# Maple integration test file: "1 Algebraic functions\1.1 Binomial products\1.1.2 Quadratic\1.1.2.2 (c x)^m (a+b x^2)^p.txt"

lst:=[

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

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

# Integrands of the form x^m (a+b x^2)^p

# p>0
[x^4*(a+b*x^2),x,2,1/5*a*x^5+1/7*b*x^7],
[x^3*(a+b*x^2),x,2,1/4*a*x^4+1/6*b*x^6],
[x^2*(a+b*x^2),x,2,1/3*a*x^3+1/5*b*x^5],
[x*(a+b*x^2),x,2,1/2*a*x^2+1/4*b*x^4],
[a+b*x^2,x,1,a*x+1/3*b*x^3],
[(a+b*x^2)/x,x,2,1/2*b*x^2+a*log(x)],
[(a+b*x^2)/x^2,x,2,-a/x+b*x],
[(a+b*x^2)/x^3,x,2,-1/2*a/x^2+b*log(x)],
[(a+b*x^2)/x^4,x,2,-1/3*a/x^3-b/x],
[(a+b*x^2)/x^5,x,2,-1/4*a/x^4-1/2*b/x^2],
[(a+b*x^2)/x^6,x,2,-1/5*a/x^5-1/3*b/x^3],
[(a+b*x^2)/x^7,x,2,-1/6*a/x^6-1/4*b/x^4],
[x^5*(a+b*x^2)^2,x,3,1/6*a^2*x^6+1/4*a*b*x^8+1/10*b^2*x^10],
[x^4*(a+b*x^2)^2,x,2,1/5*a^2*x^5+2/7*a*b*x^7+1/9*b^2*x^9],
[x^3*(a+b*x^2)^2,x,3,1/4*a^2*x^4+1/3*a*b*x^6+1/8*b^2*x^8],
[x^2*(a+b*x^2)^2,x,2,1/3*a^2*x^3+2/5*a*b*x^5+1/7*b^2*x^7],
[x*(a+b*x^2)^2,x,1,1/6*(a+b*x^2)^3/b],
[(a+b*x^2)^2,x,2,a^2*x+2/3*a*b*x^3+1/5*b^2*x^5],
[(a+b*x^2)^2/x,x,3,a*b*x^2+1/4*b^2*x^4+a^2*log(x)],
[(a+b*x^2)^2/x^2,x,2,-a^2/x+2*a*b*x+1/3*b^2*x^3],
[(a+b*x^2)^2/x^3,x,3,-1/2*a^2/x^2+1/2*b^2*x^2+2*a*b*log(x)],
[(a+b*x^2)^2/x^4,x,2,-1/3*a^2/x^3-2*a*b/x+b^2*x],
[(a+b*x^2)^2/x^5,x,3,-1/4*a^2/x^4-a*b/x^2+b^2*log(x)],
[(a+b*x^2)^2/x^6,x,2,-1/5*a^2/x^5-2/3*a*b/x^3-b^2/x],
[(a+b*x^2)^2/x^7,x,1,-1/6*(a+b*x^2)^3/(a*x^6)],
[(a+b*x^2)^2/x^8,x,2,-1/7*a^2/x^7-2/5*a*b/x^5-1/3*b^2/x^3],
[(a+b*x^2)^2/x^9,x,3,-1/8*a^2/x^8-1/3*a*b/x^6-1/4*b^2/x^4],
[(a+b*x^2)^2/x^10,x,2,-1/9*a^2/x^9-2/7*a*b/x^7-1/5*b^2/x^5],
[x^9*(a+b*x^2)^3,x,3,1/10*a^3*x^10+1/4*a^2*b*x^12+3/14*a*b^2*x^14+1/16*b^3*x^16],
[x^7*(a+b*x^2)^3,x,3,1/8*a^3*x^8+3/10*a^2*b*x^10+1/4*a*b^2*x^12+1/14*b^3*x^14],
[x^5*(a+b*x^2)^3,x,3,1/6*a^3*x^6+3/8*a^2*b*x^8+3/10*a*b^2*x^10+1/12*b^3*x^12],
[x^3*(a+b*x^2)^3,x,3,-1/8*a*(a+b*x^2)^4/b^2+1/10*(a+b*x^2)^5/b^2],
[x*(a+b*x^2)^3,x,1,1/8*(a+b*x^2)^4/b],
[(a+b*x^2)^3/x,x,3,3/2*a^2*b*x^2+3/4*a*b^2*x^4+1/6*b^3*x^6+a^3*log(x)],
[(a+b*x^2)^3/x^3,x,3,-1/2*a^3/x^2+3/2*a*b^2*x^2+1/4*b^3*x^4+3*a^2*b*log(x)],
[(a+b*x^2)^3/x^5,x,3,-1/4*a^3/x^4-3/2*a^2*b/x^2+1/2*b^3*x^2+3*a*b^2*log(x)],
[(a+b*x^2)^3/x^7,x,3,-1/6*a^3/x^6-3/4*a^2*b/x^4-3/2*a*b^2/x^2+b^3*log(x)],
[(a+b*x^2)^3/x^9,x,1,-1/8*(a+b*x^2)^4/(a*x^8)],
[(a+b*x^2)^3/x^11,x,3,-1/10*(a+b*x^2)^4/(a*x^10)+1/40*b*(a+b*x^2)^4/(a^2*x^8)],
[(a+b*x^2)^3/x^13,x,3,-1/12*a^3/x^12-3/10*a^2*b/x^10-3/8*a*b^2/x^8-1/6*b^3/x^6],
[(a+b*x^2)^3/x^15,x,3,-1/14*a^3/x^14-1/4*a^2*b/x^12-3/10*a*b^2/x^10-1/8*b^3/x^8],
[x^6*(a+b*x^2)^3,x,2,1/7*a^3*x^7+1/3*a^2*b*x^9+3/11*a*b^2*x^11+1/13*b^3*x^13],
[x^4*(a+b*x^2)^3,x,2,1/5*a^3*x^5+3/7*a^2*b*x^7+1/3*a*b^2*x^9+1/11*b^3*x^11],
[x^2*(a+b*x^2)^3,x,2,1/3*a^3*x^3+3/5*a^2*b*x^5+3/7*a*b^2*x^7+1/9*b^3*x^9],
[(a+b*x^2)^3,x,2,a^3*x+a^2*b*x^3+3/5*a*b^2*x^5+1/7*b^3*x^7],
[(a+b*x^2)^3/x^2,x,2,-a^3/x+3*a^2*b*x+a*b^2*x^3+1/5*b^3*x^5],
[(a+b*x^2)^3/x^4,x,2,-1/3*a^3/x^3-3*a^2*b/x+3*a*b^2*x+1/3*b^3*x^3],
[(a+b*x^2)^3/x^6,x,2,-1/5*a^3/x^5-a^2*b/x^3-3*a*b^2/x+b^3*x],
[(a+b*x^2)^3/x^8,x,2,-1/7*a^3/x^7-3/5*a^2*b/x^5-a*b^2/x^3-b^3/x],
[(a+b*x^2)^3/x^10,x,2,-1/9*a^3/x^9-3/7*a^2*b/x^7-3/5*a*b^2/x^5-1/3*b^3/x^3],
[(a+b*x^2)^3/x^12,x,2,-1/11*a^3/x^11-1/3*a^2*b/x^9-3/7*a*b^2/x^7-1/5*b^3/x^5],
[x^13*(a+b*x^2)^5,x,3,1/14*a^5*x^14+5/16*a^4*b*x^16+5/9*a^3*b^2*x^18+1/2*a^2*b^3*x^20+5/22*a*b^4*x^22+1/24*b^5*x^24],
[x^11*(a+b*x^2)^5,x,3,1/12*a^5*x^12+5/14*a^4*b*x^14+5/8*a^3*b^2*x^16+5/9*a^2*b^3*x^18+1/4*a*b^4*x^20+1/22*b^5*x^22],
[x^9*(a+b*x^2)^5,x,3,1/10*a^5*x^10+5/12*a^4*b*x^12+5/7*a^3*b^2*x^14+5/8*a^2*b^3*x^16+5/18*a*b^4*x^18+1/20*b^5*x^20],
[x^7*(a+b*x^2)^5,x,3,-1/12*a^3*(a+b*x^2)^6/b^4+3/14*a^2*(a+b*x^2)^7/b^4-3/16*a*(a+b*x^2)^8/b^4+1/18*(a+b*x^2)^9/b^4],
[x^5*(a+b*x^2)^5,x,3,1/12*a^2*(a+b*x^2)^6/b^3-1/7*a*(a+b*x^2)^7/b^3+1/16*(a+b*x^2)^8/b^3],
[x^3*(a+b*x^2)^5,x,3,-1/12*a*(a+b*x^2)^6/b^2+1/14*(a+b*x^2)^7/b^2],
[x*(a+b*x^2)^5,x,1,1/12*(a+b*x^2)^6/b],
[(a+b*x^2)^5/x,x,3,5/2*a^4*b*x^2+5/2*a^3*b^2*x^4+5/3*a^2*b^3*x^6+5/8*a*b^4*x^8+1/10*b^5*x^10+a^5*log(x)],
[(a+b*x^2)^5/x^3,x,3,-1/2*a^5/x^2+5*a^3*b^2*x^2+5/2*a^2*b^3*x^4+5/6*a*b^4*x^6+1/8*b^5*x^8+5*a^4*b*log(x)],
[(a+b*x^2)^5/x^5,x,3,-1/4*a^5/x^4-5/2*a^4*b/x^2+5*a^2*b^3*x^2+5/4*a*b^4*x^4+1/6*b^5*x^6+10*a^3*b^2*log(x)],
[(a+b*x^2)^5/x^7,x,3,-1/6*a^5/x^6-5/4*a^4*b/x^4-5*a^3*b^2/x^2+5/2*a*b^4*x^2+1/4*b^5*x^4+10*a^2*b^3*log(x)],
[(a+b*x^2)^5/x^9,x,3,-1/8*a^5/x^8-5/6*a^4*b/x^6-5/2*a^3*b^2/x^4-5*a^2*b^3/x^2+1/2*b^5*x^2+5*a*b^4*log(x)],
[(a+b*x^2)^5/x^11,x,3,-1/10*a^5/x^10-5/8*a^4*b/x^8-5/3*a^3*b^2/x^6-5/2*a^2*b^3/x^4-5/2*a*b^4/x^2+b^5*log(x)],
[(a+b*x^2)^5/x^13,x,1,-1/12*(a+b*x^2)^6/(a*x^12)],
[(a+b*x^2)^5/x^15,x,3,-1/14*(a+b*x^2)^6/(a*x^14)+1/84*b*(a+b*x^2)^6/(a^2*x^12)],
[(a+b*x^2)^5/x^17,x,4,-1/16*(a+b*x^2)^6/(a*x^16)+1/56*b*(a+b*x^2)^6/(a^2*x^14)-1/336*b^2*(a+b*x^2)^6/(a^3*x^12)],
[(a+b*x^2)^5/x^19,x,3,-1/18*a^5/x^18-5/16*a^4*b/x^16-5/7*a^3*b^2/x^14-5/6*a^2*b^3/x^12-1/2*a*b^4/x^10-1/8*b^5/x^8],
[(a+b*x^2)^5/x^21,x,3,-1/20*a^5/x^20-5/18*a^4*b/x^18-5/8*a^3*b^2/x^16-5/7*a^2*b^3/x^14-5/12*a*b^4/x^12-1/10*b^5/x^10],
[x^8*(a+b*x^2)^5,x,2,1/9*a^5*x^9+5/11*a^4*b*x^11+10/13*a^3*b^2*x^13+2/3*a^2*b^3*x^15+5/17*a*b^4*x^17+1/19*b^5*x^19],
[x^6*(a+b*x^2)^5,x,2,1/7*a^5*x^7+5/9*a^4*b*x^9+10/11*a^3*b^2*x^11+10/13*a^2*b^3*x^13+1/3*a*b^4*x^15+1/17*b^5*x^17],
[x^4*(a+b*x^2)^5,x,2,1/5*a^5*x^5+5/7*a^4*b*x^7+10/9*a^3*b^2*x^9+10/11*a^2*b^3*x^11+5/13*a*b^4*x^13+1/15*b^5*x^15],
[x^2*(a+b*x^2)^5,x,2,1/3*a^5*x^3+a^4*b*x^5+10/7*a^3*b^2*x^7+10/9*a^2*b^3*x^9+5/11*a*b^4*x^11+1/13*b^5*x^13],
[(a+b*x^2)^5,x,2,a^5*x+5/3*a^4*b*x^3+2*a^3*b^2*x^5+10/7*a^2*b^3*x^7+5/9*a*b^4*x^9+1/11*b^5*x^11],
[(a+b*x^2)^5/x^2,x,2,-a^5/x+5*a^4*b*x+10/3*a^3*b^2*x^3+2*a^2*b^3*x^5+5/7*a*b^4*x^7+1/9*b^5*x^9],
[(a+b*x^2)^5/x^4,x,2,-1/3*a^5/x^3-5*a^4*b/x+10*a^3*b^2*x+10/3*a^2*b^3*x^3+a*b^4*x^5+1/7*b^5*x^7],
[(a+b*x^2)^5/x^6,x,2,-1/5*a^5/x^5-5/3*a^4*b/x^3-10*a^3*b^2/x+10*a^2*b^3*x+5/3*a*b^4*x^3+1/5*b^5*x^5],
[(a+b*x^2)^5/x^8,x,2,-1/7*a^5/x^7-a^4*b/x^5-10/3*a^3*b^2/x^3-10*a^2*b^3/x+5*a*b^4*x+1/3*b^5*x^3],
[(a+b*x^2)^5/x^10,x,2,-1/9*a^5/x^9-5/7*a^4*b/x^7-2*a^3*b^2/x^5-10/3*a^2*b^3/x^3-5*a*b^4/x+b^5*x],
[(a+b*x^2)^5/x^12,x,2,-1/11*a^5/x^11-5/9*a^4*b/x^9-10/7*a^3*b^2/x^7-2*a^2*b^3/x^5-5/3*a*b^4/x^3-b^5/x],
[(a+b*x^2)^5/x^14,x,2,-1/13*a^5/x^13-5/11*a^4*b/x^11-10/9*a^3*b^2/x^9-10/7*a^2*b^3/x^7-a*b^4/x^5-1/3*b^5/x^3],
[(a+b*x^2)^5/x^16,x,2,-1/15*a^5/x^15-5/13*a^4*b/x^13-10/11*a^3*b^2/x^11-10/9*a^2*b^3/x^9-5/7*a*b^4/x^7-1/5*b^5/x^5],
[(a+b*x^2)^5/x^18,x,2,-1/17*a^5/x^17-1/3*a^4*b/x^15-10/13*a^3*b^2/x^13-10/11*a^2*b^3/x^11-5/9*a*b^4/x^9-1/7*b^5/x^7],
[(a+b*x^2)^5/x^20,x,2,-1/19*a^5/x^19-5/17*a^4*b/x^17-2/3*a^3*b^2/x^15-10/13*a^2*b^3/x^13-5/11*a*b^4/x^11-1/9*b^5/x^9],
[x^13*(a+b*x^2)^8,x,3,1/18*a^6*(a+b*x^2)^9/b^7-3/10*a^5*(a+b*x^2)^10/b^7+15/22*a^4*(a+b*x^2)^11/b^7-5/6*a^3*(a+b*x^2)^12/b^7+15/26*a^2*(a+b*x^2)^13/b^7-3/14*a*(a+b*x^2)^14/b^7+1/30*(a+b*x^2)^15/b^7],
[x^11*(a+b*x^2)^8,x,3,-1/18*a^5*(a+b*x^2)^9/b^6+1/4*a^4*(a+b*x^2)^10/b^6-5/11*a^3*(a+b*x^2)^11/b^6+5/12*a^2*(a+b*x^2)^12/b^6-5/26*a*(a+b*x^2)^13/b^6+1/28*(a+b*x^2)^14/b^6],
[x^9*(a+b*x^2)^8,x,3,1/18*a^4*(a+b*x^2)^9/b^5-1/5*a^3*(a+b*x^2)^10/b^5+3/11*a^2*(a+b*x^2)^11/b^5-1/6*a*(a+b*x^2)^12/b^5+1/26*(a+b*x^2)^13/b^5],
[x^7*(a+b*x^2)^8,x,3,-1/18*a^3*(a+b*x^2)^9/b^4+3/20*a^2*(a+b*x^2)^10/b^4-3/22*a*(a+b*x^2)^11/b^4+1/24*(a+b*x^2)^12/b^4],
[x^5*(a+b*x^2)^8,x,3,1/18*a^2*(a+b*x^2)^9/b^3-1/10*a*(a+b*x^2)^10/b^3+1/22*(a+b*x^2)^11/b^3],
[x^3*(a+b*x^2)^8,x,3,-1/18*a*(a+b*x^2)^9/b^2+1/20*(a+b*x^2)^10/b^2],
[x*(a+b*x^2)^8,x,1,1/18*(a+b*x^2)^9/b],
[(a+b*x^2)^8/x,x,3,4*a^7*b*x^2+7*a^6*b^2*x^4+28/3*a^5*b^3*x^6+35/4*a^4*b^4*x^8+28/5*a^3*b^5*x^10+7/3*a^2*b^6*x^12+4/7*a*b^7*x^14+1/16*b^8*x^16+a^8*log(x)],
[(a+b*x^2)^8/x^3,x,3,-1/2*a^8/x^2+14*a^6*b^2*x^2+14*a^5*b^3*x^4+35/3*a^4*b^4*x^6+7*a^3*b^5*x^8+14/5*a^2*b^6*x^10+2/3*a*b^7*x^12+1/14*b^8*x^14+8*a^7*b*log(x)],
[(a+b*x^2)^8/x^5,x,3,-1/4*a^8/x^4-4*a^7*b/x^2+28*a^5*b^3*x^2+35/2*a^4*b^4*x^4+28/3*a^3*b^5*x^6+7/2*a^2*b^6*x^8+4/5*a*b^7*x^10+1/12*b^8*x^12+28*a^6*b^2*log(x)],
[(a+b*x^2)^8/x^7,x,3,-1/6*a^8/x^6-2*a^7*b/x^4-14*a^6*b^2/x^2+35*a^4*b^4*x^2+14*a^3*b^5*x^4+14/3*a^2*b^6*x^6+a*b^7*x^8+1/10*b^8*x^10+56*a^5*b^3*log(x)],
[(a+b*x^2)^8/x^9,x,3,-1/8*a^8/x^8-4/3*a^7*b/x^6-7*a^6*b^2/x^4-28*a^5*b^3/x^2+28*a^3*b^5*x^2+7*a^2*b^6*x^4+4/3*a*b^7*x^6+1/8*b^8*x^8+70*a^4*b^4*log(x)],
[(a+b*x^2)^8/x^11,x,3,-1/10*a^8/x^10-a^7*b/x^8-14/3*a^6*b^2/x^6-14*a^5*b^3/x^4-35*a^4*b^4/x^2+14*a^2*b^6*x^2+2*a*b^7*x^4+1/6*b^8*x^6+56*a^3*b^5*log(x)],
[(a+b*x^2)^8/x^13,x,3,-1/12*a^8/x^12-4/5*a^7*b/x^10-7/2*a^6*b^2/x^8-28/3*a^5*b^3/x^6-35/2*a^4*b^4/x^4-28*a^3*b^5/x^2+4*a*b^7*x^2+1/4*b^8*x^4+28*a^2*b^6*log(x)],
[(a+b*x^2)^8/x^15,x,3,-1/14*a^8/x^14-2/3*a^7*b/x^12-14/5*a^6*b^2/x^10-7*a^5*b^3/x^8-35/3*a^4*b^4/x^6-14*a^3*b^5/x^4-14*a^2*b^6/x^2+1/2*b^8*x^2+8*a*b^7*log(x)],
[(a+b*x^2)^8/x^17,x,3,-1/16*a^8/x^16-4/7*a^7*b/x^14-7/3*a^6*b^2/x^12-28/5*a^5*b^3/x^10-35/4*a^4*b^4/x^8-28/3*a^3*b^5/x^6-7*a^2*b^6/x^4-4*a*b^7/x^2+b^8*log(x)],
[(a+b*x^2)^8/x^19,x,1,-1/18*(a+b*x^2)^9/(a*x^18)],
[(a+b*x^2)^8/x^21,x,3,-1/20*(a+b*x^2)^9/(a*x^20)+1/180*b*(a+b*x^2)^9/(a^2*x^18)],
[(a+b*x^2)^8/x^23,x,4,-1/22*(a+b*x^2)^9/(a*x^22)+1/110*b*(a+b*x^2)^9/(a^2*x^20)-1/990*b^2*(a+b*x^2)^9/(a^3*x^18)],
[(a+b*x^2)^8/x^25,x,5,-1/24*(a+b*x^2)^9/(a*x^24)+1/88*b*(a+b*x^2)^9/(a^2*x^22)-1/440*b^2*(a+b*x^2)^9/(a^3*x^20)+1/3960*b^3*(a+b*x^2)^9/(a^4*x^18)],
[(a+b*x^2)^8/x^27,x,6,-1/26*(a+b*x^2)^9/(a*x^26)+1/78*b*(a+b*x^2)^9/(a^2*x^24)-1/286*b^2*(a+b*x^2)^9/(a^3*x^22)+1/1430*b^3*(a+b*x^2)^9/(a^4*x^20)-1/12870*b^4*(a+b*x^2)^9/(a^5*x^18)],
[(a+b*x^2)^8/x^29,x,3,-1/28*a^8/x^28-4/13*a^7*b/x^26-7/6*a^6*b^2/x^24-28/11*a^5*b^3/x^22-7/2*a^4*b^4/x^20-28/9*a^3*b^5/x^18-7/4*a^2*b^6/x^16-4/7*a*b^7/x^14-1/12*b^8/x^12],
[(a+b*x^2)^8/x^31,x,3,-1/30*a^8/x^30-2/7*a^7*b/x^28-14/13*a^6*b^2/x^26-7/3*a^5*b^3/x^24-35/11*a^4*b^4/x^22-14/5*a^3*b^5/x^20-14/9*a^2*b^6/x^18-1/2*a*b^7/x^16-1/14*b^8/x^14],
[(a+b*x^2)^8/x^33,x,3,-1/32*a^8/x^32-4/15*a^7*b/x^30-a^6*b^2/x^28-28/13*a^5*b^3/x^26-35/12*a^4*b^4/x^24-28/11*a^3*b^5/x^22-7/5*a^2*b^6/x^20-4/9*a*b^7/x^18-1/16*b^8/x^16],
[x^8*(a+b*x^2)^8,x,2,1/9*a^8*x^9+8/11*a^7*b*x^11+28/13*a^6*b^2*x^13+56/15*a^5*b^3*x^15+70/17*a^4*b^4*x^17+56/19*a^3*b^5*x^19+4/3*a^2*b^6*x^21+8/23*a*b^7*x^23+1/25*b^8*x^25],
[x^6*(a+b*x^2)^8,x,2,1/7*a^8*x^7+8/9*a^7*b*x^9+28/11*a^6*b^2*x^11+56/13*a^5*b^3*x^13+14/3*a^4*b^4*x^15+56/17*a^3*b^5*x^17+28/19*a^2*b^6*x^19+8/21*a*b^7*x^21+1/23*b^8*x^23],
[x^4*(a+b*x^2)^8,x,2,1/5*a^8*x^5+8/7*a^7*b*x^7+28/9*a^6*b^2*x^9+56/11*a^5*b^3*x^11+70/13*a^4*b^4*x^13+56/15*a^3*b^5*x^15+28/17*a^2*b^6*x^17+8/19*a*b^7*x^19+1/21*b^8*x^21],
[x^2*(a+b*x^2)^8,x,2,1/3*a^8*x^3+8/5*a^7*b*x^5+4*a^6*b^2*x^7+56/9*a^5*b^3*x^9+70/11*a^4*b^4*x^11+56/13*a^3*b^5*x^13+28/15*a^2*b^6*x^15+8/17*a*b^7*x^17+1/19*b^8*x^19],
[(a+b*x^2)^8,x,2,a^8*x+8/3*a^7*b*x^3+28/5*a^6*b^2*x^5+8*a^5*b^3*x^7+70/9*a^4*b^4*x^9+56/11*a^3*b^5*x^11+28/13*a^2*b^6*x^13+8/15*a*b^7*x^15+1/17*b^8*x^17],
[(a+b*x^2)^8/x^2,x,2,-a^8/x+8*a^7*b*x+28/3*a^6*b^2*x^3+56/5*a^5*b^3*x^5+10*a^4*b^4*x^7+56/9*a^3*b^5*x^9+28/11*a^2*b^6*x^11+8/13*a*b^7*x^13+1/15*b^8*x^15],
[(a+b*x^2)^8/x^4,x,2,-1/3*a^8/x^3-8*a^7*b/x+28*a^6*b^2*x+56/3*a^5*b^3*x^3+14*a^4*b^4*x^5+8*a^3*b^5*x^7+28/9*a^2*b^6*x^9+8/11*a*b^7*x^11+1/13*b^8*x^13],
[(a+b*x^2)^8/x^6,x,2,-1/5*a^8/x^5-8/3*a^7*b/x^3-28*a^6*b^2/x+56*a^5*b^3*x+70/3*a^4*b^4*x^3+56/5*a^3*b^5*x^5+4*a^2*b^6*x^7+8/9*a*b^7*x^9+1/11*b^8*x^11],
[(a+b*x^2)^8/x^8,x,2,-1/7*a^8/x^7-8/5*a^7*b/x^5-28/3*a^6*b^2/x^3-56*a^5*b^3/x+70*a^4*b^4*x+56/3*a^3*b^5*x^3+28/5*a^2*b^6*x^5+8/7*a*b^7*x^7+1/9*b^8*x^9],
[(a+b*x^2)^8/x^10,x,2,-1/9*a^8/x^9-8/7*a^7*b/x^7-28/5*a^6*b^2/x^5-56/3*a^5*b^3/x^3-70*a^4*b^4/x+56*a^3*b^5*x+28/3*a^2*b^6*x^3+8/5*a*b^7*x^5+1/7*b^8*x^7],
[(a+b*x^2)^8/x^12,x,2,-1/11*a^8/x^11-8/9*a^7*b/x^9-4*a^6*b^2/x^7-56/5*a^5*b^3/x^5-70/3*a^4*b^4/x^3-56*a^3*b^5/x+28*a^2*b^6*x+8/3*a*b^7*x^3+1/5*b^8*x^5],
[(a+b*x^2)^8/x^14,x,2,-1/13*a^8/x^13-8/11*a^7*b/x^11-28/9*a^6*b^2/x^9-8*a^5*b^3/x^7-14*a^4*b^4/x^5-56/3*a^3*b^5/x^3-28*a^2*b^6/x+8*a*b^7*x+1/3*b^8*x^3],
[(a+b*x^2)^8/x^16,x,2,-1/15*a^8/x^15-8/13*a^7*b/x^13-28/11*a^6*b^2/x^11-56/9*a^5*b^3/x^9-10*a^4*b^4/x^7-56/5*a^3*b^5/x^5-28/3*a^2*b^6/x^3-8*a*b^7/x+b^8*x],
[(a+b*x^2)^8/x^18,x,2,-1/17*a^8/x^17-8/15*a^7*b/x^15-28/13*a^6*b^2/x^13-56/11*a^5*b^3/x^11-70/9*a^4*b^4/x^9-8*a^3*b^5/x^7-28/5*a^2*b^6/x^5-8/3*a*b^7/x^3-b^8/x],
[(a+b*x^2)^8/x^20,x,2,-1/19*a^8/x^19-8/17*a^7*b/x^17-28/15*a^6*b^2/x^15-56/13*a^5*b^3/x^13-70/11*a^4*b^4/x^11-56/9*a^3*b^5/x^9-4*a^2*b^6/x^7-8/5*a*b^7/x^5-1/3*b^8/x^3],

