^3*(b*c-a*d))],
[x^5*sqrt(c+d*x^3)/(a+b*x^3)^2,x,5,1/3*a*(c+d*x^3)^(3/2)/(b*(b*c-a*d)*(a+b*x^3))-1/3*(2*b*c-3*a*d)*arctanh(sqrt(b)*sqrt(c+d*x^3)/sqrt(b*c-a*d))/(b^(5/2)*sqrt(b*c-a*d))+1/3*(2*b*c-3*a*d)*sqrt(c+d*x^3)/(b^2*(b*c-a*d))],
[x^2*sqrt(c+d*x^3)/(a+b*x^3)^2,x,4,-1/3*d*arctanh(sqrt(b)*sqrt(c+d*x^3)/sqrt(b*c-a*d))/(b^(3/2)*sqrt(b*c-a*d))-1/3*sqrt(c+d*x^3)/(b*(a+b*x^3))],
[sqrt(c+d*x^3)/(x*(a+b*x^3)^2),x,7,-2/3*arctanh(sqrt(c+d*x^3)/sqrt(c))*sqrt(c)/a^2+1/3*(2*b*c-a*d)*arctanh(sqrt(b)*sqrt(c+d*x^3)/sqrt(b*c-a*d))/(a^2*sqrt(b)*sqrt(b*c-a*d))+1/3*sqrt(c+d*x^3)/(a*(a+b*x^3))],
[sqrt(c+d*x^3)/(x^4*(a+b*x^3)^2),x,8,1/3*(4*b*c-a*d)*arctanh(sqrt(c+d*x^3)/sqrt(c))/(a^3*sqrt(c))-1/3*(4*b*c-3*a*d)*arctanh(sqrt(b)*sqrt(c+d*x^3)/sqrt(b*c-a*d))*sqrt(b)/(a^3*sqrt(b*c-a*d))-2/3*b*sqrt(c+d*x^3)/(a^2*(a+b*x^3))-1/3*sqrt(c+d*x^3)/(a*x^3*(a+b*x^3))],
[x^3*sqrt(c+d*x^3)/(a+b*x^3)^2,x,2,1/4*x^4*AppellF1(4/3,2,-1/2,7/3,-b*x^3/a,-d*x^3/c)*sqrt(c+d*x^3)/(a^2*sqrt(1+d*x^3/c))],
[x*sqrt(c+d*x^3)/(a+b*x^3)^2,x,2,1/2*x^2*AppellF1(2/3,2,-1/2,5/3,-b*x^3/a,-d*x^3/c)*sqrt(c+d*x^3)/(a^2*sqrt(1+d*x^3/c))],
[sqrt(c+d*x^3)/(a+b*x^3)^2,x,2,x*AppellF1(1/3,2,-1/2,4/3,-b*x^3/a,-d*x^3/c)*sqrt(c+d*x^3)/(a^2*sqrt(1+d*x^3/c))],
[sqrt(c+d*x^3)/(x^2*(a+b*x^3)^2),x,2,-AppellF1(-1/3,2,-1/2,2/3,-b*x^3/a,-d*x^3/c)*sqrt(c+d*x^3)/(a^2*x*sqrt(1+d*x^3/c))],
[sqrt(c+d*x^3)/(x^3*(a+b*x^3)^2),x,2,-1/2*AppellF1(-2/3,2,-1/2,1/3,-b*x^3/a,-d*x^3/c)*sqrt(c+d*x^3)/(a^2*x^2*sqrt(1+d*x^3/c))],
[x^8*(c+d*x^3)^(3/2)/(a+b*x^3)^2,x,7,-1/9*a*(4*b*c-7*a*d)*(c+d*x^3)^(3/2)/(b^3*(b*c-a*d))+2/15*(c+d*x^3)^(5/2)/(b^2*d)-1/3*a^2*(c+d*x^3)^(5/2)/(b^2*(b*c-a*d)*(a+b*x^3))+1/3*a*(4*b*c-7*a*d)*arctanh(sqrt(b)*sqrt(c+d*x^3)/sqrt(b*c-a*d))*sqrt(b*c-a*d)/b^(9/2)-1/3*a*(4*b*c-7*a*d)*sqrt(c+d*x^3)/b^4],
[x^5*(c+d*x^3)^(3/2)/(a+b*x^3)^2,x,6,1/9*(2*b*c-5*a*d)*(c+d*x^3)^(3/2)/(b^2*(b*c-a*d))+1/3*a*(c+d*x^3)^(5/2)/(b*(b*c-a*d)*(a+b*x^3))-1/3*(2*b*c-5*a*d)*arctanh(sqrt(b)*sqrt(c+d*x^3)/sqrt(b*c-a*d))*sqrt(b*c-a*d)/b^(7/2)+1/3*(2*b*c-5*a*d)*sqrt(c+d*x^3)/b^3],
[x^2*(c+d*x^3)^(3/2)/(a+b*x^3)^2,x,5,-1/3*(c+d*x^3)^(3/2)/(b*(a+b*x^3))-d*arctanh(sqrt(b)*sqrt(c+d*x^3)/sqrt(b*c-a*d))*sqrt(b*c-a*d)/b^(5/2)+d*sqrt(c+d*x^3)/b^2],
[(c+d*x^3)^(3/2)/(x*(a+b*x^3)^2),x,7,-2/3*c^(3/2)*arctanh(sqrt(c+d*x^3)/sqrt(c))/a^2+1/3*(2*b*c+a*d)*arctanh(sqrt(b)*sqrt(c+d*x^3)/sqrt(b*c-a*d))*sqrt(b*c-a*d)/(a^2*b^(3/2))+1/3*(b*c-a*d)*sqrt(c+d*x^3)/(a*b*(a+b*x^3))],
[(c+d*x^3)^(3/2)/(x^4*(a+b*x^3)^2),x,8,1/3*(4*b*c-3*a*d)*arctanh(sqrt(c+d*x^3)/sqrt(c))*sqrt(c)/a^3-1/3*(4*b*c-a*d)*arctanh(sqrt(b)*sqrt(c+d*x^3)/sqrt(b*c-a*d))*sqrt(b*c-a*d)/(a^3*sqrt(b))-1/3*(2*b*c-a*d)*sqrt(c+d*x^3)/(a^2*(a+b*x^3))-1/3*c*sqrt(c+d*x^3)/(a*x^3*(a+b*x^3))],
[x^3*(c+d*x^3)^(3/2)/(a+b*x^3)^2,x,2,1/4*c*x^4*AppellF1(4/3,2,-3/2,7/3,-b*x^3/a,-d*x^3/c)*sqrt(c+d*x^3)/(a^2*sqrt(1+d*x^3/c))],
[x*(c+d*x^3)^(3/2)/(a+b*x^3)^2,x,2,1/2*c*x^2*AppellF1(2/3,2,-3/2,5/3,-b*x^3/a,-d*x^3/c)*sqrt(c+d*x^3)/(a^2*sqrt(1+d*x^3/c))],
[(c+d*x^3)^(3/2)/(a+b*x^3)^2,x,2,c*x*AppellF1(1/3,2,-3/2,4/3,-b*x^3/a,-d*x^3/c)*sqrt(c+d*x^3)/(a^2*sqrt(1+d*x^3/c))],
[(c+d*x^3)^(3/2)/(x^2*(a+b*x^3)^2),x,2,-c*AppellF1(-1/3,2,-3/2,2/3,-b*x^3/a,-d*x^3/c)*sqrt(c+d*x^3)/(a^2*x*sqrt(1+d*x^3/c))],
[(c+d*x^3)^(3/2)/(x^3*(a+b*x^3)^2),x,2,-1/2*c*AppellF1(-2/3,2,-3/2,1/3,-b*x^3/a,-d*x^3/c)*sqrt(c+d*x^3)/(a^2*x^2*sqrt(1+d*x^3/c))],

# q<0
[x^8/((a+b*x^3)^2*sqrt(c+d*x^3)),x,5,1/3*a*(4*b*c-3*a*d)*arctanh(sqrt(b)*sqrt(c+d*x^3)/sqrt(b*c-a*d))/(b^(5/2)*(b*c-a*d)^(3/2))+2/3*sqrt(c+d*x^3)/(b^2*d)-1/3*a^2*sqrt(c+d*x^3)/(b^2*(b*c-a*d)*(a+b*x^3))],
[x^5/((a+b*x^3)^2*sqrt(c+d*x^3)),x,4,-1/3*(2*b*c-a*d)*arctanh(sqrt(b)*sqrt(c+d*x^3)/sqrt(b*c-a*d))/(b^(3/2)*(b*c-a*d)^(3/2))+1/3*a*sqrt(c+d*x^3)/(b*(b*c-a*d)*(a+b*x^3))],
[x^2/((a+b*x^3)^2*sqrt(c+d*x^3)),x,4,1/3*d*arctanh(sqrt(b)*sqrt(c+d*x^3)/sqrt(b*c-a*d))/((b*c-a*d)^(3/2)*sqrt(b))-1/3*sqrt(c+d*x^3)/((b*c-a*d)*(a+b*x^3))],
[1/(x*(a+b*x^3)^2*sqrt(c+d*x^3)),x,7,1/3*(2*b*c-3*a*d)*arctanh(sqrt(b)*sqrt(c+d*x^3)/sqrt(b*c-a*d))*sqrt(b)/(a^2*(b*c-a*d)^(3/2))-2/3*arctanh(sqrt(c+d*x^3)/sqrt(c))/(a^2*sqrt(c))+1/3*b*sqrt(c+d*x^3)/(a*(b*c-a*d)*(a+b*x^3))],
[1/(x^4*(a+b*x^3)^2*sqrt(c+d*x^3)),x,8,1/3*(4*b*c+a*d)*arctanh(sqrt(c+d*x^3)/sqrt(c))/(a^3*c^(3/2))-1/3*b^(3/2)*(4*b*c-5*a*d)*arctanh(sqrt(b)*sqrt(c+d*x^3)/sqrt(b*c-a*d))/(a^3*(b*c-a*d)^(3/2))-1/3*b*(2*b*c-a*d)*sqrt(c+d*x^3)/(a^2*c*(b*c-a*d)*(a+b*x^3))-1/3*sqrt(c+d*x^3)/(a*c*x^3*(a+b*x^3))],
[x^3/((a+b*x^3)^2*sqrt(c+d*x^3)),x,2,1/4*x^4*AppellF1(4/3,2,1/2,7/3,-b*x^3/a,-d*x^3/c)*sqrt(1+d*x^3/c)/(a^2*sqrt(c+d*x^3))],
[x/((a+b*x^3)^2*sqrt(c+d*x^3)),x,2,1/2*x^2*AppellF1(2/3,2,1/2,5/3,-b*x^3/a,-d*x^3/c)*sqrt(1+d*x^3/c)/(a^2*sqrt(c+d*x^3))],
[1/((a+b*x^3)^2*sqrt(c+d*x^3)),x,2,x*AppellF1(1/3,2,1/2,4/3,-b*x^3/a,-d*x^3/c)*sqrt(1+d*x^3/c)/(a^2*sqrt(c+d*x^3))],
[1/(x^2*(a+b*x^3)^2*sqrt(c+d*x^3)),x,2,-AppellF1(-1/3,2,1/2,2/3,-b*x^3/a,-d*x^3/c)*sqrt(1+d*x^3/c)/(a^2*x*sqrt(c+d*x^3))],
[1/(x^3*(a+b*x^3)^2*sqrt(c+d*x^3)),x,2,-1/2*AppellF1(-2/3,2,1/2,1/3,-b*x^3/a,-d*x^3/c)*sqrt(1+d*x^3/c)/(a^2*x^2*sqrt(c+d*x^3))],
[x^8/((a+b*x^3)^2*(c+d*x^3)^(3/2)),x,5,1/3*a*(4*b*c-a*d)*arctanh(sqrt(b)*sqrt(c+d*x^3)/sqrt(b*c-a*d))/(b^(3/2)*(b*c-a*d)^(5/2))+1/3*(-2*b^2*c^2-a^2*d^2)/(b^2*d*(b*c-a*d)^2*sqrt(c+d*x^3))-1/3*a^2/(b^2*(b*c-a*d)*(a+b*x^3)*sqrt(c+d*x^3))],
[x^5/((a+b*x^3)^2*(c+d*x^3)^(3/2)),x,5,-1/3*(2*b*c+a*d)*arctanh(sqrt(b)*sqrt(c+d*x^3)/sqrt(b*c-a*d))/((b*c-a*d)^(5/2)*sqrt(b))+1/3*(2*b*c+a*d)/(b*(b*c-a*d)^2*sqrt(c+d*x^3))+1/3*a/(b*(b*c-a*d)*(a+b*x^3)*sqrt(c+d*x^3))],
[x^2/((a+b*x^3)^2*(c+d*x^3)^(3/2)),x,5,d*arctanh(sqrt(b)*sqrt(c+d*x^3)/sqrt(b*c-a*d))*sqrt(b)/(b*c-a*d)^(5/2)-d/((b*c-a*d)^2*sqrt(c+d*x^3))+(-1/3)/((b*c-a*d)*(a+b*x^3)*sqrt(c+d*x^3))],
[1/(x*(a+b*x^3)^2*(c+d*x^3)^(3/2)),x,8,-2/3*arctanh(sqrt(c+d*x^3)/sqrt(c))/(a^2*c^(3/2))+1/3*b^(3/2)*(2*b*c-5*a*d)*arctanh(sqrt(b)*sqrt(c+d*x^3)/sqrt(b*c-a*d))/(a^2*(b*c-a*d)^(5/2))+1/3*d*(b*c+2*a*d)/(a*c*(b*c-a*d)^2*sqrt(c+d*x^3))+1/3*b/(a*(b*c-a*d)*(a+b*x^3)*sqrt(c+d*x^3))],
[1/(x^4*(a+b*x^3)^2*(c+d*x^3)^(3/2)),x,9,1/3*(4*b*c+3*a*d)*arctanh(sqrt(c+d*x^3)/sqrt(c))/(a^3*c^(5/2))-1/3*b^(5/2)*(4*b*c-7*a*d)*arctanh(sqrt(b)*sqrt(c+d*x^3)/sqrt(b*c-a*d))/(a^3*(b*c-a*d)^(5/2))-1/3*d*(2*b^2*c^2-2*a*b*c*d+3*a^2*d^2)/(a^2*c^2*(b*c-a*d)^2*sqrt(c+d*x^3))-1/3*b*(2*b*c-a*d)/(a^2*c*(b*c-a*d)*(a+b*x^3)*sqrt(c+d*x^3))+(-1/3)/(a*c*x^3*(a+b*x^3)*sqrt(c+d*x^3))],
[x^3/((a+b*x^3)^2*(c+d*x^3)^(3/2)),x,2,1/4*x^4*AppellF1(4/3,2,3/2,7/3,-b*x^3/a,-d*x^3/c)*sqrt(1+d*x^3/c)/(a^2*c*sqrt(c+d*x^3))],
[x/((a+b*x^3)^2*(c+d*x^3)^(3/2)),x,2,1/2*x^2*AppellF1(2/3,2,3/2,5/3,-b*x^3/a,-d*x^3/c)*sqrt(1+d*x^3/c)/(a^2*c*sqrt(c+d*x^3))],
[1/((a+b*x^3)^2*(c+d*x^3)^(3/2)),x,2,x*AppellF1(1/3,2,3/2,4/3,-b*x^3/a,-d*x^3/c)*sqrt(1+d*x^3/c)/(a^2*c*sqrt(c+d*x^3))],
[1/(x^2*(a+b*x^3)^2*(c+d*x^3)^(3/2)),x,2,-AppellF1(-1/3,2,3/2,2/3,-b*x^3/a,-d*x^3/c)*sqrt(1+d*x^3/c)/(a^2*c*x*sqrt(c+d*x^3))],
[1/(x^3*(a+b*x^3)^2*(c+d*x^3)^(3/2)),x,2,-1/2*AppellF1(-2/3,2,3/2,1/3,-b*x^3/a,-d*x^3/c)*sqrt(1+d*x^3/c)/(a^2*c*x^2*sqrt(c+d*x^3))],

# Integrands of the form (e x)^m (a+b x^3)^(p/2) (c+d x^3)^q with m symbolic
[(e*x)^m*(a+b*x^3)^(5/2)*(A+B*x^3),x,3,2*B*(e*x)^(1+m)*(a+b*x^3)^(7/2)/(b*e*(23+2*m))-a^2*(2*a*B*(1+m)-A*b*(23+2*m))*(e*x)^(1+m)*hypergeom([-5/2,1/3*(1+m)],[1/3*(4+m)],-b*x^3/a)*sqrt(a+b*x^3)/(b*e*(1+m)*(23+2*m)*sqrt(1+b*x^3/a))],
[(e*x)^m*(a+b*x^3)^(3/2)*(A+B*x^3),x,3,2*B*(e*x)^(1+m)*(a+b*x^3)^(5/2)/(b*e*(17+2*m))-a*(2*a*B*(1+m)-A*b*(17+2*m))*(e*x)^(1+m)*hypergeom([-3/2,1/3*(1+m)],[1/3*(4+m)],-b*x^3/a)*sqrt(a+b*x^3)/(b*e*(1+m)*(17+2*m)*sqrt(1+b*x^3/a))],
[(e*x)^m*(a+b*x^3)^(1/2)*(A+B*x^3),x,3,2*B*(e*x)^(1+m)*(a+b*x^3)^(3/2)/(b*e*(11+2*m))-(2*a*B*(1+m)-A*b*(11+2*m))*(e*x)^(1+m)*hypergeom([-1/2,1/3*(1+m)],[1/3*(4+m)],-b*x^3/a)*sqrt(a+b*x^3)/(b*e*(1+m)*(11+2*m)*sqrt(1+b*x^3/a))],
[(e*x)^m*(A+B*x^3)/(a+b*x^3)^(1/2),x,3,2*B*(e*x)^(1+m)*sqrt(a+b*x^3)/(b*e*(5+2*m))-(2*a*B*(1+m)-A*b*(5+2*m))*(e*x)^(1+m)*hypergeom([1/2,1/3*(1+m)],[1/3*(4+m)],-b*x^3/a)*sqrt(1+b*x^3/a)/(b*e*(1+m)*(5+2*m)*sqrt(a+b*x^3))],
[(e*x)^m*(A+B*x^3)/(a+b*x^3)^(3/2),x,3,2/3*(A*b-a*B)*(e*x)^(1+m)/(a*b*e*sqrt(a+b*x^3))+1/3*(2*a*B*(1+m)+A*(b-2*b*m))*(e*x)^(1+m)*hypergeom([1/2,1/3*(1+m)],[1/3*(4+m)],-b*x^3/a)*sqrt(1+b*x^3/a)/(a*b*e*(1+m)*sqrt(a+b*x^3))],
[(e*x)^m*(A+B*x^3)/(a+b*x^3)^(5/2),x,3,2/9*(A*b-a*B)*(e*x)^(1+m)/(a*b*e*(a+b*x^3)^(3/2))+1/9*(A*b*(7-2*m)+2*a*B*(1+m))*(e*x)^(1+m)*hypergeom([3/2,1/3*(1+m)],[1/3*(4+m)],-b*x^3/a)*sqrt(1+b*x^3/a)/(a^2*b*e*(1+m)*sqrt(a+b*x^3))],

# Integrands of the form (e x)^m (a+b x^3)^(p/2) (c+d x^3)^(q/2)

# Integrands of the form (e x)^m (a+b x^3)^(p/2) (c+d x^3)^(q/2)

# p>0

# p<0
[x^5/(sqrt(a+b*x^3)*sqrt(c+d*x^3)),x,5,-1/3*(b*c+a*d)*arctanh(sqrt(d)*sqrt(a+b*x^3)/(sqrt(b)*sqrt(c+d*x^3)))/(b^(3/2)*d^(3/2))+1/3*sqrt(a+b*x^3)*sqrt(c+d*x^3)/(b*d)],
[x^2/(sqrt(a+b*x^3)*sqrt(c+d*x^3)),x,4,2/3*arctanh(sqrt(d)*sqrt(a+b*x^3)/(sqrt(b)*sqrt(c+d*x^3)))/(sqrt(b)*sqrt(d))],
[1/(x*sqrt(a+b*x^3)*sqrt(c+d*x^3)),x,3,-2/3*arctanh(sqrt(c)*sqrt(a+b*x^3)/(sqrt(a)*sqrt(c+d*x^3)))/(sqrt(a)*sqrt(c))],
[1/(x^4*sqrt(a+b*x^3)*sqrt(c+d*x^3)),x,4,1/3*(b*c+a*d)*arctanh(sqrt(c)*sqrt(a+b*x^3)/(sqrt(a)*sqrt(c+d*x^3)))/(a^(3/2)*c^(3/2))-1/3*sqrt(a+b*x^3)*sqrt(c+d*x^3)/(a*c*x^3)],
[x^4/(sqrt(a+b*x^3)*sqrt(c+d*x^3)),x,3,1/5*x^5*AppellF1(5/3,1/2,1/2,8/3,-b*x^3/a,-d*x^3/c)*sqrt(1+b*x^3/a)*sqrt(1+d*x^3/c)/(sqrt(a+b*x^3)*sqrt(c+d*x^3))],
[x^3/(sqrt(a+b*x^3)*sqrt(c+d*x^3)),x,3,1/4*x^4*AppellF1(4/3,1/2,1/2,7/3,-b*x^3/a,-d*x^3/c)*sqrt(1+b*x^3/a)*sqrt(1+d*x^3/c)/(sqrt(a+b*x^3)*sqrt(c+d*x^3))],
[x/(sqrt(a+b*x^3)*sqrt(c+d*x^3)),x,3,1/2*x^2*AppellF1(2/3,1/2,1/2,5/3,-b*x^3/a,-d*x^3/c)*sqrt(1+b*x^3/a)*sqrt(1+d*x^3/c)/(sqrt(a+b*x^3)*sqrt(c+d*x^3))],
[1/(sqrt(a+b*x^3)*sqrt(c+d*x^3)),x,3,x*AppellF1(1/3,1/2,1/2,4/3,-b*x^3/a,-d*x^3/c)*sqrt(1+b*x^3/a)*sqrt(1+d*x^3/c)/(sqrt(a+b*x^3)*sqrt(c+d*x^3))],
[1/(x^2*sqrt(a+b*x^3)*sqrt(c+d*x^3)),x,3,-AppellF1(-1/3,1/2,1/2,2/3,-b*x^3/a,-d*x^3/c)*sqrt(1+b*x^3/a)*sqrt(1+d*x^3/c)/(x*sqrt(a+b*x^3)*sqrt(c+d*x^3))],
[1/(x^3*sqrt(a+b*x^3)*sqrt(c+d*x^3)),x,3,-1/2*AppellF1(-2/3,1/2,1/2,1/3,-b*x^3/a,-d*x^3/c)*sqrt(1+b*x^3/a)*sqrt(1+d*x^3/c)/(x^2*sqrt(a+b*x^3)*sqrt(c+d*x^3))],

# Integrands of the form (e x)^(m/2) (a+b x^3)^(p/2) (c+d x^3)^q

# Integrands of the form x^(m/2) (a+b x^3)^(p/2) (c+d x^3)^1

# p>0
[(e*x)^(7/2)*(A+B*x^3)*sqrt(a+b*x^3),x,7,1/9*B*(e*x)^(9/2)*(a+b*x^3)^(3/2)/(b*e)-1/24*a^2*(2*A*b-a*B)*e^(7/2)*arctanh((e*x)^(3/2)*sqrt(b)/(e^(3/2)*sqrt(a+b*x^3)))/b^(5/2)+1/24*a*(2*A*b-a*B)*e^2*(e*x)^(3/2)*sqrt(a+b*x^3)/b^2+1/12*(2*A*b-a*B)*(e*x)^(9/2)*sqrt(a+b*x^3)/(b*e)],
[(e*x)^(5/2)*(A+B*x^3)*sqrt(a+b*x^3),x,5,1/8*B*(e*x)^(7/2)*(a+b*x^3)^(3/2)/(b*e)+1/80*(16*A*b-7*a*B)*(e*x)^(7/2)*sqrt(a+b*x^3)/(b*e)+3/320*a*(16*A*b-7*a*B)*e^2*sqrt(e*x)*sqrt(a+b*x^3)/b^2-1/640*3^(3/4)*a^(5/3)*(16*A*b-7*a*B)*e^2*(a^(1/3)+b^(1/3)*x)*sqrt(cos(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))))^2)/cos(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))))*EllipticF(sin(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3))))),sqrt(1/4*(2+sqrt(3))))*sqrt(e*x)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))^2)/(b^2*sqrt(a+b*x^3)*sqrt(b^(1/3)*x*(a^(1/3)+b^(1/3)*x)/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))^2))],
[(e*x)^(3/2)*(A+B*x^3)*sqrt(a+b*x^3),x,6,1/7*B*(e*x)^(5/2)*(a+b*x^3)^(3/2)/(b*e)+1/56*(14*A*b-5*a*B)*(e*x)^(5/2)*sqrt(a+b*x^3)/(b*e)+3/112*a*(14*A*b-5*a*B)*e*(1+sqrt(3))*sqrt(e*x)*sqrt(a+b*x^3)/(b^(5/3)*(a^(1/3)+b^(1/3)*x*(1+sqrt(3))))-3/112*3^(1/4)*a^(4/3)*(14*A*b-5*a*B)*e*(a^(1/3)+b^(1/3)*x)*sqrt(cos(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))))^2)/cos(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))))*EllipticE(sin(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3))))),sqrt(1/4*(2+sqrt(3))))*sqrt(e*x)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))^2)/(b^(5/3)*sqrt(a+b*x^3)*sqrt(b^(1/3)*x*(a^(1/3)+b^(1/3)*x)/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))^2))-1/224*3^(3/4)*a^(4/3)*(14*A*b-5*a*B)*e*(a^(1/3)+b^(1/3)*x)*sqrt(cos(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))))^2)/cos(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))))*EllipticF(sin(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3))))),sqrt(1/4*(2+sqrt(3))))*(1-sqrt(3))*sqrt(e*x)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))^2)/(b^(5/3)*sqrt(a+b*x^3)*sqrt(b^(1/3)*x*(a^(1/3)+b^(1/3)*x)/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))^2))],
[(A+B*x^3)*sqrt(e*x)*sqrt(a+b*x^3),x,6,1/6*B*(e*x)^(3/2)*(a+b*x^3)^(3/2)/(b*e)+1/12*a*(4*A*b-a*B)*arctanh((e*x)^(3/2)*sqrt(b)/(e^(3/2)*sqrt(a+b*x^3)))*sqrt(e)/b^(3/2)+1/12*(4*A*b-a*B)*(e*x)^(3/2)*sqrt(a+b*x^3)/(b*e)],
[(A+B*x^3)*sqrt(a+b*x^3)/sqrt(e*x),x,4,1/5*B*(a+b*x^3)^(3/2)*sqrt(e*x)/(b*e)+1/20*(10*A*b-a*B)*sqrt(e*x)*sqrt(a+b*x^3)/(b*e)+1/40*3^(3/4)*a^(2/3)*(10*A*b-a*B)*(a^(1/3)+b^(1/3)*x)*sqrt(cos(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))))^2)/cos(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))))*EllipticF(sin(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3))))),sqrt(1/4*(2+sqrt(3))))*sqrt(e*x)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))^2)/(b*e*sqrt(a+b*x^3)*sqrt(b^(1/3)*x*(a^(1/3)+b^(1/3)*x)/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))^2))],
[(A+B*x^3)*sqrt(a+b*x^3)/(e*x)^(3/2),x,6,-2*A*(a+b*x^3)^(3/2)/(a*e*sqrt(e*x))+1/4*(8*A*b+a*B)*(e*x)^(5/2)*sqrt(a+b*x^3)/(a*e^4)+3/8*(8*A*b+a*B)*(1+sqrt(3))*sqrt(e*x)*sqrt(a+b*x^3)/(b^(2/3)*e^2*(a^(1/3)+b^(1/3)*x*(1+sqrt(3))))-3/8*3^(1/4)*a^(1/3)*(8*A*b+a*B)*(a^(1/3)+b^(1/3)*x)*sqrt(cos(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))))^2)/cos(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))))*EllipticE(sin(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3))))),sqrt(1/4*(2+sqrt(3))))*sqrt(e*x)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))^2)/(b^(2/3)*e^2*sqrt(a+b*x^3)*sqrt(b^(1/3)*x*(a^(1/3)+b^(1/3)*x)/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))^2))-1/16*3^(3/4)*a^(1/3)*(8*A*b+a*B)*(a^(1/3)+b^(1/3)*x)*sqrt(cos(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))))^2)/cos(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))))*EllipticF(sin(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3))))),sqrt(1/4*(2+sqrt(3))))*(1-sqrt(3))*sqrt(e*x)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))^2)/(b^(2/3)*e^2*sqrt(a+b*x^3)*sqrt(b^(1/3)*x*(a^(1/3)+b^(1/3)*x)/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))^2))],
[(A+B*x^3)*sqrt(a+b*x^3)/(e*x)^(5/2),x,6,-2/3*A*(a+b*x^3)^(3/2)/(a*e*(e*x)^(3/2))+1/3*(2*A*b+a*B)*arctanh((e*x)^(3/2)*sqrt(b)/(e^(3/2)*sqrt(a+b*x^3)))/(e^(5/2)*sqrt(b))+1/3*(2*A*b+a*B)*(e*x)^(3/2)*sqrt(a+b*x^3)/(a*e^4)],
[(A+B*x^3)*sqrt(a+b*x^3)/(e*x)^(7/2),x,4,-2/5*A*(a+b*x^3)^(3/2)/(a*e*(e*x)^(5/2))+1/10*(4*A*b+5*a*B)*sqrt(e*x)*sqrt(a+b*x^3)/(a*e^4)+1/20*3^(3/4)*(4*A*b+5*a*B)*(a^(1/3)+b^(1/3)*x)*sqrt(cos(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))))^2)/cos(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))))*EllipticF(sin(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3))))),sqrt(1/4*(2+sqrt(3))))*sqrt(e*x)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))^2)/(a^(1/3)*e^4*sqrt(a+b*x^3)*sqrt(b^(1/3)*x*(a^(1/3)+b^(1/3)*x)/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))^2))],
[(A+B*x^3)*sqrt(a+b*x^3)/x^(9/2),x,6,-2/7*A*(a+b*x^3)^(3/2)/(a*x^(7/2))-2/7*(2*A*b+7*a*B)*sqrt(a+b*x^3)/(a*sqrt(x))+3/7*b^(1/3)*(2*A*b+7*a*B)*(1+sqrt(3))*sqrt(x)*sqrt(a+b*x^3)/(a*(a^(1/3)+b^(1/3)*x*(1+sqrt(3))))-3/7*3^(1/4)*b^(1/3)*(2*A*b+7*a*B)*(a^(1/3)+b^(1/3)*x)*sqrt(cos(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))))^2)/cos(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))))*EllipticE(sin(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3))))),sqrt(1/4*(2+sqrt(3))))*sqrt(x)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))^2)/(a^(2/3)*sqrt(a+b*x^3)*sqrt(b^(1/3)*x*(a^(1/3)+b^(1/3)*x)/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))^2))-1/14*3^(3/4)*b^(1/3)*(2*A*b+7*a*B)*(a^(1/3)+b^(1/3)*x)*sqrt(cos(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))))^2)/cos(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))))*EllipticF(sin(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3))))),sqrt(1/4*(2+sqrt(3))))*(1-sqrt(3))*sqrt(x)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))^2)/(a^(2/3)*sqrt(a+b*x^3)*sqrt(b^(1/3)*x*(a^(1/3)+b^(1/3)*x)/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))^2))],
[(A+B*x^3)*sqrt(a+b*x^3)/x^(11/2),x,6,-2/9*A*(a+b*x^3)^(3/2)/(a*x^(9/2))+2/3*B*arctanh(x^(3/2)*sqrt(b)/sqrt(a+b*x^3))*sqrt(b)-2/3*B*sqrt(a+b*x^3)/x^(3/2)],
[(A+B*x^3)*sqrt(a+b*x^3)/x^(13/2),x,4,-2/11*A*(a+b*x^3)^(3/2)/(a*x^(11/2))+2/55*(2*A*b-11*a*B)*sqrt(a+b*x^3)/(a*x^(5/2))-1/55*3^(3/4)*b*(2*A*b-11*a*B)*(a^(1/3)+b^(1/3)*x)*sqrt(cos(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))))^2)/cos(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))))*EllipticF(sin(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3))))),sqrt(1/4*(2+sqrt(3))))*sqrt(x)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))^2)/(a^(4/3)*sqrt(a+b*x^3)*sqrt(b^(1/3)*x*(a^(1/3)+b^(1/3)*x)/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))^2))],
[(e*x)^(7/2)*(a+b*x^3)^(3/2)*(A+B*x^3),x,8,1/72*(8*A*b-3*a*B)*(e*x)^(9/2)*(a+b*x^3)^(3/2)/(b*e)+1/12*B*(e*x)^(9/2)*(a+b*x^3)^(5/2)/(b*e)-1/192*a^3*(8*A*b-3*a*B)*e^(7/2)*arctanh((e*x)^(3/2)*sqrt(b)/(e^(3/2)*sqrt(a+b*x^3)))/b^(5/2)+1/192*a^2*(8*A*b-3*a*B)*e^2*(e*x)^(3/2)*sqrt(a+b*x^3)/b^2+1/96*a*(8*A*b-3*a*B)*(e*x)^(9/2)*sqrt(a+b*x^3)/(b*e)],
[(e*x)^(5/2)*(a+b*x^3)^(3/2)*(A+B*x^3),x,6,1/176*(22*A*b-7*a*B)*(e*x)^(7/2)*(a+b*x^3)^(3/2)/(b*e)+1/11*B*(e*x)^(7/2)*(a+b*x^3)^(5/2)/(b*e)+9/1760*a*(22*A*b-7*a*B)*(e*x)^(7/2)*sqrt(a+b*x^3)/(b*e)+27/7040*a^2*(22*A*b-7*a*B)*e^2*sqrt(e*x)*sqrt(a+b*x^3)/b^2-9/14080*3^(3/4)*a^(8/3)*(22*A*b-7*a*B)*e^2*(a^(1/3)+b^(1/3)*x)*sqrt(cos(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))))^2)/cos(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))))*EllipticF(sin(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3))))),sqrt(1/4*(2+sqrt(3))))*sqrt(e*x)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))^2)/(b^2*sqrt(a+b*x^3)*sqrt(b^(1/3)*x*(a^(1/3)+b^(1/3)*x)/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))^2))],
[(e*x)^(3/2)*(a+b*x^3)^(3/2)*(A+B*x^3),x,7,1/28*(4*A*b-a*B)*(e*x)^(5/2)*(a+b*x^3)^(3/2)/(b*e)+1/10*B*(e*x)^(5/2)*(a+b*x^3)^(5/2)/(b*e)+9/224*a*(4*A*b-a*B)*(e*x)^(5/2)*sqrt(a+b*x^3)/(b*e)+27/448*a^2*(4*A*b-a*B)*e*(1+sqrt(3))*sqrt(e*x)*sqrt(a+b*x^3)/(b^(5/3)*(a^(1/3)+b^(1/3)*x*(1+sqrt(3))))-27/448*3^(1/4)*a^(7/3)*(4*A*b-a*B)*e*(a^(1/3)+b^(1/3)*x)*sqrt(cos(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))))^2)/cos(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))))*EllipticE(sin(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3))))),sqrt(1/4*(2+sqrt(3))))*sqrt(e*x)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))^2)/(b^(5/3)*sqrt(a+b*x^3)*sqrt(b^(1/3)*x*(a^(1/3)+b^(1/3)*x)/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))^2))-9/896*3^(3/4)*a^(7/3)*(4*A*b-a*B)*e*(a^(1/3)+b^(1/3)*x)*sqrt(cos(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))))^2)/cos(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))))*EllipticF(sin(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3))))),sqrt(1/4*(2+sqrt(3))))*(1-sqrt(3))*sqrt(e*x)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))^2)/(b^(5/3)*sqrt(a+b*x^3)*sqrt(b^(1/3)*x*(a^(1/3)+b^(1/3)*x)/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))^2))],
[(a+b*x^3)^(3/2)*(A+B*x^3)*sqrt(e*x),x,7,1/36*(6*A*b-a*B)*(e*x)^(3/2)*(a+b*x^3)^(3/2)/(b*e)+1/9*B*(e*x)^(3/2)*(a+b*x^3)^(5/2)/(b*e)+1/24*a^2*(6*A*b-a*B)*arctanh((e*x)^(3/2)*sqrt(b)/(e^(3/2)*sqrt(a+b*x^3)))*sqrt(e)/b^(3/2)+1/24*a*(6*A*b-a*B)*(e*x)^(3/2)*sqrt(a+b*x^3)/(b*e)],
[(a+b*x^3)^(3/2)*(A+B*x^3)/sqrt(e*x),x,5,1/80*(16*A*b-a*B)*(a+b*x^3)^(3/2)*sqrt(e*x)/(b*e)+1/8*B*(a+b*x^3)^(5/2)*sqrt(e*x)/(b*e)+9/320*a*(16*A*b-a*B)*sqrt(e*x)*sqrt(a+b*x^3)/(b*e)+9/640*3^(3/4)*a^(5/3)*(16*A*b-a*B)*(a^(1/3)+b^(1/3)*x)*sqrt(cos(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))))^2)/cos(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))))*EllipticF(sin(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3))))),sqrt(1/4*(2+sqrt(3))))*sqrt(e*x)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))^2)/(b*e*sqrt(a+b*x^3)*sqrt(b^(1/3)*x*(a^(1/3)+b^(1/3)*x)/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))^2))],
[(a+b*x^3)^(3/2)*(A+B*x^3)/(e*x)^(3/2),x,7,1/7*(14*A*b+a*B)*(e*x)^(5/2)*(a+b*x^3)^(3/2)/(a*e^4)-2*A*(a+b*x^3)^(5/2)/(a*e*sqrt(e*x))+9/56*(14*A*b+a*B)*(e*x)^(5/2)*sqrt(a+b*x^3)/e^4+27/112*a*(14*A*b+a*B)*(1+sqrt(3))*sqrt(e*x)*sqrt(a+b*x^3)/(b^(2/3)*e^2*(a^(1/3)+b^(1/3)*x*(1+sqrt(3))))-27/112*3^(1/4)*a^(4/3)*(14*A*b+a*B)*(a^(1/3)+b^(1/3)*x)*sqrt(cos(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))))^2)/cos(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))))*EllipticE(sin(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3))))),sqrt(1/4*(2+sqrt(3))))*sqrt(e*x)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))^2)/(b^(2/3)*e^2*sqrt(a+b*x^3)*sqrt(b^(1/3)*x*(a^(1/3)+b^(1/3)*x)/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))^2))-9/224*3^(3/4)*a^(4/3)*(14*A*b+a*B)*(a^(1/3)+b^(1/3)*x)*sqrt(cos(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))))^2)/cos(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))))*EllipticF(sin(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3))))),sqrt(1/4*(2+sqrt(3))))*(1-sqrt(3))*sqrt(e*x)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))^2)/(b^(2/3)*e^2*sqrt(a+b*x^3)*sqrt(b^(1/3)*x*(a^(1/3)+b^(1/3)*x)/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))^2))],
[(a+b*x^3)^(3/2)*(A+B*x^3)/(e*x)^(5/2),x,7,1/6*(4*A*b+a*B)*(e*x)^(3/2)*(a+b*x^3)^(3/2)/(a*e^4)-2/3*A*(a+b*x^3)^(5/2)/(a*e*(e*x)^(3/2))+1/4*a*(4*A*b+a*B)*arctanh((e*x)^(3/2)*sqrt(b)/(e^(3/2)*sqrt(a+b*x^3)))/(e^(5/2)*sqrt(b))+1/4*(4*A*b+a*B)*(e*x)^(3/2)*sqrt(a+b*x^3)/e^4],
[(a+b*x^3)^(3/2)*(A+B*x^3)/(e*x)^(7/2),x,5,-2/5*A*(a+b*x^3)^(5/2)/(a*e*(e*x)^(5/2))+1/5*(2*A*b+a*B)*(a+b*x^3)^(3/2)*sqrt(e*x)/(a*e^4)+9/20*(2*A*b+a*B)*sqrt(e*x)*sqrt(a+b*x^3)/e^4+9/40*3^(3/4)*a^(2/3)*(2*A*b+a*B)*(a^(1/3)+b^(1/3)*x)*sqrt(cos(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))))^2)/cos(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))))*EllipticF(sin(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3))))),sqrt(1/4*(2+sqrt(3))))*sqrt(e*x)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))^2)/(e^4*sqrt(a+b*x^3)*sqrt(b^(1/3)*x*(a^(1/3)+b^(1/3)*x)/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))^2))],
[(e*x)^(7/2)*(a+b*x^3)^(5/2)*(A+B*x^3),x,9,1/144*a*(10*A*b-3*a*B)*(e*x)^(9/2)*(a+b*x^3)^(3/2)/(b*e)+1/120*(10*A*b-3*a*B)*(e*x)^(9/2)*(a+b*x^3)^(5/2)/(b*e)+1/15*B*(e*x)^(9/2)*(a+b*x^3)^(7/2)/(b*e)-1/384*a^4*(10*A*b-3*a*B)*e^(7/2)*arctanh((e*x)^(3/2)*sqrt(b)/(e^(3/2)*sqrt(a+b*x^3)))/b^(5/2)+1/384*a^3*(10*A*b-3*a*B)*e^2*(e*x)^(3/2)*sqrt(a+b*x^3)/b^2+1/192*a^2*(10*A*b-3*a*B)*(e*x)^(9/2)*sqrt(a+b*x^3)/(b*e)],
[(e*x)^(5/2)*(a+b*x^3)^(5/2)*(A+B*x^3),x,7,15/704*a*(4*A*b-a*B)*(e*x)^(7/2)*(a+b*x^3)^(3/2)/(b*e)+1/44*(4*A*b-a*B)*(e*x)^(7/2)*(a+b*x^3)^(5/2)/(b*e)+1/14*B*(e*x)^(7/2)*(a+b*x^3)^(7/2)/(b*e)+27/1408*a^2*(4*A*b-a*B)*(e*x)^(7/2)*sqrt(a+b*x^3)/(b*e)+81/5632*a^3*(4*A*b-a*B)*e^2*sqrt(e*x)*sqrt(a+b*x^3)/b^2-27/11264*3^(3/4)*a^(11/3)*(4*A*b-a*B)*e^2*(a^(1/3)+b^(1/3)*x)*sqrt(cos(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))))^2)/cos(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))))*EllipticF(sin(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3))))),sqrt(1/4*(2+sqrt(3))))*sqrt(e*x)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))^2)/(b^2*sqrt(a+b*x^3)*sqrt(b^(1/3)*x*(a^(1/3)+b^(1/3)*x)/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))^2))],
[(e*x)^(3/2)*(a+b*x^3)^(5/2)*(A+B*x^3),x,8,3/728*a*(26*A*b-5*a*B)*(e*x)^(5/2)*(a+b*x^3)^(3/2)/(b*e)+1/260*(26*A*b-5*a*B)*(e*x)^(5/2)*(a+b*x^3)^(5/2)/(b*e)+1/13*B*(e*x)^(5/2)*(a+b*x^3)^(7/2)/(b*e)+27/5824*a^2*(26*A*b-5*a*B)*(e*x)^(5/2)*sqrt(a+b*x^3)/(b*e)+81/11648*a^3*(26*A*b-5*a*B)*e*(1+sqrt(3))*sqrt(e*x)*sqrt(a+b*x^3)/(b^(5/3)*(a^(1/3)+b^(1/3)*x*(1+sqrt(3))))-81/11648*3^(1/4)*a^(10/3)*(26*A*b-5*a*B)*e*(a^(1/3)+b^(1/3)*x)*sqrt(cos(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))))^2)/cos(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))))*EllipticE(sin(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3))))),sqrt(1/4*(2+sqrt(3))))*sqrt(e*x)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))^2)/(b^(5/3)*sqrt(a+b*x^3)*sqrt(b^(1/3)*x*(a^(1/3)+b^(1/3)*x)/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))^2))-27/23296*3^(3/4)*a^(10/3)*(26*A*b-5*a*B)*e*(a^(1/3)+b^(1/3)*x)*sqrt(cos(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))))^2)/cos(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))))*EllipticF(sin(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3))))),sqrt(1/4*(2+sqrt(3))))*(1-sqrt(3))*sqrt(e*x)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))^2)/(b^(5/3)*sqrt(a+b*x^3)*sqrt(b^(1/3)*x*(a^(1/3)+b^(1/3)*x)/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))^2))],
[(a+b*x^3)^(5/2)*(A+B*x^3)*sqrt(e*x),x,8,5/288*a*(8*A*b-a*B)*(e*x)^(3/2)*(a+b*x^3)^(3/2)/(b*e)+1/72*(8*A*b-a*B)*(e*x)^(3/2)*(a+b*x^3)^(5/2)/(b*e)+1/12*B*(e*x)^(3/2)*(a+b*x^3)^(7/2)/(b*e)+5/192*a^3*(8*A*b-a*B)*arctanh((e*x)^(3/2)*sqrt(b)/(e^(3/2)*sqrt(a+b*x^3)))*sqrt(e)/b^(3/2)+5/192*a^2*(8*A*b-a*B)*(e*x)^(3/2)*sqrt(a+b*x^3)/(b*e)],
[(a+b*x^3)^(5/2)*(A+B*x^3)/sqrt(e*x),x,6,3/352*a*(22*A*b-a*B)*(a+b*x^3)^(3/2)*sqrt(e*x)/(b*e)+1/176*(22*A*b-a*B)*(a+b*x^3)^(5/2)*sqrt(e*x)/(b*e)+1/11*B*(a+b*x^3)^(7/2)*sqrt(e*x)/(b*e)+27/1408*a^2*(22*A*b-a*B)*sqrt(e*x)*sqrt(a+b*x^3)/(b*e)+27/2816*3^(3/4)*a^(8/3)*(22*A*b-a*B)*(a^(1/3)+b^(1/3)*x)*sqrt(cos(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))))^2)/cos(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))))*EllipticF(sin(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3))))),sqrt(1/4*(2+sqrt(3))))*sqrt(e*x)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))^2)/(b*e*sqrt(a+b*x^3)*sqrt(b^(1/3)*x*(a^(1/3)+b^(1/3)*x)/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))^2))],
[(a+b*x^3)^(5/2)*(A+B*x^3)/(e*x)^(3/2),x,8,3/28*(20*A*b+a*B)*(e*x)^(5/2)*(a+b*x^3)^(3/2)/e^4+1/10*(20*A*b+a*B)*(e*x)^(5/2)*(a+b*x^3)^(5/2)/(a*e^4)-2*A*(a+b*x^3)^(7/2)/(a*e*sqrt(e*x))+27/224*a*(20*A*b+a*B)*(e*x)^(5/2)*sqrt(a+b*x^3)/e^4+81/448*a^2*(20*A*b+a*B)*(1+sqrt(3))*sqrt(e*x)*sqrt(a+b*x^3)/(b^(2/3)*e^2*(a^(1/3)+b^(1/3)*x*(1+sqrt(3))))-81/448*3^(1/4)*a^(7/3)*(20*A*b+a*B)*(a^(1/3)+b^(1/3)*x)*sqrt(cos(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))))^2)/cos(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))))*EllipticE(sin(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3))))),sqrt(1/4*(2+sqrt(3))))*sqrt(e*x)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))^2)/(b^(2/3)*e^2*sqrt(a+b*x^3)*sqrt(b^(1/3)*x*(a^(1/3)+b^(1/3)*x)/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))^2))-27/896*3^(3/4)*a^(7/3)*(20*A*b+a*B)*(a^(1/3)+b^(1/3)*x)*sqrt(cos(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))))^2)/cos(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))))*EllipticF(sin(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3))))),sqrt(1/4*(2+sqrt(3))))*(1-sqrt(3))*sqrt(e*x)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))^2)/(b^(2/3)*e^2*sqrt(a+b*x^3)*sqrt(b^(1/3)*x*(a^(1/3)+b^(1/3)*x)/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))^2))],
[(a+b*x^3)^(5/2)*(A+B*x^3)/(e*x)^(5/2),x,8,5/36*(6*A*b+a*B)*(e*x)^(3/2)*(a+b*x^3)^(3/2)/e^4+1/9*(6*A*b+a*B)*(e*x)^(3/2)*(a+b*x^3)^(5/2)/(a*e^4)-2/3*A*(a+b*x^3)^(7/2)/(a*e*(e*x)^(3/2))+5/24*a^2*(6*A*b+a*B)*arctanh((e*x)^(3/2)*sqrt(b)/(e^(3/2)*sqrt(a+b*x^3)))/(e^(5/2)*sqrt(b))+5/24*a*(6*A*b+a*B)*(e*x)^(3/2)*sqrt(a+b*x^3)/e^4],
[(a+b*x^3)^(5/2)*(A+B*x^3)/(e*x)^(7/2),x,6,-2/5*A*(a+b*x^3)^(7/2)/(a*e*(e*x)^(5/2))+3/80*(16*A*b+5*a*B)*(a+b*x^3)^(3/2)*sqrt(e*x)/e^4+1/40*(16*A*b+5*a*B)*(a+b*x^3)^(5/2)*sqrt(e*x)/(a*e^4)+27/320*a*(16*A*b+5*a*B)*sqrt(e*x)*sqrt(a+b*x^3)/e^4+27/640*3^(3/4)*a^(5/3)*(16*A*b+5*a*B)*(a^(1/3)+b^(1/3)*x)*sqrt(cos(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))))^2)/cos(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))))*EllipticF(sin(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3))))),sqrt(1/4*(2+sqrt(3))))*sqrt(e*x)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))^2)/(e^4*sqrt(a+b*x^3)*sqrt(b^(1/3)*x*(a^(1/3)+b^(1/3)*x)/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))^2))],