# p<0
[x^11/(a+b*x^2),x,3,1/2*a^4*x^2/b^5-1/4*a^3*x^4/b^4+1/6*a^2*x^6/b^3-1/8*a*x^8/b^2+1/10*x^10/b-1/2*a^5*log(a+b*x^2)/b^6],
[x^10/(a+b*x^2),x,3,a^4*x/b^5-1/3*a^3*x^3/b^4+1/5*a^2*x^5/b^3-1/7*a*x^7/b^2+1/9*x^9/b-a^(9/2)*arctan(x*sqrt(b)/sqrt(a))/b^(11/2)],
[x^9/(a+b*x^2),x,3,-1/2*a^3*x^2/b^4+1/4*a^2*x^4/b^3-1/6*a*x^6/b^2+1/8*x^8/b+1/2*a^4*log(a+b*x^2)/b^5],
[x^8/(a+b*x^2),x,3,-a^3*x/b^4+1/3*a^2*x^3/b^3-1/5*a*x^5/b^2+1/7*x^7/b+a^(7/2)*arctan(x*sqrt(b)/sqrt(a))/b^(9/2)],
[x^7/(a+b*x^2),x,3,1/2*a^2*x^2/b^3-1/4*a*x^4/b^2+1/6*x^6/b-1/2*a^3*log(a+b*x^2)/b^4],
[x^6/(a+b*x^2),x,3,a^2*x/b^3-1/3*a*x^3/b^2+1/5*x^5/b-a^(5/2)*arctan(x*sqrt(b)/sqrt(a))/b^(7/2)],
[x^5/(a+b*x^2),x,3,-1/2*a*x^2/b^2+1/4*x^4/b+1/2*a^2*log(a+b*x^2)/b^3],
[x^4/(a+b*x^2),x,3,-a*x/b^2+1/3*x^3/b+a^(3/2)*arctan(x*sqrt(b)/sqrt(a))/b^(5/2)],
[x^3/(a+b*x^2),x,3,1/2*x^2/b-1/2*a*log(a+b*x^2)/b^2],
[x^2/(a+b*x^2),x,2,x/b-arctan(x*sqrt(b)/sqrt(a))*sqrt(a)/b^(3/2)],
[x/(a+b*x^2),x,1,1/2*log(a+b*x^2)/b],
[1/(a+b*x^2),x,1,arctan(x*sqrt(b)/sqrt(a))/(sqrt(a)*sqrt(b))],
[1/(x*(a+b*x^2)),x,4,log(x)/a-1/2*log(a+b*x^2)/a],
[1/(x^2*(a+b*x^2)),x,2,(-1)/(a*x)-arctan(x*sqrt(b)/sqrt(a))*sqrt(b)/a^(3/2)],
[1/(x^3*(a+b*x^2)),x,3,(-1/2)/(a*x^2)-b*log(x)/a^2+1/2*b*log(a+b*x^2)/a^2],
[1/(x^4*(a+b*x^2)),x,3,(-1/3)/(a*x^3)+b/(a^2*x)+b^(3/2)*arctan(x*sqrt(b)/sqrt(a))/a^(5/2)],
[1/(x^5*(a+b*x^2)),x,3,(-1/4)/(a*x^4)+1/2*b/(a^2*x^2)+b^2*log(x)/a^3-1/2*b^2*log(a+b*x^2)/a^3],
[1/(x^6*(a+b*x^2)),x,4,(-1/5)/(a*x^5)+1/3*b/(a^2*x^3)-b^2/(a^3*x)-b^(5/2)*arctan(x*sqrt(b)/sqrt(a))/a^(7/2)],
[1/(x^7*(a+b*x^2)),x,3,(-1/6)/(a*x^6)+1/4*b/(a^2*x^4)-1/2*b^2/(a^3*x^2)-b^3*log(x)/a^4+1/2*b^3*log(a+b*x^2)/a^4],
[1/(x^8*(a+b*x^2)),x,5,(-1/7)/(a*x^7)+1/5*b/(a^2*x^5)-1/3*b^2/(a^3*x^3)+b^3/(a^4*x)+b^(7/2)*arctan(x*sqrt(b)/sqrt(a))/a^(9/2)],
[1/(x^9*(a+b*x^2)),x,3,(-1/8)/(a*x^8)+1/6*b/(a^2*x^6)-1/4*b^2/(a^3*x^4)+1/2*b^3/(a^4*x^2)+b^4*log(x)/a^5-1/2*b^4*log(a+b*x^2)/a^5],
[x^13/(a+b*x^2)^2,x,3,5/2*a^4*x^2/b^6-a^3*x^4/b^5+1/2*a^2*x^6/b^4-1/4*a*x^8/b^3+1/10*x^10/b^2-1/2*a^6/(b^7*(a+b*x^2))-3*a^5*log(a+b*x^2)/b^7],
[x^12/(a+b*x^2)^2,x,4,11/2*a^4*x/b^6-11/6*a^3*x^3/b^5+11/10*a^2*x^5/b^4-11/14*a*x^7/b^3+11/18*x^9/b^2-1/2*x^11/(b*(a+b*x^2))-11/2*a^(9/2)*arctan(x*sqrt(b)/sqrt(a))/b^(13/2)],
[x^11/(a+b*x^2)^2,x,3,-2*a^3*x^2/b^5+3/4*a^2*x^4/b^4-1/3*a*x^6/b^3+1/8*x^8/b^2+1/2*a^5/(b^6*(a+b*x^2))+5/2*a^4*log(a+b*x^2)/b^6],
[x^10/(a+b*x^2)^2,x,4,-9/2*a^3*x/b^5+3/2*a^2*x^3/b^4-9/10*a*x^5/b^3+9/14*x^7/b^2-1/2*x^9/(b*(a+b*x^2))+9/2*a^(7/2)*arctan(x*sqrt(b)/sqrt(a))/b^(11/2)],
[x^9/(a+b*x^2)^2,x,3,3/2*a^2*x^2/b^4-1/2*a*x^4/b^3+1/6*x^6/b^2-1/2*a^4/(b^5*(a+b*x^2))-2*a^3*log(a+b*x^2)/b^5],
[x^8/(a+b*x^2)^2,x,4,7/2*a^2*x/b^4-7/6*a*x^3/b^3+7/10*x^5/b^2-1/2*x^7/(b*(a+b*x^2))-7/2*a^(5/2)*arctan(x*sqrt(b)/sqrt(a))/b^(9/2)],
[x^7/(a+b*x^2)^2,x,3,-a*x^2/b^3+1/4*x^4/b^2+1/2*a^3/(b^4*(a+b*x^2))+3/2*a^2*log(a+b*x^2)/b^4],
[x^6/(a+b*x^2)^2,x,4,-5/2*a*x/b^3+5/6*x^3/b^2-1/2*x^5/(b*(a+b*x^2))+5/2*a^(3/2)*arctan(x*sqrt(b)/sqrt(a))/b^(7/2)],
[x^5/(a+b*x^2)^2,x,3,1/2*x^2/b^2-1/2*a^2/(b^3*(a+b*x^2))-a*log(a+b*x^2)/b^3],
[x^4/(a+b*x^2)^2,x,3,3/2*x/b^2-1/2*x^3/(b*(a+b*x^2))-3/2*arctan(x*sqrt(b)/sqrt(a))*sqrt(a)/b^(5/2)],
[x^3/(a+b*x^2)^2,x,3,1/2*a/(b^2*(a+b*x^2))+1/2*log(a+b*x^2)/b^2],
[x^2/(a+b*x^2)^2,x,2,-1/2*x/(b*(a+b*x^2))+1/2*arctan(x*sqrt(b)/sqrt(a))/(b^(3/2)*sqrt(a))],
[x/(a+b*x^2)^2,x,1,(-1/2)/(b*(a+b*x^2))],
[1/(a+b*x^2)^2,x,2,1/2*x/(a*(a+b*x^2))+1/2*arctan(x*sqrt(b)/sqrt(a))/(a^(3/2)*sqrt(b))],
[1/(x*(a+b*x^2)^2),x,3,1/2/(a*(a+b*x^2))+log(x)/a^2-1/2*log(a+b*x^2)/a^2],
[1/(x^2*(a+b*x^2)^2),x,3,(-3/2)/(a^2*x)+1/2/(a*x*(a+b*x^2))-3/2*arctan(x*sqrt(b)/sqrt(a))*sqrt(b)/a^(5/2)],
[1/(x^3*(a+b*x^2)^2),x,3,(-1/2)/(a^2*x^2)-1/2*b/(a^2*(a+b*x^2))-2*b*log(x)/a^3+b*log(a+b*x^2)/a^3],
[1/(x^4*(a+b*x^2)^2),x,4,(-5/6)/(a^2*x^3)+5/2*b/(a^3*x)+1/2/(a*x^3*(a+b*x^2))+5/2*b^(3/2)*arctan(x*sqrt(b)/sqrt(a))/a^(7/2)],
[1/(x^5*(a+b*x^2)^2),x,3,(-1/4)/(a^2*x^4)+b/(a^3*x^2)+1/2*b^2/(a^3*(a+b*x^2))+3*b^2*log(x)/a^4-3/2*b^2*log(a+b*x^2)/a^4],
[1/(x^6*(a+b*x^2)^2),x,5,(-7/10)/(a^2*x^5)+7/6*b/(a^3*x^3)-7/2*b^2/(a^4*x)+1/2/(a*x^5*(a+b*x^2))-7/2*b^(5/2)*arctan(x*sqrt(b)/sqrt(a))/a^(9/2)],
[1/(x^7*(a+b*x^2)^2),x,3,(-1/6)/(a^2*x^6)+1/2*b/(a^3*x^4)-3/2*b^2/(a^4*x^2)-1/2*b^3/(a^4*(a+b*x^2))-4*b^3*log(x)/a^5+2*b^3*log(a+b*x^2)/a^5],
[1/(x^8*(a+b*x^2)^2),x,6,(-9/14)/(a^2*x^7)+9/10*b/(a^3*x^5)-3/2*b^2/(a^4*x^3)+9/2*b^3/(a^5*x)+1/2/(a*x^7*(a+b*x^2))+9/2*b^(7/2)*arctan(x*sqrt(b)/sqrt(a))/a^(11/2)],
[1/(x^9*(a+b*x^2)^2),x,3,(-1/8)/(a^2*x^8)+1/3*b/(a^3*x^6)-3/4*b^2/(a^4*x^4)+2*b^3/(a^5*x^2)+1/2*b^4/(a^5*(a+b*x^2))+5*b^4*log(x)/a^6-5/2*b^4*log(a+b*x^2)/a^6],
[x^15/(a+b*x^2)^3,x,3,15/2*a^4*x^2/b^7-5/2*a^3*x^4/b^6+a^2*x^6/b^5-3/8*a*x^8/b^4+1/10*x^10/b^3+1/4*a^7/(b^8*(a+b*x^2)^2)-7/2*a^6/(b^8*(a+b*x^2))-21/2*a^5*log(a+b*x^2)/b^8],
[x^13/(a+b*x^2)^3,x,3,-5*a^3*x^2/b^6+3/2*a^2*x^4/b^5-1/2*a*x^6/b^4+1/8*x^8/b^3-1/4*a^6/(b^7*(a+b*x^2)^2)+3*a^5/(b^7*(a+b*x^2))+15/2*a^4*log(a+b*x^2)/b^7],
[x^11/(a+b*x^2)^3,x,3,3*a^2*x^2/b^5-3/4*a*x^4/b^4+1/6*x^6/b^3+1/4*a^5/(b^6*(a+b*x^2)^2)-5/2*a^4/(b^6*(a+b*x^2))-5*a^3*log(a+b*x^2)/b^6],
[x^9/(a+b*x^2)^3,x,3,-3/2*a*x^2/b^4+1/4*x^4/b^3-1/4*a^4/(b^5*(a+b*x^2)^2)+2*a^3/(b^5*(a+b*x^2))+3*a^2*log(a+b*x^2)/b^5],
[x^7/(a+b*x^2)^3,x,3,1/2*x^2/b^3+1/4*a^3/(b^4*(a+b*x^2)^2)-3/2*a^2/(b^4*(a+b*x^2))-3/2*a*log(a+b*x^2)/b^4],
[x^5/(a+b*x^2)^3,x,3,-1/4*a^2/(b^3*(a+b*x^2)^2)+a/(b^3*(a+b*x^2))+1/2*log(a+b*x^2)/b^3],
[x^3/(a+b*x^2)^3,x,1,1/4*x^4/(a*(a+b*x^2)^2)],
[x/(a+b*x^2)^3,x,1,(-1/4)/(b*(a+b*x^2)^2)],
[1/(x*(a+b*x^2)^3),x,3,1/4/(a*(a+b*x^2)^2)+1/2/(a^2*(a+b*x^2))+log(x)/a^3-1/2*log(a+b*x^2)/a^3],
[1/(x^3*(a+b*x^2)^3),x,3,(-1/2)/(a^3*x^2)-1/4*b/(a^2*(a+b*x^2)^2)-b/(a^3*(a+b*x^2))-3*b*log(x)/a^4+3/2*b*log(a+b*x^2)/a^4],
[1/(x^5*(a+b*x^2)^3),x,3,(-1/4)/(a^3*x^4)+3/2*b/(a^4*x^2)+1/4*b^2/(a^3*(a+b*x^2)^2)+3/2*b^2/(a^4*(a+b*x^2))+6*b^2*log(x)/a^5-3*b^2*log(a+b*x^2)/a^5],
[1/(x^7*(a+b*x^2)^3),x,3,(-1/6)/(a^3*x^6)+3/4*b/(a^4*x^4)-3*b^2/(a^5*x^2)-1/4*b^3/(a^4*(a+b*x^2)^2)-2*b^3/(a^5*(a+b*x^2))-10*b^3*log(x)/a^6+5*b^3*log(a+b*x^2)/a^6],
[1/(x^9*(a+b*x^2)^3),x,3,(-1/8)/(a^3*x^8)+1/2*b/(a^4*x^6)-3/2*b^2/(a^5*x^4)+5*b^3/(a^6*x^2)+1/4*b^4/(a^5*(a+b*x^2)^2)+5/2*b^4/(a^6*(a+b*x^2))+15*b^4*log(x)/a^7-15/2*b^4*log(a+b*x^2)/a^7],
[x^12/(a+b*x^2)^3,x,5,-99/8*a^3*x/b^6+33/8*a^2*x^3/b^5-99/40*a*x^5/b^4+99/56*x^7/b^3-1/4*x^11/(b*(a+b*x^2)^2)-11/8*x^9/(b^2*(a+b*x^2))+99/8*a^(7/2)*arctan(x*sqrt(b)/sqrt(a))/b^(13/2)],
[x^10/(a+b*x^2)^3,x,5,63/8*a^2*x/b^5-21/8*a*x^3/b^4+63/40*x^5/b^3-1/4*x^9/(b*(a+b*x^2)^2)-9/8*x^7/(b^2*(a+b*x^2))-63/8*a^(5/2)*arctan(x*sqrt(b)/sqrt(a))/b^(11/2)],
[x^8/(a+b*x^2)^3,x,5,-35/8*a*x/b^4+35/24*x^3/b^3-1/4*x^7/(b*(a+b*x^2)^2)-7/8*x^5/(b^2*(a+b*x^2))+35/8*a^(3/2)*arctan(x*sqrt(b)/sqrt(a))/b^(9/2)],
[x^6/(a+b*x^2)^3,x,4,15/8*x/b^3-1/4*x^5/(b*(a+b*x^2)^2)-5/8*x^3/(b^2*(a+b*x^2))-15/8*arctan(x*sqrt(b)/sqrt(a))*sqrt(a)/b^(7/2)],
[x^4/(a+b*x^2)^3,x,3,-1/4*x^3/(b*(a+b*x^2)^2)-3/8*x/(b^2*(a+b*x^2))+3/8*arctan(x*sqrt(b)/sqrt(a))/(b^(5/2)*sqrt(a))],
[x^2/(a+b*x^2)^3,x,3,-1/4*x/(b*(a+b*x^2)^2)+1/8*x/(a*b*(a+b*x^2))+1/8*arctan(x*sqrt(b)/sqrt(a))/(a^(3/2)*b^(3/2))],
[1/(a+b*x^2)^3,x,3,1/4*x/(a*(a+b*x^2)^2)+3/8*x/(a^2*(a+b*x^2))+3/8*arctan(x*sqrt(b)/sqrt(a))/(a^(5/2)*sqrt(b))],
[1/(x^2*(a+b*x^2)^3),x,4,(-15/8)/(a^3*x)+1/4/(a*x*(a+b*x^2)^2)+5/8/(a^2*x*(a+b*x^2))-15/8*arctan(x*sqrt(b)/sqrt(a))*sqrt(b)/a^(7/2)],
[1/(x^4*(a+b*x^2)^3),x,5,(-35/24)/(a^3*x^3)+35/8*b/(a^4*x)+1/4/(a*x^3*(a+b*x^2)^2)+7/8/(a^2*x^3*(a+b*x^2))+35/8*b^(3/2)*arctan(x*sqrt(b)/sqrt(a))/a^(9/2)],
[1/(x^6*(a+b*x^2)^3),x,6,(-63/40)/(a^3*x^5)+21/8*b/(a^4*x^3)-63/8*b^2/(a^5*x)+1/4/(a*x^5*(a+b*x^2)^2)+9/8/(a^2*x^5*(a+b*x^2))-63/8*b^(5/2)*arctan(x*sqrt(b)/sqrt(a))/a^(11/2)],
[1/(x^8*(a+b*x^2)^3),x,7,(-99/56)/(a^3*x^7)+99/40*b/(a^4*x^5)-33/8*b^2/(a^5*x^3)+99/8*b^3/(a^6*x)+1/4/(a*x^7*(a+b*x^2)^2)+11/8/(a^2*x^7*(a+b*x^2))+99/8*b^(7/2)*arctan(x*sqrt(b)/sqrt(a))/a^(13/2)],
[x^25/(a+b*x^2)^10,x,3,55/2*a^2*x^2/b^12-5/2*a*x^4/b^11+1/6*x^6/b^10-1/18*a^12/(b^13*(a+b*x^2)^9)+3/4*a^11/(b^13*(a+b*x^2)^8)-33/7*a^10/(b^13*(a+b*x^2)^7)+55/3*a^9/(b^13*(a+b*x^2)^6)-99/2*a^8/(b^13*(a+b*x^2)^5)+99*a^7/(b^13*(a+b*x^2)^4)-154*a^6/(b^13*(a+b*x^2)^3)+198*a^5/(b^13*(a+b*x^2)^2)-495/2*a^4/(b^13*(a+b*x^2))-110*a^3*log(a+b*x^2)/b^13],
[x^23/(a+b*x^2)^10,x,3,-5*a*x^2/b^11+1/4*x^4/b^10+1/18*a^11/(b^12*(a+b*x^2)^9)-11/16*a^10/(b^12*(a+b*x^2)^8)+55/14*a^9/(b^12*(a+b*x^2)^7)-55/4*a^8/(b^12*(a+b*x^2)^6)+33*a^7/(b^12*(a+b*x^2)^5)-231/4*a^6/(b^12*(a+b*x^2)^4)+77*a^5/(b^12*(a+b*x^2)^3)-165/2*a^4/(b^12*(a+b*x^2)^2)+165/2*a^3/(b^12*(a+b*x^2))+55/2*a^2*log(a+b*x^2)/b^12],
[x^21/(a+b*x^2)^10,x,3,1/2*x^2/b^10-1/18*a^10/(b^11*(a+b*x^2)^9)+5/8*a^9/(b^11*(a+b*x^2)^8)-45/14*a^8/(b^11*(a+b*x^2)^7)+10*a^7/(b^11*(a+b*x^2)^6)-21*a^6/(b^11*(a+b*x^2)^5)+63/2*a^5/(b^11*(a+b*x^2)^4)-35*a^4/(b^11*(a+b*x^2)^3)+30*a^3/(b^11*(a+b*x^2)^2)-45/2*a^2/(b^11*(a+b*x^2))-5*a*log(a+b*x^2)/b^11],
[x^19/(a+b*x^2)^10,x,3,1/18*a^9/(b^10*(a+b*x^2)^9)-9/16*a^8/(b^10*(a+b*x^2)^8)+18/7*a^7/(b^10*(a+b*x^2)^7)-7*a^6/(b^10*(a+b*x^2)^6)+63/5*a^5/(b^10*(a+b*x^2)^5)-63/4*a^4/(b^10*(a+b*x^2)^4)+14*a^3/(b^10*(a+b*x^2)^3)-9*a^2/(b^10*(a+b*x^2)^2)+9/2*a/(b^10*(a+b*x^2))+1/2*log(a+b*x^2)/b^10],
[x^17/(a+b*x^2)^10,x,1,1/18*x^18/(a*(a+b*x^2)^9)],
[x^15/(a+b*x^2)^10,x,3,1/18*x^16/(a*(a+b*x^2)^9)+1/144*x^16/(a^2*(a+b*x^2)^8)],
[x^13/(a+b*x^2)^10,x,4,1/18*x^14/(a*(a+b*x^2)^9)+1/72*x^14/(a^2*(a+b*x^2)^8)+1/504*x^14/(a^3*(a+b*x^2)^7)],
[x^11/(a+b*x^2)^10,x,5,1/18*x^12/(a*(a+b*x^2)^9)+1/48*x^12/(a^2*(a+b*x^2)^8)+1/168*x^12/(a^3*(a+b*x^2)^7)+1/1008*x^12/(a^4*(a+b*x^2)^6)],
[x^9/(a+b*x^2)^10,x,3,-1/18*a^4/(b^5*(a+b*x^2)^9)+1/4*a^3/(b^5*(a+b*x^2)^8)-3/7*a^2/(b^5*(a+b*x^2)^7)+1/3*a/(b^5*(a+b*x^2)^6)+(-1/10)/(b^5*(a+b*x^2)^5)],
[x^7/(a+b*x^2)^10,x,3,1/18*a^3/(b^4*(a+b*x^2)^9)-3/16*a^2/(b^4*(a+b*x^2)^8)+3/14*a/(b^4*(a+b*x^2)^7)+(-1/12)/(b^4*(a+b*x^2)^6)],
[x^5/(a+b*x^2)^10,x,3,-1/18*a^2/(b^3*(a+b*x^2)^9)+1/8*a/(b^3*(a+b*x^2)^8)+(-1/14)/(b^3*(a+b*x^2)^7)],
[x^3/(a+b*x^2)^10,x,3,1/18*a/(b^2*(a+b*x^2)^9)+(-1/16)/(b^2*(a+b*x^2)^8)],
[x/(a+b*x^2)^10,x,1,(-1/18)/(b*(a+b*x^2)^9)],
[1/(x*(a+b*x^2)^10),x,3,1/18/(a*(a+b*x^2)^9)+1/16/(a^2*(a+b*x^2)^8)+1/14/(a^3*(a+b*x^2)^7)+1/12/(a^4*(a+b*x^2)^6)+1/10/(a^5*(a+b*x^2)^5)+1/8/(a^6*(a+b*x^2)^4)+1/6/(a^7*(a+b*x^2)^3)+1/4/(a^8*(a+b*x^2)^2)+1/2/(a^9*(a+b*x^2))+log(x)/a^10-1/2*log(a+b*x^2)/a^10],
[1/(x^3*(a+b*x^2)^10),x,3,(-1/2)/(a^10*x^2)-1/18*b/(a^2*(a+b*x^2)^9)-1/8*b/(a^3*(a+b*x^2)^8)-3/14*b/(a^4*(a+b*x^2)^7)-1/3*b/(a^5*(a+b*x^2)^6)-1/2*b/(a^6*(a+b*x^2)^5)-3/4*b/(a^7*(a+b*x^2)^4)-7/6*b/(a^8*(a+b*x^2)^3)-2*b/(a^9*(a+b*x^2)^2)-9/2*b/(a^10*(a+b*x^2))-10*b*log(x)/a^11+5*b*log(a+b*x^2)/a^11],
[1/(x^5*(a+b*x^2)^10),x,3,(-1/4)/(a^10*x^4)+5*b/(a^11*x^2)+1/18*b^2/(a^3*(a+b*x^2)^9)+3/16*b^2/(a^4*(a+b*x^2)^8)+3/7*b^2/(a^5*(a+b*x^2)^7)+5/6*b^2/(a^6*(a+b*x^2)^6)+3/2*b^2/(a^7*(a+b*x^2)^5)+21/8*b^2/(a^8*(a+b*x^2)^4)+14/3*b^2/(a^9*(a+b*x^2)^3)+9*b^2/(a^10*(a+b*x^2)^2)+45/2*b^2/(a^11*(a+b*x^2))+55*b^2*log(x)/a^12-55/2*b^2*log(a+b*x^2)/a^12],
[1/(x^7*(a+b*x^2)^10),x,3,(-1/6)/(a^10*x^6)+5/2*b/(a^11*x^4)-55/2*b^2/(a^12*x^2)-1/18*b^3/(a^4*(a+b*x^2)^9)-1/4*b^3/(a^5*(a+b*x^2)^8)-5/7*b^3/(a^6*(a+b*x^2)^7)-5/3*b^3/(a^7*(a+b*x^2)^6)-7/2*b^3/(a^8*(a+b*x^2)^5)-7*b^3/(a^9*(a+b*x^2)^4)-14*b^3/(a^10*(a+b*x^2)^3)-30*b^3/(a^11*(a+b*x^2)^2)-165/2*b^3/(a^12*(a+b*x^2))-220*b^3*log(x)/a^13+110*b^3*log(a+b*x^2)/a^13],
[x^24/(a+b*x^2)^10,x,12,7436429/65536*a^2*x/b^12-7436429/196608*a*x^3/b^11+7436429/327680*x^5/b^10-1/18*x^23/(b*(a+b*x^2)^9)-23/288*x^21/(b^2*(a+b*x^2)^8)-23/192*x^19/(b^3*(a+b*x^2)^7)-437/2304*x^17/(b^4*(a+b*x^2)^6)-7429/23040*x^15/(b^5*(a+b*x^2)^5)-7429/12288*x^13/(b^6*(a+b*x^2)^4)-96577/73728*x^11/(b^7*(a+b*x^2)^3)-1062347/294912*x^9/(b^8*(a+b*x^2)^2)-1062347/65536*x^7/(b^9*(a+b*x^2))-7436429/65536*a^(5/2)*arctan(x*sqrt(b)/sqrt(a))/b^(25/2)],
[x^22/(a+b*x^2)^10,x,12,-1616615/65536*a*x/b^11+1616615/196608*x^3/b^10-1/18*x^21/(b*(a+b*x^2)^9)-7/96*x^19/(b^2*(a+b*x^2)^8)-19/192*x^17/(b^3*(a+b*x^2)^7)-323/2304*x^15/(b^4*(a+b*x^2)^6)-323/1536*x^13/(b^5*(a+b*x^2)^5)-4199/12288*x^11/(b^6*(a+b*x^2)^4)-46189/73728*x^9/(b^7*(a+b*x^2)^3)-46189/32768*x^7/(b^8*(a+b*x^2)^2)-323323/65536*x^5/(b^9*(a+b*x^2))+1616615/65536*a^(3/2)*arctan(x*sqrt(b)/sqrt(a))/b^(23/2)],
[x^20/(a+b*x^2)^10,x,11,230945/65536*x/b^10-1/18*x^19/(b*(a+b*x^2)^9)-19/288*x^17/(b^2*(a+b*x^2)^8)-323/4032*x^15/(b^3*(a+b*x^2)^7)-1615/16128*x^13/(b^4*(a+b*x^2)^6)-4199/32256*x^11/(b^5*(a+b*x^2)^5)-46189/258048*x^9/(b^6*(a+b*x^2)^4)-46189/172032*x^7/(b^7*(a+b*x^2)^3)-46189/98304*x^5/(b^8*(a+b*x^2)^2)-230945/196608*x^3/(b^9*(a+b*x^2))-230945/65536*arctan(x*sqrt(b)/sqrt(a))*sqrt(a)/b^(21/2)],
[x^18/(a+b*x^2)^10,x,10,-1/18*x^17/(b*(a+b*x^2)^9)-17/288*x^15/(b^2*(a+b*x^2)^8)-85/1344*x^13/(b^3*(a+b*x^2)^7)-1105/16128*x^11/(b^4*(a+b*x^2)^6)-2431/32256*x^9/(b^5*(a+b*x^2)^5)-2431/28672*x^7/(b^6*(a+b*x^2)^4)-2431/24576*x^5/(b^7*(a+b*x^2)^3)-12155/98304*x^3/(b^8*(a+b*x^2)^2)-12155/65536*x/(b^9*(a+b*x^2))+12155/65536*arctan(x*sqrt(b)/sqrt(a))/(b^(19/2)*sqrt(a))],
[x^16/(a+b*x^2)^10,x,10,-1/18*x^15/(b*(a+b*x^2)^9)-5/96*x^13/(b^2*(a+b*x^2)^8)-65/1344*x^11/(b^3*(a+b*x^2)^7)-715/16128*x^9/(b^4*(a+b*x^2)^6)-143/3584*x^7/(b^5*(a+b*x^2)^5)-143/4096*x^5/(b^6*(a+b*x^2)^4)-715/24576*x^3/(b^7*(a+b*x^2)^3)-715/32768*x/(b^8*(a+b*x^2)^2)+715/65536*x/(a*b^8*(a+b*x^2))+715/65536*arctan(x*sqrt(b)/sqrt(a))/(a^(3/2)*b^(17/2))],
[x^14/(a+b*x^2)^10,x,10,-1/18*x^13/(b*(a+b*x^2)^9)-13/288*x^11/(b^2*(a+b*x^2)^8)-143/4032*x^9/(b^3*(a+b*x^2)^7)-143/5376*x^7/(b^4*(a+b*x^2)^6)-143/7680*x^5/(b^5*(a+b*x^2)^5)-143/12288*x^3/(b^6*(a+b*x^2)^4)-143/24576*x/(b^7*(a+b*x^2)^3)+143/98304*x/(a*b^7*(a+b*x^2)^2)+143/65536*x/(a^2*b^7*(a+b*x^2))+143/65536*arctan(x*sqrt(b)/sqrt(a))/(a^(5/2)*b^(15/2))],
[x^12/(a+b*x^2)^10,x,10,-1/18*x^11/(b*(a+b*x^2)^9)-11/288*x^9/(b^2*(a+b*x^2)^8)-11/448*x^7/(b^3*(a+b*x^2)^7)-11/768*x^5/(b^4*(a+b*x^2)^6)-11/1536*x^3/(b^5*(a+b*x^2)^5)-11/4096*x/(b^6*(a+b*x^2)^4)+11/24576*x/(a*b^6*(a+b*x^2)^3)+55/98304*x/(a^2*b^6*(a+b*x^2)^2)+55/65536*x/(a^3*b^6*(a+b*x^2))+55/65536*arctan(x*sqrt(b)/sqrt(a))/(a^(7/2)*b^(13/2))],
[x^10/(a+b*x^2)^10,x,10,-1/18*x^9/(b*(a+b*x^2)^9)-1/32*x^7/(b^2*(a+b*x^2)^8)-1/64*x^5/(b^3*(a+b*x^2)^7)-5/768*x^3/(b^4*(a+b*x^2)^6)-1/512*x/(b^5*(a+b*x^2)^5)+1/4096*x/(a*b^5*(a+b*x^2)^4)+7/24576*x/(a^2*b^5*(a+b*x^2)^3)+35/98304*x/(a^3*b^5*(a+b*x^2)^2)+35/65536*x/(a^4*b^5*(a+b*x^2))+35/65536*arctan(x*sqrt(b)/sqrt(a))/(a^(9/2)*b^(11/2))],
[x^8/(a+b*x^2)^10,x,10,-1/18*x^7/(b*(a+b*x^2)^9)-7/288*x^5/(b^2*(a+b*x^2)^8)-5/576*x^3/(b^3*(a+b*x^2)^7)-5/2304*x/(b^4*(a+b*x^2)^6)+1/4608*x/(a*b^4*(a+b*x^2)^5)+1/4096*x/(a^2*b^4*(a+b*x^2)^4)+7/24576*x/(a^3*b^4*(a+b*x^2)^3)+35/98304*x/(a^4*b^4*(a+b*x^2)^2)+35/65536*x/(a^5*b^4*(a+b*x^2))+35/65536*arctan(x*sqrt(b)/sqrt(a))/(a^(11/2)*b^(9/2))],
[x^6/(a+b*x^2)^10,x,10,-1/18*x^5/(b*(a+b*x^2)^9)-5/288*x^3/(b^2*(a+b*x^2)^8)-5/1344*x/(b^3*(a+b*x^2)^7)+5/16128*x/(a*b^3*(a+b*x^2)^6)+11/32256*x/(a^2*b^3*(a+b*x^2)^5)+11/28672*x/(a^3*b^3*(a+b*x^2)^4)+11/24576*x/(a^4*b^3*(a+b*x^2)^3)+55/98304*x/(a^5*b^3*(a+b*x^2)^2)+55/65536*x/(a^6*b^3*(a+b*x^2))+55/65536*arctan(x*sqrt(b)/sqrt(a))/(a^(13/2)*b^(7/2))],
[x^4/(a+b*x^2)^10,x,10,-1/18*x^3/(b*(a+b*x^2)^9)-1/96*x/(b^2*(a+b*x^2)^8)+1/1344*x/(a*b^2*(a+b*x^2)^7)+13/16128*x/(a^2*b^2*(a+b*x^2)^6)+143/161280*x/(a^3*b^2*(a+b*x^2)^5)+143/143360*x/(a^4*b^2*(a+b*x^2)^4)+143/122880*x/(a^5*b^2*(a+b*x^2)^3)+143/98304*x/(a^6*b^2*(a+b*x^2)^2)+143/65536*x/(a^7*b^2*(a+b*x^2))+143/65536*arctan(x*sqrt(b)/sqrt(a))/(a^(15/2)*b^(5/2))],
[x^2/(a+b*x^2)^10,x,10,-1/18*x/(b*(a+b*x^2)^9)+1/288*x/(a*b*(a+b*x^2)^8)+5/1344*x/(a^2*b*(a+b*x^2)^7)+65/16128*x/(a^3*b*(a+b*x^2)^6)+143/32256*x/(a^4*b*(a+b*x^2)^5)+143/28672*x/(a^5*b*(a+b*x^2)^4)+143/24576*x/(a^6*b*(a+b*x^2)^3)+715/98304*x/(a^7*b*(a+b*x^2)^2)+715/65536*x/(a^8*b*(a+b*x^2))+715/65536*arctan(x*sqrt(b)/sqrt(a))/(a^(17/2)*b^(3/2))],
[1/(a+b*x^2)^10,x,10,1/18*x/(a*(a+b*x^2)^9)+17/288*x/(a^2*(a+b*x^2)^8)+85/1344*x/(a^3*(a+b*x^2)^7)+1105/16128*x/(a^4*(a+b*x^2)^6)+2431/32256*x/(a^5*(a+b*x^2)^5)+2431/28672*x/(a^6*(a+b*x^2)^4)+2431/24576*x/(a^7*(a+b*x^2)^3)+12155/98304*x/(a^8*(a+b*x^2)^2)+12155/65536*x/(a^9*(a+b*x^2))+12155/65536*arctan(x*sqrt(b)/sqrt(a))/(a^(19/2)*sqrt(b))],
[1/(x^2*(a+b*x^2)^10),x,11,(-230945/65536)/(a^10*x)+1/18/(a*x*(a+b*x^2)^9)+19/288/(a^2*x*(a+b*x^2)^8)+323/4032/(a^3*x*(a+b*x^2)^7)+1615/16128/(a^4*x*(a+b*x^2)^6)+4199/32256/(a^5*x*(a+b*x^2)^5)+46189/258048/(a^6*x*(a+b*x^2)^4)+46189/172032/(a^7*x*(a+b*x^2)^3)+46189/98304/(a^8*x*(a+b*x^2)^2)+230945/196608/(a^9*x*(a+b*x^2))-230945/65536*arctan(x*sqrt(b)/sqrt(a))*sqrt(b)/a^(21/2)],
[1/(x^4*(a+b*x^2)^10),x,12,(-1616615/196608)/(a^10*x^3)+1616615/65536*b/(a^11*x)+1/18/(a*x^3*(a+b*x^2)^9)+7/96/(a^2*x^3*(a+b*x^2)^8)+19/192/(a^3*x^3*(a+b*x^2)^7)+323/2304/(a^4*x^3*(a+b*x^2)^6)+323/1536/(a^5*x^3*(a+b*x^2)^5)+4199/12288/(a^6*x^3*(a+b*x^2)^4)+46189/73728/(a^7*x^3*(a+b*x^2)^3)+46189/32768/(a^8*x^3*(a+b*x^2)^2)+323323/65536/(a^9*x^3*(a+b*x^2))+1616615/65536*b^(3/2)*arctan(x*sqrt(b)/sqrt(a))/a^(23/2)],
[1/(x^6*(a+b*x^2)^10),x,13,(-7436429/327680)/(a^10*x^5)+7436429/196608*b/(a^11*x^3)-7436429/65536*b^2/(a^12*x)+1/18/(a*x^5*(a+b*x^2)^9)+23/288/(a^2*x^5*(a+b*x^2)^8)+23/192/(a^3*x^5*(a+b*x^2)^7)+437/2304/(a^4*x^5*(a+b*x^2)^6)+7429/23040/(a^5*x^5*(a+b*x^2)^5)+7429/12288/(a^6*x^5*(a+b*x^2)^4)+96577/73728/(a^7*x^5*(a+b*x^2)^3)+1062347/294912/(a^8*x^5*(a+b*x^2)^2)+1062347/65536/(a^9*x^5*(a+b*x^2))-7436429/65536*b^(5/2)*arctan(x*sqrt(b)/sqrt(a))/a^(25/2)],
[x^3/(a-b*x^2),x,3,-1/2*x^2/b-1/2*a*log(a-b*x^2)/b^2],
[x^2/(a-b*x^2),x,2,-x/b+arctanh(x*sqrt(b)/sqrt(a))*sqrt(a)/b^(3/2)],
[x/(a-b*x^2),x,1,-1/2*log(a-b*x^2)/b],
[1/(a-b*x^2),x,1,arctanh(x*sqrt(b)/sqrt(a))/(sqrt(a)*sqrt(b))],
[1/(x*(a-b*x^2)),x,4,log(x)/a-1/2*log(a-b*x^2)/a],
[1/(x^2*(a-b*x^2)),x,2,(-1)/(a*x)+arctanh(x*sqrt(b)/sqrt(a))*sqrt(b)/a^(3/2)],
[1/(x^3*(a-b*x^2)),x,3,(-1/2)/(a*x^2)+b*log(x)/a^2-1/2*b*log(a-b*x^2)/a^2],
[x^3/(a-b*x^2)^2,x,3,1/2*a/(b^2*(a-b*x^2))+1/2*log(a-b*x^2)/b^2],
[x^2/(a-b*x^2)^2,x,2,1/2*x/(b*(a-b*x^2))-1/2*arctanh(x*sqrt(b)/sqrt(a))/(b^(3/2)*sqrt(a))],
[x/(a-b*x^2)^2,x,1,1/2/(b*(a-b*x^2))],
[1/(a-b*x^2)^2,x,2,1/2*x/(a*(a-b*x^2))+1/2*arctanh(x*sqrt(b)/sqrt(a))/(a^(3/2)*sqrt(b))],
[1/(x*(a-b*x^2)^2),x,3,1/2/(a*(a-b*x^2))+log(x)/a^2-1/2*log(a-b*x^2)/a^2],
[1/(x^2*(a-b*x^2)^2),x,3,(-3/2)/(a^2*x)+1/2/(a*x*(a-b*x^2))+3/2*arctanh(x*sqrt(b)/sqrt(a))*sqrt(b)/a^(5/2)],
[1/(x^3*(a-b*x^2)^2),x,3,(-1/2)/(a^2*x^2)+1/2*b/(a^2*(a-b*x^2))+2*b*log(x)/a^3-b*log(a-b*x^2)/a^3],
[x^3/(a-b*x^2)^3,x,1,1/4*x^4/(a*(a-b*x^2)^2)],
[x^2/(a-b*x^2)^3,x,3,1/4*x/(b*(a-b*x^2)^2)-1/8*x/(a*b*(a-b*x^2))-1/8*arctanh(x*sqrt(b)/sqrt(a))/(a^(3/2)*b^(3/2))],
[x/(a-b*x^2)^3,x,1,1/4/(b*(a-b*x^2)^2)],
[1/(a-b*x^2)^3,x,3,1/4*x/(a*(a-b*x^2)^2)+3/8*x/(a^2*(a-b*x^2))+3/8*arctanh(x*sqrt(b)/sqrt(a))/(a^(5/2)*sqrt(b))],
[1/(x*(a-b*x^2)^3),x,3,1/4/(a*(a-b*x^2)^2)+1/2/(a^2*(a-b*x^2))+log(x)/a^3-1/2*log(a-b*x^2)/a^3],
[1/(x^2*(a-b*x^2)^3),x,4,(-15/8)/(a^3*x)+1/4/(a*x*(a-b*x^2)^2)+5/8/(a^2*x*(a-b*x^2))+15/8*arctanh(x*sqrt(b)/sqrt(a))*sqrt(b)/a^(7/2)],
[1/(x^3*(a-b*x^2)^3),x,3,(-1/2)/(a^3*x^2)+1/4*b/(a^2*(a-b*x^2)^2)+b/(a^3*(a-b*x^2))+3*b*log(x)/a^4-3/2*b*log(a-b*x^2)/a^4],
[x^3/(a-b*x^2)^5,x,3,1/8*a/(b^2*(a-b*x^2)^4)+(-1/6)/(b^2*(a-b*x^2)^3)],
[x^2/(a-b*x^2)^5,x,5,1/8*x/(b*(a-b*x^2)^4)-1/48*x/(a*b*(a-b*x^2)^3)-5/192*x/(a^2*b*(a-b*x^2)^2)-5/128*x/(a^3*b*(a-b*x^2))-5/128*arctanh(x*sqrt(b)/sqrt(a))/(a^(7/2)*b^(3/2))],
[x/(a-b*x^2)^5,x,1,1/8/(b*(a-b*x^2)^4)],
[1/(a-b*x^2)^5,x,5,1/8*x/(a*(a-b*x^2)^4)+7/48*x/(a^2*(a-b*x^2)^3)+35/192*x/(a^3*(a-b*x^2)^2)+35/128*x/(a^4*(a-b*x^2))+35/128*arctanh(x*sqrt(b)/sqrt(a))/(a^(9/2)*sqrt(b))],
[1/(x*(a-b*x^2)^5),x,3,1/8/(a*(a-b*x^2)^4)+1/6/(a^2*(a-b*x^2)^3)+1/4/(a^3*(a-b*x^2)^2)+1/2/(a^4*(a-b*x^2))+log(x)/a^5-1/2*log(a-b*x^2)/a^5],
[1/(x^2*(a-b*x^2)^5),x,6,(-315/128)/(a^5*x)+1/8/(a*x*(a-b*x^2)^4)+3/16/(a^2*x*(a-b*x^2)^3)+21/64/(a^3*x*(a-b*x^2)^2)+105/128/(a^4*x*(a-b*x^2))+315/128*arctanh(x*sqrt(b)/sqrt(a))*sqrt(b)/a^(11/2)],
[1/(x^3*(a-b*x^2)^5),x,3,(-1/2)/(a^5*x^2)+1/8*b/(a^2*(a-b*x^2)^4)+1/3*b/(a^3*(a-b*x^2)^3)+3/4*b/(a^4*(a-b*x^2)^2)+2*b/(a^5*(a-b*x^2))+5*b*log(x)/a^6-5/2*b*log(a-b*x^2)/a^6],
[1/(x*(1+b*x^2)),x,4,log(x)-1/2*log(1+b*x^2)],
[1/(x*(-1+b*x^2)),x,4,-log(x)+1/2*log(1-b*x^2)],
[1/(x^3*(1+b*x^2)),x,3,(-1/2)/x^2-b*log(x)+1/2*b*log(1+b*x^2)],
[1/(x^3*(-1+b*x^2)),x,3,1/2/x^2-b*log(x)+1/2*b*log(1-b*x^2)],

#  Formerly failed because both PosQ[(1-a)/a] and PosQ[-(1-a)/a] returned False. 
[1/(-1+a+a*x^2),x,1,-arctanh(x*sqrt(a)/sqrt(1-a))/sqrt((1-a)*a)],
[1/(-c-d+(c-d)*x^2),x,1,-arctanh(x*sqrt(c-d)/sqrt(c+d))/(sqrt(c-d)*sqrt(c+d))],
[1/(x*(1+b*x^2)^2),x,3,1/2/(1+b*x^2)+log(x)-1/2*log(1+b*x^2)],
[1/(x*(-1+b*x^2)^2),x,3,1/2/(1-b*x^2)+log(x)-1/2*log(1-b*x^2)],

#  Checks to ensure PosQ[a/(b-a*c)] returns True. 
[1/(a+(b-a*c)*x^2),x,1,arctan(x*sqrt(b-a*c)/sqrt(a))/(sqrt(a)*sqrt(b-a*c))],
[1/(a-(b-a*c)*x^2),x,1,arctanh(x*sqrt(b-a*c)/sqrt(a))/(sqrt(a)*sqrt(b-a*c))],

#  Checks to ensure Rt[-c*(a-d)/(-b+c),2] returns Sqrt[c]*Sqrt[a-d]/Sqrt[b-c]. 
[1/(c*(a-d)-(b-c)*x^2),x,1,arctanh(x*sqrt(b-c)/(sqrt(c)*sqrt(a-d)))/(sqrt(b-c)*sqrt(c)*sqrt(a-d))],

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

# p>0
[x^(7/2)*(a+b*x^2),x,2,2/9*a*x^(9/2)+2/13*b*x^(13/2)],
[x^(5/2)*(a+b*x^2),x,2,2/7*a*x^(7/2)+2/11*b*x^(11/2)],
[x^(3/2)*(a+b*x^2),x,2,2/5*a*x^(5/2)+2/9*b*x^(9/2)],
[(a+b*x^2)*sqrt(x),x,2,2/3*a*x^(3/2)+2/7*b*x^(7/2)],
[(a+b*x^2)/sqrt(x),x,2,2/5*b*x^(5/2)+2*a*sqrt(x)],
[(a+b*x^2)/x^(3/2),x,2,2/3*b*x^(3/2)-2*a/sqrt(x)],
[(a+b*x^2)/x^(5/2),x,2,-2/3*a/x^(3/2)+2*b*sqrt(x)],
[(a+b*x^2)/x^(7/2),x,2,-2/5*a/x^(5/2)-2*b/sqrt(x)],
[x^(7/2)*(a+b*x^2)^2,x,2,2/9*a^2*x^(9/2)+4/13*a*b*x^(13/2)+2/17*b^2*x^(17/2)],
[x^(5/2)*(a+b*x^2)^2,x,2,2/7*a^2*x^(7/2)+4/11*a*b*x^(11/2)+2/15*b^2*x^(15/2)],
[x^(3/2)*(a+b*x^2)^2,x,2,2/5*a^2*x^(5/2)+4/9*a*b*x^(9/2)+2/13*b^2*x^(13/2)],
[(a+b*x^2)^2*sqrt(x),x,2,2/3*a^2*x^(3/2)+4/7*a*b*x^(7/2)+2/11*b^2*x^(11/2)],
[(a+b*x^2)^2/sqrt(x),x,2,4/5*a*b*x^(5/2)+2/9*b^2*x^(9/2)+2*a^2*sqrt(x)],
[(a+b*x^2)^2/x^(3/2),x,2,4/3*a*b*x^(3/2)+2/7*b^2*x^(7/2)-2*a^2/sqrt(x)],
[(a+b*x^2)^2/x^(5/2),x,2,-2/3*a^2/x^(3/2)+2/5*b^2*x^(5/2)+4*a*b*sqrt(x)],
[(a+b*x^2)^2/x^(7/2),x,2,-2/5*a^2/x^(5/2)+2/3*b^2*x^(3/2)-4*a*b/sqrt(x)],
[x^(7/2)*(a+b*x^2)^3,x,2,2/9*a^3*x^(9/2)+6/13*a^2*b*x^(13/2)+6/17*a*b^2*x^(17/2)+2/21*b^3*x^(21/2)],
[x^(5/2)*(a+b*x^2)^3,x,2,2/7*a^3*x^(7/2)+6/11*a^2*b*x^(11/2)+2/5*a*b^2*x^(15/2)+2/19*b^3*x^(19/2)],
[x^(3/2)*(a+b*x^2)^3,x,2,2/5*a^3*x^(5/2)+2/3*a^2*b*x^(9/2)+6/13*a*b^2*x^(13/2)+2/17*b^3*x^(17/2)],
[(a+b*x^2)^3*sqrt(x),x,2,2/3*a^3*x^(3/2)+6/7*a^2*b*x^(7/2)+6/11*a*b^2*x^(11/2)+2/15*b^3*x^(15/2)],
[(a+b*x^2)^3/sqrt(x),x,2,6/5*a^2*b*x^(5/2)+2/3*a*b^2*x^(9/2)+2/13*b^3*x^(13/2)+2*a^3*sqrt(x)],
[(a+b*x^2)^3/x^(3/2),x,2,2*a^2*b*x^(3/2)+6/7*a*b^2*x^(7/2)+2/11*b^3*x^(11/2)-2*a^3/sqrt(x)],
[(a+b*x^2)^3/x^(5/2),x,2,-2/3*a^3/x^(3/2)+6/5*a*b^2*x^(5/2)+2/9*b^3*x^(9/2)+6*a^2*b*sqrt(x)],
[(a+b*x^2)^3/x^(7/2),x,2,-2/5*a^3/x^(5/2)+2*a*b^2*x^(3/2)+2/7*b^3*x^(7/2)-6*a^2*b/sqrt(x)],

# p<0
[x^(7/2)/(a+b*x^2),x,12,2/5*x^(5/2)/b-a^(5/4)*arctan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(b^(9/4)*sqrt(2))+a^(5/4)*arctan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(b^(9/4)*sqrt(2))-1/2*a^(5/4)*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(b^(9/4)*sqrt(2))+1/2*a^(5/4)*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(b^(9/4)*sqrt(2))-2*a*sqrt(x)/b^2],
[x^(5/2)/(a+b*x^2),x,11,2/3*x^(3/2)/b+a^(3/4)*arctan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(b^(7/4)*sqrt(2))-a^(3/4)*arctan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(b^(7/4)*sqrt(2))-1/2*a^(3/4)*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(b^(7/4)*sqrt(2))+1/2*a^(3/4)*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(b^(7/4)*sqrt(2))],
[x^(3/2)/(a+b*x^2),x,11,a^(1/4)*arctan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(b^(5/4)*sqrt(2))-a^(1/4)*arctan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(b^(5/4)*sqrt(2))+1/2*a^(1/4)*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(b^(5/4)*sqrt(2))-1/2*a^(1/4)*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(b^(5/4)*sqrt(2))+2*sqrt(x)/b],
[sqrt(x)/(a+b*x^2),x,10,-arctan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(1/4)*b^(3/4)*sqrt(2))+arctan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(1/4)*b^(3/4)*sqrt(2))+1/2*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(1/4)*b^(3/4)*sqrt(2))-1/2*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(1/4)*b^(3/4)*sqrt(2))],
[1/((a+b*x^2)*sqrt(x)),x,10,-arctan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(3/4)*b^(1/4)*sqrt(2))+arctan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(3/4)*b^(1/4)*sqrt(2))-1/2*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(3/4)*b^(1/4)*sqrt(2))+1/2*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(3/4)*b^(1/4)*sqrt(2))],
[1/(x^(3/2)*(a+b*x^2)),x,11,b^(1/4)*arctan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(5/4)*sqrt(2))-b^(1/4)*arctan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(5/4)*sqrt(2))-1/2*b^(1/4)*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(5/4)*sqrt(2))+1/2*b^(1/4)*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(5/4)*sqrt(2))+(-2)/(a*sqrt(x))],
[1/(x^(5/2)*(a+b*x^2)),x,11,(-2/3)/(a*x^(3/2))+b^(3/4)*arctan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(7/4)*sqrt(2))-b^(3/4)*arctan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(7/4)*sqrt(2))+1/2*b^(3/4)*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(7/4)*sqrt(2))-1/2*b^(3/4)*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(7/4)*sqrt(2))],
[1/(x^(7/2)*(a+b*x^2)),x,12,(-2/5)/(a*x^(5/2))-b^(5/4)*arctan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(9/4)*sqrt(2))+b^(5/4)*arctan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(9/4)*sqrt(2))+1/2*b^(5/4)*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(9/4)*sqrt(2))-1/2*b^(5/4)*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(9/4)*sqrt(2))+2*b/(a^2*sqrt(x))],
[x^(7/2)/(a+b*x^2)^2,x,12,-1/2*x^(5/2)/(b*(a+b*x^2))+5/4*a^(1/4)*arctan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(b^(9/4)*sqrt(2))-5/4*a^(1/4)*arctan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(b^(9/4)*sqrt(2))+5/8*a^(1/4)*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(b^(9/4)*sqrt(2))-5/8*a^(1/4)*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(b^(9/4)*sqrt(2))+5/2*sqrt(x)/b^2],
[x^(5/2)/(a+b*x^2)^2,x,11,-1/2*x^(3/2)/(b*(a+b*x^2))-3/4*arctan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(1/4)*b^(7/4)*sqrt(2))+3/4*arctan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(1/4)*b^(7/4)*sqrt(2))+3/8*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(1/4)*b^(7/4)*sqrt(2))-3/8*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(1/4)*b^(7/4)*sqrt(2))],
[x^(3/2)/(a+b*x^2)^2,x,11,-1/4*arctan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(3/4)*b^(5/4)*sqrt(2))+1/4*arctan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(3/4)*b^(5/4)*sqrt(2))-1/8*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(3/4)*b^(5/4)*sqrt(2))+1/8*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(3/4)*b^(5/4)*sqrt(2))-1/2*sqrt(x)/(b*(a+b*x^2))],
[sqrt(x)/(a+b*x^2)^2,x,11,1/2*x^(3/2)/(a*(a+b*x^2))-1/4*arctan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(5/4)*b^(3/4)*sqrt(2))+1/4*arctan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(5/4)*b^(3/4)*sqrt(2))+1/8*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(5/4)*b^(3/4)*sqrt(2))-1/8*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(5/4)*b^(3/4)*sqrt(2))],
[1/((a+b*x^2)^2*sqrt(x)),x,11,-3/4*arctan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(7/4)*b^(1/4)*sqrt(2))+3/4*arctan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(7/4)*b^(1/4)*sqrt(2))-3/8*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(7/4)*b^(1/4)*sqrt(2))+3/8*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(7/4)*b^(1/4)*sqrt(2))+1/2*sqrt(x)/(a*(a+b*x^2))],
[1/(x^(3/2)*(a+b*x^2)^2),x,12,5/4*b^(1/4)*arctan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(9/4)*sqrt(2))-5/4*b^(1/4)*arctan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(9/4)*sqrt(2))-5/8*b^(1/4)*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(9/4)*sqrt(2))+5/8*b^(1/4)*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(9/4)*sqrt(2))+(-5/2)/(a^2*sqrt(x))+1/2/(a*(a+b*x^2)*sqrt(x))],
[1/(x^(5/2)*(a+b*x^2)^2),x,12,(-7/6)/(a^2*x^(3/2))+1/2/(a*x^(3/2)*(a+b*x^2))+7/4*b^(3/4)*arctan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(11/4)*sqrt(2))-7/4*b^(3/4)*arctan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(11/4)*sqrt(2))+7/8*b^(3/4)*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(11/4)*sqrt(2))-7/8*b^(3/4)*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(11/4)*sqrt(2))],
[1/(x^(7/2)*(a+b*x^2)^2),x,13,(-9/10)/(a^2*x^(5/2))+1/2/(a*x^(5/2)*(a+b*x^2))-9/4*b^(5/4)*arctan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(13/4)*sqrt(2))+9/4*b^(5/4)*arctan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(13/4)*sqrt(2))+9/8*b^(5/4)*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(13/4)*sqrt(2))-9/8*b^(5/4)*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(13/4)*sqrt(2))+9/2*b/(a^3*sqrt(x))],
[x^(7/2)/(a+b*x^2)^3,x,12,-1/4*x^(5/2)/(b*(a+b*x^2)^2)-5/32*arctan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(3/4)*b^(9/4)*sqrt(2))+5/32*arctan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(3/4)*b^(9/4)*sqrt(2))-5/64*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(3/4)*b^(9/4)*sqrt(2))+5/64*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(3/4)*b^(9/4)*sqrt(2))-5/16*sqrt(x)/(b^2*(a+b*x^2))],
[x^(5/2)/(a+b*x^2)^3,x,12,-1/4*x^(3/2)/(b*(a+b*x^2)^2)+3/16*x^(3/2)/(a*b*(a+b*x^2))-3/32*arctan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(5/4)*b^(7/4)*sqrt(2))+3/32*arctan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(5/4)*b^(7/4)*sqrt(2))+3/64*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(5/4)*b^(7/4)*sqrt(2))-3/64*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(5/4)*b^(7/4)*sqrt(2))],
[x^(3/2)/(a+b*x^2)^3,x,12,-3/32*arctan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(7/4)*b^(5/4)*sqrt(2))+3/32*arctan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(7/4)*b^(5/4)*sqrt(2))-3/64*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(7/4)*b^(5/4)*sqrt(2))+3/64*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(7/4)*b^(5/4)*sqrt(2))-1/4*sqrt(x)/(b*(a+b*x^2)^2)+1/16*sqrt(x)/(a*b*(a+b*x^2))],
[sqrt(x)/(a+b*x^2)^3,x,12,1/4*x^(3/2)/(a*(a+b*x^2)^2)+5/16*x^(3/2)/(a^2*(a+b*x^2))-5/32*arctan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(9/4)*b^(3/4)*sqrt(2))+5/32*arctan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(9/4)*b^(3/4)*sqrt(2))+5/64*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(9/4)*b^(3/4)*sqrt(2))-5/64*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(9/4)*b^(3/4)*sqrt(2))],
[1/((a+b*x^2)^3*sqrt(x)),x,12,-21/32*arctan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(11/4)*b^(1/4)*sqrt(2))+21/32*arctan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(11/4)*b^(1/4)*sqrt(2))-21/64*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(11/4)*b^(1/4)*sqrt(2))+21/64*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(11/4)*b^(1/4)*sqrt(2))+1/4*sqrt(x)/(a*(a+b*x^2)^2)+7/16*sqrt(x)/(a^2*(a+b*x^2))],
[1/(x^(3/2)*(a+b*x^2)^3),x,13,45/32*b^(1/4)*arctan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(13/4)*sqrt(2))-45/32*b^(1/4)*arctan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(13/4)*sqrt(2))-45/64*b^(1/4)*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(13/4)*sqrt(2))+45/64*b^(1/4)*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(13/4)*sqrt(2))+(-45/16)/(a^3*sqrt(x))+1/4/(a*(a+b*x^2)^2*sqrt(x))+9/16/(a^2*(a+b*x^2)*sqrt(x))],
[1/(x^(5/2)*(a+b*x^2)^3),x,13,(-77/48)/(a^3*x^(3/2))+1/4/(a*x^(3/2)*(a+b*x^2)^2)+11/16/(a^2*x^(3/2)*(a+b*x^2))+77/32*b^(3/4)*arctan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(15/4)*sqrt(2))-77/32*b^(3/4)*arctan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(15/4)*sqrt(2))+77/64*b^(3/4)*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(15/4)*sqrt(2))-77/64*b^(3/4)*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(15/4)*sqrt(2))],
[1/(x^(7/2)*(a+b*x^2)^3),x,14,(-117/80)/(a^3*x^(5/2))+1/4/(a*x^(5/2)*(a+b*x^2)^2)+13/16/(a^2*x^(5/2)*(a+b*x^2))-117/32*b^(5/4)*arctan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(17/4)*sqrt(2))+117/32*b^(5/4)*arctan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(17/4)*sqrt(2))+117/64*b^(5/4)*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(17/4)*sqrt(2))-117/64*b^(5/4)*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(17/4)*sqrt(2))+117/16*b/(a^4*sqrt(x))],
[sqrt(x)/(a-b*x^2),x,4,-arctan(b^(1/4)*sqrt(x)/a^(1/4))/(a^(1/4)*b^(3/4))+arctanh(b^(1/4)*sqrt(x)/a^(1/4))/(a^(1/4)*b^(3/4))],
[x^(7/2)/(1+x^2),x,12,2/5*x^(5/2)-arctan(1-sqrt(2)*sqrt(x))/sqrt(2)+arctan(1+sqrt(2)*sqrt(x))/sqrt(2)-1/2*log(1+x-sqrt(2)*sqrt(x))/sqrt(2)+1/2*log(1+x+sqrt(2)*sqrt(x))/sqrt(2)-2*sqrt(x)],
[x^(5/2)/(1+x^2),x,11,2/3*x^(3/2)+arctan(1-sqrt(2)*sqrt(x))/sqrt(2)-arctan(1+sqrt(2)*sqrt(x))/sqrt(2)-1/2*log(1+x-sqrt(2)*sqrt(x))/sqrt(2)+1/2*log(1+x+sqrt(2)*sqrt(x))/sqrt(2)],
[x^(3/2)/(1+x^2),x,11,arctan(1-sqrt(2)*sqrt(x))/sqrt(2)-arctan(1+sqrt(2)*sqrt(x))/sqrt(2)+1/2*log(1+x-sqrt(2)*sqrt(x))/sqrt(2)-1/2*log(1+x+sqrt(2)*sqrt(x))/sqrt(2)+2*sqrt(x)],
[sqrt(x)/(1+x^2),x,10,-arctan(1-sqrt(2)*sqrt(x))/sqrt(2)+arctan(1+sqrt(2)*sqrt(x))/sqrt(2)+1/2*log(1+x-sqrt(2)*sqrt(x))/sqrt(2)-1/2*log(1+x+sqrt(2)*sqrt(x))/sqrt(2)],
[1/((1+x^2)*sqrt(x)),x,10,-arctan(1-sqrt(2)*sqrt(x))/sqrt(2)+arctan(1+sqrt(2)*sqrt(x))/sqrt(2)-1/2*log(1+x-sqrt(2)*sqrt(x))/sqrt(2)+1/2*log(1+x+sqrt(2)*sqrt(x))/sqrt(2)],
[1/(x^(3/2)*(1+x^2)),x,11,arctan(1-sqrt(2)*sqrt(x))/sqrt(2)-arctan(1+sqrt(2)*sqrt(x))/sqrt(2)-1/2*log(1+x-sqrt(2)*sqrt(x))/sqrt(2)+1/2*log(1+x+sqrt(2)*sqrt(x))/sqrt(2)+(-2)/sqrt(x)],
[1/(x^(5/2)*(1+x^2)),x,11,(-2/3)/x^(3/2)+arctan(1-sqrt(2)*sqrt(x))/sqrt(2)-arctan(1+sqrt(2)*sqrt(x))/sqrt(2)+1/2*log(1+x-sqrt(2)*sqrt(x))/sqrt(2)-1/2*log(1+x+sqrt(2)*sqrt(x))/sqrt(2)],
[1/(x^(7/2)*(1+x^2)),x,12,(-2/5)/x^(5/2)-arctan(1-sqrt(2)*sqrt(x))/sqrt(2)+arctan(1+sqrt(2)*sqrt(x))/sqrt(2)+1/2*log(1+x-sqrt(2)*sqrt(x))/sqrt(2)-1/2*log(1+x+sqrt(2)*sqrt(x))/sqrt(2)+2/sqrt(x)],
[x^(7/2)/(1+x^2)^2,x,12,-1/2*x^(5/2)/(1+x^2)+5/4*arctan(1-sqrt(2)*sqrt(x))/sqrt(2)-5/4*arctan(1+sqrt(2)*sqrt(x))/sqrt(2)+5/8*log(1+x-sqrt(2)*sqrt(x))/sqrt(2)-5/8*log(1+x+sqrt(2)*sqrt(x))/sqrt(2)+5/2*sqrt(x)],
[x^(5/2)/(1+x^2)^2,x,11,-1/2*x^(3/2)/(1+x^2)-3/4*arctan(1-sqrt(2)*sqrt(x))/sqrt(2)+3/4*arctan(1+sqrt(2)*sqrt(x))/sqrt(2)+3/8*log(1+x-sqrt(2)*sqrt(x))/sqrt(2)-3/8*log(1+x+sqrt(2)*sqrt(x))/sqrt(2)],
[x^(3/2)/(1+x^2)^2,x,11,-1/4*arctan(1-sqrt(2)*sqrt(x))/sqrt(2)+1/4*arctan(1+sqrt(2)*sqrt(x))/sqrt(2)-1/8*log(1+x-sqrt(2)*sqrt(x))/sqrt(2)+1/8*log(1+x+sqrt(2)*sqrt(x))/sqrt(2)-1/2*sqrt(x)/(1+x^2)],
[sqrt(x)/(1+x^2)^2,x,11,1/2*x^(3/2)/(1+x^2)-1/4*arctan(1-sqrt(2)*sqrt(x))/sqrt(2)+1/4*arctan(1+sqrt(2)*sqrt(x))/sqrt(2)+1/8*log(1+x-sqrt(2)*sqrt(x))/sqrt(2)-1/8*log(1+x+sqrt(2)*sqrt(x))/sqrt(2)],
[1/((1+x^2)^2*sqrt(x)),x,11,-3/4*arctan(1-sqrt(2)*sqrt(x))/sqrt(2)+3/4*arctan(1+sqrt(2)*sqrt(x))/sqrt(2)-3/8*log(1+x-sqrt(2)*sqrt(x))/sqrt(2)+3/8*log(1+x+sqrt(2)*sqrt(x))/sqrt(2)+1/2*sqrt(x)/(1+x^2)],
[1/(x^(3/2)*(1+x^2)^2),x,12,5/4*arctan(1-sqrt(2)*sqrt(x))/sqrt(2)-5/4*arctan(1+sqrt(2)*sqrt(x))/sqrt(2)-5/8*log(1+x-sqrt(2)*sqrt(x))/sqrt(2)+5/8*log(1+x+sqrt(2)*sqrt(x))/sqrt(2)+(-5/2)/sqrt(x)+1/2/((1+x^2)*sqrt(x))],
[1/(x^(5/2)*(1+x^2)^2),x,12,(-7/6)/x^(3/2)+1/2/(x^(3/2)*(1+x^2))+7/4*arctan(1-sqrt(2)*sqrt(x))/sqrt(2)-7/4*arctan(1+sqrt(2)*sqrt(x))/sqrt(2)+7/8*log(1+x-sqrt(2)*sqrt(x))/sqrt(2)-7/8*log(1+x+sqrt(2)*sqrt(x))/sqrt(2)],
[1/(x^(7/2)*(1+x^2)^2),x,13,(-9/10)/x^(5/2)+1/2/(x^(5/2)*(1+x^2))-9/4*arctan(1-sqrt(2)*sqrt(x))/sqrt(2)+9/4*arctan(1+sqrt(2)*sqrt(x))/sqrt(2)+9/8*log(1+x-sqrt(2)*sqrt(x))/sqrt(2)-9/8*log(1+x+sqrt(2)*sqrt(x))/sqrt(2)+9/2/sqrt(x)],
[x^(7/2)/(1+x^2)^3,x,12,-1/4*x^(5/2)/(1+x^2)^2-5/32*arctan(1-sqrt(2)*sqrt(x))/sqrt(2)+5/32*arctan(1+sqrt(2)*sqrt(x))/sqrt(2)-5/64*log(1+x-sqrt(2)*sqrt(x))/sqrt(2)+5/64*log(1+x+sqrt(2)*sqrt(x))/sqrt(2)-5/16*sqrt(x)/(1+x^2)],
[x^(5/2)/(1+x^2)^3,x,12,-1/4*x^(3/2)/(1+x^2)^2+3/16*x^(3/2)/(1+x^2)-3/32*arctan(1-sqrt(2)*sqrt(x))/sqrt(2)+3/32*arctan(1+sqrt(2)*sqrt(x))/sqrt(2)+3/64*log(1+x-sqrt(2)*sqrt(x))/sqrt(2)-3/64*log(1+x+sqrt(2)*sqrt(x))/sqrt(2)],
[x^(3/2)/(1+x^2)^3,x,12,-3/32*arctan(1-sqrt(2)*sqrt(x))/sqrt(2)+3/32*arctan(1+sqrt(2)*sqrt(x))/sqrt(2)-3/64*log(1+x-sqrt(2)*sqrt(x))/sqrt(2)+3/64*log(1+x+sqrt(2)*sqrt(x))/sqrt(2)-1/4*sqrt(x)/(1+x^2)^2+1/16*sqrt(x)/(1+x^2)],
[sqrt(x)/(1+x^2)^3,x,12,1/4*x^(3/2)/(1+x^2)^2+5/16*x^(3/2)/(1+x^2)-5/32*arctan(1-sqrt(2)*sqrt(x))/sqrt(2)+5/32*arctan(1+sqrt(2)*sqrt(x))/sqrt(2)+5/64*log(1+x-sqrt(2)*sqrt(x))/sqrt(2)-5/64*log(1+x+sqrt(2)*sqrt(x))/sqrt(2)],
[1/((1+x^2)^3*sqrt(x)),x,12,-21/32*arctan(1-sqrt(2)*sqrt(x))/sqrt(2)+21/32*arctan(1+sqrt(2)*sqrt(x))/sqrt(2)-21/64*log(1+x-sqrt(2)*sqrt(x))/sqrt(2)+21/64*log(1+x+sqrt(2)*sqrt(x))/sqrt(2)+1/4*sqrt(x)/(1+x^2)^2+7/16*sqrt(x)/(1+x^2)],
[1/(x^(3/2)*(1+x^2)^3),x,13,45/32*arctan(1-sqrt(2)*sqrt(x))/sqrt(2)-45/32*arctan(1+sqrt(2)*sqrt(x))/sqrt(2)-45/64*log(1+x-sqrt(2)*sqrt(x))/sqrt(2)+45/64*log(1+x+sqrt(2)*sqrt(x))/sqrt(2)+(-45/16)/sqrt(x)+1/4/((1+x^2)^2*sqrt(x))+9/16/((1+x^2)*sqrt(x))],
[1/(x^(5/2)*(1+x^2)^3),x,13,(-77/48)/x^(3/2)+1/4/(x^(3/2)*(1+x^2)^2)+11/16/(x^(3/2)*(1+x^2))+77/32*arctan(1-sqrt(2)*sqrt(x))/sqrt(2)-77/32*arctan(1+sqrt(2)*sqrt(x))/sqrt(2)+77/64*log(1+x-sqrt(2)*sqrt(x))/sqrt(2)-77/64*log(1+x+sqrt(2)*sqrt(x))/sqrt(2)],
[1/(x^(7/2)*(1+x^2)^3),x,14,(-117/80)/x^(5/2)+1/4/(x^(5/2)*(1+x^2)^2)+13/16/(x^(5/2)*(1+x^2))-117/32*arctan(1-sqrt(2)*sqrt(x))/sqrt(2)+117/32*arctan(1+sqrt(2)*sqrt(x))/sqrt(2)+117/64*log(1+x-sqrt(2)*sqrt(x))/sqrt(2)-117/64*log(1+x+sqrt(2)*sqrt(x))/sqrt(2)+117/16/sqrt(x)],
[sqrt(x)/(1-x^2),x,4,-arctan(sqrt(x))+arctanh(sqrt(x))],

# Integrands of the form (c x)^(m/3) (a+b x^2)^p
[x^(2/3)/(1+x^2),x,11,arctan(x^(1/3))-1/2*arctan(-2*x^(1/3)+sqrt(3))+1/2*arctan(2*x^(1/3)+sqrt(3))-1/2*arctanh(x^(1/3)*sqrt(3)/(1+x^(2/3)))*sqrt(3),arctan(x^(1/3))-1/2*arctan(-2*x^(1/3)+sqrt(3))+1/2*arctan(2*x^(1/3)+sqrt(3))+1/4*log(1+x^(2/3)-x^(1/3)*sqrt(3))*sqrt(3)-1/4*log(1+x^(2/3)+x^(1/3)*sqrt(3))*sqrt(3)],

# Integrands of the form (c x)^m (a+b x^2)^p when m symbolic
[x^m*(a+b*x^2)^5,x,2,a^5*x^(1+m)/(1+m)+5*a^4*b*x^(3+m)/(3+m)+10*a^3*b^2*x^(5+m)/(5+m)+10*a^2*b^3*x^(7+m)/(7+m)+5*a*b^4*x^(9+m)/(9+m)+b^5*x^(11+m)/(11+m)],
[x^m*(a+b*x^2)^4,x,2,a^4*x^(1+m)/(1+m)+4*a^3*b*x^(3+m)/(3+m)+6*a^2*b^2*x^(5+m)/(5+m)+4*a*b^3*x^(7+m)/(7+m)+b^4*x^(9+m)/(9+m)],
[x^m*(a+b*x^2)^3,x,2,a^3*x^(1+m)/(1+m)+3*a^2*b*x^(3+m)/(3+m)+3*a*b^2*x^(5+m)/(5+m)+b^3*x^(7+m)/(7+m)],
[x^m*(a+b*x^2)^2,x,2,a^2*x^(1+m)/(1+m)+2*a*b*x^(3+m)/(3+m)+b^2*x^(5+m)/(5+m)],
[x^m*(a+b*x^2),x,2,a*x^(1+m)/(1+m)+b*x^(3+m)/(3+m)],
[x^m/(a+b*x^2),x,1,x^(1+m)*hypergeom([1,1/2*(1+m)],[1/2*(3+m)],-b*x^2/a)/(a*(1+m))],
[x^m/(a+b*x^2)^2,x,1,x^(1+m)*hypergeom([2,1/2*(1+m)],[1/2*(3+m)],-b*x^2/a)/(a^2*(1+m))],
[x^m/(a+b*x^2)^3,x,1,x^(1+m)*hypergeom([3,1/2*(1+m)],[1/2*(3+m)],-b*x^2/a)/(a^3*(1+m))],
[(c*x)^(1+m)/(a+b*x^2),x,1,(c*x)^(2+m)*hypergeom([1,1/2*(2+m)],[1/2*(4+m)],-b*x^2/a)/(a*c*(2+m))],
[(c*x)^m/(a+b*x^2),x,1,(c*x)^(1+m)*hypergeom([1,1/2*(1+m)],[1/2*(3+m)],-b*x^2/a)/(a*c*(1+m))],
[(c*x)^(-1+m)/(a+b*x^2),x,1,(c*x)^m*hypergeom([1,1/2*m],[1/2*(2+m)],-b*x^2/a)/(a*c*m)],
[(c*x)^(-2+m)/(a+b*x^2),x,1,-(c*x)^(-1+m)*hypergeom([1,1/2*(-1+m)],[1/2*(1+m)],-b*x^2/a)/(a*c*(1-m))],
[(c*x)^(-3+m)/(a+b*x^2),x,1,-(c*x)^(-2+m)*hypergeom([1,1/2*(-2+m)],[1/2*m],-b*x^2/a)/(a*c*(2-m))],
[x^m/(1+a*x^2/b)^2,x,1,x^(1+m)*hypergeom([2,1/2*(1+m)],[1/2*(3+m)],-a*x^2/b)/(1+m)],