# p<0
[(e*x)^(7/2)*(A+B*x^3)/sqrt(a+b*x^3),x,6,-1/12*a*(4*A*b-3*a*B)*e^(7/2)*arctanh((e*x)^(3/2)*sqrt(b)/(e^(3/2)*sqrt(a+b*x^3)))/b^(5/2)+1/12*(4*A*b-3*a*B)*e^2*(e*x)^(3/2)*sqrt(a+b*x^3)/b^2+1/6*B*(e*x)^(9/2)*sqrt(a+b*x^3)/(b*e)],
[(e*x)^(5/2)*(A+B*x^3)/sqrt(a+b*x^3),x,4,1/5*B*(e*x)^(7/2)*sqrt(a+b*x^3)/(b*e)+1/20*(10*A*b-7*a*B)*e^2*sqrt(e*x)*sqrt(a+b*x^3)/b^2-1/40*a^(2/3)*(10*A*b-7*a*B)*e^2*(a^(1/3)+b^(1/3)*x)*sqrt(cos(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))))^2)/cos(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))))*EllipticF(sin(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3))))),sqrt(1/4*(2+sqrt(3))))*sqrt(e*x)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))^2)/(3^(1/4)*b^2*sqrt(a+b*x^3)*sqrt(b^(1/3)*x*(a^(1/3)+b^(1/3)*x)/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))^2))],
[(e*x)^(3/2)*(A+B*x^3)/sqrt(a+b*x^3),x,5,1/4*B*(e*x)^(5/2)*sqrt(a+b*x^3)/(b*e)+1/8*(8*A*b-5*a*B)*e*(1+sqrt(3))*sqrt(e*x)*sqrt(a+b*x^3)/(b^(5/3)*(a^(1/3)+b^(1/3)*x*(1+sqrt(3))))-1/8*3^(1/4)*a^(1/3)*(8*A*b-5*a*B)*e*(a^(1/3)+b^(1/3)*x)*sqrt(cos(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))))^2)/cos(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))))*EllipticE(sin(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3))))),sqrt(1/4*(2+sqrt(3))))*sqrt(e*x)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))^2)/(b^(5/3)*sqrt(a+b*x^3)*sqrt(b^(1/3)*x*(a^(1/3)+b^(1/3)*x)/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))^2))-1/16*a^(1/3)*(8*A*b-5*a*B)*e*(a^(1/3)+b^(1/3)*x)*sqrt(cos(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))))^2)/cos(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))))*EllipticF(sin(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3))))),sqrt(1/4*(2+sqrt(3))))*(1-sqrt(3))*sqrt(e*x)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))^2)/(3^(1/4)*b^(5/3)*sqrt(a+b*x^3)*sqrt(b^(1/3)*x*(a^(1/3)+b^(1/3)*x)/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))^2))],
[(A+B*x^3)*sqrt(e*x)/sqrt(a+b*x^3),x,5,1/3*(2*A*b-a*B)*arctanh((e*x)^(3/2)*sqrt(b)/(e^(3/2)*sqrt(a+b*x^3)))*sqrt(e)/b^(3/2)+1/3*B*(e*x)^(3/2)*sqrt(a+b*x^3)/(b*e)],
[(A+B*x^3)/(sqrt(e*x)*sqrt(a+b*x^3)),x,3,1/2*B*sqrt(e*x)*sqrt(a+b*x^3)/(b*e)+1/4*(4*A*b-a*B)*(a^(1/3)+b^(1/3)*x)*sqrt(cos(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))))^2)/cos(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))))*EllipticF(sin(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3))))),sqrt(1/4*(2+sqrt(3))))*sqrt(e*x)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))^2)/(3^(1/4)*a^(1/3)*b*e*sqrt(a+b*x^3)*sqrt(b^(1/3)*x*(a^(1/3)+b^(1/3)*x)/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))^2))],
[(A+B*x^3)/((e*x)^(3/2)*sqrt(a+b*x^3)),x,5,-2*A*sqrt(a+b*x^3)/(a*e*sqrt(e*x))+(2*A*b+a*B)*(1+sqrt(3))*sqrt(e*x)*sqrt(a+b*x^3)/(a*b^(2/3)*e^2*(a^(1/3)+b^(1/3)*x*(1+sqrt(3))))-3^(1/4)*(2*A*b+a*B)*(a^(1/3)+b^(1/3)*x)*sqrt(cos(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))))^2)/cos(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))))*EllipticE(sin(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3))))),sqrt(1/4*(2+sqrt(3))))*sqrt(e*x)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))^2)/(a^(2/3)*b^(2/3)*e^2*sqrt(a+b*x^3)*sqrt(b^(1/3)*x*(a^(1/3)+b^(1/3)*x)/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))^2))-1/2*(2*A*b+a*B)*(a^(1/3)+b^(1/3)*x)*sqrt(cos(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))))^2)/cos(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))))*EllipticF(sin(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3))))),sqrt(1/4*(2+sqrt(3))))*(1-sqrt(3))*sqrt(e*x)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))^2)/(3^(1/4)*a^(2/3)*b^(2/3)*e^2*sqrt(a+b*x^3)*sqrt(b^(1/3)*x*(a^(1/3)+b^(1/3)*x)/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))^2))],
[(A+B*x^3)/((e*x)^(5/2)*sqrt(a+b*x^3)),x,5,2/3*B*arctanh((e*x)^(3/2)*sqrt(b)/(e^(3/2)*sqrt(a+b*x^3)))/(e^(5/2)*sqrt(b))-2/3*A*sqrt(a+b*x^3)/(a*e*(e*x)^(3/2))],
[(A+B*x^3)/((e*x)^(7/2)*sqrt(a+b*x^3)),x,3,-2/5*A*sqrt(a+b*x^3)/(a*e*(e*x)^(5/2))-1/5*(2*A*b-5*a*B)*(a^(1/3)+b^(1/3)*x)*sqrt(cos(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))))^2)/cos(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))))*EllipticF(sin(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3))))),sqrt(1/4*(2+sqrt(3))))*sqrt(e*x)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))^2)/(3^(1/4)*a^(4/3)*e^4*sqrt(a+b*x^3)*sqrt(b^(1/3)*x*(a^(1/3)+b^(1/3)*x)/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))^2))],
[(e*x)^(7/2)*(A+B*x^3)/(a+b*x^3)^(3/2),x,6,1/3*(2*A*b-3*a*B)*e^(7/2)*arctanh((e*x)^(3/2)*sqrt(b)/(e^(3/2)*sqrt(a+b*x^3)))/b^(5/2)-1/3*(2*A*b-3*a*B)*e^2*(e*x)^(3/2)/(b^2*sqrt(a+b*x^3))+1/3*B*(e*x)^(9/2)/(b*e*sqrt(a+b*x^3))],
[(e*x)^(5/2)*(A+B*x^3)/(a+b*x^3)^(3/2),x,4,1/2*B*(e*x)^(7/2)/(b*e*sqrt(a+b*x^3))-1/6*(4*A*b-7*a*B)*e^2*sqrt(e*x)/(b^2*sqrt(a+b*x^3))+1/12*(4*A*b-7*a*B)*e^2*(a^(1/3)+b^(1/3)*x)*sqrt(cos(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))))^2)/cos(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))))*EllipticF(sin(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3))))),sqrt(1/4*(2+sqrt(3))))*sqrt(e*x)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))^2)/(3^(1/4)*a^(1/3)*b^2*sqrt(a+b*x^3)*sqrt(b^(1/3)*x*(a^(1/3)+b^(1/3)*x)/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))^2))],
[(e*x)^(3/2)*(A+B*x^3)/(a+b*x^3)^(3/2),x,5,2/3*(A*b-a*B)*(e*x)^(5/2)/(a*b*e*sqrt(a+b*x^3))-1/3*(2*A*b-5*a*B)*e*(1+sqrt(3))*sqrt(e*x)*sqrt(a+b*x^3)/(a*b^(5/3)*(a^(1/3)+b^(1/3)*x*(1+sqrt(3))))+(2*A*b-5*a*B)*e*(a^(1/3)+b^(1/3)*x)*sqrt(cos(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))))^2)/cos(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))))*EllipticE(sin(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3))))),sqrt(1/4*(2+sqrt(3))))*sqrt(e*x)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))^2)/(3^(3/4)*a^(2/3)*b^(5/3)*sqrt(a+b*x^3)*sqrt(b^(1/3)*x*(a^(1/3)+b^(1/3)*x)/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))^2))+1/6*(2*A*b-5*a*B)*e*(a^(1/3)+b^(1/3)*x)*sqrt(cos(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))))^2)/cos(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))))*EllipticF(sin(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3))))),sqrt(1/4*(2+sqrt(3))))*(1-sqrt(3))*sqrt(e*x)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))^2)/(3^(1/4)*a^(2/3)*b^(5/3)*sqrt(a+b*x^3)*sqrt(b^(1/3)*x*(a^(1/3)+b^(1/3)*x)/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))^2))],
[(A+B*x^3)*sqrt(e*x)/(a+b*x^3)^(3/2),x,5,2/3*B*arctanh((e*x)^(3/2)*sqrt(b)/(e^(3/2)*sqrt(a+b*x^3)))*sqrt(e)/b^(3/2)+2/3*(A*b-a*B)*(e*x)^(3/2)/(a*b*e*sqrt(a+b*x^3))],
[(A+B*x^3)/((a+b*x^3)^(3/2)*sqrt(e*x)),x,3,2/3*(A*b-a*B)*sqrt(e*x)/(a*b*e*sqrt(a+b*x^3))+1/3*(2*A*b+a*B)*(a^(1/3)+b^(1/3)*x)*sqrt(cos(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))))^2)/cos(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))))*EllipticF(sin(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3))))),sqrt(1/4*(2+sqrt(3))))*sqrt(e*x)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))^2)/(3^(1/4)*a^(4/3)*b*e*sqrt(a+b*x^3)*sqrt(b^(1/3)*x*(a^(1/3)+b^(1/3)*x)/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))^2))],
[(A+B*x^3)/((e*x)^(3/2)*(a+b*x^3)^(3/2)),x,6,-2/3*(4*A*b-a*B)*(e*x)^(5/2)/(a^2*e^4*sqrt(a+b*x^3))-2*A/(a*e*sqrt(e*x)*sqrt(a+b*x^3))+2/3*(4*A*b-a*B)*(1+sqrt(3))*sqrt(e*x)*sqrt(a+b*x^3)/(a^2*b^(2/3)*e^2*(a^(1/3)+b^(1/3)*x*(1+sqrt(3))))-2*(4*A*b-a*B)*(a^(1/3)+b^(1/3)*x)*sqrt(cos(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))))^2)/cos(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))))*EllipticE(sin(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3))))),sqrt(1/4*(2+sqrt(3))))*sqrt(e*x)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))^2)/(3^(3/4)*a^(5/3)*b^(2/3)*e^2*sqrt(a+b*x^3)*sqrt(b^(1/3)*x*(a^(1/3)+b^(1/3)*x)/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))^2))-1/3*(4*A*b-a*B)*(a^(1/3)+b^(1/3)*x)*sqrt(cos(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))))^2)/cos(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))))*EllipticF(sin(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3))))),sqrt(1/4*(2+sqrt(3))))*(1-sqrt(3))*sqrt(e*x)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))^2)/(3^(1/4)*a^(5/3)*b^(2/3)*e^2*sqrt(a+b*x^3)*sqrt(b^(1/3)*x*(a^(1/3)+b^(1/3)*x)/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))^2))],
[(A+B*x^3)/((e*x)^(5/2)*(a+b*x^3)^(3/2)),x,2,-2/3*A/(a*e*(e*x)^(3/2)*sqrt(a+b*x^3))-2/3*(2*A*b-a*B)*(e*x)^(3/2)/(a^2*e^4*sqrt(a+b*x^3))],
[(A+B*x^3)/((e*x)^(7/2)*(a+b*x^3)^(3/2)),x,4,-2/5*A/(a*e*(e*x)^(5/2)*sqrt(a+b*x^3))-2/15*(8*A*b-5*a*B)*sqrt(e*x)/(a^2*e^4*sqrt(a+b*x^3))-2/15*(8*A*b-5*a*B)*(a^(1/3)+b^(1/3)*x)*sqrt(cos(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))))^2)/cos(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))))*EllipticF(sin(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3))))),sqrt(1/4*(2+sqrt(3))))*sqrt(e*x)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))^2)/(3^(1/4)*a^(7/3)*e^4*sqrt(a+b*x^3)*sqrt(b^(1/3)*x*(a^(1/3)+b^(1/3)*x)/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))^2))],
[(e*x)^(7/2)*(A+B*x^3)/(a+b*x^3)^(5/2),x,6,2/9*(A*b-a*B)*(e*x)^(9/2)/(a*b*e*(a+b*x^3)^(3/2))+2/3*B*e^(7/2)*arctanh((e*x)^(3/2)*sqrt(b)/(e^(3/2)*sqrt(a+b*x^3)))/b^(5/2)-2/3*B*e^2*(e*x)^(3/2)/(b^2*sqrt(a+b*x^3))],
[(e*x)^(5/2)*(A+B*x^3)/(a+b*x^3)^(5/2),x,4,2/9*(A*b-a*B)*(e*x)^(7/2)/(a*b*e*(a+b*x^3)^(3/2))-2/27*(2*A*b+7*a*B)*e^2*sqrt(e*x)/(a*b^2*sqrt(a+b*x^3))+1/27*(2*A*b+7*a*B)*e^2*(a^(1/3)+b^(1/3)*x)*sqrt(cos(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))))^2)/cos(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))))*EllipticF(sin(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3))))),sqrt(1/4*(2+sqrt(3))))*sqrt(e*x)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))^2)/(3^(1/4)*a^(4/3)*b^2*sqrt(a+b*x^3)*sqrt(b^(1/3)*x*(a^(1/3)+b^(1/3)*x)/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))^2))],
[(e*x)^(3/2)*(A+B*x^3)/(a+b*x^3)^(5/2),x,6,2/9*(A*b-a*B)*(e*x)^(5/2)/(a*b*e*(a+b*x^3)^(3/2))+2/27*(4*A*b+5*a*B)*(e*x)^(5/2)/(a^2*b*e*sqrt(a+b*x^3))-2/27*(4*A*b+5*a*B)*e*(1+sqrt(3))*sqrt(e*x)*sqrt(a+b*x^3)/(a^2*b^(5/3)*(a^(1/3)+b^(1/3)*x*(1+sqrt(3))))+2/9*(4*A*b+5*a*B)*e*(a^(1/3)+b^(1/3)*x)*sqrt(cos(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))))^2)/cos(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))))*EllipticE(sin(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3))))),sqrt(1/4*(2+sqrt(3))))*sqrt(e*x)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))^2)/(3^(3/4)*a^(5/3)*b^(5/3)*sqrt(a+b*x^3)*sqrt(b^(1/3)*x*(a^(1/3)+b^(1/3)*x)/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))^2))+1/27*(4*A*b+5*a*B)*e*(a^(1/3)+b^(1/3)*x)*sqrt(cos(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))))^2)/cos(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))))*EllipticF(sin(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3))))),sqrt(1/4*(2+sqrt(3))))*(1-sqrt(3))*sqrt(e*x)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))^2)/(3^(1/4)*a^(5/3)*b^(5/3)*sqrt(a+b*x^3)*sqrt(b^(1/3)*x*(a^(1/3)+b^(1/3)*x)/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))^2))],
[(A+B*x^3)*sqrt(e*x)/(a+b*x^3)^(5/2),x,2,2/9*(A*b-a*B)*(e*x)^(3/2)/(a*b*e*(a+b*x^3)^(3/2))+2/9*(2*A*b+a*B)*(e*x)^(3/2)/(a^2*b*e*sqrt(a+b*x^3))],
[(A+B*x^3)/((a+b*x^3)^(5/2)*sqrt(e*x)),x,4,2/9*(A*b-a*B)*sqrt(e*x)/(a*b*e*(a+b*x^3)^(3/2))+2/27*(8*A*b+a*B)*sqrt(e*x)/(a^2*b*e*sqrt(a+b*x^3))+2/27*(8*A*b+a*B)*(a^(1/3)+b^(1/3)*x)*sqrt(cos(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))))^2)/cos(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))))*EllipticF(sin(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3))))),sqrt(1/4*(2+sqrt(3))))*sqrt(e*x)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))^2)/(3^(1/4)*a^(7/3)*b*e*sqrt(a+b*x^3)*sqrt(b^(1/3)*x*(a^(1/3)+b^(1/3)*x)/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))^2))],
[(A+B*x^3)/((e*x)^(3/2)*(a+b*x^3)^(5/2)),x,7,-2/9*(10*A*b-a*B)*(e*x)^(5/2)/(a^2*e^4*(a+b*x^3)^(3/2))-2*A/(a*e*(a+b*x^3)^(3/2)*sqrt(e*x))-8/27*(10*A*b-a*B)*(e*x)^(5/2)/(a^3*e^4*sqrt(a+b*x^3))+8/27*(10*A*b-a*B)*(1+sqrt(3))*sqrt(e*x)*sqrt(a+b*x^3)/(a^3*b^(2/3)*e^2*(a^(1/3)+b^(1/3)*x*(1+sqrt(3))))-8/9*(10*A*b-a*B)*(a^(1/3)+b^(1/3)*x)*sqrt(cos(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))))^2)/cos(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))))*EllipticE(sin(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3))))),sqrt(1/4*(2+sqrt(3))))*sqrt(e*x)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))^2)/(3^(3/4)*a^(8/3)*b^(2/3)*e^2*sqrt(a+b*x^3)*sqrt(b^(1/3)*x*(a^(1/3)+b^(1/3)*x)/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))^2))-4/27*(10*A*b-a*B)*(a^(1/3)+b^(1/3)*x)*sqrt(cos(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))))^2)/cos(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))))*EllipticF(sin(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3))))),sqrt(1/4*(2+sqrt(3))))*(1-sqrt(3))*sqrt(e*x)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))^2)/(3^(1/4)*a^(8/3)*b^(2/3)*e^2*sqrt(a+b*x^3)*sqrt(b^(1/3)*x*(a^(1/3)+b^(1/3)*x)/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))^2))],
[(A+B*x^3)/((e*x)^(5/2)*(a+b*x^3)^(5/2)),x,3,-2/3*A/(a*e*(e*x)^(3/2)*(a+b*x^3)^(3/2))-2/9*(4*A*b-a*B)*(e*x)^(3/2)/(a^2*e^4*(a+b*x^3)^(3/2))-4/9*(4*A*b-a*B)*(e*x)^(3/2)/(a^3*e^4*sqrt(a+b*x^3))],
[(A+B*x^3)/((e*x)^(7/2)*(a+b*x^3)^(5/2)),x,5,-2/5*A/(a*e*(e*x)^(5/2)*(a+b*x^3)^(3/2))-2/45*(14*A*b-5*a*B)*sqrt(e*x)/(a^2*e^4*(a+b*x^3)^(3/2))-16/135*(14*A*b-5*a*B)*sqrt(e*x)/(a^3*e^4*sqrt(a+b*x^3))-16/135*(14*A*b-5*a*B)*(a^(1/3)+b^(1/3)*x)*sqrt(cos(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))))^2)/cos(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))))*EllipticF(sin(arccos((a^(1/3)+b^(1/3)*x*(1-sqrt(3)))/(a^(1/3)+b^(1/3)*x*(1+sqrt(3))))),sqrt(1/4*(2+sqrt(3))))*sqrt(e*x)*sqrt((a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))^2)/(3^(1/4)*a^(10/3)*e^4*sqrt(a+b*x^3)*sqrt(b^(1/3)*x*(a^(1/3)+b^(1/3)*x)/(a^(1/3)+b^(1/3)*x*(1+sqrt(3)))^2))],

# Integrands of the form (e x)^m (a+b x^3)^(p/3) (c+d x^3)^q

# Integrands of the form x^m (a+b x^3)^(p/3) / (c+d x^3) when b c+a d=0

# p>0
[x^11*(a+b*x^3)^(1/3)/(a*d-b*d*x^3),x,8,-a^3*(a+b*x^3)^(1/3)/(b^4*d)-1/4*a^2*(a+b*x^3)^(4/3)/(b^4*d)+1/7*a*(a+b*x^3)^(7/3)/(b^4*d)-1/10*(a+b*x^3)^(10/3)/(b^4*d)+1/3*a^(10/3)*log(a-b*x^3)/(2^(2/3)*b^4*d)-a^(10/3)*log(2^(1/3)*a^(1/3)-(a+b*x^3)^(1/3))/(2^(2/3)*b^4*d)+2^(1/3)*a^(10/3)*arctan((a^(1/3)+2^(2/3)*(a+b*x^3)^(1/3))/(a^(1/3)*sqrt(3)))/(b^4*d*sqrt(3))],
[x^8*(a+b*x^3)^(1/3)/(a*d-b*d*x^3),x,8,-a^2*(a+b*x^3)^(1/3)/(b^3*d)-1/7*(a+b*x^3)^(7/3)/(b^3*d)+1/3*a^(7/3)*log(a-b*x^3)/(2^(2/3)*b^3*d)-a^(7/3)*log(2^(1/3)*a^(1/3)-(a+b*x^3)^(1/3))/(2^(2/3)*b^3*d)+2^(1/3)*a^(7/3)*arctan((a^(1/3)+2^(2/3)*(a+b*x^3)^(1/3))/(a^(1/3)*sqrt(3)))/(b^3*d*sqrt(3))],
[x^5*(a+b*x^3)^(1/3)/(a*d-b*d*x^3),x,7,-a*(a+b*x^3)^(1/3)/(b^2*d)-1/4*(a+b*x^3)^(4/3)/(b^2*d)+1/3*a^(4/3)*log(a-b*x^3)/(2^(2/3)*b^2*d)-a^(4/3)*log(2^(1/3)*a^(1/3)-(a+b*x^3)^(1/3))/(2^(2/3)*b^2*d)+2^(1/3)*a^(4/3)*arctan((a^(1/3)+2^(2/3)*(a+b*x^3)^(1/3))/(a^(1/3)*sqrt(3)))/(b^2*d*sqrt(3))],
[x^2*(a+b*x^3)^(1/3)/(a*d-b*d*x^3),x,6,-(a+b*x^3)^(1/3)/(b*d)+1/3*a^(1/3)*log(a-b*x^3)/(2^(2/3)*b*d)-a^(1/3)*log(2^(1/3)*a^(1/3)-(a+b*x^3)^(1/3))/(2^(2/3)*b*d)+2^(1/3)*a^(1/3)*arctan((a^(1/3)+2^(2/3)*(a+b*x^3)^(1/3))/(a^(1/3)*sqrt(3)))/(b*d*sqrt(3))],
[(a+b*x^3)^(1/3)/(x*(a*d-b*d*x^3)),x,10,-1/2*log(x)/(a^(2/3)*d)+1/3*log(a-b*x^3)/(2^(2/3)*a^(2/3)*d)+1/2*log(a^(1/3)-(a+b*x^3)^(1/3))/(a^(2/3)*d)-log(2^(1/3)*a^(1/3)-(a+b*x^3)^(1/3))/(2^(2/3)*a^(2/3)*d)-arctan((a^(1/3)+2*(a+b*x^3)^(1/3))/(a^(1/3)*sqrt(3)))/(a^(2/3)*d*sqrt(3))+2^(1/3)*arctan((a^(1/3)+2^(2/3)*(a+b*x^3)^(1/3))/(a^(1/3)*sqrt(3)))/(a^(2/3)*d*sqrt(3))],
[(a+b*x^3)^(1/3)/(x^4*(a*d-b*d*x^3)),x,13,1/3*b*(a+b*x^3)^(1/3)/(a^2*d)-1/3*(a+b*x^3)^(4/3)/(a^2*d*x^3)-2/3*b*log(x)/(a^(5/3)*d)+1/3*b*log(a-b*x^3)/(2^(2/3)*a^(5/3)*d)+2/3*b*log(a^(1/3)-(a+b*x^3)^(1/3))/(a^(5/3)*d)-b*log(2^(1/3)*a^(1/3)-(a+b*x^3)^(1/3))/(2^(2/3)*a^(5/3)*d)-4/3*b*arctan((a^(1/3)+2*(a+b*x^3)^(1/3))/(a^(1/3)*sqrt(3)))/(a^(5/3)*d*sqrt(3))+2^(1/3)*b*arctan((a^(1/3)+2^(2/3)*(a+b*x^3)^(1/3))/(a^(1/3)*sqrt(3)))/(a^(5/3)*d*sqrt(3))],
[(a+b*x^3)^(1/3)/(x^7*(a*d-b*d*x^3)),x,12,-2/9*b*(a+b*x^3)^(1/3)/(a^2*d*x^3)-1/6*(a+b*x^3)^(4/3)/(a^2*d*x^6)-11/18*b^2*log(x)/(a^(8/3)*d)+1/3*b^2*log(a-b*x^3)/(2^(2/3)*a^(8/3)*d)+11/18*b^2*log(a^(1/3)-(a+b*x^3)^(1/3))/(a^(8/3)*d)-b^2*log(2^(1/3)*a^(1/3)-(a+b*x^3)^(1/3))/(2^(2/3)*a^(8/3)*d)-11/9*b^2*arctan((a^(1/3)+2*(a+b*x^3)^(1/3))/(a^(1/3)*sqrt(3)))/(a^(8/3)*d*sqrt(3))+2^(1/3)*b^2*arctan((a^(1/3)+2^(2/3)*(a+b*x^3)^(1/3))/(a^(1/3)*sqrt(3)))/(a^(8/3)*d*sqrt(3))],
[x^7*(a+b*x^3)^(1/3)/(a*d-b*d*x^3),x,6,-7/18*a*x^2*(a+b*x^3)^(1/3)/(b^2*d)-1/6*x^5*(a+b*x^3)^(1/3)/(b*d)+1/3*a^2*log(a*d-b*d*x^3)/(2^(2/3)*b^(8/3)*d)+11/18*a^2*log(b^(1/3)*x-(a+b*x^3)^(1/3))/(b^(8/3)*d)-a^2*log(2^(1/3)*b^(1/3)*x-(a+b*x^3)^(1/3))/(2^(2/3)*b^(8/3)*d)+11/9*a^2*arctan((1+2*b^(1/3)*x/(a+b*x^3)^(1/3))/sqrt(3))/(b^(8/3)*d*sqrt(3))-2^(1/3)*a^2*arctan((1+2*2^(1/3)*b^(1/3)*x/(a+b*x^3)^(1/3))/sqrt(3))/(b^(8/3)*d*sqrt(3))],
[x^4*(a+b*x^3)^(1/3)/(a*d-b*d*x^3),x,5,-1/3*x^2*(a+b*x^3)^(1/3)/(b*d)+1/3*a*log(a*d-b*d*x^3)/(2^(2/3)*b^(5/3)*d)+2/3*a*log(b^(1/3)*x-(a+b*x^3)^(1/3))/(b^(5/3)*d)-a*log(2^(1/3)*b^(1/3)*x-(a+b*x^3)^(1/3))/(2^(2/3)*b^(5/3)*d)+4/3*a*arctan((1+2*b^(1/3)*x/(a+b*x^3)^(1/3))/sqrt(3))/(b^(5/3)*d*sqrt(3))-2^(1/3)*a*arctan((1+2*2^(1/3)*b^(1/3)*x/(a+b*x^3)^(1/3))/sqrt(3))/(b^(5/3)*d*sqrt(3))],
[x*(a+b*x^3)^(1/3)/(a*d-b*d*x^3),x,3,1/3*log(a*d-b*d*x^3)/(2^(2/3)*b^(2/3)*d)+1/2*log(b^(1/3)*x-(a+b*x^3)^(1/3))/(b^(2/3)*d)-log(2^(1/3)*b^(1/3)*x-(a+b*x^3)^(1/3))/(2^(2/3)*b^(2/3)*d)+arctan((1+2*b^(1/3)*x/(a+b*x^3)^(1/3))/sqrt(3))/(b^(2/3)*d*sqrt(3))-2^(1/3)*arctan((1+2*2^(1/3)*b^(1/3)*x/(a+b*x^3)^(1/3))/sqrt(3))/(b^(2/3)*d*sqrt(3))],
[(a+b*x^3)^(1/3)/(x^2*(a*d-b*d*x^3)),x,3,-(a+b*x^3)^(1/3)/(a*d*x)+1/3*b^(1/3)*log(a*d-b*d*x^3)/(2^(2/3)*a*d)-b^(1/3)*log(2^(1/3)*b^(1/3)*x-(a+b*x^3)^(1/3))/(2^(2/3)*a*d)-2^(1/3)*b^(1/3)*arctan((1+2*2^(1/3)*b^(1/3)*x/(a+b*x^3)^(1/3))/sqrt(3))/(a*d*sqrt(3))],
[(a+b*x^3)^(1/3)/(x^5*(a*d-b*d*x^3)),x,4,-1/4*(a+b*x^3)^(1/3)/(a*d*x^4)-5/4*b*(a+b*x^3)^(1/3)/(a^2*d*x)+1/3*b^(4/3)*log(a*d-b*d*x^3)/(2^(2/3)*a^2*d)-b^(4/3)*log(2^(1/3)*b^(1/3)*x-(a+b*x^3)^(1/3))/(2^(2/3)*a^2*d)-2^(1/3)*b^(4/3)*arctan((1+2*2^(1/3)*b^(1/3)*x/(a+b*x^3)^(1/3))/sqrt(3))/(a^2*d*sqrt(3))],
[(a+b*x^3)^(1/3)/(x^8*(a*d-b*d*x^3)),x,5,-1/7*(a+b*x^3)^(1/3)/(a*d*x^7)-2/7*b*(a+b*x^3)^(1/3)/(a^2*d*x^4)-8/7*b^2*(a+b*x^3)^(1/3)/(a^3*d*x)+1/3*b^(7/3)*log(a*d-b*d*x^3)/(2^(2/3)*a^3*d)-b^(7/3)*log(2^(1/3)*b^(1/3)*x-(a+b*x^3)^(1/3))/(2^(2/3)*a^3*d)-2^(1/3)*b^(7/3)*arctan((1+2*2^(1/3)*b^(1/3)*x/(a+b*x^3)^(1/3))/sqrt(3))/(a^3*d*sqrt(3))],
[(a+b*x^3)^(1/3)/(x^11*(a*d-b*d*x^3)),x,6,-1/10*(a+b*x^3)^(1/3)/(a*d*x^10)-11/70*b*(a+b*x^3)^(1/3)/(a^2*d*x^7)-37/140*b^2*(a+b*x^3)^(1/3)/(a^3*d*x^4)-169/140*b^3*(a+b*x^3)^(1/3)/(a^4*d*x)+1/3*b^(10/3)*log(a*d-b*d*x^3)/(2^(2/3)*a^4*d)-b^(10/3)*log(2^(1/3)*b^(1/3)*x-(a+b*x^3)^(1/3))/(2^(2/3)*a^4*d)-2^(1/3)*b^(10/3)*arctan((1+2*2^(1/3)*b^(1/3)*x/(a+b*x^3)^(1/3))/sqrt(3))/(a^4*d*sqrt(3))],
[x^6*(a+b*x^3)^(1/3)/(a*d-b*d*x^3),x,22,-3/5*a*x*(a+b*x^3)^(1/3)/(b^2*d)-1/5*x^4*(a+b*x^3)^(1/3)/(b*d)-2/5*a^2*x*(1+b*x^3/a)^(2/3)*hypergeom([1/3,2/3],[4/3],-b*x^3/a)/(b^2*d*(a+b*x^3)^(2/3))-1/3*a^(5/3)*log(2^(2/3)+(-a^(1/3)-b^(1/3)*x)/(a+b*x^3)^(1/3))/(2^(2/3)*b^(7/3)*d)+1/3*a^(5/3)*log(1+2^(2/3)*(a^(1/3)+b^(1/3)*x)^2/(a+b*x^3)^(2/3)-2^(1/3)*(a^(1/3)+b^(1/3)*x)/(a+b*x^3)^(1/3))/(2^(2/3)*b^(7/3)*d)-1/3*2^(1/3)*a^(5/3)*log(1+2^(1/3)*(a^(1/3)+b^(1/3)*x)/(a+b*x^3)^(1/3))/(b^(7/3)*d)+1/6*a^(5/3)*log(2*2^(1/3)+(a^(1/3)+b^(1/3)*x)^2/(a+b*x^3)^(2/3)+2^(2/3)*(a^(1/3)+b^(1/3)*x)/(a+b*x^3)^(1/3))/(2^(2/3)*b^(7/3)*d)-2^(1/3)*a^(5/3)*arctan((1-2*2^(1/3)*(a^(1/3)+b^(1/3)*x)/(a+b*x^3)^(1/3))/sqrt(3))/(b^(7/3)*d*sqrt(3))-a^(5/3)*arctan((1+2^(1/3)*(a^(1/3)+b^(1/3)*x)/(a+b*x^3)^(1/3))/sqrt(3))/(2^(2/3)*b^(7/3)*d*sqrt(3))],
[x^3*(a+b*x^3)^(1/3)/(a*d-b*d*x^3),x,21,-1/2*x*(a+b*x^3)^(1/3)/(b*d)-1/2*a*x*(1+b*x^3/a)^(2/3)*hypergeom([1/3,2/3],[4/3],-b*x^3/a)/(b*d*(a+b*x^3)^(2/3))-1/3*a^(2/3)*log(2^(2/3)+(-a^(1/3)-b^(1/3)*x)/(a+b*x^3)^(1/3))/(2^(2/3)*b^(4/3)*d)+1/3*a^(2/3)*log(1+2^(2/3)*(a^(1/3)+b^(1/3)*x)^2/(a+b*x^3)^(2/3)-2^(1/3)*(a^(1/3)+b^(1/3)*x)/(a+b*x^3)^(1/3))/(2^(2/3)*b^(4/3)*d)-1/3*2^(1/3)*a^(2/3)*log(1+2^(1/3)*(a^(1/3)+b^(1/3)*x)/(a+b*x^3)^(1/3))/(b^(4/3)*d)+1/6*a^(2/3)*log(2*2^(1/3)+(a^(1/3)+b^(1/3)*x)^2/(a+b*x^3)^(2/3)+2^(2/3)*(a^(1/3)+b^(1/3)*x)/(a+b*x^3)^(1/3))/(2^(2/3)*b^(4/3)*d)-2^(1/3)*a^(2/3)*arctan((1-2*2^(1/3)*(a^(1/3)+b^(1/3)*x)/(a+b*x^3)^(1/3))/sqrt(3))/(b^(4/3)*d*sqrt(3))-a^(2/3)*arctan((1+2^(1/3)*(a^(1/3)+b^(1/3)*x)/(a+b*x^3)^(1/3))/sqrt(3))/(2^(2/3)*b^(4/3)*d*sqrt(3))],
[(a+b*x^3)^(1/3)/(a*d-b*d*x^3),x,14,-1/3*log(2^(2/3)+(-a^(1/3)-b^(1/3)*x)/(a+b*x^3)^(1/3))/(2^(2/3)*a^(1/3)*b^(1/3)*d)+1/3*log(1+2^(2/3)*(a^(1/3)+b^(1/3)*x)^2/(a+b*x^3)^(2/3)-2^(1/3)*(a^(1/3)+b^(1/3)*x)/(a+b*x^3)^(1/3))/(2^(2/3)*a^(1/3)*b^(1/3)*d)-1/3*2^(1/3)*log(1+2^(1/3)*(a^(1/3)+b^(1/3)*x)/(a+b*x^3)^(1/3))/(a^(1/3)*b^(1/3)*d)+1/6*log(2*2^(1/3)+(a^(1/3)+b^(1/3)*x)^2/(a+b*x^3)^(2/3)+2^(2/3)*(a^(1/3)+b^(1/3)*x)/(a+b*x^3)^(1/3))/(2^(2/3)*a^(1/3)*b^(1/3)*d)-2^(1/3)*arctan((1-2*2^(1/3)*(a^(1/3)+b^(1/3)*x)/(a+b*x^3)^(1/3))/sqrt(3))/(a^(1/3)*b^(1/3)*d*sqrt(3))-arctan((1+2^(1/3)*(a^(1/3)+b^(1/3)*x)/(a+b*x^3)^(1/3))/sqrt(3))/(2^(2/3)*a^(1/3)*b^(1/3)*d*sqrt(3))],
[(a+b*x^3)^(1/3)/(x^3*(a*d-b*d*x^3)),x,21,-1/2*(a+b*x^3)^(1/3)/(a*d*x^2)+1/2*b*x*(1+b*x^3/a)^(2/3)*hypergeom([1/3,2/3],[4/3],-b*x^3/a)/(a*d*(a+b*x^3)^(2/3))-1/3*b^(2/3)*log(2^(2/3)+(-a^(1/3)-b^(1/3)*x)/(a+b*x^3)^(1/3))/(2^(2/3)*a^(4/3)*d)+1/3*b^(2/3)*log(1+2^(2/3)*(a^(1/3)+b^(1/3)*x)^2/(a+b*x^3)^(2/3)-2^(1/3)*(a^(1/3)+b^(1/3)*x)/(a+b*x^3)^(1/3))/(2^(2/3)*a^(4/3)*d)-1/3*2^(1/3)*b^(2/3)*log(1+2^(1/3)*(a^(1/3)+b^(1/3)*x)/(a+b*x^3)^(1/3))/(a^(4/3)*d)+1/6*b^(2/3)*log(2*2^(1/3)+(a^(1/3)+b^(1/3)*x)^2/(a+b*x^3)^(2/3)+2^(2/3)*(a^(1/3)+b^(1/3)*x)/(a+b*x^3)^(1/3))/(2^(2/3)*a^(4/3)*d)-2^(1/3)*b^(2/3)*arctan((1-2*2^(1/3)*(a^(1/3)+b^(1/3)*x)/(a+b*x^3)^(1/3))/sqrt(3))/(a^(4/3)*d*sqrt(3))-b^(2/3)*arctan((1+2^(1/3)*(a^(1/3)+b^(1/3)*x)/(a+b*x^3)^(1/3))/sqrt(3))/(2^(2/3)*a^(4/3)*d*sqrt(3))],
[(a+b*x^3)^(1/3)/(x^6*(a*d-b*d*x^3)),x,22,-1/5*(a+b*x^3)^(1/3)/(a*d*x^5)-3/5*b*(a+b*x^3)^(1/3)/(a^2*d*x^2)+2/5*b^2*x*(1+b*x^3/a)^(2/3)*hypergeom([1/3,2/3],[4/3],-b*x^3/a)/(a^2*d*(a+b*x^3)^(2/3))-1/3*b^(5/3)*log(2^(2/3)+(-a^(1/3)-b^(1/3)*x)/(a+b*x^3)^(1/3))/(2^(2/3)*a^(7/3)*d)+1/3*b^(5/3)*log(1+2^(2/3)*(a^(1/3)+b^(1/3)*x)^2/(a+b*x^3)^(2/3)-2^(1/3)*(a^(1/3)+b^(1/3)*x)/(a+b*x^3)^(1/3))/(2^(2/3)*a^(7/3)*d)-1/3*2^(1/3)*b^(5/3)*log(1+2^(1/3)*(a^(1/3)+b^(1/3)*x)/(a+b*x^3)^(1/3))/(a^(7/3)*d)+1/6*b^(5/3)*log(2*2^(1/3)+(a^(1/3)+b^(1/3)*x)^2/(a+b*x^3)^(2/3)+2^(2/3)*(a^(1/3)+b^(1/3)*x)/(a+b*x^3)^(1/3))/(2^(2/3)*a^(7/3)*d)-2^(1/3)*b^(5/3)*arctan((1-2*2^(1/3)*(a^(1/3)+b^(1/3)*x)/(a+b*x^3)^(1/3))/sqrt(3))/(a^(7/3)*d*sqrt(3))-b^(5/3)*arctan((1+2^(1/3)*(a^(1/3)+b^(1/3)*x)/(a+b*x^3)^(1/3))/sqrt(3))/(2^(2/3)*a^(7/3)*d*sqrt(3))],
[x^11*(a+b*x^3)^(2/3)/(a*d-b*d*x^3),x,8,-1/2*a^3*(a+b*x^3)^(2/3)/(b^4*d)-1/5*a^2*(a+b*x^3)^(5/3)/(b^4*d)+1/8*a*(a+b*x^3)^(8/3)/(b^4*d)-1/11*(a+b*x^3)^(11/3)/(b^4*d)+1/3*a^(11/3)*log(a-b*x^3)/(2^(1/3)*b^4*d)-a^(11/3)*log(2^(1/3)*a^(1/3)-(a+b*x^3)^(1/3))/(2^(1/3)*b^4*d)-2^(2/3)*a^(11/3)*arctan((a^(1/3)+2^(2/3)*(a+b*x^3)^(1/3))/(a^(1/3)*sqrt(3)))/(b^4*d*sqrt(3))],
[x^8*(a+b*x^3)^(2/3)/(a*d-b*d*x^3),x,8,-1/2*a^2*(a+b*x^3)^(2/3)/(b^3*d)-1/8*(a+b*x^3)^(8/3)/(b^3*d)+1/3*a^(8/3)*log(a-b*x^3)/(2^(1/3)*b^3*d)-a^(8/3)*log(2^(1/3)*a^(1/3)-(a+b*x^3)^(1/3))/(2^(1/3)*b^3*d)-2^(2/3)*a^(8/3)*arctan((a^(1/3)+2^(2/3)*(a+b*x^3)^(1/3))/(a^(1/3)*sqrt(3)))/(b^3*d*sqrt(3))],
[x^5*(a+b*x^3)^(2/3)/(a*d-b*d*x^3),x,7,-1/2*a*(a+b*x^3)^(2/3)/(b^2*d)-1/5*(a+b*x^3)^(5/3)/(b^2*d)+1/3*a^(5/3)*log(a-b*x^3)/(2^(1/3)*b^2*d)-a^(5/3)*log(2^(1/3)*a^(1/3)-(a+b*x^3)^(1/3))/(2^(1/3)*b^2*d)-2^(2/3)*a^(5/3)*arctan((a^(1/3)+2^(2/3)*(a+b*x^3)^(1/3))/(a^(1/3)*sqrt(3)))/(b^2*d*sqrt(3))],
[x^2*(a+b*x^3)^(2/3)/(a*d-b*d*x^3),x,6,-1/2*(a+b*x^3)^(2/3)/(b*d)+1/3*a^(2/3)*log(a-b*x^3)/(2^(1/3)*b*d)-a^(2/3)*log(2^(1/3)*a^(1/3)-(a+b*x^3)^(1/3))/(2^(1/3)*b*d)-2^(2/3)*a^(2/3)*arctan((a^(1/3)+2^(2/3)*(a+b*x^3)^(1/3))/(a^(1/3)*sqrt(3)))/(b*d*sqrt(3))],
[(a+b*x^3)^(2/3)/(x*(a*d-b*d*x^3)),x,10,-1/2*log(x)/(a^(1/3)*d)+1/3*log(a-b*x^3)/(2^(1/3)*a^(1/3)*d)+1/2*log(a^(1/3)-(a+b*x^3)^(1/3))/(a^(1/3)*d)-log(2^(1/3)*a^(1/3)-(a+b*x^3)^(1/3))/(2^(1/3)*a^(1/3)*d)+arctan((a^(1/3)+2*(a+b*x^3)^(1/3))/(a^(1/3)*sqrt(3)))/(a^(1/3)*d*sqrt(3))-2^(2/3)*arctan((a^(1/3)+2^(2/3)*(a+b*x^3)^(1/3))/(a^(1/3)*sqrt(3)))/(a^(1/3)*d*sqrt(3))],
[(a+b*x^3)^(2/3)/(x^4*(a*d-b*d*x^3)),x,13,1/3*b*(a+b*x^3)^(2/3)/(a^2*d)-1/3*(a+b*x^3)^(5/3)/(a^2*d*x^3)-5/6*b*log(x)/(a^(4/3)*d)+1/3*b*log(a-b*x^3)/(2^(1/3)*a^(4/3)*d)+5/6*b*log(a^(1/3)-(a+b*x^3)^(1/3))/(a^(4/3)*d)-b*log(2^(1/3)*a^(1/3)-(a+b*x^3)^(1/3))/(2^(1/3)*a^(4/3)*d)+5/3*b*arctan((a^(1/3)+2*(a+b*x^3)^(1/3))/(a^(1/3)*sqrt(3)))/(a^(4/3)*d*sqrt(3))-2^(2/3)*b*arctan((a^(1/3)+2^(2/3)*(a+b*x^3)^(1/3))/(a^(1/3)*sqrt(3)))/(a^(4/3)*d*sqrt(3))],
[(a+b*x^3)^(2/3)/(x^7*(a*d-b*d*x^3)),x,12,-5/18*b*(a+b*x^3)^(2/3)/(a^2*d*x^3)-1/6*(a+b*x^3)^(5/3)/(a^2*d*x^6)-7/9*b^2*log(x)/(a^(7/3)*d)+1/3*b^2*log(a-b*x^3)/(2^(1/3)*a^(7/3)*d)+7/9*b^2*log(a^(1/3)-(a+b*x^3)^(1/3))/(a^(7/3)*d)-b^2*log(2^(1/3)*a^(1/3)-(a+b*x^3)^(1/3))/(2^(1/3)*a^(7/3)*d)+14/9*b^2*arctan((a^(1/3)+2*(a+b*x^3)^(1/3))/(a^(1/3)*sqrt(3)))/(a^(7/3)*d*sqrt(3))-2^(2/3)*b^2*arctan((a^(1/3)+2^(2/3)*(a+b*x^3)^(1/3))/(a^(1/3)*sqrt(3)))/(a^(7/3)*d*sqrt(3))],
[x^6*(a+b*x^3)^(2/3)/(a*d-b*d*x^3),x,5,-4/9*a*x*(a+b*x^3)^(2/3)/(b^2*d)-1/6*x^4*(a+b*x^3)^(2/3)/(b*d)+1/3*a^2*log(a*d-b*d*x^3)/(2^(1/3)*b^(7/3)*d)-a^2*log(2^(1/3)*b^(1/3)*x-(a+b*x^3)^(1/3))/(2^(1/3)*b^(7/3)*d)+7/9*a^2*log(-b^(1/3)*x+(a+b*x^3)^(1/3))/(b^(7/3)*d)-14/9*a^2*arctan((1+2*b^(1/3)*x/(a+b*x^3)^(1/3))/sqrt(3))/(b^(7/3)*d*sqrt(3))+2^(2/3)*a^2*arctan((1+2*2^(1/3)*b^(1/3)*x/(a+b*x^3)^(1/3))/sqrt(3))/(b^(7/3)*d*sqrt(3))],
[x^3*(a+b*x^3)^(2/3)/(a*d-b*d*x^3),x,4,-1/3*x*(a+b*x^3)^(2/3)/(b*d)+1/3*a*log(a*d-b*d*x^3)/(2^(1/3)*b^(4/3)*d)-a*log(2^(1/3)*b^(1/3)*x-(a+b*x^3)^(1/3))/(2^(1/3)*b^(4/3)*d)+5/6*a*log(-b^(1/3)*x+(a+b*x^3)^(1/3))/(b^(4/3)*d)-5/3*a*arctan((1+2*b^(1/3)*x/(a+b*x^3)^(1/3))/sqrt(3))/(b^(4/3)*d*sqrt(3))+2^(2/3)*a*arctan((1+2*2^(1/3)*b^(1/3)*x/(a+b*x^3)^(1/3))/sqrt(3))/(b^(4/3)*d*sqrt(3))],
[(a+b*x^3)^(2/3)/(a*d-b*d*x^3),x,3,1/3*log(a*d-b*d*x^3)/(2^(1/3)*b^(1/3)*d)-log(2^(1/3)*b^(1/3)*x-(a+b*x^3)^(1/3))/(2^(1/3)*b^(1/3)*d)+1/2*log(-b^(1/3)*x+(a+b*x^3)^(1/3))/(b^(1/3)*d)-arctan((1+2*b^(1/3)*x/(a+b*x^3)^(1/3))/sqrt(3))/(b^(1/3)*d*sqrt(3))+2^(2/3)*arctan((1+2*2^(1/3)*b^(1/3)*x/(a+b*x^3)^(1/3))/sqrt(3))/(b^(1/3)*d*sqrt(3))],
[(a+b*x^3)^(2/3)/(x^3*(a*d-b*d*x^3)),x,3,-1/2*(a+b*x^3)^(2/3)/(a*d*x^2)+1/3*b^(2/3)*log(a*d-b*d*x^3)/(2^(1/3)*a*d)-b^(2/3)*log(2^(1/3)*b^(1/3)*x-(a+b*x^3)^(1/3))/(2^(1/3)*a*d)+2^(2/3)*b^(2/3)*arctan((1+2*2^(1/3)*b^(1/3)*x/(a+b*x^3)^(1/3))/sqrt(3))/(a*d*sqrt(3))],
[(a+b*x^3)^(2/3)/(x^6*(a*d-b*d*x^3)),x,4,-1/5*(a+b*x^3)^(2/3)/(a*d*x^5)-7/10*b*(a+b*x^3)^(2/3)/(a^2*d*x^2)+1/3*b^(5/3)*log(a*d-b*d*x^3)/(2^(1/3)*a^2*d)-b^(5/3)*log(2^(1/3)*b^(1/3)*x-(a+b*x^3)^(1/3))/(2^(1/3)*a^2*d)+2^(2/3)*b^(5/3)*arctan((1+2*2^(1/3)*b^(1/3)*x/(a+b*x^3)^(1/3))/sqrt(3))/(a^2*d*sqrt(3))],
[(a+b*x^3)^(2/3)/(x^9*(a*d-b*d*x^3)),x,5,-1/8*(a+b*x^3)^(2/3)/(a*d*x^8)-1/4*b*(a+b*x^3)^(2/3)/(a^2*d*x^5)-5/8*b^2*(a+b*x^3)^(2/3)/(a^3*d*x^2)+1/3*b^(8/3)*log(a*d-b*d*x^3)/(2^(1/3)*a^3*d)-b^(8/3)*log(2^(1/3)*b^(1/3)*x-(a+b*x^3)^(1/3))/(2^(1/3)*a^3*d)+2^(2/3)*b^(8/3)*arctan((1+2*2^(1/3)*b^(1/3)*x/(a+b*x^3)^(1/3))/sqrt(3))/(a^3*d*sqrt(3))],
[(a+b*x^3)^(2/3)/(x^12*(a*d-b*d*x^3)),x,6,-1/11*(a+b*x^3)^(2/3)/(a*d*x^11)-13/88*b*(a+b*x^3)^(2/3)/(a^2*d*x^8)-49/220*b^2*(a+b*x^3)^(2/3)/(a^3*d*x^5)-293/440*b^3*(a+b*x^3)^(2/3)/(a^4*d*x^2)+1/3*b^(11/3)*log(a*d-b*d*x^3)/(2^(1/3)*a^4*d)-b^(11/3)*log(2^(1/3)*b^(1/3)*x-(a+b*x^3)^(1/3))/(2^(1/3)*a^4*d)+2^(2/3)*b^(11/3)*arctan((1+2*2^(1/3)*b^(1/3)*x/(a+b*x^3)^(1/3))/sqrt(3))/(a^4*d*sqrt(3))],
[x^7*(a+b*x^3)^(2/3)/(a*d-b*d*x^3),x,14,-9/28*a*x^2*(a+b*x^3)^(2/3)/(b^2*d)-1/7*x^5*(a+b*x^3)^(2/3)/(b*d)-19/28*a^2*x^2*(1+b*x^3/a)^(1/3)*hypergeom([1/3,2/3],[5/3],-b*x^3/a)/(b^2*d*(a+b*x^3)^(1/3))+1/6*a^(7/3)*log((a^(1/3)-b^(1/3)*x)^2*(a^(1/3)+b^(1/3)*x)/a)/(2^(1/3)*b^(8/3)*d)+1/3*a^(7/3)*log(1+2^(2/3)*(a^(1/3)+b^(1/3)*x)^2/(a+b*x^3)^(2/3)-2^(1/3)*(a^(1/3)+b^(1/3)*x)/(a+b*x^3)^(1/3))/(2^(1/3)*b^(8/3)*d)-1/3*2^(2/3)*a^(7/3)*log(1+2^(1/3)*(a^(1/3)+b^(1/3)*x)/(a+b*x^3)^(1/3))/(b^(8/3)*d)-1/2*a^(7/3)*log(b^(1/3)*(a^(1/3)+b^(1/3)*x)/a^(1/3)-2^(2/3)*b^(1/3)*(a+b*x^3)^(1/3)/a^(1/3))/(2^(1/3)*b^(8/3)*d)+2^(2/3)*a^(7/3)*arctan((1-2*2^(1/3)*(a^(1/3)+b^(1/3)*x)/(a+b*x^3)^(1/3))/sqrt(3))/(b^(8/3)*d*sqrt(3))+a^(7/3)*arctan((1+2^(1/3)*(a^(1/3)+b^(1/3)*x)/(a+b*x^3)^(1/3))/sqrt(3))/(2^(1/3)*b^(8/3)*d*sqrt(3))],
[x^4*(a+b*x^3)^(2/3)/(a*d-b*d*x^3),x,13,-1/4*x^2*(a+b*x^3)^(2/3)/(b*d)-3/4*a*x^2*(1+b*x^3/a)^(1/3)*hypergeom([1/3,2/3],[5/3],-b*x^3/a)/(b*d*(a+b*x^3)^(1/3))+1/6*a^(4/3)*log((a^(1/3)-b^(1/3)*x)^2*(a^(1/3)+b^(1/3)*x)/a)/(2^(1/3)*b^(5/3)*d)+1/3*a^(4/3)*log(1+2^(2/3)*(a^(1/3)+b^(1/3)*x)^2/(a+b*x^3)^(2/3)-2^(1/3)*(a^(1/3)+b^(1/3)*x)/(a+b*x^3)^(1/3))/(2^(1/3)*b^(5/3)*d)-1/3*2^(2/3)*a^(4/3)*log(1+2^(1/3)*(a^(1/3)+b^(1/3)*x)/(a+b*x^3)^(1/3))/(b^(5/3)*d)-1/2*a^(4/3)*log(b^(1/3)*(a^(1/3)+b^(1/3)*x)/a^(1/3)-2^(2/3)*b^(1/3)*(a+b*x^3)^(1/3)/a^(1/3))/(2^(1/3)*b^(5/3)*d)+2^(2/3)*a^(4/3)*arctan((1-2*2^(1/3)*(a^(1/3)+b^(1/3)*x)/(a+b*x^3)^(1/3))/sqrt(3))/(b^(5/3)*d*sqrt(3))+a^(4/3)*arctan((1+2^(1/3)*(a^(1/3)+b^(1/3)*x)/(a+b*x^3)^(1/3))/sqrt(3))/(2^(1/3)*b^(5/3)*d*sqrt(3))],
[x*(a+b*x^3)^(2/3)/(a*d-b*d*x^3),x,11,-1/2*x^2*(1+b*x^3/a)^(1/3)*hypergeom([1/3,2/3],[5/3],-b*x^3/a)/(d*(a+b*x^3)^(1/3))+1/6*a^(1/3)*log((a^(1/3)-b^(1/3)*x)^2*(a^(1/3)+b^(1/3)*x)/a)/(2^(1/3)*b^(2/3)*d)+1/3*a^(1/3)*log(1+2^(2/3)*(a^(1/3)+b^(1/3)*x)^2/(a+b*x^3)^(2/3)-2^(1/3)*(a^(1/3)+b^(1/3)*x)/(a+b*x^3)^(1/3))/(2^(1/3)*b^(2/3)*d)-1/3*2^(2/3)*a^(1/3)*log(1+2^(1/3)*(a^(1/3)+b^(1/3)*x)/(a+b*x^3)^(1/3))/(b^(2/3)*d)-1/2*a^(1/3)*log(b^(1/3)*(a^(1/3)+b^(1/3)*x)/a^(1/3)-2^(2/3)*b^(1/3)*(a+b*x^3)^(1/3)/a^(1/3))/(2^(1/3)*b^(2/3)*d)+2^(2/3)*a^(1/3)*arctan((1-2*2^(1/3)*(a^(1/3)+b^(1/3)*x)/(a+b*x^3)^(1/3))/sqrt(3))/(b^(2/3)*d*sqrt(3))+a^(1/3)*arctan((1+2^(1/3)*(a^(1/3)+b^(1/3)*x)/(a+b*x^3)^(1/3))/sqrt(3))/(2^(1/3)*b^(2/3)*d*sqrt(3))],
[(a+b*x^3)^(2/3)/(x^2*(a*d-b*d*x^3)),x,13,-(a+b*x^3)^(2/3)/(a*d*x)+1/2*b*x^2*(1+b*x^3/a)^(1/3)*hypergeom([1/3,2/3],[5/3],-b*x^3/a)/(a*d*(a+b*x^3)^(1/3))+1/6*b^(1/3)*log((a^(1/3)-b^(1/3)*x)^2*(a^(1/3)+b^(1/3)*x)/a)/(2^(1/3)*a^(2/3)*d)+1/3*b^(1/3)*log(1+2^(2/3)*(a^(1/3)+b^(1/3)*x)^2/(a+b*x^3)^(2/3)-2^(1/3)*(a^(1/3)+b^(1/3)*x)/(a+b*x^3)^(1/3))/(2^(1/3)*a^(2/3)*d)-1/3*2^(2/3)*b^(1/3)*log(1+2^(1/3)*(a^(1/3)+b^(1/3)*x)/(a+b*x^3)^(1/3))/(a^(2/3)*d)-1/2*b^(1/3)*log(b^(1/3)*(a^(1/3)+b^(1/3)*x)/a^(1/3)-2^(2/3)*b^(1/3)*(a+b*x^3)^(1/3)/a^(1/3))/(2^(1/3)*a^(2/3)*d)+2^(2/3)*b^(1/3)*arctan((1-2*2^(1/3)*(a^(1/3)+b^(1/3)*x)/(a+b*x^3)^(1/3))/sqrt(3))/(a^(2/3)*d*sqrt(3))+b^(1/3)*arctan((1+2^(1/3)*(a^(1/3)+b^(1/3)*x)/(a+b*x^3)^(1/3))/sqrt(3))/(2^(1/3)*a^(2/3)*d*sqrt(3))],
[(a+b*x^3)^(2/3)/(x^5*(a*d-b*d*x^3)),x,14,-1/4*(a+b*x^3)^(2/3)/(a*d*x^4)-3/2*b*(a+b*x^3)^(2/3)/(a^2*d*x)+3/4*b^2*x^2*(1+b*x^3/a)^(1/3)*hypergeom([1/3,2/3],[5/3],-b*x^3/a)/(a^2*d*(a+b*x^3)^(1/3))+1/6*b^(4/3)*log((a^(1/3)-b^(1/3)*x)^2*(a^(1/3)+b^(1/3)*x)/a)/(2^(1/3)*a^(5/3)*d)+1/3*b^(4/3)*log(1+2^(2/3)*(a^(1/3)+b^(1/3)*x)^2/(a+b*x^3)^(2/3)-2^(1/3)*(a^(1/3)+b^(1/3)*x)/(a+b*x^3)^(1/3))/(2^(1/3)*a^(5/3)*d)-1/3*2^(2/3)*b^(4/3)*log(1+2^(1/3)*(a^(1/3)+b^(1/3)*x)/(a+b*x^3)^(1/3))/(a^(5/3)*d)-1/2*b^(4/3)*log(b^(1/3)*(a^(1/3)+b^(1/3)*x)/a^(1/3)-2^(2/3)*b^(1/3)*(a+b*x^3)^(1/3)/a^(1/3))/(2^(1/3)*a^(5/3)*d)+2^(2/3)*b^(4/3)*arctan((1-2*2^(1/3)*(a^(1/3)+b^(1/3)*x)/(a+b*x^3)^(1/3))/sqrt(3))/(a^(5/3)*d*sqrt(3))+b^(4/3)*arctan((1+2^(1/3)*(a^(1/3)+b^(1/3)*x)/(a+b*x^3)^(1/3))/sqrt(3))/(2^(1/3)*a^(5/3)*d*sqrt(3))],