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

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

# p>0
[x^7*sqrt(a+b*x^2),x,3,-1/3*a^3*(a+b*x^2)^(3/2)/b^4+3/5*a^2*(a+b*x^2)^(5/2)/b^4-3/7*a*(a+b*x^2)^(7/2)/b^4+1/9*(a+b*x^2)^(9/2)/b^4],
[x^5*sqrt(a+b*x^2),x,3,1/3*a^2*(a+b*x^2)^(3/2)/b^3-2/5*a*(a+b*x^2)^(5/2)/b^3+1/7*(a+b*x^2)^(7/2)/b^3],
[x^3*sqrt(a+b*x^2),x,3,-1/3*a*(a+b*x^2)^(3/2)/b^2+1/5*(a+b*x^2)^(5/2)/b^2],
[x*sqrt(a+b*x^2),x,1,1/3*(a+b*x^2)^(3/2)/b],
[sqrt(a+b*x^2)/x,x,4,-arctanh(sqrt(a+b*x^2)/sqrt(a))*sqrt(a)+sqrt(a+b*x^2)],
[sqrt(a+b*x^2)/x^3,x,4,-1/2*b*arctanh(sqrt(a+b*x^2)/sqrt(a))/sqrt(a)-1/2*sqrt(a+b*x^2)/x^2],
[sqrt(a+b*x^2)/x^5,x,5,1/8*b^2*arctanh(sqrt(a+b*x^2)/sqrt(a))/a^(3/2)-1/4*sqrt(a+b*x^2)/x^4-1/8*b*sqrt(a+b*x^2)/(a*x^2)],
[sqrt(a+b*x^2)/x^7,x,6,-1/16*b^3*arctanh(sqrt(a+b*x^2)/sqrt(a))/a^(5/2)-1/6*sqrt(a+b*x^2)/x^6-1/24*b*sqrt(a+b*x^2)/(a*x^4)+1/16*b^2*sqrt(a+b*x^2)/(a^2*x^2)],
[x^4*sqrt(a+b*x^2),x,5,1/16*a^3*arctanh(x*sqrt(b)/sqrt(a+b*x^2))/b^(5/2)-1/16*a^2*x*sqrt(a+b*x^2)/b^2+1/24*a*x^3*sqrt(a+b*x^2)/b+1/6*x^5*sqrt(a+b*x^2)],
[x^2*sqrt(a+b*x^2),x,4,-1/8*a^2*arctanh(x*sqrt(b)/sqrt(a+b*x^2))/b^(3/2)+1/8*a*x*sqrt(a+b*x^2)/b+1/4*x^3*sqrt(a+b*x^2)],
[sqrt(a+b*x^2),x,3,1/2*a*arctanh(x*sqrt(b)/sqrt(a+b*x^2))/sqrt(b)+1/2*x*sqrt(a+b*x^2)],
[sqrt(a+b*x^2)/x^2,x,3,arctanh(x*sqrt(b)/sqrt(a+b*x^2))*sqrt(b)-sqrt(a+b*x^2)/x],
[sqrt(a+b*x^2)/x^4,x,1,-1/3*(a+b*x^2)^(3/2)/(a*x^3)],
[sqrt(a+b*x^2)/x^6,x,2,-1/5*(a+b*x^2)^(3/2)/(a*x^5)+2/15*b*(a+b*x^2)^(3/2)/(a^2*x^3)],
[sqrt(a+b*x^2)/x^8,x,3,-1/7*(a+b*x^2)^(3/2)/(a*x^7)+4/35*b*(a+b*x^2)^(3/2)/(a^2*x^5)-8/105*b^2*(a+b*x^2)^(3/2)/(a^3*x^3)],
[sqrt(a+b*x^2)/x^10,x,4,-1/9*(a+b*x^2)^(3/2)/(a*x^9)+2/21*b*(a+b*x^2)^(3/2)/(a^2*x^7)-8/105*b^2*(a+b*x^2)^(3/2)/(a^3*x^5)+16/315*b^3*(a+b*x^2)^(3/2)/(a^4*x^3)],
[x^7*(a+b*x^2)^(3/2),x,3,-1/5*a^3*(a+b*x^2)^(5/2)/b^4+3/7*a^2*(a+b*x^2)^(7/2)/b^4-1/3*a*(a+b*x^2)^(9/2)/b^4+1/11*(a+b*x^2)^(11/2)/b^4],
[x^5*(a+b*x^2)^(3/2),x,3,1/5*a^2*(a+b*x^2)^(5/2)/b^3-2/7*a*(a+b*x^2)^(7/2)/b^3+1/9*(a+b*x^2)^(9/2)/b^3],
[x^3*(a+b*x^2)^(3/2),x,3,-1/5*a*(a+b*x^2)^(5/2)/b^2+1/7*(a+b*x^2)^(7/2)/b^2],
[x*(a+b*x^2)^(3/2),x,1,1/5*(a+b*x^2)^(5/2)/b],
[(a+b*x^2)^(3/2)/x,x,5,1/3*(a+b*x^2)^(3/2)-a^(3/2)*arctanh(sqrt(a+b*x^2)/sqrt(a))+a*sqrt(a+b*x^2)],
[(a+b*x^2)^(3/2)/x^3,x,5,-1/2*(a+b*x^2)^(3/2)/x^2-3/2*b*arctanh(sqrt(a+b*x^2)/sqrt(a))*sqrt(a)+3/2*b*sqrt(a+b*x^2)],
[(a+b*x^2)^(3/2)/x^5,x,5,-1/4*(a+b*x^2)^(3/2)/x^4-3/8*b^2*arctanh(sqrt(a+b*x^2)/sqrt(a))/sqrt(a)-3/8*b*sqrt(a+b*x^2)/x^2],
[(a+b*x^2)^(3/2)/x^7,x,6,-1/6*(a+b*x^2)^(3/2)/x^6+1/16*b^3*arctanh(sqrt(a+b*x^2)/sqrt(a))/a^(3/2)-1/8*b*sqrt(a+b*x^2)/x^4-1/16*b^2*sqrt(a+b*x^2)/(a*x^2)],
[(a+b*x^2)^(3/2)/x^9,x,7,-1/8*(a+b*x^2)^(3/2)/x^8-3/128*b^4*arctanh(sqrt(a+b*x^2)/sqrt(a))/a^(5/2)-1/16*b*sqrt(a+b*x^2)/x^6-1/64*b^2*sqrt(a+b*x^2)/(a*x^4)+3/128*b^3*sqrt(a+b*x^2)/(a^2*x^2)],
[x^4*(a+b*x^2)^(3/2),x,6,1/8*x^5*(a+b*x^2)^(3/2)+3/128*a^4*arctanh(x*sqrt(b)/sqrt(a+b*x^2))/b^(5/2)-3/128*a^3*x*sqrt(a+b*x^2)/b^2+1/64*a^2*x^3*sqrt(a+b*x^2)/b+1/16*a*x^5*sqrt(a+b*x^2)],
[x^2*(a+b*x^2)^(3/2),x,5,1/6*x^3*(a+b*x^2)^(3/2)-1/16*a^3*arctanh(x*sqrt(b)/sqrt(a+b*x^2))/b^(3/2)+1/16*a^2*x*sqrt(a+b*x^2)/b+1/8*a*x^3*sqrt(a+b*x^2)],
[(a+b*x^2)^(3/2),x,4,1/4*x*(a+b*x^2)^(3/2)+3/8*a^2*arctanh(x*sqrt(b)/sqrt(a+b*x^2))/sqrt(b)+3/8*a*x*sqrt(a+b*x^2)],
[(a+b*x^2)^(3/2)/x^2,x,4,-(a+b*x^2)^(3/2)/x+3/2*a*arctanh(x*sqrt(b)/sqrt(a+b*x^2))*sqrt(b)+3/2*b*x*sqrt(a+b*x^2)],
[(a+b*x^2)^(3/2)/x^4,x,4,-1/3*(a+b*x^2)^(3/2)/x^3+b^(3/2)*arctanh(x*sqrt(b)/sqrt(a+b*x^2))-b*sqrt(a+b*x^2)/x],
[(a+b*x^2)^(3/2)/x^6,x,1,-1/5*(a+b*x^2)^(5/2)/(a*x^5)],
[(a+b*x^2)^(3/2)/x^8,x,2,-1/7*(a+b*x^2)^(5/2)/(a*x^7)+2/35*b*(a+b*x^2)^(5/2)/(a^2*x^5)],
[(a+b*x^2)^(3/2)/x^10,x,3,-1/9*(a+b*x^2)^(5/2)/(a*x^9)+4/63*b*(a+b*x^2)^(5/2)/(a^2*x^7)-8/315*b^2*(a+b*x^2)^(5/2)/(a^3*x^5)],
[(a+b*x^2)^(3/2)/x^12,x,4,-1/11*(a+b*x^2)^(5/2)/(a*x^11)+2/33*b*(a+b*x^2)^(5/2)/(a^2*x^9)-8/231*b^2*(a+b*x^2)^(5/2)/(a^3*x^7)+16/1155*b^3*(a+b*x^2)^(5/2)/(a^4*x^5)],
[x^7*(a+b*x^2)^(5/2),x,3,-1/7*a^3*(a+b*x^2)^(7/2)/b^4+1/3*a^2*(a+b*x^2)^(9/2)/b^4-3/11*a*(a+b*x^2)^(11/2)/b^4+1/13*(a+b*x^2)^(13/2)/b^4],
[x^5*(a+b*x^2)^(5/2),x,3,1/7*a^2*(a+b*x^2)^(7/2)/b^3-2/9*a*(a+b*x^2)^(9/2)/b^3+1/11*(a+b*x^2)^(11/2)/b^3],
[x^3*(a+b*x^2)^(5/2),x,3,-1/7*a*(a+b*x^2)^(7/2)/b^2+1/9*(a+b*x^2)^(9/2)/b^2],
[x*(a+b*x^2)^(5/2),x,1,1/7*(a+b*x^2)^(7/2)/b],
[(a+b*x^2)^(5/2)/x,x,6,1/3*a*(a+b*x^2)^(3/2)+1/5*(a+b*x^2)^(5/2)-a^(5/2)*arctanh(sqrt(a+b*x^2)/sqrt(a))+a^2*sqrt(a+b*x^2)],
[(a+b*x^2)^(5/2)/x^3,x,6,5/6*b*(a+b*x^2)^(3/2)-1/2*(a+b*x^2)^(5/2)/x^2-5/2*a^(3/2)*b*arctanh(sqrt(a+b*x^2)/sqrt(a))+5/2*a*b*sqrt(a+b*x^2)],
[(a+b*x^2)^(5/2)/x^5,x,6,-5/8*b*(a+b*x^2)^(3/2)/x^2-1/4*(a+b*x^2)^(5/2)/x^4-15/8*b^2*arctanh(sqrt(a+b*x^2)/sqrt(a))*sqrt(a)+15/8*b^2*sqrt(a+b*x^2)],
[(a+b*x^2)^(5/2)/x^7,x,6,-5/24*b*(a+b*x^2)^(3/2)/x^4-1/6*(a+b*x^2)^(5/2)/x^6-5/16*b^3*arctanh(sqrt(a+b*x^2)/sqrt(a))/sqrt(a)-5/16*b^2*sqrt(a+b*x^2)/x^2],
[(a+b*x^2)^(5/2)/x^9,x,7,-5/48*b*(a+b*x^2)^(3/2)/x^6-1/8*(a+b*x^2)^(5/2)/x^8+5/128*b^4*arctanh(sqrt(a+b*x^2)/sqrt(a))/a^(3/2)-5/64*b^2*sqrt(a+b*x^2)/x^4-5/128*b^3*sqrt(a+b*x^2)/(a*x^2)],
[(a+b*x^2)^(5/2)/x^11,x,8,-1/16*b*(a+b*x^2)^(3/2)/x^8-1/10*(a+b*x^2)^(5/2)/x^10-3/256*b^5*arctanh(sqrt(a+b*x^2)/sqrt(a))/a^(5/2)-1/32*b^2*sqrt(a+b*x^2)/x^6-1/128*b^3*sqrt(a+b*x^2)/(a*x^4)+3/256*b^4*sqrt(a+b*x^2)/(a^2*x^2)],
[x^4*(a+b*x^2)^(5/2),x,7,1/16*a*x^5*(a+b*x^2)^(3/2)+1/10*x^5*(a+b*x^2)^(5/2)+3/256*a^5*arctanh(x*sqrt(b)/sqrt(a+b*x^2))/b^(5/2)-3/256*a^4*x*sqrt(a+b*x^2)/b^2+1/128*a^3*x^3*sqrt(a+b*x^2)/b+1/32*a^2*x^5*sqrt(a+b*x^2)],
[x^2*(a+b*x^2)^(5/2),x,6,5/48*a*x^3*(a+b*x^2)^(3/2)+1/8*x^3*(a+b*x^2)^(5/2)-5/128*a^4*arctanh(x*sqrt(b)/sqrt(a+b*x^2))/b^(3/2)+5/128*a^3*x*sqrt(a+b*x^2)/b+5/64*a^2*x^3*sqrt(a+b*x^2)],
[(a+b*x^2)^(5/2),x,5,5/24*a*x*(a+b*x^2)^(3/2)+1/6*x*(a+b*x^2)^(5/2)+5/16*a^3*arctanh(x*sqrt(b)/sqrt(a+b*x^2))/sqrt(b)+5/16*a^2*x*sqrt(a+b*x^2)],
[(a+b*x^2)^(5/2)/x^2,x,5,5/4*b*x*(a+b*x^2)^(3/2)-(a+b*x^2)^(5/2)/x+15/8*a^2*arctanh(x*sqrt(b)/sqrt(a+b*x^2))*sqrt(b)+15/8*a*b*x*sqrt(a+b*x^2)],
[(a+b*x^2)^(5/2)/x^4,x,5,-5/3*b*(a+b*x^2)^(3/2)/x-1/3*(a+b*x^2)^(5/2)/x^3+5/2*a*b^(3/2)*arctanh(x*sqrt(b)/sqrt(a+b*x^2))+5/2*b^2*x*sqrt(a+b*x^2)],
[(a+b*x^2)^(5/2)/x^6,x,5,-1/3*b*(a+b*x^2)^(3/2)/x^3-1/5*(a+b*x^2)^(5/2)/x^5+b^(5/2)*arctanh(x*sqrt(b)/sqrt(a+b*x^2))-b^2*sqrt(a+b*x^2)/x],
[(a+b*x^2)^(5/2)/x^8,x,1,-1/7*(a+b*x^2)^(7/2)/(a*x^7)],
[(a+b*x^2)^(5/2)/x^10,x,2,-1/9*(a+b*x^2)^(7/2)/(a*x^9)+2/63*b*(a+b*x^2)^(7/2)/(a^2*x^7)],
[(a+b*x^2)^(5/2)/x^12,x,3,-1/11*(a+b*x^2)^(7/2)/(a*x^11)+4/99*b*(a+b*x^2)^(7/2)/(a^2*x^9)-8/693*b^2*(a+b*x^2)^(7/2)/(a^3*x^7)],
[(a+b*x^2)^(5/2)/x^14,x,4,-1/13*(a+b*x^2)^(7/2)/(a*x^13)+6/143*b*(a+b*x^2)^(7/2)/(a^2*x^11)-8/429*b^2*(a+b*x^2)^(7/2)/(a^3*x^9)+16/3003*b^3*(a+b*x^2)^(7/2)/(a^4*x^7)],
[(a+b*x^2)^(5/2)/x^16,x,5,-1/15*(a+b*x^2)^(7/2)/(a*x^15)+8/195*b*(a+b*x^2)^(7/2)/(a^2*x^13)-16/715*b^2*(a+b*x^2)^(7/2)/(a^3*x^11)+64/6435*b^3*(a+b*x^2)^(7/2)/(a^4*x^9)-128/45045*b^4*(a+b*x^2)^(7/2)/(a^5*x^7)],
[(a+b*x^2)^(5/2)/x^18,x,6,-1/17*(a+b*x^2)^(7/2)/(a*x^17)+2/51*b*(a+b*x^2)^(7/2)/(a^2*x^15)-16/663*b^2*(a+b*x^2)^(7/2)/(a^3*x^13)+32/2431*b^3*(a+b*x^2)^(7/2)/(a^4*x^11)-128/21879*b^4*(a+b*x^2)^(7/2)/(a^5*x^9)+256/153153*b^5*(a+b*x^2)^(7/2)/(a^6*x^7)],
[x^15*(a+b*x^2)^(9/2),x,3,-1/11*a^7*(a+b*x^2)^(11/2)/b^8+7/13*a^6*(a+b*x^2)^(13/2)/b^8-7/5*a^5*(a+b*x^2)^(15/2)/b^8+35/17*a^4*(a+b*x^2)^(17/2)/b^8-35/19*a^3*(a+b*x^2)^(19/2)/b^8+a^2*(a+b*x^2)^(21/2)/b^8-7/23*a*(a+b*x^2)^(23/2)/b^8+1/25*(a+b*x^2)^(25/2)/b^8],
[x^13*(a+b*x^2)^(9/2),x,3,1/11*a^6*(a+b*x^2)^(11/2)/b^7-6/13*a^5*(a+b*x^2)^(13/2)/b^7+a^4*(a+b*x^2)^(15/2)/b^7-20/17*a^3*(a+b*x^2)^(17/2)/b^7+15/19*a^2*(a+b*x^2)^(19/2)/b^7-2/7*a*(a+b*x^2)^(21/2)/b^7+1/23*(a+b*x^2)^(23/2)/b^7],
[x^11*(a+b*x^2)^(9/2),x,3,-1/11*a^5*(a+b*x^2)^(11/2)/b^6+5/13*a^4*(a+b*x^2)^(13/2)/b^6-2/3*a^3*(a+b*x^2)^(15/2)/b^6+10/17*a^2*(a+b*x^2)^(17/2)/b^6-5/19*a*(a+b*x^2)^(19/2)/b^6+1/21*(a+b*x^2)^(21/2)/b^6],
[x^9*(a+b*x^2)^(9/2),x,3,1/11*a^4*(a+b*x^2)^(11/2)/b^5-4/13*a^3*(a+b*x^2)^(13/2)/b^5+2/5*a^2*(a+b*x^2)^(15/2)/b^5-4/17*a*(a+b*x^2)^(17/2)/b^5+1/19*(a+b*x^2)^(19/2)/b^5],
[x^7*(a+b*x^2)^(9/2),x,3,-1/11*a^3*(a+b*x^2)^(11/2)/b^4+3/13*a^2*(a+b*x^2)^(13/2)/b^4-1/5*a*(a+b*x^2)^(15/2)/b^4+1/17*(a+b*x^2)^(17/2)/b^4],
[x^5*(a+b*x^2)^(9/2),x,3,1/11*a^2*(a+b*x^2)^(11/2)/b^3-2/13*a*(a+b*x^2)^(13/2)/b^3+1/15*(a+b*x^2)^(15/2)/b^3],
[x^3*(a+b*x^2)^(9/2),x,3,-1/11*a*(a+b*x^2)^(11/2)/b^2+1/13*(a+b*x^2)^(13/2)/b^2],
[x*(a+b*x^2)^(9/2),x,1,1/11*(a+b*x^2)^(11/2)/b],
[(a+b*x^2)^(9/2)/x,x,8,1/3*a^3*(a+b*x^2)^(3/2)+1/5*a^2*(a+b*x^2)^(5/2)+1/7*a*(a+b*x^2)^(7/2)+1/9*(a+b*x^2)^(9/2)-a^(9/2)*arctanh(sqrt(a+b*x^2)/sqrt(a))+a^4*sqrt(a+b*x^2)],
[(a+b*x^2)^(9/2)/x^3,x,8,3/2*a^2*b*(a+b*x^2)^(3/2)+9/10*a*b*(a+b*x^2)^(5/2)+9/14*b*(a+b*x^2)^(7/2)-1/2*(a+b*x^2)^(9/2)/x^2-9/2*a^(7/2)*b*arctanh(sqrt(a+b*x^2)/sqrt(a))+9/2*a^3*b*sqrt(a+b*x^2)],
[(a+b*x^2)^(9/2)/x^5,x,8,21/8*a*b^2*(a+b*x^2)^(3/2)+63/40*b^2*(a+b*x^2)^(5/2)-9/8*b*(a+b*x^2)^(7/2)/x^2-1/4*(a+b*x^2)^(9/2)/x^4-63/8*a^(5/2)*b^2*arctanh(sqrt(a+b*x^2)/sqrt(a))+63/8*a^2*b^2*sqrt(a+b*x^2)],
[(a+b*x^2)^(9/2)/x^7,x,8,35/16*b^3*(a+b*x^2)^(3/2)-21/16*b^2*(a+b*x^2)^(5/2)/x^2-3/8*b*(a+b*x^2)^(7/2)/x^4-1/6*(a+b*x^2)^(9/2)/x^6-105/16*a^(3/2)*b^3*arctanh(sqrt(a+b*x^2)/sqrt(a))+105/16*a*b^3*sqrt(a+b*x^2)],
[(a+b*x^2)^(9/2)/x^9,x,8,-105/128*b^3*(a+b*x^2)^(3/2)/x^2-21/64*b^2*(a+b*x^2)^(5/2)/x^4-3/16*b*(a+b*x^2)^(7/2)/x^6-1/8*(a+b*x^2)^(9/2)/x^8-315/128*b^4*arctanh(sqrt(a+b*x^2)/sqrt(a))*sqrt(a)+315/128*b^4*sqrt(a+b*x^2)],
[(a+b*x^2)^(9/2)/x^11,x,8,-21/128*b^3*(a+b*x^2)^(3/2)/x^4-21/160*b^2*(a+b*x^2)^(5/2)/x^6-9/80*b*(a+b*x^2)^(7/2)/x^8-1/10*(a+b*x^2)^(9/2)/x^10-63/256*b^5*arctanh(sqrt(a+b*x^2)/sqrt(a))/sqrt(a)-63/256*b^4*sqrt(a+b*x^2)/x^2],
[(a+b*x^2)^(9/2)/x^13,x,9,-7/128*b^3*(a+b*x^2)^(3/2)/x^6-21/320*b^2*(a+b*x^2)^(5/2)/x^8-3/40*b*(a+b*x^2)^(7/2)/x^10-1/12*(a+b*x^2)^(9/2)/x^12+21/1024*b^6*arctanh(sqrt(a+b*x^2)/sqrt(a))/a^(3/2)-21/512*b^4*sqrt(a+b*x^2)/x^4-21/1024*b^5*sqrt(a+b*x^2)/(a*x^2)],
[(a+b*x^2)^(9/2)/x^15,x,10,-3/128*b^3*(a+b*x^2)^(3/2)/x^8-3/80*b^2*(a+b*x^2)^(5/2)/x^10-3/56*b*(a+b*x^2)^(7/2)/x^12-1/14*(a+b*x^2)^(9/2)/x^14-9/2048*b^7*arctanh(sqrt(a+b*x^2)/sqrt(a))/a^(5/2)-3/256*b^4*sqrt(a+b*x^2)/x^6-3/1024*b^5*sqrt(a+b*x^2)/(a*x^4)+9/2048*b^6*sqrt(a+b*x^2)/(a^2*x^2)],
[x^6*(a+b*x^2)^(9/2),x,10,3/256*a^3*x^7*(a+b*x^2)^(3/2)+3/128*a^2*x^7*(a+b*x^2)^(5/2)+9/224*a*x^7*(a+b*x^2)^(7/2)+1/16*x^7*(a+b*x^2)^(9/2)-45/32768*a^8*arctanh(x*sqrt(b)/sqrt(a+b*x^2))/b^(7/2)+45/32768*a^7*x*sqrt(a+b*x^2)/b^3-15/16384*a^6*x^3*sqrt(a+b*x^2)/b^2+3/4096*a^5*x^5*sqrt(a+b*x^2)/b+9/2048*a^4*x^7*sqrt(a+b*x^2)],
[x^4*(a+b*x^2)^(9/2),x,9,3/128*a^3*x^5*(a+b*x^2)^(3/2)+3/80*a^2*x^5*(a+b*x^2)^(5/2)+3/56*a*x^5*(a+b*x^2)^(7/2)+1/14*x^5*(a+b*x^2)^(9/2)+9/2048*a^7*arctanh(x*sqrt(b)/sqrt(a+b*x^2))/b^(5/2)-9/2048*a^6*x*sqrt(a+b*x^2)/b^2+3/1024*a^5*x^3*sqrt(a+b*x^2)/b+3/256*a^4*x^5*sqrt(a+b*x^2)],
[x^2*(a+b*x^2)^(9/2),x,8,7/128*a^3*x^3*(a+b*x^2)^(3/2)+21/320*a^2*x^3*(a+b*x^2)^(5/2)+3/40*a*x^3*(a+b*x^2)^(7/2)+1/12*x^3*(a+b*x^2)^(9/2)-21/1024*a^6*arctanh(x*sqrt(b)/sqrt(a+b*x^2))/b^(3/2)+21/1024*a^5*x*sqrt(a+b*x^2)/b+21/512*a^4*x^3*sqrt(a+b*x^2)],
[(a+b*x^2)^(9/2),x,7,21/128*a^3*x*(a+b*x^2)^(3/2)+21/160*a^2*x*(a+b*x^2)^(5/2)+9/80*a*x*(a+b*x^2)^(7/2)+1/10*x*(a+b*x^2)^(9/2)+63/256*a^5*arctanh(x*sqrt(b)/sqrt(a+b*x^2))/sqrt(b)+63/256*a^4*x*sqrt(a+b*x^2)],
[(a+b*x^2)^(9/2)/x^2,x,7,105/64*a^2*b*x*(a+b*x^2)^(3/2)+21/16*a*b*x*(a+b*x^2)^(5/2)+9/8*b*x*(a+b*x^2)^(7/2)-(a+b*x^2)^(9/2)/x+315/128*a^4*arctanh(x*sqrt(b)/sqrt(a+b*x^2))*sqrt(b)+315/128*a^3*b*x*sqrt(a+b*x^2)],
[(a+b*x^2)^(9/2)/x^4,x,7,35/8*a*b^2*x*(a+b*x^2)^(3/2)+7/2*b^2*x*(a+b*x^2)^(5/2)-3*b*(a+b*x^2)^(7/2)/x-1/3*(a+b*x^2)^(9/2)/x^3+105/16*a^3*b^(3/2)*arctanh(x*sqrt(b)/sqrt(a+b*x^2))+105/16*a^2*b^2*x*sqrt(a+b*x^2)],
[(a+b*x^2)^(9/2)/x^6,x,7,21/4*b^3*x*(a+b*x^2)^(3/2)-21/5*b^2*(a+b*x^2)^(5/2)/x-3/5*b*(a+b*x^2)^(7/2)/x^3-1/5*(a+b*x^2)^(9/2)/x^5+63/8*a^2*b^(5/2)*arctanh(x*sqrt(b)/sqrt(a+b*x^2))+63/8*a*b^3*x*sqrt(a+b*x^2)],
[(a+b*x^2)^(9/2)/x^8,x,7,-3*b^3*(a+b*x^2)^(3/2)/x-3/5*b^2*(a+b*x^2)^(5/2)/x^3-9/35*b*(a+b*x^2)^(7/2)/x^5-1/7*(a+b*x^2)^(9/2)/x^7+9/2*a*b^(7/2)*arctanh(x*sqrt(b)/sqrt(a+b*x^2))+9/2*b^4*x*sqrt(a+b*x^2)],
[(a+b*x^2)^(9/2)/x^10,x,7,-1/3*b^3*(a+b*x^2)^(3/2)/x^3-1/5*b^2*(a+b*x^2)^(5/2)/x^5-1/7*b*(a+b*x^2)^(7/2)/x^7-1/9*(a+b*x^2)^(9/2)/x^9+b^(9/2)*arctanh(x*sqrt(b)/sqrt(a+b*x^2))-b^4*sqrt(a+b*x^2)/x],
[(a+b*x^2)^(9/2)/x^12,x,1,-1/11*(a+b*x^2)^(11/2)/(a*x^11)],
[(a+b*x^2)^(9/2)/x^14,x,2,-1/13*(a+b*x^2)^(11/2)/(a*x^13)+2/143*b*(a+b*x^2)^(11/2)/(a^2*x^11)],
[(a+b*x^2)^(9/2)/x^16,x,3,-1/15*(a+b*x^2)^(11/2)/(a*x^15)+4/195*b*(a+b*x^2)^(11/2)/(a^2*x^13)-8/2145*b^2*(a+b*x^2)^(11/2)/(a^3*x^11)],
[(a+b*x^2)^(9/2)/x^18,x,4,-1/17*(a+b*x^2)^(11/2)/(a*x^17)+2/85*b*(a+b*x^2)^(11/2)/(a^2*x^15)-8/1105*b^2*(a+b*x^2)^(11/2)/(a^3*x^13)+16/12155*b^3*(a+b*x^2)^(11/2)/(a^4*x^11)],
[(a+b*x^2)^(9/2)/x^20,x,5,-1/19*(a+b*x^2)^(11/2)/(a*x^19)+8/323*b*(a+b*x^2)^(11/2)/(a^2*x^17)-16/1615*b^2*(a+b*x^2)^(11/2)/(a^3*x^15)+64/20995*b^3*(a+b*x^2)^(11/2)/(a^4*x^13)-128/230945*b^4*(a+b*x^2)^(11/2)/(a^5*x^11)],
[(a+b*x^2)^(9/2)/x^22,x,6,-1/21*(a+b*x^2)^(11/2)/(a*x^21)+10/399*b*(a+b*x^2)^(11/2)/(a^2*x^19)-80/6783*b^2*(a+b*x^2)^(11/2)/(a^3*x^17)+32/6783*b^3*(a+b*x^2)^(11/2)/(a^4*x^15)-128/88179*b^4*(a+b*x^2)^(11/2)/(a^5*x^13)+256/969969*b^5*(a+b*x^2)^(11/2)/(a^6*x^11)],
[(a+b*x^2)^(9/2)/x^24,x,7,-1/23*(a+b*x^2)^(11/2)/(a*x^23)+4/161*b*(a+b*x^2)^(11/2)/(a^2*x^21)-40/3059*b^2*(a+b*x^2)^(11/2)/(a^3*x^19)+320/52003*b^3*(a+b*x^2)^(11/2)/(a^4*x^17)-128/52003*b^4*(a+b*x^2)^(11/2)/(a^5*x^15)+512/676039*b^5*(a+b*x^2)^(11/2)/(a^6*x^13)-1024/7436429*b^6*(a+b*x^2)^(11/2)/(a^7*x^11)],
[x^5*sqrt(9+4*x^2),x,3,27/64*(9+4*x^2)^(3/2)-9/160*(9+4*x^2)^(5/2)+1/448*(9+4*x^2)^(7/2)],
[x^4*sqrt(9+4*x^2),x,4,729/512*arcsinh(2/3*x)-81/256*x*sqrt(9+4*x^2)+3/32*x^3*sqrt(9+4*x^2)+1/6*x^5*sqrt(9+4*x^2)],
[x^3*sqrt(9+4*x^2),x,3,-3/16*(9+4*x^2)^(3/2)+1/80*(9+4*x^2)^(5/2)],
[x^2*sqrt(9+4*x^2),x,3,-81/64*arcsinh(2/3*x)+9/32*x*sqrt(9+4*x^2)+1/4*x^3*sqrt(9+4*x^2)],
[x*sqrt(9+4*x^2),x,1,1/12*(9+4*x^2)^(3/2)],
[sqrt(9+4*x^2),x,2,9/4*arcsinh(2/3*x)+1/2*x*sqrt(9+4*x^2)],
[sqrt(9+4*x^2)/x,x,4,-3*arctanh(1/3*sqrt(9+4*x^2))+sqrt(9+4*x^2)],
[sqrt(9+4*x^2)/x^2,x,2,2*arcsinh(2/3*x)-sqrt(9+4*x^2)/x],
[sqrt(9+4*x^2)/x^3,x,4,-2/3*arctanh(1/3*sqrt(9+4*x^2))-1/2*sqrt(9+4*x^2)/x^2],
[sqrt(9+4*x^2)/x^4,x,1,-1/27*(9+4*x^2)^(3/2)/x^3],
[sqrt(9+4*x^2)/x^5,x,5,2/27*arctanh(1/3*sqrt(9+4*x^2))-1/4*sqrt(9+4*x^2)/x^4-1/18*sqrt(9+4*x^2)/x^2],
[x^5*sqrt(9-4*x^2),x,3,-27/64*(9-4*x^2)^(3/2)+9/160*(9-4*x^2)^(5/2)-1/448*(9-4*x^2)^(7/2)],
[x^4*sqrt(9-4*x^2),x,4,729/512*arcsin(2/3*x)-81/256*x*sqrt(9-4*x^2)-3/32*x^3*sqrt(9-4*x^2)+1/6*x^5*sqrt(9-4*x^2)],
[x^3*sqrt(9-4*x^2),x,3,-3/16*(9-4*x^2)^(3/2)+1/80*(9-4*x^2)^(5/2)],
[x^2*sqrt(9-4*x^2),x,3,81/64*arcsin(2/3*x)-9/32*x*sqrt(9-4*x^2)+1/4*x^3*sqrt(9-4*x^2)],
[x*sqrt(9-4*x^2),x,1,-1/12*(9-4*x^2)^(3/2)],
[sqrt(9-4*x^2),x,2,9/4*arcsin(2/3*x)+1/2*x*sqrt(9-4*x^2)],
[sqrt(9-4*x^2)/x,x,4,-3*arctanh(1/3*sqrt(9-4*x^2))+sqrt(9-4*x^2)],
[sqrt(9-4*x^2)/x^2,x,2,-2*arcsin(2/3*x)-sqrt(9-4*x^2)/x],
[sqrt(9-4*x^2)/x^3,x,4,2/3*arctanh(1/3*sqrt(9-4*x^2))-1/2*sqrt(9-4*x^2)/x^2],
[sqrt(9-4*x^2)/x^4,x,1,-1/27*(9-4*x^2)^(3/2)/x^3],
[sqrt(9-4*x^2)/x^5,x,5,2/27*arctanh(1/3*sqrt(9-4*x^2))-1/4*sqrt(9-4*x^2)/x^4+1/18*sqrt(9-4*x^2)/x^2],
[x^5*sqrt(-9+4*x^2),x,3,27/64*(-9+4*x^2)^(3/2)+9/160*(-9+4*x^2)^(5/2)+1/448*(-9+4*x^2)^(7/2)],
[x^4*sqrt(-9+4*x^2),x,5,-729/512*arctanh(2*x/sqrt(-9+4*x^2))-81/256*x*sqrt(-9+4*x^2)-3/32*x^3*sqrt(-9+4*x^2)+1/6*x^5*sqrt(-9+4*x^2)],
[x^3*sqrt(-9+4*x^2),x,3,3/16*(-9+4*x^2)^(3/2)+1/80*(-9+4*x^2)^(5/2)],
[x^2*sqrt(-9+4*x^2),x,4,-81/64*arctanh(2*x/sqrt(-9+4*x^2))-9/32*x*sqrt(-9+4*x^2)+1/4*x^3*sqrt(-9+4*x^2)],
[x*sqrt(-9+4*x^2),x,1,1/12*(-9+4*x^2)^(3/2)],
[sqrt(-9+4*x^2),x,3,-9/4*arctanh(2*x/sqrt(-9+4*x^2))+1/2*x*sqrt(-9+4*x^2)],
[sqrt(-9+4*x^2)/x,x,4,-3*arctan(1/3*sqrt(-9+4*x^2))+sqrt(-9+4*x^2)],
[sqrt(-9+4*x^2)/x^2,x,3,2*arctanh(2*x/sqrt(-9+4*x^2))-sqrt(-9+4*x^2)/x],
[sqrt(-9+4*x^2)/x^3,x,4,2/3*arctan(1/3*sqrt(-9+4*x^2))-1/2*sqrt(-9+4*x^2)/x^2],
[sqrt(-9+4*x^2)/x^4,x,1,1/27*(-9+4*x^2)^(3/2)/x^3],
[sqrt(-9+4*x^2)/x^5,x,5,2/27*arctan(1/3*sqrt(-9+4*x^2))-1/4*sqrt(-9+4*x^2)/x^4+1/18*sqrt(-9+4*x^2)/x^2],
[x^5*sqrt(-9-4*x^2),x,3,-27/64*(-9-4*x^2)^(3/2)-9/160*(-9-4*x^2)^(5/2)-1/448*(-9-4*x^2)^(7/2)],
[x^4*sqrt(-9-4*x^2),x,5,-729/512*arctan(2*x/sqrt(-9-4*x^2))-81/256*x*sqrt(-9-4*x^2)+3/32*x^3*sqrt(-9-4*x^2)+1/6*x^5*sqrt(-9-4*x^2)],
[x^3*sqrt(-9-4*x^2),x,3,3/16*(-9-4*x^2)^(3/2)+1/80*(-9-4*x^2)^(5/2)],
[x^2*sqrt(-9-4*x^2),x,4,81/64*arctan(2*x/sqrt(-9-4*x^2))+9/32*x*sqrt(-9-4*x^2)+1/4*x^3*sqrt(-9-4*x^2)],
[x*sqrt(-9-4*x^2),x,1,-1/12*(-9-4*x^2)^(3/2)],
[sqrt(-9-4*x^2),x,3,-9/4*arctan(2*x/sqrt(-9-4*x^2))+1/2*x*sqrt(-9-4*x^2)],
[sqrt(-9-4*x^2)/x,x,4,-3*arctan(1/3*sqrt(-9-4*x^2))+sqrt(-9-4*x^2)],
[sqrt(-9-4*x^2)/x^2,x,3,-2*arctan(2*x/sqrt(-9-4*x^2))-sqrt(-9-4*x^2)/x],
[sqrt(-9-4*x^2)/x^3,x,4,-2/3*arctan(1/3*sqrt(-9-4*x^2))-1/2*sqrt(-9-4*x^2)/x^2],
[sqrt(-9-4*x^2)/x^4,x,1,1/27*(-9-4*x^2)^(3/2)/x^3],
[sqrt(-9-4*x^2)/x^5,x,5,2/27*arctan(1/3*sqrt(-9-4*x^2))-1/4*sqrt(-9-4*x^2)/x^4-1/18*sqrt(-9-4*x^2)/x^2],

# p<0
[x^5/sqrt(a+b*x^2),x,3,-2/3*a*(a+b*x^2)^(3/2)/b^3+1/5*(a+b*x^2)^(5/2)/b^3+a^2*sqrt(a+b*x^2)/b^3],
[x^4/sqrt(a+b*x^2),x,4,3/8*a^2*arctanh(x*sqrt(b)/sqrt(a+b*x^2))/b^(5/2)-3/8*a*x*sqrt(a+b*x^2)/b^2+1/4*x^3*sqrt(a+b*x^2)/b],
[x^3/sqrt(a+b*x^2),x,3,1/3*(a+b*x^2)^(3/2)/b^2-a*sqrt(a+b*x^2)/b^2],
[x^2/sqrt(a+b*x^2),x,3,-1/2*a*arctanh(x*sqrt(b)/sqrt(a+b*x^2))/b^(3/2)+1/2*x*sqrt(a+b*x^2)/b],
[x/sqrt(a+b*x^2),x,1,sqrt(a+b*x^2)/b],
[1/sqrt(a+b*x^2),x,2,arctanh(x*sqrt(b)/sqrt(a+b*x^2))/sqrt(b)],
[1/(x*sqrt(a+b*x^2)),x,3,-arctanh(sqrt(a+b*x^2)/sqrt(a))/sqrt(a)],
[1/(x^2*sqrt(a+b*x^2)),x,1,-sqrt(a+b*x^2)/(a*x)],
[1/(x^3*sqrt(a+b*x^2)),x,4,1/2*b*arctanh(sqrt(a+b*x^2)/sqrt(a))/a^(3/2)-1/2*sqrt(a+b*x^2)/(a*x^2)],
[1/(x^4*sqrt(a+b*x^2)),x,2,-1/3*sqrt(a+b*x^2)/(a*x^3)+2/3*b*sqrt(a+b*x^2)/(a^2*x)],
[1/(x^5*sqrt(a+b*x^2)),x,5,-3/8*b^2*arctanh(sqrt(a+b*x^2)/sqrt(a))/a^(5/2)-1/4*sqrt(a+b*x^2)/(a*x^4)+3/8*b*sqrt(a+b*x^2)/(a^2*x^2)],
[x^5/(a+b*x^2)^(3/2),x,3,1/3*(a+b*x^2)^(3/2)/b^3-a^2/(b^3*sqrt(a+b*x^2))-2*a*sqrt(a+b*x^2)/b^3],
[x^4/(a+b*x^2)^(3/2),x,4,-3/2*a*arctanh(x*sqrt(b)/sqrt(a+b*x^2))/b^(5/2)-x^3/(b*sqrt(a+b*x^2))+3/2*x*sqrt(a+b*x^2)/b^2],
[x^3/(a+b*x^2)^(3/2),x,3,a/(b^2*sqrt(a+b*x^2))+sqrt(a+b*x^2)/b^2],
[x^2/(a+b*x^2)^(3/2),x,3,arctanh(x*sqrt(b)/sqrt(a+b*x^2))/b^(3/2)-x/(b*sqrt(a+b*x^2))],
[x/(a+b*x^2)^(3/2),x,1,(-1)/(b*sqrt(a+b*x^2))],
[1/(a+b*x^2)^(3/2),x,1,x/(a*sqrt(a+b*x^2))],
[1/(x*(a+b*x^2)^(3/2)),x,4,-arctanh(sqrt(a+b*x^2)/sqrt(a))/a^(3/2)+1/(a*sqrt(a+b*x^2))],
[1/(x^2*(a+b*x^2)^(3/2)),x,2,(-1)/(a*x*sqrt(a+b*x^2))-2*b*x/(a^2*sqrt(a+b*x^2))],
[1/(x^3*(a+b*x^2)^(3/2)),x,5,3/2*b*arctanh(sqrt(a+b*x^2)/sqrt(a))/a^(5/2)-3/2*b/(a^2*sqrt(a+b*x^2))+(-1/2)/(a*x^2*sqrt(a+b*x^2))],
[1/(x^4*(a+b*x^2)^(3/2)),x,3,(-1/3)/(a*x^3*sqrt(a+b*x^2))+4/3*b/(a^2*x*sqrt(a+b*x^2))+8/3*b^2*x/(a^3*sqrt(a+b*x^2))],
[x^6/(a+b*x^2)^(5/2),x,5,-1/3*x^5/(b*(a+b*x^2)^(3/2))-5/2*a*arctanh(x*sqrt(b)/sqrt(a+b*x^2))/b^(7/2)-5/3*x^3/(b^2*sqrt(a+b*x^2))+5/2*x*sqrt(a+b*x^2)/b^3],
[x^5/(a+b*x^2)^(5/2),x,3,-1/3*a^2/(b^3*(a+b*x^2)^(3/2))+2*a/(b^3*sqrt(a+b*x^2))+sqrt(a+b*x^2)/b^3],
[x^4/(a+b*x^2)^(5/2),x,4,-1/3*x^3/(b*(a+b*x^2)^(3/2))+arctanh(x*sqrt(b)/sqrt(a+b*x^2))/b^(5/2)-x/(b^2*sqrt(a+b*x^2))],
[x^3/(a+b*x^2)^(5/2),x,3,1/3*a/(b^2*(a+b*x^2)^(3/2))+(-1)/(b^2*sqrt(a+b*x^2))],
[x^2/(a+b*x^2)^(5/2),x,1,1/3*x^3/(a*(a+b*x^2)^(3/2))],
[x/(a+b*x^2)^(5/2),x,1,(-1/3)/(b*(a+b*x^2)^(3/2))],
[1/(a+b*x^2)^(5/2),x,2,1/3*x/(a*(a+b*x^2)^(3/2))+2/3*x/(a^2*sqrt(a+b*x^2))],
[1/(x*(a+b*x^2)^(5/2)),x,5,1/3/(a*(a+b*x^2)^(3/2))-arctanh(sqrt(a+b*x^2)/sqrt(a))/a^(5/2)+1/(a^2*sqrt(a+b*x^2))],
[1/(x^2*(a+b*x^2)^(5/2)),x,3,(-1)/(a*x*(a+b*x^2)^(3/2))-4/3*b*x/(a^2*(a+b*x^2)^(3/2))-8/3*b*x/(a^3*sqrt(a+b*x^2))],
[1/(x^3*(a+b*x^2)^(5/2)),x,6,-5/6*b/(a^2*(a+b*x^2)^(3/2))+(-1/2)/(a*x^2*(a+b*x^2)^(3/2))+5/2*b*arctanh(sqrt(a+b*x^2)/sqrt(a))/a^(7/2)-5/2*b/(a^3*sqrt(a+b*x^2))],
[1/(x^4*(a+b*x^2)^(5/2)),x,4,(-1/3)/(a*x^3*(a+b*x^2)^(3/2))+2*b/(a^2*x*(a+b*x^2)^(3/2))+8/3*b^2*x/(a^3*(a+b*x^2)^(3/2))+16/3*b^2*x/(a^4*sqrt(a+b*x^2))],
[x^10/(a+b*x^2)^(9/2),x,7,-1/7*x^9/(b*(a+b*x^2)^(7/2))-9/35*x^7/(b^2*(a+b*x^2)^(5/2))-3/5*x^5/(b^3*(a+b*x^2)^(3/2))-9/2*a*arctanh(x*sqrt(b)/sqrt(a+b*x^2))/b^(11/2)-3*x^3/(b^4*sqrt(a+b*x^2))+9/2*x*sqrt(a+b*x^2)/b^5],
[x^9/(a+b*x^2)^(9/2),x,3,-1/7*a^4/(b^5*(a+b*x^2)^(7/2))+4/5*a^3/(b^5*(a+b*x^2)^(5/2))-2*a^2/(b^5*(a+b*x^2)^(3/2))+4*a/(b^5*sqrt(a+b*x^2))+sqrt(a+b*x^2)/b^5],
[x^8/(a+b*x^2)^(9/2),x,6,-1/7*x^7/(b*(a+b*x^2)^(7/2))-1/5*x^5/(b^2*(a+b*x^2)^(5/2))-1/3*x^3/(b^3*(a+b*x^2)^(3/2))+arctanh(x*sqrt(b)/sqrt(a+b*x^2))/b^(9/2)-x/(b^4*sqrt(a+b*x^2))],
[x^7/(a+b*x^2)^(9/2),x,3,1/7*a^3/(b^4*(a+b*x^2)^(7/2))-3/5*a^2/(b^4*(a+b*x^2)^(5/2))+a/(b^4*(a+b*x^2)^(3/2))+(-1)/(b^4*sqrt(a+b*x^2))],
[x^6/(a+b*x^2)^(9/2),x,1,1/7*x^7/(a*(a+b*x^2)^(7/2))],
[x^5/(a+b*x^2)^(9/2),x,3,-1/7*a^2/(b^3*(a+b*x^2)^(7/2))+2/5*a/(b^3*(a+b*x^2)^(5/2))+(-1/3)/(b^3*(a+b*x^2)^(3/2))],
[x^4/(a+b*x^2)^(9/2),x,2,1/5*x^5/(a*(a+b*x^2)^(7/2))+2/35*b*x^7/(a^2*(a+b*x^2)^(7/2))],
[x^3/(a+b*x^2)^(9/2),x,3,1/7*a/(b^2*(a+b*x^2)^(7/2))+(-1/5)/(b^2*(a+b*x^2)^(5/2))],
[x^2/(a+b*x^2)^(9/2),x,3,1/3*x^3/(a*(a+b*x^2)^(7/2))+4/15*b*x^5/(a^2*(a+b*x^2)^(7/2))+8/105*b^2*x^7/(a^3*(a+b*x^2)^(7/2))],
[x/(a+b*x^2)^(9/2),x,1,(-1/7)/(b*(a+b*x^2)^(7/2))],
[1/(a+b*x^2)^(9/2),x,4,1/7*x/(a*(a+b*x^2)^(7/2))+6/35*x/(a^2*(a+b*x^2)^(5/2))+8/35*x/(a^3*(a+b*x^2)^(3/2))+16/35*x/(a^4*sqrt(a+b*x^2))],
[1/(x*(a+b*x^2)^(9/2)),x,7,1/7/(a*(a+b*x^2)^(7/2))+1/5/(a^2*(a+b*x^2)^(5/2))+1/3/(a^3*(a+b*x^2)^(3/2))-arctanh(sqrt(a+b*x^2)/sqrt(a))/a^(9/2)+1/(a^4*sqrt(a+b*x^2))],
[1/(x^2*(a+b*x^2)^(9/2)),x,5,(-1)/(a*x*(a+b*x^2)^(7/2))-8/7*b*x/(a^2*(a+b*x^2)^(7/2))-48/35*b*x/(a^3*(a+b*x^2)^(5/2))-64/35*b*x/(a^4*(a+b*x^2)^(3/2))-128/35*b*x/(a^5*sqrt(a+b*x^2))],
[1/(x^3*(a+b*x^2)^(9/2)),x,8,-9/14*b/(a^2*(a+b*x^2)^(7/2))+(-1/2)/(a*x^2*(a+b*x^2)^(7/2))-9/10*b/(a^3*(a+b*x^2)^(5/2))-3/2*b/(a^4*(a+b*x^2)^(3/2))+9/2*b*arctanh(sqrt(a+b*x^2)/sqrt(a))/a^(11/2)-9/2*b/(a^5*sqrt(a+b*x^2))],
[1/(x^4*(a+b*x^2)^(9/2)),x,6,(-1/3)/(a*x^3*(a+b*x^2)^(7/2))+10/3*b/(a^2*x*(a+b*x^2)^(7/2))+80/21*b^2*x/(a^3*(a+b*x^2)^(7/2))+32/7*b^2*x/(a^4*(a+b*x^2)^(5/2))+128/21*b^2*x/(a^5*(a+b*x^2)^(3/2))+256/21*b^2*x/(a^6*sqrt(a+b*x^2))],
[x^5/sqrt(9+4*x^2),x,3,-3/32*(9+4*x^2)^(3/2)+1/320*(9+4*x^2)^(5/2)+81/64*sqrt(9+4*x^2)],
[x^4/sqrt(9+4*x^2),x,3,243/256*arcsinh(2/3*x)-27/128*x*sqrt(9+4*x^2)+1/16*x^3*sqrt(9+4*x^2)],
[x^3/sqrt(9+4*x^2),x,3,1/48*(9+4*x^2)^(3/2)-9/16*sqrt(9+4*x^2)],
[x^2/sqrt(9+4*x^2),x,2,-9/16*arcsinh(2/3*x)+1/8*x*sqrt(9+4*x^2)],
[x/sqrt(9+4*x^2),x,1,1/4*sqrt(9+4*x^2)],
[1/sqrt(9+4*x^2),x,1,1/2*arcsinh(2/3*x)],
[1/(x*sqrt(9+4*x^2)),x,3,-1/3*arctanh(1/3*sqrt(9+4*x^2))],
[1/(x^2*sqrt(9+4*x^2)),x,1,-1/9*sqrt(9+4*x^2)/x],
[1/(x^3*sqrt(9+4*x^2)),x,4,2/27*arctanh(1/3*sqrt(9+4*x^2))-1/18*sqrt(9+4*x^2)/x^2],
[1/(x^4*sqrt(9+4*x^2)),x,2,-1/27*sqrt(9+4*x^2)/x^3+8/243*sqrt(9+4*x^2)/x],
[1/(x^5*sqrt(9+4*x^2)),x,5,-2/81*arctanh(1/3*sqrt(9+4*x^2))-1/36*sqrt(9+4*x^2)/x^4+1/54*sqrt(9+4*x^2)/x^2],
[x^5/sqrt(9-4*x^2),x,3,3/32*(9-4*x^2)^(3/2)-1/320*(9-4*x^2)^(5/2)-81/64*sqrt(9-4*x^2)],
[x^4/sqrt(9-4*x^2),x,3,243/256*arcsin(2/3*x)-27/128*x*sqrt(9-4*x^2)-1/16*x^3*sqrt(9-4*x^2)],
[x^3/sqrt(9-4*x^2),x,3,1/48*(9-4*x^2)^(3/2)-9/16*sqrt(9-4*x^2)],
[x^2/sqrt(9-4*x^2),x,2,9/16*arcsin(2/3*x)-1/8*x*sqrt(9-4*x^2)],
[x/sqrt(9-4*x^2),x,1,-1/4*sqrt(9-4*x^2)],
[1/sqrt(9-4*x^2),x,1,1/2*arcsin(2/3*x)],
[1/(x*sqrt(9-4*x^2)),x,3,-1/3*arctanh(1/3*sqrt(9-4*x^2))],
[1/(x^2*sqrt(9-4*x^2)),x,1,-1/9*sqrt(9-4*x^2)/x],
[1/(x^3*sqrt(9-4*x^2)),x,4,-2/27*arctanh(1/3*sqrt(9-4*x^2))-1/18*sqrt(9-4*x^2)/x^2],
[1/(x^4*sqrt(9-4*x^2)),x,2,-1/27*sqrt(9-4*x^2)/x^3-8/243*sqrt(9-4*x^2)/x],
[1/(x^5*sqrt(9-4*x^2)),x,5,-2/81*arctanh(1/3*sqrt(9-4*x^2))-1/36*sqrt(9-4*x^2)/x^4-1/54*sqrt(9-4*x^2)/x^2],
[x^5/sqrt(-9+4*x^2),x,3,3/32*(-9+4*x^2)^(3/2)+1/320*(-9+4*x^2)^(5/2)+81/64*sqrt(-9+4*x^2)],
[x^4/sqrt(-9+4*x^2),x,4,243/256*arctanh(2*x/sqrt(-9+4*x^2))+27/128*x*sqrt(-9+4*x^2)+1/16*x^3*sqrt(-9+4*x^2)],
[x^3/sqrt(-9+4*x^2),x,3,1/48*(-9+4*x^2)^(3/2)+9/16*sqrt(-9+4*x^2)],
[x^2/sqrt(-9+4*x^2),x,3,9/16*arctanh(2*x/sqrt(-9+4*x^2))+1/8*x*sqrt(-9+4*x^2)],
[x/sqrt(-9+4*x^2),x,1,1/4*sqrt(-9+4*x^2)],
[1/sqrt(-9+4*x^2),x,2,1/2*arctanh(2*x/sqrt(-9+4*x^2))],
[1/(x*sqrt(-9+4*x^2)),x,3,1/3*arctan(1/3*sqrt(-9+4*x^2))],
[1/(x^2*sqrt(-9+4*x^2)),x,1,1/9*sqrt(-9+4*x^2)/x],
[1/(x^3*sqrt(-9+4*x^2)),x,4,2/27*arctan(1/3*sqrt(-9+4*x^2))+1/18*sqrt(-9+4*x^2)/x^2],
[1/(x^4*sqrt(-9+4*x^2)),x,2,1/27*sqrt(-9+4*x^2)/x^3+8/243*sqrt(-9+4*x^2)/x],
[1/(x^5*sqrt(-9+4*x^2)),x,5,2/81*arctan(1/3*sqrt(-9+4*x^2))+1/36*sqrt(-9+4*x^2)/x^4+1/54*sqrt(-9+4*x^2)/x^2],
[x^5/sqrt(-9-4*x^2),x,3,-3/32*(-9-4*x^2)^(3/2)-1/320*(-9-4*x^2)^(5/2)-81/64*sqrt(-9-4*x^2)],
[x^4/sqrt(-9-4*x^2),x,4,243/256*arctan(2*x/sqrt(-9-4*x^2))+27/128*x*sqrt(-9-4*x^2)-1/16*x^3*sqrt(-9-4*x^2)],
[x^3/sqrt(-9-4*x^2),x,3,1/48*(-9-4*x^2)^(3/2)+9/16*sqrt(-9-4*x^2)],
[x^2/sqrt(-9-4*x^2),x,3,-9/16*arctan(2*x/sqrt(-9-4*x^2))-1/8*x*sqrt(-9-4*x^2)],
[x/sqrt(-9-4*x^2),x,1,-1/4*sqrt(-9-4*x^2)],
[1/sqrt(-9-4*x^2),x,2,1/2*arctan(2*x/sqrt(-9-4*x^2))],
[1/(x*sqrt(-9-4*x^2)),x,3,1/3*arctan(1/3*sqrt(-9-4*x^2))],
[1/(x^2*sqrt(-9-4*x^2)),x,1,1/9*sqrt(-9-4*x^2)/x],
[1/(x^3*sqrt(-9-4*x^2)),x,4,-2/27*arctan(1/3*sqrt(-9-4*x^2))+1/18*sqrt(-9-4*x^2)/x^2],
[1/(x^4*sqrt(-9-4*x^2)),x,2,1/27*sqrt(-9-4*x^2)/x^3-8/243*sqrt(-9-4*x^2)/x],
[1/(x^5*sqrt(-9-4*x^2)),x,5,2/81*arctan(1/3*sqrt(-9-4*x^2))+1/36*sqrt(-9-4*x^2)/x^4-1/54*sqrt(-9-4*x^2)/x^2],
[1/sqrt(9+b*x^2),x,1,arcsinh(1/3*x*sqrt(b))/sqrt(b)],
[1/sqrt(9-b*x^2),x,1,arcsin(1/3*x*sqrt(b))/sqrt(b)],
[1/sqrt(-9+b*x^2),x,2,arctanh(x*sqrt(b)/sqrt(-9+b*x^2))/sqrt(b)],
[1/sqrt(-9-b*x^2),x,2,arctan(x*sqrt(b)/sqrt(-9-b*x^2))/sqrt(b)],
[1/sqrt(Pi+b*x^2),x,1,arcsinh(x*sqrt(b)/sqrt(Pi))/sqrt(b)],
[1/sqrt(Pi-b*x^2),x,1,arcsin(x*sqrt(b)/sqrt(Pi))/sqrt(b)],
[1/sqrt(-Pi+b*x^2),x,2,arctanh(x*sqrt(b)/sqrt(-Pi+b*x^2))/sqrt(b)],
[1/sqrt(-Pi-b*x^2),x,2,arctan(x*sqrt(b)/sqrt(-Pi-b*x^2))/sqrt(b)],
[1/sqrt(a+b*x^2),x,2,arctanh(x*sqrt(b)/sqrt(a+b*x^2))/sqrt(b)],
[1/sqrt(a-b*x^2),x,2,arctan(x*sqrt(b)/sqrt(a-b*x^2))/sqrt(b)],
[1/sqrt(-a+b*x^2),x,2,arctanh(x*sqrt(b)/sqrt(-a+b*x^2))/sqrt(b)],
[1/sqrt(-a-b*x^2),x,2,arctan(x*sqrt(b)/sqrt(-a-b*x^2))/sqrt(b)],
[1/sqrt(a^2-x^2),x,2,arctan(x/sqrt(a^2-x^2))],

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

# p>0
[(c*x)^(7/2)*sqrt(a+b*x^2),x,5,4/77*a*c*(c*x)^(5/2)*sqrt(a+b*x^2)/b+2/11*(c*x)^(9/2)*sqrt(a+b*x^2)/c-20/231*a^2*c^3*sqrt(c*x)*sqrt(a+b*x^2)/b^2+10/231*a^(11/4)*c^(7/2)*sqrt(cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))^2)/cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))*EllipticF(sin(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c)))),sqrt(1/2))*(sqrt(a)+x*sqrt(b))*sqrt((a+b*x^2)/(sqrt(a)+x*sqrt(b))^2)/(b^(9/4)*sqrt(a+b*x^2))],
[(c*x)^(5/2)*sqrt(a+b*x^2),x,6,4/45*a*c*(c*x)^(3/2)*sqrt(a+b*x^2)/b+2/9*(c*x)^(7/2)*sqrt(a+b*x^2)/c-4/15*a^2*c^2*sqrt(c*x)*sqrt(a+b*x^2)/(b^(3/2)*(sqrt(a)+x*sqrt(b)))+4/15*a^(9/4)*c^(5/2)*sqrt(cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))^2)/cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))*EllipticE(sin(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c)))),sqrt(1/2))*(sqrt(a)+x*sqrt(b))*sqrt((a+b*x^2)/(sqrt(a)+x*sqrt(b))^2)/(b^(7/4)*sqrt(a+b*x^2))-2/15*a^(9/4)*c^(5/2)*sqrt(cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))^2)/cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))*EllipticF(sin(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c)))),sqrt(1/2))*(sqrt(a)+x*sqrt(b))*sqrt((a+b*x^2)/(sqrt(a)+x*sqrt(b))^2)/(b^(7/4)*sqrt(a+b*x^2))],
[(c*x)^(3/2)*sqrt(a+b*x^2),x,4,2/7*(c*x)^(5/2)*sqrt(a+b*x^2)/c+4/21*a*c*sqrt(c*x)*sqrt(a+b*x^2)/b-2/21*a^(7/4)*c^(3/2)*sqrt(cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))^2)/cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))*EllipticF(sin(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c)))),sqrt(1/2))*(sqrt(a)+x*sqrt(b))*sqrt((a+b*x^2)/(sqrt(a)+x*sqrt(b))^2)/(b^(5/4)*sqrt(a+b*x^2))],
[(c*x)^(1/2)*sqrt(a+b*x^2),x,5,2/5*(c*x)^(3/2)*sqrt(a+b*x^2)/c+4/5*a*sqrt(c*x)*sqrt(a+b*x^2)/(sqrt(b)*(sqrt(a)+x*sqrt(b)))-4/5*a^(5/4)*sqrt(cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))^2)/cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))*EllipticE(sin(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c)))),sqrt(1/2))*(sqrt(a)+x*sqrt(b))*sqrt(c)*sqrt((a+b*x^2)/(sqrt(a)+x*sqrt(b))^2)/(b^(3/4)*sqrt(a+b*x^2))+2/5*a^(5/4)*sqrt(cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))^2)/cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))*EllipticF(sin(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c)))),sqrt(1/2))*(sqrt(a)+x*sqrt(b))*sqrt(c)*sqrt((a+b*x^2)/(sqrt(a)+x*sqrt(b))^2)/(b^(3/4)*sqrt(a+b*x^2))],
[sqrt(a+b*x^2)/(c*x)^(1/2),x,3,2/3*sqrt(c*x)*sqrt(a+b*x^2)/c+2/3*a^(3/4)*sqrt(cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))^2)/cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))*EllipticF(sin(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c)))),sqrt(1/2))*(sqrt(a)+x*sqrt(b))*sqrt((a+b*x^2)/(sqrt(a)+x*sqrt(b))^2)/(b^(1/4)*sqrt(c)*sqrt(a+b*x^2))],
[sqrt(a+b*x^2)/(c*x)^(3/2),x,5,-2*sqrt(a+b*x^2)/(c*sqrt(c*x))+4*sqrt(b)*sqrt(c*x)*sqrt(a+b*x^2)/(c^2*(sqrt(a)+x*sqrt(b)))-4*a^(1/4)*b^(1/4)*sqrt(cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))^2)/cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))*EllipticE(sin(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c)))),sqrt(1/2))*(sqrt(a)+x*sqrt(b))*sqrt((a+b*x^2)/(sqrt(a)+x*sqrt(b))^2)/(c^(3/2)*sqrt(a+b*x^2))+2*a^(1/4)*b^(1/4)*sqrt(cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))^2)/cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))*EllipticF(sin(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c)))),sqrt(1/2))*(sqrt(a)+x*sqrt(b))*sqrt((a+b*x^2)/(sqrt(a)+x*sqrt(b))^2)/(c^(3/2)*sqrt(a+b*x^2))],
[sqrt(a+b*x^2)/(c*x)^(5/2),x,3,-2/3*sqrt(a+b*x^2)/(c*(c*x)^(3/2))+2/3*b^(3/4)*sqrt(cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))^2)/cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))*EllipticF(sin(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c)))),sqrt(1/2))*(sqrt(a)+x*sqrt(b))*sqrt((a+b*x^2)/(sqrt(a)+x*sqrt(b))^2)/(a^(1/4)*c^(5/2)*sqrt(a+b*x^2))],
[sqrt(a+b*x^2)/(c*x)^(7/2),x,6,-2/5*sqrt(a+b*x^2)/(c*(c*x)^(5/2))-4/5*b*sqrt(a+b*x^2)/(a*c^3*sqrt(c*x))+4/5*b^(3/2)*sqrt(c*x)*sqrt(a+b*x^2)/(a*c^4*(sqrt(a)+x*sqrt(b)))-4/5*b^(5/4)*sqrt(cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))^2)/cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))*EllipticE(sin(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c)))),sqrt(1/2))*(sqrt(a)+x*sqrt(b))*sqrt((a+b*x^2)/(sqrt(a)+x*sqrt(b))^2)/(a^(3/4)*c^(7/2)*sqrt(a+b*x^2))+2/5*b^(5/4)*sqrt(cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))^2)/cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))*EllipticF(sin(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c)))),sqrt(1/2))*(sqrt(a)+x*sqrt(b))*sqrt((a+b*x^2)/(sqrt(a)+x*sqrt(b))^2)/(a^(3/4)*c^(7/2)*sqrt(a+b*x^2))],
[(c*x)^(7/2)*(a+b*x^2)^(3/2),x,6,2/15*(c*x)^(9/2)*(a+b*x^2)^(3/2)/c+8/385*a^2*c*(c*x)^(5/2)*sqrt(a+b*x^2)/b+4/55*a*(c*x)^(9/2)*sqrt(a+b*x^2)/c-8/231*a^3*c^3*sqrt(c*x)*sqrt(a+b*x^2)/b^2+4/231*a^(15/4)*c^(7/2)*sqrt(cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))^2)/cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))*EllipticF(sin(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c)))),sqrt(1/2))*(sqrt(a)+x*sqrt(b))*sqrt((a+b*x^2)/(sqrt(a)+x*sqrt(b))^2)/(b^(9/4)*sqrt(a+b*x^2))],
[(c*x)^(5/2)*(a+b*x^2)^(3/2),x,7,2/13*(c*x)^(7/2)*(a+b*x^2)^(3/2)/c+8/195*a^2*c*(c*x)^(3/2)*sqrt(a+b*x^2)/b+4/39*a*(c*x)^(7/2)*sqrt(a+b*x^2)/c-8/65*a^3*c^2*sqrt(c*x)*sqrt(a+b*x^2)/(b^(3/2)*(sqrt(a)+x*sqrt(b)))+8/65*a^(13/4)*c^(5/2)*sqrt(cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))^2)/cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))*EllipticE(sin(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c)))),sqrt(1/2))*(sqrt(a)+x*sqrt(b))*sqrt((a+b*x^2)/(sqrt(a)+x*sqrt(b))^2)/(b^(7/4)*sqrt(a+b*x^2))-4/65*a^(13/4)*c^(5/2)*sqrt(cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))^2)/cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))*EllipticF(sin(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c)))),sqrt(1/2))*(sqrt(a)+x*sqrt(b))*sqrt((a+b*x^2)/(sqrt(a)+x*sqrt(b))^2)/(b^(7/4)*sqrt(a+b*x^2))],
[(c*x)^(3/2)*(a+b*x^2)^(3/2),x,5,2/11*(c*x)^(5/2)*(a+b*x^2)^(3/2)/c+12/77*a*(c*x)^(5/2)*sqrt(a+b*x^2)/c+8/77*a^2*c*sqrt(c*x)*sqrt(a+b*x^2)/b-4/77*a^(11/4)*c^(3/2)*sqrt(cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))^2)/cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))*EllipticF(sin(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c)))),sqrt(1/2))*(sqrt(a)+x*sqrt(b))*sqrt((a+b*x^2)/(sqrt(a)+x*sqrt(b))^2)/(b^(5/4)*sqrt(a+b*x^2))],
[(c*x)^(1/2)*(a+b*x^2)^(3/2),x,6,2/9*(c*x)^(3/2)*(a+b*x^2)^(3/2)/c+4/15*a*(c*x)^(3/2)*sqrt(a+b*x^2)/c+8/15*a^2*sqrt(c*x)*sqrt(a+b*x^2)/(sqrt(b)*(sqrt(a)+x*sqrt(b)))-8/15*a^(9/4)*sqrt(cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))^2)/cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))*EllipticE(sin(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c)))),sqrt(1/2))*(sqrt(a)+x*sqrt(b))*sqrt(c)*sqrt((a+b*x^2)/(sqrt(a)+x*sqrt(b))^2)/(b^(3/4)*sqrt(a+b*x^2))+4/15*a^(9/4)*sqrt(cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))^2)/cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))*EllipticF(sin(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c)))),sqrt(1/2))*(sqrt(a)+x*sqrt(b))*sqrt(c)*sqrt((a+b*x^2)/(sqrt(a)+x*sqrt(b))^2)/(b^(3/4)*sqrt(a+b*x^2))],
[(a+b*x^2)^(3/2)/(c*x)^(1/2),x,4,2/7*(a+b*x^2)^(3/2)*sqrt(c*x)/c+4/7*a*sqrt(c*x)*sqrt(a+b*x^2)/c+4/7*a^(7/4)*sqrt(cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))^2)/cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))*EllipticF(sin(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c)))),sqrt(1/2))*(sqrt(a)+x*sqrt(b))*sqrt((a+b*x^2)/(sqrt(a)+x*sqrt(b))^2)/(b^(1/4)*sqrt(c)*sqrt(a+b*x^2))],
[(a+b*x^2)^(3/2)/(c*x)^(3/2),x,6,-2*(a+b*x^2)^(3/2)/(c*sqrt(c*x))+12/5*b*(c*x)^(3/2)*sqrt(a+b*x^2)/c^3+24/5*a*sqrt(b)*sqrt(c*x)*sqrt(a+b*x^2)/(c^2*(sqrt(a)+x*sqrt(b)))-24/5*a^(5/4)*b^(1/4)*sqrt(cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))^2)/cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))*EllipticE(sin(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c)))),sqrt(1/2))*(sqrt(a)+x*sqrt(b))*sqrt((a+b*x^2)/(sqrt(a)+x*sqrt(b))^2)/(c^(3/2)*sqrt(a+b*x^2))+12/5*a^(5/4)*b^(1/4)*sqrt(cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))^2)/cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))*EllipticF(sin(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c)))),sqrt(1/2))*(sqrt(a)+x*sqrt(b))*sqrt((a+b*x^2)/(sqrt(a)+x*sqrt(b))^2)/(c^(3/2)*sqrt(a+b*x^2))],
[(a+b*x^2)^(3/2)/(c*x)^(5/2),x,4,-2/3*(a+b*x^2)^(3/2)/(c*(c*x)^(3/2))+4/3*b*sqrt(c*x)*sqrt(a+b*x^2)/c^3+4/3*a^(3/4)*b^(3/4)*sqrt(cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))^2)/cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))*EllipticF(sin(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c)))),sqrt(1/2))*(sqrt(a)+x*sqrt(b))*sqrt((a+b*x^2)/(sqrt(a)+x*sqrt(b))^2)/(c^(5/2)*sqrt(a+b*x^2))],
[(a+b*x^2)^(3/2)/(c*x)^(7/2),x,6,-2/5*(a+b*x^2)^(3/2)/(c*(c*x)^(5/2))-12/5*b*sqrt(a+b*x^2)/(c^3*sqrt(c*x))+24/5*b^(3/2)*sqrt(c*x)*sqrt(a+b*x^2)/(c^4*(sqrt(a)+x*sqrt(b)))-24/5*a^(1/4)*b^(5/4)*sqrt(cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))^2)/cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))*EllipticE(sin(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c)))),sqrt(1/2))*(sqrt(a)+x*sqrt(b))*sqrt((a+b*x^2)/(sqrt(a)+x*sqrt(b))^2)/(c^(7/2)*sqrt(a+b*x^2))+12/5*a^(1/4)*b^(5/4)*sqrt(cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))^2)/cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))*EllipticF(sin(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c)))),sqrt(1/2))*(sqrt(a)+x*sqrt(b))*sqrt((a+b*x^2)/(sqrt(a)+x*sqrt(b))^2)/(c^(7/2)*sqrt(a+b*x^2))],
[(a+b*x^2)^(3/2)/(c*x)^(9/2),x,4,-2/7*(a+b*x^2)^(3/2)/(c*(c*x)^(7/2))-4/7*b*sqrt(a+b*x^2)/(c^3*(c*x)^(3/2))+4/7*b^(7/4)*sqrt(cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))^2)/cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))*EllipticF(sin(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c)))),sqrt(1/2))*(sqrt(a)+x*sqrt(b))*sqrt((a+b*x^2)/(sqrt(a)+x*sqrt(b))^2)/(a^(1/4)*c^(9/2)*sqrt(a+b*x^2))],
[(a+b*x^2)^(3/2)/(c*x)^(11/2),x,7,-2/9*(a+b*x^2)^(3/2)/(c*(c*x)^(9/2))-4/15*b*sqrt(a+b*x^2)/(c^3*(c*x)^(5/2))-8/15*b^2*sqrt(a+b*x^2)/(a*c^5*sqrt(c*x))+8/15*b^(5/2)*sqrt(c*x)*sqrt(a+b*x^2)/(a*c^6*(sqrt(a)+x*sqrt(b)))-8/15*b^(9/4)*sqrt(cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))^2)/cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))*EllipticE(sin(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c)))),sqrt(1/2))*(sqrt(a)+x*sqrt(b))*sqrt((a+b*x^2)/(sqrt(a)+x*sqrt(b))^2)/(a^(3/4)*c^(11/2)*sqrt(a+b*x^2))+4/15*b^(9/4)*sqrt(cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))^2)/cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))*EllipticF(sin(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c)))),sqrt(1/2))*(sqrt(a)+x*sqrt(b))*sqrt((a+b*x^2)/(sqrt(a)+x*sqrt(b))^2)/(a^(3/4)*c^(11/2)*sqrt(a+b*x^2))],
[(c*x)^(5/2)*sqrt(3*a-2*a*x^2),x,6,-3/5*6^(1/4)*a*c^2*EllipticE(sqrt(3-x*sqrt(6))/sqrt(6),sqrt(2))*sqrt(c*x)*sqrt(3-2*x^2)/(sqrt(x)*sqrt(3*a-2*a*x^2))-2/15*c*(c*x)^(3/2)*sqrt(3*a-2*a*x^2)+2/9*(c*x)^(7/2)*sqrt(3*a-2*a*x^2)/c],
[(c*x)^(3/2)*sqrt(3*a-2*a*x^2),x,5,1/7*6^(3/4)*a*c^(3/2)*EllipticF((2/3)^(1/4)*sqrt(c*x)/sqrt(c),I)*sqrt(3-2*x^2)/sqrt(a*(3-2*x^2))+2/7*(c*x)^(5/2)*sqrt(3*a-2*a*x^2)/c-2/7*c*sqrt(c*x)*sqrt(3*a-2*a*x^2)],
[(c*x)^(1/2)*sqrt(3*a-2*a*x^2),x,5,-6/5*6^(1/4)*a*EllipticE(sqrt(3-x*sqrt(6))/sqrt(6),sqrt(2))*sqrt(c*x)*sqrt(3-2*x^2)/(sqrt(x)*sqrt(3*a-2*a*x^2))+2/5*(c*x)^(3/2)*sqrt(3*a-2*a*x^2)/c],
[sqrt(3*a-2*a*x^2)/(c*x)^(1/2),x,4,2*2^(3/4)*a*EllipticF((2/3)^(1/4)*sqrt(c*x)/sqrt(c),I)*sqrt(3-2*x^2)/(3^(1/4)*sqrt(c)*sqrt(a*(3-2*x^2)))+2/3*sqrt(c*x)*sqrt(3*a-2*a*x^2)/c],
[sqrt(3*a-2*a*x^2)/(c*x)^(3/2),x,5,4*6^(1/4)*a*EllipticE(sqrt(3-x*sqrt(6))/sqrt(6),sqrt(2))*sqrt(c*x)*sqrt(3-2*x^2)/(c^2*sqrt(x)*sqrt(3*a-2*a*x^2))-2*sqrt(3*a-2*a*x^2)/(c*sqrt(c*x))],
[sqrt(3*a-2*a*x^2)/(c*x)^(5/2),x,4,-4/3*2^(3/4)*a*EllipticF((2/3)^(1/4)*sqrt(c*x)/sqrt(c),I)*sqrt(3-2*x^2)/(3^(1/4)*c^(5/2)*sqrt(a*(3-2*x^2)))-2/3*sqrt(3*a-2*a*x^2)/(c*(c*x)^(3/2))],

# p<0
[(c*x)^(7/2)/sqrt(a+b*x^2),x,4,2/7*c*(c*x)^(5/2)*sqrt(a+b*x^2)/b-10/21*a*c^3*sqrt(c*x)*sqrt(a+b*x^2)/b^2+5/21*a^(7/4)*c^(7/2)*sqrt(cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))^2)/cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))*EllipticF(sin(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c)))),sqrt(1/2))*(sqrt(a)+x*sqrt(b))*sqrt((a+b*x^2)/(sqrt(a)+x*sqrt(b))^2)/(b^(9/4)*sqrt(a+b*x^2))],
[(c*x)^(5/2)/sqrt(a+b*x^2),x,5,2/5*c*(c*x)^(3/2)*sqrt(a+b*x^2)/b-6/5*a*c^2*sqrt(c*x)*sqrt(a+b*x^2)/(b^(3/2)*(sqrt(a)+x*sqrt(b)))+6/5*a^(5/4)*c^(5/2)*sqrt(cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))^2)/cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))*EllipticE(sin(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c)))),sqrt(1/2))*(sqrt(a)+x*sqrt(b))*sqrt((a+b*x^2)/(sqrt(a)+x*sqrt(b))^2)/(b^(7/4)*sqrt(a+b*x^2))-3/5*a^(5/4)*c^(5/2)*sqrt(cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))^2)/cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))*EllipticF(sin(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c)))),sqrt(1/2))*(sqrt(a)+x*sqrt(b))*sqrt((a+b*x^2)/(sqrt(a)+x*sqrt(b))^2)/(b^(7/4)*sqrt(a+b*x^2))],
[(c*x)^(3/2)/sqrt(a+b*x^2),x,3,2/3*c*sqrt(c*x)*sqrt(a+b*x^2)/b-1/3*a^(3/4)*c^(3/2)*sqrt(cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))^2)/cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))*EllipticF(sin(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c)))),sqrt(1/2))*(sqrt(a)+x*sqrt(b))*sqrt((a+b*x^2)/(sqrt(a)+x*sqrt(b))^2)/(b^(5/4)*sqrt(a+b*x^2))],
[(c*x)^(1/2)/sqrt(a+b*x^2),x,4,2*sqrt(c*x)*sqrt(a+b*x^2)/(sqrt(b)*(sqrt(a)+x*sqrt(b)))-2*a^(1/4)*sqrt(cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))^2)/cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))*EllipticE(sin(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c)))),sqrt(1/2))*(sqrt(a)+x*sqrt(b))*sqrt(c)*sqrt((a+b*x^2)/(sqrt(a)+x*sqrt(b))^2)/(b^(3/4)*sqrt(a+b*x^2))+a^(1/4)*sqrt(cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))^2)/cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))*EllipticF(sin(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c)))),sqrt(1/2))*(sqrt(a)+x*sqrt(b))*sqrt(c)*sqrt((a+b*x^2)/(sqrt(a)+x*sqrt(b))^2)/(b^(3/4)*sqrt(a+b*x^2))],
[1/((c*x)^(1/2)*sqrt(a+b*x^2)),x,2,sqrt(cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))^2)/cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))*EllipticF(sin(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c)))),sqrt(1/2))*(sqrt(a)+x*sqrt(b))*sqrt((a+b*x^2)/(sqrt(a)+x*sqrt(b))^2)/(a^(1/4)*b^(1/4)*sqrt(c)*sqrt(a+b*x^2))],
[1/((c*x)^(3/2)*sqrt(a+b*x^2)),x,5,-2*sqrt(a+b*x^2)/(a*c*sqrt(c*x))+2*sqrt(b)*sqrt(c*x)*sqrt(a+b*x^2)/(a*c^2*(sqrt(a)+x*sqrt(b)))-2*b^(1/4)*sqrt(cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))^2)/cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))*EllipticE(sin(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c)))),sqrt(1/2))*(sqrt(a)+x*sqrt(b))*sqrt((a+b*x^2)/(sqrt(a)+x*sqrt(b))^2)/(a^(3/4)*c^(3/2)*sqrt(a+b*x^2))+b^(1/4)*sqrt(cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))^2)/cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))*EllipticF(sin(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c)))),sqrt(1/2))*(sqrt(a)+x*sqrt(b))*sqrt((a+b*x^2)/(sqrt(a)+x*sqrt(b))^2)/(a^(3/4)*c^(3/2)*sqrt(a+b*x^2))],
[1/((c*x)^(5/2)*sqrt(a+b*x^2)),x,3,-2/3*sqrt(a+b*x^2)/(a*c*(c*x)^(3/2))-1/3*b^(3/4)*sqrt(cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))^2)/cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))*EllipticF(sin(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c)))),sqrt(1/2))*(sqrt(a)+x*sqrt(b))*sqrt((a+b*x^2)/(sqrt(a)+x*sqrt(b))^2)/(a^(5/4)*c^(5/2)*sqrt(a+b*x^2))],
[1/((c*x)^(7/2)*sqrt(a+b*x^2)),x,6,-2/5*sqrt(a+b*x^2)/(a*c*(c*x)^(5/2))+6/5*b*sqrt(a+b*x^2)/(a^2*c^3*sqrt(c*x))-6/5*b^(3/2)*sqrt(c*x)*sqrt(a+b*x^2)/(a^2*c^4*(sqrt(a)+x*sqrt(b)))+6/5*b^(5/4)*sqrt(cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))^2)/cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))*EllipticE(sin(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c)))),sqrt(1/2))*(sqrt(a)+x*sqrt(b))*sqrt((a+b*x^2)/(sqrt(a)+x*sqrt(b))^2)/(a^(7/4)*c^(7/2)*sqrt(a+b*x^2))-3/5*b^(5/4)*sqrt(cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))^2)/cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))*EllipticF(sin(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c)))),sqrt(1/2))*(sqrt(a)+x*sqrt(b))*sqrt((a+b*x^2)/(sqrt(a)+x*sqrt(b))^2)/(a^(7/4)*c^(7/2)*sqrt(a+b*x^2))],
[(c*x)^(7/2)/(a+b*x^2)^(3/2),x,4,-c*(c*x)^(5/2)/(b*sqrt(a+b*x^2))+5/3*c^3*sqrt(c*x)*sqrt(a+b*x^2)/b^2-5/6*a^(3/4)*c^(7/2)*sqrt(cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))^2)/cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))*EllipticF(sin(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c)))),sqrt(1/2))*(sqrt(a)+x*sqrt(b))*sqrt((a+b*x^2)/(sqrt(a)+x*sqrt(b))^2)/(b^(9/4)*sqrt(a+b*x^2))],
[(c*x)^(5/2)/(a+b*x^2)^(3/2),x,5,-c*(c*x)^(3/2)/(b*sqrt(a+b*x^2))+3*c^2*sqrt(c*x)*sqrt(a+b*x^2)/(b^(3/2)*(sqrt(a)+x*sqrt(b)))-3*a^(1/4)*c^(5/2)*sqrt(cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))^2)/cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))*EllipticE(sin(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c)))),sqrt(1/2))*(sqrt(a)+x*sqrt(b))*sqrt((a+b*x^2)/(sqrt(a)+x*sqrt(b))^2)/(b^(7/4)*sqrt(a+b*x^2))+3/2*a^(1/4)*c^(5/2)*sqrt(cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))^2)/cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))*EllipticF(sin(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c)))),sqrt(1/2))*(sqrt(a)+x*sqrt(b))*sqrt((a+b*x^2)/(sqrt(a)+x*sqrt(b))^2)/(b^(7/4)*sqrt(a+b*x^2))],
[(c*x)^(3/2)/(a+b*x^2)^(3/2),x,3,-c*sqrt(c*x)/(b*sqrt(a+b*x^2))+1/2*c^(3/2)*sqrt(cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))^2)/cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))*EllipticF(sin(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c)))),sqrt(1/2))*(sqrt(a)+x*sqrt(b))*sqrt((a+b*x^2)/(sqrt(a)+x*sqrt(b))^2)/(a^(1/4)*b^(5/4)*sqrt(a+b*x^2))],
[(c*x)^(1/2)/(a+b*x^2)^(3/2),x,5,(c*x)^(3/2)/(a*c*sqrt(a+b*x^2))-sqrt(c*x)*sqrt(a+b*x^2)/(a*sqrt(b)*(sqrt(a)+x*sqrt(b)))+sqrt(cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))^2)/cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))*EllipticE(sin(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c)))),sqrt(1/2))*(sqrt(a)+x*sqrt(b))*sqrt(c)*sqrt((a+b*x^2)/(sqrt(a)+x*sqrt(b))^2)/(a^(3/4)*b^(3/4)*sqrt(a+b*x^2))-1/2*sqrt(cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))^2)/cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))*EllipticF(sin(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c)))),sqrt(1/2))*(sqrt(a)+x*sqrt(b))*sqrt(c)*sqrt((a+b*x^2)/(sqrt(a)+x*sqrt(b))^2)/(a^(3/4)*b^(3/4)*sqrt(a+b*x^2))],
[1/((c*x)^(1/2)*(a+b*x^2)^(3/2)),x,3,sqrt(c*x)/(a*c*sqrt(a+b*x^2))+1/2*sqrt(cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))^2)/cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))*EllipticF(sin(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c)))),sqrt(1/2))*(sqrt(a)+x*sqrt(b))*sqrt((a+b*x^2)/(sqrt(a)+x*sqrt(b))^2)/(a^(5/4)*b^(1/4)*sqrt(c)*sqrt(a+b*x^2))],
[1/((c*x)^(3/2)*(a+b*x^2)^(3/2)),x,6,1/(a*c*sqrt(c*x)*sqrt(a+b*x^2))-3*sqrt(a+b*x^2)/(a^2*c*sqrt(c*x))+3*sqrt(b)*sqrt(c*x)*sqrt(a+b*x^2)/(a^2*c^2*(sqrt(a)+x*sqrt(b)))-3*b^(1/4)*sqrt(cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))^2)/cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))*EllipticE(sin(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c)))),sqrt(1/2))*(sqrt(a)+x*sqrt(b))*sqrt((a+b*x^2)/(sqrt(a)+x*sqrt(b))^2)/(a^(7/4)*c^(3/2)*sqrt(a+b*x^2))+3/2*b^(1/4)*sqrt(cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))^2)/cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))*EllipticF(sin(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c)))),sqrt(1/2))*(sqrt(a)+x*sqrt(b))*sqrt((a+b*x^2)/(sqrt(a)+x*sqrt(b))^2)/(a^(7/4)*c^(3/2)*sqrt(a+b*x^2))],
[1/((c*x)^(5/2)*(a+b*x^2)^(3/2)),x,4,1/(a*c*(c*x)^(3/2)*sqrt(a+b*x^2))-5/3*sqrt(a+b*x^2)/(a^2*c*(c*x)^(3/2))-5/6*b^(3/4)*sqrt(cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))^2)/cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))*EllipticF(sin(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c)))),sqrt(1/2))*(sqrt(a)+x*sqrt(b))*sqrt((a+b*x^2)/(sqrt(a)+x*sqrt(b))^2)/(a^(9/4)*c^(5/2)*sqrt(a+b*x^2))],
[1/((c*x)^(7/2)*(a+b*x^2)^(3/2)),x,7,1/(a*c*(c*x)^(5/2)*sqrt(a+b*x^2))-7/5*sqrt(a+b*x^2)/(a^2*c*(c*x)^(5/2))+21/5*b*sqrt(a+b*x^2)/(a^3*c^3*sqrt(c*x))-21/5*b^(3/2)*sqrt(c*x)*sqrt(a+b*x^2)/(a^3*c^4*(sqrt(a)+x*sqrt(b)))+21/5*b^(5/4)*sqrt(cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))^2)/cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))*EllipticE(sin(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c)))),sqrt(1/2))*(sqrt(a)+x*sqrt(b))*sqrt((a+b*x^2)/(sqrt(a)+x*sqrt(b))^2)/(a^(11/4)*c^(7/2)*sqrt(a+b*x^2))-21/10*b^(5/4)*sqrt(cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))^2)/cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))*EllipticF(sin(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c)))),sqrt(1/2))*(sqrt(a)+x*sqrt(b))*sqrt((a+b*x^2)/(sqrt(a)+x*sqrt(b))^2)/(a^(11/4)*c^(7/2)*sqrt(a+b*x^2))],
[(c*x)^(7/2)/(a+b*x^2)^(5/2),x,4,-1/3*c*(c*x)^(5/2)/(b*(a+b*x^2)^(3/2))-5/6*c^3*sqrt(c*x)/(b^2*sqrt(a+b*x^2))+5/12*c^(7/2)*sqrt(cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))^2)/cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))*EllipticF(sin(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c)))),sqrt(1/2))*(sqrt(a)+x*sqrt(b))*sqrt((a+b*x^2)/(sqrt(a)+x*sqrt(b))^2)/(a^(1/4)*b^(9/4)*sqrt(a+b*x^2))],
[(c*x)^(5/2)/(a+b*x^2)^(5/2),x,6,-1/3*c*(c*x)^(3/2)/(b*(a+b*x^2)^(3/2))+1/2*c*(c*x)^(3/2)/(a*b*sqrt(a+b*x^2))-1/2*c^2*sqrt(c*x)*sqrt(a+b*x^2)/(a*b^(3/2)*(sqrt(a)+x*sqrt(b)))+1/2*c^(5/2)*sqrt(cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))^2)/cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))*EllipticE(sin(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c)))),sqrt(1/2))*(sqrt(a)+x*sqrt(b))*sqrt((a+b*x^2)/(sqrt(a)+x*sqrt(b))^2)/(a^(3/4)*b^(7/4)*sqrt(a+b*x^2))-1/4*c^(5/2)*sqrt(cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))^2)/cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))*EllipticF(sin(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c)))),sqrt(1/2))*(sqrt(a)+x*sqrt(b))*sqrt((a+b*x^2)/(sqrt(a)+x*sqrt(b))^2)/(a^(3/4)*b^(7/4)*sqrt(a+b*x^2))],
[(c*x)^(3/2)/(a+b*x^2)^(5/2),x,4,-1/3*c*sqrt(c*x)/(b*(a+b*x^2)^(3/2))+1/6*c*sqrt(c*x)/(a*b*sqrt(a+b*x^2))+1/12*c^(3/2)*sqrt(cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))^2)/cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))*EllipticF(sin(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c)))),sqrt(1/2))*(sqrt(a)+x*sqrt(b))*sqrt((a+b*x^2)/(sqrt(a)+x*sqrt(b))^2)/(a^(5/4)*b^(5/4)*sqrt(a+b*x^2))],
[(c*x)^(1/2)/(a+b*x^2)^(5/2),x,6,1/3*(c*x)^(3/2)/(a*c*(a+b*x^2)^(3/2))+1/2*(c*x)^(3/2)/(a^2*c*sqrt(a+b*x^2))-1/2*sqrt(c*x)*sqrt(a+b*x^2)/(a^2*sqrt(b)*(sqrt(a)+x*sqrt(b)))+1/2*sqrt(cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))^2)/cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))*EllipticE(sin(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c)))),sqrt(1/2))*(sqrt(a)+x*sqrt(b))*sqrt(c)*sqrt((a+b*x^2)/(sqrt(a)+x*sqrt(b))^2)/(a^(7/4)*b^(3/4)*sqrt(a+b*x^2))-1/4*sqrt(cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))^2)/cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))*EllipticF(sin(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c)))),sqrt(1/2))*(sqrt(a)+x*sqrt(b))*sqrt(c)*sqrt((a+b*x^2)/(sqrt(a)+x*sqrt(b))^2)/(a^(7/4)*b^(3/4)*sqrt(a+b*x^2))],
[1/((c*x)^(1/2)*(a+b*x^2)^(5/2)),x,4,1/3*sqrt(c*x)/(a*c*(a+b*x^2)^(3/2))+5/6*sqrt(c*x)/(a^2*c*sqrt(a+b*x^2))+5/12*sqrt(cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))^2)/cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))*EllipticF(sin(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c)))),sqrt(1/2))*(sqrt(a)+x*sqrt(b))*sqrt((a+b*x^2)/(sqrt(a)+x*sqrt(b))^2)/(a^(9/4)*b^(1/4)*sqrt(c)*sqrt(a+b*x^2))],
[1/((c*x)^(3/2)*(a+b*x^2)^(5/2)),x,7,1/3/(a*c*(a+b*x^2)^(3/2)*sqrt(c*x))+7/6/(a^2*c*sqrt(c*x)*sqrt(a+b*x^2))-7/2*sqrt(a+b*x^2)/(a^3*c*sqrt(c*x))+7/2*sqrt(b)*sqrt(c*x)*sqrt(a+b*x^2)/(a^3*c^2*(sqrt(a)+x*sqrt(b)))-7/2*b^(1/4)*sqrt(cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))^2)/cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))*EllipticE(sin(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c)))),sqrt(1/2))*(sqrt(a)+x*sqrt(b))*sqrt((a+b*x^2)/(sqrt(a)+x*sqrt(b))^2)/(a^(11/4)*c^(3/2)*sqrt(a+b*x^2))+7/4*b^(1/4)*sqrt(cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))^2)/cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))*EllipticF(sin(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c)))),sqrt(1/2))*(sqrt(a)+x*sqrt(b))*sqrt((a+b*x^2)/(sqrt(a)+x*sqrt(b))^2)/(a^(11/4)*c^(3/2)*sqrt(a+b*x^2))],
[1/((c*x)^(5/2)*(a+b*x^2)^(5/2)),x,5,1/3/(a*c*(c*x)^(3/2)*(a+b*x^2)^(3/2))+3/2/(a^2*c*(c*x)^(3/2)*sqrt(a+b*x^2))-5/2*sqrt(a+b*x^2)/(a^3*c*(c*x)^(3/2))-5/4*b^(3/4)*sqrt(cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))^2)/cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))*EllipticF(sin(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c)))),sqrt(1/2))*(sqrt(a)+x*sqrt(b))*sqrt((a+b*x^2)/(sqrt(a)+x*sqrt(b))^2)/(a^(13/4)*c^(5/2)*sqrt(a+b*x^2))],
[1/((c*x)^(7/2)*(a+b*x^2)^(5/2)),x,8,1/3/(a*c*(c*x)^(5/2)*(a+b*x^2)^(3/2))+11/6/(a^2*c*(c*x)^(5/2)*sqrt(a+b*x^2))-77/30*sqrt(a+b*x^2)/(a^3*c*(c*x)^(5/2))+77/10*b*sqrt(a+b*x^2)/(a^4*c^3*sqrt(c*x))-77/10*b^(3/2)*sqrt(c*x)*sqrt(a+b*x^2)/(a^4*c^4*(sqrt(a)+x*sqrt(b)))+77/10*b^(5/4)*sqrt(cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))^2)/cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))*EllipticE(sin(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c)))),sqrt(1/2))*(sqrt(a)+x*sqrt(b))*sqrt((a+b*x^2)/(sqrt(a)+x*sqrt(b))^2)/(a^(15/4)*c^(7/2)*sqrt(a+b*x^2))-77/20*b^(5/4)*sqrt(cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))^2)/cos(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c))))*EllipticF(sin(2*arctan(b^(1/4)*sqrt(c*x)/(a^(1/4)*sqrt(c)))),sqrt(1/2))*(sqrt(a)+x*sqrt(b))*sqrt((a+b*x^2)/(sqrt(a)+x*sqrt(b))^2)/(a^(15/4)*c^(7/2)*sqrt(a+b*x^2))],
[(c*x)^(5/2)/sqrt(3*a-2*a*x^2),x,5,-9/5*3^(1/4)*c^2*EllipticE(sqrt(3-x*sqrt(6))/sqrt(6),sqrt(2))*sqrt(c*x)*sqrt(3-2*x^2)/(2^(3/4)*sqrt(x)*sqrt(3*a-2*a*x^2))-1/5*c*(c*x)^(3/2)*sqrt(3*a-2*a*x^2)/a],
[(c*x)^(3/2)/sqrt(3*a-2*a*x^2),x,4,c^(3/2)*EllipticF((2/3)^(1/4)*sqrt(c*x)/sqrt(c),I)*sqrt(3-2*x^2)/(6^(1/4)*sqrt(a*(3-2*x^2)))-1/3*c*sqrt(c*x)*sqrt(3*a-2*a*x^2)/a],
[(c*x)^(1/2)/sqrt(3*a-2*a*x^2),x,4,-6^(1/4)*EllipticE(sqrt(3-x*sqrt(6))/sqrt(6),sqrt(2))*sqrt(c*x)*sqrt(3-2*x^2)/(sqrt(x)*sqrt(3*a-2*a*x^2))],
[1/((c*x)^(1/2)*sqrt(3*a-2*a*x^2)),x,3,2^(3/4)*EllipticF((2/3)^(1/4)*sqrt(c*x)/sqrt(c),I)*sqrt(3-2*x^2)/(3^(1/4)*sqrt(c)*sqrt(a*(3-2*x^2)))],
[1/((c*x)^(3/2)*sqrt(3*a-2*a*x^2)),x,5,2*2^(1/4)*EllipticE(sqrt(3-x*sqrt(6))/sqrt(6),sqrt(2))*sqrt(c*x)*sqrt(3-2*x^2)/(3^(3/4)*c^2*sqrt(x)*sqrt(3*a-2*a*x^2))-2/3*sqrt(3*a-2*a*x^2)/(a*c*sqrt(c*x))],
[1/((c*x)^(5/2)*sqrt(3*a-2*a*x^2)),x,4,2/9*2^(3/4)*EllipticF((2/3)^(1/4)*sqrt(c*x)/sqrt(c),I)*sqrt(3-2*x^2)/(3^(1/4)*c^(5/2)*sqrt(a*(3-2*x^2)))-2/9*sqrt(3*a-2*a*x^2)/(a*c*(c*x)^(3/2))],
[(c*x)^(5/2)/(3*a-2*a*x^2)^(3/2),x,5,1/2*c*(c*x)^(3/2)/(a*sqrt(3*a-2*a*x^2))+3/2*3^(1/4)*c^2*EllipticE(sqrt(3-x*sqrt(6))/sqrt(6),sqrt(2))*sqrt(c*x)*sqrt(3-2*x^2)/(2^(3/4)*a*sqrt(x)*sqrt(3*a-2*a*x^2))],
[(c*x)^(3/2)/(3*a-2*a*x^2)^(3/2),x,4,-1/2*c^(3/2)*EllipticF((2/3)^(1/4)*sqrt(c*x)/sqrt(c),I)*sqrt(3-2*x^2)/(6^(1/4)*a*sqrt(a*(3-2*x^2)))+1/2*c*sqrt(c*x)/(a*sqrt(3*a-2*a*x^2))],
[(c*x)^(1/2)/(3*a-2*a*x^2)^(3/2),x,5,1/3*(c*x)^(3/2)/(a*c*sqrt(3*a-2*a*x^2))+EllipticE(sqrt(3-x*sqrt(6))/sqrt(6),sqrt(2))*sqrt(c*x)*sqrt(3-2*x^2)/(6^(3/4)*a*sqrt(x)*sqrt(3*a-2*a*x^2))],
[1/((c*x)^(1/2)*(3*a-2*a*x^2)^(3/2)),x,4,1/3*EllipticF((2/3)^(1/4)*sqrt(c*x)/sqrt(c),I)*sqrt(3-2*x^2)/(6^(1/4)*a*sqrt(c)*sqrt(a*(3-2*x^2)))+1/3*sqrt(c*x)/(a*c*sqrt(3*a-2*a*x^2))],
[1/((c*x)^(3/2)*(3*a-2*a*x^2)^(3/2)),x,6,1/3/(a*c*sqrt(c*x)*sqrt(3*a-2*a*x^2))+2^(1/4)*EllipticE(sqrt(3-x*sqrt(6))/sqrt(6),sqrt(2))*sqrt(c*x)*sqrt(3-2*x^2)/(3^(3/4)*a*c^2*sqrt(x)*sqrt(3*a-2*a*x^2))-1/3*sqrt(3*a-2*a*x^2)/(a^2*c*sqrt(c*x))],
[1/((c*x)^(5/2)*(3*a-2*a*x^2)^(3/2)),x,5,5/27*2^(3/4)*EllipticF((2/3)^(1/4)*sqrt(c*x)/sqrt(c),I)*sqrt(3-2*x^2)/(3^(1/4)*a*c^(5/2)*sqrt(a*(3-2*x^2)))+1/3/(a*c*(c*x)^(3/2)*sqrt(3*a-2*a*x^2))-5/27*sqrt(3*a-2*a*x^2)/(a^2*c*(c*x)^(3/2))],