# p<0
[x^14/((1-x^3)^(1/3)*(1+x^3)),x,7,2/5*(1-x^3)^(5/3)-1/4*(1-x^3)^(8/3)+1/11*(1-x^3)^(11/3)-1/6*log(1+x^3)/2^(1/3)+1/2*log(2^(1/3)-(1-x^3)^(1/3))/2^(1/3)+arctan((1+2^(2/3)*(1-x^3)^(1/3))/sqrt(3))/(2^(1/3)*sqrt(3))],
[x^11/((1-x^3)^(1/3)*(1+x^3)),x,7,-1/2*(1-x^3)^(2/3)+1/5*(1-x^3)^(5/3)-1/8*(1-x^3)^(8/3)+1/6*log(1+x^3)/2^(1/3)-1/2*log(2^(1/3)-(1-x^3)^(1/3))/2^(1/3)-arctan((1+2^(2/3)*(1-x^3)^(1/3))/sqrt(3))/(2^(1/3)*sqrt(3))],
[x^8/((1-x^3)^(1/3)*(1+x^3)),x,7,1/5*(1-x^3)^(5/3)-1/6*log(1+x^3)/2^(1/3)+1/2*log(2^(1/3)-(1-x^3)^(1/3))/2^(1/3)+arctan((1+2^(2/3)*(1-x^3)^(1/3))/sqrt(3))/(2^(1/3)*sqrt(3))],
[x^5/((1-x^3)^(1/3)*(1+x^3)),x,6,-1/2*(1-x^3)^(2/3)+1/6*log(1+x^3)/2^(1/3)-1/2*log(2^(1/3)-(1-x^3)^(1/3))/2^(1/3)-arctan((1+2^(2/3)*(1-x^3)^(1/3))/sqrt(3))/(2^(1/3)*sqrt(3))],
[x^2/((1-x^3)^(1/3)*(1+x^3)),x,5,-1/6*log(1+x^3)/2^(1/3)+1/2*log(2^(1/3)-(1-x^3)^(1/3))/2^(1/3)+arctan((1+2^(2/3)*(1-x^3)^(1/3))/sqrt(3))/(2^(1/3)*sqrt(3))],
[1/(x*(1-x^3)^(1/3)*(1+x^3)),x,10,-1/2*log(x)+1/6*log(1+x^3)/2^(1/3)+1/2*log(1-(1-x^3)^(1/3))-1/2*log(2^(1/3)-(1-x^3)^(1/3))/2^(1/3)+arctan((1+2*(1-x^3)^(1/3))/sqrt(3))/sqrt(3)-arctan((1+2^(2/3)*(1-x^3)^(1/3))/sqrt(3))/(2^(1/3)*sqrt(3))],
[1/(x^4*(1-x^3)^(1/3)*(1+x^3)),x,11,-1/3*(1-x^3)^(2/3)/x^3+1/3*log(x)-1/6*log(1+x^3)/2^(1/3)-1/3*log(1-(1-x^3)^(1/3))+1/2*log(2^(1/3)-(1-x^3)^(1/3))/2^(1/3)-2/3*arctan((1+2*(1-x^3)^(1/3))/sqrt(3))/sqrt(3)+arctan((1+2^(2/3)*(1-x^3)^(1/3))/sqrt(3))/(2^(1/3)*sqrt(3))],
[x^6/((1-x^3)^(1/3)*(1+x^3)),x,4,-1/3*x*(1-x^3)^(2/3)-1/6*log(1+x^3)/2^(1/3)+1/2*log(-2^(1/3)*x-(1-x^3)^(1/3))/2^(1/3)-1/3*log(x+(1-x^3)^(1/3))+2/3*arctan((1-2*x/(1-x^3)^(1/3))/sqrt(3))/sqrt(3)-arctan((1-2*2^(1/3)*x/(1-x^3)^(1/3))/sqrt(3))/(2^(1/3)*sqrt(3))],
[x^3/((1-x^3)^(1/3)*(1+x^3)),x,3,1/6*log(1+x^3)/2^(1/3)-1/2*log(-2^(1/3)*x-(1-x^3)^(1/3))/2^(1/3)+1/2*log(x+(1-x^3)^(1/3))-arctan((1-2*x/(1-x^3)^(1/3))/sqrt(3))/sqrt(3)+arctan((1-2*2^(1/3)*x/(1-x^3)^(1/3))/sqrt(3))/(2^(1/3)*sqrt(3))],
[1/((1-x^3)^(1/3)*(1+x^3)),x,1,-1/6*log(1+x^3)/2^(1/3)+1/2*log(-2^(1/3)*x-(1-x^3)^(1/3))/2^(1/3)-arctan((1-2*2^(1/3)*x/(1-x^3)^(1/3))/sqrt(3))/(2^(1/3)*sqrt(3))],
[1/(x^3*(1-x^3)^(1/3)*(1+x^3)),x,3,-1/2*(1-x^3)^(2/3)/x^2+1/6*log(1+x^3)/2^(1/3)-1/2*log(-2^(1/3)*x-(1-x^3)^(1/3))/2^(1/3)+arctan((1-2*2^(1/3)*x/(1-x^3)^(1/3))/sqrt(3))/(2^(1/3)*sqrt(3))],
[1/(x^6*(1-x^3)^(1/3)*(1+x^3)),x,4,-1/5*(1-x^3)^(2/3)/x^5+1/5*(1-x^3)^(2/3)/x^2-1/6*log(1+x^3)/2^(1/3)+1/2*log(-2^(1/3)*x-(1-x^3)^(1/3))/2^(1/3)-arctan((1-2*2^(1/3)*x/(1-x^3)^(1/3))/sqrt(3))/(2^(1/3)*sqrt(3))],
[1/(x^9*(1-x^3)^(1/3)*(1+x^3)),x,5,-1/8*(1-x^3)^(2/3)/x^8+1/20*(1-x^3)^(2/3)/x^5-17/40*(1-x^3)^(2/3)/x^2+1/6*log(1+x^3)/2^(1/3)-1/2*log(-2^(1/3)*x-(1-x^3)^(1/3))/2^(1/3)+arctan((1-2*2^(1/3)*x/(1-x^3)^(1/3))/sqrt(3))/(2^(1/3)*sqrt(3))],
[x^7/((1-x^3)^(1/3)*(1+x^3)),x,12,-1/4*x^2*(1-x^3)^(2/3)-1/4*x^2*hypergeom([1/3,2/3],[5/3],x^3)+1/12*log((1-x)*(1+x)^2)/2^(1/3)+1/6*log(1+2^(2/3)*(1-x)^2/(1-x^3)^(2/3)-2^(1/3)*(1-x)/(1-x^3)^(1/3))/2^(1/3)-1/3*log(1+2^(1/3)*(1-x)/(1-x^3)^(1/3))/2^(1/3)-1/4*log(-1+x+2^(2/3)*(1-x^3)^(1/3))/2^(1/3)+arctan((1-2*2^(1/3)*(1-x)/(1-x^3)^(1/3))/sqrt(3))/(2^(1/3)*sqrt(3))+1/2*arctan((1+2^(1/3)*(1-x)/(1-x^3)^(1/3))/sqrt(3))/(2^(1/3)*sqrt(3))],
[x^4/((1-x^3)^(1/3)*(1+x^3)),x,10,1/2*x^2*hypergeom([1/3,2/3],[5/3],x^3)-1/12*log((1-x)*(1+x)^2)/2^(1/3)-1/6*log(1+2^(2/3)*(1-x)^2/(1-x^3)^(2/3)-2^(1/3)*(1-x)/(1-x^3)^(1/3))/2^(1/3)+1/3*log(1+2^(1/3)*(1-x)/(1-x^3)^(1/3))/2^(1/3)+1/4*log(-1+x+2^(2/3)*(1-x^3)^(1/3))/2^(1/3)-arctan((1-2*2^(1/3)*(1-x)/(1-x^3)^(1/3))/sqrt(3))/(2^(1/3)*sqrt(3))-1/2*arctan((1+2^(1/3)*(1-x)/(1-x^3)^(1/3))/sqrt(3))/(2^(1/3)*sqrt(3))],
[x/((1-x^3)^(1/3)*(1+x^3)),x,8,1/12*log((1-x)*(1+x)^2)/2^(1/3)+1/6*log(1+2^(2/3)*(1-x)^2/(1-x^3)^(2/3)-2^(1/3)*(1-x)/(1-x^3)^(1/3))/2^(1/3)-1/3*log(1+2^(1/3)*(1-x)/(1-x^3)^(1/3))/2^(1/3)-1/4*log(-1+x+2^(2/3)*(1-x^3)^(1/3))/2^(1/3)+arctan((1-2*2^(1/3)*(1-x)/(1-x^3)^(1/3))/sqrt(3))/(2^(1/3)*sqrt(3))+1/2*arctan((1+2^(1/3)*(1-x)/(1-x^3)^(1/3))/sqrt(3))/(2^(1/3)*sqrt(3))],
[1/(x^2*(1-x^3)^(1/3)*(1+x^3)),x,12,-(1-x^3)^(2/3)/x-1/2*x^2*hypergeom([1/3,2/3],[5/3],x^3)-1/12*log((1-x)*(1+x)^2)/2^(1/3)-1/6*log(1+2^(2/3)*(1-x)^2/(1-x^3)^(2/3)-2^(1/3)*(1-x)/(1-x^3)^(1/3))/2^(1/3)+1/3*log(1+2^(1/3)*(1-x)/(1-x^3)^(1/3))/2^(1/3)+1/4*log(-1+x+2^(2/3)*(1-x^3)^(1/3))/2^(1/3)-arctan((1-2*2^(1/3)*(1-x)/(1-x^3)^(1/3))/sqrt(3))/(2^(1/3)*sqrt(3))-1/2*arctan((1+2^(1/3)*(1-x)/(1-x^3)^(1/3))/sqrt(3))/(2^(1/3)*sqrt(3))],
[1/(x^5*(1-x^3)^(1/3)*(1+x^3)),x,14,-1/4*(1-x^3)^(2/3)/x^4+1/2*(1-x^3)^(2/3)/x+1/4*x^2*hypergeom([1/3,2/3],[5/3],x^3)+1/12*log((1-x)*(1+x)^2)/2^(1/3)+1/6*log(1+2^(2/3)*(1-x)^2/(1-x^3)^(2/3)-2^(1/3)*(1-x)/(1-x^3)^(1/3))/2^(1/3)-1/3*log(1+2^(1/3)*(1-x)/(1-x^3)^(1/3))/2^(1/3)-1/4*log(-1+x+2^(2/3)*(1-x^3)^(1/3))/2^(1/3)+arctan((1-2*2^(1/3)*(1-x)/(1-x^3)^(1/3))/sqrt(3))/(2^(1/3)*sqrt(3))+1/2*arctan((1+2^(1/3)*(1-x)/(1-x^3)^(1/3))/sqrt(3))/(2^(1/3)*sqrt(3))],
[x^11/((1-x^3)^(2/3)*(1+x^3)),x,7,-(1-x^3)^(1/3)+1/4*(1-x^3)^(4/3)-1/7*(1-x^3)^(7/3)+1/6*log(1+x^3)/2^(2/3)-1/2*log(2^(1/3)-(1-x^3)^(1/3))/2^(2/3)+arctan((1+2^(2/3)*(1-x^3)^(1/3))/sqrt(3))/(2^(2/3)*sqrt(3))],
[x^8/((1-x^3)^(2/3)*(1+x^3)),x,7,1/4*(1-x^3)^(4/3)-1/6*log(1+x^3)/2^(2/3)+1/2*log(2^(1/3)-(1-x^3)^(1/3))/2^(2/3)-arctan((1+2^(2/3)*(1-x^3)^(1/3))/sqrt(3))/(2^(2/3)*sqrt(3))],
[x^5/((1-x^3)^(2/3)*(1+x^3)),x,6,-(1-x^3)^(1/3)+1/6*log(1+x^3)/2^(2/3)-1/2*log(2^(1/3)-(1-x^3)^(1/3))/2^(2/3)+arctan((1+2^(2/3)*(1-x^3)^(1/3))/sqrt(3))/(2^(2/3)*sqrt(3))],
[x^2/((1-x^3)^(2/3)*(1+x^3)),x,5,-1/6*log(1+x^3)/2^(2/3)+1/2*log(2^(1/3)-(1-x^3)^(1/3))/2^(2/3)-arctan((1+2^(2/3)*(1-x^3)^(1/3))/sqrt(3))/(2^(2/3)*sqrt(3))],
[1/(x*(1-x^3)^(2/3)*(1+x^3)),x,10,-1/2*log(x)+1/6*log(1+x^3)/2^(2/3)+1/2*log(1-(1-x^3)^(1/3))-1/2*log(2^(1/3)-(1-x^3)^(1/3))/2^(2/3)-arctan((1+2*(1-x^3)^(1/3))/sqrt(3))/sqrt(3)+arctan((1+2^(2/3)*(1-x^3)^(1/3))/sqrt(3))/(2^(2/3)*sqrt(3))],
[1/(x^4*(1-x^3)^(2/3)*(1+x^3)),x,11,-1/3*(1-x^3)^(1/3)/x^3+1/6*log(x)-1/6*log(1+x^3)/2^(2/3)-1/6*log(1-(1-x^3)^(1/3))+1/2*log(2^(1/3)-(1-x^3)^(1/3))/2^(2/3)+1/3*arctan((1+2*(1-x^3)^(1/3))/sqrt(3))/sqrt(3)-arctan((1+2^(2/3)*(1-x^3)^(1/3))/sqrt(3))/(2^(2/3)*sqrt(3))],
[x^7/((1-x^3)^(2/3)*(1+x^3)),x,5,-1/3*x^2*(1-x^3)^(1/3)+1/6*log(1+x^3)/2^(2/3)+1/6*log(-x-(1-x^3)^(1/3))-1/2*log(-2^(1/3)*x-(1-x^3)^(1/3))/2^(2/3)+1/3*arctan((1-2*x/(1-x^3)^(1/3))/sqrt(3))/sqrt(3)-arctan((1-2*2^(1/3)*x/(1-x^3)^(1/3))/sqrt(3))/(2^(2/3)*sqrt(3))],
[x^4/((1-x^3)^(2/3)*(1+x^3)),x,3,-1/6*log(1+x^3)/2^(2/3)-1/2*log(-x-(1-x^3)^(1/3))+1/2*log(-2^(1/3)*x-(1-x^3)^(1/3))/2^(2/3)-arctan((1-2*x/(1-x^3)^(1/3))/sqrt(3))/sqrt(3)+arctan((1-2*2^(1/3)*x/(1-x^3)^(1/3))/sqrt(3))/(2^(2/3)*sqrt(3))],
[x/((1-x^3)^(2/3)*(1+x^3)),x,1,1/6*log(1+x^3)/2^(2/3)-1/2*log(-2^(1/3)*x-(1-x^3)^(1/3))/2^(2/3)-arctan((1-2*2^(1/3)*x/(1-x^3)^(1/3))/sqrt(3))/(2^(2/3)*sqrt(3))],
[1/(x^2*(1-x^3)^(2/3)*(1+x^3)),x,2,-(1-x^3)^(1/3)/x-1/6*log(1+x^3)/2^(2/3)+1/2*log(-2^(1/3)*x-(1-x^3)^(1/3))/2^(2/3)+arctan((1-2*2^(1/3)*x/(1-x^3)^(1/3))/sqrt(3))/(2^(2/3)*sqrt(3))],
[1/(x^5*(1-x^3)^(2/3)*(1+x^3)),x,4,-1/4*(1-x^3)^(1/3)/x^4+1/4*(1-x^3)^(1/3)/x+1/6*log(1+x^3)/2^(2/3)-1/2*log(-2^(1/3)*x-(1-x^3)^(1/3))/2^(2/3)-arctan((1-2*2^(1/3)*x/(1-x^3)^(1/3))/sqrt(3))/(2^(2/3)*sqrt(3))],
[x^6/((1-x^3)^(2/3)*(1+x^3)),x,15,-1/2*x*(1-x^3)^(1/3)+1/6*log(2^(2/3)+(-1+x)/(1-x^3)^(1/3))/2^(2/3)-1/6*log(1+2^(2/3)*(1-x)^2/(1-x^3)^(2/3)-2^(1/3)*(1-x)/(1-x^3)^(1/3))/2^(2/3)+1/3*log(1+2^(1/3)*(1-x)/(1-x^3)^(1/3))/2^(2/3)-1/12*log(2*2^(1/3)+(1-x)^2/(1-x^3)^(2/3)+2^(2/3)*(1-x)/(1-x^3)^(1/3))/2^(2/3)+arctan((1-2*2^(1/3)*(1-x)/(1-x^3)^(1/3))/sqrt(3))/(2^(2/3)*sqrt(3))+1/2*arctan((1+2^(1/3)*(1-x)/(1-x^3)^(1/3))/sqrt(3))/(2^(2/3)*sqrt(3))],
[x^3/((1-x^3)^(2/3)*(1+x^3)),x,18,1/2*x*hypergeom([1/3,2/3],[4/3],x^3)-1/6*log(2^(2/3)+(-1+x)/(1-x^3)^(1/3))/2^(2/3)+1/6*log(1+2^(2/3)*(1-x)^2/(1-x^3)^(2/3)-2^(1/3)*(1-x)/(1-x^3)^(1/3))/2^(2/3)-1/3*log(1+2^(1/3)*(1-x)/(1-x^3)^(1/3))/2^(2/3)+1/12*log(2*2^(1/3)+(1-x)^2/(1-x^3)^(2/3)+2^(2/3)*(1-x)/(1-x^3)^(1/3))/2^(2/3)-arctan((1-2*2^(1/3)*(1-x)/(1-x^3)^(1/3))/sqrt(3))/(2^(2/3)*sqrt(3))-1/2*arctan((1+2^(1/3)*(1-x)/(1-x^3)^(1/3))/sqrt(3))/(2^(2/3)*sqrt(3))],
[1/((1-x^3)^(2/3)*(1+x^3)),x,16,1/2*x*hypergeom([1/3,2/3],[4/3],x^3)+1/6*log(2^(2/3)+(-1+x)/(1-x^3)^(1/3))/2^(2/3)-1/6*log(1+2^(2/3)*(1-x)^2/(1-x^3)^(2/3)-2^(1/3)*(1-x)/(1-x^3)^(1/3))/2^(2/3)+1/3*log(1+2^(1/3)*(1-x)/(1-x^3)^(1/3))/2^(2/3)-1/12*log(2*2^(1/3)+(1-x)^2/(1-x^3)^(2/3)+2^(2/3)*(1-x)/(1-x^3)^(1/3))/2^(2/3)+arctan((1-2*2^(1/3)*(1-x)/(1-x^3)^(1/3))/sqrt(3))/(2^(2/3)*sqrt(3))+1/2*arctan((1+2^(1/3)*(1-x)/(1-x^3)^(1/3))/sqrt(3))/(2^(2/3)*sqrt(3))],
[1/(x^3*(1-x^3)^(2/3)*(1+x^3)),x,16,-1/2*(1-x^3)^(1/3)/x^2-1/6*log(2^(2/3)+(-1+x)/(1-x^3)^(1/3))/2^(2/3)+1/6*log(1+2^(2/3)*(1-x)^2/(1-x^3)^(2/3)-2^(1/3)*(1-x)/(1-x^3)^(1/3))/2^(2/3)-1/3*log(1+2^(1/3)*(1-x)/(1-x^3)^(1/3))/2^(2/3)+1/12*log(2*2^(1/3)+(1-x)^2/(1-x^3)^(2/3)+2^(2/3)*(1-x)/(1-x^3)^(1/3))/2^(2/3)-arctan((1-2*2^(1/3)*(1-x)/(1-x^3)^(1/3))/sqrt(3))/(2^(2/3)*sqrt(3))-1/2*arctan((1+2^(1/3)*(1-x)/(1-x^3)^(1/3))/sqrt(3))/(2^(2/3)*sqrt(3))],
[x^14/((1-x^3)^(4/3)*(1+x^3)),x,11,1/2/(1-x^3)^(1/3)+(1-x^3)^(2/3)-2/5*(1-x^3)^(5/3)+1/8*(1-x^3)^(8/3)-1/12*log(1+x^3)/2^(1/3)+1/4*log(2^(1/3)-(1-x^3)^(1/3))/2^(1/3)+1/2*arctan((1+2^(2/3)*(1-x^3)^(1/3))/sqrt(3))/(2^(1/3)*sqrt(3))],
[x^11/((1-x^3)^(4/3)*(1+x^3)),x,11,1/2/(1-x^3)^(1/3)+1/2*(1-x^3)^(2/3)-1/5*(1-x^3)^(5/3)+1/12*log(1+x^3)/2^(1/3)-1/4*log(2^(1/3)-(1-x^3)^(1/3))/2^(1/3)-1/2*arctan((1+2^(2/3)*(1-x^3)^(1/3))/sqrt(3))/(2^(1/3)*sqrt(3))],
[x^8/((1-x^3)^(4/3)*(1+x^3)),x,9,1/2/(1-x^3)^(1/3)+1/2*(1-x^3)^(2/3)-1/12*log(1+x^3)/2^(1/3)+1/4*log(2^(1/3)-(1-x^3)^(1/3))/2^(1/3)+1/2*arctan((1+2^(2/3)*(1-x^3)^(1/3))/sqrt(3))/(2^(1/3)*sqrt(3))],
[x^5/((1-x^3)^(4/3)*(1+x^3)),x,6,1/2/(1-x^3)^(1/3)+1/12*log(1+x^3)/2^(1/3)-1/4*log(2^(1/3)-(1-x^3)^(1/3))/2^(1/3)-1/2*arctan((1+2^(2/3)*(1-x^3)^(1/3))/sqrt(3))/(2^(1/3)*sqrt(3))],
[x^2/((1-x^3)^(4/3)*(1+x^3)),x,6,1/2/(1-x^3)^(1/3)-1/12*log(1+x^3)/2^(1/3)+1/4*log(2^(1/3)-(1-x^3)^(1/3))/2^(1/3)+1/2*arctan((1+2^(2/3)*(1-x^3)^(1/3))/sqrt(3))/(2^(1/3)*sqrt(3))],
[1/(x*(1-x^3)^(4/3)*(1+x^3)),x,11,1/2/(1-x^3)^(1/3)-1/2*log(x)+1/12*log(1+x^3)/2^(1/3)+1/2*log(1-(1-x^3)^(1/3))-1/4*log(2^(1/3)-(1-x^3)^(1/3))/2^(1/3)+arctan((1+2*(1-x^3)^(1/3))/sqrt(3))/sqrt(3)-1/2*arctan((1+2^(2/3)*(1-x^3)^(1/3))/sqrt(3))/(2^(1/3)*sqrt(3))],
[1/(x^4*(1-x^3)^(4/3)*(1+x^3)),x,13,5/6/(1-x^3)^(1/3)+(-1/3)/(x^3*(1-x^3)^(1/3))-1/6*log(x)-1/12*log(1+x^3)/2^(1/3)+1/6*log(1-(1-x^3)^(1/3))+1/4*log(2^(1/3)-(1-x^3)^(1/3))/2^(1/3)+1/3*arctan((1+2*(1-x^3)^(1/3))/sqrt(3))/sqrt(3)+1/2*arctan((1+2^(2/3)*(1-x^3)^(1/3))/sqrt(3))/(2^(1/3)*sqrt(3))],
[x^9/((1-x^3)^(4/3)*(1+x^3)),x,5,1/2*x^4/(1-x^3)^(1/3)+5/6*x*(1-x^3)^(2/3)+1/12*log(1+x^3)/2^(1/3)-1/4*log(-2^(1/3)*x-(1-x^3)^(1/3))/2^(1/3)-1/6*log(x+(1-x^3)^(1/3))+1/3*arctan((1-2*x/(1-x^3)^(1/3))/sqrt(3))/sqrt(3)+1/2*arctan((1-2*2^(1/3)*x/(1-x^3)^(1/3))/sqrt(3))/(2^(1/3)*sqrt(3))],
[x^6/((1-x^3)^(4/3)*(1+x^3)),x,4,1/2*x/(1-x^3)^(1/3)-1/12*log(1+x^3)/2^(1/3)+1/4*log(-2^(1/3)*x-(1-x^3)^(1/3))/2^(1/3)-1/2*log(x+(1-x^3)^(1/3))+arctan((1-2*x/(1-x^3)^(1/3))/sqrt(3))/sqrt(3)-1/2*arctan((1-2*2^(1/3)*x/(1-x^3)^(1/3))/sqrt(3))/(2^(1/3)*sqrt(3))],
[x^3/((1-x^3)^(4/3)*(1+x^3)),x,2,1/2*x/(1-x^3)^(1/3)+1/12*log(1+x^3)/2^(1/3)-1/4*log(-2^(1/3)*x-(1-x^3)^(1/3))/2^(1/3)+1/2*arctan((1-2*2^(1/3)*x/(1-x^3)^(1/3))/sqrt(3))/(2^(1/3)*sqrt(3))],
[1/((1-x^3)^(4/3)*(1+x^3)),x,2,1/2*x/(1-x^3)^(1/3)-1/12*log(1+x^3)/2^(1/3)+1/4*log(-2^(1/3)*x-(1-x^3)^(1/3))/2^(1/3)-1/2*arctan((1-2*2^(1/3)*x/(1-x^3)^(1/3))/sqrt(3))/(2^(1/3)*sqrt(3))],
[1/(x^3*(1-x^3)^(4/3)*(1+x^3)),x,4,1/2/(x^2*(1-x^3)^(1/3))-(1-x^3)^(2/3)/x^2+1/12*log(1+x^3)/2^(1/3)-1/4*log(-2^(1/3)*x-(1-x^3)^(1/3))/2^(1/3)+1/2*arctan((1-2*2^(1/3)*x/(1-x^3)^(1/3))/sqrt(3))/(2^(1/3)*sqrt(3))],
[1/(x^6*(1-x^3)^(4/3)*(1+x^3)),x,5,1/2/(x^5*(1-x^3)^(1/3))-7/10*(1-x^3)^(2/3)/x^5-4/5*(1-x^3)^(2/3)/x^2-1/12*log(1+x^3)/2^(1/3)+1/4*log(-2^(1/3)*x-(1-x^3)^(1/3))/2^(1/3)-1/2*arctan((1-2*2^(1/3)*x/(1-x^3)^(1/3))/sqrt(3))/(2^(1/3)*sqrt(3))],
[1/(x^9*(1-x^3)^(4/3)*(1+x^3)),x,6,1/2/(x^8*(1-x^3)^(1/3))-5/8*(1-x^3)^(2/3)/x^8-13/20*(1-x^3)^(2/3)/x^5-49/40*(1-x^3)^(2/3)/x^2+1/12*log(1+x^3)/2^(1/3)-1/4*log(-2^(1/3)*x-(1-x^3)^(1/3))/2^(1/3)+1/2*arctan((1-2*2^(1/3)*x/(1-x^3)^(1/3))/sqrt(3))/(2^(1/3)*sqrt(3))],
[x^10/((1-x^3)^(4/3)*(1+x^3)),x,13,1/2*x^5/(1-x^3)^(1/3)+3/4*x^2*(1-x^3)^(2/3)-1/2*x^2*hypergeom([1/3,2/3],[5/3],x^3)-1/24*log((1-x)*(1+x)^2)/2^(1/3)-1/12*log(1+2^(2/3)*(1-x)^2/(1-x^3)^(2/3)-2^(1/3)*(1-x)/(1-x^3)^(1/3))/2^(1/3)+1/6*log(1+2^(1/3)*(1-x)/(1-x^3)^(1/3))/2^(1/3)+1/8*log(-1+x+2^(2/3)*(1-x^3)^(1/3))/2^(1/3)-1/2*arctan((1-2*2^(1/3)*(1-x)/(1-x^3)^(1/3))/sqrt(3))/(2^(1/3)*sqrt(3))-1/4*arctan((1+2^(1/3)*(1-x)/(1-x^3)^(1/3))/sqrt(3))/(2^(1/3)*sqrt(3))],
[x^7/((1-x^3)^(4/3)*(1+x^3)),x,12,1/2*x^2/(1-x^3)^(1/3)-3/4*x^2*hypergeom([1/3,2/3],[5/3],x^3)+1/24*log((1-x)*(1+x)^2)/2^(1/3)+1/12*log(1+2^(2/3)*(1-x)^2/(1-x^3)^(2/3)-2^(1/3)*(1-x)/(1-x^3)^(1/3))/2^(1/3)-1/6*log(1+2^(1/3)*(1-x)/(1-x^3)^(1/3))/2^(1/3)-1/8*log(-1+x+2^(2/3)*(1-x^3)^(1/3))/2^(1/3)+1/2*arctan((1-2*2^(1/3)*(1-x)/(1-x^3)^(1/3))/sqrt(3))/(2^(1/3)*sqrt(3))+1/4*arctan((1+2^(1/3)*(1-x)/(1-x^3)^(1/3))/sqrt(3))/(2^(1/3)*sqrt(3))],
[x^4/((1-x^3)^(4/3)*(1+x^3)),x,12,1/2*x^2/(1-x^3)^(1/3)-1/4*x^2*hypergeom([1/3,2/3],[5/3],x^3)-1/24*log((1-x)*(1+x)^2)/2^(1/3)-1/12*log(1+2^(2/3)*(1-x)^2/(1-x^3)^(2/3)-2^(1/3)*(1-x)/(1-x^3)^(1/3))/2^(1/3)+1/6*log(1+2^(1/3)*(1-x)/(1-x^3)^(1/3))/2^(1/3)+1/8*log(-1+x+2^(2/3)*(1-x^3)^(1/3))/2^(1/3)-1/2*arctan((1-2*2^(1/3)*(1-x)/(1-x^3)^(1/3))/sqrt(3))/(2^(1/3)*sqrt(3))-1/4*arctan((1+2^(1/3)*(1-x)/(1-x^3)^(1/3))/sqrt(3))/(2^(1/3)*sqrt(3))],
[x/((1-x^3)^(4/3)*(1+x^3)),x,11,1/2*x^2/(1-x^3)^(1/3)-1/4*x^2*hypergeom([1/3,2/3],[5/3],x^3)+1/24*log((1-x)*(1+x)^2)/2^(1/3)+1/12*log(1+2^(2/3)*(1-x)^2/(1-x^3)^(2/3)-2^(1/3)*(1-x)/(1-x^3)^(1/3))/2^(1/3)-1/6*log(1+2^(1/3)*(1-x)/(1-x^3)^(1/3))/2^(1/3)-1/8*log(-1+x+2^(2/3)*(1-x^3)^(1/3))/2^(1/3)+1/2*arctan((1-2*2^(1/3)*(1-x)/(1-x^3)^(1/3))/sqrt(3))/(2^(1/3)*sqrt(3))+1/4*arctan((1+2^(1/3)*(1-x)/(1-x^3)^(1/3))/sqrt(3))/(2^(1/3)*sqrt(3))],
[1/(x^2*(1-x^3)^(4/3)*(1+x^3)),x,13,1/2/(x*(1-x^3)^(1/3))-3/2*(1-x^3)^(2/3)/x-3/4*x^2*hypergeom([1/3,2/3],[5/3],x^3)-1/24*log((1-x)*(1+x)^2)/2^(1/3)-1/12*log(1+2^(2/3)*(1-x)^2/(1-x^3)^(2/3)-2^(1/3)*(1-x)/(1-x^3)^(1/3))/2^(1/3)+1/6*log(1+2^(1/3)*(1-x)/(1-x^3)^(1/3))/2^(1/3)+1/8*log(-1+x+2^(2/3)*(1-x^3)^(1/3))/2^(1/3)-1/2*arctan((1-2*2^(1/3)*(1-x)/(1-x^3)^(1/3))/sqrt(3))/(2^(1/3)*sqrt(3))-1/4*arctan((1+2^(1/3)*(1-x)/(1-x^3)^(1/3))/sqrt(3))/(2^(1/3)*sqrt(3))],
[1/(x^5*(1-x^3)^(4/3)*(1+x^3)),x,14,1/2/(x^4*(1-x^3)^(1/3))-3/4*(1-x^3)^(2/3)/x^4-(1-x^3)^(2/3)/x-1/2*x^2*hypergeom([1/3,2/3],[5/3],x^3)+1/24*log((1-x)*(1+x)^2)/2^(1/3)+1/12*log(1+2^(2/3)*(1-x)^2/(1-x^3)^(2/3)-2^(1/3)*(1-x)/(1-x^3)^(1/3))/2^(1/3)-1/6*log(1+2^(1/3)*(1-x)/(1-x^3)^(1/3))/2^(1/3)-1/8*log(-1+x+2^(2/3)*(1-x^3)^(1/3))/2^(1/3)+1/2*arctan((1-2*2^(1/3)*(1-x)/(1-x^3)^(1/3))/sqrt(3))/(2^(1/3)*sqrt(3))+1/4*arctan((1+2^(1/3)*(1-x)/(1-x^3)^(1/3))/sqrt(3))/(2^(1/3)*sqrt(3))],

# Integrands of the form x^m (a+b x^3)^(p/3) / (c+d x^3)

# p>0
[x^11*(a+b*x^3)^(1/3)/(c+d*x^3),x,8,-c^3*(a+b*x^3)^(1/3)/d^4+1/4*(b^2*c^2+a*b*c*d+a^2*d^2)*(a+b*x^3)^(4/3)/(b^3*d^3)-1/7*(b*c+2*a*d)*(a+b*x^3)^(7/3)/(b^3*d^2)+1/10*(a+b*x^3)^(10/3)/(b^3*d)-1/6*c^3*(b*c-a*d)^(1/3)*log(c+d*x^3)/d^(13/3)+1/2*c^3*(b*c-a*d)^(1/3)*log((b*c-a*d)^(1/3)+d^(1/3)*(a+b*x^3)^(1/3))/d^(13/3)-c^3*(b*c-a*d)^(1/3)*arctan((1-2*d^(1/3)*(a+b*x^3)^(1/3)/(b*c-a*d)^(1/3))/sqrt(3))/(d^(13/3)*sqrt(3))],
[x^8*(a+b*x^3)^(1/3)/(c+d*x^3),x,8,c^2*(a+b*x^3)^(1/3)/d^3-1/4*(b*c+a*d)*(a+b*x^3)^(4/3)/(b^2*d^2)+1/7*(a+b*x^3)^(7/3)/(b^2*d)+1/6*c^2*(b*c-a*d)^(1/3)*log(c+d*x^3)/d^(10/3)-1/2*c^2*(b*c-a*d)^(1/3)*log((b*c-a*d)^(1/3)+d^(1/3)*(a+b*x^3)^(1/3))/d^(10/3)+c^2*(b*c-a*d)^(1/3)*arctan((1-2*d^(1/3)*(a+b*x^3)^(1/3)/(b*c-a*d)^(1/3))/sqrt(3))/(d^(10/3)*sqrt(3))],
[x^5*(a+b*x^3)^(1/3)/(c+d*x^3),x,7,-c*(a+b*x^3)^(1/3)/d^2+1/4*(a+b*x^3)^(4/3)/(b*d)-1/6*c*(b*c-a*d)^(1/3)*log(c+d*x^3)/d^(7/3)+1/2*c*(b*c-a*d)^(1/3)*log((b*c-a*d)^(1/3)+d^(1/3)*(a+b*x^3)^(1/3))/d^(7/3)-c*(b*c-a*d)^(1/3)*arctan((1-2*d^(1/3)*(a+b*x^3)^(1/3)/(b*c-a*d)^(1/3))/sqrt(3))/(d^(7/3)*sqrt(3))],
[x^2*(a+b*x^3)^(1/3)/(c+d*x^3),x,6,(a+b*x^3)^(1/3)/d+1/6*(b*c-a*d)^(1/3)*log(c+d*x^3)/d^(4/3)-1/2*(b*c-a*d)^(1/3)*log((b*c-a*d)^(1/3)+d^(1/3)*(a+b*x^3)^(1/3))/d^(4/3)+(b*c-a*d)^(1/3)*arctan((1-2*d^(1/3)*(a+b*x^3)^(1/3)/(b*c-a*d)^(1/3))/sqrt(3))/(d^(4/3)*sqrt(3))],
[(a+b*x^3)^(1/3)/(x*(c+d*x^3)),x,10,-1/2*a^(1/3)*log(x)/c-1/6*(b*c-a*d)^(1/3)*log(c+d*x^3)/(c*d^(1/3))+1/2*a^(1/3)*log(a^(1/3)-(a+b*x^3)^(1/3))/c+1/2*(b*c-a*d)^(1/3)*log((b*c-a*d)^(1/3)+d^(1/3)*(a+b*x^3)^(1/3))/(c*d^(1/3))-a^(1/3)*arctan((a^(1/3)+2*(a+b*x^3)^(1/3))/(a^(1/3)*sqrt(3)))/(c*sqrt(3))-(b*c-a*d)^(1/3)*arctan((1-2*d^(1/3)*(a+b*x^3)^(1/3)/(b*c-a*d)^(1/3))/sqrt(3))/(c*d^(1/3)*sqrt(3))],
[(a+b*x^3)^(1/3)/(x^4*(c+d*x^3)),x,13,d*(a+b*x^3)^(1/3)/c^2+1/3*(b*c-3*a*d)*(a+b*x^3)^(1/3)/(a*c^2)-1/3*(a+b*x^3)^(4/3)/(a*c*x^3)-1/6*(b*c-3*a*d)*log(x)/(a^(2/3)*c^2)+1/6*d^(2/3)*(b*c-a*d)^(1/3)*log(c+d*x^3)/c^2+1/6*(b*c-3*a*d)*log(a^(1/3)-(a+b*x^3)^(1/3))/(a^(2/3)*c^2)-1/2*d^(2/3)*(b*c-a*d)^(1/3)*log((b*c-a*d)^(1/3)+d^(1/3)*(a+b*x^3)^(1/3))/c^2-1/3*(b*c-3*a*d)*arctan((a^(1/3)+2*(a+b*x^3)^(1/3))/(a^(1/3)*sqrt(3)))/(a^(2/3)*c^2*sqrt(3))+d^(2/3)*(b*c-a*d)^(1/3)*arctan((1-2*d^(1/3)*(a+b*x^3)^(1/3)/(b*c-a*d)^(1/3))/sqrt(3))/(c^2*sqrt(3))],
[(a+b*x^3)^(1/3)/(x^7*(c+d*x^3)),x,12,1/9*(b*c+3*a*d)*(a+b*x^3)^(1/3)/(a*c^2*x^3)-1/6*(a+b*x^3)^(4/3)/(a*c*x^6)+1/18*(b^2*c^2+3*a*b*c*d-9*a^2*d^2)*log(x)/(a^(5/3)*c^3)-1/6*d^(5/3)*(b*c-a*d)^(1/3)*log(c+d*x^3)/c^3-1/18*(b^2*c^2+3*a*b*c*d-9*a^2*d^2)*log(a^(1/3)-(a+b*x^3)^(1/3))/(a^(5/3)*c^3)+1/2*d^(5/3)*(b*c-a*d)^(1/3)*log((b*c-a*d)^(1/3)+d^(1/3)*(a+b*x^3)^(1/3))/c^3+1/9*(b^2*c^2+3*a*b*c*d-9*a^2*d^2)*arctan((a^(1/3)+2*(a+b*x^3)^(1/3))/(a^(1/3)*sqrt(3)))/(a^(5/3)*c^3*sqrt(3))-d^(5/3)*(b*c-a*d)^(1/3)*arctan((1-2*d^(1/3)*(a+b*x^3)^(1/3)/(b*c-a*d)^(1/3))/sqrt(3))/(c^3*sqrt(3))],
[x^7*(a+b*x^3)^(1/3)/(c+d*x^3),x,6,-1/18*(6*b*c-a*d)*x^2*(a+b*x^3)^(1/3)/(b*d^2)+1/6*x^5*(a+b*x^3)^(1/3)/d-1/6*c^(5/3)*(b*c-a*d)^(1/3)*log(c+d*x^3)/d^3-1/18*(9*b^2*c^2-3*a*b*c*d-a^2*d^2)*log(b^(1/3)*x-(a+b*x^3)^(1/3))/(b^(5/3)*d^3)+1/2*c^(5/3)*(b*c-a*d)^(1/3)*log((b*c-a*d)^(1/3)*x/c^(1/3)-(a+b*x^3)^(1/3))/d^3-1/9*(9*b^2*c^2-3*a*b*c*d-a^2*d^2)*arctan((1+2*b^(1/3)*x/(a+b*x^3)^(1/3))/sqrt(3))/(b^(5/3)*d^3*sqrt(3))+c^(5/3)*(b*c-a*d)^(1/3)*arctan((1+2*(b*c-a*d)^(1/3)*x/(c^(1/3)*(a+b*x^3)^(1/3)))/sqrt(3))/(d^3*sqrt(3))],
[x^4*(a+b*x^3)^(1/3)/(c+d*x^3),x,5,1/3*x^2*(a+b*x^3)^(1/3)/d+1/6*c^(2/3)*(b*c-a*d)^(1/3)*log(c+d*x^3)/d^2+1/6*(3*b*c-a*d)*log(b^(1/3)*x-(a+b*x^3)^(1/3))/(b^(2/3)*d^2)-1/2*c^(2/3)*(b*c-a*d)^(1/3)*log((b*c-a*d)^(1/3)*x/c^(1/3)-(a+b*x^3)^(1/3))/d^2+1/3*(3*b*c-a*d)*arctan((1+2*b^(1/3)*x/(a+b*x^3)^(1/3))/sqrt(3))/(b^(2/3)*d^2*sqrt(3))-c^(2/3)*(b*c-a*d)^(1/3)*arctan((1+2*(b*c-a*d)^(1/3)*x/(c^(1/3)*(a+b*x^3)^(1/3)))/sqrt(3))/(d^2*sqrt(3))],
[x*(a+b*x^3)^(1/3)/(c+d*x^3),x,3,-1/6*(b*c-a*d)^(1/3)*log(c+d*x^3)/(c^(1/3)*d)-1/2*b^(1/3)*log(b^(1/3)*x-(a+b*x^3)^(1/3))/d+1/2*(b*c-a*d)^(1/3)*log((b*c-a*d)^(1/3)*x/c^(1/3)-(a+b*x^3)^(1/3))/(c^(1/3)*d)-b^(1/3)*arctan((1+2*b^(1/3)*x/(a+b*x^3)^(1/3))/sqrt(3))/(d*sqrt(3))+(b*c-a*d)^(1/3)*arctan((1+2*(b*c-a*d)^(1/3)*x/(c^(1/3)*(a+b*x^3)^(1/3)))/sqrt(3))/(c^(1/3)*d*sqrt(3))],
[(a+b*x^3)^(1/3)/(x^2*(c+d*x^3)),x,3,-(a+b*x^3)^(1/3)/(c*x)+1/6*(b*c-a*d)^(1/3)*log(c+d*x^3)/c^(4/3)-1/2*(b*c-a*d)^(1/3)*log((b*c-a*d)^(1/3)*x/c^(1/3)-(a+b*x^3)^(1/3))/c^(4/3)-(b*c-a*d)^(1/3)*arctan((1+2*(b*c-a*d)^(1/3)*x/(c^(1/3)*(a+b*x^3)^(1/3)))/sqrt(3))/(c^(4/3)*sqrt(3))],
[(a+b*x^3)^(1/3)/(x^5*(c+d*x^3)),x,4,-1/4*(a+b*x^3)^(1/3)/(c*x^4)-1/4*(b*c-4*a*d)*(a+b*x^3)^(1/3)/(a*c^2*x)-1/6*d*(b*c-a*d)^(1/3)*log(c+d*x^3)/c^(7/3)+1/2*d*(b*c-a*d)^(1/3)*log((b*c-a*d)^(1/3)*x/c^(1/3)-(a+b*x^3)^(1/3))/c^(7/3)+d*(b*c-a*d)^(1/3)*arctan((1+2*(b*c-a*d)^(1/3)*x/(c^(1/3)*(a+b*x^3)^(1/3)))/sqrt(3))/(c^(7/3)*sqrt(3))],
[(a+b*x^3)^(1/3)/(x^8*(c+d*x^3)),x,5,-1/7*(a+b*x^3)^(1/3)/(c*x^7)-1/28*(b*c-7*a*d)*(a+b*x^3)^(1/3)/(a*c^2*x^4)+1/28*(3*b^2*c^2+7*a*b*c*d-28*a^2*d^2)*(a+b*x^3)^(1/3)/(a^2*c^3*x)+1/6*d^2*(b*c-a*d)^(1/3)*log(c+d*x^3)/c^(10/3)-1/2*d^2*(b*c-a*d)^(1/3)*log((b*c-a*d)^(1/3)*x/c^(1/3)-(a+b*x^3)^(1/3))/c^(10/3)-d^2*(b*c-a*d)^(1/3)*arctan((1+2*(b*c-a*d)^(1/3)*x/(c^(1/3)*(a+b*x^3)^(1/3)))/sqrt(3))/(c^(10/3)*sqrt(3))],
[(a+b*x^3)^(1/3)/(x^11*(c+d*x^3)),x,6,-1/10*(a+b*x^3)^(1/3)/(c*x^10)-1/70*(b*c-10*a*d)*(a+b*x^3)^(1/3)/(a*c^2*x^7)+1/140*(3*b^2*c^2+5*a*b*c*d-35*a^2*d^2)*(a+b*x^3)^(1/3)/(a^2*c^3*x^4)-1/140*(9*b^3*c^3+15*a*b^2*c^2*d+35*a^2*b*c*d^2-140*a^3*d^3)*(a+b*x^3)^(1/3)/(a^3*c^4*x)-1/6*d^3*(b*c-a*d)^(1/3)*log(c+d*x^3)/c^(13/3)+1/2*d^3*(b*c-a*d)^(1/3)*log((b*c-a*d)^(1/3)*x/c^(1/3)-(a+b*x^3)^(1/3))/c^(13/3)+d^3*(b*c-a*d)^(1/3)*arctan((1+2*(b*c-a*d)^(1/3)*x/(c^(1/3)*(a+b*x^3)^(1/3)))/sqrt(3))/(c^(13/3)*sqrt(3))],
[x^6*(a+b*x^3)^(1/3)/(c+d*x^3),x,2,1/7*x^7*(a+b*x^3)^(1/3)*AppellF1(7/3,-1/3,1,10/3,-b*x^3/a,-d*x^3/c)/(c*(1+b*x^3/a)^(1/3))],
[x^3*(a+b*x^3)^(1/3)/(c+d*x^3),x,2,1/4*x^4*(a+b*x^3)^(1/3)*AppellF1(4/3,-1/3,1,7/3,-b*x^3/a,-d*x^3/c)/(c*(1+b*x^3/a)^(1/3))],
[(a+b*x^3)^(1/3)/(c+d*x^3),x,2,x*(a+b*x^3)^(1/3)*AppellF1(1/3,-1/3,1,4/3,-b*x^3/a,-d*x^3/c)/(c*(1+b*x^3/a)^(1/3))],
[(a+b*x^3)^(1/3)/(x^3*(c+d*x^3)),x,2,-1/2*(a+b*x^3)^(1/3)*AppellF1(-2/3,-1/3,1,1/3,-b*x^3/a,-d*x^3/c)/(c*x^2*(1+b*x^3/a)^(1/3))],
[(a+b*x^3)^(1/3)/(x^6*(c+d*x^3)),x,2,-1/5*(a+b*x^3)^(1/3)*AppellF1(-5/3,-1/3,1,-2/3,-b*x^3/a,-d*x^3/c)/(c*x^5*(1+b*x^3/a)^(1/3))],
[x^11*(a+b*x^3)^(2/3)/(c+d*x^3),x,8,-1/2*c^3*(a+b*x^3)^(2/3)/d^4+1/5*(b^2*c^2+a*b*c*d+a^2*d^2)*(a+b*x^3)^(5/3)/(b^3*d^3)-1/8*(b*c+2*a*d)*(a+b*x^3)^(8/3)/(b^3*d^2)+1/11*(a+b*x^3)^(11/3)/(b^3*d)+1/6*c^3*(b*c-a*d)^(2/3)*log(c+d*x^3)/d^(14/3)-1/2*c^3*(b*c-a*d)^(2/3)*log((b*c-a*d)^(1/3)+d^(1/3)*(a+b*x^3)^(1/3))/d^(14/3)-c^3*(b*c-a*d)^(2/3)*arctan((1-2*d^(1/3)*(a+b*x^3)^(1/3)/(b*c-a*d)^(1/3))/sqrt(3))/(d^(14/3)*sqrt(3))],
[x^8*(a+b*x^3)^(2/3)/(c+d*x^3),x,8,1/2*c^2*(a+b*x^3)^(2/3)/d^3-1/5*(b*c+a*d)*(a+b*x^3)^(5/3)/(b^2*d^2)+1/8*(a+b*x^3)^(8/3)/(b^2*d)-1/6*c^2*(b*c-a*d)^(2/3)*log(c+d*x^3)/d^(11/3)+1/2*c^2*(b*c-a*d)^(2/3)*log((b*c-a*d)^(1/3)+d^(1/3)*(a+b*x^3)^(1/3))/d^(11/3)+c^2*(b*c-a*d)^(2/3)*arctan((1-2*d^(1/3)*(a+b*x^3)^(1/3)/(b*c-a*d)^(1/3))/sqrt(3))/(d^(11/3)*sqrt(3))],
[x^5*(a+b*x^3)^(2/3)/(c+d*x^3),x,7,-1/2*c*(a+b*x^3)^(2/3)/d^2+1/5*(a+b*x^3)^(5/3)/(b*d)+1/6*c*(b*c-a*d)^(2/3)*log(c+d*x^3)/d^(8/3)-1/2*c*(b*c-a*d)^(2/3)*log((b*c-a*d)^(1/3)+d^(1/3)*(a+b*x^3)^(1/3))/d^(8/3)-c*(b*c-a*d)^(2/3)*arctan((1-2*d^(1/3)*(a+b*x^3)^(1/3)/(b*c-a*d)^(1/3))/sqrt(3))/(d^(8/3)*sqrt(3))],
[x^2*(a+b*x^3)^(2/3)/(c+d*x^3),x,6,1/2*(a+b*x^3)^(2/3)/d-1/6*(b*c-a*d)^(2/3)*log(c+d*x^3)/d^(5/3)+1/2*(b*c-a*d)^(2/3)*log((b*c-a*d)^(1/3)+d^(1/3)*(a+b*x^3)^(1/3))/d^(5/3)+(b*c-a*d)^(2/3)*arctan((1-2*d^(1/3)*(a+b*x^3)^(1/3)/(b*c-a*d)^(1/3))/sqrt(3))/(d^(5/3)*sqrt(3))],
[(a+b*x^3)^(2/3)/(x*(c+d*x^3)),x,10,-1/2*a^(2/3)*log(x)/c+1/6*(b*c-a*d)^(2/3)*log(c+d*x^3)/(c*d^(2/3))+1/2*a^(2/3)*log(a^(1/3)-(a+b*x^3)^(1/3))/c-1/2*(b*c-a*d)^(2/3)*log((b*c-a*d)^(1/3)+d^(1/3)*(a+b*x^3)^(1/3))/(c*d^(2/3))+a^(2/3)*arctan((a^(1/3)+2*(a+b*x^3)^(1/3))/(a^(1/3)*sqrt(3)))/(c*sqrt(3))-(b*c-a*d)^(2/3)*arctan((1-2*d^(1/3)*(a+b*x^3)^(1/3)/(b*c-a*d)^(1/3))/sqrt(3))/(c*d^(2/3)*sqrt(3))],
[(a+b*x^3)^(2/3)/(x^4*(c+d*x^3)),x,13,1/2*d*(a+b*x^3)^(2/3)/c^2+1/6*(2*b*c-3*a*d)*(a+b*x^3)^(2/3)/(a*c^2)-1/3*(a+b*x^3)^(5/3)/(a*c*x^3)-1/6*(2*b*c-3*a*d)*log(x)/(a^(1/3)*c^2)-1/6*d^(1/3)*(b*c-a*d)^(2/3)*log(c+d*x^3)/c^2+1/6*(2*b*c-3*a*d)*log(a^(1/3)-(a+b*x^3)^(1/3))/(a^(1/3)*c^2)+1/2*d^(1/3)*(b*c-a*d)^(2/3)*log((b*c-a*d)^(1/3)+d^(1/3)*(a+b*x^3)^(1/3))/c^2+1/3*(2*b*c-3*a*d)*arctan((a^(1/3)+2*(a+b*x^3)^(1/3))/(a^(1/3)*sqrt(3)))/(a^(1/3)*c^2*sqrt(3))+d^(1/3)*(b*c-a*d)^(2/3)*arctan((1-2*d^(1/3)*(a+b*x^3)^(1/3)/(b*c-a*d)^(1/3))/sqrt(3))/(c^2*sqrt(3))],
[(a+b*x^3)^(2/3)/(x^7*(c+d*x^3)),x,12,1/18*(b*c+6*a*d)*(a+b*x^3)^(2/3)/(a*c^2*x^3)-1/6*(a+b*x^3)^(5/3)/(a*c*x^6)+1/18*(b^2*c^2+6*a*b*c*d-9*a^2*d^2)*log(x)/(a^(4/3)*c^3)+1/6*d^(4/3)*(b*c-a*d)^(2/3)*log(c+d*x^3)/c^3-1/18*(b^2*c^2+6*a*b*c*d-9*a^2*d^2)*log(a^(1/3)-(a+b*x^3)^(1/3))/(a^(4/3)*c^3)-1/2*d^(4/3)*(b*c-a*d)^(2/3)*log((b*c-a*d)^(1/3)+d^(1/3)*(a+b*x^3)^(1/3))/c^3-1/9*(b^2*c^2+6*a*b*c*d-9*a^2*d^2)*arctan((a^(1/3)+2*(a+b*x^3)^(1/3))/(a^(1/3)*sqrt(3)))/(a^(4/3)*c^3*sqrt(3))-d^(4/3)*(b*c-a*d)^(2/3)*arctan((1-2*d^(1/3)*(a+b*x^3)^(1/3)/(b*c-a*d)^(1/3))/sqrt(3))/(c^3*sqrt(3))],
[x^6*(a+b*x^3)^(2/3)/(c+d*x^3),x,5,-1/9*(3*b*c-a*d)*x*(a+b*x^3)^(2/3)/(b*d^2)+1/6*x^4*(a+b*x^3)^(2/3)/d-1/6*c^(4/3)*(b*c-a*d)^(2/3)*log(c+d*x^3)/d^3+1/2*c^(4/3)*(b*c-a*d)^(2/3)*log((b*c-a*d)^(1/3)*x/c^(1/3)-(a+b*x^3)^(1/3))/d^3-1/18*(9*b^2*c^2-6*a*b*c*d-a^2*d^2)*log(-b^(1/3)*x+(a+b*x^3)^(1/3))/(b^(4/3)*d^3)+1/9*(9*b^2*c^2-6*a*b*c*d-a^2*d^2)*arctan((1+2*b^(1/3)*x/(a+b*x^3)^(1/3))/sqrt(3))/(b^(4/3)*d^3*sqrt(3))-c^(4/3)*(b*c-a*d)^(2/3)*arctan((1+2*(b*c-a*d)^(1/3)*x/(c^(1/3)*(a+b*x^3)^(1/3)))/sqrt(3))/(d^3*sqrt(3))],
[x^3*(a+b*x^3)^(2/3)/(c+d*x^3),x,4,1/3*x*(a+b*x^3)^(2/3)/d+1/6*c^(1/3)*(b*c-a*d)^(2/3)*log(c+d*x^3)/d^2-1/2*c^(1/3)*(b*c-a*d)^(2/3)*log((b*c-a*d)^(1/3)*x/c^(1/3)-(a+b*x^3)^(1/3))/d^2+1/6*(3*b*c-2*a*d)*log(-b^(1/3)*x+(a+b*x^3)^(1/3))/(b^(1/3)*d^2)-1/3*(3*b*c-2*a*d)*arctan((1+2*b^(1/3)*x/(a+b*x^3)^(1/3))/sqrt(3))/(b^(1/3)*d^2*sqrt(3))+c^(1/3)*(b*c-a*d)^(2/3)*arctan((1+2*(b*c-a*d)^(1/3)*x/(c^(1/3)*(a+b*x^3)^(1/3)))/sqrt(3))/(d^2*sqrt(3))],
[(a+b*x^3)^(2/3)/(c+d*x^3),x,3,-1/6*(b*c-a*d)^(2/3)*log(c+d*x^3)/(c^(2/3)*d)+1/2*(b*c-a*d)^(2/3)*log((b*c-a*d)^(1/3)*x/c^(1/3)-(a+b*x^3)^(1/3))/(c^(2/3)*d)-1/2*b^(2/3)*log(-b^(1/3)*x+(a+b*x^3)^(1/3))/d+b^(2/3)*arctan((1+2*b^(1/3)*x/(a+b*x^3)^(1/3))/sqrt(3))/(d*sqrt(3))-(b*c-a*d)^(2/3)*arctan((1+2*(b*c-a*d)^(1/3)*x/(c^(1/3)*(a+b*x^3)^(1/3)))/sqrt(3))/(c^(2/3)*d*sqrt(3))],
[(a+b*x^3)^(2/3)/(x^3*(c+d*x^3)),x,3,-1/2*(a+b*x^3)^(2/3)/(c*x^2)+1/6*(b*c-a*d)^(2/3)*log(c+d*x^3)/c^(5/3)-1/2*(b*c-a*d)^(2/3)*log((b*c-a*d)^(1/3)*x/c^(1/3)-(a+b*x^3)^(1/3))/c^(5/3)+(b*c-a*d)^(2/3)*arctan((1+2*(b*c-a*d)^(1/3)*x/(c^(1/3)*(a+b*x^3)^(1/3)))/sqrt(3))/(c^(5/3)*sqrt(3))],
[(a+b*x^3)^(2/3)/(x^6*(c+d*x^3)),x,4,-1/5*(a+b*x^3)^(2/3)/(c*x^5)-1/10*(2*b*c-5*a*d)*(a+b*x^3)^(2/3)/(a*c^2*x^2)-1/6*d*(b*c-a*d)^(2/3)*log(c+d*x^3)/c^(8/3)+1/2*d*(b*c-a*d)^(2/3)*log((b*c-a*d)^(1/3)*x/c^(1/3)-(a+b*x^3)^(1/3))/c^(8/3)-d*(b*c-a*d)^(2/3)*arctan((1+2*(b*c-a*d)^(1/3)*x/(c^(1/3)*(a+b*x^3)^(1/3)))/sqrt(3))/(c^(8/3)*sqrt(3))],
[(a+b*x^3)^(2/3)/(x^9*(c+d*x^3)),x,5,-1/8*(a+b*x^3)^(2/3)/(c*x^8)-1/20*(b*c-4*a*d)*(a+b*x^3)^(2/3)/(a*c^2*x^5)+1/40*(3*b^2*c^2+8*a*b*c*d-20*a^2*d^2)*(a+b*x^3)^(2/3)/(a^2*c^3*x^2)+1/6*d^2*(b*c-a*d)^(2/3)*log(c+d*x^3)/c^(11/3)-1/2*d^2*(b*c-a*d)^(2/3)*log((b*c-a*d)^(1/3)*x/c^(1/3)-(a+b*x^3)^(1/3))/c^(11/3)+d^2*(b*c-a*d)^(2/3)*arctan((1+2*(b*c-a*d)^(1/3)*x/(c^(1/3)*(a+b*x^3)^(1/3)))/sqrt(3))/(c^(11/3)*sqrt(3))],
[(a+b*x^3)^(2/3)/(x^12*(c+d*x^3)),x,6,-1/11*(a+b*x^3)^(2/3)/(c*x^11)-1/88*(2*b*c-11*a*d)*(a+b*x^3)^(2/3)/(a*c^2*x^8)+1/220*(6*b^2*c^2+11*a*b*c*d-44*a^2*d^2)*(a+b*x^3)^(2/3)/(a^2*c^3*x^5)-1/440*(18*b^3*c^3+33*a*b^2*c^2*d+88*a^2*b*c*d^2-220*a^3*d^3)*(a+b*x^3)^(2/3)/(a^3*c^4*x^2)-1/6*d^3*(b*c-a*d)^(2/3)*log(c+d*x^3)/c^(14/3)+1/2*d^3*(b*c-a*d)^(2/3)*log((b*c-a*d)^(1/3)*x/c^(1/3)-(a+b*x^3)^(1/3))/c^(14/3)-d^3*(b*c-a*d)^(2/3)*arctan((1+2*(b*c-a*d)^(1/3)*x/(c^(1/3)*(a+b*x^3)^(1/3)))/sqrt(3))/(c^(14/3)*sqrt(3))],
[x^7*(a+b*x^3)^(2/3)/(c+d*x^3),x,2,1/8*x^8*(a+b*x^3)^(2/3)*AppellF1(8/3,-2/3,1,11/3,-b*x^3/a,-d*x^3/c)/(c*(1+b*x^3/a)^(2/3))],
[x^4*(a+b*x^3)^(2/3)/(c+d*x^3),x,2,1/5*x^5*(a+b*x^3)^(2/3)*AppellF1(5/3,-2/3,1,8/3,-b*x^3/a,-d*x^3/c)/(c*(1+b*x^3/a)^(2/3))],
[x*(a+b*x^3)^(2/3)/(c+d*x^3),x,2,1/2*x^2*(a+b*x^3)^(2/3)*AppellF1(2/3,-2/3,1,5/3,-b*x^3/a,-d*x^3/c)/(c*(1+b*x^3/a)^(2/3))],
[(a+b*x^3)^(2/3)/(x^2*(c+d*x^3)),x,2,-(a+b*x^3)^(2/3)*AppellF1(-1/3,-2/3,1,2/3,-b*x^3/a,-d*x^3/c)/(c*x*(1+b*x^3/a)^(2/3))],
[(a+b*x^3)^(2/3)/(x^5*(c+d*x^3)),x,2,-1/4*(a+b*x^3)^(2/3)*AppellF1(-4/3,-2/3,1,-1/3,-b*x^3/a,-d*x^3/c)/(c*x^4*(1+b*x^3/a)^(2/3))],
[x^8*(a+b*x^3)^(4/3)/(c+d*x^3),x,9,-c^2*(b*c-a*d)*(a+b*x^3)^(1/3)/d^4+1/4*c^2*(a+b*x^3)^(4/3)/d^3-1/7*(b*c+a*d)*(a+b*x^3)^(7/3)/(b^2*d^2)+1/10*(a+b*x^3)^(10/3)/(b^2*d)-1/6*c^2*(b*c-a*d)^(4/3)*log(c+d*x^3)/d^(13/3)+1/2*c^2*(b*c-a*d)^(4/3)*log((b*c-a*d)^(1/3)+d^(1/3)*(a+b*x^3)^(1/3))/d^(13/3)-c^2*(b*c-a*d)^(4/3)*arctan((1-2*d^(1/3)*(a+b*x^3)^(1/3)/(b*c-a*d)^(1/3))/sqrt(3))/(d^(13/3)*sqrt(3))],
[x^5*(a+b*x^3)^(4/3)/(c+d*x^3),x,8,c*(b*c-a*d)*(a+b*x^3)^(1/3)/d^3-1/4*c*(a+b*x^3)^(4/3)/d^2+1/7*(a+b*x^3)^(7/3)/(b*d)+1/6*c*(b*c-a*d)^(4/3)*log(c+d*x^3)/d^(10/3)-1/2*c*(b*c-a*d)^(4/3)*log((b*c-a*d)^(1/3)+d^(1/3)*(a+b*x^3)^(1/3))/d^(10/3)+c*(b*c-a*d)^(4/3)*arctan((1-2*d^(1/3)*(a+b*x^3)^(1/3)/(b*c-a*d)^(1/3))/sqrt(3))/(d^(10/3)*sqrt(3))],
[x^2*(a+b*x^3)^(4/3)/(c+d*x^3),x,7,-(b*c-a*d)*(a+b*x^3)^(1/3)/d^2+1/4*(a+b*x^3)^(4/3)/d-1/6*(b*c-a*d)^(4/3)*log(c+d*x^3)/d^(7/3)+1/2*(b*c-a*d)^(4/3)*log((b*c-a*d)^(1/3)+d^(1/3)*(a+b*x^3)^(1/3))/d^(7/3)-(b*c-a*d)^(4/3)*arctan((1-2*d^(1/3)*(a+b*x^3)^(1/3)/(b*c-a*d)^(1/3))/sqrt(3))/(d^(7/3)*sqrt(3))],
[(a+b*x^3)^(4/3)/(x*(c+d*x^3)),x,11,b*(a+b*x^3)^(1/3)/d-1/2*a^(4/3)*log(x)/c+1/6*(b*c-a*d)^(4/3)*log(c+d*x^3)/(c*d^(4/3))+1/2*a^(4/3)*log(a^(1/3)-(a+b*x^3)^(1/3))/c-1/2*(b*c-a*d)^(4/3)*log((b*c-a*d)^(1/3)+d^(1/3)*(a+b*x^3)^(1/3))/(c*d^(4/3))-a^(4/3)*arctan((a^(1/3)+2*(a+b*x^3)^(1/3))/(a^(1/3)*sqrt(3)))/(c*sqrt(3))+(b*c-a*d)^(4/3)*arctan((1-2*d^(1/3)*(a+b*x^3)^(1/3)/(b*c-a*d)^(1/3))/sqrt(3))/(c*d^(4/3)*sqrt(3))],
[(a+b*x^3)^(4/3)/(x^4*(c+d*x^3)),x,15,1/3*(4*b*c-3*a*d)*(a+b*x^3)^(1/3)/c^2-(b*c-a*d)*(a+b*x^3)^(1/3)/c^2+1/4*d*(a+b*x^3)^(4/3)/c^2+1/12*(4*b*c-3*a*d)*(a+b*x^3)^(4/3)/(a*c^2)-1/3*(a+b*x^3)^(7/3)/(a*c*x^3)-1/6*a^(1/3)*(4*b*c-3*a*d)*log(x)/c^2-1/6*(b*c-a*d)^(4/3)*log(c+d*x^3)/(c^2*d^(1/3))+1/6*a^(1/3)*(4*b*c-3*a*d)*log(a^(1/3)-(a+b*x^3)^(1/3))/c^2+1/2*(b*c-a*d)^(4/3)*log((b*c-a*d)^(1/3)+d^(1/3)*(a+b*x^3)^(1/3))/(c^2*d^(1/3))-1/3*a^(1/3)*(4*b*c-3*a*d)*arctan((a^(1/3)+2*(a+b*x^3)^(1/3))/(a^(1/3)*sqrt(3)))/(c^2*sqrt(3))-(b*c-a*d)^(4/3)*arctan((1-2*d^(1/3)*(a+b*x^3)^(1/3)/(b*c-a*d)^(1/3))/sqrt(3))/(c^2*d^(1/3)*sqrt(3))],
[(a+b*x^3)^(4/3)/(x^7*(c+d*x^3)),x,14,d*(b*c-a*d)*(a+b*x^3)^(1/3)/c^3+1/9*(2*b^2*c^2-12*a*b*c*d+9*a^2*d^2)*(a+b*x^3)^(1/3)/(a*c^3)-1/18*(b*c-6*a*d)*(a+b*x^3)^(4/3)/(a*c^2*x^3)-1/6*(a+b*x^3)^(7/3)/(a*c*x^6)-1/18*(2*b^2*c^2-12*a*b*c*d+9*a^2*d^2)*log(x)/(a^(2/3)*c^3)+1/6*d^(2/3)*(b*c-a*d)^(4/3)*log(c+d*x^3)/c^3+1/18*(2*b^2*c^2-12*a*b*c*d+9*a^2*d^2)*log(a^(1/3)-(a+b*x^3)^(1/3))/(a^(2/3)*c^3)-1/2*d^(2/3)*(b*c-a*d)^(4/3)*log((b*c-a*d)^(1/3)+d^(1/3)*(a+b*x^3)^(1/3))/c^3-1/9*(2*b^2*c^2-12*a*b*c*d+9*a^2*d^2)*arctan((a^(1/3)+2*(a+b*x^3)^(1/3))/(a^(1/3)*sqrt(3)))/(a^(2/3)*c^3*sqrt(3))+d^(2/3)*(b*c-a*d)^(4/3)*arctan((1-2*d^(1/3)*(a+b*x^3)^(1/3)/(b*c-a*d)^(1/3))/sqrt(3))/(c^3*sqrt(3))],
[x^4*(a+b*x^3)^(4/3)/(c+d*x^3),x,6,-1/18*(6*b*c-7*a*d)*x^2*(a+b*x^3)^(1/3)/d^2+1/6*b*x^5*(a+b*x^3)^(1/3)/d-1/6*c^(2/3)*(b*c-a*d)^(4/3)*log(c+d*x^3)/d^3-1/18*(9*b^2*c^2-12*a*b*c*d+2*a^2*d^2)*log(b^(1/3)*x-(a+b*x^3)^(1/3))/(b^(2/3)*d^3)+1/2*c^(2/3)*(b*c-a*d)^(4/3)*log((b*c-a*d)^(1/3)*x/c^(1/3)-(a+b*x^3)^(1/3))/d^3-1/9*(9*b^2*c^2-12*a*b*c*d+2*a^2*d^2)*arctan((1+2*b^(1/3)*x/(a+b*x^3)^(1/3))/sqrt(3))/(b^(2/3)*d^3*sqrt(3))+c^(2/3)*(b*c-a*d)^(4/3)*arctan((1+2*(b*c-a*d)^(1/3)*x/(c^(1/3)*(a+b*x^3)^(1/3)))/sqrt(3))/(d^3*sqrt(3))],
[x*(a+b*x^3)^(4/3)/(c+d*x^3),x,5,1/3*b*x^2*(a+b*x^3)^(1/3)/d+1/6*(b*c-a*d)^(4/3)*log(c+d*x^3)/(c^(1/3)*d^2)+1/6*b^(1/3)*(3*b*c-4*a*d)*log(b^(1/3)*x-(a+b*x^3)^(1/3))/d^2-1/2*(b*c-a*d)^(4/3)*log((b*c-a*d)^(1/3)*x/c^(1/3)-(a+b*x^3)^(1/3))/(c^(1/3)*d^2)+1/3*b^(1/3)*(3*b*c-4*a*d)*arctan((1+2*b^(1/3)*x/(a+b*x^3)^(1/3))/sqrt(3))/(d^2*sqrt(3))-(b*c-a*d)^(4/3)*arctan((1+2*(b*c-a*d)^(1/3)*x/(c^(1/3)*(a+b*x^3)^(1/3)))/sqrt(3))/(c^(1/3)*d^2*sqrt(3))],
[(a+b*x^3)^(4/3)/(x^2*(c+d*x^3)),x,5,-a*(a+b*x^3)^(1/3)/(c*x)-1/6*(b*c-a*d)^(4/3)*log(c+d*x^3)/(c^(4/3)*d)-1/2*b^(4/3)*log(b^(1/3)*x-(a+b*x^3)^(1/3))/d+1/2*(b*c-a*d)^(4/3)*log((b*c-a*d)^(1/3)*x/c^(1/3)-(a+b*x^3)^(1/3))/(c^(4/3)*d)-b^(4/3)*arctan((1+2*b^(1/3)*x/(a+b*x^3)^(1/3))/sqrt(3))/(d*sqrt(3))+(b*c-a*d)^(4/3)*arctan((1+2*(b*c-a*d)^(1/3)*x/(c^(1/3)*(a+b*x^3)^(1/3)))/sqrt(3))/(c^(4/3)*d*sqrt(3))],
[(a+b*x^3)^(4/3)/(x^5*(c+d*x^3)),x,4,-1/4*a*(a+b*x^3)^(1/3)/(c*x^4)-1/4*(5*b*c-4*a*d)*(a+b*x^3)^(1/3)/(c^2*x)+1/6*(b*c-a*d)^(4/3)*log(c+d*x^3)/c^(7/3)-1/2*(b*c-a*d)^(4/3)*log((b*c-a*d)^(1/3)*x/c^(1/3)-(a+b*x^3)^(1/3))/c^(7/3)-(b*c-a*d)^(4/3)*arctan((1+2*(b*c-a*d)^(1/3)*x/(c^(1/3)*(a+b*x^3)^(1/3)))/sqrt(3))/(c^(7/3)*sqrt(3))],
[(a+b*x^3)^(4/3)/(x^8*(c+d*x^3)),x,5,-1/7*a*(a+b*x^3)^(1/3)/(c*x^7)-1/28*(8*b*c-7*a*d)*(a+b*x^3)^(1/3)/(c^2*x^4)-1/28*(4*b^2*c^2-35*a*b*c*d+28*a^2*d^2)*(a+b*x^3)^(1/3)/(a*c^3*x)-1/6*d*(b*c-a*d)^(4/3)*log(c+d*x^3)/c^(10/3)+1/2*d*(b*c-a*d)^(4/3)*log((b*c-a*d)^(1/3)*x/c^(1/3)-(a+b*x^3)^(1/3))/c^(10/3)+d*(b*c-a*d)^(4/3)*arctan((1+2*(b*c-a*d)^(1/3)*x/(c^(1/3)*(a+b*x^3)^(1/3)))/sqrt(3))/(c^(10/3)*sqrt(3))],
[(a+b*x^3)^(4/3)/(x^11*(c+d*x^3)),x,6,-1/10*a*(a+b*x^3)^(1/3)/(c*x^10)-1/70*(11*b*c-10*a*d)*(a+b*x^3)^(1/3)/(c^2*x^7)-1/140*(2*b^2*c^2-40*a*b*c*d+35*a^2*d^2)*(a+b*x^3)^(1/3)/(a*c^3*x^4)+1/140*(6*b^3*c^3+20*a*b^2*c^2*d-175*a^2*b*c*d^2+140*a^3*d^3)*(a+b*x^3)^(1/3)/(a^2*c^4*x)+1/6*d^2*(b*c-a*d)^(4/3)*log(c+d*x^3)/c^(13/3)-1/2*d^2*(b*c-a*d)^(4/3)*log((b*c-a*d)^(1/3)*x/c^(1/3)-(a+b*x^3)^(1/3))/c^(13/3)-d^2*(b*c-a*d)^(4/3)*arctan((1+2*(b*c-a*d)^(1/3)*x/(c^(1/3)*(a+b*x^3)^(1/3)))/sqrt(3))/(c^(13/3)*sqrt(3))],
[(a+b*x^3)^(4/3)/(x^14*(c+d*x^3)),x,7,-1/13*a*(a+b*x^3)^(1/3)/(c*x^13)-1/130*(14*b*c-13*a*d)*(a+b*x^3)^(1/3)/(c^2*x^10)-1/910*(4*b^2*c^2-143*a*b*c*d+130*a^2*d^2)*(a+b*x^3)^(1/3)/(a*c^3*x^7)+1/1820*(12*b^3*c^3+26*a*b^2*c^2*d-520*a^2*b*c*d^2+455*a^3*d^3)*(a+b*x^3)^(1/3)/(a^2*c^4*x^4)-1/1820*(36*b^4*c^4+78*a*b^3*c^3*d+260*a^2*b^2*c^2*d^2-2275*a^3*b*c*d^3+1820*a^4*d^4)*(a+b*x^3)^(1/3)/(a^3*c^5*x)-1/6*d^3*(b*c-a*d)^(4/3)*log(c+d*x^3)/c^(16/3)+1/2*d^3*(b*c-a*d)^(4/3)*log((b*c-a*d)^(1/3)*x/c^(1/3)-(a+b*x^3)^(1/3))/c^(16/3)+d^3*(b*c-a*d)^(4/3)*arctan((1+2*(b*c-a*d)^(1/3)*x/(c^(1/3)*(a+b*x^3)^(1/3)))/sqrt(3))/(c^(16/3)*sqrt(3))],
[x^6*(a+b*x^3)^(4/3)/(c+d*x^3),x,2,1/7*a*x^7*(a+b*x^3)^(1/3)*AppellF1(7/3,-4/3,1,10/3,-b*x^3/a,-d*x^3/c)/(c*(1+b*x^3/a)^(1/3))],
[x^3*(a+b*x^3)^(4/3)/(c+d*x^3),x,2,1/4*a*x^4*(a+b*x^3)^(1/3)*AppellF1(4/3,-4/3,1,7/3,-b*x^3/a,-d*x^3/c)/(c*(1+b*x^3/a)^(1/3))],
[(a+b*x^3)^(4/3)/(c+d*x^3),x,2,a*x*(a+b*x^3)^(1/3)*AppellF1(1/3,-4/3,1,4/3,-b*x^3/a,-d*x^3/c)/(c*(1+b*x^3/a)^(1/3))],
[(a+b*x^3)^(4/3)/(x^3*(c+d*x^3)),x,2,-1/2*a*(a+b*x^3)^(1/3)*AppellF1(-2/3,-4/3,1,1/3,-b*x^3/a,-d*x^3/c)/(c*x^2*(1+b*x^3/a)^(1/3))],
[(a+b*x^3)^(4/3)/(x^6*(c+d*x^3)),x,2,-1/5*a*(a+b*x^3)^(1/3)*AppellF1(-5/3,-4/3,1,-2/3,-b*x^3/a,-d*x^3/c)/(c*x^5*(1+b*x^3/a)^(1/3))],

# p<0
[x^14/((a+b*x^3)^(1/3)*(c+d*x^3)),x,7,-1/2*(b*c+a*d)*(b^2*c^2+a^2*d^2)*(a+b*x^3)^(2/3)/(b^4*d^4)+1/5*(b^2*c^2+2*a*b*c*d+3*a^2*d^2)*(a+b*x^3)^(5/3)/(b^4*d^3)-1/8*(b*c+3*a*d)*(a+b*x^3)^(8/3)/(b^4*d^2)+1/11*(a+b*x^3)^(11/3)/(b^4*d)+1/6*c^4*log(c+d*x^3)/(d^(14/3)*(b*c-a*d)^(1/3))-1/2*c^4*log((b*c-a*d)^(1/3)+d^(1/3)*(a+b*x^3)^(1/3))/(d^(14/3)*(b*c-a*d)^(1/3))-c^4*arctan((1-2*d^(1/3)*(a+b*x^3)^(1/3)/(b*c-a*d)^(1/3))/sqrt(3))/(d^(14/3)*(b*c-a*d)^(1/3)*sqrt(3))],
[x^11/((a+b*x^3)^(1/3)*(c+d*x^3)),x,7,1/2*(b^2*c^2+a*b*c*d+a^2*d^2)*(a+b*x^3)^(2/3)/(b^3*d^3)-1/5*(b*c+2*a*d)*(a+b*x^3)^(5/3)/(b^3*d^2)+1/8*(a+b*x^3)^(8/3)/(b^3*d)-1/6*c^3*log(c+d*x^3)/(d^(11/3)*(b*c-a*d)^(1/3))+1/2*c^3*log((b*c-a*d)^(1/3)+d^(1/3)*(a+b*x^3)^(1/3))/(d^(11/3)*(b*c-a*d)^(1/3))+c^3*arctan((1-2*d^(1/3)*(a+b*x^3)^(1/3)/(b*c-a*d)^(1/3))/sqrt(3))/(d^(11/3)*(b*c-a*d)^(1/3)*sqrt(3))],
[x^8/((a+b*x^3)^(1/3)*(c+d*x^3)),x,7,-1/2*(b*c+a*d)*(a+b*x^3)^(2/3)/(b^2*d^2)+1/5*(a+b*x^3)^(5/3)/(b^2*d)+1/6*c^2*log(c+d*x^3)/(d^(8/3)*(b*c-a*d)^(1/3))-1/2*c^2*log((b*c-a*d)^(1/3)+d^(1/3)*(a+b*x^3)^(1/3))/(d^(8/3)*(b*c-a*d)^(1/3))-c^2*arctan((1-2*d^(1/3)*(a+b*x^3)^(1/3)/(b*c-a*d)^(1/3))/sqrt(3))/(d^(8/3)*(b*c-a*d)^(1/3)*sqrt(3))],
[x^5/((a+b*x^3)^(1/3)*(c+d*x^3)),x,6,1/2*(a+b*x^3)^(2/3)/(b*d)-1/6*c*log(c+d*x^3)/(d^(5/3)*(b*c-a*d)^(1/3))+1/2*c*log((b*c-a*d)^(1/3)+d^(1/3)*(a+b*x^3)^(1/3))/(d^(5/3)*(b*c-a*d)^(1/3))+c*arctan((1-2*d^(1/3)*(a+b*x^3)^(1/3)/(b*c-a*d)^(1/3))/sqrt(3))/(d^(5/3)*(b*c-a*d)^(1/3)*sqrt(3))],
[x^2/((a+b*x^3)^(1/3)*(c+d*x^3)),x,5,1/6*log(c+d*x^3)/(d^(2/3)*(b*c-a*d)^(1/3))-1/2*log((b*c-a*d)^(1/3)+d^(1/3)*(a+b*x^3)^(1/3))/(d^(2/3)*(b*c-a*d)^(1/3))-arctan((1-2*d^(1/3)*(a+b*x^3)^(1/3)/(b*c-a*d)^(1/3))/sqrt(3))/(d^(2/3)*(b*c-a*d)^(1/3)*sqrt(3))],
[1/(x*(a+b*x^3)^(1/3)*(c+d*x^3)),x,10,-1/2*log(x)/(a^(1/3)*c)-1/6*d^(1/3)*log(c+d*x^3)/(c*(b*c-a*d)^(1/3))+1/2*log(a^(1/3)-(a+b*x^3)^(1/3))/(a^(1/3)*c)+1/2*d^(1/3)*log((b*c-a*d)^(1/3)+d^(1/3)*(a+b*x^3)^(1/3))/(c*(b*c-a*d)^(1/3))+arctan((a^(1/3)+2*(a+b*x^3)^(1/3))/(a^(1/3)*sqrt(3)))/(a^(1/3)*c*sqrt(3))+d^(1/3)*arctan((1-2*d^(1/3)*(a+b*x^3)^(1/3)/(b*c-a*d)^(1/3))/sqrt(3))/(c*(b*c-a*d)^(1/3)*sqrt(3))],
[1/(x^4*(a+b*x^3)^(1/3)*(c+d*x^3)),x,11,-1/3*(a+b*x^3)^(2/3)/(a*c*x^3)+1/6*(b*c+3*a*d)*log(x)/(a^(4/3)*c^2)+1/6*d^(4/3)*log(c+d*x^3)/(c^2*(b*c-a*d)^(1/3))-1/6*(b*c+3*a*d)*log(a^(1/3)-(a+b*x^3)^(1/3))/(a^(4/3)*c^2)-1/2*d^(4/3)*log((b*c-a*d)^(1/3)+d^(1/3)*(a+b*x^3)^(1/3))/(c^2*(b*c-a*d)^(1/3))-1/3*(b*c+3*a*d)*arctan((a^(1/3)+2*(a+b*x^3)^(1/3))/(a^(1/3)*sqrt(3)))/(a^(4/3)*c^2*sqrt(3))-d^(4/3)*arctan((1-2*d^(1/3)*(a+b*x^3)^(1/3)/(b*c-a*d)^(1/3))/sqrt(3))/(c^2*(b*c-a*d)^(1/3)*sqrt(3))],
[x^6/((a+b*x^3)^(1/3)*(c+d*x^3)),x,4,1/3*x*(a+b*x^3)^(2/3)/(b*d)+1/6*c^(4/3)*log(c+d*x^3)/(d^2*(b*c-a*d)^(1/3))-1/2*c^(4/3)*log((b*c-a*d)^(1/3)*x/c^(1/3)-(a+b*x^3)^(1/3))/(d^2*(b*c-a*d)^(1/3))+1/6*(3*b*c+a*d)*log(-b^(1/3)*x+(a+b*x^3)^(1/3))/(b^(4/3)*d^2)-1/3*(3*b*c+a*d)*arctan((1+2*b^(1/3)*x/(a+b*x^3)^(1/3))/sqrt(3))/(b^(4/3)*d^2*sqrt(3))+c^(4/3)*arctan((1+2*(b*c-a*d)^(1/3)*x/(c^(1/3)*(a+b*x^3)^(1/3)))/sqrt(3))/(d^2*(b*c-a*d)^(1/3)*sqrt(3))],
[x^3/((a+b*x^3)^(1/3)*(c+d*x^3)),x,3,-1/6*c^(1/3)*log(c+d*x^3)/(d*(b*c-a*d)^(1/3))+1/2*c^(1/3)*log((b*c-a*d)^(1/3)*x/c^(1/3)-(a+b*x^3)^(1/3))/(d*(b*c-a*d)^(1/3))-1/2*log(-b^(1/3)*x+(a+b*x^3)^(1/3))/(b^(1/3)*d)+arctan((1+2*b^(1/3)*x/(a+b*x^3)^(1/3))/sqrt(3))/(b^(1/3)*d*sqrt(3))-c^(1/3)*arctan((1+2*(b*c-a*d)^(1/3)*x/(c^(1/3)*(a+b*x^3)^(1/3)))/sqrt(3))/(d*(b*c-a*d)^(1/3)*sqrt(3))],
[1/((a+b*x^3)^(1/3)*(c+d*x^3)),x,1,1/6*log(c+d*x^3)/(c^(2/3)*(b*c-a*d)^(1/3))-1/2*log((b*c-a*d)^(1/3)*x/c^(1/3)-(a+b*x^3)^(1/3))/(c^(2/3)*(b*c-a*d)^(1/3))+arctan((1+2*(b*c-a*d)^(1/3)*x/(c^(1/3)*(a+b*x^3)^(1/3)))/sqrt(3))/(c^(2/3)*(b*c-a*d)^(1/3)*sqrt(3))],
[1/(x^3*(a+b*x^3)^(1/3)*(c+d*x^3)),x,3,-1/2*(a+b*x^3)^(2/3)/(a*c*x^2)-1/6*d*log(c+d*x^3)/(c^(5/3)*(b*c-a*d)^(1/3))+1/2*d*log((b*c-a*d)^(1/3)*x/c^(1/3)-(a+b*x^3)^(1/3))/(c^(5/3)*(b*c-a*d)^(1/3))-d*arctan((1+2*(b*c-a*d)^(1/3)*x/(c^(1/3)*(a+b*x^3)^(1/3)))/sqrt(3))/(c^(5/3)*(b*c-a*d)^(1/3)*sqrt(3))],
[1/(x^6*(a+b*x^3)^(1/3)*(c+d*x^3)),x,4,-1/5*(a+b*x^3)^(2/3)/(a*c*x^5)+1/10*(3*b*c+5*a*d)*(a+b*x^3)^(2/3)/(a^2*c^2*x^2)+1/6*d^2*log(c+d*x^3)/(c^(8/3)*(b*c-a*d)^(1/3))-1/2*d^2*log((b*c-a*d)^(1/3)*x/c^(1/3)-(a+b*x^3)^(1/3))/(c^(8/3)*(b*c-a*d)^(1/3))+d^2*arctan((1+2*(b*c-a*d)^(1/3)*x/(c^(1/3)*(a+b*x^3)^(1/3)))/sqrt(3))/(c^(8/3)*(b*c-a*d)^(1/3)*sqrt(3))],
[1/(x^9*(a+b*x^3)^(1/3)*(c+d*x^3)),x,5,-1/8*(a+b*x^3)^(2/3)/(a*c*x^8)+1/20*(3*b*c+4*a*d)*(a+b*x^3)^(2/3)/(a^2*c^2*x^5)-1/40*(9*b^2*c^2+12*a*b*c*d+20*a^2*d^2)*(a+b*x^3)^(2/3)/(a^3*c^3*x^2)-1/6*d^3*log(c+d*x^3)/(c^(11/3)*(b*c-a*d)^(1/3))+1/2*d^3*log((b*c-a*d)^(1/3)*x/c^(1/3)-(a+b*x^3)^(1/3))/(c^(11/3)*(b*c-a*d)^(1/3))-d^3*arctan((1+2*(b*c-a*d)^(1/3)*x/(c^(1/3)*(a+b*x^3)^(1/3)))/sqrt(3))/(c^(11/3)*(b*c-a*d)^(1/3)*sqrt(3))],
[x^7/((a+b*x^3)^(1/3)*(c+d*x^3)),x,2,1/8*x^8*(1+b*x^3/a)^(1/3)*AppellF1(8/3,1/3,1,11/3,-b*x^3/a,-d*x^3/c)/(c*(a+b*x^3)^(1/3))],
[x^4/((a+b*x^3)^(1/3)*(c+d*x^3)),x,2,1/5*x^5*(1+b*x^3/a)^(1/3)*AppellF1(5/3,1/3,1,8/3,-b*x^3/a,-d*x^3/c)/(c*(a+b*x^3)^(1/3))],
[x/((a+b*x^3)^(1/3)*(c+d*x^3)),x,2,1/2*x^2*(1+b*x^3/a)^(1/3)*AppellF1(2/3,1/3,1,5/3,-b*x^3/a,-d*x^3/c)/(c*(a+b*x^3)^(1/3))],
[1/(x^2*(a+b*x^3)^(1/3)*(c+d*x^3)),x,2,-(1+b*x^3/a)^(1/3)*AppellF1(-1/3,1/3,1,2/3,-b*x^3/a,-d*x^3/c)/(c*x*(a+b*x^3)^(1/3))],
[1/(x^5*(a+b*x^3)^(1/3)*(c+d*x^3)),x,2,-1/4*(1+b*x^3/a)^(1/3)*AppellF1(-4/3,1/3,1,-1/3,-b*x^3/a,-d*x^3/c)/(c*x^4*(a+b*x^3)^(1/3))],
[x^11/((a+b*x^3)^(2/3)*(c+d*x^3)),x,7,(b^2*c^2+a*b*c*d+a^2*d^2)*(a+b*x^3)^(1/3)/(b^3*d^3)-1/4*(b*c+2*a*d)*(a+b*x^3)^(4/3)/(b^3*d^2)+1/7*(a+b*x^3)^(7/3)/(b^3*d)+1/6*c^3*log(c+d*x^3)/(d^(10/3)*(b*c-a*d)^(2/3))-1/2*c^3*log((b*c-a*d)^(1/3)+d^(1/3)*(a+b*x^3)^(1/3))/(d^(10/3)*(b*c-a*d)^(2/3))+c^3*arctan((1-2*d^(1/3)*(a+b*x^3)^(1/3)/(b*c-a*d)^(1/3))/sqrt(3))/(d^(10/3)*(b*c-a*d)^(2/3)*sqrt(3))],
[x^8/((a+b*x^3)^(2/3)*(c+d*x^3)),x,7,-(b*c+a*d)*(a+b*x^3)^(1/3)/(b^2*d^2)+1/4*(a+b*x^3)^(4/3)/(b^2*d)-1/6*c^2*log(c+d*x^3)/(d^(7/3)*(b*c-a*d)^(2/3))+1/2*c^2*log((b*c-a*d)^(1/3)+d^(1/3)*(a+b*x^3)^(1/3))/(d^(7/3)*(b*c-a*d)^(2/3))-c^2*arctan((1-2*d^(1/3)*(a+b*x^3)^(1/3)/(b*c-a*d)^(1/3))/sqrt(3))/(d^(7/3)*(b*c-a*d)^(2/3)*sqrt(3))],
[x^5/((a+b*x^3)^(2/3)*(c+d*x^3)),x,6,(a+b*x^3)^(1/3)/(b*d)+1/6*c*log(c+d*x^3)/(d^(4/3)*(b*c-a*d)^(2/3))-1/2*c*log((b*c-a*d)^(1/3)+d^(1/3)*(a+b*x^3)^(1/3))/(d^(4/3)*(b*c-a*d)^(2/3))+c*arctan((1-2*d^(1/3)*(a+b*x^3)^(1/3)/(b*c-a*d)^(1/3))/sqrt(3))/(d^(4/3)*(b*c-a*d)^(2/3)*sqrt(3))],
[x^2/((a+b*x^3)^(2/3)*(c+d*x^3)),x,5,-1/6*log(c+d*x^3)/(d^(1/3)*(b*c-a*d)^(2/3))+1/2*log((b*c-a*d)^(1/3)+d^(1/3)*(a+b*x^3)^(1/3))/(d^(1/3)*(b*c-a*d)^(2/3))-arctan((1-2*d^(1/3)*(a+b*x^3)^(1/3)/(b*c-a*d)^(1/3))/sqrt(3))/(d^(1/3)*(b*c-a*d)^(2/3)*sqrt(3))],
[1/(x*(a+b*x^3)^(2/3)*(c+d*x^3)),x,10,-1/2*log(x)/(a^(2/3)*c)+1/6*d^(2/3)*log(c+d*x^3)/(c*(b*c-a*d)^(2/3))+1/2*log(a^(1/3)-(a+b*x^3)^(1/3))/(a^(2/3)*c)-1/2*d^(2/3)*log((b*c-a*d)^(1/3)+d^(1/3)*(a+b*x^3)^(1/3))/(c*(b*c-a*d)^(2/3))-arctan((a^(1/3)+2*(a+b*x^3)^(1/3))/(a^(1/3)*sqrt(3)))/(a^(2/3)*c*sqrt(3))+d^(2/3)*arctan((1-2*d^(1/3)*(a+b*x^3)^(1/3)/(b*c-a*d)^(1/3))/sqrt(3))/(c*(b*c-a*d)^(2/3)*sqrt(3))],
[1/(x^4*(a+b*x^3)^(2/3)*(c+d*x^3)),x,11,-1/3*(a+b*x^3)^(1/3)/(a*c*x^3)+1/6*(2*b*c+3*a*d)*log(x)/(a^(5/3)*c^2)-1/6*d^(5/3)*log(c+d*x^3)/(c^2*(b*c-a*d)^(2/3))-1/6*(2*b*c+3*a*d)*log(a^(1/3)-(a+b*x^3)^(1/3))/(a^(5/3)*c^2)+1/2*d^(5/3)*log((b*c-a*d)^(1/3)+d^(1/3)*(a+b*x^3)^(1/3))/(c^2*(b*c-a*d)^(2/3))+1/3*(2*b*c+3*a*d)*arctan((a^(1/3)+2*(a+b*x^3)^(1/3))/(a^(1/3)*sqrt(3)))/(a^(5/3)*c^2*sqrt(3))-d^(5/3)*arctan((1-2*d^(1/3)*(a+b*x^3)^(1/3)/(b*c-a*d)^(1/3))/sqrt(3))/(c^2*(b*c-a*d)^(2/3)*sqrt(3))],
[x^7/((a+b*x^3)^(2/3)*(c+d*x^3)),x,5,1/3*x^2*(a+b*x^3)^(1/3)/(b*d)+1/6*c^(5/3)*log(c+d*x^3)/(d^2*(b*c-a*d)^(2/3))+1/6*(3*b*c+2*a*d)*log(b^(1/3)*x-(a+b*x^3)^(1/3))/(b^(5/3)*d^2)-1/2*c^(5/3)*log((b*c-a*d)^(1/3)*x/c^(1/3)-(a+b*x^3)^(1/3))/(d^2*(b*c-a*d)^(2/3))+1/3*(3*b*c+2*a*d)*arctan((1+2*b^(1/3)*x/(a+b*x^3)^(1/3))/sqrt(3))/(b^(5/3)*d^2*sqrt(3))-c^(5/3)*arctan((1+2*(b*c-a*d)^(1/3)*x/(c^(1/3)*(a+b*x^3)^(1/3)))/sqrt(3))/(d^2*(b*c-a*d)^(2/3)*sqrt(3))],
[x^4/((a+b*x^3)^(2/3)*(c+d*x^3)),x,3,-1/6*c^(2/3)*log(c+d*x^3)/(d*(b*c-a*d)^(2/3))-1/2*log(b^(1/3)*x-(a+b*x^3)^(1/3))/(b^(2/3)*d)+1/2*c^(2/3)*log((b*c-a*d)^(1/3)*x/c^(1/3)-(a+b*x^3)^(1/3))/(d*(b*c-a*d)^(2/3))-arctan((1+2*b^(1/3)*x/(a+b*x^3)^(1/3))/sqrt(3))/(b^(2/3)*d*sqrt(3))+c^(2/3)*arctan((1+2*(b*c-a*d)^(1/3)*x/(c^(1/3)*(a+b*x^3)^(1/3)))/sqrt(3))/(d*(b*c-a*d)^(2/3)*sqrt(3))],
[x/((a+b*x^3)^(2/3)*(c+d*x^3)),x,1,1/6*log(c+d*x^3)/(c^(1/3)*(b*c-a*d)^(2/3))-1/2*log((b*c-a*d)^(1/3)*x/c^(1/3)-(a+b*x^3)^(1/3))/(c^(1/3)*(b*c-a*d)^(2/3))-arctan((1+2*(b*c-a*d)^(1/3)*x/(c^(1/3)*(a+b*x^3)^(1/3)))/sqrt(3))/(c^(1/3)*(b*c-a*d)^(2/3)*sqrt(3))],
[1/(x^2*(a+b*x^3)^(2/3)*(c+d*x^3)),x,3,-(a+b*x^3)^(1/3)/(a*c*x)-1/6*d*log(c+d*x^3)/(c^(4/3)*(b*c-a*d)^(2/3))+1/2*d*log((b*c-a*d)^(1/3)*x/c^(1/3)-(a+b*x^3)^(1/3))/(c^(4/3)*(b*c-a*d)^(2/3))+d*arctan((1+2*(b*c-a*d)^(1/3)*x/(c^(1/3)*(a+b*x^3)^(1/3)))/sqrt(3))/(c^(4/3)*(b*c-a*d)^(2/3)*sqrt(3))],
[1/(x^5*(a+b*x^3)^(2/3)*(c+d*x^3)),x,4,-1/4*(a+b*x^3)^(1/3)/(a*c*x^4)+1/4*(3*b*c+4*a*d)*(a+b*x^3)^(1/3)/(a^2*c^2*x)+1/6*d^2*log(c+d*x^3)/(c^(7/3)*(b*c-a*d)^(2/3))-1/2*d^2*log((b*c-a*d)^(1/3)*x/c^(1/3)-(a+b*x^3)^(1/3))/(c^(7/3)*(b*c-a*d)^(2/3))-d^2*arctan((1+2*(b*c-a*d)^(1/3)*x/(c^(1/3)*(a+b*x^3)^(1/3)))/sqrt(3))/(c^(7/3)*(b*c-a*d)^(2/3)*sqrt(3))],
[x^6/((a+b*x^3)^(2/3)*(c+d*x^3)),x,2,1/7*x^7*(1+b*x^3/a)^(2/3)*AppellF1(7/3,2/3,1,10/3,-b*x^3/a,-d*x^3/c)/(c*(a+b*x^3)^(2/3))],
[x^3/((a+b*x^3)^(2/3)*(c+d*x^3)),x,2,1/4*x^4*(1+b*x^3/a)^(2/3)*AppellF1(4/3,2/3,1,7/3,-b*x^3/a,-d*x^3/c)/(c*(a+b*x^3)^(2/3))],
[1/((a+b*x^3)^(2/3)*(c+d*x^3)),x,2,x*(1+b*x^3/a)^(2/3)*AppellF1(1/3,2/3,1,4/3,-b*x^3/a,-d*x^3/c)/(c*(a+b*x^3)^(2/3))],
[1/(x^3*(a+b*x^3)^(2/3)*(c+d*x^3)),x,2,-1/2*(1+b*x^3/a)^(2/3)*AppellF1(-2/3,2/3,1,1/3,-b*x^3/a,-d*x^3/c)/(c*x^2*(a+b*x^3)^(2/3))],
[x^14/((a+b*x^3)^(4/3)*(c+d*x^3)),x,11,-a^4/(b^4*(b*c-a*d)*(a+b*x^3)^(1/3))+1/2*a^2*(a+b*x^3)^(2/3)/(b^4*d)+1/2*a*(b*c+a*d)*(a+b*x^3)^(2/3)/(b^4*d^2)+1/2*(b^2*c^2+a*b*c*d+a^2*d^2)*(a+b*x^3)^(2/3)/(b^4*d^3)-2/5*a*(a+b*x^3)^(5/3)/(b^4*d)-1/5*(b*c+a*d)*(a+b*x^3)^(5/3)/(b^4*d^2)+1/8*(a+b*x^3)^(8/3)/(b^4*d)-1/6*c^4*log(c+d*x^3)/(d^(11/3)*(b*c-a*d)^(4/3))+1/2*c^4*log((b*c-a*d)^(1/3)+d^(1/3)*(a+b*x^3)^(1/3))/(d^(11/3)*(b*c-a*d)^(4/3))+c^4*arctan((1-2*d^(1/3)*(a+b*x^3)^(1/3)/(b*c-a*d)^(1/3))/sqrt(3))/(d^(11/3)*(b*c-a*d)^(4/3)*sqrt(3))],
[x^11/((a+b*x^3)^(4/3)*(c+d*x^3)),x,9,a^3/(b^3*(b*c-a*d)*(a+b*x^3)^(1/3))-1/2*a*(a+b*x^3)^(2/3)/(b^3*d)-1/2*(b*c+a*d)*(a+b*x^3)^(2/3)/(b^3*d^2)+1/5*(a+b*x^3)^(5/3)/(b^3*d)+1/6*c^3*log(c+d*x^3)/(d^(8/3)*(b*c-a*d)^(4/3))-1/2*c^3*log((b*c-a*d)^(1/3)+d^(1/3)*(a+b*x^3)^(1/3))/(d^(8/3)*(b*c-a*d)^(4/3))-c^3*arctan((1-2*d^(1/3)*(a+b*x^3)^(1/3)/(b*c-a*d)^(1/3))/sqrt(3))/(d^(8/3)*(b*c-a*d)^(4/3)*sqrt(3))],
[x^8/((a+b*x^3)^(4/3)*(c+d*x^3)),x,7,-a^2/(b^2*(b*c-a*d)*(a+b*x^3)^(1/3))+1/2*(a+b*x^3)^(2/3)/(b^2*d)-1/6*c^2*log(c+d*x^3)/(d^(5/3)*(b*c-a*d)^(4/3))+1/2*c^2*log((b*c-a*d)^(1/3)+d^(1/3)*(a+b*x^3)^(1/3))/(d^(5/3)*(b*c-a*d)^(4/3))+c^2*arctan((1-2*d^(1/3)*(a+b*x^3)^(1/3)/(b*c-a*d)^(1/3))/sqrt(3))/(d^(5/3)*(b*c-a*d)^(4/3)*sqrt(3))],
[x^5/((a+b*x^3)^(4/3)*(c+d*x^3)),x,6,a/(b*(b*c-a*d)*(a+b*x^3)^(1/3))+1/6*c*log(c+d*x^3)/(d^(2/3)*(b*c-a*d)^(4/3))-1/2*c*log((b*c-a*d)^(1/3)+d^(1/3)*(a+b*x^3)^(1/3))/(d^(2/3)*(b*c-a*d)^(4/3))-c*arctan((1-2*d^(1/3)*(a+b*x^3)^(1/3)/(b*c-a*d)^(1/3))/sqrt(3))/(d^(2/3)*(b*c-a*d)^(4/3)*sqrt(3))],
[x^2/((a+b*x^3)^(4/3)*(c+d*x^3)),x,6,(-1)/((b*c-a*d)*(a+b*x^3)^(1/3))-1/6*d^(1/3)*log(c+d*x^3)/(b*c-a*d)^(4/3)+1/2*d^(1/3)*log((b*c-a*d)^(1/3)+d^(1/3)*(a+b*x^3)^(1/3))/(b*c-a*d)^(4/3)+d^(1/3)*arctan((1-2*d^(1/3)*(a+b*x^3)^(1/3)/(b*c-a*d)^(1/3))/sqrt(3))/((b*c-a*d)^(4/3)*sqrt(3))],
[1/(x*(a+b*x^3)^(4/3)*(c+d*x^3)),x,11,b/(a*(b*c-a*d)*(a+b*x^3)^(1/3))-1/2*log(x)/(a^(4/3)*c)+1/6*d^(4/3)*log(c+d*x^3)/(c*(b*c-a*d)^(4/3))+1/2*log(a^(1/3)-(a+b*x^3)^(1/3))/(a^(4/3)*c)-1/2*d^(4/3)*log((b*c-a*d)^(1/3)+d^(1/3)*(a+b*x^3)^(1/3))/(c*(b*c-a*d)^(4/3))+arctan((a^(1/3)+2*(a+b*x^3)^(1/3))/(a^(1/3)*sqrt(3)))/(a^(4/3)*c*sqrt(3))-d^(4/3)*arctan((1-2*d^(1/3)*(a+b*x^3)^(1/3)/(b*c-a*d)^(1/3))/sqrt(3))/(c*(b*c-a*d)^(4/3)*sqrt(3))],
[1/(x^4*(a+b*x^3)^(4/3)*(c+d*x^3)),x,13,-d^2/(c^2*(b*c-a*d)*(a+b*x^3)^(1/3))+1/3*(-4*b*c-3*a*d)/(a^2*c^2*(a+b*x^3)^(1/3))+(-1/3)/(a*c*x^3*(a+b*x^3)^(1/3))+1/6*(4*b*c+3*a*d)*log(x)/(a^(7/3)*c^2)-1/6*d^(7/3)*log(c+d*x^3)/(c^2*(b*c-a*d)^(4/3))-1/6*(4*b*c+3*a*d)*log(a^(1/3)-(a+b*x^3)^(1/3))/(a^(7/3)*c^2)+1/2*d^(7/3)*log((b*c-a*d)^(1/3)+d^(1/3)*(a+b*x^3)^(1/3))/(c^2*(b*c-a*d)^(4/3))-1/3*(4*b*c+3*a*d)*arctan((a^(1/3)+2*(a+b*x^3)^(1/3))/(a^(1/3)*sqrt(3)))/(a^(7/3)*c^2*sqrt(3))+d^(7/3)*arctan((1-2*d^(1/3)*(a+b*x^3)^(1/3)/(b*c-a*d)^(1/3))/sqrt(3))/(c^2*(b*c-a*d)^(4/3)*sqrt(3))],
[x^9/((a+b*x^3)^(4/3)*(c+d*x^3)),x,5,a*x^4/(b*(b*c-a*d)*(a+b*x^3)^(1/3))+1/3*(b*c-4*a*d)*x*(a+b*x^3)^(2/3)/(b^2*d*(b*c-a*d))+1/6*c^(7/3)*log(c+d*x^3)/(d^2*(b*c-a*d)^(4/3))-1/2*c^(7/3)*log((b*c-a*d)^(1/3)*x/c^(1/3)-(a+b*x^3)^(1/3))/(d^2*(b*c-a*d)^(4/3))+1/6*(3*b*c+4*a*d)*log(-b^(1/3)*x+(a+b*x^3)^(1/3))/(b^(7/3)*d^2)-1/3*(3*b*c+4*a*d)*arctan((1+2*b^(1/3)*x/(a+b*x^3)^(1/3))/sqrt(3))/(b^(7/3)*d^2*sqrt(3))+c^(7/3)*arctan((1+2*(b*c-a*d)^(1/3)*x/(c^(1/3)*(a+b*x^3)^(1/3)))/sqrt(3))/(d^2*(b*c-a*d)^(4/3)*sqrt(3))],
[x^6/((a+b*x^3)^(4/3)*(c+d*x^3)),x,4,a*x/(b*(b*c-a*d)*(a+b*x^3)^(1/3))-1/6*c^(4/3)*log(c+d*x^3)/(d*(b*c-a*d)^(4/3))+1/2*c^(4/3)*log((b*c-a*d)^(1/3)*x/c^(1/3)-(a+b*x^3)^(1/3))/(d*(b*c-a*d)^(4/3))-1/2*log(-b^(1/3)*x+(a+b*x^3)^(1/3))/(b^(4/3)*d)+arctan((1+2*b^(1/3)*x/(a+b*x^3)^(1/3))/sqrt(3))/(b^(4/3)*d*sqrt(3))-c^(4/3)*arctan((1+2*(b*c-a*d)^(1/3)*x/(c^(1/3)*(a+b*x^3)^(1/3)))/sqrt(3))/(d*(b*c-a*d)^(4/3)*sqrt(3))],
[x^3/((a+b*x^3)^(4/3)*(c+d*x^3)),x,3,-x/((b*c-a*d)*(a+b*x^3)^(1/3))+1/6*c^(1/3)*log(c+d*x^3)/(b*c-a*d)^(4/3)-1/2*c^(1/3)*log((b*c-a*d)^(1/3)*x/c^(1/3)-(a+b*x^3)^(1/3))/(b*c-a*d)^(4/3)+c^(1/3)*arctan((1+2*(b*c-a*d)^(1/3)*x/(c^(1/3)*(a+b*x^3)^(1/3)))/sqrt(3))/((b*c-a*d)^(4/3)*sqrt(3))],
[1/((a+b*x^3)^(4/3)*(c+d*x^3)),x,2,b*x/(a*(b*c-a*d)*(a+b*x^3)^(1/3))-1/6*d*log(c+d*x^3)/(c^(2/3)*(b*c-a*d)^(4/3))+1/2*d*log((b*c-a*d)^(1/3)*x/c^(1/3)-(a+b*x^3)^(1/3))/(c^(2/3)*(b*c-a*d)^(4/3))-d*arctan((1+2*(b*c-a*d)^(1/3)*x/(c^(1/3)*(a+b*x^3)^(1/3)))/sqrt(3))/(c^(2/3)*(b*c-a*d)^(4/3)*sqrt(3))],
[1/(x^3*(a+b*x^3)^(4/3)*(c+d*x^3)),x,4,b/(a*(b*c-a*d)*x^2*(a+b*x^3)^(1/3))-1/2*(3*b*c-a*d)*(a+b*x^3)^(2/3)/(a^2*c*(b*c-a*d)*x^2)+1/6*d^2*log(c+d*x^3)/(c^(5/3)*(b*c-a*d)^(4/3))-1/2*d^2*log((b*c-a*d)^(1/3)*x/c^(1/3)-(a+b*x^3)^(1/3))/(c^(5/3)*(b*c-a*d)^(4/3))+d^2*arctan((1+2*(b*c-a*d)^(1/3)*x/(c^(1/3)*(a+b*x^3)^(1/3)))/sqrt(3))/(c^(5/3)*(b*c-a*d)^(4/3)*sqrt(3))],
[1/(x^6*(a+b*x^3)^(4/3)*(c+d*x^3)),x,5,b/(a*(b*c-a*d)*x^5*(a+b*x^3)^(1/3))-1/5*(6*b*c-a*d)*(a+b*x^3)^(2/3)/(a^2*c*(b*c-a*d)*x^5)+1/10*(18*b^2*c^2-3*a*b*c*d-5*a^2*d^2)*(a+b*x^3)^(2/3)/(a^3*c^2*(b*c-a*d)*x^2)-1/6*d^3*log(c+d*x^3)/(c^(8/3)*(b*c-a*d)^(4/3))+1/2*d^3*log((b*c-a*d)^(1/3)*x/c^(1/3)-(a+b*x^3)^(1/3))/(c^(8/3)*(b*c-a*d)^(4/3))-d^3*arctan((1+2*(b*c-a*d)^(1/3)*x/(c^(1/3)*(a+b*x^3)^(1/3)))/sqrt(3))/(c^(8/3)*(b*c-a*d)^(4/3)*sqrt(3))],
[1/(x^9*(a+b*x^3)^(4/3)*(c+d*x^3)),x,6,b/(a*(b*c-a*d)*x^8*(a+b*x^3)^(1/3))-1/8*(9*b*c-a*d)*(a+b*x^3)^(2/3)/(a^2*c*(b*c-a*d)*x^8)+1/20*(9*b*c-4*a*d)*(3*b*c+a*d)*(a+b*x^3)^(2/3)/(a^3*c^2*(b*c-a*d)*x^5)-1/40*(81*b^3*c^3-9*a*b^2*c^2*d-12*a^2*b*c*d^2-20*a^3*d^3)*(a+b*x^3)^(2/3)/(a^4*c^3*(b*c-a*d)*x^2)+1/6*d^4*log(c+d*x^3)/(c^(11/3)*(b*c-a*d)^(4/3))-1/2*d^4*log((b*c-a*d)^(1/3)*x/c^(1/3)-(a+b*x^3)^(1/3))/(c^(11/3)*(b*c-a*d)^(4/3))+d^4*arctan((1+2*(b*c-a*d)^(1/3)*x/(c^(1/3)*(a+b*x^3)^(1/3)))/sqrt(3))/(c^(11/3)*(b*c-a*d)^(4/3)*sqrt(3))],
[x^10/((a+b*x^3)^(4/3)*(c+d*x^3)),x,2,1/11*x^11*(1+b*x^3/a)^(1/3)*AppellF1(11/3,4/3,1,14/3,-b*x^3/a,-d*x^3/c)/(a*c*(a+b*x^3)^(1/3))],
[x^7/((a+b*x^3)^(4/3)*(c+d*x^3)),x,2,1/8*x^8*(1+b*x^3/a)^(1/3)*AppellF1(8/3,4/3,1,11/3,-b*x^3/a,-d*x^3/c)/(a*c*(a+b*x^3)^(1/3))],
[x^4/((a+b*x^3)^(4/3)*(c+d*x^3)),x,2,1/5*x^5*(1+b*x^3/a)^(1/3)*AppellF1(5/3,4/3,1,8/3,-b*x^3/a,-d*x^3/c)/(a*c*(a+b*x^3)^(1/3))],
[x/((a+b*x^3)^(4/3)*(c+d*x^3)),x,2,1/2*x^2*(1+b*x^3/a)^(1/3)*AppellF1(2/3,4/3,1,5/3,-b*x^3/a,-d*x^3/c)/(a*c*(a+b*x^3)^(1/3))],
[1/(x^2*(a+b*x^3)^(4/3)*(c+d*x^3)),x,2,-(1+b*x^3/a)^(1/3)*AppellF1(-1/3,4/3,1,2/3,-b*x^3/a,-d*x^3/c)/(a*c*x*(a+b*x^3)^(1/3))],
[1/(x^5*(a+b*x^3)^(4/3)*(c+d*x^3)),x,2,-1/4*(1+b*x^3/a)^(1/3)*AppellF1(-4/3,4/3,1,-1/3,-b*x^3/a,-d*x^3/c)/(a*c*x^4*(a+b*x^3)^(1/3))],