#  Compare with Mathematica's more complicated complex result. 
[1/(sqrt(x)*sqrt(1-a^2*x^2)),x,2,2*EllipticF(sqrt(a)*sqrt(x),I)/sqrt(a)],
[1/(sqrt(x)*sqrt(1+a*x^2)),x,2,sqrt(cos(2*arctan(a^(1/4)*sqrt(x)))^2)/cos(2*arctan(a^(1/4)*sqrt(x)))*EllipticF(sin(2*arctan(a^(1/4)*sqrt(x))),sqrt(1/2))*(1+x*sqrt(a))*sqrt((1+a*x^2)/(1+x*sqrt(a))^2)/(a^(1/4)*sqrt(1+a*x^2))],

# Integrands of the form (c x)^m (a+b x^2)^(p/2) when m symbolic
[x^m*(a+b*x^2)^(3/2),x,2,x^(1+m)*(a+b*x^2)^(5/2)*hypergeom([1,1/2*(6+m)],[1/2*(3+m)],-b*x^2/a)/(a*(1+m)),a*x^(1+m)*hypergeom([-3/2,1/2*(1+m)],[1/2*(3+m)],-b*x^2/a)*sqrt(a+b*x^2)/((1+m)*sqrt(1+b*x^2/a))],
[x^m*(a+b*x^2)^(1/2),x,2,x^(1+m)*(a+b*x^2)^(3/2)*hypergeom([1,1/2*(4+m)],[1/2*(3+m)],-b*x^2/a)/(a*(1+m)),x^(1+m)*hypergeom([-1/2,1/2*(1+m)],[1/2*(3+m)],-b*x^2/a)*sqrt(a+b*x^2)/((1+m)*sqrt(1+b*x^2/a))],
[x^m/(a+b*x^2)^(1/2),x,2,x^(1+m)*hypergeom([1,1/2*(2+m)],[1/2*(3+m)],-b*x^2/a)*sqrt(a+b*x^2)/(a*(1+m)),x^(1+m)*hypergeom([1/2,1/2*(1+m)],[1/2*(3+m)],-b*x^2/a)*sqrt(1+b*x^2/a)/((1+m)*sqrt(a+b*x^2))],
[x^m/(a+b*x^2)^(3/2),x,2,x^(1+m)*hypergeom([1,1/2*m],[1/2*(3+m)],-b*x^2/a)/(a*(1+m)*sqrt(a+b*x^2)),x^(1+m)*hypergeom([3/2,1/2*(1+m)],[1/2*(3+m)],-b*x^2/a)*sqrt(1+b*x^2/a)/(a*(1+m)*sqrt(a+b*x^2))],
[x^m/(a+b*x^2)^(5/2),x,2,x^(1+m)*hypergeom([1,1/2*(-2+m)],[1/2*(3+m)],-b*x^2/a)/(a*(1+m)*(a+b*x^2)^(3/2)),x^(1+m)*hypergeom([5/2,1/2*(1+m)],[1/2*(3+m)],-b*x^2/a)*sqrt(1+b*x^2/a)/(a^2*(1+m)*sqrt(a+b*x^2))],
[x^(2+m)/sqrt(a+b*x^2),x,2,x^(3+m)*hypergeom([1,1/2*(4+m)],[1/2*(5+m)],-b*x^2/a)*sqrt(a+b*x^2)/(a*(3+m)),x^(3+m)*hypergeom([1/2,1/2*(3+m)],[1/2*(5+m)],-b*x^2/a)*sqrt(1+b*x^2/a)/((3+m)*sqrt(a+b*x^2))],
[x^(1+m)/sqrt(a+b*x^2),x,2,x^(2+m)*hypergeom([1,1/2*(3+m)],[1/2*(4+m)],-b*x^2/a)*sqrt(a+b*x^2)/(a*(2+m)),x^(2+m)*hypergeom([1/2,1/2*(2+m)],[1/2*(4+m)],-b*x^2/a)*sqrt(1+b*x^2/a)/((2+m)*sqrt(a+b*x^2))],
[x^m/sqrt(a+b*x^2),x,2,x^(1+m)*hypergeom([1,1/2*(2+m)],[1/2*(3+m)],-b*x^2/a)*sqrt(a+b*x^2)/(a*(1+m)),x^(1+m)*hypergeom([1/2,1/2*(1+m)],[1/2*(3+m)],-b*x^2/a)*sqrt(1+b*x^2/a)/((1+m)*sqrt(a+b*x^2))],
[x^(-1+m)/sqrt(a+b*x^2),x,2,x^m*hypergeom([1,1/2*(1+m)],[1/2*(2+m)],-b*x^2/a)*sqrt(a+b*x^2)/(a*m),x^m*hypergeom([1/2,1/2*m],[1/2*(2+m)],-b*x^2/a)*sqrt(1+b*x^2/a)/(m*sqrt(a+b*x^2))],
[x^(-2+m)/sqrt(a+b*x^2),x,2,-x^(-1+m)*hypergeom([1,1/2*m],[1/2*(1+m)],-b*x^2/a)*sqrt(a+b*x^2)/(a*(1-m)),-x^(-1+m)*hypergeom([1/2,1/2*(-1+m)],[1/2*(1+m)],-b*x^2/a)*sqrt(1+b*x^2/a)/((1-m)*sqrt(a+b*x^2))],
[x^(1+m)*(a*(2+m)+b*(3+m)*x^2)/sqrt(a+b*x^2),x,1,x^(2+m)*sqrt(a+b*x^2)],
[a*(2+m)*x^(1+m)/sqrt(a+b*x^2)+b*(3+m)*x^(3+m)/sqrt(a+b*x^2),x,-5,x^(2+m)*sqrt(a+b*x^2)],
[x^(-1+m)*(a*m+b*(-1+m)*x^2)/(a+b*x^2)^(3/2),x,1,x^m/sqrt(a+b*x^2)],
[-b*x^(1+m)/(a+b*x^2)^(3/2)+m*x^(-1+m)/sqrt(a+b*x^2),x,-5,x^m/sqrt(a+b*x^2),-b*x^(2+m)/(a*sqrt(a+b*x^2))+x^m*sqrt(a+b*x^2)/a],

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

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

# p>0
[x^7*(a+b*x^2)^(1/3),x,3,-3/8*a^3*(a+b*x^2)^(4/3)/b^4+9/14*a^2*(a+b*x^2)^(7/3)/b^4-9/20*a*(a+b*x^2)^(10/3)/b^4+3/26*(a+b*x^2)^(13/3)/b^4],
[x^5*(a+b*x^2)^(1/3),x,3,3/8*a^2*(a+b*x^2)^(4/3)/b^3-3/7*a*(a+b*x^2)^(7/3)/b^3+3/20*(a+b*x^2)^(10/3)/b^3],
[x^3*(a+b*x^2)^(1/3),x,3,-3/8*a*(a+b*x^2)^(4/3)/b^2+3/14*(a+b*x^2)^(7/3)/b^2],
[x*(a+b*x^2)^(1/3),x,1,3/8*(a+b*x^2)^(4/3)/b],
[(a+b*x^2)^(1/3)/x,x,6,3/2*(a+b*x^2)^(1/3)-1/2*a^(1/3)*log(x)+3/4*a^(1/3)*log(a^(1/3)-(a+b*x^2)^(1/3))-1/2*a^(1/3)*arctan((a^(1/3)+2*(a+b*x^2)^(1/3))/(a^(1/3)*sqrt(3)))*sqrt(3)],
[(a+b*x^2)^(1/3)/x^3,x,6,-1/2*(a+b*x^2)^(1/3)/x^2-1/6*b*log(x)/a^(2/3)+1/4*b*log(a^(1/3)-(a+b*x^2)^(1/3))/a^(2/3)-1/2*b*arctan((a^(1/3)+2*(a+b*x^2)^(1/3))/(a^(1/3)*sqrt(3)))/(a^(2/3)*sqrt(3))],
[(a+b*x^2)^(1/3)/x^5,x,7,-1/4*(a+b*x^2)^(1/3)/x^4-1/12*b*(a+b*x^2)^(1/3)/(a*x^2)+1/18*b^2*log(x)/a^(5/3)-1/12*b^2*log(a^(1/3)-(a+b*x^2)^(1/3))/a^(5/3)+1/6*b^2*arctan((a^(1/3)+2*(a+b*x^2)^(1/3))/(a^(1/3)*sqrt(3)))/(a^(5/3)*sqrt(3))],
[x^4*(a+b*x^2)^(1/3),x,5,-54/935*a^2*x*(a+b*x^2)^(1/3)/b^2+6/187*a*x^3*(a+b*x^2)^(1/3)/b+3/17*x^5*(a+b*x^2)^(1/3)-54/935*3^(3/4)*a^3*(a^(1/3)-(a+b*x^2)^(1/3))*EllipticF((-(a+b*x^2)^(1/3)+a^(1/3)*(1+sqrt(3)))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3))),sqrt(-7+4*sqrt(3)))*sqrt((a^(2/3)+a^(1/3)*(a+b*x^2)^(1/3)+(a+b*x^2)^(2/3))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3)))^2)*sqrt(2-sqrt(3))/(b^3*x*sqrt(-a^(1/3)*(a^(1/3)-(a+b*x^2)^(1/3))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3)))^2))],
[x^2*(a+b*x^2)^(1/3),x,4,6/55*a*x*(a+b*x^2)^(1/3)/b+3/11*x^3*(a+b*x^2)^(1/3)+6/55*3^(3/4)*a^2*(a^(1/3)-(a+b*x^2)^(1/3))*EllipticF((-(a+b*x^2)^(1/3)+a^(1/3)*(1+sqrt(3)))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3))),sqrt(-7+4*sqrt(3)))*sqrt((a^(2/3)+a^(1/3)*(a+b*x^2)^(1/3)+(a+b*x^2)^(2/3))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3)))^2)*sqrt(2-sqrt(3))/(b^2*x*sqrt(-a^(1/3)*(a^(1/3)-(a+b*x^2)^(1/3))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3)))^2))],
[(a+b*x^2)^(1/3),x,3,3/5*x*(a+b*x^2)^(1/3)-2/5*3^(3/4)*a*(a^(1/3)-(a+b*x^2)^(1/3))*EllipticF((-(a+b*x^2)^(1/3)+a^(1/3)*(1+sqrt(3)))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3))),sqrt(-7+4*sqrt(3)))*sqrt((a^(2/3)+a^(1/3)*(a+b*x^2)^(1/3)+(a+b*x^2)^(2/3))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3)))^2)*sqrt(2-sqrt(3))/(b*x*sqrt(-a^(1/3)*(a^(1/3)-(a+b*x^2)^(1/3))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3)))^2))],
[(a+b*x^2)^(1/3)/x^2,x,3,-(a+b*x^2)^(1/3)/x-2*(a^(1/3)-(a+b*x^2)^(1/3))*EllipticF((-(a+b*x^2)^(1/3)+a^(1/3)*(1+sqrt(3)))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3))),sqrt(-7+4*sqrt(3)))*sqrt((a^(2/3)+a^(1/3)*(a+b*x^2)^(1/3)+(a+b*x^2)^(2/3))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3)))^2)*sqrt(2-sqrt(3))/(3^(1/4)*x*sqrt(-a^(1/3)*(a^(1/3)-(a+b*x^2)^(1/3))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3)))^2))],
[(a+b*x^2)^(1/3)/x^4,x,4,-1/3*(a+b*x^2)^(1/3)/x^3-2/9*b*(a+b*x^2)^(1/3)/(a*x)+2/9*b*(a^(1/3)-(a+b*x^2)^(1/3))*EllipticF((-(a+b*x^2)^(1/3)+a^(1/3)*(1+sqrt(3)))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3))),sqrt(-7+4*sqrt(3)))*sqrt((a^(2/3)+a^(1/3)*(a+b*x^2)^(1/3)+(a+b*x^2)^(2/3))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3)))^2)*sqrt(2-sqrt(3))/(3^(1/4)*a*x*sqrt(-a^(1/3)*(a^(1/3)-(a+b*x^2)^(1/3))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3)))^2))],
[x^7*(a+b*x^2)^(2/3),x,3,-3/10*a^3*(a+b*x^2)^(5/3)/b^4+9/16*a^2*(a+b*x^2)^(8/3)/b^4-9/22*a*(a+b*x^2)^(11/3)/b^4+3/28*(a+b*x^2)^(14/3)/b^4],
[x^5*(a+b*x^2)^(2/3),x,3,3/10*a^2*(a+b*x^2)^(5/3)/b^3-3/8*a*(a+b*x^2)^(8/3)/b^3+3/22*(a+b*x^2)^(11/3)/b^3],
[x^3*(a+b*x^2)^(2/3),x,3,-3/10*a*(a+b*x^2)^(5/3)/b^2+3/16*(a+b*x^2)^(8/3)/b^2],
[x*(a+b*x^2)^(2/3),x,1,3/10*(a+b*x^2)^(5/3)/b],
[(a+b*x^2)^(2/3)/x,x,6,3/4*(a+b*x^2)^(2/3)-1/2*a^(2/3)*log(x)+3/4*a^(2/3)*log(a^(1/3)-(a+b*x^2)^(1/3))+1/2*a^(2/3)*arctan((a^(1/3)+2*(a+b*x^2)^(1/3))/(a^(1/3)*sqrt(3)))*sqrt(3)],
[(a+b*x^2)^(2/3)/x^3,x,6,-1/2*(a+b*x^2)^(2/3)/x^2-1/3*b*log(x)/a^(1/3)+1/2*b*log(a^(1/3)-(a+b*x^2)^(1/3))/a^(1/3)+b*arctan((a^(1/3)+2*(a+b*x^2)^(1/3))/(a^(1/3)*sqrt(3)))/(a^(1/3)*sqrt(3))],
[(a+b*x^2)^(2/3)/x^5,x,7,-1/4*(a+b*x^2)^(2/3)/x^4-1/6*b*(a+b*x^2)^(2/3)/(a*x^2)+1/18*b^2*log(x)/a^(4/3)-1/12*b^2*log(a^(1/3)-(a+b*x^2)^(1/3))/a^(4/3)-1/6*b^2*arctan((a^(1/3)+2*(a+b*x^2)^(1/3))/(a^(1/3)*sqrt(3)))/(a^(4/3)*sqrt(3))],
[x^4*(a+b*x^2)^(2/3),x,7,-108/1729*a^2*x*(a+b*x^2)^(2/3)/b^2+12/247*a*x^3*(a+b*x^2)^(2/3)/b+3/19*x^5*(a+b*x^2)^(2/3)-324/1729*a^3*x/(b^2*(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3))))-108/1729*3^(3/4)*a^(10/3)*(a^(1/3)-(a+b*x^2)^(1/3))*EllipticF((-(a+b*x^2)^(1/3)+a^(1/3)*(1+sqrt(3)))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3))),sqrt(-7+4*sqrt(3)))*sqrt(2)*sqrt((a^(2/3)+a^(1/3)*(a+b*x^2)^(1/3)+(a+b*x^2)^(2/3))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3)))^2)/(b^3*x*sqrt(-a^(1/3)*(a^(1/3)-(a+b*x^2)^(1/3))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3)))^2))+162/1729*3^(1/4)*a^(10/3)*(a^(1/3)-(a+b*x^2)^(1/3))*EllipticE((-(a+b*x^2)^(1/3)+a^(1/3)*(1+sqrt(3)))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3))),sqrt(-7+4*sqrt(3)))*sqrt((a^(2/3)+a^(1/3)*(a+b*x^2)^(1/3)+(a+b*x^2)^(2/3))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3)))^2)*sqrt(2+sqrt(3))/(b^3*x*sqrt(-a^(1/3)*(a^(1/3)-(a+b*x^2)^(1/3))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3)))^2))],
[x^2*(a+b*x^2)^(2/3),x,6,12/91*a*x*(a+b*x^2)^(2/3)/b+3/13*x^3*(a+b*x^2)^(2/3)+36/91*a^2*x/(b*(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3))))+12/91*3^(3/4)*a^(7/3)*(a^(1/3)-(a+b*x^2)^(1/3))*EllipticF((-(a+b*x^2)^(1/3)+a^(1/3)*(1+sqrt(3)))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3))),sqrt(-7+4*sqrt(3)))*sqrt(2)*sqrt((a^(2/3)+a^(1/3)*(a+b*x^2)^(1/3)+(a+b*x^2)^(2/3))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3)))^2)/(b^2*x*sqrt(-a^(1/3)*(a^(1/3)-(a+b*x^2)^(1/3))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3)))^2))-18/91*3^(1/4)*a^(7/3)*(a^(1/3)-(a+b*x^2)^(1/3))*EllipticE((-(a+b*x^2)^(1/3)+a^(1/3)*(1+sqrt(3)))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3))),sqrt(-7+4*sqrt(3)))*sqrt((a^(2/3)+a^(1/3)*(a+b*x^2)^(1/3)+(a+b*x^2)^(2/3))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3)))^2)*sqrt(2+sqrt(3))/(b^2*x*sqrt(-a^(1/3)*(a^(1/3)-(a+b*x^2)^(1/3))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3)))^2))],
[(a+b*x^2)^(2/3),x,5,3/7*x*(a+b*x^2)^(2/3)-12/7*a*x/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3)))-4/7*3^(3/4)*a^(4/3)*(a^(1/3)-(a+b*x^2)^(1/3))*EllipticF((-(a+b*x^2)^(1/3)+a^(1/3)*(1+sqrt(3)))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3))),sqrt(-7+4*sqrt(3)))*sqrt(2)*sqrt((a^(2/3)+a^(1/3)*(a+b*x^2)^(1/3)+(a+b*x^2)^(2/3))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3)))^2)/(b*x*sqrt(-a^(1/3)*(a^(1/3)-(a+b*x^2)^(1/3))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3)))^2))+6/7*3^(1/4)*a^(4/3)*(a^(1/3)-(a+b*x^2)^(1/3))*EllipticE((-(a+b*x^2)^(1/3)+a^(1/3)*(1+sqrt(3)))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3))),sqrt(-7+4*sqrt(3)))*sqrt((a^(2/3)+a^(1/3)*(a+b*x^2)^(1/3)+(a+b*x^2)^(2/3))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3)))^2)*sqrt(2+sqrt(3))/(b*x*sqrt(-a^(1/3)*(a^(1/3)-(a+b*x^2)^(1/3))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3)))^2))],
[(a+b*x^2)^(2/3)/x^2,x,5,-(a+b*x^2)^(2/3)/x-4*b*x/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3)))-4*a^(1/3)*(a^(1/3)-(a+b*x^2)^(1/3))*EllipticF((-(a+b*x^2)^(1/3)+a^(1/3)*(1+sqrt(3)))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3))),sqrt(-7+4*sqrt(3)))*sqrt(2)*sqrt((a^(2/3)+a^(1/3)*(a+b*x^2)^(1/3)+(a+b*x^2)^(2/3))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3)))^2)/(3^(1/4)*x*sqrt(-a^(1/3)*(a^(1/3)-(a+b*x^2)^(1/3))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3)))^2))+2*3^(1/4)*a^(1/3)*(a^(1/3)-(a+b*x^2)^(1/3))*EllipticE((-(a+b*x^2)^(1/3)+a^(1/3)*(1+sqrt(3)))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3))),sqrt(-7+4*sqrt(3)))*sqrt((a^(2/3)+a^(1/3)*(a+b*x^2)^(1/3)+(a+b*x^2)^(2/3))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3)))^2)*sqrt(2+sqrt(3))/(x*sqrt(-a^(1/3)*(a^(1/3)-(a+b*x^2)^(1/3))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3)))^2))],
[(a+b*x^2)^(2/3)/x^4,x,6,-1/3*(a+b*x^2)^(2/3)/x^3-4/9*b*(a+b*x^2)^(2/3)/(a*x)-4/9*b^2*x/(a*(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3))))-4/9*b*(a^(1/3)-(a+b*x^2)^(1/3))*EllipticF((-(a+b*x^2)^(1/3)+a^(1/3)*(1+sqrt(3)))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3))),sqrt(-7+4*sqrt(3)))*sqrt(2)*sqrt((a^(2/3)+a^(1/3)*(a+b*x^2)^(1/3)+(a+b*x^2)^(2/3))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3)))^2)/(3^(1/4)*a^(2/3)*x*sqrt(-a^(1/3)*(a^(1/3)-(a+b*x^2)^(1/3))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3)))^2))+2/3*b*(a^(1/3)-(a+b*x^2)^(1/3))*EllipticE((-(a+b*x^2)^(1/3)+a^(1/3)*(1+sqrt(3)))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3))),sqrt(-7+4*sqrt(3)))*sqrt((a^(2/3)+a^(1/3)*(a+b*x^2)^(1/3)+(a+b*x^2)^(2/3))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3)))^2)*sqrt(2+sqrt(3))/(3^(3/4)*a^(2/3)*x*sqrt(-a^(1/3)*(a^(1/3)-(a+b*x^2)^(1/3))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3)))^2))],
[x^7*(a+b*x^2)^(4/3),x,3,-3/14*a^3*(a+b*x^2)^(7/3)/b^4+9/20*a^2*(a+b*x^2)^(10/3)/b^4-9/26*a*(a+b*x^2)^(13/3)/b^4+3/32*(a+b*x^2)^(16/3)/b^4],
[x^5*(a+b*x^2)^(4/3),x,3,3/14*a^2*(a+b*x^2)^(7/3)/b^3-3/10*a*(a+b*x^2)^(10/3)/b^3+3/26*(a+b*x^2)^(13/3)/b^3],
[x^3*(a+b*x^2)^(4/3),x,3,-3/14*a*(a+b*x^2)^(7/3)/b^2+3/20*(a+b*x^2)^(10/3)/b^2],
[x*(a+b*x^2)^(4/3),x,1,3/14*(a+b*x^2)^(7/3)/b],
[(a+b*x^2)^(4/3)/x,x,7,3/2*a*(a+b*x^2)^(1/3)+3/8*(a+b*x^2)^(4/3)-1/2*a^(4/3)*log(x)+3/4*a^(4/3)*log(a^(1/3)-(a+b*x^2)^(1/3))-1/2*a^(4/3)*arctan((a^(1/3)+2*(a+b*x^2)^(1/3))/(a^(1/3)*sqrt(3)))*sqrt(3)],
[(a+b*x^2)^(4/3)/x^3,x,7,2*b*(a+b*x^2)^(1/3)-1/2*(a+b*x^2)^(4/3)/x^2-2/3*a^(1/3)*b*log(x)+a^(1/3)*b*log(a^(1/3)-(a+b*x^2)^(1/3))-2*a^(1/3)*b*arctan((a^(1/3)+2*(a+b*x^2)^(1/3))/(a^(1/3)*sqrt(3)))/sqrt(3)],
[(a+b*x^2)^(4/3)/x^5,x,7,-1/3*b*(a+b*x^2)^(1/3)/x^2-1/4*(a+b*x^2)^(4/3)/x^4-1/9*b^2*log(x)/a^(2/3)+1/6*b^2*log(a^(1/3)-(a+b*x^2)^(1/3))/a^(2/3)-1/3*b^2*arctan((a^(1/3)+2*(a+b*x^2)^(1/3))/(a^(1/3)*sqrt(3)))/(a^(2/3)*sqrt(3))],
[x^4*(a+b*x^2)^(4/3),x,6,-432/21505*a^3*x*(a+b*x^2)^(1/3)/b^2+48/4301*a^2*x^3*(a+b*x^2)^(1/3)/b+24/391*a*x^5*(a+b*x^2)^(1/3)+3/23*x^5*(a+b*x^2)^(4/3)-432/21505*3^(3/4)*a^4*(a^(1/3)-(a+b*x^2)^(1/3))*EllipticF((-(a+b*x^2)^(1/3)+a^(1/3)*(1+sqrt(3)))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3))),sqrt(-7+4*sqrt(3)))*sqrt((a^(2/3)+a^(1/3)*(a+b*x^2)^(1/3)+(a+b*x^2)^(2/3))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3)))^2)*sqrt(2-sqrt(3))/(b^3*x*sqrt(-a^(1/3)*(a^(1/3)-(a+b*x^2)^(1/3))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3)))^2))],
[x^2*(a+b*x^2)^(4/3),x,5,48/935*a^2*x*(a+b*x^2)^(1/3)/b+24/187*a*x^3*(a+b*x^2)^(1/3)+3/17*x^3*(a+b*x^2)^(4/3)+48/935*3^(3/4)*a^3*(a^(1/3)-(a+b*x^2)^(1/3))*EllipticF((-(a+b*x^2)^(1/3)+a^(1/3)*(1+sqrt(3)))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3))),sqrt(-7+4*sqrt(3)))*sqrt((a^(2/3)+a^(1/3)*(a+b*x^2)^(1/3)+(a+b*x^2)^(2/3))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3)))^2)*sqrt(2-sqrt(3))/(b^2*x*sqrt(-a^(1/3)*(a^(1/3)-(a+b*x^2)^(1/3))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3)))^2))],
[(a+b*x^2)^(4/3),x,4,24/55*a*x*(a+b*x^2)^(1/3)+3/11*x*(a+b*x^2)^(4/3)-16/55*3^(3/4)*a^2*(a^(1/3)-(a+b*x^2)^(1/3))*EllipticF((-(a+b*x^2)^(1/3)+a^(1/3)*(1+sqrt(3)))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3))),sqrt(-7+4*sqrt(3)))*sqrt((a^(2/3)+a^(1/3)*(a+b*x^2)^(1/3)+(a+b*x^2)^(2/3))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3)))^2)*sqrt(2-sqrt(3))/(b*x*sqrt(-a^(1/3)*(a^(1/3)-(a+b*x^2)^(1/3))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3)))^2))],
[(a+b*x^2)^(4/3)/x^2,x,4,8/5*b*x*(a+b*x^2)^(1/3)-(a+b*x^2)^(4/3)/x-16/5*a*(a^(1/3)-(a+b*x^2)^(1/3))*EllipticF((-(a+b*x^2)^(1/3)+a^(1/3)*(1+sqrt(3)))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3))),sqrt(-7+4*sqrt(3)))*sqrt((a^(2/3)+a^(1/3)*(a+b*x^2)^(1/3)+(a+b*x^2)^(2/3))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3)))^2)*sqrt(2-sqrt(3))/(3^(1/4)*x*sqrt(-a^(1/3)*(a^(1/3)-(a+b*x^2)^(1/3))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3)))^2))],
[(a+b*x^2)^(4/3)/x^4,x,4,-8/9*b*(a+b*x^2)^(1/3)/x-1/3*(a+b*x^2)^(4/3)/x^3-16/9*b*(a^(1/3)-(a+b*x^2)^(1/3))*EllipticF((-(a+b*x^2)^(1/3)+a^(1/3)*(1+sqrt(3)))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3))),sqrt(-7+4*sqrt(3)))*sqrt((a^(2/3)+a^(1/3)*(a+b*x^2)^(1/3)+(a+b*x^2)^(2/3))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3)))^2)*sqrt(2-sqrt(3))/(3^(1/4)*x*sqrt(-a^(1/3)*(a^(1/3)-(a+b*x^2)^(1/3))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3)))^2))],
[x*(-1+x^2)^(7/3),x,1,3/20*(-1+x^2)^(10/3)],

# p<0
[x^7/(a+b*x^2)^(1/3),x,3,-3/4*a^3*(a+b*x^2)^(2/3)/b^4+9/10*a^2*(a+b*x^2)^(5/3)/b^4-9/16*a*(a+b*x^2)^(8/3)/b^4+3/22*(a+b*x^2)^(11/3)/b^4],
[x^5/(a+b*x^2)^(1/3),x,3,3/4*a^2*(a+b*x^2)^(2/3)/b^3-3/5*a*(a+b*x^2)^(5/3)/b^3+3/16*(a+b*x^2)^(8/3)/b^3],
[x^3/(a+b*x^2)^(1/3),x,3,-3/4*a*(a+b*x^2)^(2/3)/b^2+3/10*(a+b*x^2)^(5/3)/b^2],
[x/(a+b*x^2)^(1/3),x,1,3/4*(a+b*x^2)^(2/3)/b],
[1/(x*(a+b*x^2)^(1/3)),x,5,-1/2*log(x)/a^(1/3)+3/4*log(a^(1/3)-(a+b*x^2)^(1/3))/a^(1/3)+1/2*arctan((a^(1/3)+2*(a+b*x^2)^(1/3))/(a^(1/3)*sqrt(3)))*sqrt(3)/a^(1/3)],
[1/(x^3*(a+b*x^2)^(1/3)),x,6,-1/2*(a+b*x^2)^(2/3)/(a*x^2)+1/6*b*log(x)/a^(4/3)-1/4*b*log(a^(1/3)-(a+b*x^2)^(1/3))/a^(4/3)-1/2*b*arctan((a^(1/3)+2*(a+b*x^2)^(1/3))/(a^(1/3)*sqrt(3)))/(a^(4/3)*sqrt(3))],
[1/(x^5*(a+b*x^2)^(1/3)),x,7,-1/4*(a+b*x^2)^(2/3)/(a*x^4)+1/3*b*(a+b*x^2)^(2/3)/(a^2*x^2)-1/9*b^2*log(x)/a^(7/3)+1/6*b^2*log(a^(1/3)-(a+b*x^2)^(1/3))/a^(7/3)+1/3*b^2*arctan((a^(1/3)+2*(a+b*x^2)^(1/3))/(a^(1/3)*sqrt(3)))/(a^(7/3)*sqrt(3))],
[x^4/(a+b*x^2)^(1/3),x,6,-27/91*a*x*(a+b*x^2)^(2/3)/b^2+3/13*x^3*(a+b*x^2)^(2/3)/b-81/91*a^2*x/(b^2*(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3))))-27/91*3^(3/4)*a^(7/3)*(a^(1/3)-(a+b*x^2)^(1/3))*EllipticF((-(a+b*x^2)^(1/3)+a^(1/3)*(1+sqrt(3)))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3))),sqrt(-7+4*sqrt(3)))*sqrt(2)*sqrt((a^(2/3)+a^(1/3)*(a+b*x^2)^(1/3)+(a+b*x^2)^(2/3))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3)))^2)/(b^3*x*sqrt(-a^(1/3)*(a^(1/3)-(a+b*x^2)^(1/3))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3)))^2))+81/182*3^(1/4)*a^(7/3)*(a^(1/3)-(a+b*x^2)^(1/3))*EllipticE((-(a+b*x^2)^(1/3)+a^(1/3)*(1+sqrt(3)))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3))),sqrt(-7+4*sqrt(3)))*sqrt((a^(2/3)+a^(1/3)*(a+b*x^2)^(1/3)+(a+b*x^2)^(2/3))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3)))^2)*sqrt(2+sqrt(3))/(b^3*x*sqrt(-a^(1/3)*(a^(1/3)-(a+b*x^2)^(1/3))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3)))^2))],
[x^2/(a+b*x^2)^(1/3),x,5,3/7*x*(a+b*x^2)^(2/3)/b+9/7*a*x/(b*(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3))))+3/7*3^(3/4)*a^(4/3)*(a^(1/3)-(a+b*x^2)^(1/3))*EllipticF((-(a+b*x^2)^(1/3)+a^(1/3)*(1+sqrt(3)))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3))),sqrt(-7+4*sqrt(3)))*sqrt(2)*sqrt((a^(2/3)+a^(1/3)*(a+b*x^2)^(1/3)+(a+b*x^2)^(2/3))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3)))^2)/(b^2*x*sqrt(-a^(1/3)*(a^(1/3)-(a+b*x^2)^(1/3))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3)))^2))-9/14*3^(1/4)*a^(4/3)*(a^(1/3)-(a+b*x^2)^(1/3))*EllipticE((-(a+b*x^2)^(1/3)+a^(1/3)*(1+sqrt(3)))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3))),sqrt(-7+4*sqrt(3)))*sqrt((a^(2/3)+a^(1/3)*(a+b*x^2)^(1/3)+(a+b*x^2)^(2/3))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3)))^2)*sqrt(2+sqrt(3))/(b^2*x*sqrt(-a^(1/3)*(a^(1/3)-(a+b*x^2)^(1/3))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3)))^2))],
[1/(a+b*x^2)^(1/3),x,4,-3*x/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3)))-3^(3/4)*a^(1/3)*(a^(1/3)-(a+b*x^2)^(1/3))*EllipticF((-(a+b*x^2)^(1/3)+a^(1/3)*(1+sqrt(3)))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3))),sqrt(-7+4*sqrt(3)))*sqrt(2)*sqrt((a^(2/3)+a^(1/3)*(a+b*x^2)^(1/3)+(a+b*x^2)^(2/3))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3)))^2)/(b*x*sqrt(-a^(1/3)*(a^(1/3)-(a+b*x^2)^(1/3))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3)))^2))+3/2*3^(1/4)*a^(1/3)*(a^(1/3)-(a+b*x^2)^(1/3))*EllipticE((-(a+b*x^2)^(1/3)+a^(1/3)*(1+sqrt(3)))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3))),sqrt(-7+4*sqrt(3)))*sqrt((a^(2/3)+a^(1/3)*(a+b*x^2)^(1/3)+(a+b*x^2)^(2/3))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3)))^2)*sqrt(2+sqrt(3))/(b*x*sqrt(-a^(1/3)*(a^(1/3)-(a+b*x^2)^(1/3))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3)))^2))],
[1/(x^2*(a+b*x^2)^(1/3)),x,5,-(a+b*x^2)^(2/3)/(a*x)-b*x/(a*(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3))))-(a^(1/3)-(a+b*x^2)^(1/3))*EllipticF((-(a+b*x^2)^(1/3)+a^(1/3)*(1+sqrt(3)))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3))),sqrt(-7+4*sqrt(3)))*sqrt(2)*sqrt((a^(2/3)+a^(1/3)*(a+b*x^2)^(1/3)+(a+b*x^2)^(2/3))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3)))^2)/(3^(1/4)*a^(2/3)*x*sqrt(-a^(1/3)*(a^(1/3)-(a+b*x^2)^(1/3))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3)))^2))+1/2*3^(1/4)*(a^(1/3)-(a+b*x^2)^(1/3))*EllipticE((-(a+b*x^2)^(1/3)+a^(1/3)*(1+sqrt(3)))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3))),sqrt(-7+4*sqrt(3)))*sqrt((a^(2/3)+a^(1/3)*(a+b*x^2)^(1/3)+(a+b*x^2)^(2/3))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3)))^2)*sqrt(2+sqrt(3))/(a^(2/3)*x*sqrt(-a^(1/3)*(a^(1/3)-(a+b*x^2)^(1/3))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3)))^2))],
[1/(x^4*(a+b*x^2)^(1/3)),x,6,-1/3*(a+b*x^2)^(2/3)/(a*x^3)+5/9*b*(a+b*x^2)^(2/3)/(a^2*x)+5/9*b^2*x/(a^2*(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3))))+5/9*b*(a^(1/3)-(a+b*x^2)^(1/3))*EllipticF((-(a+b*x^2)^(1/3)+a^(1/3)*(1+sqrt(3)))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3))),sqrt(-7+4*sqrt(3)))*sqrt(2)*sqrt((a^(2/3)+a^(1/3)*(a+b*x^2)^(1/3)+(a+b*x^2)^(2/3))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3)))^2)/(3^(1/4)*a^(5/3)*x*sqrt(-a^(1/3)*(a^(1/3)-(a+b*x^2)^(1/3))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3)))^2))-5/6*b*(a^(1/3)-(a+b*x^2)^(1/3))*EllipticE((-(a+b*x^2)^(1/3)+a^(1/3)*(1+sqrt(3)))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3))),sqrt(-7+4*sqrt(3)))*sqrt((a^(2/3)+a^(1/3)*(a+b*x^2)^(1/3)+(a+b*x^2)^(2/3))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3)))^2)*sqrt(2+sqrt(3))/(3^(3/4)*a^(5/3)*x*sqrt(-a^(1/3)*(a^(1/3)-(a+b*x^2)^(1/3))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3)))^2))],
[x^7/(a+b*x^2)^(2/3),x,3,-3/2*a^3*(a+b*x^2)^(1/3)/b^4+9/8*a^2*(a+b*x^2)^(4/3)/b^4-9/14*a*(a+b*x^2)^(7/3)/b^4+3/20*(a+b*x^2)^(10/3)/b^4],
[x^5/(a+b*x^2)^(2/3),x,3,3/2*a^2*(a+b*x^2)^(1/3)/b^3-3/4*a*(a+b*x^2)^(4/3)/b^3+3/14*(a+b*x^2)^(7/3)/b^3],
[x^3/(a+b*x^2)^(2/3),x,3,-3/2*a*(a+b*x^2)^(1/3)/b^2+3/8*(a+b*x^2)^(4/3)/b^2],
[x/(a+b*x^2)^(2/3),x,1,3/2*(a+b*x^2)^(1/3)/b],
[1/(x*(a+b*x^2)^(2/3)),x,5,-1/2*log(x)/a^(2/3)+3/4*log(a^(1/3)-(a+b*x^2)^(1/3))/a^(2/3)-1/2*arctan((a^(1/3)+2*(a+b*x^2)^(1/3))/(a^(1/3)*sqrt(3)))*sqrt(3)/a^(2/3)],
[1/(x^3*(a+b*x^2)^(2/3)),x,6,-1/2*(a+b*x^2)^(1/3)/(a*x^2)+1/3*b*log(x)/a^(5/3)-1/2*b*log(a^(1/3)-(a+b*x^2)^(1/3))/a^(5/3)+b*arctan((a^(1/3)+2*(a+b*x^2)^(1/3))/(a^(1/3)*sqrt(3)))/(a^(5/3)*sqrt(3))],
[1/(x^5*(a+b*x^2)^(2/3)),x,7,-1/4*(a+b*x^2)^(1/3)/(a*x^4)+5/12*b*(a+b*x^2)^(1/3)/(a^2*x^2)-5/18*b^2*log(x)/a^(8/3)+5/12*b^2*log(a^(1/3)-(a+b*x^2)^(1/3))/a^(8/3)-5/6*b^2*arctan((a^(1/3)+2*(a+b*x^2)^(1/3))/(a^(1/3)*sqrt(3)))/(a^(8/3)*sqrt(3))],
[x^4/(a+b*x^2)^(2/3),x,4,-27/55*a*x*(a+b*x^2)^(1/3)/b^2+3/11*x^3*(a+b*x^2)^(1/3)/b-27/55*3^(3/4)*a^2*(a^(1/3)-(a+b*x^2)^(1/3))*EllipticF((-(a+b*x^2)^(1/3)+a^(1/3)*(1+sqrt(3)))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3))),sqrt(-7+4*sqrt(3)))*sqrt((a^(2/3)+a^(1/3)*(a+b*x^2)^(1/3)+(a+b*x^2)^(2/3))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3)))^2)*sqrt(2-sqrt(3))/(b^3*x*sqrt(-a^(1/3)*(a^(1/3)-(a+b*x^2)^(1/3))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3)))^2))],
[x^2/(a+b*x^2)^(2/3),x,3,3/5*x*(a+b*x^2)^(1/3)/b+3/5*3^(3/4)*a*(a^(1/3)-(a+b*x^2)^(1/3))*EllipticF((-(a+b*x^2)^(1/3)+a^(1/3)*(1+sqrt(3)))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3))),sqrt(-7+4*sqrt(3)))*sqrt((a^(2/3)+a^(1/3)*(a+b*x^2)^(1/3)+(a+b*x^2)^(2/3))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3)))^2)*sqrt(2-sqrt(3))/(b^2*x*sqrt(-a^(1/3)*(a^(1/3)-(a+b*x^2)^(1/3))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3)))^2))],
[1/(a+b*x^2)^(2/3),x,2,-3^(3/4)*(a^(1/3)-(a+b*x^2)^(1/3))*EllipticF((-(a+b*x^2)^(1/3)+a^(1/3)*(1+sqrt(3)))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3))),sqrt(-7+4*sqrt(3)))*sqrt((a^(2/3)+a^(1/3)*(a+b*x^2)^(1/3)+(a+b*x^2)^(2/3))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3)))^2)*sqrt(2-sqrt(3))/(b*x*sqrt(-a^(1/3)*(a^(1/3)-(a+b*x^2)^(1/3))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3)))^2))],
[1/(x^2*(a+b*x^2)^(2/3)),x,3,-(a+b*x^2)^(1/3)/(a*x)+(a^(1/3)-(a+b*x^2)^(1/3))*EllipticF((-(a+b*x^2)^(1/3)+a^(1/3)*(1+sqrt(3)))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3))),sqrt(-7+4*sqrt(3)))*sqrt((a^(2/3)+a^(1/3)*(a+b*x^2)^(1/3)+(a+b*x^2)^(2/3))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3)))^2)*sqrt(2-sqrt(3))/(3^(1/4)*a*x*sqrt(-a^(1/3)*(a^(1/3)-(a+b*x^2)^(1/3))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3)))^2))],
[1/(x^4*(a+b*x^2)^(2/3)),x,4,-1/3*(a+b*x^2)^(1/3)/(a*x^3)+7/9*b*(a+b*x^2)^(1/3)/(a^2*x)-7/9*b*(a^(1/3)-(a+b*x^2)^(1/3))*EllipticF((-(a+b*x^2)^(1/3)+a^(1/3)*(1+sqrt(3)))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3))),sqrt(-7+4*sqrt(3)))*sqrt((a^(2/3)+a^(1/3)*(a+b*x^2)^(1/3)+(a+b*x^2)^(2/3))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3)))^2)*sqrt(2-sqrt(3))/(3^(1/4)*a^2*x*sqrt(-a^(1/3)*(a^(1/3)-(a+b*x^2)^(1/3))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3)))^2))],
[x^7/(a+b*x^2)^(4/3),x,3,3/2*a^3/(b^4*(a+b*x^2)^(1/3))+9/4*a^2*(a+b*x^2)^(2/3)/b^4-9/10*a*(a+b*x^2)^(5/3)/b^4+3/16*(a+b*x^2)^(8/3)/b^4],
[x^5/(a+b*x^2)^(4/3),x,3,-3/2*a^2/(b^3*(a+b*x^2)^(1/3))-3/2*a*(a+b*x^2)^(2/3)/b^3+3/10*(a+b*x^2)^(5/3)/b^3],
[x^3/(a+b*x^2)^(4/3),x,3,3/2*a/(b^2*(a+b*x^2)^(1/3))+3/4*(a+b*x^2)^(2/3)/b^2],
[x/(a+b*x^2)^(4/3),x,1,(-3/2)/(b*(a+b*x^2)^(1/3))],
[1/(x*(a+b*x^2)^(4/3)),x,6,3/2/(a*(a+b*x^2)^(1/3))-1/2*log(x)/a^(4/3)+3/4*log(a^(1/3)-(a+b*x^2)^(1/3))/a^(4/3)+1/2*arctan((a^(1/3)+2*(a+b*x^2)^(1/3))/(a^(1/3)*sqrt(3)))*sqrt(3)/a^(4/3)],
[1/(x^3*(a+b*x^2)^(4/3)),x,7,-2*b/(a^2*(a+b*x^2)^(1/3))+(-1/2)/(a*x^2*(a+b*x^2)^(1/3))+2/3*b*log(x)/a^(7/3)-b*log(a^(1/3)-(a+b*x^2)^(1/3))/a^(7/3)-2*b*arctan((a^(1/3)+2*(a+b*x^2)^(1/3))/(a^(1/3)*sqrt(3)))/(a^(7/3)*sqrt(3))],
[1/(x^5*(a+b*x^2)^(4/3)),x,8,7/3*b^2/(a^3*(a+b*x^2)^(1/3))+(-1/4)/(a*x^4*(a+b*x^2)^(1/3))+7/12*b/(a^2*x^2*(a+b*x^2)^(1/3))-7/9*b^2*log(x)/a^(10/3)+7/6*b^2*log(a^(1/3)-(a+b*x^2)^(1/3))/a^(10/3)+7/3*b^2*arctan((a^(1/3)+2*(a+b*x^2)^(1/3))/(a^(1/3)*sqrt(3)))/(a^(10/3)*sqrt(3))],
[x^4/(a+b*x^2)^(4/3),x,6,-3/2*x^3/(b*(a+b*x^2)^(1/3))+27/14*x*(a+b*x^2)^(2/3)/b^2+81/14*a*x/(b^2*(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3))))+27/7*3^(3/4)*a^(4/3)*(a^(1/3)-(a+b*x^2)^(1/3))*EllipticF((-(a+b*x^2)^(1/3)+a^(1/3)*(1+sqrt(3)))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3))),sqrt(-7+4*sqrt(3)))*sqrt((a^(2/3)+a^(1/3)*(a+b*x^2)^(1/3)+(a+b*x^2)^(2/3))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3)))^2)/(b^3*x*sqrt(2)*sqrt(-a^(1/3)*(a^(1/3)-(a+b*x^2)^(1/3))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3)))^2))-81/28*3^(1/4)*a^(4/3)*(a^(1/3)-(a+b*x^2)^(1/3))*EllipticE((-(a+b*x^2)^(1/3)+a^(1/3)*(1+sqrt(3)))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3))),sqrt(-7+4*sqrt(3)))*sqrt((a^(2/3)+a^(1/3)*(a+b*x^2)^(1/3)+(a+b*x^2)^(2/3))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3)))^2)*sqrt(2+sqrt(3))/(b^3*x*sqrt(-a^(1/3)*(a^(1/3)-(a+b*x^2)^(1/3))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3)))^2))],
[x^2/(a+b*x^2)^(4/3),x,5,-3/2*x/(b*(a+b*x^2)^(1/3))-9/2*x/(b*(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3))))-3*3^(3/4)*a^(1/3)*(a^(1/3)-(a+b*x^2)^(1/3))*EllipticF((-(a+b*x^2)^(1/3)+a^(1/3)*(1+sqrt(3)))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3))),sqrt(-7+4*sqrt(3)))*sqrt((a^(2/3)+a^(1/3)*(a+b*x^2)^(1/3)+(a+b*x^2)^(2/3))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3)))^2)/(b^2*x*sqrt(2)*sqrt(-a^(1/3)*(a^(1/3)-(a+b*x^2)^(1/3))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3)))^2))+9/4*3^(1/4)*a^(1/3)*(a^(1/3)-(a+b*x^2)^(1/3))*EllipticE((-(a+b*x^2)^(1/3)+a^(1/3)*(1+sqrt(3)))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3))),sqrt(-7+4*sqrt(3)))*sqrt((a^(2/3)+a^(1/3)*(a+b*x^2)^(1/3)+(a+b*x^2)^(2/3))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3)))^2)*sqrt(2+sqrt(3))/(b^2*x*sqrt(-a^(1/3)*(a^(1/3)-(a+b*x^2)^(1/3))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3)))^2))],
[1/(a+b*x^2)^(4/3),x,5,3/2*x/(a*(a+b*x^2)^(1/3))+3/2*x/(a*(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3))))+3^(3/4)*(a^(1/3)-(a+b*x^2)^(1/3))*EllipticF((-(a+b*x^2)^(1/3)+a^(1/3)*(1+sqrt(3)))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3))),sqrt(-7+4*sqrt(3)))*sqrt((a^(2/3)+a^(1/3)*(a+b*x^2)^(1/3)+(a+b*x^2)^(2/3))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3)))^2)/(a^(2/3)*b*x*sqrt(2)*sqrt(-a^(1/3)*(a^(1/3)-(a+b*x^2)^(1/3))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3)))^2))-3/4*3^(1/4)*(a^(1/3)-(a+b*x^2)^(1/3))*EllipticE((-(a+b*x^2)^(1/3)+a^(1/3)*(1+sqrt(3)))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3))),sqrt(-7+4*sqrt(3)))*sqrt((a^(2/3)+a^(1/3)*(a+b*x^2)^(1/3)+(a+b*x^2)^(2/3))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3)))^2)*sqrt(2+sqrt(3))/(a^(2/3)*b*x*sqrt(-a^(1/3)*(a^(1/3)-(a+b*x^2)^(1/3))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3)))^2))],
[1/(x^2*(a+b*x^2)^(4/3)),x,6,3/2/(a*x*(a+b*x^2)^(1/3))-5/2*(a+b*x^2)^(2/3)/(a^2*x)-5/2*b*x/(a^2*(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3))))-5*(a^(1/3)-(a+b*x^2)^(1/3))*EllipticF((-(a+b*x^2)^(1/3)+a^(1/3)*(1+sqrt(3)))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3))),sqrt(-7+4*sqrt(3)))*sqrt((a^(2/3)+a^(1/3)*(a+b*x^2)^(1/3)+(a+b*x^2)^(2/3))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3)))^2)/(3^(1/4)*a^(5/3)*x*sqrt(2)*sqrt(-a^(1/3)*(a^(1/3)-(a+b*x^2)^(1/3))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3)))^2))+5/4*3^(1/4)*(a^(1/3)-(a+b*x^2)^(1/3))*EllipticE((-(a+b*x^2)^(1/3)+a^(1/3)*(1+sqrt(3)))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3))),sqrt(-7+4*sqrt(3)))*sqrt((a^(2/3)+a^(1/3)*(a+b*x^2)^(1/3)+(a+b*x^2)^(2/3))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3)))^2)*sqrt(2+sqrt(3))/(a^(5/3)*x*sqrt(-a^(1/3)*(a^(1/3)-(a+b*x^2)^(1/3))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3)))^2))],
[1/(x^4*(a+b*x^2)^(4/3)),x,7,3/2/(a*x^3*(a+b*x^2)^(1/3))-11/6*(a+b*x^2)^(2/3)/(a^2*x^3)+55/18*b*(a+b*x^2)^(2/3)/(a^3*x)+55/18*b^2*x/(a^3*(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3))))+55/9*b*(a^(1/3)-(a+b*x^2)^(1/3))*EllipticF((-(a+b*x^2)^(1/3)+a^(1/3)*(1+sqrt(3)))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3))),sqrt(-7+4*sqrt(3)))*sqrt((a^(2/3)+a^(1/3)*(a+b*x^2)^(1/3)+(a+b*x^2)^(2/3))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3)))^2)/(3^(1/4)*a^(8/3)*x*sqrt(2)*sqrt(-a^(1/3)*(a^(1/3)-(a+b*x^2)^(1/3))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3)))^2))-55/12*b*(a^(1/3)-(a+b*x^2)^(1/3))*EllipticE((-(a+b*x^2)^(1/3)+a^(1/3)*(1+sqrt(3)))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3))),sqrt(-7+4*sqrt(3)))*sqrt((a^(2/3)+a^(1/3)*(a+b*x^2)^(1/3)+(a+b*x^2)^(2/3))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3)))^2)*sqrt(2+sqrt(3))/(3^(3/4)*a^(8/3)*x*sqrt(-a^(1/3)*(a^(1/3)-(a+b*x^2)^(1/3))/(-(a+b*x^2)^(1/3)+a^(1/3)*(1-sqrt(3)))^2))],

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

# p>0
[(c*x)^(13/3)*(a+b*x^2)^(1/3),x,6,-5/108*a^2*c^3*(c*x)^(4/3)*(a+b*x^2)^(1/3)/b^2+1/36*a*c*(c*x)^(10/3)*(a+b*x^2)^(1/3)/b+1/6*(c*x)^(16/3)*(a+b*x^2)^(1/3)/c-5/108*a^3*c^(13/3)*log(b^(1/3)*(c*x)^(2/3)-c^(2/3)*(a+b*x^2)^(1/3))/b^(8/3)-5/54*a^3*c^(13/3)*arctan((1+2*b^(1/3)*(c*x)^(2/3)/(c^(2/3)*(a+b*x^2)^(1/3)))/sqrt(3))/(b^(8/3)*sqrt(3))],
[(c*x)^(7/3)*(a+b*x^2)^(1/3),x,5,1/12*a*c*(c*x)^(4/3)*(a+b*x^2)^(1/3)/b+1/4*(c*x)^(10/3)*(a+b*x^2)^(1/3)/c+1/12*a^2*c^(7/3)*log(b^(1/3)*(c*x)^(2/3)-c^(2/3)*(a+b*x^2)^(1/3))/b^(5/3)+1/6*a^2*c^(7/3)*arctan((1+2*b^(1/3)*(c*x)^(2/3)/(c^(2/3)*(a+b*x^2)^(1/3)))/sqrt(3))/(b^(5/3)*sqrt(3))],
[(c*x)^(1/3)*(a+b*x^2)^(1/3),x,4,1/2*(c*x)^(4/3)*(a+b*x^2)^(1/3)/c-1/4*a*c^(1/3)*log(b^(1/3)*(c*x)^(2/3)-c^(2/3)*(a+b*x^2)^(1/3))/b^(2/3)-1/2*a*c^(1/3)*arctan((1+2*b^(1/3)*(c*x)^(2/3)/(c^(2/3)*(a+b*x^2)^(1/3)))/sqrt(3))/(b^(2/3)*sqrt(3))],
[(a+b*x^2)^(1/3)/(c*x)^(5/3),x,4,-3/2*(a+b*x^2)^(1/3)/(c*(c*x)^(2/3))-3/4*b^(1/3)*log(b^(1/3)*(c*x)^(2/3)-c^(2/3)*(a+b*x^2)^(1/3))/c^(5/3)-1/2*b^(1/3)*arctan((1+2*b^(1/3)*(c*x)^(2/3)/(c^(2/3)*(a+b*x^2)^(1/3)))/sqrt(3))*sqrt(3)/c^(5/3)],
[(a+b*x^2)^(1/3)/(c*x)^(11/3),x,1,-3/8*(a+b*x^2)^(4/3)/(a*c*(c*x)^(8/3))],
[(a+b*x^2)^(1/3)/(c*x)^(17/3),x,2,-3/8*(a+b*x^2)^(4/3)/(a*c*(c*x)^(14/3))+9/56*(a+b*x^2)^(7/3)/(a^2*c*(c*x)^(14/3))],
[(a+b*x^2)^(1/3)/(c*x)^(23/3),x,3,-3/8*(a+b*x^2)^(4/3)/(a*c*(c*x)^(20/3))+9/28*(a+b*x^2)^(7/3)/(a^2*c*(c*x)^(20/3))-27/280*(a+b*x^2)^(10/3)/(a^3*c*(c*x)^(20/3))],
[(a+b*x^2)^(1/3)/(c*x)^(29/3),x,4,-3/8*(a+b*x^2)^(4/3)/(a*c*(c*x)^(26/3))+27/56*(a+b*x^2)^(7/3)/(a^2*c*(c*x)^(26/3))-81/280*(a+b*x^2)^(10/3)/(a^3*c*(c*x)^(26/3))+243/3640*(a+b*x^2)^(13/3)/(a^4*c*(c*x)^(26/3))],
[(c*x)^(10/3)*(a+b*x^2)^(1/3),x,6,-14/135*a^2*c^3*(c*x)^(1/3)*(a+b*x^2)^(1/3)/b^2+2/45*a*c*(c*x)^(7/3)*(a+b*x^2)^(1/3)/b+1/5*(c*x)^(13/3)*(a+b*x^2)^(1/3)/c+7/135*a^2*c^(7/3)*(c*x)^(1/3)*(a+b*x^2)^(1/3)*(c^(2/3)-b^(1/3)*(c*x)^(2/3)/(a+b*x^2)^(1/3))*sqrt(cos(arccos((c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1-sqrt(3))/(a+b*x^2)^(1/3))/(c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1+sqrt(3))/(a+b*x^2)^(1/3))))^2)/cos(arccos((c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1-sqrt(3))/(a+b*x^2)^(1/3))/(c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1+sqrt(3))/(a+b*x^2)^(1/3))))*EllipticF(sin(arccos((c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1-sqrt(3))/(a+b*x^2)^(1/3))/(c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1+sqrt(3))/(a+b*x^2)^(1/3)))),sqrt(1/4*(2+sqrt(3))))*sqrt((c^(4/3)+b^(2/3)*(c*x)^(4/3)/(a+b*x^2)^(2/3)+b^(1/3)*c^(2/3)*(c*x)^(2/3)/(a+b*x^2)^(1/3))/(c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1+sqrt(3))/(a+b*x^2)^(1/3))^2)/(3^(1/4)*b^2*sqrt(-b^(1/3)*(c*x)^(2/3)*(c^(2/3)-b^(1/3)*(c*x)^(2/3)/(a+b*x^2)^(1/3))/((a+b*x^2)^(1/3)*(c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1+sqrt(3))/(a+b*x^2)^(1/3))^2)))],
[(c*x)^(4/3)*(a+b*x^2)^(1/3),x,5,2/9*a*c*(c*x)^(1/3)*(a+b*x^2)^(1/3)/b+1/3*(c*x)^(7/3)*(a+b*x^2)^(1/3)/c-1/9*a*c^(1/3)*(c*x)^(1/3)*(a+b*x^2)^(1/3)*(c^(2/3)-b^(1/3)*(c*x)^(2/3)/(a+b*x^2)^(1/3))*sqrt(cos(arccos((c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1-sqrt(3))/(a+b*x^2)^(1/3))/(c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1+sqrt(3))/(a+b*x^2)^(1/3))))^2)/cos(arccos((c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1-sqrt(3))/(a+b*x^2)^(1/3))/(c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1+sqrt(3))/(a+b*x^2)^(1/3))))*EllipticF(sin(arccos((c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1-sqrt(3))/(a+b*x^2)^(1/3))/(c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1+sqrt(3))/(a+b*x^2)^(1/3)))),sqrt(1/4*(2+sqrt(3))))*sqrt((c^(4/3)+b^(2/3)*(c*x)^(4/3)/(a+b*x^2)^(2/3)+b^(1/3)*c^(2/3)*(c*x)^(2/3)/(a+b*x^2)^(1/3))/(c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1+sqrt(3))/(a+b*x^2)^(1/3))^2)/(3^(1/4)*b*sqrt(-b^(1/3)*(c*x)^(2/3)*(c^(2/3)-b^(1/3)*(c*x)^(2/3)/(a+b*x^2)^(1/3))/((a+b*x^2)^(1/3)*(c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1+sqrt(3))/(a+b*x^2)^(1/3))^2)))],
[(a+b*x^2)^(1/3)/(c*x)^(2/3),x,4,(c*x)^(1/3)*(a+b*x^2)^(1/3)/c+(c*x)^(1/3)*(a+b*x^2)^(1/3)*(c^(2/3)-b^(1/3)*(c*x)^(2/3)/(a+b*x^2)^(1/3))*sqrt(cos(arccos((c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1-sqrt(3))/(a+b*x^2)^(1/3))/(c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1+sqrt(3))/(a+b*x^2)^(1/3))))^2)/cos(arccos((c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1-sqrt(3))/(a+b*x^2)^(1/3))/(c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1+sqrt(3))/(a+b*x^2)^(1/3))))*EllipticF(sin(arccos((c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1-sqrt(3))/(a+b*x^2)^(1/3))/(c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1+sqrt(3))/(a+b*x^2)^(1/3)))),sqrt(1/4*(2+sqrt(3))))*sqrt((c^(4/3)+b^(2/3)*(c*x)^(4/3)/(a+b*x^2)^(2/3)+b^(1/3)*c^(2/3)*(c*x)^(2/3)/(a+b*x^2)^(1/3))/(c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1+sqrt(3))/(a+b*x^2)^(1/3))^2)/(3^(1/4)*c^(5/3)*sqrt(-b^(1/3)*(c*x)^(2/3)*(c^(2/3)-b^(1/3)*(c*x)^(2/3)/(a+b*x^2)^(1/3))/((a+b*x^2)^(1/3)*(c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1+sqrt(3))/(a+b*x^2)^(1/3))^2)))],
[(a+b*x^2)^(1/3)/(c*x)^(8/3),x,4,-3/5*(a+b*x^2)^(1/3)/(c*(c*x)^(5/3))+1/5*3^(3/4)*b*(c*x)^(1/3)*(a+b*x^2)^(1/3)*(c^(2/3)-b^(1/3)*(c*x)^(2/3)/(a+b*x^2)^(1/3))*sqrt(cos(arccos((c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1-sqrt(3))/(a+b*x^2)^(1/3))/(c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1+sqrt(3))/(a+b*x^2)^(1/3))))^2)/cos(arccos((c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1-sqrt(3))/(a+b*x^2)^(1/3))/(c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1+sqrt(3))/(a+b*x^2)^(1/3))))*EllipticF(sin(arccos((c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1-sqrt(3))/(a+b*x^2)^(1/3))/(c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1+sqrt(3))/(a+b*x^2)^(1/3)))),sqrt(1/4*(2+sqrt(3))))*sqrt((c^(4/3)+b^(2/3)*(c*x)^(4/3)/(a+b*x^2)^(2/3)+b^(1/3)*c^(2/3)*(c*x)^(2/3)/(a+b*x^2)^(1/3))/(c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1+sqrt(3))/(a+b*x^2)^(1/3))^2)/(a*c^(11/3)*sqrt(-b^(1/3)*(c*x)^(2/3)*(c^(2/3)-b^(1/3)*(c*x)^(2/3)/(a+b*x^2)^(1/3))/((a+b*x^2)^(1/3)*(c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1+sqrt(3))/(a+b*x^2)^(1/3))^2)))],
[(a+b*x^2)^(1/3)/(c*x)^(14/3),x,5,-3/11*(a+b*x^2)^(1/3)/(c*(c*x)^(11/3))-6/55*b*(a+b*x^2)^(1/3)/(a*c^3*(c*x)^(5/3))-3/55*3^(3/4)*b^2*(c*x)^(1/3)*(a+b*x^2)^(1/3)*(c^(2/3)-b^(1/3)*(c*x)^(2/3)/(a+b*x^2)^(1/3))*sqrt(cos(arccos((c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1-sqrt(3))/(a+b*x^2)^(1/3))/(c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1+sqrt(3))/(a+b*x^2)^(1/3))))^2)/cos(arccos((c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1-sqrt(3))/(a+b*x^2)^(1/3))/(c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1+sqrt(3))/(a+b*x^2)^(1/3))))*EllipticF(sin(arccos((c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1-sqrt(3))/(a+b*x^2)^(1/3))/(c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1+sqrt(3))/(a+b*x^2)^(1/3)))),sqrt(1/4*(2+sqrt(3))))*sqrt((c^(4/3)+b^(2/3)*(c*x)^(4/3)/(a+b*x^2)^(2/3)+b^(1/3)*c^(2/3)*(c*x)^(2/3)/(a+b*x^2)^(1/3))/(c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1+sqrt(3))/(a+b*x^2)^(1/3))^2)/(a^2*c^(17/3)*sqrt(-b^(1/3)*(c*x)^(2/3)*(c^(2/3)-b^(1/3)*(c*x)^(2/3)/(a+b*x^2)^(1/3))/((a+b*x^2)^(1/3)*(c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1+sqrt(3))/(a+b*x^2)^(1/3))^2)))],
[(c*x)^(2/3)*(a+b*x^2)^(1/3),x,2,3/5*(c*x)^(5/3)*(a+b*x^2)^(1/3)*hypergeom([-1/3,5/6],[11/6],-b*x^2/a)/(c*(1+b*x^2/a)^(1/3))],
[(a+b*x^2)^(1/3)/(c*x)^(1/3),x,2,3/2*(c*x)^(2/3)*(a+b*x^2)^(1/3)*hypergeom([-1/3,1/3],[4/3],-b*x^2/a)/(c*(1+b*x^2/a)^(1/3))],
[(a+b*x^2)^(1/3)/(c*x)^(4/3),x,2,-3*(a+b*x^2)^(1/3)*hypergeom([-1/3,-1/6],[5/6],-b*x^2/a)/(c*(c*x)^(1/3)*(1+b*x^2/a)^(1/3))],
[(c*x)^(13/3)*(a+b*x^2)^(4/3),x,7,-5/324*a^3*c^3*(c*x)^(4/3)*(a+b*x^2)^(1/3)/b^2+1/108*a^2*c*(c*x)^(10/3)*(a+b*x^2)^(1/3)/b+1/18*a*(c*x)^(16/3)*(a+b*x^2)^(1/3)/c+1/8*(c*x)^(16/3)*(a+b*x^2)^(4/3)/c-5/324*a^4*c^(13/3)*log(b^(1/3)*(c*x)^(2/3)-c^(2/3)*(a+b*x^2)^(1/3))/b^(8/3)-5/162*a^4*c^(13/3)*arctan((1+2*b^(1/3)*(c*x)^(2/3)/(c^(2/3)*(a+b*x^2)^(1/3)))/sqrt(3))/(b^(8/3)*sqrt(3))],
[(c*x)^(7/3)*(a+b*x^2)^(4/3),x,6,1/27*a^2*c*(c*x)^(4/3)*(a+b*x^2)^(1/3)/b+1/9*a*(c*x)^(10/3)*(a+b*x^2)^(1/3)/c+1/6*(c*x)^(10/3)*(a+b*x^2)^(4/3)/c+1/27*a^3*c^(7/3)*log(b^(1/3)*(c*x)^(2/3)-c^(2/3)*(a+b*x^2)^(1/3))/b^(5/3)+2/27*a^3*c^(7/3)*arctan((1+2*b^(1/3)*(c*x)^(2/3)/(c^(2/3)*(a+b*x^2)^(1/3)))/sqrt(3))/(b^(5/3)*sqrt(3))],
[(c*x)^(1/3)*(a+b*x^2)^(4/3),x,5,1/3*a*(c*x)^(4/3)*(a+b*x^2)^(1/3)/c+1/4*(c*x)^(4/3)*(a+b*x^2)^(4/3)/c-1/6*a^2*c^(1/3)*log(b^(1/3)*(c*x)^(2/3)-c^(2/3)*(a+b*x^2)^(1/3))/b^(2/3)-1/3*a^2*c^(1/3)*arctan((1+2*b^(1/3)*(c*x)^(2/3)/(c^(2/3)*(a+b*x^2)^(1/3)))/sqrt(3))/(b^(2/3)*sqrt(3))],
[(a+b*x^2)^(4/3)/(c*x)^(5/3),x,5,2*b*(c*x)^(4/3)*(a+b*x^2)^(1/3)/c^3-3/2*(a+b*x^2)^(4/3)/(c*(c*x)^(2/3))-a*b^(1/3)*log(b^(1/3)*(c*x)^(2/3)-c^(2/3)*(a+b*x^2)^(1/3))/c^(5/3)-2*a*b^(1/3)*arctan((1+2*b^(1/3)*(c*x)^(2/3)/(c^(2/3)*(a+b*x^2)^(1/3)))/sqrt(3))/(c^(5/3)*sqrt(3))],
[(a+b*x^2)^(4/3)/(c*x)^(11/3),x,5,-3/2*b*(a+b*x^2)^(1/3)/(c^3*(c*x)^(2/3))-3/8*(a+b*x^2)^(4/3)/(c*(c*x)^(8/3))-3/4*b^(4/3)*log(b^(1/3)*(c*x)^(2/3)-c^(2/3)*(a+b*x^2)^(1/3))/c^(11/3)-1/2*b^(4/3)*arctan((1+2*b^(1/3)*(c*x)^(2/3)/(c^(2/3)*(a+b*x^2)^(1/3)))/sqrt(3))*sqrt(3)/c^(11/3)],
[(a+b*x^2)^(4/3)/(c*x)^(17/3),x,1,-3/14*(a+b*x^2)^(7/3)/(a*c*(c*x)^(14/3))],
[(a+b*x^2)^(4/3)/(c*x)^(23/3),x,2,-3/14*(a+b*x^2)^(7/3)/(a*c*(c*x)^(20/3))+9/140*(a+b*x^2)^(10/3)/(a^2*c*(c*x)^(20/3))],
[(a+b*x^2)^(4/3)/(c*x)^(29/3),x,3,-3/14*(a+b*x^2)^(7/3)/(a*c*(c*x)^(26/3))+9/70*(a+b*x^2)^(10/3)/(a^2*c*(c*x)^(26/3))-27/910*(a+b*x^2)^(13/3)/(a^3*c*(c*x)^(26/3))],
[(c*x)^(10/3)*(a+b*x^2)^(4/3),x,7,-16/405*a^3*c^3*(c*x)^(1/3)*(a+b*x^2)^(1/3)/b^2+16/945*a^2*c*(c*x)^(7/3)*(a+b*x^2)^(1/3)/b+8/105*a*(c*x)^(13/3)*(a+b*x^2)^(1/3)/c+1/7*(c*x)^(13/3)*(a+b*x^2)^(4/3)/c+8/405*a^3*c^(7/3)*(c*x)^(1/3)*(a+b*x^2)^(1/3)*(c^(2/3)-b^(1/3)*(c*x)^(2/3)/(a+b*x^2)^(1/3))*sqrt(cos(arccos((c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1-sqrt(3))/(a+b*x^2)^(1/3))/(c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1+sqrt(3))/(a+b*x^2)^(1/3))))^2)/cos(arccos((c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1-sqrt(3))/(a+b*x^2)^(1/3))/(c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1+sqrt(3))/(a+b*x^2)^(1/3))))*EllipticF(sin(arccos((c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1-sqrt(3))/(a+b*x^2)^(1/3))/(c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1+sqrt(3))/(a+b*x^2)^(1/3)))),sqrt(1/4*(2+sqrt(3))))*sqrt((c^(4/3)+b^(2/3)*(c*x)^(4/3)/(a+b*x^2)^(2/3)+b^(1/3)*c^(2/3)*(c*x)^(2/3)/(a+b*x^2)^(1/3))/(c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1+sqrt(3))/(a+b*x^2)^(1/3))^2)/(3^(1/4)*b^2*sqrt(-b^(1/3)*(c*x)^(2/3)*(c^(2/3)-b^(1/3)*(c*x)^(2/3)/(a+b*x^2)^(1/3))/((a+b*x^2)^(1/3)*(c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1+sqrt(3))/(a+b*x^2)^(1/3))^2)))],
[(c*x)^(4/3)*(a+b*x^2)^(4/3),x,6,16/135*a^2*c*(c*x)^(1/3)*(a+b*x^2)^(1/3)/b+8/45*a*(c*x)^(7/3)*(a+b*x^2)^(1/3)/c+1/5*(c*x)^(7/3)*(a+b*x^2)^(4/3)/c-8/135*a^2*c^(1/3)*(c*x)^(1/3)*(a+b*x^2)^(1/3)*(c^(2/3)-b^(1/3)*(c*x)^(2/3)/(a+b*x^2)^(1/3))*sqrt(cos(arccos((c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1-sqrt(3))/(a+b*x^2)^(1/3))/(c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1+sqrt(3))/(a+b*x^2)^(1/3))))^2)/cos(arccos((c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1-sqrt(3))/(a+b*x^2)^(1/3))/(c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1+sqrt(3))/(a+b*x^2)^(1/3))))*EllipticF(sin(arccos((c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1-sqrt(3))/(a+b*x^2)^(1/3))/(c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1+sqrt(3))/(a+b*x^2)^(1/3)))),sqrt(1/4*(2+sqrt(3))))*sqrt((c^(4/3)+b^(2/3)*(c*x)^(4/3)/(a+b*x^2)^(2/3)+b^(1/3)*c^(2/3)*(c*x)^(2/3)/(a+b*x^2)^(1/3))/(c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1+sqrt(3))/(a+b*x^2)^(1/3))^2)/(3^(1/4)*b*sqrt(-b^(1/3)*(c*x)^(2/3)*(c^(2/3)-b^(1/3)*(c*x)^(2/3)/(a+b*x^2)^(1/3))/((a+b*x^2)^(1/3)*(c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1+sqrt(3))/(a+b*x^2)^(1/3))^2)))],
[(a+b*x^2)^(4/3)/(c*x)^(2/3),x,5,8/9*a*(c*x)^(1/3)*(a+b*x^2)^(1/3)/c+1/3*(c*x)^(1/3)*(a+b*x^2)^(4/3)/c+8/9*a*(c*x)^(1/3)*(a+b*x^2)^(1/3)*(c^(2/3)-b^(1/3)*(c*x)^(2/3)/(a+b*x^2)^(1/3))*sqrt(cos(arccos((c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1-sqrt(3))/(a+b*x^2)^(1/3))/(c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1+sqrt(3))/(a+b*x^2)^(1/3))))^2)/cos(arccos((c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1-sqrt(3))/(a+b*x^2)^(1/3))/(c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1+sqrt(3))/(a+b*x^2)^(1/3))))*EllipticF(sin(arccos((c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1-sqrt(3))/(a+b*x^2)^(1/3))/(c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1+sqrt(3))/(a+b*x^2)^(1/3)))),sqrt(1/4*(2+sqrt(3))))*sqrt((c^(4/3)+b^(2/3)*(c*x)^(4/3)/(a+b*x^2)^(2/3)+b^(1/3)*c^(2/3)*(c*x)^(2/3)/(a+b*x^2)^(1/3))/(c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1+sqrt(3))/(a+b*x^2)^(1/3))^2)/(3^(1/4)*c^(5/3)*sqrt(-b^(1/3)*(c*x)^(2/3)*(c^(2/3)-b^(1/3)*(c*x)^(2/3)/(a+b*x^2)^(1/3))/((a+b*x^2)^(1/3)*(c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1+sqrt(3))/(a+b*x^2)^(1/3))^2)))],
[(a+b*x^2)^(4/3)/(c*x)^(8/3),x,5,8/5*b*(c*x)^(1/3)*(a+b*x^2)^(1/3)/c^3-3/5*(a+b*x^2)^(4/3)/(c*(c*x)^(5/3))+8/5*b*(c*x)^(1/3)*(a+b*x^2)^(1/3)*(c^(2/3)-b^(1/3)*(c*x)^(2/3)/(a+b*x^2)^(1/3))*sqrt(cos(arccos((c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1-sqrt(3))/(a+b*x^2)^(1/3))/(c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1+sqrt(3))/(a+b*x^2)^(1/3))))^2)/cos(arccos((c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1-sqrt(3))/(a+b*x^2)^(1/3))/(c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1+sqrt(3))/(a+b*x^2)^(1/3))))*EllipticF(sin(arccos((c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1-sqrt(3))/(a+b*x^2)^(1/3))/(c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1+sqrt(3))/(a+b*x^2)^(1/3)))),sqrt(1/4*(2+sqrt(3))))*sqrt((c^(4/3)+b^(2/3)*(c*x)^(4/3)/(a+b*x^2)^(2/3)+b^(1/3)*c^(2/3)*(c*x)^(2/3)/(a+b*x^2)^(1/3))/(c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1+sqrt(3))/(a+b*x^2)^(1/3))^2)/(3^(1/4)*c^(11/3)*sqrt(-b^(1/3)*(c*x)^(2/3)*(c^(2/3)-b^(1/3)*(c*x)^(2/3)/(a+b*x^2)^(1/3))/((a+b*x^2)^(1/3)*(c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1+sqrt(3))/(a+b*x^2)^(1/3))^2)))],
[(a+b*x^2)^(4/3)/(c*x)^(14/3),x,5,-24/55*b*(a+b*x^2)^(1/3)/(c^3*(c*x)^(5/3))-3/11*(a+b*x^2)^(4/3)/(c*(c*x)^(11/3))+8/55*3^(3/4)*b^2*(c*x)^(1/3)*(a+b*x^2)^(1/3)*(c^(2/3)-b^(1/3)*(c*x)^(2/3)/(a+b*x^2)^(1/3))*sqrt(cos(arccos((c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1-sqrt(3))/(a+b*x^2)^(1/3))/(c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1+sqrt(3))/(a+b*x^2)^(1/3))))^2)/cos(arccos((c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1-sqrt(3))/(a+b*x^2)^(1/3))/(c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1+sqrt(3))/(a+b*x^2)^(1/3))))*EllipticF(sin(arccos((c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1-sqrt(3))/(a+b*x^2)^(1/3))/(c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1+sqrt(3))/(a+b*x^2)^(1/3)))),sqrt(1/4*(2+sqrt(3))))*sqrt((c^(4/3)+b^(2/3)*(c*x)^(4/3)/(a+b*x^2)^(2/3)+b^(1/3)*c^(2/3)*(c*x)^(2/3)/(a+b*x^2)^(1/3))/(c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1+sqrt(3))/(a+b*x^2)^(1/3))^2)/(a*c^(17/3)*sqrt(-b^(1/3)*(c*x)^(2/3)*(c^(2/3)-b^(1/3)*(c*x)^(2/3)/(a+b*x^2)^(1/3))/((a+b*x^2)^(1/3)*(c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1+sqrt(3))/(a+b*x^2)^(1/3))^2)))],
[(a+b*x^2)^(4/3)/(c*x)^(20/3),x,6,-24/187*b*(a+b*x^2)^(1/3)/(c^3*(c*x)^(11/3))-48/935*b^2*(a+b*x^2)^(1/3)/(a*c^5*(c*x)^(5/3))-3/17*(a+b*x^2)^(4/3)/(c*(c*x)^(17/3))-24/935*3^(3/4)*b^3*(c*x)^(1/3)*(a+b*x^2)^(1/3)*(c^(2/3)-b^(1/3)*(c*x)^(2/3)/(a+b*x^2)^(1/3))*sqrt(cos(arccos((c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1-sqrt(3))/(a+b*x^2)^(1/3))/(c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1+sqrt(3))/(a+b*x^2)^(1/3))))^2)/cos(arccos((c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1-sqrt(3))/(a+b*x^2)^(1/3))/(c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1+sqrt(3))/(a+b*x^2)^(1/3))))*EllipticF(sin(arccos((c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1-sqrt(3))/(a+b*x^2)^(1/3))/(c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1+sqrt(3))/(a+b*x^2)^(1/3)))),sqrt(1/4*(2+sqrt(3))))*sqrt((c^(4/3)+b^(2/3)*(c*x)^(4/3)/(a+b*x^2)^(2/3)+b^(1/3)*c^(2/3)*(c*x)^(2/3)/(a+b*x^2)^(1/3))/(c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1+sqrt(3))/(a+b*x^2)^(1/3))^2)/(a^2*c^(23/3)*sqrt(-b^(1/3)*(c*x)^(2/3)*(c^(2/3)-b^(1/3)*(c*x)^(2/3)/(a+b*x^2)^(1/3))/((a+b*x^2)^(1/3)*(c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1+sqrt(3))/(a+b*x^2)^(1/3))^2)))],
[(c*x)^(2/3)*(a+b*x^2)^(4/3),x,2,3/5*a*(c*x)^(5/3)*(a+b*x^2)^(1/3)*hypergeom([-4/3,5/6],[11/6],-b*x^2/a)/(c*(1+b*x^2/a)^(1/3))],
[(a+b*x^2)^(4/3)/(c*x)^(1/3),x,2,3/2*a*(c*x)^(2/3)*(a+b*x^2)^(1/3)*hypergeom([-4/3,1/3],[4/3],-b*x^2/a)/(c*(1+b*x^2/a)^(1/3))],
[(a+b*x^2)^(4/3)/(c*x)^(4/3),x,2,-3*a*(a+b*x^2)^(1/3)*hypergeom([-4/3,-1/6],[5/6],-b*x^2/a)/(c*(c*x)^(1/3)*(1+b*x^2/a)^(1/3))],