# Integrands of the form (e x)^m (a+b x^4)^p (c+d x^4)^q

# Integrands of the form (e x)^m (a+b x^4)^p (c+d x^4)^q

# q>0

# q<0
[x^15/((a+b*x^4)*(c+d*x^4)),x,3,-1/4*(b*c+a*d)*x^4/(b^2*d^2)+1/8*x^8/(b*d)-1/4*a^3*log(a+b*x^4)/(b^3*(b*c-a*d))+1/4*c^3*log(c+d*x^4)/(d^3*(b*c-a*d))],
[x^11/((a+b*x^4)*(c+d*x^4)),x,3,1/4*x^4/(b*d)+1/4*a^2*log(a+b*x^4)/(b^2*(b*c-a*d))-1/4*c^2*log(c+d*x^4)/(d^2*(b*c-a*d))],
[x^7/((a+b*x^4)*(c+d*x^4)),x,3,-1/4*a*log(a+b*x^4)/(b*(b*c-a*d))+1/4*c*log(c+d*x^4)/(d*(b*c-a*d))],
[x^3/((a+b*x^4)*(c+d*x^4)),x,4,1/4*log(a+b*x^4)/(b*c-a*d)-1/4*log(c+d*x^4)/(b*c-a*d)],
[1/(x*(a+b*x^4)*(c+d*x^4)),x,3,log(x)/(a*c)-1/4*b*log(a+b*x^4)/(a*(b*c-a*d))+1/4*d*log(c+d*x^4)/(c*(b*c-a*d))],
[1/(x^5*(a+b*x^4)*(c+d*x^4)),x,3,(-1/4)/(a*c*x^4)-(b*c+a*d)*log(x)/(a^2*c^2)+1/4*b^2*log(a+b*x^4)/(a^2*(b*c-a*d))-1/4*d^2*log(c+d*x^4)/(c^2*(b*c-a*d))],
[x^13/((a+b*x^4)*(c+d*x^4)),x,6,-1/2*(b*c+a*d)*x^2/(b^2*d^2)+1/6*x^6/(b*d)-1/2*a^(5/2)*arctan(x^2*sqrt(b)/sqrt(a))/(b^(5/2)*(b*c-a*d))+1/2*c^(5/2)*arctan(x^2*sqrt(d)/sqrt(c))/(d^(5/2)*(b*c-a*d))],
[x^9/((a+b*x^4)*(c+d*x^4)),x,5,1/2*x^2/(b*d)+1/2*a^(3/2)*arctan(x^2*sqrt(b)/sqrt(a))/(b^(3/2)*(b*c-a*d))-1/2*c^(3/2)*arctan(x^2*sqrt(d)/sqrt(c))/(d^(3/2)*(b*c-a*d))],
[x^5/((a+b*x^4)*(c+d*x^4)),x,4,-1/2*arctan(x^2*sqrt(b)/sqrt(a))*sqrt(a)/((b*c-a*d)*sqrt(b))+1/2*arctan(x^2*sqrt(d)/sqrt(c))*sqrt(c)/((b*c-a*d)*sqrt(d))],
[x/((a+b*x^4)*(c+d*x^4)),x,4,1/2*arctan(x^2*sqrt(b)/sqrt(a))*sqrt(b)/((b*c-a*d)*sqrt(a))-1/2*arctan(x^2*sqrt(d)/sqrt(c))*sqrt(d)/((b*c-a*d)*sqrt(c))],
[1/(x^3*(a+b*x^4)*(c+d*x^4)),x,5,(-1/2)/(a*c*x^2)-1/2*b^(3/2)*arctan(x^2*sqrt(b)/sqrt(a))/(a^(3/2)*(b*c-a*d))+1/2*d^(3/2)*arctan(x^2*sqrt(d)/sqrt(c))/(c^(3/2)*(b*c-a*d))],
[1/(x^7*(a+b*x^4)*(c+d*x^4)),x,6,(-1/6)/(a*c*x^6)+1/2*(b*c+a*d)/(a^2*c^2*x^2)+1/2*b^(5/2)*arctan(x^2*sqrt(b)/sqrt(a))/(a^(5/2)*(b*c-a*d))-1/2*d^(5/2)*arctan(x^2*sqrt(d)/sqrt(c))/(c^(5/2)*(b*c-a*d))],
[x^8/((a+b*x^4)*(c+d*x^4)),x,20,x/(b*d)-1/2*a^(5/4)*arctan(1-b^(1/4)*x*sqrt(2)/a^(1/4))/(b^(5/4)*(b*c-a*d)*sqrt(2))+1/2*a^(5/4)*arctan(1+b^(1/4)*x*sqrt(2)/a^(1/4))/(b^(5/4)*(b*c-a*d)*sqrt(2))+1/2*c^(5/4)*arctan(1-d^(1/4)*x*sqrt(2)/c^(1/4))/(d^(5/4)*(b*c-a*d)*sqrt(2))-1/2*c^(5/4)*arctan(1+d^(1/4)*x*sqrt(2)/c^(1/4))/(d^(5/4)*(b*c-a*d)*sqrt(2))-1/4*a^(5/4)*log(-a^(1/4)*b^(1/4)*x*sqrt(2)+sqrt(a)+x^2*sqrt(b))/(b^(5/4)*(b*c-a*d)*sqrt(2))+1/4*a^(5/4)*log(a^(1/4)*b^(1/4)*x*sqrt(2)+sqrt(a)+x^2*sqrt(b))/(b^(5/4)*(b*c-a*d)*sqrt(2))+1/4*c^(5/4)*log(-c^(1/4)*d^(1/4)*x*sqrt(2)+sqrt(c)+x^2*sqrt(d))/(d^(5/4)*(b*c-a*d)*sqrt(2))-1/4*c^(5/4)*log(c^(1/4)*d^(1/4)*x*sqrt(2)+sqrt(c)+x^2*sqrt(d))/(d^(5/4)*(b*c-a*d)*sqrt(2))],
[x^6/((a+b*x^4)*(c+d*x^4)),x,19,1/2*a^(3/4)*arctan(1-b^(1/4)*x*sqrt(2)/a^(1/4))/(b^(3/4)*(b*c-a*d)*sqrt(2))-1/2*a^(3/4)*arctan(1+b^(1/4)*x*sqrt(2)/a^(1/4))/(b^(3/4)*(b*c-a*d)*sqrt(2))-1/2*c^(3/4)*arctan(1-d^(1/4)*x*sqrt(2)/c^(1/4))/(d^(3/4)*(b*c-a*d)*sqrt(2))+1/2*c^(3/4)*arctan(1+d^(1/4)*x*sqrt(2)/c^(1/4))/(d^(3/4)*(b*c-a*d)*sqrt(2))-1/4*a^(3/4)*log(-a^(1/4)*b^(1/4)*x*sqrt(2)+sqrt(a)+x^2*sqrt(b))/(b^(3/4)*(b*c-a*d)*sqrt(2))+1/4*a^(3/4)*log(a^(1/4)*b^(1/4)*x*sqrt(2)+sqrt(a)+x^2*sqrt(b))/(b^(3/4)*(b*c-a*d)*sqrt(2))+1/4*c^(3/4)*log(-c^(1/4)*d^(1/4)*x*sqrt(2)+sqrt(c)+x^2*sqrt(d))/(d^(3/4)*(b*c-a*d)*sqrt(2))-1/4*c^(3/4)*log(c^(1/4)*d^(1/4)*x*sqrt(2)+sqrt(c)+x^2*sqrt(d))/(d^(3/4)*(b*c-a*d)*sqrt(2))],
[x^4/((a+b*x^4)*(c+d*x^4)),x,19,1/2*a^(1/4)*arctan(1-b^(1/4)*x*sqrt(2)/a^(1/4))/(b^(1/4)*(b*c-a*d)*sqrt(2))-1/2*a^(1/4)*arctan(1+b^(1/4)*x*sqrt(2)/a^(1/4))/(b^(1/4)*(b*c-a*d)*sqrt(2))-1/2*c^(1/4)*arctan(1-d^(1/4)*x*sqrt(2)/c^(1/4))/(d^(1/4)*(b*c-a*d)*sqrt(2))+1/2*c^(1/4)*arctan(1+d^(1/4)*x*sqrt(2)/c^(1/4))/(d^(1/4)*(b*c-a*d)*sqrt(2))+1/4*a^(1/4)*log(-a^(1/4)*b^(1/4)*x*sqrt(2)+sqrt(a)+x^2*sqrt(b))/(b^(1/4)*(b*c-a*d)*sqrt(2))-1/4*a^(1/4)*log(a^(1/4)*b^(1/4)*x*sqrt(2)+sqrt(a)+x^2*sqrt(b))/(b^(1/4)*(b*c-a*d)*sqrt(2))-1/4*c^(1/4)*log(-c^(1/4)*d^(1/4)*x*sqrt(2)+sqrt(c)+x^2*sqrt(d))/(d^(1/4)*(b*c-a*d)*sqrt(2))+1/4*c^(1/4)*log(c^(1/4)*d^(1/4)*x*sqrt(2)+sqrt(c)+x^2*sqrt(d))/(d^(1/4)*(b*c-a*d)*sqrt(2))],
[x^2/((a+b*x^4)*(c+d*x^4)),x,19,-1/2*b^(1/4)*arctan(1-b^(1/4)*x*sqrt(2)/a^(1/4))/(a^(1/4)*(b*c-a*d)*sqrt(2))+1/2*b^(1/4)*arctan(1+b^(1/4)*x*sqrt(2)/a^(1/4))/(a^(1/4)*(b*c-a*d)*sqrt(2))+1/2*d^(1/4)*arctan(1-d^(1/4)*x*sqrt(2)/c^(1/4))/(c^(1/4)*(b*c-a*d)*sqrt(2))-1/2*d^(1/4)*arctan(1+d^(1/4)*x*sqrt(2)/c^(1/4))/(c^(1/4)*(b*c-a*d)*sqrt(2))+1/4*b^(1/4)*log(-a^(1/4)*b^(1/4)*x*sqrt(2)+sqrt(a)+x^2*sqrt(b))/(a^(1/4)*(b*c-a*d)*sqrt(2))-1/4*b^(1/4)*log(a^(1/4)*b^(1/4)*x*sqrt(2)+sqrt(a)+x^2*sqrt(b))/(a^(1/4)*(b*c-a*d)*sqrt(2))-1/4*d^(1/4)*log(-c^(1/4)*d^(1/4)*x*sqrt(2)+sqrt(c)+x^2*sqrt(d))/(c^(1/4)*(b*c-a*d)*sqrt(2))+1/4*d^(1/4)*log(c^(1/4)*d^(1/4)*x*sqrt(2)+sqrt(c)+x^2*sqrt(d))/(c^(1/4)*(b*c-a*d)*sqrt(2))],
[1/((a+b*x^4)*(c+d*x^4)),x,19,-1/2*b^(3/4)*arctan(1-b^(1/4)*x*sqrt(2)/a^(1/4))/(a^(3/4)*(b*c-a*d)*sqrt(2))+1/2*b^(3/4)*arctan(1+b^(1/4)*x*sqrt(2)/a^(1/4))/(a^(3/4)*(b*c-a*d)*sqrt(2))+1/2*d^(3/4)*arctan(1-d^(1/4)*x*sqrt(2)/c^(1/4))/(c^(3/4)*(b*c-a*d)*sqrt(2))-1/2*d^(3/4)*arctan(1+d^(1/4)*x*sqrt(2)/c^(1/4))/(c^(3/4)*(b*c-a*d)*sqrt(2))-1/4*b^(3/4)*log(-a^(1/4)*b^(1/4)*x*sqrt(2)+sqrt(a)+x^2*sqrt(b))/(a^(3/4)*(b*c-a*d)*sqrt(2))+1/4*b^(3/4)*log(a^(1/4)*b^(1/4)*x*sqrt(2)+sqrt(a)+x^2*sqrt(b))/(a^(3/4)*(b*c-a*d)*sqrt(2))+1/4*d^(3/4)*log(-c^(1/4)*d^(1/4)*x*sqrt(2)+sqrt(c)+x^2*sqrt(d))/(c^(3/4)*(b*c-a*d)*sqrt(2))-1/4*d^(3/4)*log(c^(1/4)*d^(1/4)*x*sqrt(2)+sqrt(c)+x^2*sqrt(d))/(c^(3/4)*(b*c-a*d)*sqrt(2))],
[1/(x^2*(a+b*x^4)*(c+d*x^4)),x,21,(-1)/(a*c*x)+1/2*b^(5/4)*arctan(1-b^(1/4)*x*sqrt(2)/a^(1/4))/(a^(5/4)*(b*c-a*d)*sqrt(2))-1/2*b^(5/4)*arctan(1+b^(1/4)*x*sqrt(2)/a^(1/4))/(a^(5/4)*(b*c-a*d)*sqrt(2))-1/2*d^(5/4)*arctan(1-d^(1/4)*x*sqrt(2)/c^(1/4))/(c^(5/4)*(b*c-a*d)*sqrt(2))+1/2*d^(5/4)*arctan(1+d^(1/4)*x*sqrt(2)/c^(1/4))/(c^(5/4)*(b*c-a*d)*sqrt(2))-1/4*b^(5/4)*log(-a^(1/4)*b^(1/4)*x*sqrt(2)+sqrt(a)+x^2*sqrt(b))/(a^(5/4)*(b*c-a*d)*sqrt(2))+1/4*b^(5/4)*log(a^(1/4)*b^(1/4)*x*sqrt(2)+sqrt(a)+x^2*sqrt(b))/(a^(5/4)*(b*c-a*d)*sqrt(2))+1/4*d^(5/4)*log(-c^(1/4)*d^(1/4)*x*sqrt(2)+sqrt(c)+x^2*sqrt(d))/(c^(5/4)*(b*c-a*d)*sqrt(2))-1/4*d^(5/4)*log(c^(1/4)*d^(1/4)*x*sqrt(2)+sqrt(c)+x^2*sqrt(d))/(c^(5/4)*(b*c-a*d)*sqrt(2))],
[1/(x^4*(a+b*x^4)*(c+d*x^4)),x,20,(-1/3)/(a*c*x^3)+1/2*b^(7/4)*arctan(1-b^(1/4)*x*sqrt(2)/a^(1/4))/(a^(7/4)*(b*c-a*d)*sqrt(2))-1/2*b^(7/4)*arctan(1+b^(1/4)*x*sqrt(2)/a^(1/4))/(a^(7/4)*(b*c-a*d)*sqrt(2))-1/2*d^(7/4)*arctan(1-d^(1/4)*x*sqrt(2)/c^(1/4))/(c^(7/4)*(b*c-a*d)*sqrt(2))+1/2*d^(7/4)*arctan(1+d^(1/4)*x*sqrt(2)/c^(1/4))/(c^(7/4)*(b*c-a*d)*sqrt(2))+1/4*b^(7/4)*log(-a^(1/4)*b^(1/4)*x*sqrt(2)+sqrt(a)+x^2*sqrt(b))/(a^(7/4)*(b*c-a*d)*sqrt(2))-1/4*b^(7/4)*log(a^(1/4)*b^(1/4)*x*sqrt(2)+sqrt(a)+x^2*sqrt(b))/(a^(7/4)*(b*c-a*d)*sqrt(2))-1/4*d^(7/4)*log(-c^(1/4)*d^(1/4)*x*sqrt(2)+sqrt(c)+x^2*sqrt(d))/(c^(7/4)*(b*c-a*d)*sqrt(2))+1/4*d^(7/4)*log(c^(1/4)*d^(1/4)*x*sqrt(2)+sqrt(c)+x^2*sqrt(d))/(c^(7/4)*(b*c-a*d)*sqrt(2))],
[1/(x^6*(a+b*x^4)*(c+d*x^4)),x,22,(-1/5)/(a*c*x^5)+(b*c+a*d)/(a^2*c^2*x)-1/2*b^(9/4)*arctan(1-b^(1/4)*x*sqrt(2)/a^(1/4))/(a^(9/4)*(b*c-a*d)*sqrt(2))+1/2*b^(9/4)*arctan(1+b^(1/4)*x*sqrt(2)/a^(1/4))/(a^(9/4)*(b*c-a*d)*sqrt(2))+1/2*d^(9/4)*arctan(1-d^(1/4)*x*sqrt(2)/c^(1/4))/(c^(9/4)*(b*c-a*d)*sqrt(2))-1/2*d^(9/4)*arctan(1+d^(1/4)*x*sqrt(2)/c^(1/4))/(c^(9/4)*(b*c-a*d)*sqrt(2))+1/4*b^(9/4)*log(-a^(1/4)*b^(1/4)*x*sqrt(2)+sqrt(a)+x^2*sqrt(b))/(a^(9/4)*(b*c-a*d)*sqrt(2))-1/4*b^(9/4)*log(a^(1/4)*b^(1/4)*x*sqrt(2)+sqrt(a)+x^2*sqrt(b))/(a^(9/4)*(b*c-a*d)*sqrt(2))-1/4*d^(9/4)*log(-c^(1/4)*d^(1/4)*x*sqrt(2)+sqrt(c)+x^2*sqrt(d))/(c^(9/4)*(b*c-a*d)*sqrt(2))+1/4*d^(9/4)*log(c^(1/4)*d^(1/4)*x*sqrt(2)+sqrt(c)+x^2*sqrt(d))/(c^(9/4)*(b*c-a*d)*sqrt(2))],

# Integrands of the form (e x)^m (a+b x^4)^p (c+d x^4)^(q/2)

# Integrands of the form (e x)^m (a+b x^4)^p (c+d x^4)^(1/2)

# p>0

# p<0
[x^7*sqrt(c+d*x^4)/(a+b*x^4),x,5,1/6*(c+d*x^4)^(3/2)/(b*d)+1/2*a*arctanh(sqrt(b)*sqrt(c+d*x^4)/sqrt(b*c-a*d))*sqrt(b*c-a*d)/b^(5/2)-1/2*a*sqrt(c+d*x^4)/b^2],
[x^5*sqrt(c+d*x^4)/(a+b*x^4),x,7,1/4*(b*c-2*a*d)*arctanh(x^2*sqrt(d)/sqrt(c+d*x^4))/(b^2*sqrt(d))-1/2*arctan(x^2*sqrt(b*c-a*d)/(sqrt(a)*sqrt(c+d*x^4)))*sqrt(a)*sqrt(b*c-a*d)/b^2+1/4*x^2*sqrt(c+d*x^4)/b],
[x^3*sqrt(c+d*x^4)/(a+b*x^4),x,4,-1/2*arctanh(sqrt(b)*sqrt(c+d*x^4)/sqrt(b*c-a*d))*sqrt(b*c-a*d)/b^(3/2)+1/2*sqrt(c+d*x^4)/b],
[x*sqrt(c+d*x^4)/(a+b*x^4),x,6,1/2*arctanh(x^2*sqrt(d)/sqrt(c+d*x^4))*sqrt(d)/b+1/2*arctan(x^2*sqrt(b*c-a*d)/(sqrt(a)*sqrt(c+d*x^4)))*sqrt(b*c-a*d)/(b*sqrt(a))],
[sqrt(c+d*x^4)/(x*(a+b*x^4)),x,6,-1/2*arctanh(sqrt(c+d*x^4)/sqrt(c))*sqrt(c)/a+1/2*arctanh(sqrt(b)*sqrt(c+d*x^4)/sqrt(b*c-a*d))*sqrt(b*c-a*d)/(a*sqrt(b))],
[sqrt(c+d*x^4)/(x^3*(a+b*x^4)),x,5,-1/2*arctan(x^2*sqrt(b*c-a*d)/(sqrt(a)*sqrt(c+d*x^4)))*sqrt(b*c-a*d)/a^(3/2)-1/2*sqrt(c+d*x^4)/(a*x^2)],
[sqrt(c+d*x^4)/(x^5*(a+b*x^4)),x,7,1/4*(2*b*c-a*d)*arctanh(sqrt(c+d*x^4)/sqrt(c))/(a^2*sqrt(c))-1/2*arctanh(sqrt(b)*sqrt(c+d*x^4)/sqrt(b*c-a*d))*sqrt(b)*sqrt(b*c-a*d)/a^2-1/4*sqrt(c+d*x^4)/(a*x^4)],
[sqrt(c+d*x^4)/(x^7*(a+b*x^4)),x,6,1/2*b*arctan(x^2*sqrt(b*c-a*d)/(sqrt(a)*sqrt(c+d*x^4)))*sqrt(b*c-a*d)/a^(5/2)-1/6*sqrt(c+d*x^4)/(a*x^6)+1/6*(3*b*c-a*d)*sqrt(c+d*x^4)/(a^2*c*x^2)],
[x^6*sqrt(c+d*x^4)/(a+b*x^4),x,13,1/5*x^3*sqrt(c+d*x^4)/b+1/5*(2*b*c-5*a*d)*x*sqrt(c+d*x^4)/(b^2*sqrt(d)*(sqrt(c)+x^2*sqrt(d)))-1/4*a*arctan(x*sqrt((-b*c+a*d)/(sqrt(-a)*sqrt(b)))/sqrt(c+d*x^4))*sqrt((-b*c+a*d)/(sqrt(-a)*sqrt(b)))/b^2-1/4*a*arctan(x*sqrt((b*c-a*d)/(sqrt(-a)*sqrt(b)))/sqrt(c+d*x^4))*sqrt((b*c-a*d)/(sqrt(-a)*sqrt(b)))/b^2-1/5*c^(1/4)*(2*b*c-5*a*d)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticE(sin(2*arctan(d^(1/4)*x/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(b^2*d^(3/4)*sqrt(c+d*x^4))+1/5*c^(1/4)*(b^2*c^2+a*b*c*d-5*a^2*d^2)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(b^2*d^(3/4)*(b*c+a*d)*sqrt(c+d*x^4))+1/8*a*(b*c-a*d)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticPi(sin(2*arctan(d^(1/4)*x/c^(1/4))),1/4*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))^2/(sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(b^(5/2)*c^(1/4)*d^(1/4)*(sqrt(-a)*sqrt(b)*sqrt(c)-a*sqrt(d))*sqrt(c+d*x^4))-1/8*a*(b*c-a*d)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticPi(sin(2*arctan(d^(1/4)*x/c^(1/4))),-1/4*sqrt(c)*(sqrt(b)-sqrt(-a)*sqrt(d)/sqrt(c))^2/(sqrt(-a)*sqrt(b)*sqrt(d)),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(b^(5/2)*c^(1/4)*d^(1/4)*(sqrt(-a)*sqrt(b)*sqrt(c)+a*sqrt(d))*sqrt(c+d*x^4)),1/4*(-a)^(3/4)*arctan(x*sqrt(b*c-a*d)/((-a)^(1/4)*b^(1/4)*sqrt(c+d*x^4)))*sqrt(b*c-a*d)/b^(9/4)+1/4*(-a)^(3/4)*arctan(x*sqrt(-b*c+a*d)/((-a)^(1/4)*b^(1/4)*sqrt(c+d*x^4)))*sqrt(-b*c+a*d)/b^(9/4)+1/5*x^3*sqrt(c+d*x^4)/b+1/5*(2*b*c-5*a*d)*x*sqrt(c+d*x^4)/(b^2*sqrt(d)*(sqrt(c)+x^2*sqrt(d)))-1/5*c^(1/4)*(2*b*c-5*a*d)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticE(sin(2*arctan(d^(1/4)*x/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(b^2*d^(3/4)*sqrt(c+d*x^4))+1/10*c^(1/4)*(2*b*c-5*a*d)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(b^2*d^(3/4)*sqrt(c+d*x^4))-1/8*(b*c-a*d)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticPi(sin(2*arctan(d^(1/4)*x/c^(1/4))),1/4*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))^2/(sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)),sqrt(1/2))*sqrt(-a)*(sqrt(c)+x^2*sqrt(d))*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))^2*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(b^(5/2)*c^(1/4)*d^(1/4)*(b*c+a*d)*sqrt(c+d*x^4))+1/8*(b*c-a*d)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticPi(sin(2*arctan(d^(1/4)*x/c^(1/4))),-1/4*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))^2/(sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)),sqrt(1/2))*sqrt(-a)*(sqrt(c)+x^2*sqrt(d))*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))^2*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(b^(5/2)*c^(1/4)*d^(1/4)*(b*c+a*d)*sqrt(c+d*x^4))+1/4*a*d^(1/4)*(b*c-a*d)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*(sqrt(c)-sqrt(-a)*sqrt(d)/sqrt(b))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(b^2*c^(1/4)*(b*c+a*d)*sqrt(c+d*x^4))+1/4*a*d^(1/4)*(b*c-a*d)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*(sqrt(c)+sqrt(-a)*sqrt(d)/sqrt(b))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(b^2*c^(1/4)*(b*c+a*d)*sqrt(c+d*x^4))],
[x^4*sqrt(c+d*x^4)/(a+b*x^4),x,10,1/3*x*sqrt(c+d*x^4)/b-1/4*(b*c-a*d)*arctan(x*sqrt((b*c/a-d)*sqrt(-a)/sqrt(b))/sqrt(c+d*x^4))/(b^2*sqrt((-b*c+a*d)/(sqrt(-a)*sqrt(b))))-1/4*(b*c-a*d)*arctan(x*sqrt((b*c-a*d)/(sqrt(-a)*sqrt(b)))/sqrt(c+d*x^4))/(b^2*sqrt((b*c-a*d)/(sqrt(-a)*sqrt(b))))+1/3*c^(3/4)*(b*c-2*a*d)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(b*d^(1/4)*(b*c+a*d)*sqrt(c+d*x^4))-1/8*(b*c-a*d)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticPi(sin(2*arctan(d^(1/4)*x/c^(1/4))),1/4*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))^2/(sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(b^2*c^(1/4)*d^(1/4)*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))*sqrt(c+d*x^4))-1/8*(b*c-a*d)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticPi(sin(2*arctan(d^(1/4)*x/c^(1/4))),-1/4*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))^2/(sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(b^2*c^(1/4)*d^(1/4)*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))*sqrt(c+d*x^4)),-1/4*(-a)^(1/4)*arctan(x*sqrt(b*c-a*d)/((-a)^(1/4)*b^(1/4)*sqrt(c+d*x^4)))*sqrt(b*c-a*d)/b^(7/4)+1/4*(-a)^(1/4)*arctan(x*sqrt(-b*c+a*d)/((-a)^(1/4)*b^(1/4)*sqrt(c+d*x^4)))*sqrt(-b*c+a*d)/b^(7/4)+1/3*x*sqrt(c+d*x^4)/b+1/6*(2*b*c-3*a*d)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(b^2*c^(1/4)*d^(1/4)*sqrt(c+d*x^4))-1/4*a*d^(1/4)*(b*c-a*d)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x/c^(1/4))),sqrt(1/2))*(sqrt(b)*sqrt(c)/sqrt(-a)+sqrt(d))*(sqrt(c)+x^2*sqrt(d))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(b^2*c^(1/4)*(b*c+a*d)*sqrt(c+d*x^4))-1/4*d^(1/4)*(b*c-a*d)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x/c^(1/4))),sqrt(1/2))*sqrt(-a)*(sqrt(c)+x^2*sqrt(d))*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(b^2*c^(1/4)*(b*c+a*d)*sqrt(c+d*x^4))-1/8*(b*c-a*d)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticPi(sin(2*arctan(d^(1/4)*x/c^(1/4))),1/4*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))^2/(sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))^2*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(b^2*c^(1/4)*d^(1/4)*(b*c+a*d)*sqrt(c+d*x^4))-1/8*(b*c-a*d)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticPi(sin(2*arctan(d^(1/4)*x/c^(1/4))),-1/4*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))^2/(sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))^2*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(b^2*c^(1/4)*d^(1/4)*(b*c+a*d)*sqrt(c+d*x^4))],
[x^2*sqrt(c+d*x^4)/(a+b*x^4),x,11,x*sqrt(d)*sqrt(c+d*x^4)/(b*(sqrt(c)+x^2*sqrt(d)))+1/4*arctan(x*sqrt((-b*c+a*d)/(sqrt(-a)*sqrt(b)))/sqrt(c+d*x^4))*sqrt((-b*c+a*d)/(sqrt(-a)*sqrt(b)))/b+1/4*arctan(x*sqrt((b*c-a*d)/(sqrt(-a)*sqrt(b)))/sqrt(c+d*x^4))*sqrt((b*c-a*d)/(sqrt(-a)*sqrt(b)))/b-c^(1/4)*d^(1/4)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticE(sin(2*arctan(d^(1/4)*x/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(b*sqrt(c+d*x^4))+a*c^(1/4)*d^(5/4)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(b*(b*c+a*d)*sqrt(c+d*x^4))-1/8*(b*c-a*d)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticPi(sin(2*arctan(d^(1/4)*x/c^(1/4))),1/4*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))^2/(sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(b^(3/2)*c^(1/4)*d^(1/4)*(sqrt(-a)*sqrt(b)*sqrt(c)-a*sqrt(d))*sqrt(c+d*x^4))+1/8*(b*c-a*d)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticPi(sin(2*arctan(d^(1/4)*x/c^(1/4))),-1/4*sqrt(c)*(sqrt(b)-sqrt(-a)*sqrt(d)/sqrt(c))^2/(sqrt(-a)*sqrt(b)*sqrt(d)),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(b^(3/2)*c^(1/4)*d^(1/4)*(sqrt(-a)*sqrt(b)*sqrt(c)+a*sqrt(d))*sqrt(c+d*x^4)),1/4*arctan(x*sqrt(b*c-a*d)/((-a)^(1/4)*b^(1/4)*sqrt(c+d*x^4)))*sqrt(b*c-a*d)/((-a)^(1/4)*b^(5/4))+1/4*arctan(x*sqrt(-b*c+a*d)/((-a)^(1/4)*b^(1/4)*sqrt(c+d*x^4)))*sqrt(-b*c+a*d)/((-a)^(1/4)*b^(5/4))+x*sqrt(d)*sqrt(c+d*x^4)/(b*(sqrt(c)+x^2*sqrt(d)))-c^(1/4)*d^(1/4)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticE(sin(2*arctan(d^(1/4)*x/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(b*sqrt(c+d*x^4))+1/2*c^(1/4)*d^(1/4)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(b*sqrt(c+d*x^4))-1/8*(b*c-a*d)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticPi(sin(2*arctan(d^(1/4)*x/c^(1/4))),1/4*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))^2/(sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))^2*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(b^(3/2)*c^(1/4)*d^(1/4)*(b*c+a*d)*sqrt(-a)*sqrt(c+d*x^4))+1/8*(b*c-a*d)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticPi(sin(2*arctan(d^(1/4)*x/c^(1/4))),-1/4*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))^2/(sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))^2*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(b^(3/2)*c^(1/4)*d^(1/4)*(b*c+a*d)*sqrt(-a)*sqrt(c+d*x^4))-1/4*d^(1/4)*(b*c-a*d)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*(sqrt(c)-sqrt(-a)*sqrt(d)/sqrt(b))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(b*c^(1/4)*(b*c+a*d)*sqrt(c+d*x^4))-1/4*d^(1/4)*(b*c-a*d)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*(sqrt(c)+sqrt(-a)*sqrt(d)/sqrt(b))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(b*c^(1/4)*(b*c+a*d)*sqrt(c+d*x^4))],
[sqrt(c+d*x^4)/(a+b*x^4),x,9,1/4*(b*c-a*d)*arctan(x*sqrt((b*c/a-d)*sqrt(-a)/sqrt(b))/sqrt(c+d*x^4))/(a*b*sqrt((-b*c+a*d)/(sqrt(-a)*sqrt(b))))+1/4*(b*c-a*d)*arctan(x*sqrt((b*c-a*d)/(sqrt(-a)*sqrt(b)))/sqrt(c+d*x^4))/(a*b*sqrt((b*c-a*d)/(sqrt(-a)*sqrt(b))))+c^(3/4)*d^(3/4)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/((b*c+a*d)*sqrt(c+d*x^4))+1/8*(b*c-a*d)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticPi(sin(2*arctan(d^(1/4)*x/c^(1/4))),1/4*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))^2/(sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(a*b*c^(1/4)*d^(1/4)*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))*sqrt(c+d*x^4))+1/8*(b*c-a*d)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticPi(sin(2*arctan(d^(1/4)*x/c^(1/4))),-1/4*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))^2/(sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(a*b*c^(1/4)*d^(1/4)*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))*sqrt(c+d*x^4)),-1/4*arctan(x*sqrt(b*c-a*d)/((-a)^(1/4)*b^(1/4)*sqrt(c+d*x^4)))*sqrt(b*c-a*d)/((-a)^(3/4)*b^(3/4))+1/4*arctan(x*sqrt(-b*c+a*d)/((-a)^(1/4)*b^(1/4)*sqrt(c+d*x^4)))*sqrt(-b*c+a*d)/((-a)^(3/4)*b^(3/4))+1/2*d^(3/4)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(b*c^(1/4)*sqrt(c+d*x^4))+1/4*d^(1/4)*(b*c-a*d)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x/c^(1/4))),sqrt(1/2))*(sqrt(b)*sqrt(c)/sqrt(-a)+sqrt(d))*(sqrt(c)+x^2*sqrt(d))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(b*c^(1/4)*(b*c+a*d)*sqrt(c+d*x^4))-1/4*d^(1/4)*(b*c-a*d)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(b*c^(1/4)*(b*c+a*d)*sqrt(-a)*sqrt(c+d*x^4))+1/8*(b*c-a*d)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticPi(sin(2*arctan(d^(1/4)*x/c^(1/4))),1/4*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))^2/(sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))^2*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(a*b*c^(1/4)*d^(1/4)*(b*c+a*d)*sqrt(c+d*x^4))+1/8*(b*c-a*d)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticPi(sin(2*arctan(d^(1/4)*x/c^(1/4))),-1/4*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))^2/(sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))^2*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(a*b*c^(1/4)*d^(1/4)*(b*c+a*d)*sqrt(c+d*x^4))],
[sqrt(c+d*x^4)/(x^2*(a+b*x^4)),x,13,-sqrt(c+d*x^4)/(a*x)+x*sqrt(d)*sqrt(c+d*x^4)/(a*(sqrt(c)+x^2*sqrt(d)))-1/4*arctan(x*sqrt((-b*c+a*d)/(sqrt(-a)*sqrt(b)))/sqrt(c+d*x^4))*sqrt((-b*c+a*d)/(sqrt(-a)*sqrt(b)))/a-1/4*arctan(x*sqrt((b*c-a*d)/(sqrt(-a)*sqrt(b)))/sqrt(c+d*x^4))*sqrt((b*c-a*d)/(sqrt(-a)*sqrt(b)))/a-c^(1/4)*d^(1/4)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticE(sin(2*arctan(d^(1/4)*x/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(a*sqrt(c+d*x^4))+b*c^(5/4)*d^(1/4)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(a*(b*c+a*d)*sqrt(c+d*x^4))-1/8*(b*c-a*d)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticPi(sin(2*arctan(d^(1/4)*x/c^(1/4))),1/4*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))^2/(sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(c^(1/4)*d^(1/4)*sqrt(b)*((-a)^(3/2)*sqrt(b)*sqrt(c)+a^2*sqrt(d))*sqrt(c+d*x^4))-1/8*(b*c-a*d)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticPi(sin(2*arctan(d^(1/4)*x/c^(1/4))),-1/4*sqrt(c)*(sqrt(b)-sqrt(-a)*sqrt(d)/sqrt(c))^2/(sqrt(-a)*sqrt(b)*sqrt(d)),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(a*c^(1/4)*d^(1/4)*sqrt(b)*(sqrt(-a)*sqrt(b)*sqrt(c)+a*sqrt(d))*sqrt(c+d*x^4)),1/4*arctan(x*sqrt(b*c-a*d)/((-a)^(1/4)*b^(1/4)*sqrt(c+d*x^4)))*sqrt(b*c-a*d)/((-a)^(5/4)*b^(1/4))+1/4*arctan(x*sqrt(-b*c+a*d)/((-a)^(1/4)*b^(1/4)*sqrt(c+d*x^4)))*sqrt(-b*c+a*d)/((-a)^(5/4)*b^(1/4))-sqrt(c+d*x^4)/(a*x)+x*sqrt(d)*sqrt(c+d*x^4)/(a*(sqrt(c)+x^2*sqrt(d)))-c^(1/4)*d^(1/4)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticE(sin(2*arctan(d^(1/4)*x/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(a*sqrt(c+d*x^4))+1/2*c^(1/4)*d^(1/4)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(a*sqrt(c+d*x^4))-1/8*(b*c-a*d)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticPi(sin(2*arctan(d^(1/4)*x/c^(1/4))),1/4*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))^2/(sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))^2*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/((-a)^(3/2)*c^(1/4)*d^(1/4)*(b*c+a*d)*sqrt(b)*sqrt(c+d*x^4))+1/8*(b*c-a*d)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticPi(sin(2*arctan(d^(1/4)*x/c^(1/4))),-1/4*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))^2/(sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))^2*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/((-a)^(3/2)*c^(1/4)*d^(1/4)*(b*c+a*d)*sqrt(b)*sqrt(c+d*x^4))+1/4*d^(1/4)*(b*c-a*d)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*(sqrt(c)-sqrt(-a)*sqrt(d)/sqrt(b))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(a*c^(1/4)*(b*c+a*d)*sqrt(c+d*x^4))+1/4*d^(1/4)*(b*c-a*d)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*(sqrt(c)+sqrt(-a)*sqrt(d)/sqrt(b))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(a*c^(1/4)*(b*c+a*d)*sqrt(c+d*x^4))],
[sqrt(c+d*x^4)/(x^4*(a+b*x^4)),x,10,-1/3*sqrt(c+d*x^4)/(a*x^3)-1/4*(b*c-a*d)*arctan(x*sqrt((b*c/a-d)*sqrt(-a)/sqrt(b))/sqrt(c+d*x^4))/(a^2*sqrt((-b*c+a*d)/(sqrt(-a)*sqrt(b))))-1/4*(b*c-a*d)*arctan(x*sqrt((b*c-a*d)/(sqrt(-a)*sqrt(b)))/sqrt(c+d*x^4))/(a^2*sqrt((b*c-a*d)/(sqrt(-a)*sqrt(b))))-1/3*d^(3/4)*(2*b*c-a*d)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(a*c^(1/4)*(b*c+a*d)*sqrt(c+d*x^4))-1/8*(b*c-a*d)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticPi(sin(2*arctan(d^(1/4)*x/c^(1/4))),1/4*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))^2/(sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(a^2*c^(1/4)*d^(1/4)*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))*sqrt(c+d*x^4))-1/8*(b*c-a*d)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticPi(sin(2*arctan(d^(1/4)*x/c^(1/4))),-1/4*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))^2/(sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(a^2*c^(1/4)*d^(1/4)*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))*sqrt(c+d*x^4)),-1/4*b^(1/4)*arctan(x*sqrt(b*c-a*d)/((-a)^(1/4)*b^(1/4)*sqrt(c+d*x^4)))*sqrt(b*c-a*d)/(-a)^(7/4)+1/4*b^(1/4)*arctan(x*sqrt(-b*c+a*d)/((-a)^(1/4)*b^(1/4)*sqrt(c+d*x^4)))*sqrt(-b*c+a*d)/(-a)^(7/4)-1/3*sqrt(c+d*x^4)/(a*x^3)-1/6*d^(3/4)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(a*c^(1/4)*sqrt(c+d*x^4))-1/4*d^(1/4)*(b*c-a*d)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x/c^(1/4))),sqrt(1/2))*(sqrt(b)*sqrt(c)/sqrt(-a)+sqrt(d))*(sqrt(c)+x^2*sqrt(d))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(a*c^(1/4)*(b*c+a*d)*sqrt(c+d*x^4))-1/4*d^(1/4)*(b*c-a*d)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/((-a)^(3/2)*c^(1/4)*(b*c+a*d)*sqrt(c+d*x^4))-1/8*(b*c-a*d)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticPi(sin(2*arctan(d^(1/4)*x/c^(1/4))),1/4*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))^2/(sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))^2*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(a^2*c^(1/4)*d^(1/4)*(b*c+a*d)*sqrt(c+d*x^4))-1/8*(b*c-a*d)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticPi(sin(2*arctan(d^(1/4)*x/c^(1/4))),-1/4*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))^2/(sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))^2*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(a^2*c^(1/4)*d^(1/4)*(b*c+a*d)*sqrt(c+d*x^4))],

# Integrands of the form (e x)^(m/2) (a+b x^4)^p (c+d x^4)^(1/2)

# p>0

# p<0
[(e*x)^(3/2)*sqrt(c+d*x^4)/(a+b*x^4),x,3,2/5*(e*x)^(5/2)*AppellF1(5/8,1,-1/2,13/8,-b*x^4/a,-d*x^4/c)*sqrt(c+d*x^4)/(a*e*sqrt(1+d*x^4/c))],
[(e*x)^(1/2)*sqrt(c+d*x^4)/(a+b*x^4),x,3,2/3*(e*x)^(3/2)*AppellF1(3/8,1,-1/2,11/8,-b*x^4/a,-d*x^4/c)*sqrt(c+d*x^4)/(a*e*sqrt(1+d*x^4/c))],
[sqrt(c+d*x^4)/((e*x)^(1/2)*(a+b*x^4)),x,3,2*AppellF1(1/8,1,-1/2,9/8,-b*x^4/a,-d*x^4/c)*sqrt(e*x)*sqrt(c+d*x^4)/(a*e*sqrt(1+d*x^4/c))],
[sqrt(c+d*x^4)/((e*x)^(3/2)*(a+b*x^4)),x,3,-2*AppellF1(-1/8,1,-1/2,7/8,-b*x^4/a,-d*x^4/c)*sqrt(c+d*x^4)/(a*e*sqrt(e*x)*sqrt(1+d*x^4/c))],

# Integrands of the form (e x)^m (a+b x^4)^p / (c+d x^4)^(1/2)

# p>0

# p<0
[x^11/((a+b*x^4)*sqrt(c+d*x^4)),x,5,1/6*(c+d*x^4)^(3/2)/(b*d^2)-1/2*a^2*arctanh(sqrt(b)*sqrt(c+d*x^4)/sqrt(b*c-a*d))/(b^(5/2)*sqrt(b*c-a*d))-1/2*(b*c+a*d)*sqrt(c+d*x^4)/(b^2*d^2)],
[x^7/((a+b*x^4)*sqrt(c+d*x^4)),x,4,1/2*a*arctanh(sqrt(b)*sqrt(c+d*x^4)/sqrt(b*c-a*d))/(b^(3/2)*sqrt(b*c-a*d))+1/2*sqrt(c+d*x^4)/(b*d)],
[x^3/((a+b*x^4)*sqrt(c+d*x^4)),x,3,-1/2*arctanh(sqrt(b)*sqrt(c+d*x^4)/sqrt(b*c-a*d))/(sqrt(b)*sqrt(b*c-a*d))],
[1/(x*(a+b*x^4)*sqrt(c+d*x^4)),x,6,-1/2*arctanh(sqrt(c+d*x^4)/sqrt(c))/(a*sqrt(c))+1/2*arctanh(sqrt(b)*sqrt(c+d*x^4)/sqrt(b*c-a*d))*sqrt(b)/(a*sqrt(b*c-a*d))],
[1/(x^5*(a+b*x^4)*sqrt(c+d*x^4)),x,7,1/4*(2*b*c+a*d)*arctanh(sqrt(c+d*x^4)/sqrt(c))/(a^2*c^(3/2))-1/2*b^(3/2)*arctanh(sqrt(b)*sqrt(c+d*x^4)/sqrt(b*c-a*d))/(a^2*sqrt(b*c-a*d))-1/4*sqrt(c+d*x^4)/(a*c*x^4)],
[x^9/((a+b*x^4)*sqrt(c+d*x^4)),x,7,-1/4*(b*c+2*a*d)*arctanh(x^2*sqrt(d)/sqrt(c+d*x^4))/(b^2*d^(3/2))+1/2*a^(3/2)*arctan(x^2*sqrt(b*c-a*d)/(sqrt(a)*sqrt(c+d*x^4)))/(b^2*sqrt(b*c-a*d))+1/4*x^2*sqrt(c+d*x^4)/(b*d)],
[x^5/((a+b*x^4)*sqrt(c+d*x^4)),x,6,1/2*arctanh(x^2*sqrt(d)/sqrt(c+d*x^4))/(b*sqrt(d))-1/2*arctan(x^2*sqrt(b*c-a*d)/(sqrt(a)*sqrt(c+d*x^4)))*sqrt(a)/(b*sqrt(b*c-a*d))],
[x/((a+b*x^4)*sqrt(c+d*x^4)),x,3,1/2*arctan(x^2*sqrt(b*c-a*d)/(sqrt(a)*sqrt(c+d*x^4)))/(sqrt(a)*sqrt(b*c-a*d))],
[1/(x^3*(a+b*x^4)*sqrt(c+d*x^4)),x,5,-1/2*b*arctan(x^2*sqrt(b*c-a*d)/(sqrt(a)*sqrt(c+d*x^4)))/(a^(3/2)*sqrt(b*c-a*d))-1/2*sqrt(c+d*x^4)/(a*c*x^2)],
[1/(x^7*(a+b*x^4)*sqrt(c+d*x^4)),x,6,1/2*b^2*arctan(x^2*sqrt(b*c-a*d)/(sqrt(a)*sqrt(c+d*x^4)))/(a^(5/2)*sqrt(b*c-a*d))-1/6*sqrt(c+d*x^4)/(a*c*x^6)+1/6*(3*b*c+2*a*d)*sqrt(c+d*x^4)/(a^2*c^2*x^2)],
[x^8/((a+b*x^4)*sqrt(c+d*x^4)),x,10,-1/4*(-a)^(5/4)*arctan(x*sqrt(b*c-a*d)/((-a)^(1/4)*b^(1/4)*sqrt(c+d*x^4)))/(b^(7/4)*sqrt(b*c-a*d))-1/4*(-a)^(5/4)*arctan(x*sqrt(-b*c+a*d)/((-a)^(1/4)*b^(1/4)*sqrt(c+d*x^4)))/(b^(7/4)*sqrt(-b*c+a*d))+1/3*x*sqrt(c+d*x^4)/(b*d)-1/6*(b*c+3*a*d)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(b^2*c^(1/4)*d^(5/4)*sqrt(c+d*x^4))+1/4*a^2*d^(1/4)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x/c^(1/4))),sqrt(1/2))*(sqrt(b)*sqrt(c)/sqrt(-a)+sqrt(d))*(sqrt(c)+x^2*sqrt(d))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(b^2*c^(1/4)*(b*c+a*d)*sqrt(c+d*x^4))+1/4*a*d^(1/4)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x/c^(1/4))),sqrt(1/2))*(sqrt(-a)*sqrt(b)*sqrt(c)+a*sqrt(d))*(sqrt(c)+x^2*sqrt(d))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(b^2*c^(1/4)*(b*c+a*d)*sqrt(c+d*x^4))+1/8*a*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticPi(sin(2*arctan(d^(1/4)*x/c^(1/4))),1/4*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))^2/(sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))^2*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(b^2*c^(1/4)*d^(1/4)*(b*c+a*d)*sqrt(c+d*x^4))+1/8*a*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticPi(sin(2*arctan(d^(1/4)*x/c^(1/4))),-1/4*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))^2/(sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))^2*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(b^2*c^(1/4)*d^(1/4)*(b*c+a*d)*sqrt(c+d*x^4))],
[x^4/((a+b*x^4)*sqrt(c+d*x^4)),x,9,-1/4*arctan(x*sqrt((b*c/a-d)*sqrt(-a)/sqrt(b))/sqrt(c+d*x^4))/(b*sqrt((-b*c+a*d)/(sqrt(-a)*sqrt(b))))-1/4*arctan(x*sqrt((b*c-a*d)/(sqrt(-a)*sqrt(b)))/sqrt(c+d*x^4))/(b*sqrt((b*c-a*d)/(sqrt(-a)*sqrt(b))))+1/2*c^(3/4)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(d^(1/4)*(b*c+a*d)*sqrt(c+d*x^4))-1/8*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticPi(sin(2*arctan(d^(1/4)*x/c^(1/4))),1/4*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))^2/(sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(b*c^(1/4)*d^(1/4)*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))*sqrt(c+d*x^4))-1/8*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticPi(sin(2*arctan(d^(1/4)*x/c^(1/4))),-1/4*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))^2/(sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(b*c^(1/4)*d^(1/4)*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))*sqrt(c+d*x^4)),-1/4*(-a)^(1/4)*arctan(x*sqrt(b*c-a*d)/((-a)^(1/4)*b^(1/4)*sqrt(c+d*x^4)))/(b^(3/4)*sqrt(b*c-a*d))-1/4*(-a)^(1/4)*arctan(x*sqrt(-b*c+a*d)/((-a)^(1/4)*b^(1/4)*sqrt(c+d*x^4)))/(b^(3/4)*sqrt(-b*c+a*d))+1/2*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(b*c^(1/4)*d^(1/4)*sqrt(c+d*x^4))-1/4*a*d^(1/4)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x/c^(1/4))),sqrt(1/2))*(sqrt(b)*sqrt(c)/sqrt(-a)+sqrt(d))*(sqrt(c)+x^2*sqrt(d))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(b*c^(1/4)*(b*c+a*d)*sqrt(c+d*x^4))-1/4*d^(1/4)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x/c^(1/4))),sqrt(1/2))*(sqrt(-a)*sqrt(b)*sqrt(c)+a*sqrt(d))*(sqrt(c)+x^2*sqrt(d))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(b*c^(1/4)*(b*c+a*d)*sqrt(c+d*x^4))-1/8*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticPi(sin(2*arctan(d^(1/4)*x/c^(1/4))),1/4*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))^2/(sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))^2*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(b*c^(1/4)*d^(1/4)*(b*c+a*d)*sqrt(c+d*x^4))-1/8*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticPi(sin(2*arctan(d^(1/4)*x/c^(1/4))),-1/4*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))^2/(sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))^2*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(b*c^(1/4)*d^(1/4)*(b*c+a*d)*sqrt(c+d*x^4))],
[1/((a+b*x^4)*sqrt(c+d*x^4)),x,7,1/4*arctan(x*sqrt((b*c/a-d)*sqrt(-a)/sqrt(b))/sqrt(c+d*x^4))/(a*sqrt((-b*c+a*d)/(sqrt(-a)*sqrt(b))))+1/4*arctan(x*sqrt((b*c-a*d)/(sqrt(-a)*sqrt(b)))/sqrt(c+d*x^4))/(a*sqrt((b*c-a*d)/(sqrt(-a)*sqrt(b))))+1/2*d^(3/4)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(c^(1/4)*(b*c+a*d)*sqrt(c+d*x^4))+1/8*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticPi(sin(2*arctan(d^(1/4)*x/c^(1/4))),1/4*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))^2/(sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(a*c^(1/4)*d^(1/4)*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))*sqrt(c+d*x^4))+1/8*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticPi(sin(2*arctan(d^(1/4)*x/c^(1/4))),-1/4*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))^2/(sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(a*c^(1/4)*d^(1/4)*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))*sqrt(c+d*x^4)),-1/4*b^(1/4)*arctan(x*sqrt(b*c-a*d)/((-a)^(1/4)*b^(1/4)*sqrt(c+d*x^4)))/((-a)^(3/4)*sqrt(b*c-a*d))-1/4*b^(1/4)*arctan(x*sqrt(-b*c+a*d)/((-a)^(1/4)*b^(1/4)*sqrt(c+d*x^4)))/((-a)^(3/4)*sqrt(-b*c+a*d))+1/4*d^(1/4)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x/c^(1/4))),sqrt(1/2))*(sqrt(b)*sqrt(c)/sqrt(-a)+sqrt(d))*(sqrt(c)+x^2*sqrt(d))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(c^(1/4)*(b*c+a*d)*sqrt(c+d*x^4))+1/4*d^(1/4)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x/c^(1/4))),sqrt(1/2))*(sqrt(-a)*sqrt(b)*sqrt(c)+a*sqrt(d))*(sqrt(c)+x^2*sqrt(d))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(a*c^(1/4)*(b*c+a*d)*sqrt(c+d*x^4))+1/8*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticPi(sin(2*arctan(d^(1/4)*x/c^(1/4))),1/4*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))^2/(sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))^2*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(a*c^(1/4)*d^(1/4)*(b*c+a*d)*sqrt(c+d*x^4))+1/8*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticPi(sin(2*arctan(d^(1/4)*x/c^(1/4))),-1/4*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))^2/(sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))^2*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(a*c^(1/4)*d^(1/4)*(b*c+a*d)*sqrt(c+d*x^4))],
[1/(x^4*(a+b*x^4)*sqrt(c+d*x^4)),x,10,-1/3*sqrt(c+d*x^4)/(a*c*x^3)-1/4*b*arctan(x*sqrt((b*c/a-d)*sqrt(-a)/sqrt(b))/sqrt(c+d*x^4))/(a^2*sqrt((-b*c+a*d)/(sqrt(-a)*sqrt(b))))-1/4*b*arctan(x*sqrt((b*c-a*d)/(sqrt(-a)*sqrt(b)))/sqrt(c+d*x^4))/(a^2*sqrt((b*c-a*d)/(sqrt(-a)*sqrt(b))))-1/6*d^(3/4)*(4*b*c+a*d)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(a*c^(5/4)*(b*c+a*d)*sqrt(c+d*x^4))-1/8*b*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticPi(sin(2*arctan(d^(1/4)*x/c^(1/4))),1/4*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))^2/(sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(a^2*c^(1/4)*d^(1/4)*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))*sqrt(c+d*x^4))-1/8*b*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticPi(sin(2*arctan(d^(1/4)*x/c^(1/4))),-1/4*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))^2/(sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(a^2*c^(1/4)*d^(1/4)*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))*sqrt(c+d*x^4)),-1/4*b^(5/4)*arctan(x*sqrt(b*c-a*d)/((-a)^(1/4)*b^(1/4)*sqrt(c+d*x^4)))/((-a)^(7/4)*sqrt(b*c-a*d))-1/4*b^(5/4)*arctan(x*sqrt(-b*c+a*d)/((-a)^(1/4)*b^(1/4)*sqrt(c+d*x^4)))/((-a)^(7/4)*sqrt(-b*c+a*d))-1/3*sqrt(c+d*x^4)/(a*c*x^3)-1/6*d^(3/4)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(a*c^(5/4)*sqrt(c+d*x^4))-1/4*b*d^(1/4)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x/c^(1/4))),sqrt(1/2))*(sqrt(b)*sqrt(c)/sqrt(-a)+sqrt(d))*(sqrt(c)+x^2*sqrt(d))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(a*c^(1/4)*(b*c+a*d)*sqrt(c+d*x^4))-1/4*b*d^(1/4)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x/c^(1/4))),sqrt(1/2))*(sqrt(-a)*sqrt(b)*sqrt(c)+a*sqrt(d))*(sqrt(c)+x^2*sqrt(d))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(a^2*c^(1/4)*(b*c+a*d)*sqrt(c+d*x^4))-1/8*b*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticPi(sin(2*arctan(d^(1/4)*x/c^(1/4))),1/4*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))^2/(sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))^2*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(a^2*c^(1/4)*d^(1/4)*(b*c+a*d)*sqrt(c+d*x^4))-1/8*b*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticPi(sin(2*arctan(d^(1/4)*x/c^(1/4))),-1/4*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))^2/(sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))^2*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(a^2*c^(1/4)*d^(1/4)*(b*c+a*d)*sqrt(c+d*x^4))],
[x^6/((a+b*x^4)*sqrt(c+d*x^4)),x,11,x*sqrt(c+d*x^4)/(b*sqrt(d)*(sqrt(c)+x^2*sqrt(d)))-1/4*a*arctan(x*sqrt((-b*c+a*d)/(sqrt(-a)*sqrt(b)))/sqrt(c+d*x^4))*sqrt((-b*c+a*d)/(sqrt(-a)*sqrt(b)))/(b*(b*c-a*d))-1/4*a*arctan(x*sqrt((b*c-a*d)/(sqrt(-a)*sqrt(b)))/sqrt(c+d*x^4))*sqrt((b*c-a*d)/(sqrt(-a)*sqrt(b)))/(b*(b*c-a*d))-c^(1/4)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticE(sin(2*arctan(d^(1/4)*x/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(b*d^(3/4)*sqrt(c+d*x^4))+1/2*c^(1/4)*(b*c+2*a*d)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(b*d^(3/4)*(b*c+a*d)*sqrt(c+d*x^4))+1/8*a*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticPi(sin(2*arctan(d^(1/4)*x/c^(1/4))),1/4*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))^2/(sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(b^(3/2)*c^(1/4)*d^(1/4)*(sqrt(-a)*sqrt(b)*sqrt(c)-a*sqrt(d))*sqrt(c+d*x^4))-1/8*a*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticPi(sin(2*arctan(d^(1/4)*x/c^(1/4))),-1/4*sqrt(c)*(sqrt(b)-sqrt(-a)*sqrt(d)/sqrt(c))^2/(sqrt(-a)*sqrt(b)*sqrt(d)),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(b^(3/2)*c^(1/4)*d^(1/4)*(sqrt(-a)*sqrt(b)*sqrt(c)+a*sqrt(d))*sqrt(c+d*x^4)),1/4*(-a)^(3/4)*arctan(x*sqrt(b*c-a*d)/((-a)^(1/4)*b^(1/4)*sqrt(c+d*x^4)))/(b^(5/4)*sqrt(b*c-a*d))-1/4*(-a)^(3/4)*arctan(x*sqrt(-b*c+a*d)/((-a)^(1/4)*b^(1/4)*sqrt(c+d*x^4)))/(b^(5/4)*sqrt(-b*c+a*d))+x*sqrt(c+d*x^4)/(b*sqrt(d)*(sqrt(c)+x^2*sqrt(d)))-c^(1/4)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticE(sin(2*arctan(d^(1/4)*x/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(b*d^(3/4)*sqrt(c+d*x^4))+1/2*c^(1/4)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(b*d^(3/4)*sqrt(c+d*x^4))-1/8*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticPi(sin(2*arctan(d^(1/4)*x/c^(1/4))),1/4*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))^2/(sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)),sqrt(1/2))*sqrt(-a)*(sqrt(c)+x^2*sqrt(d))*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))^2*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(b^(3/2)*c^(1/4)*d^(1/4)*(b*c+a*d)*sqrt(c+d*x^4))+1/8*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticPi(sin(2*arctan(d^(1/4)*x/c^(1/4))),-1/4*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))^2/(sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)),sqrt(1/2))*sqrt(-a)*(sqrt(c)+x^2*sqrt(d))*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))^2*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(b^(3/2)*c^(1/4)*d^(1/4)*(b*c+a*d)*sqrt(c+d*x^4))+1/4*a*d^(1/4)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*(sqrt(c)-sqrt(-a)*sqrt(d)/sqrt(b))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(b*c^(1/4)*(b*c+a*d)*sqrt(c+d*x^4))+1/4*a*d^(1/4)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*(sqrt(c)+sqrt(-a)*sqrt(d)/sqrt(b))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(b*c^(1/4)*(b*c+a*d)*sqrt(c+d*x^4))],
[x^2/((a+b*x^4)*sqrt(c+d*x^4)),x,7,1/4*arctan(x*sqrt((-b*c+a*d)/(sqrt(-a)*sqrt(b)))/sqrt(c+d*x^4))*sqrt((-b*c+a*d)/(sqrt(-a)*sqrt(b)))/(b*c-a*d)+1/4*arctan(x*sqrt((b*c-a*d)/(sqrt(-a)*sqrt(b)))/sqrt(c+d*x^4))*sqrt((b*c-a*d)/(sqrt(-a)*sqrt(b)))/(b*c-a*d)-1/2*c^(1/4)*d^(1/4)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/((b*c+a*d)*sqrt(c+d*x^4))-1/8*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticPi(sin(2*arctan(d^(1/4)*x/c^(1/4))),1/4*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))^2/(sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(c^(1/4)*d^(1/4)*sqrt(b)*(sqrt(-a)*sqrt(b)*sqrt(c)-a*sqrt(d))*sqrt(c+d*x^4))+1/8*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticPi(sin(2*arctan(d^(1/4)*x/c^(1/4))),-1/4*sqrt(c)*(sqrt(b)-sqrt(-a)*sqrt(d)/sqrt(c))^2/(sqrt(-a)*sqrt(b)*sqrt(d)),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(c^(1/4)*d^(1/4)*sqrt(b)*(sqrt(-a)*sqrt(b)*sqrt(c)+a*sqrt(d))*sqrt(c+d*x^4)),1/4*arctan(x*sqrt(b*c-a*d)/((-a)^(1/4)*b^(1/4)*sqrt(c+d*x^4)))/((-a)^(1/4)*b^(1/4)*sqrt(b*c-a*d))-1/4*arctan(x*sqrt(-b*c+a*d)/((-a)^(1/4)*b^(1/4)*sqrt(c+d*x^4)))/((-a)^(1/4)*b^(1/4)*sqrt(-b*c+a*d))-1/8*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticPi(sin(2*arctan(d^(1/4)*x/c^(1/4))),1/4*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))^2/(sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))^2*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(c^(1/4)*d^(1/4)*(b*c+a*d)*sqrt(-a)*sqrt(b)*sqrt(c+d*x^4))+1/8*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticPi(sin(2*arctan(d^(1/4)*x/c^(1/4))),-1/4*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))^2/(sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))^2*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(c^(1/4)*d^(1/4)*(b*c+a*d)*sqrt(-a)*sqrt(b)*sqrt(c+d*x^4))-1/4*d^(1/4)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*(sqrt(c)-sqrt(-a)*sqrt(d)/sqrt(b))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(c^(1/4)*(b*c+a*d)*sqrt(c+d*x^4))-1/4*d^(1/4)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*(sqrt(c)+sqrt(-a)*sqrt(d)/sqrt(b))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(c^(1/4)*(b*c+a*d)*sqrt(c+d*x^4))],
[1/(x^2*(a+b*x^4)*sqrt(c+d*x^4)),x,13,-sqrt(c+d*x^4)/(a*c*x)+x*sqrt(d)*sqrt(c+d*x^4)/(a*c*(sqrt(c)+x^2*sqrt(d)))-1/4*b*arctan(x*sqrt((-b*c+a*d)/(sqrt(-a)*sqrt(b)))/sqrt(c+d*x^4))*sqrt((-b*c+a*d)/(sqrt(-a)*sqrt(b)))/(a*(b*c-a*d))-1/4*b*arctan(x*sqrt((b*c-a*d)/(sqrt(-a)*sqrt(b)))/sqrt(c+d*x^4))*sqrt((b*c-a*d)/(sqrt(-a)*sqrt(b)))/(a*(b*c-a*d))-d^(1/4)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticE(sin(2*arctan(d^(1/4)*x/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(a*c^(3/4)*sqrt(c+d*x^4))+1/2*d^(1/4)*(2*b*c+a*d)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(a*c^(3/4)*(b*c+a*d)*sqrt(c+d*x^4))+1/8*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticPi(sin(2*arctan(d^(1/4)*x/c^(1/4))),1/4*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))^2/(sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)),sqrt(1/2))*sqrt(b)*(-d^(1/4)*sqrt(-a)/c^(1/4)+c^(1/4)*sqrt(b)/d^(1/4))*(sqrt(c)+x^2*sqrt(d))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(a*(sqrt(-a)*sqrt(b)*sqrt(c)-a*sqrt(d))*sqrt(c+d*x^4))-1/8*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticPi(sin(2*arctan(d^(1/4)*x/c^(1/4))),-1/4*sqrt(c)*(sqrt(b)-sqrt(-a)*sqrt(d)/sqrt(c))^2/(sqrt(-a)*sqrt(b)*sqrt(d)),sqrt(1/2))*sqrt(b)*(d^(1/4)*sqrt(-a)/c^(1/4)+c^(1/4)*sqrt(b)/d^(1/4))*(sqrt(c)+x^2*sqrt(d))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(a*(sqrt(-a)*sqrt(b)*sqrt(c)+a*sqrt(d))*sqrt(c+d*x^4)),1/4*b^(3/4)*arctan(x*sqrt(b*c-a*d)/((-a)^(1/4)*b^(1/4)*sqrt(c+d*x^4)))/((-a)^(5/4)*sqrt(b*c-a*d))-1/4*b^(3/4)*arctan(x*sqrt(-b*c+a*d)/((-a)^(1/4)*b^(1/4)*sqrt(c+d*x^4)))/((-a)^(5/4)*sqrt(-b*c+a*d))-sqrt(c+d*x^4)/(a*c*x)+x*sqrt(d)*sqrt(c+d*x^4)/(a*c*(sqrt(c)+x^2*sqrt(d)))-d^(1/4)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticE(sin(2*arctan(d^(1/4)*x/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(a*c^(3/4)*sqrt(c+d*x^4))+1/2*d^(1/4)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(a*c^(3/4)*sqrt(c+d*x^4))-1/8*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticPi(sin(2*arctan(d^(1/4)*x/c^(1/4))),1/4*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))^2/(sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)),sqrt(1/2))*sqrt(b)*(sqrt(c)+x^2*sqrt(d))*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))^2*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/((-a)^(3/2)*c^(1/4)*d^(1/4)*(b*c+a*d)*sqrt(c+d*x^4))+1/8*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticPi(sin(2*arctan(d^(1/4)*x/c^(1/4))),-1/4*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))^2/(sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)),sqrt(1/2))*sqrt(b)*(sqrt(c)+x^2*sqrt(d))*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))^2*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/((-a)^(3/2)*c^(1/4)*d^(1/4)*(b*c+a*d)*sqrt(c+d*x^4))+1/4*b*d^(1/4)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*(sqrt(c)-sqrt(-a)*sqrt(d)/sqrt(b))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(a*c^(1/4)*(b*c+a*d)*sqrt(c+d*x^4))+1/4*b*d^(1/4)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*(sqrt(c)+sqrt(-a)*sqrt(d)/sqrt(b))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(a*c^(1/4)*(b*c+a*d)*sqrt(c+d*x^4))],
[x^15/((a+b*x^4)^2*sqrt(c+d*x^4)),x,5,-1/4*a^2*(6*b*c-5*a*d)*arctanh(sqrt(b)*sqrt(c+d*x^4)/sqrt(b*c-a*d))/(b^(7/2)*(b*c-a*d)^(3/2))+1/4*a*x^8*sqrt(c+d*x^4)/(b*(b*c-a*d)*(a+b*x^4))-1/12*(4*b^2*c^2+8*a*b*c*d-15*a^2*d^2-b*d*(2*b*c-5*a*d)*x^4)*sqrt(c+d*x^4)/(b^3*d^2*(b*c-a*d))],
[x^11/((a+b*x^4)^2*sqrt(c+d*x^4)),x,5,1/4*a*(4*b*c-3*a*d)*arctanh(sqrt(b)*sqrt(c+d*x^4)/sqrt(b*c-a*d))/(b^(5/2)*(b*c-a*d)^(3/2))+1/2*sqrt(c+d*x^4)/(b^2*d)-1/4*a^2*sqrt(c+d*x^4)/(b^2*(b*c-a*d)*(a+b*x^4))],
[x^7/((a+b*x^4)^2*sqrt(c+d*x^4)),x,4,-1/4*(2*b*c-a*d)*arctanh(sqrt(b)*sqrt(c+d*x^4)/sqrt(b*c-a*d))/(b^(3/2)*(b*c-a*d)^(3/2))+1/4*a*sqrt(c+d*x^4)/(b*(b*c-a*d)*(a+b*x^4))],
[x^3/((a+b*x^4)^2*sqrt(c+d*x^4)),x,4,1/4*d*arctanh(sqrt(b)*sqrt(c+d*x^4)/sqrt(b*c-a*d))/((b*c-a*d)^(3/2)*sqrt(b))-1/4*sqrt(c+d*x^4)/((b*c-a*d)*(a+b*x^4))],
[1/(x*(a+b*x^4)^2*sqrt(c+d*x^4)),x,7,1/4*(2*b*c-3*a*d)*arctanh(sqrt(b)*sqrt(c+d*x^4)/sqrt(b*c-a*d))*sqrt(b)/(a^2*(b*c-a*d)^(3/2))-1/2*arctanh(sqrt(c+d*x^4)/sqrt(c))/(a^2*sqrt(c))+1/4*b*sqrt(c+d*x^4)/(a*(b*c-a*d)*(a+b*x^4))],
[1/(x^5*(a+b*x^4)^2*sqrt(c+d*x^4)),x,8,1/4*(4*b*c+a*d)*arctanh(sqrt(c+d*x^4)/sqrt(c))/(a^3*c^(3/2))-1/4*b^(3/2)*(4*b*c-5*a*d)*arctanh(sqrt(b)*sqrt(c+d*x^4)/sqrt(b*c-a*d))/(a^3*(b*c-a*d)^(3/2))-1/4*b*(2*b*c-a*d)*sqrt(c+d*x^4)/(a^2*c*(b*c-a*d)*(a+b*x^4))-1/4*sqrt(c+d*x^4)/(a*c*x^4*(a+b*x^4))],
[x^13/((a+b*x^4)^2*sqrt(c+d*x^4)),x,8,1/4*a^(3/2)*(5*b*c-4*a*d)*arctan(x^2*sqrt(b*c-a*d)/(sqrt(a)*sqrt(c+d*x^4)))/(b^3*(b*c-a*d)^(3/2))-1/4*(b*c+4*a*d)*arctanh(x^2*sqrt(d)/sqrt(c+d*x^4))/(b^3*d^(3/2))+1/4*(b*c-2*a*d)*x^2*sqrt(c+d*x^4)/(b^2*d*(b*c-a*d))+1/4*a*x^6*sqrt(c+d*x^4)/(b*(b*c-a*d)*(a+b*x^4))],
[x^9/((a+b*x^4)^2*sqrt(c+d*x^4)),x,7,-1/4*(3*b*c-2*a*d)*arctan(x^2*sqrt(b*c-a*d)/(sqrt(a)*sqrt(c+d*x^4)))*sqrt(a)/(b^2*(b*c-a*d)^(3/2))+1/2*arctanh(x^2*sqrt(d)/sqrt(c+d*x^4))/(b^2*sqrt(d))+1/4*a*x^2*sqrt(c+d*x^4)/(b*(b*c-a*d)*(a+b*x^4))],
[x^5/((a+b*x^4)^2*sqrt(c+d*x^4)),x,5,1/4*c*arctan(x^2*sqrt(b*c-a*d)/(sqrt(a)*sqrt(c+d*x^4)))/((b*c-a*d)^(3/2)*sqrt(a))-1/4*x^2*sqrt(c+d*x^4)/((b*c-a*d)*(a+b*x^4))],
[x/((a+b*x^4)^2*sqrt(c+d*x^4)),x,4,1/4*(b*c-2*a*d)*arctan(x^2*sqrt(b*c-a*d)/(sqrt(a)*sqrt(c+d*x^4)))/(a^(3/2)*(b*c-a*d)^(3/2))+1/4*b*x^2*sqrt(c+d*x^4)/(a*(b*c-a*d)*(a+b*x^4))],
[1/(x^3*(a+b*x^4)^2*sqrt(c+d*x^4)),x,6,-1/4*b*(3*b*c-4*a*d)*arctan(x^2*sqrt(b*c-a*d)/(sqrt(a)*sqrt(c+d*x^4)))/(a^(5/2)*(b*c-a*d)^(3/2))-1/4*(3*b*c-2*a*d)*sqrt(c+d*x^4)/(a^2*c*(b*c-a*d)*x^2)+1/4*b*sqrt(c+d*x^4)/(a*(b*c-a*d)*x^2*(a+b*x^4))],
[1/(x^7*(a+b*x^4)^2*sqrt(c+d*x^4)),x,7,1/4*b^2*(5*b*c-6*a*d)*arctan(x^2*sqrt(b*c-a*d)/(sqrt(a)*sqrt(c+d*x^4)))/(a^(7/2)*(b*c-a*d)^(3/2))-1/12*(5*b*c-2*a*d)*sqrt(c+d*x^4)/(a^2*c*(b*c-a*d)*x^6)+1/12*(15*b^2*c^2-8*a*b*c*d-4*a^2*d^2)*sqrt(c+d*x^4)/(a^3*c^2*(b*c-a*d)*x^2)+1/4*b*sqrt(c+d*x^4)/(a*(b*c-a*d)*x^6*(a+b*x^4))],
[x^8/((a+b*x^4)^2*sqrt(c+d*x^4)),x,10,-1/16*(-a)^(1/4)*(5*b*c-3*a*d)*arctan(x*sqrt(b*c-a*d)/((-a)^(1/4)*b^(1/4)*sqrt(c+d*x^4)))/(b^(7/4)*(b*c-a*d)^(3/2))+1/16*(-a)^(1/4)*(5*b*c-3*a*d)*arctan(x*sqrt(-b*c+a*d)/((-a)^(1/4)*b^(1/4)*sqrt(c+d*x^4)))/(b^(7/4)*(-b*c+a*d)^(3/2))+1/4*a*x*sqrt(c+d*x^4)/(b*(b*c-a*d)*(a+b*x^4))+1/8*(4*b*c-3*a*d)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(b^2*c^(1/4)*d^(1/4)*(b*c-a*d)*sqrt(c+d*x^4))-1/16*a*d^(1/4)*(5*b*c-3*a*d)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x/c^(1/4))),sqrt(1/2))*(sqrt(b)*sqrt(c)/sqrt(-a)+sqrt(d))*(sqrt(c)+x^2*sqrt(d))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(b^2*c^(1/4)*(b*c-a*d)*(b*c+a*d)*sqrt(c+d*x^4))-1/16*d^(1/4)*(5*b*c-3*a*d)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x/c^(1/4))),sqrt(1/2))*sqrt(-a)*(sqrt(c)+x^2*sqrt(d))*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(b^2*c^(1/4)*(b^2*c^2-a^2*d^2)*sqrt(c+d*x^4))-1/32*(5*b*c-3*a*d)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticPi(sin(2*arctan(d^(1/4)*x/c^(1/4))),1/4*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))^2/(sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))^2*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(b^2*c^(1/4)*d^(1/4)*(b^2*c^2-a^2*d^2)*sqrt(c+d*x^4))-1/32*(5*b*c-3*a*d)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticPi(sin(2*arctan(d^(1/4)*x/c^(1/4))),-1/4*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))^2/(sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))^2*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(b^2*c^(1/4)*d^(1/4)*(b^2*c^2-a^2*d^2)*sqrt(c+d*x^4))],
[x^4/((a+b*x^4)^2*sqrt(c+d*x^4)),x,10,-1/16*(b*c+a*d)*arctan(x*sqrt(b*c-a*d)/((-a)^(1/4)*b^(1/4)*sqrt(c+d*x^4)))/((-a)^(3/4)*b^(3/4)*(b*c-a*d)^(3/2))+1/16*(b*c+a*d)*arctan(x*sqrt(-b*c+a*d)/((-a)^(1/4)*b^(1/4)*sqrt(c+d*x^4)))/((-a)^(3/4)*b^(3/4)*(-b*c+a*d)^(3/2))-1/4*x*sqrt(c+d*x^4)/((b*c-a*d)*(a+b*x^4))-1/8*d^(3/4)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(b*c^(1/4)*(b*c-a*d)*sqrt(c+d*x^4))+1/16*d^(1/4)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x/c^(1/4))),sqrt(1/2))*(sqrt(b)*sqrt(c)/sqrt(-a)+sqrt(d))*(sqrt(c)+x^2*sqrt(d))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(b*c^(1/4)*(b*c-a*d)*sqrt(c+d*x^4))+1/16*d^(1/4)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x/c^(1/4))),sqrt(1/2))*(sqrt(-a)*sqrt(b)*sqrt(c)+a*sqrt(d))*(sqrt(c)+x^2*sqrt(d))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(a*b*c^(1/4)*(b*c-a*d)*sqrt(c+d*x^4))+1/32*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticPi(sin(2*arctan(d^(1/4)*x/c^(1/4))),1/4*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))^2/(sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))^2*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(a*b*c^(1/4)*d^(1/4)*(b*c-a*d)*sqrt(c+d*x^4))+1/32*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticPi(sin(2*arctan(d^(1/4)*x/c^(1/4))),-1/4*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))^2/(sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))^2*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(a*b*c^(1/4)*d^(1/4)*(b*c-a*d)*sqrt(c+d*x^4))],
[1/((a+b*x^4)^2*sqrt(c+d*x^4)),x,10,1/16*b^(1/4)*(3*b*c-5*a*d)*arctan(x*sqrt(b*c-a*d)/((-a)^(1/4)*b^(1/4)*sqrt(c+d*x^4)))/((-a)^(7/4)*(b*c-a*d)^(3/2))-1/16*b^(1/4)*(3*b*c-5*a*d)*arctan(x*sqrt(-b*c+a*d)/((-a)^(1/4)*b^(1/4)*sqrt(c+d*x^4)))/((-a)^(7/4)*(-b*c+a*d)^(3/2))+1/4*b*x*sqrt(c+d*x^4)/(a*(b*c-a*d)*(a+b*x^4))+1/8*d^(3/4)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(a*c^(1/4)*(b*c-a*d)*sqrt(c+d*x^4))+1/16*d^(1/4)*(3*b*c-5*a*d)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x/c^(1/4))),sqrt(1/2))*(sqrt(b)*sqrt(c)/sqrt(-a)+sqrt(d))*(sqrt(c)+x^2*sqrt(d))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(a*c^(1/4)*(b*c-a*d)*(b*c+a*d)*sqrt(c+d*x^4))+1/16*d^(1/4)*(3*b*c-5*a*d)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/((-a)^(3/2)*c^(1/4)*(b*c-a*d)*(b*c+a*d)*sqrt(c+d*x^4))+1/32*(3*b*c-5*a*d)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticPi(sin(2*arctan(d^(1/4)*x/c^(1/4))),1/4*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))^2/(sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))^2*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(a^2*c^(1/4)*d^(1/4)*(b^2*c^2-a^2*d^2)*sqrt(c+d*x^4))+1/32*(3*b*c-5*a*d)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticPi(sin(2*arctan(d^(1/4)*x/c^(1/4))),-1/4*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))^2/(sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))^2*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(a^2*c^(1/4)*d^(1/4)*(b^2*c^2-a^2*d^2)*sqrt(c+d*x^4))],
[1/(x^4*(a+b*x^4)^2*sqrt(c+d*x^4)),x,11,1/16*b^(5/4)*(7*b*c-9*a*d)*arctan(x*sqrt(b*c-a*d)/((-a)^(1/4)*b^(1/4)*sqrt(c+d*x^4)))/((-a)^(11/4)*(b*c-a*d)^(3/2))-1/16*b^(5/4)*(7*b*c-9*a*d)*arctan(x*sqrt(-b*c+a*d)/((-a)^(1/4)*b^(1/4)*sqrt(c+d*x^4)))/((-a)^(11/4)*(-b*c+a*d)^(3/2))-1/12*(7*b*c-4*a*d)*sqrt(c+d*x^4)/(a^2*c*(b*c-a*d)*x^3)+1/4*b*sqrt(c+d*x^4)/(a*(b*c-a*d)*x^3*(a+b*x^4))-1/24*d^(3/4)*(7*b*c-4*a*d)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(a^2*c^(5/4)*(b*c-a*d)*sqrt(c+d*x^4))+1/16*b*d^(1/4)*(7*b*c-9*a*d)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/((-a)^(5/2)*c^(1/4)*(b*c-a*d)*(b*c+a*d)*sqrt(c+d*x^4))-1/32*b*(7*b*c-9*a*d)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticPi(sin(2*arctan(d^(1/4)*x/c^(1/4))),1/4*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))^2/(sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))^2*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(a^3*c^(1/4)*d^(1/4)*(b^2*c^2-a^2*d^2)*sqrt(c+d*x^4))-1/16*b*d^(1/4)*(7*b*c-9*a*d)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/((-a)^(5/2)*c^(1/4)*(b*c-a*d)*(b*c+a*d)*sqrt(c+d*x^4))-1/32*b*(7*b*c-9*a*d)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticPi(sin(2*arctan(d^(1/4)*x/c^(1/4))),-1/4*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))^2/(sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))^2*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(a^3*c^(1/4)*d^(1/4)*(b^2*c^2-a^2*d^2)*sqrt(c+d*x^4))],
[x^6/((a+b*x^4)^2*sqrt(c+d*x^4)),x,13,1/16*(3*b*c-a*d)*arctan(x*sqrt(b*c-a*d)/((-a)^(1/4)*b^(1/4)*sqrt(c+d*x^4)))/((-a)^(1/4)*b^(5/4)*(b*c-a*d)^(3/2))+1/16*(3*b*c-a*d)*arctan(x*sqrt(-b*c+a*d)/((-a)^(1/4)*b^(1/4)*sqrt(c+d*x^4)))/((-a)^(1/4)*b^(5/4)*(-b*c+a*d)^(3/2))-1/4*x^3*sqrt(c+d*x^4)/((b*c-a*d)*(a+b*x^4))+1/4*x*sqrt(d)*sqrt(c+d*x^4)/(b*(b*c-a*d)*(sqrt(c)+x^2*sqrt(d)))-1/4*c^(1/4)*d^(1/4)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticE(sin(2*arctan(d^(1/4)*x/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(b*(b*c-a*d)*sqrt(c+d*x^4))+1/8*c^(1/4)*d^(1/4)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(b*(b*c-a*d)*sqrt(c+d*x^4))-1/16*d^(1/4)*(3*b*c-a*d)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(b^(3/2)*c^(1/4)*(b^2*c^2-a^2*d^2)*sqrt(c+d*x^4))-1/32*(3*b*c-a*d)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticPi(sin(2*arctan(d^(1/4)*x/c^(1/4))),1/4*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))^2/(sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))^2*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(b^(3/2)*c^(1/4)*d^(1/4)*(b*c-a*d)*(b*c+a*d)*sqrt(-a)*sqrt(c+d*x^4))-1/16*d^(1/4)*(3*b*c-a*d)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(b^(3/2)*c^(1/4)*(b^2*c^2-a^2*d^2)*sqrt(c+d*x^4))+1/32*(3*b*c-a*d)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticPi(sin(2*arctan(d^(1/4)*x/c^(1/4))),-1/4*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))^2/(sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))^2*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(b^(3/2)*c^(1/4)*d^(1/4)*(b*c-a*d)*(b*c+a*d)*sqrt(-a)*sqrt(c+d*x^4))],
[x^2/((a+b*x^4)^2*sqrt(c+d*x^4)),x,13,-1/16*(b*c-3*a*d)*arctan(x*sqrt(b*c-a*d)/((-a)^(1/4)*b^(1/4)*sqrt(c+d*x^4)))/((-a)^(5/4)*b^(1/4)*(b*c-a*d)^(3/2))-1/16*(b*c-3*a*d)*arctan(x*sqrt(-b*c+a*d)/((-a)^(1/4)*b^(1/4)*sqrt(c+d*x^4)))/((-a)^(5/4)*b^(1/4)*(-b*c+a*d)^(3/2))+1/4*b*x^3*sqrt(c+d*x^4)/(a*(b*c-a*d)*(a+b*x^4))-1/4*x*sqrt(d)*sqrt(c+d*x^4)/(a*(b*c-a*d)*(sqrt(c)+x^2*sqrt(d)))+1/4*c^(1/4)*d^(1/4)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticE(sin(2*arctan(d^(1/4)*x/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(a*(b*c-a*d)*sqrt(c+d*x^4))-1/8*c^(1/4)*d^(1/4)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(a*(b*c-a*d)*sqrt(c+d*x^4))+1/32*(b*c-3*a*d)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticPi(sin(2*arctan(d^(1/4)*x/c^(1/4))),1/4*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))^2/(sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))^2*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/((-a)^(3/2)*c^(1/4)*d^(1/4)*(b*c-a*d)*(b*c+a*d)*sqrt(b)*sqrt(c+d*x^4))-1/32*(b*c-3*a*d)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticPi(sin(2*arctan(d^(1/4)*x/c^(1/4))),-1/4*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))^2/(sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))^2*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/((-a)^(3/2)*c^(1/4)*d^(1/4)*(b*c-a*d)*(b*c+a*d)*sqrt(b)*sqrt(c+d*x^4))-1/16*d^(1/4)*(b*c-3*a*d)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*(sqrt(c)-sqrt(-a)*sqrt(d)/sqrt(b))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(a*c^(1/4)*(b*c-a*d)*(b*c+a*d)*sqrt(c+d*x^4))-1/16*d^(1/4)*(b*c-3*a*d)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*(sqrt(c)+sqrt(-a)*sqrt(d)/sqrt(b))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(a*c^(1/4)*(b*c-a*d)*(b*c+a*d)*sqrt(c+d*x^4))],
[1/(x^2*(a+b*x^4)^2*sqrt(c+d*x^4)),x,14,-1/16*b^(3/4)*(5*b*c-7*a*d)*arctan(x*sqrt(b*c-a*d)/((-a)^(1/4)*b^(1/4)*sqrt(c+d*x^4)))/((-a)^(9/4)*(b*c-a*d)^(3/2))-1/16*b^(3/4)*(5*b*c-7*a*d)*arctan(x*sqrt(-b*c+a*d)/((-a)^(1/4)*b^(1/4)*sqrt(c+d*x^4)))/((-a)^(9/4)*(-b*c+a*d)^(3/2))-1/4*(5*b*c-4*a*d)*sqrt(c+d*x^4)/(a^2*c*(b*c-a*d)*x)+1/4*b*sqrt(c+d*x^4)/(a*(b*c-a*d)*x*(a+b*x^4))+1/4*(5*b*c-4*a*d)*x*sqrt(d)*sqrt(c+d*x^4)/(a^2*c*(b*c-a*d)*(sqrt(c)+x^2*sqrt(d)))-1/4*d^(1/4)*(5*b*c-4*a*d)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticE(sin(2*arctan(d^(1/4)*x/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(a^2*c^(3/4)*(b*c-a*d)*sqrt(c+d*x^4))+1/8*d^(1/4)*(5*b*c-4*a*d)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(a^2*c^(3/4)*(b*c-a*d)*sqrt(c+d*x^4))+1/32*(5*b*c-7*a*d)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticPi(sin(2*arctan(d^(1/4)*x/c^(1/4))),1/4*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))^2/(sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)),sqrt(1/2))*sqrt(b)*(sqrt(c)+x^2*sqrt(d))*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))^2*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/((-a)^(5/2)*c^(1/4)*d^(1/4)*(b*c-a*d)*(b*c+a*d)*sqrt(c+d*x^4))-1/32*(5*b*c-7*a*d)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticPi(sin(2*arctan(d^(1/4)*x/c^(1/4))),-1/4*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))^2/(sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)),sqrt(1/2))*sqrt(b)*(sqrt(c)+x^2*sqrt(d))*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))^2*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/((-a)^(5/2)*c^(1/4)*d^(1/4)*(b*c-a*d)*(b*c+a*d)*sqrt(c+d*x^4))+1/16*b*d^(1/4)*(5*b*c-7*a*d)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*(sqrt(c)-sqrt(-a)*sqrt(d)/sqrt(b))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(a^2*c^(1/4)*(b*c-a*d)*(b*c+a*d)*sqrt(c+d*x^4))+1/16*b*d^(1/4)*(5*b*c-7*a*d)*sqrt(cos(2*arctan(d^(1/4)*x/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^2*sqrt(d))*(sqrt(c)+sqrt(-a)*sqrt(d)/sqrt(b))*sqrt((c+d*x^4)/(sqrt(c)+x^2*sqrt(d))^2)/(a^2*c^(1/4)*(b*c-a*d)*(b*c+a*d)*sqrt(c+d*x^4))],

# Integrands of the form (e x)^m (a+b x^4)^p (c+d x^4)^(q/2) with m symbolic

# q>0

# q<0
[(e*x)^m*(a+b*x^4)^2/sqrt(c+d*x^4),x,4,-b*(b*c*(5+m)-2*a*d*(7+m))*(e*x)^(1+m)*sqrt(c+d*x^4)/(d^2*e*(3+m)*(7+m))+b^2*(e*x)^(5+m)*sqrt(c+d*x^4)/(d*e^5*(7+m))+(a^2*d^2*(3+m)*(7+m)+b*c*(1+m)*(b*c*(5+m)-2*a*d*(7+m)))*(e*x)^(1+m)*hypergeom([1/2,1/4*(1+m)],[1/4*(5+m)],-d*x^4/c)*sqrt(1+d*x^4/c)/(d^2*e*(1+m)*(3+m)*(7+m)*sqrt(c+d*x^4))],
[(e*x)^m*(a+b*x^4)/sqrt(c+d*x^4),x,3,b*(e*x)^(1+m)*sqrt(c+d*x^4)/(d*e*(3+m))-(b*c*(1+m)-a*d*(3+m))*(e*x)^(1+m)*hypergeom([1/2,1/4*(1+m)],[1/4*(5+m)],-d*x^4/c)*sqrt(1+d*x^4/c)/(d*e*(1+m)*(3+m)*sqrt(c+d*x^4))],
[(e*x)^m/sqrt(c+d*x^4),x,2,(e*x)^(1+m)*hypergeom([1/2,1/4*(1+m)],[1/4*(5+m)],-d*x^4/c)*sqrt(1+d*x^4/c)/(e*(1+m)*sqrt(c+d*x^4))],
[(e*x)^m/((a+b*x^4)*sqrt(c+d*x^4)),x,2,(e*x)^(1+m)*AppellF1(1/4*(1+m),1,1/2,1/4*(5+m),-b*x^4/a,-d*x^4/c)*sqrt(1+d*x^4/c)/(a*e*(1+m)*sqrt(c+d*x^4))],
[(e*x)^m/((a+b*x^4)^2*sqrt(c+d*x^4)),x,2,(e*x)^(1+m)*AppellF1(1/4*(1+m),2,1/2,1/4*(5+m),-b*x^4/a,-d*x^4/c)*sqrt(1+d*x^4/c)/(a^2*e*(1+m)*sqrt(c+d*x^4))],
[(e*x)^m/((a+b*x^4)^3*sqrt(c+d*x^4)),x,2,(e*x)^(1+m)*AppellF1(1/4*(1+m),3,1/2,1/4*(5+m),-b*x^4/a,-d*x^4/c)*sqrt(1+d*x^4/c)/(a^3*e*(1+m)*sqrt(c+d*x^4))],
[(e*x)^m*(a+b*x^4)^2/(c+d*x^4)^(3/2),x,4,1/2*(b*c-a*d)^2*(e*x)^(1+m)/(c*d^2*e*sqrt(c+d*x^4))+b^2*(e*x)^(1+m)*sqrt(c+d*x^4)/(d^2*e*(3+m))-1/2*(2*b^2*c^2*(1+m)-(3+m)*(2*a^2*d^2-(b*c-a*d)^2*(1+m)))*(e*x)^(1+m)*hypergeom([1/2,1/4*(1+m)],[1/4*(5+m)],-d*x^4/c)*sqrt(1+d*x^4/c)/(c*d^2*e*(1+m)*(3+m)*sqrt(c+d*x^4))],
[(e*x)^m*(a+b*x^4)/(c+d*x^4)^(3/2),x,3,-1/2*(b*c-a*d)*(e*x)^(1+m)/(c*d*e*sqrt(c+d*x^4))+1/2*(a*d*(1-m)+b*c*(1+m))*(e*x)^(1+m)*hypergeom([1/2,1/4*(1+m)],[1/4*(5+m)],-d*x^4/c)*sqrt(1+d*x^4/c)/(c*d*e*(1+m)*sqrt(c+d*x^4))],
[(e*x)^m/(c+d*x^4)^(3/2),x,2,(e*x)^(1+m)*hypergeom([3/2,1/4*(1+m)],[1/4*(5+m)],-d*x^4/c)*sqrt(1+d*x^4/c)/(c*e*(1+m)*sqrt(c+d*x^4))],
[(e*x)^m/((a+b*x^4)*(c+d*x^4)^(3/2)),x,2,(e*x)^(1+m)*AppellF1(1/4*(1+m),1,3/2,1/4*(5+m),-b*x^4/a,-d*x^4/c)*sqrt(1+d*x^4/c)/(a*c*e*(1+m)*sqrt(c+d*x^4))],
[(e*x)^m/((a+b*x^4)^2*(c+d*x^4)^(3/2)),x,2,(e*x)^(1+m)*AppellF1(1/4*(1+m),2,3/2,1/4*(5+m),-b*x^4/a,-d*x^4/c)*sqrt(1+d*x^4/c)/(a^2*c*e*(1+m)*sqrt(c+d*x^4))],
[(e*x)^m/((a+b*x^4)^3*(c+d*x^4)^(3/2)),x,2,(e*x)^(1+m)*AppellF1(1/4*(1+m),3,3/2,1/4*(5+m),-b*x^4/a,-d*x^4/c)*sqrt(1+d*x^4/c)/(a^3*c*e*(1+m)*sqrt(c+d*x^4))],

# Integrands of the form (e x)^m (a+b x^6)^p (c+d x^6)^q

# Integrands of the form (e x)^m (a+b x^6)^p (c+d x^6)^(q/2)

# Integrands of the form x^m (a+b x^6)^p (c+d x^6)^(1/2)

# Integrands of the form x^m (a+b x^6)^p / (c+d x^6)^(1/2)

# p>0

# p<0
[x^17/((a+b*x^6)*sqrt(c+d*x^6)),x,5,1/9*(c+d*x^6)^(3/2)/(b*d^2)-1/3*a^2*arctanh(sqrt(b)*sqrt(c+d*x^6)/sqrt(b*c-a*d))/(b^(5/2)*sqrt(b*c-a*d))-1/3*(b*c+a*d)*sqrt(c+d*x^6)/(b^2*d^2)],
[x^11/((a+b*x^6)*sqrt(c+d*x^6)),x,4,1/3*a*arctanh(sqrt(b)*sqrt(c+d*x^6)/sqrt(b*c-a*d))/(b^(3/2)*sqrt(b*c-a*d))+1/3*sqrt(c+d*x^6)/(b*d)],
[x^5/((a+b*x^6)*sqrt(c+d*x^6)),x,3,-1/3*arctanh(sqrt(b)*sqrt(c+d*x^6)/sqrt(b*c-a*d))/(sqrt(b)*sqrt(b*c-a*d))],
[1/(x*(a+b*x^6)*sqrt(c+d*x^6)),x,6,-1/3*arctanh(sqrt(c+d*x^6)/sqrt(c))/(a*sqrt(c))+1/3*arctanh(sqrt(b)*sqrt(c+d*x^6)/sqrt(b*c-a*d))*sqrt(b)/(a*sqrt(b*c-a*d))],
[1/(x^7*(a+b*x^6)*sqrt(c+d*x^6)),x,7,1/6*(2*b*c+a*d)*arctanh(sqrt(c+d*x^6)/sqrt(c))/(a^2*c^(3/2))-1/3*b^(3/2)*arctanh(sqrt(b)*sqrt(c+d*x^6)/sqrt(b*c-a*d))/(a^2*sqrt(b*c-a*d))-1/6*sqrt(c+d*x^6)/(a*c*x^6)],
[x^14/((a+b*x^6)*sqrt(c+d*x^6)),x,7,-1/6*(b*c+2*a*d)*arctanh(x^3*sqrt(d)/sqrt(c+d*x^6))/(b^2*d^(3/2))+1/3*a^(3/2)*arctan(x^3*sqrt(b*c-a*d)/(sqrt(a)*sqrt(c+d*x^6)))/(b^2*sqrt(b*c-a*d))+1/6*x^3*sqrt(c+d*x^6)/(b*d)],
[x^8/((a+b*x^6)*sqrt(c+d*x^6)),x,6,1/3*arctanh(x^3*sqrt(d)/sqrt(c+d*x^6))/(b*sqrt(d))-1/3*arctan(x^3*sqrt(b*c-a*d)/(sqrt(a)*sqrt(c+d*x^6)))*sqrt(a)/(b*sqrt(b*c-a*d))],
[x^2/((a+b*x^6)*sqrt(c+d*x^6)),x,3,1/3*arctan(x^3*sqrt(b*c-a*d)/(sqrt(a)*sqrt(c+d*x^6)))/(sqrt(a)*sqrt(b*c-a*d))],
[1/(x^4*(a+b*x^6)*sqrt(c+d*x^6)),x,5,-1/3*b*arctan(x^3*sqrt(b*c-a*d)/(sqrt(a)*sqrt(c+d*x^6)))/(a^(3/2)*sqrt(b*c-a*d))-1/3*sqrt(c+d*x^6)/(a*c*x^3)],
[1/(x^10*(a+b*x^6)*sqrt(c+d*x^6)),x,6,1/3*b^2*arctan(x^3*sqrt(b*c-a*d)/(sqrt(a)*sqrt(c+d*x^6)))/(a^(5/2)*sqrt(b*c-a*d))-1/9*sqrt(c+d*x^6)/(a*c*x^9)+1/9*(3*b*c+2*a*d)*sqrt(c+d*x^6)/(a^2*c^2*x^3)],
[x^4/((a+b*x^6)*sqrt(c+d*x^6)),x,2,1/5*x^5*AppellF1(5/6,1,1/2,11/6,-b*x^6/a,-d*x^6/c)*sqrt(1+d*x^6/c)/(a*sqrt(c+d*x^6))],
[x^3/((a+b*x^6)*sqrt(c+d*x^6)),x,3,1/4*x^4*AppellF1(2/3,1,1/2,5/3,-b*x^6/a,-d*x^6/c)*sqrt(1+d*x^6/c)/(a*sqrt(c+d*x^6))],
[x/((a+b*x^6)*sqrt(c+d*x^6)),x,3,1/2*x^2*AppellF1(1/3,1,1/2,4/3,-b*x^6/a,-d*x^6/c)*sqrt(1+d*x^6/c)/(a*sqrt(c+d*x^6))],
[1/((a+b*x^6)*sqrt(c+d*x^6)),x,2,x*AppellF1(1/6,1,1/2,7/6,-b*x^6/a,-d*x^6/c)*sqrt(1+d*x^6/c)/(a*sqrt(c+d*x^6))],
[1/(x^2*(a+b*x^6)*sqrt(c+d*x^6)),x,2,-AppellF1(-1/6,1,1/2,5/6,-b*x^6/a,-d*x^6/c)*sqrt(1+d*x^6/c)/(a*x*sqrt(c+d*x^6))],
[1/(x^3*(a+b*x^6)*sqrt(c+d*x^6)),x,3,-1/2*AppellF1(-1/3,1,1/2,2/3,-b*x^6/a,-d*x^6/c)*sqrt(1+d*x^6/c)/(a*x^2*sqrt(c+d*x^6))],
[1/(x^5*(a+b*x^6)*sqrt(c+d*x^6)),x,3,-1/4*AppellF1(-2/3,1,1/2,1/3,-b*x^6/a,-d*x^6/c)*sqrt(1+d*x^6/c)/(a*x^4*sqrt(c+d*x^6))],
[x^17/((a+b*x^6)^2*sqrt(c+d*x^6)),x,5,1/6*a*(4*b*c-3*a*d)*arctanh(sqrt(b)*sqrt(c+d*x^6)/sqrt(b*c-a*d))/(b^(5/2)*(b*c-a*d)^(3/2))+1/3*sqrt(c+d*x^6)/(b^2*d)-1/6*a^2*sqrt(c+d*x^6)/(b^2*(b*c-a*d)*(a+b*x^6))],
[x^11/((a+b*x^6)^2*sqrt(c+d*x^6)),x,4,-1/6*(2*b*c-a*d)*arctanh(sqrt(b)*sqrt(c+d*x^6)/sqrt(b*c-a*d))/(b^(3/2)*(b*c-a*d)^(3/2))+1/6*a*sqrt(c+d*x^6)/(b*(b*c-a*d)*(a+b*x^6))],
[x^5/((a+b*x^6)^2*sqrt(c+d*x^6)),x,4,1/6*d*arctanh(sqrt(b)*sqrt(c+d*x^6)/sqrt(b*c-a*d))/((b*c-a*d)^(3/2)*sqrt(b))-1/6*sqrt(c+d*x^6)/((b*c-a*d)*(a+b*x^6))],
[1/(x*(a+b*x^6)^2*sqrt(c+d*x^6)),x,7,1/6*(2*b*c-3*a*d)*arctanh(sqrt(b)*sqrt(c+d*x^6)/sqrt(b*c-a*d))*sqrt(b)/(a^2*(b*c-a*d)^(3/2))-1/3*arctanh(sqrt(c+d*x^6)/sqrt(c))/(a^2*sqrt(c))+1/6*b*sqrt(c+d*x^6)/(a*(b*c-a*d)*(a+b*x^6))],
[1/(x^7*(a+b*x^6)^2*sqrt(c+d*x^6)),x,8,1/6*(4*b*c+a*d)*arctanh(sqrt(c+d*x^6)/sqrt(c))/(a^3*c^(3/2))-1/6*b^(3/2)*(4*b*c-5*a*d)*arctanh(sqrt(b)*sqrt(c+d*x^6)/sqrt(b*c-a*d))/(a^3*(b*c-a*d)^(3/2))-1/6*b*(2*b*c-a*d)*sqrt(c+d*x^6)/(a^2*c*(b*c-a*d)*(a+b*x^6))-1/6*sqrt(c+d*x^6)/(a*c*x^6*(a+b*x^6))],
[x^14/((a+b*x^6)^2*sqrt(c+d*x^6)),x,7,-1/6*(3*b*c-2*a*d)*arctan(x^3*sqrt(b*c-a*d)/(sqrt(a)*sqrt(c+d*x^6)))*sqrt(a)/(b^2*(b*c-a*d)^(3/2))+1/3*arctanh(x^3*sqrt(d)/sqrt(c+d*x^6))/(b^2*sqrt(d))+1/6*a*x^3*sqrt(c+d*x^6)/(b*(b*c-a*d)*(a+b*x^6))],
[x^8/((a+b*x^6)^2*sqrt(c+d*x^6)),x,5,1/6*c*arctan(x^3*sqrt(b*c-a*d)/(sqrt(a)*sqrt(c+d*x^6)))/((b*c-a*d)^(3/2)*sqrt(a))-1/6*x^3*sqrt(c+d*x^6)/((b*c-a*d)*(a+b*x^6))],
[x^2/((a+b*x^6)^2*sqrt(c+d*x^6)),x,4,1/6*(b*c-2*a*d)*arctan(x^3*sqrt(b*c-a*d)/(sqrt(a)*sqrt(c+d*x^6)))/(a^(3/2)*(b*c-a*d)^(3/2))+1/6*b*x^3*sqrt(c+d*x^6)/(a*(b*c-a*d)*(a+b*x^6))],
[1/(x^4*(a+b*x^6)^2*sqrt(c+d*x^6)),x,6,-1/6*b*(3*b*c-4*a*d)*arctan(x^3*sqrt(b*c-a*d)/(sqrt(a)*sqrt(c+d*x^6)))/(a^(5/2)*(b*c-a*d)^(3/2))-1/6*(3*b*c-2*a*d)*sqrt(c+d*x^6)/(a^2*c*(b*c-a*d)*x^3)+1/6*b*sqrt(c+d*x^6)/(a*(b*c-a*d)*x^3*(a+b*x^6))],
[1/(x^10*(a+b*x^6)^2*sqrt(c+d*x^6)),x,7,1/6*b^2*(5*b*c-6*a*d)*arctan(x^3*sqrt(b*c-a*d)/(sqrt(a)*sqrt(c+d*x^6)))/(a^(7/2)*(b*c-a*d)^(3/2))-1/18*(5*b*c-2*a*d)*sqrt(c+d*x^6)/(a^2*c*(b*c-a*d)*x^9)+1/18*(15*b^2*c^2-8*a*b*c*d-4*a^2*d^2)*sqrt(c+d*x^6)/(a^3*c^2*(b*c-a*d)*x^3)+1/6*b*sqrt(c+d*x^6)/(a*(b*c-a*d)*x^9*(a+b*x^6))],
[x^4/((a+b*x^6)^2*sqrt(c+d*x^6)),x,2,1/5*x^5*AppellF1(5/6,2,1/2,11/6,-b*x^6/a,-d*x^6/c)*sqrt(1+d*x^6/c)/(a^2*sqrt(c+d*x^6))],
[x^3/((a+b*x^6)^2*sqrt(c+d*x^6)),x,3,1/4*x^4*AppellF1(2/3,2,1/2,5/3,-b*x^6/a,-d*x^6/c)*sqrt(1+d*x^6/c)/(a^2*sqrt(c+d*x^6))],
[x/((a+b*x^6)^2*sqrt(c+d*x^6)),x,3,1/2*x^2*AppellF1(1/3,2,1/2,4/3,-b*x^6/a,-d*x^6/c)*sqrt(1+d*x^6/c)/(a^2*sqrt(c+d*x^6))],
[1/((a+b*x^6)^2*sqrt(c+d*x^6)),x,2,x*AppellF1(1/6,2,1/2,7/6,-b*x^6/a,-d*x^6/c)*sqrt(1+d*x^6/c)/(a^2*sqrt(c+d*x^6))],
[1/(x^2*(a+b*x^6)^2*sqrt(c+d*x^6)),x,2,-AppellF1(-1/6,2,1/2,5/6,-b*x^6/a,-d*x^6/c)*sqrt(1+d*x^6/c)/(a^2*x*sqrt(c+d*x^6))],
[1/(x^3*(a+b*x^6)^2*sqrt(c+d*x^6)),x,3,-1/2*AppellF1(-1/3,2,1/2,2/3,-b*x^6/a,-d*x^6/c)*sqrt(1+d*x^6/c)/(a^2*x^2*sqrt(c+d*x^6))],
[1/(x^5*(a+b*x^6)^2*sqrt(c+d*x^6)),x,3,-1/4*AppellF1(-2/3,2,1/2,1/3,-b*x^6/a,-d*x^6/c)*sqrt(1+d*x^6/c)/(a^2*x^4*sqrt(c+d*x^6))],