# p<0
[(c*x)^(19/3)/(a+b*x^2)^(2/3),x,6,10/27*a^2*c^5*(c*x)^(4/3)*(a+b*x^2)^(1/3)/b^3-2/9*a*c^3*(c*x)^(10/3)*(a+b*x^2)^(1/3)/b^2+1/6*c*(c*x)^(16/3)*(a+b*x^2)^(1/3)/b+10/27*a^3*c^(19/3)*log(b^(1/3)*(c*x)^(2/3)-c^(2/3)*(a+b*x^2)^(1/3))/b^(11/3)+20/27*a^3*c^(19/3)*arctan((1+2*b^(1/3)*(c*x)^(2/3)/(c^(2/3)*(a+b*x^2)^(1/3)))/sqrt(3))/(b^(11/3)*sqrt(3))],
[(c*x)^(13/3)/(a+b*x^2)^(2/3),x,5,-5/12*a*c^3*(c*x)^(4/3)*(a+b*x^2)^(1/3)/b^2+1/4*c*(c*x)^(10/3)*(a+b*x^2)^(1/3)/b-5/12*a^2*c^(13/3)*log(b^(1/3)*(c*x)^(2/3)-c^(2/3)*(a+b*x^2)^(1/3))/b^(8/3)-5/6*a^2*c^(13/3)*arctan((1+2*b^(1/3)*(c*x)^(2/3)/(c^(2/3)*(a+b*x^2)^(1/3)))/sqrt(3))/(b^(8/3)*sqrt(3))],
[(c*x)^(7/3)/(a+b*x^2)^(2/3),x,4,1/2*c*(c*x)^(4/3)*(a+b*x^2)^(1/3)/b+1/2*a*c^(7/3)*log(b^(1/3)*(c*x)^(2/3)-c^(2/3)*(a+b*x^2)^(1/3))/b^(5/3)+a*c^(7/3)*arctan((1+2*b^(1/3)*(c*x)^(2/3)/(c^(2/3)*(a+b*x^2)^(1/3)))/sqrt(3))/(b^(5/3)*sqrt(3))],
[(c*x)^(1/3)/(a+b*x^2)^(2/3),x,3,-3/4*c^(1/3)*log(b^(1/3)*(c*x)^(2/3)-c^(2/3)*(a+b*x^2)^(1/3))/b^(2/3)-1/2*c^(1/3)*arctan((1+2*b^(1/3)*(c*x)^(2/3)/(c^(2/3)*(a+b*x^2)^(1/3)))/sqrt(3))*sqrt(3)/b^(2/3)],
[1/((c*x)^(5/3)*(a+b*x^2)^(2/3)),x,1,-3/2*(a+b*x^2)^(1/3)/(a*c*(c*x)^(2/3))],
[1/((c*x)^(11/3)*(a+b*x^2)^(2/3)),x,2,-3/2*(a+b*x^2)^(1/3)/(a*c*(c*x)^(8/3))+9/8*(a+b*x^2)^(4/3)/(a^2*c*(c*x)^(8/3))],
[1/((c*x)^(17/3)*(a+b*x^2)^(2/3)),x,3,-3/2*(a+b*x^2)^(1/3)/(a*c*(c*x)^(14/3))+9/4*(a+b*x^2)^(4/3)/(a^2*c*(c*x)^(14/3))-27/28*(a+b*x^2)^(7/3)/(a^3*c*(c*x)^(14/3))],
[1/((c*x)^(23/3)*(a+b*x^2)^(2/3)),x,4,-3/2*(a+b*x^2)^(1/3)/(a*c*(c*x)^(20/3))+27/8*(a+b*x^2)^(4/3)/(a^2*c*(c*x)^(20/3))-81/28*(a+b*x^2)^(7/3)/(a^3*c*(c*x)^(20/3))+243/280*(a+b*x^2)^(10/3)/(a^4*c*(c*x)^(20/3))],
[(c*x)^(10/3)/(a+b*x^2)^(2/3),x,5,-7/9*a*c^3*(c*x)^(1/3)*(a+b*x^2)^(1/3)/b^2+1/3*c*(c*x)^(7/3)*(a+b*x^2)^(1/3)/b+7/18*a*c^(7/3)*(c*x)^(1/3)*(a+b*x^2)^(1/3)*(c^(2/3)-b^(1/3)*(c*x)^(2/3)/(a+b*x^2)^(1/3))*sqrt(cos(arccos((c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1-sqrt(3))/(a+b*x^2)^(1/3))/(c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1+sqrt(3))/(a+b*x^2)^(1/3))))^2)/cos(arccos((c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1-sqrt(3))/(a+b*x^2)^(1/3))/(c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1+sqrt(3))/(a+b*x^2)^(1/3))))*EllipticF(sin(arccos((c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1-sqrt(3))/(a+b*x^2)^(1/3))/(c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1+sqrt(3))/(a+b*x^2)^(1/3)))),sqrt(1/4*(2+sqrt(3))))*sqrt((c^(4/3)+b^(2/3)*(c*x)^(4/3)/(a+b*x^2)^(2/3)+b^(1/3)*c^(2/3)*(c*x)^(2/3)/(a+b*x^2)^(1/3))/(c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1+sqrt(3))/(a+b*x^2)^(1/3))^2)/(3^(1/4)*b^2*sqrt(-b^(1/3)*(c*x)^(2/3)*(c^(2/3)-b^(1/3)*(c*x)^(2/3)/(a+b*x^2)^(1/3))/((a+b*x^2)^(1/3)*(c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1+sqrt(3))/(a+b*x^2)^(1/3))^2)))],
[(c*x)^(4/3)/(a+b*x^2)^(2/3),x,4,c*(c*x)^(1/3)*(a+b*x^2)^(1/3)/b-1/2*c^(1/3)*(c*x)^(1/3)*(a+b*x^2)^(1/3)*(c^(2/3)-b^(1/3)*(c*x)^(2/3)/(a+b*x^2)^(1/3))*sqrt(cos(arccos((c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1-sqrt(3))/(a+b*x^2)^(1/3))/(c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1+sqrt(3))/(a+b*x^2)^(1/3))))^2)/cos(arccos((c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1-sqrt(3))/(a+b*x^2)^(1/3))/(c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1+sqrt(3))/(a+b*x^2)^(1/3))))*EllipticF(sin(arccos((c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1-sqrt(3))/(a+b*x^2)^(1/3))/(c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1+sqrt(3))/(a+b*x^2)^(1/3)))),sqrt(1/4*(2+sqrt(3))))*sqrt((c^(4/3)+b^(2/3)*(c*x)^(4/3)/(a+b*x^2)^(2/3)+b^(1/3)*c^(2/3)*(c*x)^(2/3)/(a+b*x^2)^(1/3))/(c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1+sqrt(3))/(a+b*x^2)^(1/3))^2)/(3^(1/4)*b*sqrt(-b^(1/3)*(c*x)^(2/3)*(c^(2/3)-b^(1/3)*(c*x)^(2/3)/(a+b*x^2)^(1/3))/((a+b*x^2)^(1/3)*(c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1+sqrt(3))/(a+b*x^2)^(1/3))^2)))],
[1/((c*x)^(2/3)*(a+b*x^2)^(2/3)),x,3,1/2*3^(3/4)*(c*x)^(1/3)*(a+b*x^2)^(1/3)*(c^(2/3)-b^(1/3)*(c*x)^(2/3)/(a+b*x^2)^(1/3))*sqrt(cos(arccos((c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1-sqrt(3))/(a+b*x^2)^(1/3))/(c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1+sqrt(3))/(a+b*x^2)^(1/3))))^2)/cos(arccos((c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1-sqrt(3))/(a+b*x^2)^(1/3))/(c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1+sqrt(3))/(a+b*x^2)^(1/3))))*EllipticF(sin(arccos((c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1-sqrt(3))/(a+b*x^2)^(1/3))/(c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1+sqrt(3))/(a+b*x^2)^(1/3)))),sqrt(1/4*(2+sqrt(3))))*sqrt((c^(4/3)+b^(2/3)*(c*x)^(4/3)/(a+b*x^2)^(2/3)+b^(1/3)*c^(2/3)*(c*x)^(2/3)/(a+b*x^2)^(1/3))/(c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1+sqrt(3))/(a+b*x^2)^(1/3))^2)/(a*c^(5/3)*sqrt(-b^(1/3)*(c*x)^(2/3)*(c^(2/3)-b^(1/3)*(c*x)^(2/3)/(a+b*x^2)^(1/3))/((a+b*x^2)^(1/3)*(c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1+sqrt(3))/(a+b*x^2)^(1/3))^2)))],
[1/((c*x)^(8/3)*(a+b*x^2)^(2/3)),x,4,-3/5*(a+b*x^2)^(1/3)/(a*c*(c*x)^(5/3))-3/10*3^(3/4)*b*(c*x)^(1/3)*(a+b*x^2)^(1/3)*(c^(2/3)-b^(1/3)*(c*x)^(2/3)/(a+b*x^2)^(1/3))*sqrt(cos(arccos((c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1-sqrt(3))/(a+b*x^2)^(1/3))/(c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1+sqrt(3))/(a+b*x^2)^(1/3))))^2)/cos(arccos((c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1-sqrt(3))/(a+b*x^2)^(1/3))/(c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1+sqrt(3))/(a+b*x^2)^(1/3))))*EllipticF(sin(arccos((c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1-sqrt(3))/(a+b*x^2)^(1/3))/(c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1+sqrt(3))/(a+b*x^2)^(1/3)))),sqrt(1/4*(2+sqrt(3))))*sqrt((c^(4/3)+b^(2/3)*(c*x)^(4/3)/(a+b*x^2)^(2/3)+b^(1/3)*c^(2/3)*(c*x)^(2/3)/(a+b*x^2)^(1/3))/(c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1+sqrt(3))/(a+b*x^2)^(1/3))^2)/(a^2*c^(11/3)*sqrt(-b^(1/3)*(c*x)^(2/3)*(c^(2/3)-b^(1/3)*(c*x)^(2/3)/(a+b*x^2)^(1/3))/((a+b*x^2)^(1/3)*(c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1+sqrt(3))/(a+b*x^2)^(1/3))^2)))],
[1/((c*x)^(14/3)*(a+b*x^2)^(2/3)),x,5,-3/11*(a+b*x^2)^(1/3)/(a*c*(c*x)^(11/3))+27/55*b*(a+b*x^2)^(1/3)/(a^2*c^3*(c*x)^(5/3))+27/110*3^(3/4)*b^2*(c*x)^(1/3)*(a+b*x^2)^(1/3)*(c^(2/3)-b^(1/3)*(c*x)^(2/3)/(a+b*x^2)^(1/3))*sqrt(cos(arccos((c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1-sqrt(3))/(a+b*x^2)^(1/3))/(c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1+sqrt(3))/(a+b*x^2)^(1/3))))^2)/cos(arccos((c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1-sqrt(3))/(a+b*x^2)^(1/3))/(c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1+sqrt(3))/(a+b*x^2)^(1/3))))*EllipticF(sin(arccos((c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1-sqrt(3))/(a+b*x^2)^(1/3))/(c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1+sqrt(3))/(a+b*x^2)^(1/3)))),sqrt(1/4*(2+sqrt(3))))*sqrt((c^(4/3)+b^(2/3)*(c*x)^(4/3)/(a+b*x^2)^(2/3)+b^(1/3)*c^(2/3)*(c*x)^(2/3)/(a+b*x^2)^(1/3))/(c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1+sqrt(3))/(a+b*x^2)^(1/3))^2)/(a^3*c^(17/3)*sqrt(-b^(1/3)*(c*x)^(2/3)*(c^(2/3)-b^(1/3)*(c*x)^(2/3)/(a+b*x^2)^(1/3))/((a+b*x^2)^(1/3)*(c^(2/3)-b^(1/3)*(c*x)^(2/3)*(1+sqrt(3))/(a+b*x^2)^(1/3))^2)))],
[(c*x)^(2/3)/(a+b*x^2)^(2/3),x,2,3/5*(c*x)^(5/3)*(1+b*x^2/a)^(2/3)*hypergeom([2/3,5/6],[11/6],-b*x^2/a)/(c*(a+b*x^2)^(2/3))],
[1/((c*x)^(1/3)*(a+b*x^2)^(2/3)),x,2,3/2*(c*x)^(2/3)*(1+b*x^2/a)^(2/3)*hypergeom([1/3,2/3],[4/3],-b*x^2/a)/(c*(a+b*x^2)^(2/3))],
[1/((c*x)^(4/3)*(a+b*x^2)^(2/3)),x,2,-3*(1+b*x^2/a)^(2/3)*hypergeom([-1/6,2/3],[5/6],-b*x^2/a)/(c*(c*x)^(1/3)*(a+b*x^2)^(2/3))],

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

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

# p>0
[x^4*(a+b*x^2)^(1/4),x,5,-4/77*a^2*x*(a+b*x^2)^(1/4)/b^2+2/77*a*x^3*(a+b*x^2)^(1/4)/b+2/11*x^5*(a+b*x^2)^(1/4)+8/77*a^(7/2)*(1+b*x^2/a)^(3/4)*sqrt(cos(1/2*arctan(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arctan(x*sqrt(b)/sqrt(a)))*EllipticF(sin(1/2*arctan(x*sqrt(b)/sqrt(a))),sqrt(2))/(b^(5/2)*(a+b*x^2)^(3/4))],
[x^2*(a+b*x^2)^(1/4),x,4,2/21*a*x*(a+b*x^2)^(1/4)/b+2/7*x^3*(a+b*x^2)^(1/4)-4/21*a^(5/2)*(1+b*x^2/a)^(3/4)*sqrt(cos(1/2*arctan(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arctan(x*sqrt(b)/sqrt(a)))*EllipticF(sin(1/2*arctan(x*sqrt(b)/sqrt(a))),sqrt(2))/(b^(3/2)*(a+b*x^2)^(3/4))],
[(a+b*x^2)^(1/4),x,3,2/3*x*(a+b*x^2)^(1/4)+2/3*a^(3/2)*(1+b*x^2/a)^(3/4)*sqrt(cos(1/2*arctan(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arctan(x*sqrt(b)/sqrt(a)))*EllipticF(sin(1/2*arctan(x*sqrt(b)/sqrt(a))),sqrt(2))/((a+b*x^2)^(3/4)*sqrt(b))],
[(a+b*x^2)^(1/4)/x^2,x,3,-(a+b*x^2)^(1/4)/x+(1+b*x^2/a)^(3/4)*sqrt(cos(1/2*arctan(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arctan(x*sqrt(b)/sqrt(a)))*EllipticF(sin(1/2*arctan(x*sqrt(b)/sqrt(a))),sqrt(2))*sqrt(a)*sqrt(b)/(a+b*x^2)^(3/4)],
[(a+b*x^2)^(1/4)/x^4,x,4,-1/3*(a+b*x^2)^(1/4)/x^3-1/6*b*(a+b*x^2)^(1/4)/(a*x)-1/6*b^(3/2)*(1+b*x^2/a)^(3/4)*sqrt(cos(1/2*arctan(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arctan(x*sqrt(b)/sqrt(a)))*EllipticF(sin(1/2*arctan(x*sqrt(b)/sqrt(a))),sqrt(2))/((a+b*x^2)^(3/4)*sqrt(a))],
[(a+b*x^2)^(1/4)/x^6,x,5,-1/5*(a+b*x^2)^(1/4)/x^5-1/30*b*(a+b*x^2)^(1/4)/(a*x^3)+1/12*b^2*(a+b*x^2)^(1/4)/(a^2*x)+1/12*b^(5/2)*(1+b*x^2/a)^(3/4)*sqrt(cos(1/2*arctan(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arctan(x*sqrt(b)/sqrt(a)))*EllipticF(sin(1/2*arctan(x*sqrt(b)/sqrt(a))),sqrt(2))/(a^(3/2)*(a+b*x^2)^(3/4))],
[x^4*(a-b*x^2)^(1/4),x,5,-4/77*a^2*x*(a-b*x^2)^(1/4)/b^2-2/77*a*x^3*(a-b*x^2)^(1/4)/b+2/11*x^5*(a-b*x^2)^(1/4)+8/77*a^(7/2)*(1-b*x^2/a)^(3/4)*sqrt(cos(1/2*arcsin(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arcsin(x*sqrt(b)/sqrt(a)))*EllipticF(sin(1/2*arcsin(x*sqrt(b)/sqrt(a))),sqrt(2))/(b^(5/2)*(a-b*x^2)^(3/4))],
[x^2*(a-b*x^2)^(1/4),x,4,-2/21*a*x*(a-b*x^2)^(1/4)/b+2/7*x^3*(a-b*x^2)^(1/4)+4/21*a^(5/2)*(1-b*x^2/a)^(3/4)*sqrt(cos(1/2*arcsin(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arcsin(x*sqrt(b)/sqrt(a)))*EllipticF(sin(1/2*arcsin(x*sqrt(b)/sqrt(a))),sqrt(2))/(b^(3/2)*(a-b*x^2)^(3/4))],
[(a-b*x^2)^(1/4),x,3,2/3*x*(a-b*x^2)^(1/4)+2/3*a^(3/2)*(1-b*x^2/a)^(3/4)*sqrt(cos(1/2*arcsin(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arcsin(x*sqrt(b)/sqrt(a)))*EllipticF(sin(1/2*arcsin(x*sqrt(b)/sqrt(a))),sqrt(2))/((a-b*x^2)^(3/4)*sqrt(b))],
[(a-b*x^2)^(1/4)/x^2,x,3,-(a-b*x^2)^(1/4)/x-(1-b*x^2/a)^(3/4)*sqrt(cos(1/2*arcsin(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arcsin(x*sqrt(b)/sqrt(a)))*EllipticF(sin(1/2*arcsin(x*sqrt(b)/sqrt(a))),sqrt(2))*sqrt(a)*sqrt(b)/(a-b*x^2)^(3/4)],
[(a-b*x^2)^(1/4)/x^4,x,4,-1/3*(a-b*x^2)^(1/4)/x^3+1/6*b*(a-b*x^2)^(1/4)/(a*x)-1/6*b^(3/2)*(1-b*x^2/a)^(3/4)*sqrt(cos(1/2*arcsin(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arcsin(x*sqrt(b)/sqrt(a)))*EllipticF(sin(1/2*arcsin(x*sqrt(b)/sqrt(a))),sqrt(2))/((a-b*x^2)^(3/4)*sqrt(a))],
[(a-b*x^2)^(1/4)/x^6,x,5,-1/5*(a-b*x^2)^(1/4)/x^5+1/30*b*(a-b*x^2)^(1/4)/(a*x^3)+1/12*b^2*(a-b*x^2)^(1/4)/(a^2*x)-1/12*b^(5/2)*(1-b*x^2/a)^(3/4)*sqrt(cos(1/2*arcsin(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arcsin(x*sqrt(b)/sqrt(a)))*EllipticF(sin(1/2*arcsin(x*sqrt(b)/sqrt(a))),sqrt(2))/(a^(3/2)*(a-b*x^2)^(3/4))],
[x^4*(a+b*x^2)^(3/4),x,6,8/65*a^3*x/(b^2*(a+b*x^2)^(1/4))-4/65*a^2*x*(a+b*x^2)^(3/4)/b^2+2/39*a*x^3*(a+b*x^2)^(3/4)/b+2/13*x^5*(a+b*x^2)^(3/4)-8/65*a^(7/2)*(1+b*x^2/a)^(1/4)*sqrt(cos(1/2*arctan(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arctan(x*sqrt(b)/sqrt(a)))*EllipticE(sin(1/2*arctan(x*sqrt(b)/sqrt(a))),sqrt(2))/(b^(5/2)*(a+b*x^2)^(1/4))],
[x^2*(a+b*x^2)^(3/4),x,5,-4/15*a^2*x/(b*(a+b*x^2)^(1/4))+2/15*a*x*(a+b*x^2)^(3/4)/b+2/9*x^3*(a+b*x^2)^(3/4)+4/15*a^(5/2)*(1+b*x^2/a)^(1/4)*sqrt(cos(1/2*arctan(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arctan(x*sqrt(b)/sqrt(a)))*EllipticE(sin(1/2*arctan(x*sqrt(b)/sqrt(a))),sqrt(2))/(b^(3/2)*(a+b*x^2)^(1/4))],
[(a+b*x^2)^(3/4),x,4,6/5*a*x/(a+b*x^2)^(1/4)+2/5*x*(a+b*x^2)^(3/4)-6/5*a^(3/2)*(1+b*x^2/a)^(1/4)*sqrt(cos(1/2*arctan(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arctan(x*sqrt(b)/sqrt(a)))*EllipticE(sin(1/2*arctan(x*sqrt(b)/sqrt(a))),sqrt(2))/((a+b*x^2)^(1/4)*sqrt(b))],
[(a+b*x^2)^(3/4)/x^2,x,4,3*b*x/(a+b*x^2)^(1/4)-(a+b*x^2)^(3/4)/x-3*(1+b*x^2/a)^(1/4)*sqrt(cos(1/2*arctan(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arctan(x*sqrt(b)/sqrt(a)))*EllipticE(sin(1/2*arctan(x*sqrt(b)/sqrt(a))),sqrt(2))*sqrt(a)*sqrt(b)/(a+b*x^2)^(1/4)],
[(a+b*x^2)^(3/4)/x^4,x,5,1/2*b^2*x/(a*(a+b*x^2)^(1/4))-1/3*(a+b*x^2)^(3/4)/x^3-1/2*b*(a+b*x^2)^(3/4)/(a*x)-1/2*b^(3/2)*(1+b*x^2/a)^(1/4)*sqrt(cos(1/2*arctan(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arctan(x*sqrt(b)/sqrt(a)))*EllipticE(sin(1/2*arctan(x*sqrt(b)/sqrt(a))),sqrt(2))/((a+b*x^2)^(1/4)*sqrt(a))],
[(a+b*x^2)^(3/4)/x^6,x,6,-3/20*b^3*x/(a^2*(a+b*x^2)^(1/4))-1/5*(a+b*x^2)^(3/4)/x^5-1/10*b*(a+b*x^2)^(3/4)/(a*x^3)+3/20*b^2*(a+b*x^2)^(3/4)/(a^2*x)+3/20*b^(5/2)*(1+b*x^2/a)^(1/4)*sqrt(cos(1/2*arctan(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arctan(x*sqrt(b)/sqrt(a)))*EllipticE(sin(1/2*arctan(x*sqrt(b)/sqrt(a))),sqrt(2))/(a^(3/2)*(a+b*x^2)^(1/4))],
[x^4*(a-b*x^2)^(3/4),x,5,-4/65*a^2*x*(a-b*x^2)^(3/4)/b^2-2/39*a*x^3*(a-b*x^2)^(3/4)/b+2/13*x^5*(a-b*x^2)^(3/4)+8/65*a^(7/2)*(1-b*x^2/a)^(1/4)*sqrt(cos(1/2*arcsin(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arcsin(x*sqrt(b)/sqrt(a)))*EllipticE(sin(1/2*arcsin(x*sqrt(b)/sqrt(a))),sqrt(2))/(b^(5/2)*(a-b*x^2)^(1/4))],
[x^2*(a-b*x^2)^(3/4),x,4,-2/15*a*x*(a-b*x^2)^(3/4)/b+2/9*x^3*(a-b*x^2)^(3/4)+4/15*a^(5/2)*(1-b*x^2/a)^(1/4)*sqrt(cos(1/2*arcsin(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arcsin(x*sqrt(b)/sqrt(a)))*EllipticE(sin(1/2*arcsin(x*sqrt(b)/sqrt(a))),sqrt(2))/(b^(3/2)*(a-b*x^2)^(1/4))],
[(a-b*x^2)^(3/4),x,3,2/5*x*(a-b*x^2)^(3/4)+6/5*a^(3/2)*(1-b*x^2/a)^(1/4)*sqrt(cos(1/2*arcsin(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arcsin(x*sqrt(b)/sqrt(a)))*EllipticE(sin(1/2*arcsin(x*sqrt(b)/sqrt(a))),sqrt(2))/((a-b*x^2)^(1/4)*sqrt(b))],
[(a-b*x^2)^(3/4)/x^2,x,3,-(a-b*x^2)^(3/4)/x-3*(1-b*x^2/a)^(1/4)*sqrt(cos(1/2*arcsin(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arcsin(x*sqrt(b)/sqrt(a)))*EllipticE(sin(1/2*arcsin(x*sqrt(b)/sqrt(a))),sqrt(2))*sqrt(a)*sqrt(b)/(a-b*x^2)^(1/4)],
[(a-b*x^2)^(3/4)/x^4,x,4,-1/3*(a-b*x^2)^(3/4)/x^3+1/2*b*(a-b*x^2)^(3/4)/(a*x)+1/2*b^(3/2)*(1-b*x^2/a)^(1/4)*sqrt(cos(1/2*arcsin(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arcsin(x*sqrt(b)/sqrt(a)))*EllipticE(sin(1/2*arcsin(x*sqrt(b)/sqrt(a))),sqrt(2))/((a-b*x^2)^(1/4)*sqrt(a))],
[(a-b*x^2)^(3/4)/x^6,x,5,-1/5*(a-b*x^2)^(3/4)/x^5+1/10*b*(a-b*x^2)^(3/4)/(a*x^3)+3/20*b^2*(a-b*x^2)^(3/4)/(a^2*x)+3/20*b^(5/2)*(1-b*x^2/a)^(1/4)*sqrt(cos(1/2*arcsin(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arcsin(x*sqrt(b)/sqrt(a)))*EllipticE(sin(1/2*arcsin(x*sqrt(b)/sqrt(a))),sqrt(2))/(a^(3/2)*(a-b*x^2)^(1/4))],
[(a+b*x^2)^(5/4),x,4,10/21*a*x*(a+b*x^2)^(1/4)+2/7*x*(a+b*x^2)^(5/4)+10/21*a^(5/2)*(1+b*x^2/a)^(3/4)*sqrt(cos(1/2*arctan(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arctan(x*sqrt(b)/sqrt(a)))*EllipticF(sin(1/2*arctan(x*sqrt(b)/sqrt(a))),sqrt(2))/((a+b*x^2)^(3/4)*sqrt(b))],
[(a-b*x^2)^(5/4),x,4,10/21*a*x*(a-b*x^2)^(1/4)+2/7*x*(a-b*x^2)^(5/4)+10/21*a^(5/2)*(1-b*x^2/a)^(3/4)*sqrt(cos(1/2*arcsin(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arcsin(x*sqrt(b)/sqrt(a)))*EllipticF(sin(1/2*arcsin(x*sqrt(b)/sqrt(a))),sqrt(2))/((a-b*x^2)^(3/4)*sqrt(b))],
[(a+b*x^2)^(7/4),x,5,14/15*a^2*x/(a+b*x^2)^(1/4)+14/45*a*x*(a+b*x^2)^(3/4)+2/9*x*(a+b*x^2)^(7/4)-14/15*a^(5/2)*(1+b*x^2/a)^(1/4)*sqrt(cos(1/2*arctan(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arctan(x*sqrt(b)/sqrt(a)))*EllipticE(sin(1/2*arctan(x*sqrt(b)/sqrt(a))),sqrt(2))/((a+b*x^2)^(1/4)*sqrt(b))],
[(a-b*x^2)^(7/4),x,4,14/45*a*x*(a-b*x^2)^(3/4)+2/9*x*(a-b*x^2)^(7/4)+14/15*a^(5/2)*(1-b*x^2/a)^(1/4)*sqrt(cos(1/2*arcsin(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arcsin(x*sqrt(b)/sqrt(a)))*EllipticE(sin(1/2*arcsin(x*sqrt(b)/sqrt(a))),sqrt(2))/((a-b*x^2)^(1/4)*sqrt(b))],

# p<0
[x^6/(a+b*x^2)^(1/4),x,6,-16/39*a^3*x/(b^3*(a+b*x^2)^(1/4))+8/39*a^2*x*(a+b*x^2)^(3/4)/b^3-20/117*a*x^3*(a+b*x^2)^(3/4)/b^2+2/13*x^5*(a+b*x^2)^(3/4)/b+16/39*a^(7/2)*(1+b*x^2/a)^(1/4)*sqrt(cos(1/2*arctan(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arctan(x*sqrt(b)/sqrt(a)))*EllipticE(sin(1/2*arctan(x*sqrt(b)/sqrt(a))),sqrt(2))/(b^(7/2)*(a+b*x^2)^(1/4))],
[x^4/(a+b*x^2)^(1/4),x,5,8/15*a^2*x/(b^2*(a+b*x^2)^(1/4))-4/15*a*x*(a+b*x^2)^(3/4)/b^2+2/9*x^3*(a+b*x^2)^(3/4)/b-8/15*a^(5/2)*(1+b*x^2/a)^(1/4)*sqrt(cos(1/2*arctan(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arctan(x*sqrt(b)/sqrt(a)))*EllipticE(sin(1/2*arctan(x*sqrt(b)/sqrt(a))),sqrt(2))/(b^(5/2)*(a+b*x^2)^(1/4))],
[x^2/(a+b*x^2)^(1/4),x,4,-4/5*a*x/(b*(a+b*x^2)^(1/4))+2/5*x*(a+b*x^2)^(3/4)/b+4/5*a^(3/2)*(1+b*x^2/a)^(1/4)*sqrt(cos(1/2*arctan(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arctan(x*sqrt(b)/sqrt(a)))*EllipticE(sin(1/2*arctan(x*sqrt(b)/sqrt(a))),sqrt(2))/(b^(3/2)*(a+b*x^2)^(1/4))],
[1/(a+b*x^2)^(1/4),x,3,2*x/(a+b*x^2)^(1/4)-2*(1+b*x^2/a)^(1/4)*sqrt(cos(1/2*arctan(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arctan(x*sqrt(b)/sqrt(a)))*EllipticE(sin(1/2*arctan(x*sqrt(b)/sqrt(a))),sqrt(2))*sqrt(a)/((a+b*x^2)^(1/4)*sqrt(b))],
[1/(x^2*(a+b*x^2)^(1/4)),x,4,b*x/(a*(a+b*x^2)^(1/4))-(a+b*x^2)^(3/4)/(a*x)-(1+b*x^2/a)^(1/4)*sqrt(cos(1/2*arctan(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arctan(x*sqrt(b)/sqrt(a)))*EllipticE(sin(1/2*arctan(x*sqrt(b)/sqrt(a))),sqrt(2))*sqrt(b)/((a+b*x^2)^(1/4)*sqrt(a))],
[1/(x^4*(a+b*x^2)^(1/4)),x,5,-1/2*b^2*x/(a^2*(a+b*x^2)^(1/4))-1/3*(a+b*x^2)^(3/4)/(a*x^3)+1/2*b*(a+b*x^2)^(3/4)/(a^2*x)+1/2*b^(3/2)*(1+b*x^2/a)^(1/4)*sqrt(cos(1/2*arctan(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arctan(x*sqrt(b)/sqrt(a)))*EllipticE(sin(1/2*arctan(x*sqrt(b)/sqrt(a))),sqrt(2))/(a^(3/2)*(a+b*x^2)^(1/4))],
[1/(x^6*(a+b*x^2)^(1/4)),x,6,7/20*b^3*x/(a^3*(a+b*x^2)^(1/4))-1/5*(a+b*x^2)^(3/4)/(a*x^5)+7/30*b*(a+b*x^2)^(3/4)/(a^2*x^3)-7/20*b^2*(a+b*x^2)^(3/4)/(a^3*x)-7/20*b^(5/2)*(1+b*x^2/a)^(1/4)*sqrt(cos(1/2*arctan(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arctan(x*sqrt(b)/sqrt(a)))*EllipticE(sin(1/2*arctan(x*sqrt(b)/sqrt(a))),sqrt(2))/(a^(5/2)*(a+b*x^2)^(1/4))],
[x^6/(a-b*x^2)^(1/4),x,5,-8/39*a^2*x*(a-b*x^2)^(3/4)/b^3-20/117*a*x^3*(a-b*x^2)^(3/4)/b^2-2/13*x^5*(a-b*x^2)^(3/4)/b+16/39*a^(7/2)*(1-b*x^2/a)^(1/4)*sqrt(cos(1/2*arcsin(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arcsin(x*sqrt(b)/sqrt(a)))*EllipticE(sin(1/2*arcsin(x*sqrt(b)/sqrt(a))),sqrt(2))/(b^(7/2)*(a-b*x^2)^(1/4))],
[x^4/(a-b*x^2)^(1/4),x,4,-4/15*a*x*(a-b*x^2)^(3/4)/b^2-2/9*x^3*(a-b*x^2)^(3/4)/b+8/15*a^(5/2)*(1-b*x^2/a)^(1/4)*sqrt(cos(1/2*arcsin(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arcsin(x*sqrt(b)/sqrt(a)))*EllipticE(sin(1/2*arcsin(x*sqrt(b)/sqrt(a))),sqrt(2))/(b^(5/2)*(a-b*x^2)^(1/4))],
[x^2/(a-b*x^2)^(1/4),x,3,-2/5*x*(a-b*x^2)^(3/4)/b+4/5*a^(3/2)*(1-b*x^2/a)^(1/4)*sqrt(cos(1/2*arcsin(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arcsin(x*sqrt(b)/sqrt(a)))*EllipticE(sin(1/2*arcsin(x*sqrt(b)/sqrt(a))),sqrt(2))/(b^(3/2)*(a-b*x^2)^(1/4))],
[1/(a-b*x^2)^(1/4),x,2,2*(1-b*x^2/a)^(1/4)*sqrt(cos(1/2*arcsin(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arcsin(x*sqrt(b)/sqrt(a)))*EllipticE(sin(1/2*arcsin(x*sqrt(b)/sqrt(a))),sqrt(2))*sqrt(a)/((a-b*x^2)^(1/4)*sqrt(b))],
[1/(x^2*(a-b*x^2)^(1/4)),x,3,-(a-b*x^2)^(3/4)/(a*x)-(1-b*x^2/a)^(1/4)*sqrt(cos(1/2*arcsin(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arcsin(x*sqrt(b)/sqrt(a)))*EllipticE(sin(1/2*arcsin(x*sqrt(b)/sqrt(a))),sqrt(2))*sqrt(b)/((a-b*x^2)^(1/4)*sqrt(a))],
[1/(x^4*(a-b*x^2)^(1/4)),x,4,-1/3*(a-b*x^2)^(3/4)/(a*x^3)-1/2*b*(a-b*x^2)^(3/4)/(a^2*x)-1/2*b^(3/2)*(1-b*x^2/a)^(1/4)*sqrt(cos(1/2*arcsin(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arcsin(x*sqrt(b)/sqrt(a)))*EllipticE(sin(1/2*arcsin(x*sqrt(b)/sqrt(a))),sqrt(2))/(a^(3/2)*(a-b*x^2)^(1/4))],
[1/(x^6*(a-b*x^2)^(1/4)),x,5,-1/5*(a-b*x^2)^(3/4)/(a*x^5)-7/30*b*(a-b*x^2)^(3/4)/(a^2*x^3)-7/20*b^2*(a-b*x^2)^(3/4)/(a^3*x)-7/20*b^(5/2)*(1-b*x^2/a)^(1/4)*sqrt(cos(1/2*arcsin(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arcsin(x*sqrt(b)/sqrt(a)))*EllipticE(sin(1/2*arcsin(x*sqrt(b)/sqrt(a))),sqrt(2))/(a^(5/2)*(a-b*x^2)^(1/4))],
[x^6/(a+b*x^2)^(3/4),x,5,40/77*a^2*x*(a+b*x^2)^(1/4)/b^3-20/77*a*x^3*(a+b*x^2)^(1/4)/b^2+2/11*x^5*(a+b*x^2)^(1/4)/b-80/77*a^(7/2)*(1+b*x^2/a)^(3/4)*sqrt(cos(1/2*arctan(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arctan(x*sqrt(b)/sqrt(a)))*EllipticF(sin(1/2*arctan(x*sqrt(b)/sqrt(a))),sqrt(2))/(b^(7/2)*(a+b*x^2)^(3/4))],
[x^4/(a+b*x^2)^(3/4),x,4,-4/7*a*x*(a+b*x^2)^(1/4)/b^2+2/7*x^3*(a+b*x^2)^(1/4)/b+8/7*a^(5/2)*(1+b*x^2/a)^(3/4)*sqrt(cos(1/2*arctan(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arctan(x*sqrt(b)/sqrt(a)))*EllipticF(sin(1/2*arctan(x*sqrt(b)/sqrt(a))),sqrt(2))/(b^(5/2)*(a+b*x^2)^(3/4))],
[x^2/(a+b*x^2)^(3/4),x,3,2/3*x*(a+b*x^2)^(1/4)/b-4/3*a^(3/2)*(1+b*x^2/a)^(3/4)*sqrt(cos(1/2*arctan(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arctan(x*sqrt(b)/sqrt(a)))*EllipticF(sin(1/2*arctan(x*sqrt(b)/sqrt(a))),sqrt(2))/(b^(3/2)*(a+b*x^2)^(3/4))],
[1/(a+b*x^2)^(3/4),x,2,2*(1+b*x^2/a)^(3/4)*sqrt