# Integrands of the form (e x)^m (a+b x^8)^p (c+d x^8)^q

# Integrands of the form (e x)^m (a+b x^8)^p (c+d x^8)^(q/2)

# Integrands of the form (e x)^m (a+b x^8)^p (c+d x^8)^(1/2)

# Integrands of the form (e x)^m (a+b x^8)^p / (c+d x^8)^(1/2)

# p>0

# p<0
[x^23/((a+b*x^8)*sqrt(c+d*x^8)),x,5,1/12*(c+d*x^8)^(3/2)/(b*d^2)-1/4*a^2*arctanh(sqrt(b)*sqrt(c+d*x^8)/sqrt(b*c-a*d))/(b^(5/2)*sqrt(b*c-a*d))-1/4*(b*c+a*d)*sqrt(c+d*x^8)/(b^2*d^2)],
[x^15/((a+b*x^8)*sqrt(c+d*x^8)),x,4,1/4*a*arctanh(sqrt(b)*sqrt(c+d*x^8)/sqrt(b*c-a*d))/(b^(3/2)*sqrt(b*c-a*d))+1/4*sqrt(c+d*x^8)/(b*d)],
[x^7/((a+b*x^8)*sqrt(c+d*x^8)),x,3,-1/4*arctanh(sqrt(b)*sqrt(c+d*x^8)/sqrt(b*c-a*d))/(sqrt(b)*sqrt(b*c-a*d))],
[1/(x*(a+b*x^8)*sqrt(c+d*x^8)),x,6,-1/4*arctanh(sqrt(c+d*x^8)/sqrt(c))/(a*sqrt(c))+1/4*arctanh(sqrt(b)*sqrt(c+d*x^8)/sqrt(b*c-a*d))*sqrt(b)/(a*sqrt(b*c-a*d))],
[1/(x^9*(a+b*x^8)*sqrt(c+d*x^8)),x,7,1/8*(2*b*c+a*d)*arctanh(sqrt(c+d*x^8)/sqrt(c))/(a^2*c^(3/2))-1/4*b^(3/2)*arctanh(sqrt(b)*sqrt(c+d*x^8)/sqrt(b*c-a*d))/(a^2*sqrt(b*c-a*d))-1/8*sqrt(c+d*x^8)/(a*c*x^8)],
[x^19/((a+b*x^8)*sqrt(c+d*x^8)),x,7,-1/8*(b*c+2*a*d)*arctanh(x^4*sqrt(d)/sqrt(c+d*x^8))/(b^2*d^(3/2))+1/4*a^(3/2)*arctan(x^4*sqrt(b*c-a*d)/(sqrt(a)*sqrt(c+d*x^8)))/(b^2*sqrt(b*c-a*d))+1/8*x^4*sqrt(c+d*x^8)/(b*d)],
[x^11/((a+b*x^8)*sqrt(c+d*x^8)),x,6,1/4*arctanh(x^4*sqrt(d)/sqrt(c+d*x^8))/(b*sqrt(d))-1/4*arctan(x^4*sqrt(b*c-a*d)/(sqrt(a)*sqrt(c+d*x^8)))*sqrt(a)/(b*sqrt(b*c-a*d))],
[x^3/((a+b*x^8)*sqrt(c+d*x^8)),x,3,1/4*arctan(x^4*sqrt(b*c-a*d)/(sqrt(a)*sqrt(c+d*x^8)))/(sqrt(a)*sqrt(b*c-a*d))],
[1/(x^5*(a+b*x^8)*sqrt(c+d*x^8)),x,5,-1/4*b*arctan(x^4*sqrt(b*c-a*d)/(sqrt(a)*sqrt(c+d*x^8)))/(a^(3/2)*sqrt(b*c-a*d))-1/4*sqrt(c+d*x^8)/(a*c*x^4)],
[1/(x^13*(a+b*x^8)*sqrt(c+d*x^8)),x,6,1/4*b^2*arctan(x^4*sqrt(b*c-a*d)/(sqrt(a)*sqrt(c+d*x^8)))/(a^(5/2)*sqrt(b*c-a*d))-1/12*sqrt(c+d*x^8)/(a*c*x^12)+1/12*(3*b*c+2*a*d)*sqrt(c+d*x^8)/(a^2*c^2*x^4)],
[x^9/((a+b*x^8)*sqrt(c+d*x^8)),x,10,-1/8*(-a)^(1/4)*arctan(x^2*sqrt(b*c-a*d)/((-a)^(1/4)*b^(1/4)*sqrt(c+d*x^8)))/(b^(3/4)*sqrt(b*c-a*d))-1/8*(-a)^(1/4)*arctan(x^2*sqrt(-b*c+a*d)/((-a)^(1/4)*b^(1/4)*sqrt(c+d*x^8)))/(b^(3/4)*sqrt(-b*c+a*d))+1/4*sqrt(cos(2*arctan(d^(1/4)*x^2/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x^2/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x^2/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^4*sqrt(d))*sqrt((c+d*x^8)/(sqrt(c)+x^4*sqrt(d))^2)/(b*c^(1/4)*d^(1/4)*sqrt(c+d*x^8))-1/8*a*d^(1/4)*sqrt(cos(2*arctan(d^(1/4)*x^2/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x^2/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x^2/c^(1/4))),sqrt(1/2))*(sqrt(b)*sqrt(c)/sqrt(-a)+sqrt(d))*(sqrt(c)+x^4*sqrt(d))*sqrt((c+d*x^8)/(sqrt(c)+x^4*sqrt(d))^2)/(b*c^(1/4)*(b*c+a*d)*sqrt(c+d*x^8))-1/8*d^(1/4)*sqrt(cos(2*arctan(d^(1/4)*x^2/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x^2/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x^2/c^(1/4))),sqrt(1/2))*(sqrt(-a)*sqrt(b)*sqrt(c)+a*sqrt(d))*(sqrt(c)+x^4*sqrt(d))*sqrt((c+d*x^8)/(sqrt(c)+x^4*sqrt(d))^2)/(b*c^(1/4)*(b*c+a*d)*sqrt(c+d*x^8))-1/16*sqrt(cos(2*arctan(d^(1/4)*x^2/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x^2/c^(1/4)))*EllipticPi(sin(2*arctan(d^(1/4)*x^2/c^(1/4))),1/4*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))^2/(sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)),sqrt(1/2))*(sqrt(c)+x^4*sqrt(d))*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))^2*sqrt((c+d*x^8)/(sqrt(c)+x^4*sqrt(d))^2)/(b*c^(1/4)*d^(1/4)*(b*c+a*d)*sqrt(c+d*x^8))-1/16*sqrt(cos(2*arctan(d^(1/4)*x^2/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x^2/c^(1/4)))*EllipticPi(sin(2*arctan(d^(1/4)*x^2/c^(1/4))),-1/4*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))^2/(sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)),sqrt(1/2))*(sqrt(c)+x^4*sqrt(d))*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))^2*sqrt((c+d*x^8)/(sqrt(c)+x^4*sqrt(d))^2)/(b*c^(1/4)*d^(1/4)*(b*c+a*d)*sqrt(c+d*x^8))],
[x/((a+b*x^8)*sqrt(c+d*x^8)),x,8,-1/8*b^(1/4)*arctan(x^2*sqrt(b*c-a*d)/((-a)^(1/4)*b^(1/4)*sqrt(c+d*x^8)))/((-a)^(3/4)*sqrt(b*c-a*d))-1/8*b^(1/4)*arctan(x^2*sqrt(-b*c+a*d)/((-a)^(1/4)*b^(1/4)*sqrt(c+d*x^8)))/((-a)^(3/4)*sqrt(-b*c+a*d))+1/8*d^(1/4)*sqrt(cos(2*arctan(d^(1/4)*x^2/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x^2/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x^2/c^(1/4))),sqrt(1/2))*(sqrt(b)*sqrt(c)/sqrt(-a)+sqrt(d))*(sqrt(c)+x^4*sqrt(d))*sqrt((c+d*x^8)/(sqrt(c)+x^4*sqrt(d))^2)/(c^(1/4)*(b*c+a*d)*sqrt(c+d*x^8))+1/8*d^(1/4)*sqrt(cos(2*arctan(d^(1/4)*x^2/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x^2/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x^2/c^(1/4))),sqrt(1/2))*(sqrt(-a)*sqrt(b)*sqrt(c)+a*sqrt(d))*(sqrt(c)+x^4*sqrt(d))*sqrt((c+d*x^8)/(sqrt(c)+x^4*sqrt(d))^2)/(a*c^(1/4)*(b*c+a*d)*sqrt(c+d*x^8))+1/16*sqrt(cos(2*arctan(d^(1/4)*x^2/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x^2/c^(1/4)))*EllipticPi(sin(2*arctan(d^(1/4)*x^2/c^(1/4))),1/4*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))^2/(sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)),sqrt(1/2))*(sqrt(c)+x^4*sqrt(d))*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))^2*sqrt((c+d*x^8)/(sqrt(c)+x^4*sqrt(d))^2)/(a*c^(1/4)*d^(1/4)*(b*c+a*d)*sqrt(c+d*x^8))+1/16*sqrt(cos(2*arctan(d^(1/4)*x^2/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x^2/c^(1/4)))*EllipticPi(sin(2*arctan(d^(1/4)*x^2/c^(1/4))),-1/4*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))^2/(sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)),sqrt(1/2))*(sqrt(c)+x^4*sqrt(d))*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))^2*sqrt((c+d*x^8)/(sqrt(c)+x^4*sqrt(d))^2)/(a*c^(1/4)*d^(1/4)*(b*c+a*d)*sqrt(c+d*x^8))],
[1/(x^7*(a+b*x^8)*sqrt(c+d*x^8)),x,11,-1/8*b^(5/4)*arctan(x^2*sqrt(b*c-a*d)/((-a)^(1/4)*b^(1/4)*sqrt(c+d*x^8)))/((-a)^(7/4)*sqrt(b*c-a*d))-1/8*b^(5/4)*arctan(x^2*sqrt(-b*c+a*d)/((-a)^(1/4)*b^(1/4)*sqrt(c+d*x^8)))/((-a)^(7/4)*sqrt(-b*c+a*d))-1/6*sqrt(c+d*x^8)/(a*c*x^6)-1/12*d^(3/4)*sqrt(cos(2*arctan(d^(1/4)*x^2/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x^2/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x^2/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^4*sqrt(d))*sqrt((c+d*x^8)/(sqrt(c)+x^4*sqrt(d))^2)/(a*c^(5/4)*sqrt(c+d*x^8))-1/8*b*d^(1/4)*sqrt(cos(2*arctan(d^(1/4)*x^2/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x^2/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x^2/c^(1/4))),sqrt(1/2))*(sqrt(b)*sqrt(c)/sqrt(-a)+sqrt(d))*(sqrt(c)+x^4*sqrt(d))*sqrt((c+d*x^8)/(sqrt(c)+x^4*sqrt(d))^2)/(a*c^(1/4)*(b*c+a*d)*sqrt(c+d*x^8))-1/8*b*d^(1/4)*sqrt(cos(2*arctan(d^(1/4)*x^2/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x^2/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x^2/c^(1/4))),sqrt(1/2))*(sqrt(-a)*sqrt(b)*sqrt(c)+a*sqrt(d))*(sqrt(c)+x^4*sqrt(d))*sqrt((c+d*x^8)/(sqrt(c)+x^4*sqrt(d))^2)/(a^2*c^(1/4)*(b*c+a*d)*sqrt(c+d*x^8))-1/16*b*sqrt(cos(2*arctan(d^(1/4)*x^2/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x^2/c^(1/4)))*EllipticPi(sin(2*arctan(d^(1/4)*x^2/c^(1/4))),1/4*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))^2/(sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)),sqrt(1/2))*(sqrt(c)+x^4*sqrt(d))*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))^2*sqrt((c+d*x^8)/(sqrt(c)+x^4*sqrt(d))^2)/(a^2*c^(1/4)*d^(1/4)*(b*c+a*d)*sqrt(c+d*x^8))-1/16*b*sqrt(cos(2*arctan(d^(1/4)*x^2/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x^2/c^(1/4)))*EllipticPi(sin(2*arctan(d^(1/4)*x^2/c^(1/4))),-1/4*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))^2/(sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)),sqrt(1/2))*(sqrt(c)+x^4*sqrt(d))*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))^2*sqrt((c+d*x^8)/(sqrt(c)+x^4*sqrt(d))^2)/(a^2*c^(1/4)*d^(1/4)*(b*c+a*d)*sqrt(c+d*x^8))],
[x^13/((a+b*x^8)*sqrt(c+d*x^8)),x,12,1/8*(-a)^(3/4)*arctan(x^2*sqrt(b*c-a*d)/((-a)^(1/4)*b^(1/4)*sqrt(c+d*x^8)))/(b^(5/4)*sqrt(b*c-a*d))-1/8*(-a)^(3/4)*arctan(x^2*sqrt(-b*c+a*d)/((-a)^(1/4)*b^(1/4)*sqrt(c+d*x^8)))/(b^(5/4)*sqrt(-b*c+a*d))+1/2*x^2*sqrt(c+d*x^8)/(b*sqrt(d)*(sqrt(c)+x^4*sqrt(d)))-1/2*c^(1/4)*sqrt(cos(2*arctan(d^(1/4)*x^2/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x^2/c^(1/4)))*EllipticE(sin(2*arctan(d^(1/4)*x^2/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^4*sqrt(d))*sqrt((c+d*x^8)/(sqrt(c)+x^4*sqrt(d))^2)/(b*d^(3/4)*sqrt(c+d*x^8))+1/4*c^(1/4)*sqrt(cos(2*arctan(d^(1/4)*x^2/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x^2/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x^2/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^4*sqrt(d))*sqrt((c+d*x^8)/(sqrt(c)+x^4*sqrt(d))^2)/(b*d^(3/4)*sqrt(c+d*x^8))-1/16*sqrt(cos(2*arctan(d^(1/4)*x^2/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x^2/c^(1/4)))*EllipticPi(sin(2*arctan(d^(1/4)*x^2/c^(1/4))),1/4*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))^2/(sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)),sqrt(1/2))*sqrt(-a)*(sqrt(c)+x^4*sqrt(d))*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))^2*sqrt((c+d*x^8)/(sqrt(c)+x^4*sqrt(d))^2)/(b^(3/2)*c^(1/4)*d^(1/4)*(b*c+a*d)*sqrt(c+d*x^8))+1/16*sqrt(cos(2*arctan(d^(1/4)*x^2/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x^2/c^(1/4)))*EllipticPi(sin(2*arctan(d^(1/4)*x^2/c^(1/4))),-1/4*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))^2/(sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)),sqrt(1/2))*sqrt(-a)*(sqrt(c)+x^4*sqrt(d))*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))^2*sqrt((c+d*x^8)/(sqrt(c)+x^4*sqrt(d))^2)/(b^(3/2)*c^(1/4)*d^(1/4)*(b*c+a*d)*sqrt(c+d*x^8))+1/8*a*d^(1/4)*sqrt(cos(2*arctan(d^(1/4)*x^2/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x^2/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x^2/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^4*sqrt(d))*(sqrt(c)-sqrt(-a)*sqrt(d)/sqrt(b))*sqrt((c+d*x^8)/(sqrt(c)+x^4*sqrt(d))^2)/(b*c^(1/4)*(b*c+a*d)*sqrt(c+d*x^8))+1/8*a*d^(1/4)*sqrt(cos(2*arctan(d^(1/4)*x^2/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x^2/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x^2/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^4*sqrt(d))*(sqrt(c)+sqrt(-a)*sqrt(d)/sqrt(b))*sqrt((c+d*x^8)/(sqrt(c)+x^4*sqrt(d))^2)/(b*c^(1/4)*(b*c+a*d)*sqrt(c+d*x^8))],
[x^5/((a+b*x^8)*sqrt(c+d*x^8)),x,8,1/8*arctan(x^2*sqrt(b*c-a*d)/((-a)^(1/4)*b^(1/4)*sqrt(c+d*x^8)))/((-a)^(1/4)*b^(1/4)*sqrt(b*c-a*d))-1/8*arctan(x^2*sqrt(-b*c+a*d)/((-a)^(1/4)*b^(1/4)*sqrt(c+d*x^8)))/((-a)^(1/4)*b^(1/4)*sqrt(-b*c+a*d))-1/16*sqrt(cos(2*arctan(d^(1/4)*x^2/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x^2/c^(1/4)))*EllipticPi(sin(2*arctan(d^(1/4)*x^2/c^(1/4))),1/4*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))^2/(sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)),sqrt(1/2))*(sqrt(c)+x^4*sqrt(d))*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))^2*sqrt((c+d*x^8)/(sqrt(c)+x^4*sqrt(d))^2)/(c^(1/4)*d^(1/4)*(b*c+a*d)*sqrt(-a)*sqrt(b)*sqrt(c+d*x^8))+1/16*sqrt(cos(2*arctan(d^(1/4)*x^2/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x^2/c^(1/4)))*EllipticPi(sin(2*arctan(d^(1/4)*x^2/c^(1/4))),-1/4*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))^2/(sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)),sqrt(1/2))*(sqrt(c)+x^4*sqrt(d))*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))^2*sqrt((c+d*x^8)/(sqrt(c)+x^4*sqrt(d))^2)/(c^(1/4)*d^(1/4)*(b*c+a*d)*sqrt(-a)*sqrt(b)*sqrt(c+d*x^8))-1/8*d^(1/4)*sqrt(cos(2*arctan(d^(1/4)*x^2/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x^2/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x^2/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^4*sqrt(d))*(sqrt(c)-sqrt(-a)*sqrt(d)/sqrt(b))*sqrt((c+d*x^8)/(sqrt(c)+x^4*sqrt(d))^2)/(c^(1/4)*(b*c+a*d)*sqrt(c+d*x^8))-1/8*d^(1/4)*sqrt(cos(2*arctan(d^(1/4)*x^2/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x^2/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x^2/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^4*sqrt(d))*(sqrt(c)+sqrt(-a)*sqrt(d)/sqrt(b))*sqrt((c+d*x^8)/(sqrt(c)+x^4*sqrt(d))^2)/(c^(1/4)*(b*c+a*d)*sqrt(c+d*x^8))],
[1/(x^3*(a+b*x^8)*sqrt(c+d*x^8)),x,14,1/8*b^(3/4)*arctan(x^2*sqrt(b*c-a*d)/((-a)^(1/4)*b^(1/4)*sqrt(c+d*x^8)))/((-a)^(5/4)*sqrt(b*c-a*d))-1/8*b^(3/4)*arctan(x^2*sqrt(-b*c+a*d)/((-a)^(1/4)*b^(1/4)*sqrt(c+d*x^8)))/((-a)^(5/4)*sqrt(-b*c+a*d))-1/2*sqrt(c+d*x^8)/(a*c*x^2)+1/2*x^2*sqrt(d)*sqrt(c+d*x^8)/(a*c*(sqrt(c)+x^4*sqrt(d)))-1/2*d^(1/4)*sqrt(cos(2*arctan(d^(1/4)*x^2/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x^2/c^(1/4)))*EllipticE(sin(2*arctan(d^(1/4)*x^2/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^4*sqrt(d))*sqrt((c+d*x^8)/(sqrt(c)+x^4*sqrt(d))^2)/(a*c^(3/4)*sqrt(c+d*x^8))+1/4*d^(1/4)*sqrt(cos(2*arctan(d^(1/4)*x^2/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x^2/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x^2/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^4*sqrt(d))*sqrt((c+d*x^8)/(sqrt(c)+x^4*sqrt(d))^2)/(a*c^(3/4)*sqrt(c+d*x^8))-1/16*sqrt(cos(2*arctan(d^(1/4)*x^2/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x^2/c^(1/4)))*EllipticPi(sin(2*arctan(d^(1/4)*x^2/c^(1/4))),1/4*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))^2/(sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)),sqrt(1/2))*sqrt(b)*(sqrt(c)+x^4*sqrt(d))*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))^2*sqrt((c+d*x^8)/(sqrt(c)+x^4*sqrt(d))^2)/((-a)^(3/2)*c^(1/4)*d^(1/4)*(b*c+a*d)*sqrt(c+d*x^8))+1/16*sqrt(cos(2*arctan(d^(1/4)*x^2/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x^2/c^(1/4)))*EllipticPi(sin(2*arctan(d^(1/4)*x^2/c^(1/4))),-1/4*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))^2/(sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)),sqrt(1/2))*sqrt(b)*(sqrt(c)+x^4*sqrt(d))*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))^2*sqrt((c+d*x^8)/(sqrt(c)+x^4*sqrt(d))^2)/((-a)^(3/2)*c^(1/4)*d^(1/4)*(b*c+a*d)*sqrt(c+d*x^8))+1/8*b*d^(1/4)*sqrt(cos(2*arctan(d^(1/4)*x^2/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x^2/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x^2/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^4*sqrt(d))*(sqrt(c)-sqrt(-a)*sqrt(d)/sqrt(b))*sqrt((c+d*x^8)/(sqrt(c)+x^4*sqrt(d))^2)/(a*c^(1/4)*(b*c+a*d)*sqrt(c+d*x^8))+1/8*b*d^(1/4)*sqrt(cos(2*arctan(d^(1/4)*x^2/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x^2/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x^2/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^4*sqrt(d))*(sqrt(c)+sqrt(-a)*sqrt(d)/sqrt(b))*sqrt((c+d*x^8)/(sqrt(c)+x^4*sqrt(d))^2)/(a*c^(1/4)*(b*c+a*d)*sqrt(c+d*x^8))],
[x^4/((a+b*x^8)*sqrt(c+d*x^8)),x,2,1/5*x^5*AppellF1(5/8,1,1/2,13/8,-b*x^8/a,-d*x^8/c)*sqrt(1+d*x^8/c)/(a*sqrt(c+d*x^8))],
[x^2/((a+b*x^8)*sqrt(c+d*x^8)),x,2,1/3*x^3*AppellF1(3/8,1,1/2,11/8,-b*x^8/a,-d*x^8/c)*sqrt(1+d*x^8/c)/(a*sqrt(c+d*x^8))],
[1/((a+b*x^8)*sqrt(c+d*x^8)),x,2,x*AppellF1(1/8,1,1/2,9/8,-b*x^8/a,-d*x^8/c)*sqrt(1+d*x^8/c)/(a*sqrt(c+d*x^8))],
[1/(x^2*(a+b*x^8)*sqrt(c+d*x^8)),x,2,-AppellF1(-1/8,1,1/2,7/8,-b*x^8/a,-d*x^8/c)*sqrt(1+d*x^8/c)/(a*x*sqrt(c+d*x^8))],
[1/(x^4*(a+b*x^8)*sqrt(c+d*x^8)),x,2,-1/3*AppellF1(-3/8,1,1/2,5/8,-b*x^8/a,-d*x^8/c)*sqrt(1+d*x^8/c)/(a*x^3*sqrt(c+d*x^8))],
[x^23/((a+b*x^8)^2*sqrt(c+d*x^8)),x,5,1/8*a*(4*b*c-3*a*d)*arctanh(sqrt(b)*sqrt(c+d*x^8)/sqrt(b*c-a*d))/(b^(5/2)*(b*c-a*d)^(3/2))+1/4*sqrt(c+d*x^8)/(b^2*d)-1/8*a^2*sqrt(c+d*x^8)/(b^2*(b*c-a*d)*(a+b*x^8))],
[x^15/((a+b*x^8)^2*sqrt(c+d*x^8)),x,4,-1/8*(2*b*c-a*d)*arctanh(sqrt(b)*sqrt(c+d*x^8)/sqrt(b*c-a*d))/(b^(3/2)*(b*c-a*d)^(3/2))+1/8*a*sqrt(c+d*x^8)/(b*(b*c-a*d)*(a+b*x^8))],
[x^7/((a+b*x^8)^2*sqrt(c+d*x^8)),x,4,1/8*d*arctanh(sqrt(b)*sqrt(c+d*x^8)/sqrt(b*c-a*d))/((b*c-a*d)^(3/2)*sqrt(b))-1/8*sqrt(c+d*x^8)/((b*c-a*d)*(a+b*x^8))],
[1/(x*(a+b*x^8)^2*sqrt(c+d*x^8)),x,7,1/8*(2*b*c-3*a*d)*arctanh(sqrt(b)*sqrt(c+d*x^8)/sqrt(b*c-a*d))*sqrt(b)/(a^2*(b*c-a*d)^(3/2))-1/4*arctanh(sqrt(c+d*x^8)/sqrt(c))/(a^2*sqrt(c))+1/8*b*sqrt(c+d*x^8)/(a*(b*c-a*d)*(a+b*x^8))],
[1/(x^9*(a+b*x^8)^2*sqrt(c+d*x^8)),x,8,1/8*(4*b*c+a*d)*arctanh(sqrt(c+d*x^8)/sqrt(c))/(a^3*c^(3/2))-1/8*b^(3/2)*(4*b*c-5*a*d)*arctanh(sqrt(b)*sqrt(c+d*x^8)/sqrt(b*c-a*d))/(a^3*(b*c-a*d)^(3/2))-1/8*b*(2*b*c-a*d)*sqrt(c+d*x^8)/(a^2*c*(b*c-a*d)*(a+b*x^8))-1/8*sqrt(c+d*x^8)/(a*c*x^8*(a+b*x^8))],
[x^19/((a+b*x^8)^2*sqrt(c+d*x^8)),x,7,-1/8*(3*b*c-2*a*d)*arctan(x^4*sqrt(b*c-a*d)/(sqrt(a)*sqrt(c+d*x^8)))*sqrt(a)/(b^2*(b*c-a*d)^(3/2))+1/4*arctanh(x^4*sqrt(d)/sqrt(c+d*x^8))/(b^2*sqrt(d))+1/8*a*x^4*sqrt(c+d*x^8)/(b*(b*c-a*d)*(a+b*x^8))],
[x^11/((a+b*x^8)^2*sqrt(c+d*x^8)),x,5,1/8*c*arctan(x^4*sqrt(b*c-a*d)/(sqrt(a)*sqrt(c+d*x^8)))/((b*c-a*d)^(3/2)*sqrt(a))-1/8*x^4*sqrt(c+d*x^8)/((b*c-a*d)*(a+b*x^8))],
[x^3/((a+b*x^8)^2*sqrt(c+d*x^8)),x,4,1/8*(b*c-2*a*d)*arctan(x^4*sqrt(b*c-a*d)/(sqrt(a)*sqrt(c+d*x^8)))/(a^(3/2)*(b*c-a*d)^(3/2))+1/8*b*x^4*sqrt(c+d*x^8)/(a*(b*c-a*d)*(a+b*x^8))],
[1/(x^5*(a+b*x^8)^2*sqrt(c+d*x^8)),x,6,-1/8*b*(3*b*c-4*a*d)*arctan(x^4*sqrt(b*c-a*d)/(sqrt(a)*sqrt(c+d*x^8)))/(a^(5/2)*(b*c-a*d)^(3/2))-1/8*(3*b*c-2*a*d)*sqrt(c+d*x^8)/(a^2*c*(b*c-a*d)*x^4)+1/8*b*sqrt(c+d*x^8)/(a*(b*c-a*d)*x^4*(a+b*x^8))],
[1/(x^13*(a+b*x^8)^2*sqrt(c+d*x^8)),x,7,1/8*b^2*(5*b*c-6*a*d)*arctan(x^4*sqrt(b*c-a*d)/(sqrt(a)*sqrt(c+d*x^8)))/(a^(7/2)*(b*c-a*d)^(3/2))-1/24*(5*b*c-2*a*d)*sqrt(c+d*x^8)/(a^2*c*(b*c-a*d)*x^12)+1/24*(15*b^2*c^2-8*a*b*c*d-4*a^2*d^2)*sqrt(c+d*x^8)/(a^3*c^2*(b*c-a*d)*x^4)+1/8*b*sqrt(c+d*x^8)/(a*(b*c-a*d)*x^12*(a+b*x^8))],
[x^9/((a+b*x^8)^2*sqrt(c+d*x^8)),x,11,-1/32*(b*c+a*d)*arctan(x^2*sqrt(b*c-a*d)/((-a)^(1/4)*b^(1/4)*sqrt(c+d*x^8)))/((-a)^(3/4)*b^(3/4)*(b*c-a*d)^(3/2))+1/32*(b*c+a*d)*arctan(x^2*sqrt(-b*c+a*d)/((-a)^(1/4)*b^(1/4)*sqrt(c+d*x^8)))/((-a)^(3/4)*b^(3/4)*(-b*c+a*d)^(3/2))-1/8*x^2*sqrt(c+d*x^8)/((b*c-a*d)*(a+b*x^8))-1/16*d^(3/4)*sqrt(cos(2*arctan(d^(1/4)*x^2/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x^2/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x^2/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^4*sqrt(d))*sqrt((c+d*x^8)/(sqrt(c)+x^4*sqrt(d))^2)/(b*c^(1/4)*(b*c-a*d)*sqrt(c+d*x^8))+1/32*d^(1/4)*sqrt(cos(2*arctan(d^(1/4)*x^2/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x^2/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x^2/c^(1/4))),sqrt(1/2))*(sqrt(b)*sqrt(c)/sqrt(-a)+sqrt(d))*(sqrt(c)+x^4*sqrt(d))*sqrt((c+d*x^8)/(sqrt(c)+x^4*sqrt(d))^2)/(b*c^(1/4)*(b*c-a*d)*sqrt(c+d*x^8))+1/32*d^(1/4)*sqrt(cos(2*arctan(d^(1/4)*x^2/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x^2/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x^2/c^(1/4))),sqrt(1/2))*(sqrt(-a)*sqrt(b)*sqrt(c)+a*sqrt(d))*(sqrt(c)+x^4*sqrt(d))*sqrt((c+d*x^8)/(sqrt(c)+x^4*sqrt(d))^2)/(a*b*c^(1/4)*(b*c-a*d)*sqrt(c+d*x^8))+1/64*sqrt(cos(2*arctan(d^(1/4)*x^2/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x^2/c^(1/4)))*EllipticPi(sin(2*arctan(d^(1/4)*x^2/c^(1/4))),1/4*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))^2/(sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)),sqrt(1/2))*(sqrt(c)+x^4*sqrt(d))*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))^2*sqrt((c+d*x^8)/(sqrt(c)+x^4*sqrt(d))^2)/(a*b*c^(1/4)*d^(1/4)*(b*c-a*d)*sqrt(c+d*x^8))+1/64*sqrt(cos(2*arctan(d^(1/4)*x^2/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x^2/c^(1/4)))*EllipticPi(sin(2*arctan(d^(1/4)*x^2/c^(1/4))),-1/4*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))^2/(sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)),sqrt(1/2))*(sqrt(c)+x^4*sqrt(d))*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))^2*sqrt((c+d*x^8)/(sqrt(c)+x^4*sqrt(d))^2)/(a*b*c^(1/4)*d^(1/4)*(b*c-a*d)*sqrt(c+d*x^8))],
[x/((a+b*x^8)^2*sqrt(c+d*x^8)),x,11,1/32*b^(1/4)*(3*b*c-5*a*d)*arctan(x^2*sqrt(b*c-a*d)/((-a)^(1/4)*b^(1/4)*sqrt(c+d*x^8)))/((-a)^(7/4)*(b*c-a*d)^(3/2))-1/32*b^(1/4)*(3*b*c-5*a*d)*arctan(x^2*sqrt(-b*c+a*d)/((-a)^(1/4)*b^(1/4)*sqrt(c+d*x^8)))/((-a)^(7/4)*(-b*c+a*d)^(3/2))+1/8*b*x^2*sqrt(c+d*x^8)/(a*(b*c-a*d)*(a+b*x^8))+1/16*d^(3/4)*sqrt(cos(2*arctan(d^(1/4)*x^2/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x^2/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x^2/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^4*sqrt(d))*sqrt((c+d*x^8)/(sqrt(c)+x^4*sqrt(d))^2)/(a*c^(1/4)*(b*c-a*d)*sqrt(c+d*x^8))+1/32*d^(1/4)*(3*b*c-5*a*d)*sqrt(cos(2*arctan(d^(1/4)*x^2/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x^2/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x^2/c^(1/4))),sqrt(1/2))*(sqrt(b)*sqrt(c)/sqrt(-a)+sqrt(d))*(sqrt(c)+x^4*sqrt(d))*sqrt((c+d*x^8)/(sqrt(c)+x^4*sqrt(d))^2)/(a*c^(1/4)*(b*c-a*d)*(b*c+a*d)*sqrt(c+d*x^8))+1/32*d^(1/4)*(3*b*c-5*a*d)*sqrt(cos(2*arctan(d^(1/4)*x^2/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x^2/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x^2/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^4*sqrt(d))*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))*sqrt((c+d*x^8)/(sqrt(c)+x^4*sqrt(d))^2)/((-a)^(3/2)*c^(1/4)*(b*c-a*d)*(b*c+a*d)*sqrt(c+d*x^8))+1/64*(3*b*c-5*a*d)*sqrt(cos(2*arctan(d^(1/4)*x^2/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x^2/c^(1/4)))*EllipticPi(sin(2*arctan(d^(1/4)*x^2/c^(1/4))),1/4*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))^2/(sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)),sqrt(1/2))*(sqrt(c)+x^4*sqrt(d))*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))^2*sqrt((c+d*x^8)/(sqrt(c)+x^4*sqrt(d))^2)/(a^2*c^(1/4)*d^(1/4)*(b^2*c^2-a^2*d^2)*sqrt(c+d*x^8))+1/64*(3*b*c-5*a*d)*sqrt(cos(2*arctan(d^(1/4)*x^2/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x^2/c^(1/4)))*EllipticPi(sin(2*arctan(d^(1/4)*x^2/c^(1/4))),-1/4*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))^2/(sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)),sqrt(1/2))*(sqrt(c)+x^4*sqrt(d))*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))^2*sqrt((c+d*x^8)/(sqrt(c)+x^4*sqrt(d))^2)/(a^2*c^(1/4)*d^(1/4)*(b^2*c^2-a^2*d^2)*sqrt(c+d*x^8))],
[1/(x^7*(a+b*x^8)^2*sqrt(c+d*x^8)),x,12,1/32*b^(5/4)*(7*b*c-9*a*d)*arctan(x^2*sqrt(b*c-a*d)/((-a)^(1/4)*b^(1/4)*sqrt(c+d*x^8)))/((-a)^(11/4)*(b*c-a*d)^(3/2))-1/32*b^(5/4)*(7*b*c-9*a*d)*arctan(x^2*sqrt(-b*c+a*d)/((-a)^(1/4)*b^(1/4)*sqrt(c+d*x^8)))/((-a)^(11/4)*(-b*c+a*d)^(3/2))-1/24*(7*b*c-4*a*d)*sqrt(c+d*x^8)/(a^2*c*(b*c-a*d)*x^6)+1/8*b*sqrt(c+d*x^8)/(a*(b*c-a*d)*x^6*(a+b*x^8))-1/48*d^(3/4)*(7*b*c-4*a*d)*sqrt(cos(2*arctan(d^(1/4)*x^2/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x^2/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x^2/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^4*sqrt(d))*sqrt((c+d*x^8)/(sqrt(c)+x^4*sqrt(d))^2)/(a^2*c^(5/4)*(b*c-a*d)*sqrt(c+d*x^8))+1/32*b*d^(1/4)*(7*b*c-9*a*d)*sqrt(cos(2*arctan(d^(1/4)*x^2/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x^2/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x^2/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^4*sqrt(d))*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))*sqrt((c+d*x^8)/(sqrt(c)+x^4*sqrt(d))^2)/((-a)^(5/2)*c^(1/4)*(b*c-a*d)*(b*c+a*d)*sqrt(c+d*x^8))-1/64*b*(7*b*c-9*a*d)*sqrt(cos(2*arctan(d^(1/4)*x^2/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x^2/c^(1/4)))*EllipticPi(sin(2*arctan(d^(1/4)*x^2/c^(1/4))),1/4*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))^2/(sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)),sqrt(1/2))*(sqrt(c)+x^4*sqrt(d))*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))^2*sqrt((c+d*x^8)/(sqrt(c)+x^4*sqrt(d))^2)/(a^3*c^(1/4)*d^(1/4)*(b^2*c^2-a^2*d^2)*sqrt(c+d*x^8))-1/32*b*d^(1/4)*(7*b*c-9*a*d)*sqrt(cos(2*arctan(d^(1/4)*x^2/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x^2/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x^2/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^4*sqrt(d))*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))*sqrt((c+d*x^8)/(sqrt(c)+x^4*sqrt(d))^2)/((-a)^(5/2)*c^(1/4)*(b*c-a*d)*(b*c+a*d)*sqrt(c+d*x^8))-1/64*b*(7*b*c-9*a*d)*sqrt(cos(2*arctan(d^(1/4)*x^2/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x^2/c^(1/4)))*EllipticPi(sin(2*arctan(d^(1/4)*x^2/c^(1/4))),-1/4*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))^2/(sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)),sqrt(1/2))*(sqrt(c)+x^4*sqrt(d))*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))^2*sqrt((c+d*x^8)/(sqrt(c)+x^4*sqrt(d))^2)/(a^3*c^(1/4)*d^(1/4)*(b^2*c^2-a^2*d^2)*sqrt(c+d*x^8))],
[x^13/((a+b*x^8)^2*sqrt(c+d*x^8)),x,14,1/32*(3*b*c-a*d)*arctan(x^2*sqrt(b*c-a*d)/((-a)^(1/4)*b^(1/4)*sqrt(c+d*x^8)))/((-a)^(1/4)*b^(5/4)*(b*c-a*d)^(3/2))+1/32*(3*b*c-a*d)*arctan(x^2*sqrt(-b*c+a*d)/((-a)^(1/4)*b^(1/4)*sqrt(c+d*x^8)))/((-a)^(1/4)*b^(5/4)*(-b*c+a*d)^(3/2))-1/8*x^6*sqrt(c+d*x^8)/((b*c-a*d)*(a+b*x^8))+1/8*x^2*sqrt(d)*sqrt(c+d*x^8)/(b*(b*c-a*d)*(sqrt(c)+x^4*sqrt(d)))-1/8*c^(1/4)*d^(1/4)*sqrt(cos(2*arctan(d^(1/4)*x^2/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x^2/c^(1/4)))*EllipticE(sin(2*arctan(d^(1/4)*x^2/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^4*sqrt(d))*sqrt((c+d*x^8)/(sqrt(c)+x^4*sqrt(d))^2)/(b*(b*c-a*d)*sqrt(c+d*x^8))+1/16*c^(1/4)*d^(1/4)*sqrt(cos(2*arctan(d^(1/4)*x^2/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x^2/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x^2/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^4*sqrt(d))*sqrt((c+d*x^8)/(sqrt(c)+x^4*sqrt(d))^2)/(b*(b*c-a*d)*sqrt(c+d*x^8))-1/32*d^(1/4)*(3*b*c-a*d)*sqrt(cos(2*arctan(d^(1/4)*x^2/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x^2/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x^2/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^4*sqrt(d))*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))*sqrt((c+d*x^8)/(sqrt(c)+x^4*sqrt(d))^2)/(b^(3/2)*c^(1/4)*(b^2*c^2-a^2*d^2)*sqrt(c+d*x^8))-1/64*(3*b*c-a*d)*sqrt(cos(2*arctan(d^(1/4)*x^2/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x^2/c^(1/4)))*EllipticPi(sin(2*arctan(d^(1/4)*x^2/c^(1/4))),1/4*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))^2/(sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)),sqrt(1/2))*(sqrt(c)+x^4*sqrt(d))*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))^2*sqrt((c+d*x^8)/(sqrt(c)+x^4*sqrt(d))^2)/(b^(3/2)*c^(1/4)*d^(1/4)*(b*c-a*d)*(b*c+a*d)*sqrt(-a)*sqrt(c+d*x^8))-1/32*d^(1/4)*(3*b*c-a*d)*sqrt(cos(2*arctan(d^(1/4)*x^2/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x^2/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x^2/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^4*sqrt(d))*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))*sqrt((c+d*x^8)/(sqrt(c)+x^4*sqrt(d))^2)/(b^(3/2)*c^(1/4)*(b^2*c^2-a^2*d^2)*sqrt(c+d*x^8))+1/64*(3*b*c-a*d)*sqrt(cos(2*arctan(d^(1/4)*x^2/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x^2/c^(1/4)))*EllipticPi(sin(2*arctan(d^(1/4)*x^2/c^(1/4))),-1/4*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))^2/(sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)),sqrt(1/2))*(sqrt(c)+x^4*sqrt(d))*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))^2*sqrt((c+d*x^8)/(sqrt(c)+x^4*sqrt(d))^2)/(b^(3/2)*c^(1/4)*d^(1/4)*(b*c-a*d)*(b*c+a*d)*sqrt(-a)*sqrt(c+d*x^8))],
[x^5/((a+b*x^8)^2*sqrt(c+d*x^8)),x,14,-1/32*(b*c-3*a*d)*arctan(x^2*sqrt(b*c-a*d)/((-a)^(1/4)*b^(1/4)*sqrt(c+d*x^8)))/((-a)^(5/4)*b^(1/4)*(b*c-a*d)^(3/2))-1/32*(b*c-3*a*d)*arctan(x^2*sqrt(-b*c+a*d)/((-a)^(1/4)*b^(1/4)*sqrt(c+d*x^8)))/((-a)^(5/4)*b^(1/4)*(-b*c+a*d)^(3/2))+1/8*b*x^6*sqrt(c+d*x^8)/(a*(b*c-a*d)*(a+b*x^8))-1/8*x^2*sqrt(d)*sqrt(c+d*x^8)/(a*(b*c-a*d)*(sqrt(c)+x^4*sqrt(d)))+1/8*c^(1/4)*d^(1/4)*sqrt(cos(2*arctan(d^(1/4)*x^2/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x^2/c^(1/4)))*EllipticE(sin(2*arctan(d^(1/4)*x^2/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^4*sqrt(d))*sqrt((c+d*x^8)/(sqrt(c)+x^4*sqrt(d))^2)/(a*(b*c-a*d)*sqrt(c+d*x^8))-1/16*c^(1/4)*d^(1/4)*sqrt(cos(2*arctan(d^(1/4)*x^2/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x^2/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x^2/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^4*sqrt(d))*sqrt((c+d*x^8)/(sqrt(c)+x^4*sqrt(d))^2)/(a*(b*c-a*d)*sqrt(c+d*x^8))+1/64*(b*c-3*a*d)*sqrt(cos(2*arctan(d^(1/4)*x^2/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x^2/c^(1/4)))*EllipticPi(sin(2*arctan(d^(1/4)*x^2/c^(1/4))),1/4*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))^2/(sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)),sqrt(1/2))*(sqrt(c)+x^4*sqrt(d))*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))^2*sqrt((c+d*x^8)/(sqrt(c)+x^4*sqrt(d))^2)/((-a)^(3/2)*c^(1/4)*d^(1/4)*(b*c-a*d)*(b*c+a*d)*sqrt(b)*sqrt(c+d*x^8))-1/64*(b*c-3*a*d)*sqrt(cos(2*arctan(d^(1/4)*x^2/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x^2/c^(1/4)))*EllipticPi(sin(2*arctan(d^(1/4)*x^2/c^(1/4))),-1/4*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))^2/(sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)),sqrt(1/2))*(sqrt(c)+x^4*sqrt(d))*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))^2*sqrt((c+d*x^8)/(sqrt(c)+x^4*sqrt(d))^2)/((-a)^(3/2)*c^(1/4)*d^(1/4)*(b*c-a*d)*(b*c+a*d)*sqrt(b)*sqrt(c+d*x^8))-1/32*d^(1/4)*(b*c-3*a*d)*sqrt(cos(2*arctan(d^(1/4)*x^2/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x^2/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x^2/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^4*sqrt(d))*(sqrt(c)-sqrt(-a)*sqrt(d)/sqrt(b))*sqrt((c+d*x^8)/(sqrt(c)+x^4*sqrt(d))^2)/(a*c^(1/4)*(b*c-a*d)*(b*c+a*d)*sqrt(c+d*x^8))-1/32*d^(1/4)*(b*c-3*a*d)*sqrt(cos(2*arctan(d^(1/4)*x^2/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x^2/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x^2/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^4*sqrt(d))*(sqrt(c)+sqrt(-a)*sqrt(d)/sqrt(b))*sqrt((c+d*x^8)/(sqrt(c)+x^4*sqrt(d))^2)/(a*c^(1/4)*(b*c-a*d)*(b*c+a*d)*sqrt(c+d*x^8))],
[1/(x^3*(a+b*x^8)^2*sqrt(c+d*x^8)),x,15,-1/32*b^(3/4)*(5*b*c-7*a*d)*arctan(x^2*sqrt(b*c-a*d)/((-a)^(1/4)*b^(1/4)*sqrt(c+d*x^8)))/((-a)^(9/4)*(b*c-a*d)^(3/2))-1/32*b^(3/4)*(5*b*c-7*a*d)*arctan(x^2*sqrt(-b*c+a*d)/((-a)^(1/4)*b^(1/4)*sqrt(c+d*x^8)))/((-a)^(9/4)*(-b*c+a*d)^(3/2))-1/8*(5*b*c-4*a*d)*sqrt(c+d*x^8)/(a^2*c*(b*c-a*d)*x^2)+1/8*b*sqrt(c+d*x^8)/(a*(b*c-a*d)*x^2*(a+b*x^8))+1/8*(5*b*c-4*a*d)*x^2*sqrt(d)*sqrt(c+d*x^8)/(a^2*c*(b*c-a*d)*(sqrt(c)+x^4*sqrt(d)))-1/8*d^(1/4)*(5*b*c-4*a*d)*sqrt(cos(2*arctan(d^(1/4)*x^2/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x^2/c^(1/4)))*EllipticE(sin(2*arctan(d^(1/4)*x^2/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^4*sqrt(d))*sqrt((c+d*x^8)/(sqrt(c)+x^4*sqrt(d))^2)/(a^2*c^(3/4)*(b*c-a*d)*sqrt(c+d*x^8))+1/16*d^(1/4)*(5*b*c-4*a*d)*sqrt(cos(2*arctan(d^(1/4)*x^2/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x^2/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x^2/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^4*sqrt(d))*sqrt((c+d*x^8)/(sqrt(c)+x^4*sqrt(d))^2)/(a^2*c^(3/4)*(b*c-a*d)*sqrt(c+d*x^8))+1/64*(5*b*c-7*a*d)*sqrt(cos(2*arctan(d^(1/4)*x^2/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x^2/c^(1/4)))*EllipticPi(sin(2*arctan(d^(1/4)*x^2/c^(1/4))),1/4*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))^2/(sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)),sqrt(1/2))*sqrt(b)*(sqrt(c)+x^4*sqrt(d))*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))^2*sqrt((c+d*x^8)/(sqrt(c)+x^4*sqrt(d))^2)/((-a)^(5/2)*c^(1/4)*d^(1/4)*(b*c-a*d)*(b*c+a*d)*sqrt(c+d*x^8))-1/64*(5*b*c-7*a*d)*sqrt(cos(2*arctan(d^(1/4)*x^2/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x^2/c^(1/4)))*EllipticPi(sin(2*arctan(d^(1/4)*x^2/c^(1/4))),-1/4*(sqrt(b)*sqrt(c)-sqrt(-a)*sqrt(d))^2/(sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)),sqrt(1/2))*sqrt(b)*(sqrt(c)+x^4*sqrt(d))*(sqrt(b)*sqrt(c)+sqrt(-a)*sqrt(d))^2*sqrt((c+d*x^8)/(sqrt(c)+x^4*sqrt(d))^2)/((-a)^(5/2)*c^(1/4)*d^(1/4)*(b*c-a*d)*(b*c+a*d)*sqrt(c+d*x^8))+1/32*b*d^(1/4)*(5*b*c-7*a*d)*sqrt(cos(2*arctan(d^(1/4)*x^2/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x^2/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x^2/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^4*sqrt(d))*(sqrt(c)-sqrt(-a)*sqrt(d)/sqrt(b))*sqrt((c+d*x^8)/(sqrt(c)+x^4*sqrt(d))^2)/(a^2*c^(1/4)*(b*c-a*d)*(b*c+a*d)*sqrt(c+d*x^8))+1/32*b*d^(1/4)*(5*b*c-7*a*d)*sqrt(cos(2*arctan(d^(1/4)*x^2/c^(1/4)))^2)/cos(2*arctan(d^(1/4)*x^2/c^(1/4)))*EllipticF(sin(2*arctan(d^(1/4)*x^2/c^(1/4))),sqrt(1/2))*(sqrt(c)+x^4*sqrt(d))*(sqrt(c)+sqrt(-a)*sqrt(d)/sqrt(b))*sqrt((c+d*x^8)/(sqrt(c)+x^4*sqrt(d))^2)/(a^2*c^(1/4)*(b*c-a*d)*(b*c+a*d)*sqrt(c+d*x^8))],
[x^4/((a+b*x^8)^2*sqrt(c+d*x^8)),x,2,1/5*x^5*AppellF1(5/8,2,1/2,13/8,-b*x^8/a,-d*x^8/c)*sqrt(1+d*x^8/c)/(a^2*sqrt(c+d*x^8))],
[x^2/((a+b*x^8)^2*sqrt(c+d*x^8)),x,2,1/3*x^3*AppellF1(3/8,2,1/2,11/8,-b*x^8/a,-d*x^8/c)*sqrt(1+d*x^8/c)/(a^2*sqrt(c+d*x^8))],
[1/((a+b*x^8)^2*sqrt(c+d*x^8)),x,2,x*AppellF1(1/8,2,1/2,9/8,-b*x^8/a,-d*x^8/c)*sqrt(1+d*x^8/c)/(a^2*sqrt(c+d*x^8))],
[1/(x^2*(a+b*x^8)^2*sqrt(c+d*x^8)),x,2,-AppellF1(-1/8,2,1/2,7/8,-b*x^8/a,-d*x^8/c)*sqrt(1+d*x^8/c)/(a^2*x*sqrt(c+d*x^8))],
[1/(x^4*(a+b*x^8)^2*sqrt(c+d*x^8)),x,2,-1/3*AppellF1(-3/8,2,1/2,5/8,-b*x^8/a,-d*x^8/c)*sqrt(1+d*x^8/c)/(a^2*x^3*sqrt(c+d*x^8))],

# Integrands of the form (e x)^m (a+b/x^2)^p (c+d/x^2)^q

# Integrands of the form (e x)^m (a+b/x^2)^p (c+d/x^2)^(q/2)

# Integrands of the form (e x)^m (a+b/x^2)^1 (c+d/x^2)^(q/2)

# q>0
[(a+b/x^2)*x^5*sqrt(c+d/x^2),x,6,1/6*a*(c+d/x^2)^(3/2)*x^6/c-1/16*d^2*(2*b*c-a*d)*arctanh(sqrt(c+d/x^2)/sqrt(c))/c^(5/2)+1/16*d*(2*b*c-a*d)*x^2*sqrt(c+d/x^2)/c^2+1/8*(2*b*c-a*d)*x^4*sqrt(c+d/x^2)/c],
[(a+b/x^2)*x^3*sqrt(c+d/x^2),x,5,1/4*a*(c+d/x^2)^(3/2)*x^4/c+1/8*d*(4*b*c-a*d)*arctanh(sqrt(c+d/x^2)/sqrt(c))/c^(3/2)+1/8*(4*b*c-a*d)*x^2*sqrt(c+d/x^2)/c],
[(a+b/x^2)*x*sqrt(c+d/x^2),x,5,1/2*a*(c+d/x^2)^(3/2)*x^2/c+1/2*(2*b*c+a*d)*arctanh(sqrt(c+d/x^2)/sqrt(c))/sqrt(c)-1/2*(2*b*c+a*d)*sqrt(c+d/x^2)/c],
[(a+b/x^2)*sqrt(c+d/x^2)/x,x,5,-1/3*b*(c+d/x^2)^(3/2)/d+a*arctanh(sqrt(c+d/x^2)/sqrt(c))*sqrt(c)-a*sqrt(c+d/x^2)],
[(a+b/x^2)*sqrt(c+d/x^2)/x^3,x,3,1/3*(b*c-a*d)*(c+d/x^2)^(3/2)/d^2-1/5*b*(c+d/x^2)^(5/2)/d^2],
[(a+b/x^2)*sqrt(c+d/x^2)/x^5,x,3,-1/3*c*(b*c-a*d)*(c+d/x^2)^(3/2)/d^3+1/5*(2*b*c-a*d)*(c+d/x^2)^(5/2)/d^3-1/7*b*(c+d/x^2)^(7/2)/d^3],
[(a+b/x^2)*sqrt(c+d/x^2)/x^7,x,3,1/3*c^2*(b*c-a*d)*(c+d/x^2)^(3/2)/d^4-1/5*c*(3*b*c-2*a*d)*(c+d/x^2)^(5/2)/d^4+1/7*(3*b*c-a*d)*(c+d/x^2)^(7/2)/d^4-1/9*b*(c+d/x^2)^(9/2)/d^4],
[(a+b/x^2)*sqrt(c+d/x^2)/x^9,x,3,-1/3*c^3*(b*c-a*d)*(c+d/x^2)^(3/2)/d^5+1/5*c^2*(4*b*c-3*a*d)*(c+d/x^2)^(5/2)/d^5-3/7*c*(2*b*c-a*d)*(c+d/x^2)^(7/2)/d^5+1/9*(4*b*c-a*d)*(c+d/x^2)^(9/2)/d^5-1/11*b*(c+d/x^2)^(11/2)/d^5],
[(a+b/x^2)*x^10*sqrt(c+d/x^2),x,5,-16/3465*d^3*(11*b*c-8*a*d)*(c+d/x^2)^(3/2)*x^3/c^5+8/1155*d^2*(11*b*c-8*a*d)*(c+d/x^2)^(3/2)*x^5/c^4-2/231*d*(11*b*c-8*a*d)*(c+d/x^2)^(3/2)*x^7/c^3+1/99*(11*b*c-8*a*d)*(c+d/x^2)^(3/2)*x^9/c^2+1/11*a*(c+d/x^2)^(3/2)*x^11/c],
[(a+b/x^2)*x^8*sqrt(c+d/x^2),x,4,8/315*d^2*(3*b*c-2*a*d)*(c+d/x^2)^(3/2)*x^3/c^4-4/105*d*(3*b*c-2*a*d)*(c+d/x^2)^(3/2)*x^5/c^3+1/21*(3*b*c-2*a*d)*(c+d/x^2)^(3/2)*x^7/c^2+1/9*a*(c+d/x^2)^(3/2)*x^9/c],
[(a+b/x^2)*x^6*sqrt(c+d/x^2),x,3,-2/105*d*(7*b*c-4*a*d)*(c+d/x^2)^(3/2)*x^3/c^3+1/35*(7*b*c-4*a*d)*(c+d/x^2)^(3/2)*x^5/c^2+1/7*a*(c+d/x^2)^(3/2)*x^7/c],
[(a+b/x^2)*x^4*sqrt(c+d/x^2),x,2,1/15*(5*b*c-2*a*d)*(c+d/x^2)^(3/2)*x^3/c^2+1/5*a*(c+d/x^2)^(3/2)*x^5/c],
[(a+b/x^2)*x^2*sqrt(c+d/x^2),x,5,1/3*a*(c+d/x^2)^(3/2)*x^3/c-b*arctanh(sqrt(d)/(x*sqrt(c+d/x^2)))*sqrt(d)+b*x*sqrt(c+d/x^2)],
[(a+b/x^2)*sqrt(c+d/x^2),x,5,a*(c+d/x^2)^(3/2)*x/c-1/2*(b*c+2*a*d)*arctanh(sqrt(d)/(x*sqrt(c+d/x^2)))/sqrt(d)-1/2*(b*c+2*a*d)*sqrt(c+d/x^2)/(c*x)],
[(a+b/x^2)*sqrt(c+d/x^2)/x^2,x,5,-1/4*b*(c+d/x^2)^(3/2)/(d*x)+1/8*c*(b*c-4*a*d)*arctanh(sqrt(d)/(x*sqrt(c+d/x^2)))/d^(3/2)+1/8*(b*c-4*a*d)*sqrt(c+d/x^2)/(d*x)],
[(a+b/x^2)*sqrt(c+d/x^2)/x^4,x,6,-1/6*b*(c+d/x^2)^(3/2)/(d*x^3)-1/16*c^2*(b*c-2*a*d)*arctanh(sqrt(d)/(x*sqrt(c+d/x^2)))/d^(5/2)+1/8*(b*c-2*a*d)*sqrt(c+d/x^2)/(d*x^3)+1/16*c*(b*c-2*a*d)*sqrt(c+d/x^2)/(d^2*x)],
[(a+b/x^2)*(c+d/x^2)^(3/2)*x^5,x,6,1/24*(6*b*c-a*d)*(c+d/x^2)^(3/2)*x^4/c+1/6*a*(c+d/x^2)^(5/2)*x^6/c+1/16*d^2*(6*b*c-a*d)*arctanh(sqrt(c+d/x^2)/sqrt(c))/c^(3/2)+1/16*d*(6*b*c-a*d)*x^2*sqrt(c+d/x^2)/c],
[(a+b/x^2)*(c+d/x^2)^(3/2)*x^3,x,6,1/8*(4*b*c+a*d)*(c+d/x^2)^(3/2)*x^2/c+1/4*a*(c+d/x^2)^(5/2)*x^4/c+3/8*d*(4*b*c+a*d)*arctanh(sqrt(c+d/x^2)/sqrt(c))/sqrt(c)-3/8*d*(4*b*c+a*d)*sqrt(c+d/x^2)/c],
[(a+b/x^2)*(c+d/x^2)^(3/2)*x,x,6,-1/6*(2*b*c+3*a*d)*(c+d/x^2)^(3/2)/c+1/2*a*(c+d/x^2)^(5/2)*x^2/c+1/2*(2*b*c+3*a*d)*arctanh(sqrt(c+d/x^2)/sqrt(c))*sqrt(c)-1/2*(2*b*c+3*a*d)*sqrt(c+d/x^2)],
[(a+b/x^2)*(c+d/x^2)^(3/2)/x,x,6,-1/3*a*(c+d/x^2)^(3/2)-1/5*b*(c+d/x^2)^(5/2)/d+a*c^(3/2)*arctanh(sqrt(c+d/x^2)/sqrt(c))-a*c*sqrt(c+d/x^2)],
[(a+b/x^2)*(c+d/x^2)^(3/2)/x^3,x,3,1/5*(b*c-a*d)*(c+d/x^2)^(5/2)/d^2-1/7*b*(c+d/x^2)^(7/2)/d^2],
[(a+b/x^2)*(c+d/x^2)^(3/2)/x^5,x,3,-1/5*c*(b*c-a*d)*(c+d/x^2)^(5/2)/d^3+1/7*(2*b*c-a*d)*(c+d/x^2)^(7/2)/d^3-1/9*b*(c+d/x^2)^(9/2)/d^3],
[(a+b/x^2)*(c+d/x^2)^(3/2)/x^7,x,3,1/5*c^2*(b*c-a*d)*(c+d/x^2)^(5/2)/d^4-1/7*c*(3*b*c-2*a*d)*(c+d/x^2)^(7/2)/d^4+1/9*(3*b*c-a*d)*(c+d/x^2)^(9/2)/d^4-1/11*b*(c+d/x^2)^(11/2)/d^4],
[(a+b/x^2)*(c+d/x^2)^(3/2)/x^9,x,3,-1/5*c^3*(b*c-a*d)*(c+d/x^2)^(5/2)/d^5+1/7*c^2*(4*b*c-3*a*d)*(c+d/x^2)^(7/2)/d^5-1/3*c*(2*b*c-a*d)*(c+d/x^2)^(9/2)/d^5+1/11*(4*b*c-a*d)*(c+d/x^2)^(11/2)/d^5-1/13*b*(c+d/x^2)^(13/2)/d^5],
[(a+b/x^2)*(c+d/x^2)^(3/2)*x^12,x,5,-16/15015*d^3*(13*b*c-8*a*d)*(c+d/x^2)^(5/2)*x^5/c^5+8/3003*d^2*(13*b*c-8*a*d)*(c+d/x^2)^(5/2)*x^7/c^4-2/429*d*(13*b*c-8*a*d)*(c+d/x^2)^(5/2)*x^9/c^3+1/143*(13*b*c-8*a*d)*(c+d/x^2)^(5/2)*x^11/c^2+1/13*a*(c+d/x^2)^(5/2)*x^13/c],
[(a+b/x^2)*(c+d/x^2)^(3/2)*x^10,x,4,8/3465*d^2*(11*b*c-6*a*d)*(c+d/x^2)^(5/2)*x^5/c^4-4/693*d*(11*b*c-6*a*d)*(c+d/x^2)^(5/2)*x^7/c^3+1/99*(11*b*c-6*a*d)*(c+d/x^2)^(5/2)*x^9/c^2+1/11*a*(c+d/x^2)^(5/2)*x^11/c],
[(a+b/x^2)*(c+d/x^2)^(3/2)*x^8,x,3,-2/315*d*(9*b*c-4*a*d)*(c+d/x^2)^(5/2)*x^5/c^3+1/63*(9*b*c-4*a*d)*(c+d/x^2)^(5/2)*x^7/c^2+1/9*a*(c+d/x^2)^(5/2)*x^9/c],
[(a+b/x^2)*(c+d/x^2)^(3/2)*x^6,x,2,1/35*(7*b*c-2*a*d)*(c+d/x^2)^(5/2)*x^5/c^2+1/7*a*(c+d/x^2)^(5/2)*x^7/c],
[(a+b/x^2)*(c+d/x^2)^(3/2)*x^4,x,6,1/3*b*(c+d/x^2)^(3/2)*x^3+1/5*a*(c+d/x^2)^(5/2)*x^5/c-b*d^(3/2)*arctanh(sqrt(d)/(x*sqrt(c+d/x^2)))+b*d*x*sqrt(c+d/x^2)],
[(a+b/x^2)*(c+d/x^2)^(3/2)*x^2,x,6,1/3*(3*b*c+2*a*d)*(c+d/x^2)^(3/2)*x/c+1/3*a*(c+d/x^2)^(5/2)*x^3/c-1/2*(3*b*c+2*a*d)*arctanh(sqrt(d)/(x*sqrt(c+d/x^2)))*sqrt(d)-1/2*d*(3*b*c+2*a*d)*sqrt(c+d/x^2)/(c*x)],
[(a+b/x^2)*(c+d/x^2)^(3/2),x,6,-1/4*(b*c+4*a*d)*(c+d/x^2)^(3/2)/(c*x)+a*(c+d/x^2)^(5/2)*x/c-3/8*c*(b*c+4*a*d)*arctanh(sqrt(d)/(x*sqrt(c+d/x^2)))/sqrt(d)-3/8*(b*c+4*a*d)*sqrt(c+d/x^2)/x],
[(a+b/x^2)*(c+d/x^2)^(3/2)/x^2,x,6,1/24*(b*c-6*a*d)*(c+d/x^2)^(3/2)/(d*x)-1/6*b*(c+d/x^2)^(5/2)/(d*x)+1/16*c^2*(b*c-6*a*d)*arctanh(sqrt(d)/(x*sqrt(c+d/x^2)))/d^(3/2)+1/16*c*(b*c-6*a*d)*sqrt(c+d/x^2)/(d*x)],
[(a+b/x^2)*(c+d/x^2)^(3/2)/x^4,x,7,1/48*(3*b*c-8*a*d)*(c+d/x^2)^(3/2)/(d*x^3)-1/8*b*(c+d/x^2)^(5/2)/(d*x^3)-1/128*c^3*(3*b*c-8*a*d)*arctanh(sqrt(d)/(x*sqrt(c+d/x^2)))/d^(5/2)+1/64*c*(3*b*c-8*a*d)*sqrt(c+d/x^2)/(d*x^3)+1/128*c^2*(3*b*c-8*a*d)*sqrt(c+d/x^2)/(d^2*x)],

# q<0
[(a+b/x^2)*x^3/sqrt(c+d/x^2),x,5,-1/8*d*(4*b*c-3*a*d)*arctanh(sqrt(c+d/x^2)/sqrt(c))/c^(5/2)+1/8*(4*b*c-3*a*d)*x^2*sqrt(c+d/x^2)/c^2+1/4*a*x^4*sqrt(c+d/x^2)/c],
[(a+b/x^2)*x/sqrt(c+d/x^2),x,4,1/2*(2*b*c-a*d)*arctanh(sqrt(c+d/x^2)/sqrt(c))/c^(3/2)+1/2*a*x^2*sqrt(c+d/x^2)/c],
[(a+b/x^2)/(x*sqrt(c+d/x^2)),x,4,a*arctanh(sqrt(c+d/x^2)/sqrt(c))/sqrt(c)-b*sqrt(c+d/x^2)/d],
[(a+b/x^2)/(x^3*sqrt(c+d/x^2)),x,3,-1/3*b*(c+d/x^2)^(3/2)/d^2+(b*c-a*d)*sqrt(c+d/x^2)/d^2],
[(a+b/x^2)/(x^5*sqrt(c+d/x^2)),x,3,1/3*(2*b*c-a*d)*(c+d/x^2)^(3/2)/d^3-1/5*b*(c+d/x^2)^(5/2)/d^3-c*(b*c-a*d)*sqrt(c+d/x^2)/d^3],
[(a+b/x^2)/(x^7*sqrt(c+d/x^2)),x,3,-1/3*c*(3*b*c-2*a*d)*(c+d/x^2)^(3/2)/d^4+1/5*(3*b*c-a*d)*(c+d/x^2)^(5/2)/d^4-1/7*b*(c+d/x^2)^(7/2)/d^4+c^2*(b*c-a*d)*sqrt(c+d/x^2)/d^4],
[(a+b/x^2)*x^4/sqrt(c+d/x^2),x,3,-2/15*d*(5*b*c-4*a*d)*x*sqrt(c+d/x^2)/c^3+1/15*(5*b*c-4*a*d)*x^3*sqrt(c+d/x^2)/c^2+1/5*a*x^5*sqrt(c+d/x^2)/c],
[(a+b/x^2)*x^2/sqrt(c+d/x^2),x,2,1/3*(3*b*c-2*a*d)*x*sqrt(c+d/x^2)/c^2+1/3*a*x^3*sqrt(c+d/x^2)/c],
[(a+b/x^2)/sqrt(c+d/x^2),x,4,-b*arctanh(sqrt(d)/(x*sqrt(c+d/x^2)))/sqrt(d)+a*x*sqrt(c+d/x^2)/c],
[(a+b/x^2)/(x^2*sqrt(c+d/x^2)),x,4,1/2*(b*c-2*a*d)*arctanh(sqrt(d)/(x*sqrt(c+d/x^2)))/d^(3/2)-1/2*b*sqrt(c+d/x^2)/(d*x)],
[(a+b/x^2)/(x^4*sqrt(c+d/x^2)),x,5,-1/8*c*(3*b*c-4*a*d)*arctanh(sqrt(d)/(x*sqrt(c+d/x^2)))/d^(5/2)-1/4*b*sqrt(c+d/x^2)/(d*x^3)+1/8*(3*b*c-4*a*d)*sqrt(c+d/x^2)/(d^2*x)],
[(a+b/x^2)*x^3/(c+d/x^2)^(3/2),x,6,-3/8*d*(4*b*c-5*a*d)*arctanh(sqrt(c+d/x^2)/sqrt(c))/c^(7/2)+3/8*d*(4*b*c-5*a*d)/(c^3*sqrt(c+d/x^2))+1/8*(4*b*c-5*a*d)*x^2/(c^2*sqrt(c+d/x^2))+1/4*a*x^4/(c*sqrt(c+d/x^2))],
[(a+b/x^2)*x/(c+d/x^2)^(3/2),x,5,1/2*(2*b*c-3*a*d)*arctanh(sqrt(c+d/x^2)/sqrt(c))/c^(5/2)+1/2*(-2*b*c+3*a*d)/(c^2*sqrt(c+d/x^2))+1/2*a*x^2/(c*sqrt(c+d/x^2))],
[(a+b/x^2)/((c+d/x^2)^(3/2)*x),x,4,a*arctanh(sqrt(c+d/x^2)/sqrt(c))/c^(3/2)+(b*c-a*d)/(c*d*sqrt(c+d/x^2))],
[(a+b/x^2)/((c+d/x^2)^(3/2)*x^3),x,3,(-b*c+a*d)/(d^2*sqrt(c+d/x^2))-b*sqrt(c+d/x^2)/d^2],
[(a+b/x^2)/((c+d/x^2)^(3/2)*x^5),x,3,-1/3*b*(c+d/x^2)^(3/2)/d^3+c*(b*c-a*d)/(d^3*sqrt(c+d/x^2))+(2*b*c-a*d)*sqrt(c+d/x^2)/d^3],
[(a+b/x^2)/((c+d/x^2)^(3/2)*x^7),x,3,1/3*(3*b*c-a*d)*(c+d/x^2)^(3/2)/d^4-1/5*b*(c+d/x^2)^(5/2)/d^4-c^2*(b*c-a*d)/(d^4*sqrt(c+d/x^2))-c*(3*b*c-2*a*d)*sqrt(c+d/x^2)/d^4],
[(a+b/x^2)/((c+d/x^2)^(3/2)*x^9),x,3,-c*(2*b*c-a*d)*(c+d/x^2)^(3/2)/d^5+1/5*(4*b*c-a*d)*(c+d/x^2)^(5/2)/d^5-1/7*b*(c+d/x^2)^(7/2)/d^5+c^3*(b*c-a*d)/(d^5*sqrt(c+d/x^2))+c^2*(4*b*c-3*a*d)*sqrt(c+d/x^2)/d^5],
[(a+b/x^2)*x^4/(c+d/x^2)^(3/2),x,4,4/15*d*(5*b*c-6*a*d)*x/(c^3*sqrt(c+d/x^2))+1/15*(5*b*c-6*a*d)*x^3/(c^2*sqrt(c+d/x^2))+1/5*a*x^5/(c*sqrt(c+d/x^2))-8/15*d*(5*b*c-6*a*d)*x*sqrt(c+d/x^2)/c^4],
[(a+b/x^2)*x^2/(c+d/x^2)^(3/2),x,3,-1/3*(3*b*c-4*a*d)*x/(c^2*sqrt(c+d/x^2))+1/3*a*x^3/(c*sqrt(c+d/x^2))+2/3*(3*b*c-4*a*d)*x*sqrt(c+d/x^2)/c^3],
[(a+b/x^2)/(c+d/x^2)^(3/2),x,3,(-b*c+2*a*d)/(c^2*x*sqrt(c+d/x^2))+a*x/(c*sqrt(c+d/x^2))],
[(a+b/x^2)/((c+d/x^2)^(3/2)*x^2),x,4,-b*arctanh(sqrt(d)/(x*sqrt(c+d/x^2)))/d^(3/2)+(b*c-a*d)/(c*d*x*sqrt(c+d/x^2))],
[(a+b/x^2)/((c+d/x^2)^(3/2)*x^4),x,5,1/2*(3*b*c-2*a*d)*arctanh(sqrt(d)/(x*sqrt(c+d/x^2)))/d^(5/2)-1/2*b/(d*x^3*sqrt(c+d/x^2))+1/2*(-3*b*c+2*a*d)/(d^2*x*sqrt(c+d/x^2))],
[(a+b/x^2)/((c+d/x^2)^(3/2)*x^6),x,6,-3/8*c*(5*b*c-4*a*d)*arctanh(sqrt(d)/(x*sqrt(c+d/x^2)))/d^(7/2)-1/4*b/(d*x^5*sqrt(c+d/x^2))+1/4*(-5*b*c+4*a*d)/(d^2*x^3*sqrt(c+d/x^2))+3/8*(5*b*c-4*a*d)*sqrt(c+d/x^2)/(d^3*x)],

# Integrands of the form (e x)^m (a+b/x^2)^p (c+d/x^2)^q with p and/or q symbolic
[(a+b/x^2)^p*(c+d/x^2)^q*(e*x)^m,x,4,(a+b/x^2)^p*(c+d/x^2)^q*(e*x)^(1+m)*AppellF1(1/2*(-1-m),-p,-q,1/2*(1-m),-b/(a*x^2),-d/(c*x^2))/(e*(1+m)*(1+b/(a*x^2))^p*(1+d/(c*x^2))^q),(a+b/x^2)^p*(c+d/x^2)^q*x*(e*x)^m*AppellF1(1/2*(-1-m),-p,-q,1/2*(1-m),-b/(a*x^2),-d/(c*x^2))/((1+m)*(1+b/(a*x^2))^p*(1+d/(c*x^2))^q)],
[(a+b/x^2)^p*(c+d/x^2)^q*x^4,x,4,1/5*(a+b/x^2)^p*(c+d/x^2)^q*x^5*AppellF1(-5/2,-p,-q,-3/2,-b/(a*x^2),-d/(c*x^2))/((1+b/(a*x^2))^p*(1+d/(c*x^2))^q)],
[(a+b/x^2)^p*(c+d/x^2)^q*x^3,x,3,1/2*b^2*(a+b/x^2)^(1+p)*(c+d/x^2)^q*AppellF1(1+p,-q,3,2+p,-d*(a+b/x^2)/(b*c-a*d),(a+b/x^2)/a)/(a^3*(1+p)*(b*(c+d/x^2)/(b*c-a*d))^q)],
[(a+b/x^2)^p*(c+d/x^2)^q*x^2,x,4,1/3*(a+b/x^2)^p*(c+d/x^2)^q*x^3*AppellF1(-3/2,-p,-q,-1/2,-b/(a*x^2),-d/(c*x^2))/((1+b/(a*x^2))^p*(1+d/(c*x^2))^q)],
[(a+b/x^2)^p*(c+d/x^2)^q*x,x,3,-1/2*b*(a+b/x^2)^(1+p)*(c+d/x^2)^q*AppellF1(1+p,-q,2,2+p,-d*(a+b/x^2)/(b*c-a*d),(a+b/x^2)/a)/(a^2*(1+p)*(b*(c+d/x^2)/(b*c-a*d))^q)],
[(a+b/x^2)^p*(c+d/x^2)^q,x,4,(a+b/x^2)^p*(c+d/x^2)^q*x*AppellF1(-1/2,-p,-q,1/2,-b/(a*x^2),-d/(c*x^2))/((1+b/(a*x^2))^p*(1+d/(c*x^2))^q)],
[(a+b/x^2)^p*(c+d/x^2)^q/x,x,3,1/2*(a+b/x^2)^(1+p)*(c+d/x^2)^q*AppellF1(1+p,-q,1,2+p,-d*(a+b/x^2)/(b*c-a*d),(a+b/x^2)/a)/(a*(1+p)*(b*(c+d/x^2)/(b*c-a*d))^q)],
[(a+b/x^2)^p*(c+d/x^2)^q/x^2,x,4,-(a+b/x^2)^p*(c+d/x^2)^q*AppellF1(1/2,-p,-q,3/2,-b/(a*x^2),-d/(c*x^2))/((1+b/(a*x^2))^p*(1+d/(c*x^2))^q*x)],
[(a+b/x^2)^p*(c+d/x^2)^q/x^3,x,3,-1/2*(a+b/x^2)^(1+p)*(c+d/x^2)^q*hypergeom([1+p,-q],[2+p],-d*(a+b/x^2)/(b*c-a*d))/(b*(1+p)*(b*(c+d/x^2)/(b*c-a*d))^q)],
[(a+b/x^2)^p*(c+d/x^2)^q/x^4,x,4,-1/3*(a+b/x^2)^p*(c+d/x^2)^q*AppellF1(3/2,-p,-q,5/2,-b/(a*x^2),-d/(c*x^2))/((1+b/(a*x^2))^p*(1+d/(c*x^2))^q*x^3)],

# Integrands of the form (e x)^(m/2) (a+b/x^2)^p (c+d/x^2)^q with p and/or q symbolic
[(a+b/x^2)^p*(c+d/x^2)^q*(e*x)^(5/2),x,4,2/7*(a+b/x^2)^p*(c+d/x^2)^q*(e*x)^(7/2)*AppellF1(-7/4,-p,-q,-3/4,-b/(a*x^2),-d/(c*x^2))/(e*(1+b/(a*x^2))^p*(1+d/(c*x^2))^q)],
[(a+b/x^2)^p*(c+d/x^2)^q*(e*x)^(3/2),x,4,2/5*(a+b/x^2)^p*(c+d/x^2)^q*(e*x)^(5/2)*AppellF1(-5/4,-p,-q,-1/4,-b/(a*x^2),-d/(c*x^2))/(e*(1+b/(a*x^2))^p*(1+d/(c*x^2))^q)],
[(a+b/x^2)^p*(c+d/x^2)^q*(e*x)^(1/2),x,4,2/3*(a+b/x^2)^p*(c+d/x^2)^q*(e*x)^(3/2)*AppellF1(-3/4,-p,-q,1/4,-b/(a*x^2),-d/(c*x^2))/(e*(1+b/(a*x^2))^p*(1+d/(c*x^2))^q)],
[(a+b/x^2)^p*(c+d/x^2)^q/(e*x)^(1/2),x,4,2*(a+b/x^2)^p*(c+d/x^2)^q*AppellF1(-1/4,-p,-q,3/4,-b/(a*x^2),-d/(c*x^2))*sqrt(e*x)/(e*(1+b/(a*x^2))^p*(1+d/(c*x^2))^q)],
[(a+b/x^2)^p*(c+d/x^2)^q/(e*x)^(3/2),x,4,-2*(a+b/x^2)^p*(c+d/x^2)^q*AppellF1(1/4,-p,-q,5/4,-b/(a*x^2),-d/(c*x^2))/(e*(1+b/(a*x^2))^p*(1+d/(c*x^2))^q*sqrt(e*x))],
[(a+b/x^2)^p*(c+d/x^2)^q/(e*x)^(5/2),x,4,-2/3*(a+b/x^2)^p*(c+d/x^2)^q*AppellF1(3/4,-p,-q,7/4,-b/(a*x^2),-d/(c*x^2))/(e*(1+b/(a*x^2))^p*(1+d/(c*x^2))^q*(e*x)^(3/2))],

# Integrands of the form (e x)^m (a+b x^n)^p (c+d x^n)^q

# Integrands of the form (e x)^m (a+b x^n)^p (c+d x^n)^p with p=q and b c+a d=0

# Integrands of the form (e x)^(m/2) (a+b x^(n/2))^(p/2) (c+d x^(n/2))^(q/2) with p=q and b c+a d=0

# p>0
[x^(5/2)*sqrt(-1+sqrt(x))*sqrt(1+sqrt(x)),x,6,-5/64*arccosh(sqrt(x))-5/96*x^(3/2)*sqrt(-1+sqrt(x))*sqrt(1+sqrt(x))-1/24*x^(5/2)*sqrt(-1+sqrt(x))*sqrt(1+sqrt(x))+1/4*x^(7/2)*sqrt(-1+sqrt(x))*sqrt(1+sqrt(x))-5/64*sqrt(x)*sqrt(-1+sqrt(x))*sqrt(1+sqrt(x))],
[x^(3/2)*sqrt(-1+sqrt(x))*sqrt(1+sqrt(x)),x,5,-1/8*arccosh(sqrt(x))-1/12*x^(3/2)*sqrt(-1+sqrt(x))*sqrt(1+sqrt(x))+1/3*x^(5/2)*sqrt(-1+sqrt(x))*sqrt(1+sqrt(x))-1/8*sqrt(x)*sqrt(-1+sqrt(x))*sqrt(1+sqrt(x))],
[x^(1/2)*sqrt(-1+sqrt(x))*sqrt(1+sqrt(x)),x,4,-1/4*arccosh(sqrt(x))+1/2*x^(3/2)*sqrt(-1+sqrt(x))*sqrt(1+sqrt(x))-1/4*sqrt(x)*sqrt(-1+sqrt(x))*sqrt(1+sqrt(x))],
[sqrt(-1+sqrt(x))*sqrt(1+sqrt(x))/x^(1/2),x,3,-arccosh(sqrt(x))+sqrt(x)*sqrt(-1+sqrt(x))*sqrt(1+sqrt(x))],
[sqrt(-1+sqrt(x))*sqrt(1+sqrt(x))/x^(3/2),x,4,2*arccosh(sqrt(x))+2*(-1+sqrt(x))^(3/2)*(1+sqrt(x))^(3/2)/sqrt(x)-2*sqrt(x)*sqrt(-1+sqrt(x))*sqrt(1+sqrt(x))],
[sqrt(-1+sqrt(x))*sqrt(1+sqrt(x))/x^(5/2),x,1,2/3*(-1+sqrt(x))^(3/2)*(1+sqrt(x))^(3/2)/x^(3/2)],
[sqrt(-1+sqrt(x))*sqrt(1+sqrt(x))/x^(7/2),x,2,2/5*(-1+sqrt(x))^(3/2)*(1+sqrt(x))^(3/2)/x^(5/2)+4/15*(-1+sqrt(x))^(3/2)*(1+sqrt(x))^(3/2)/x^(3/2)],
[sqrt(-1+sqrt(x))*sqrt(1+sqrt(x))/x^(9/2),x,3,2/7*(-1+sqrt(x))^(3/2)*(1+sqrt(x))^(3/2)/x^(7/2)+8/35*(-1+sqrt(x))^(3/2)*(1+sqrt(x))^(3/2)/x^(5/2)+16/105*(-1+sqrt(x))^(3/2)*(1+sqrt(x))^(3/2)/x^(3/2)],
[sqrt(-1+sqrt(x))*sqrt(1+sqrt(x))/x^(11/2),x,4,2/9*(-1+sqrt(x))^(3/2)*(1+sqrt(x))^(3/2)/x^(9/2)+4/21*(-1+sqrt(x))^(3/2)*(1+sqrt(x))^(3/2)/x^(7/2)+16/105*(-1+sqrt(x))^(3/2)*(1+sqrt(x))^(3/2)/x^(5/2)+32/315*(-1+sqrt(x))^(3/2)*(1+sqrt(x))^(3/2)/x^(3/2)],

# p<0
[x^(5/2)/(sqrt(-1+sqrt(x))*sqrt(1+sqrt(x))),x,5,5/8*arccosh(sqrt(x))+5/12*x^(3/2)*sqrt(-1+sqrt(x))*sqrt(1+sqrt(x))+1/3*x^(5/2)*sqrt(-1+sqrt(x))*sqrt(1+sqrt(x))+5/8*sqrt(x)*sqrt(-1+sqrt(x))*sqrt(1+sqrt(x))],
[x^(3/2)/(sqrt(-1+sqrt(x))*sqrt(1+sqrt(x))),x,4,3/4*arccosh(sqrt(x))+1/2*x^(3/2)*sqrt(-1+sqrt(x))*sqrt(1+sqrt(x))+3/4*sqrt(x)*sqrt(-1+sqrt(x))*sqrt(1+sqrt(x))],
[x^(1/2)/(sqrt(-1+sqrt(x))*sqrt(1+sqrt(x))),x,3,arccosh(sqrt(x))+sqrt(x)*sqrt(-1+sqrt(x))*sqrt(1+sqrt(x))],
[1/(x^(1/2)*sqrt(-1+sqrt(x))*sqrt(1+sqrt(x))),x,2,2*arccosh(sqrt(x))],
[1/(x^(3/2)*sqrt(-1+sqrt(x))*sqrt(1+sqrt(x))),x,1,2*sqrt(-1+sqrt(x))*sqrt(1+sqrt(x))/sqrt(x)],
[1/(x^(5/2)*sqrt(-1+sqrt(x))*sqrt(1+sqrt(x))),x,2,2/3*sqrt(-1+sqrt(x))*sqrt(1+sqrt(x))/x^(3/2)+4/3*sqrt(-1+sqrt(x))*sqrt(1+sqrt(x))/sqrt(x)],
[1/(x^(7/2)*sqrt(-1+sqrt(x))*sqrt(1+sqrt(x))),x,3,2/5*sqrt(-1+sqrt(x))*sqrt(1+sqrt(x))/x^(5/2)+8/15*sqrt(-1+sqrt(x))*sqrt(1+sqrt(x))/x^(3/2)+16/15*sqrt(-1+sqrt(x))*sqrt(1+sqrt(x))/sqrt(x)],

# Integrands of the form (e x)^m (a+b x^n)^p (c+d x^n)^q with p=q, b c+a d=0 and p symbolic
[x^2*(-a+b*x^n)^p*(a+b*x^n)^p,x,3,1/3*x^3*(-a+b*x^n)^p*(a+b*x^n)^p*hypergeom([3/2/n,-p],[1+3/2/n],b^2*x^(2*n)/a^2)/(1-b^2*x^(2*n)/a^2)^p],
[x*(-a+b*x^n)^p*(a+b*x^n)^p,x,3,1/2*x^2*(-a+b*x^n)^p*(a+b*x^n)^p*hypergeom([1/n,-p],[1+1/n],b^2*x^(2*n)/a^2)/(1-b^2*x^(2*n)/a^2)^p],
[(-a+b*x^n)^p*(a+b*x^n)^p,x,3,x*(-a+b*x^n)^p*(a+b*x^n)^p*hypergeom([1/2/n,-p],[1/2*(2+1/n)],b^2*x^(2*n)/a^2)/(1-b^2*x^(2*n)/a^2)^p],
[(-a+b*x^n)^p*(a+b*x^n)^p/x,x,4,-1/2*(-a+b*x^n)^p*(a+b*x^n)^p*(a^2-b^2*x^(2*n))*hypergeom([1,1+p],[2+p],1-b^2*x^(2*n)/a^2)/(a^2*n*(1+p))],
[(-a+b*x^n)^p*(a+b*x^n)^p/x^2,x,3,-(-a+b*x^n)^p*(a+b*x^n)^p*hypergeom([(-1/2)/n,-p],[1+(-1/2)/n],b^2*x^(2*n)/a^2)/(x*(1-b^2*x^(2*n)/a^2)^p)],

# Integrands of the form (e x)^m (a+b x^n)^p (c+d x^n)^q

# Integrands of the form (e x)^m (a+b x^n)^p (c+d x^n)
[(1+x^6)/(x*(1-x^6)),x,3,log(x)-1/3*log(1-x^6)],
[(e*x)^m*(a+b*x^n)^p*(a*(1+m)+b*(1+m+n+n*p)*x^n),x,1,(e*x)^(1+m)*(a+b*x^n)^(1+p)/e],

# Integrands of the form (e x)^m (a+b x^n)^p / (c+d x^n)

# p>0

# p<0
[(e*x)^m/((a+b*x^n)*(c+d*x^n)),x,3,b*(e*x)^(1+m)*hypergeom([1,(1+m)/n],[(1+m+n)/n],-b*x^n/a)/(a*(b*c-a*d)*e*(1+m))-d*(e*x)^(1+m)*hypergeom([1,(1+m)/n],[(1+m+n)/n],-d*x^n/c)/(c*(b*c-a*d)*e*(1+m))],
[x^2/((a+b*x^n)*(c+d*x^n)),x,3,1/3*b*x^3*hypergeom([1,3/n],[(3+n)/n],-b*x^n/a)/(a*(b*c-a*d))-1/3*d*x^3*hypergeom([1,3/n],[(3+n)/n],-d*x^n/c)/(c*(b*c-a*d))],
[x/((a+b*x^n)*(c+d*x^n)),x,3,1/2*b*x^2*hypergeom([1,2/n],[(2+n)/n],-b*x^n/a)/(a*(b*c-a*d))-1/2*d*x^2*hypergeom([1,2/n],[(2+n)/n],-d*x^n/c)/(c*(b*c-a*d))],
[1/((a+b*x^n)*(c+d*x^n)),x,3,b*x*hypergeom([1,1/n],[1+1/n],-b*x^n/a)/(a*(b*c-a*d))-d*x*hypergeom([1,1/n],[1+1/n],-d*x^n/c)/(c*(b*c-a*d))],
[1/(x*(a+b*x^n)*(c+d*x^n)),x,3,log(x)/(a*c)-b*log(a+b*x^n)/(a*(b*c-a*d)*n)+d*log(c+d*x^n)/(c*(b*c-a*d)*n)],
[1/(x^2*(a+b*x^n)*(c+d*x^n)),x,3,-b*hypergeom([1,(-1)/n],[(-1+n)/n],-b*x^n/a)/(a*(b*c-a*d)*x)+d*hypergeom([1,(-1)/n],[(-1+n)/n],-d*x^n/c)/(c*(b*c-a*d)*x)],
[1/(x^3*(a+b*x^n)*(c+d*x^n)),x,3,-1/2*b*hypergeom([1,(-2)/n],[(-2+n)/n],-b*x^n/a)/(a*(b*c-a*d)*x^2)+1/2*d*hypergeom([1,(-2)/n],[(-2+n)/n],-d*x^n/c)/(c*(b*c-a*d)*x^2)],
[(e*x)^m/((a+b*x^n)^2*(c+d*x^n)),x,5,b*(e*x)^(1+m)/(a*(b*c-a*d)*e*n*(a+b*x^n))+b*(a*d*(1+m-2*n)-b*c*(1+m-n))*(e*x)^(1+m)*hypergeom([1,(1+m)/n],[(1+m+n)/n],-b*x^n/a)/(a^2*(b*c-a*d)^2*e*(1+m)*n)+d^2*(e*x)^(1+m)*hypergeom([1,(1+m)/n],[(1+m+n)/n],-d*x^n/c)/(c*(b*c-a*d)^2*e*(1+m))],
[x^2/((a+b*x^n)^2*(c+d*x^n)),x,5,b*x^3/(a*(b*c-a*d)*n*(a+b*x^n))+1/3*b*(a*d*(3-2*n)-b*c*(3-n))*x^3*hypergeom([1,3/n],[(3+n)/n],-b*x^n/a)/(a^2*(b*c-a*d)^2*n)+1/3*d^2*x^3*hypergeom([1,3/n],[(3+n)/n],-d*x^n/c)/(c*(b*c-a*d)^2)],
[x/((a+b*x^n)^2*(c+d*x^n)),x,5,b*x^2/(a*(b*c-a*d)*n*(a+b*x^n))+1/2*b*(2*a*d*(1-n)-b*c*(2-n))*x^2*hypergeom([1,2/n],[(2+n)/n],-b*x^n/a)/(a^2*(b*c-a*d)^2*n)+1/2*d^2*x^2*hypergeom([1,2/n],[(2+n)/n],-d*x^n/c)/(c*(b*c-a*d)^2)],
[1/((a+b*x^n)^2*(c+d*x^n)),x,4,b*x/(a*(b*c-a*d)*n*(a+b*x^n))+b*(a*d*(1-2*n)-b*c*(1-n))*x*hypergeom([1,1/n],[1+1/n],-b*x^n/a)/(a^2*(b*c-a*d)^2*n)+d^2*x*hypergeom([1,1/n],[1+1/n],-d*x^n/c)/(c*(b*c-a*d)^2)],
[1/(x*(a+b*x^n)^2*(c+d*x^n)),x,3,b/(a*(b*c-a*d)*n*(a+b*x^n))+log(x)/(a^2*c)-b*(b*c-2*a*d)*log(a+b*x^n)/(a^2*(b*c-a*d)^2*n)-d^2*log(c+d*x^n)/(c*(b*c-a*d)^2*n)],
[1/(x^2*(a+b*x^n)^2*(c+d*x^n)),x,5,b/(a*(b*c-a*d)*n*x*(a+b*x^n))-b*(b*c*(1+n)-a*d*(1+2*n))*hypergeom([1,(-1)/n],[(-1+n)/n],-b*x^n/a)/(a^2*(b*c-a*d)^2*n*x)-d^2*hypergeom([1,(-1)/n],[(-1+n)/n],-d*x^n/c)/(c*(b*c-a*d)^2*x)],
[1/(x^3*(a+b*x^n)^2*(c+d*x^n)),x,5,b/(a*(b*c-a*d)*n*x^2*(a+b*x^n))+1/2*b*(2*a*d*(1+n)-b*c*(2+n))*hypergeom([1,(-2)/n],[(-2+n)/n],-b*x^n/a)/(a^2*(b*c-a*d)^2*n*x^2)-1/2*d^2*hypergeom([1,(-2)/n],[(-2+n)/n],-d*x^n/c)/(c*(b*c-a*d)^2*x^2)],

# Integrands of the form x^(k n-1) (a+b x^n)^p / (c+d x^n)
[x^(-1+2*n)*(a+b*x^n)^3/(c+d*x^n),x,3,-(b*c-a*d)^3*x^n/(d^4*n)+1/2*b*(b^2*c^2-3*a*b*c*d+3*a^2*d^2)*x^(2*n)/(d^3*n)-1/3*b^2*(b*c-3*a*d)*x^(3*n)/(d^2*n)+1/4*b^3*x^(4*n)/(d*n)+c*(b*c-a*d)^3*log(c+d*x^n)/(d^5*n)],
[x^(-1+2*n)*(a+b*x^n)^2/(c+d*x^n),x,3,(b*c-a*d)^2*x^n/(d^3*n)-1/2*b*(b*c-2*a*d)*x^(2*n)/(d^2*n)+1/3*b^2*x^(3*n)/(d*n)-c*(b*c-a*d)^2*log(c+d*x^n)/(d^4*n)],
[x^(-1+2*n)*(a+b*x^n)/(c+d*x^n),x,3,-(b*c-a*d)*x^n/(d^2*n)+1/2*b*x^(2*n)/(d*n)+c*(b*c-a*d)*log(c+d*x^n)/(d^3*n)],
[x^(-1+2*n)/((a+b*x^n)*(c+d*x^n)),x,3,-a*log(a+b*x^n)/(b*(b*c-a*d)*n)+c*log(c+d*x^n)/(d*(b*c-a*d)*n)],
[x^(-1+2*n)/((a+b*x^n)^2*(c+d*x^n)),x,3,a/(b*(b*c-a*d)*n*(a+b*x^n))+c*log(a+b*x^n)/((b*c-a*d)^2*n)-c*log(c+d*x^n)/((b*c-a*d)^2*n)],
[x^(-1+2*n)/((a+b*x^n)^3*(c+d*x^n)),x,3,1/2*a/(b*(b*c-a*d)*n*(a+b*x^n)^2)-c/((b*c-a*d)^2*n*(a+b*x^n))-c*d*log(a+b*x^n)/((b*c-a*d)^3*n)+c*d*log(c+d*x^n)/((b*c-a*d)^3*n)],
[x^(-1+3*n)*(a+b*x^n)^3/(c+d*x^n),x,3,c*(b*c-a*d)^3*x^n/(d^5*n)-1/2*(b*c-a*d)^3*x^(2*n)/(d^4*n)+1/3*b*(b^2*c^2-3*a*b*c*d+3*a^2*d^2)*x^(3*n)/(d^3*n)-1/4*b^2*(b*c-3*a*d)*x^(4*n)/(d^2*n)+1/5*b^3*x^(5*n)/(d*n)-c^2*(b*c-a*d)^3*log(c+d*x^n)/(d^6*n)],
[x^(-1+3*n)*(a+b*x^n)^2/(c+d*x^n),x,3,-c*(b*c-a*d)^2*x^n/(d^4*n)+1/2*(b*c-a*d)^2*x^(2*n)/(d^3*n)-1/3*b*(b*c-2*a*d)*x^(3*n)/(d^2*n)+1/4*b^2*x^(4*n)/(d*n)+c^2*(b*c-a*d)^2*log(c+d*x^n)/(d^5*n)],
[x^(-1+3*n)*(a+b*x^n)/(c+d*x^n),x,3,c*(b*c-a*d)*x^n/(d^3*n)-1/2*(b*c-a*d)*x^(2*n)/(d^2*n)+1/3*b*x^(3*n)/(d*n)-c^2*(b*c-a*d)*log(c+d*x^n)/(d^4*n)],
[x^(-1+3*n)/((a+b*x^n)*(c+d*x^n)),x,3,x^n/(b*d*n)+a^2*log(a+b*x^n)/(b^2*(b*c-a*d)*n)-c^2*log(c+d*x^n)/(d^2*(b*c-a*d)*n)],
[x^(-1+3*n)/((a+b*x^n)^2*(c+d*x^n)),x,3,-a^2/(b^2*(b*c-a*d)*n*(a+b*x^n))-a*(2*b*c-a*d)*log(a+b*x^n)/(b^2*(b*c-a*d)^2*n)+c^2*log(c+d*x^n)/(d*(b*c-a*d)^2*n)],
[x^(-1+3*n)/((a+b*x^n)^3*(c+d*x^n)),x,3,-1/2*a^2/(b^2*(b*c-a*d)*n*(a+b*x^n)^2)+a*(2*b*c-a*d)/(b^2*(b*c-a*d)^2*n*(a+b*x^n))+c^2*log(a+b*x^n)/((b*c-a*d)^3*n)-c^2*log(c+d*x^n)/((b*c-a*d)^3*n)],
[x^13*(b+c*x)^13*(b+2*c*x),x,1,1/14*x^14*(b+c*x)^14],
[x^27*(b+c*x^2)^13*(b+2*c*x^2),x,2,1/28*x^28*(b+c*x^2)^14],
[x^41*(b+c*x^3)^13*(b+2*c*x^3),x,2,1/42*x^42*(b+c*x^3)^14],
[x^(-1+14*n)*(b+c*x^n)^13*(b+2*c*x^n),x,2,1/14*x^(14*n)*(b+c*x^n)^14/n],
[x^(-1+m)*(a+b*x^n)^(-1+p)*(a*m+b*(m+n*p)*x^n),x,1,x^m*(a+b*x^n)^p],
[(b+2*c*x)/(x*(b+c*x)),x,2,log(x*(b+c*x)),log(x)+log(b+c*x)],
[(b+2*c*x^2)/(x*(b+c*x^2)),x,3,log(x)+1/2*log(b+c*x^2)],
[(b+2*c*x^3)/(x*(b+c*x^3)),x,3,log(x)+1/3*log(b+c*x^3)],
[(b+2*c*x^n)/(x*(b+c*x^n)),x,3,log(x)+log(b+c*x^n)/n],
[(b+2*c*x)/(x^8*(b+c*x)^8),x,1,(-1/7)/(x^7*(b+c*x)^7)],
[(b+2*c*x^2)/(x^15*(b+c*x^2)^8),x,2,(-1/14)/(x^14*(b+c*x^2)^7)],
[(b+2*c*x^3)/(x^22*(b+c*x^3)^8),x,2,(-1/21)/(x^21*(b+c*x^3)^7)],
[x^(-1-7*n)*(b+2*c*x^n)/(b+c*x^n)^8,x,2,(-1/7)/(n*x^(7*n)*(b+c*x^n)^7)],

# Integrands of the form x^m (a+b x^n)^p (c+d x^n)^(q/2)
[x^31*sqrt(1+x^16)/(1-x^16),x,5,-1/24*(1+x^16)^(3/2)+1/4*arctanh(sqrt(1+x^16)/sqrt(2))/sqrt(2)-1/8*sqrt(1+x^16)],

# Integrands of the form x^m (a+b x^n)^(p/2) (c+d x^n)^(q/2)
[sqrt(c+d/x)/(x*sqrt(a+b/x)),x,8,2*arctanh(sqrt(c)*sqrt(a+b/x)/(sqrt(a)*sqrt(c+d/x)))*sqrt(c)/sqrt(a)-2*arctanh(sqrt(d)*sqrt(a+b/x)/(sqrt(b)*sqrt(c+d/x)))*sqrt(d)/sqrt(b)],
[x^(-1+2*n)*(a+b*x^n)^(5/2)/sqrt(c+d*x^n),x,8,5/64*(b*c-a*d)^3*(7*b*c+a*d)*arctanh(sqrt(d)*sqrt(a+b*x^n)/(sqrt(b)*sqrt(c+d*x^n)))/(b^(3/2)*d^(9/2)*n)+5/96*(b*c-a*d)*(7*b*c+a*d)*(a+b*x^n)^(3/2)*sqrt(c+d*x^n)/(b*d^3*n)-1/24*(7*b*c+a*d)*(a+b*x^n)^(5/2)*sqrt(c+d*x^n)/(b*d^2*n)+1/4*(a+b*x^n)^(7/2)*sqrt(c+d*x^n)/(b*d*n)-5/64*(b*c-a*d)^2*(7*b*c+a*d)*sqrt(a+b*x^n)*sqrt(c+d*x^n)/(b*d^4*n)],
[x^(-1+2*n)*(a+b*x^n)^(3/2)/sqrt(c+d*x^n),x,7,-1/8*(b*c-a*d)^2*(5*b*c+a*d)*arctanh(sqrt(d)*sqrt(a+b*x^n)/(sqrt(b)*sqrt(c+d*x^n)))/(b^(3/2)*d^(7/2)*n)-1/12*(5*b*c+a*d)*(a+b*x^n)^(3/2)*sqrt(c+d*x^n)/(b*d^2*n)+1/3*(a+b*x^n)^(5/2)*sqrt(c+d*x^n)/(b*d*n)+1/8*(b*c-a*d)*(5*b*c+a*d)*sqrt(a+b*x^n)*sqrt(c+d*x^n)/(b*d^3*n)],
[x^(-1+2*n)*sqrt(a+b*x^n)/sqrt(c+d*x^n),x,6,1/4*(b*c-a*d)*(3*b*c+a*d)*arctanh(sqrt(d)*sqrt(a+b*x^n)/(sqrt(b)*sqrt(c+d*x^n)))/(b^(3/2)*d^(5/2)*n)+1/2*(a+b*x^n)^(3/2)*sqrt(c+d*x^n)/(b*d*n)-1/4*(3*b*c+a*d)*sqrt(a+b*x^n)*sqrt(c+d*x^n)/(b*d^2*n)],
[x^(-1+2*n)/(sqrt(a+b*x^n)*sqrt(c+d*x^n)),x,5,-(b*c+a*d)*arctanh(sqrt(d)*sqrt(a+b*x^n)/(sqrt(b)*sqrt(c+d*x^n)))/(b^(3/2)*d^(3/2)*n)+sqrt(a+b*x^n)*sqrt(c+d*x^n)/(b*d*n)],
[x^(-1+2*n)/((a+b*x^n)^(3/2)*sqrt(c+d*x^n)),x,5,2*arctanh(sqrt(d)*sqrt(a+b*x^n)/(sqrt(b)*sqrt(c+d*x^n)))/(b^(3/2)*n*sqrt(d))+2*a*sqrt(c+d*x^n)/(b*(b*c-a*d)*n*sqrt(a+b*x^n))],
[x^(-1+2*n)/((a+b*x^n)^(5/2)*sqrt(c+d*x^n)),x,3,2/3*a*sqrt(c+d*x^n)/(b*(b*c-a*d)*n*(a+b*x^n)^(3/2))-2/3*(3*b*c-a*d)*sqrt(c+d*x^n)/(b*(b*c-a*d)^2*n*sqrt(a+b*x^n))],
[x^(-1+3*n)*(a+b*x^n)^(5/2)/sqrt(c+d*x^n),x,9,-1/128*(b*c-a*d)^3*(63*b^2*c^2+14*a*b*c*d+3*a^2*d^2)*arctanh(sqrt(d)*sqrt(a+b*x^n)/(sqrt(b)*sqrt(c+d*x^n)))/(b^(5/2)*d^(11/2)*n)-1/192*(b*c-a*d)*(63*b^2*c^2+14*a*b*c*d+3*a^2*d^2)*(a+b*x^n)^(3/2)*sqrt(c+d*x^n)/(b^2*d^4*n)+1/240*(63*b^2*c^2+14*a*b*c*d+3*a^2*d^2)*(a+b*x^n)^(5/2)*sqrt(c+d*x^n)/(b^2*d^3*n)-3/40*(3*b*c+a*d)*(a+b*x^n)^(7/2)*sqrt(c+d*x^n)/(b^2*d^2*n)+1/5*x^n*(a+b*x^n)^(7/2)*sqrt(c+d*x^n)/(b*d*n)+1/128*(b*c-a*d)^2*(63*b^2*c^2+14*a*b*c*d+3*a^2*d^2)*sqrt(a+b*x^n)*sqrt(c+d*x^n)/(b^2*d^5*n)],
[x^(-1+3*n)*(a+b*x^n)^(3/2)/sqrt(c+d*x^n),x,8,1/64*(b*c-a*d)^2*(35*b^2*c^2+10*a*b*c*d+3*a^2*d^2)*arctanh(sqrt(d)*sqrt(a+b*x^n)/(sqrt(b)*sqrt(c+d*x^n)))/(b^(5/2)*d^(9/2)*n)+1/96*(35*b^2*c^2+10*a*b*c*d+3*a^2*d^2)*(a+b*x^n)^(3/2)*sqrt(c+d*x^n)/(b^2*d^3*n)-1/24*(7*b*c+3*a*d)*(a+b*x^n)^(5/2)*sqrt(c+d*x^n)/(b^2*d^2*n)+1/4*x^n*(a+b*x^n)^(5/2)*sqrt(c+d*x^n)/(b*d*n)-1/64*(b*c-a*d)*(35*b^2*c^2+10*a*b*c*d+3*a^2*d^2)*sqrt(a+b*x^n)*sqrt(c+d*x^n)/(b^2*d^4*n)],
[x^(-1+3*n)*sqrt(a+b*x^n)/sqrt(c+d*x^n),x,7,-1/8*(b*c-a*d)*(5*b^2*c^2+2*a*b*c*d+a^2*d^2)*arctanh(sqrt(d)*sqrt(a+b*x^n)/(sqrt(b)*sqrt(c+d*x^n)))/(b^(5/2)*d^(7/2)*n)-1/12*(5*b*c+3*a*d)*(a+b*x^n)^(3/2)*sqrt(c+d*x^n)/(b^2*d^2*n)+1/3*x^n*(a+b*x^n)^(3/2)*sqrt(c+d*x^n)/(b*d*n)+1/8*(5*b^2*c^2+2*a*b*c*d+a^2*d^2)*sqrt(a+b*x^n)*sqrt(c+d*x^n)/(b^2*d^3*n)],
[x^(-1+3*n)/(sqrt(a+b*x^n)*sqrt(c+d*x^n)),x,6,-1/4*(4*a*b*c*d-3*(b*c+a*d)^2)*arctanh(sqrt(d)*sqrt(a+b*x^n)/(sqrt(b)*sqrt(c+d*x^n)))/(b^(5/2)*d^(5/2)*n)-3/4*(b*c+a*d)*sqrt(a+b*x^n)*sqrt(c+d*x^n)/(b^2*d^2*n)+1/2*x^n*sqrt(a+b*x^n)*sqrt(c+d*x^n)/(b*d*n)],
[x^(-1+3*n)/((a+b*x^n)^(3/2)*sqrt(c+d*x^n)),x,6,-(b*c+3*a*d)*arctanh(sqrt(d)*sqrt(a+b*x^n)/(sqrt(b)*sqrt(c+d*x^n)))/(b^(5/2)*d^(3/2)*n)-2*a^2*sqrt(c+d*x^n)/(b^2*(b*c-a*d)*n*sqrt(a+b*x^n))+sqrt(a+b*x^n)*sqrt(c+d*x^n)/(b^2*d*n)],
[x^(-1+3*n)/((a+b*x^n)^(5/2)*sqrt(c+d*x^n)),x,6,2*arctanh(sqrt(d)*sqrt(a+b*x^n)/(sqrt(b)*sqrt(c+d*x^n)))/(b^(5/2)*n*sqrt(d))-2/3*a^2*sqrt(c+d*x^n)/(b^2*(b*c-a*d)*n*(a+b*x^n)^(3/2))+4/3*a*(3*b*c-2*a*d)*sqrt(c+d*x^n)/(b^2*(b*c-a*d)^2*n*sqrt(a+b*x^n))],

# Integrands of the form x^(m/2) (a+b x^n)^(p/2) (c+d x^n)^(q/2)

# Integrands of the form x^m (a+b x^n)^p (c+d x^n)^q when q is symbolic
[x^p*(b+c*x)^p*(b+2*c*x),x,1,x^(1+p)*(b+c*x)^(1+p)/(1+p)],
[x^(-1+2*(1+p))*(b+c*x^2)^p*(b+2*c*x^2),x,1,1/2*x^(2*(1+p))*(b+c*x^2)^(1+p)/(1+p)],
[x^(-1+3*(1+p))*(b+c*x^3)^p*(b+2*c*x^3),x,1,1/3*x^(3*(1+p))*(b+c*x^3)^(1+p)/(1+p)],
[x^(-1+n*(1+p))*(b+c*x^n)^p*(b+2*c*x^n),x,1,x^(n*(1+p))*(b+c*x^n)^(1+p)/(n*(1+p))]]:
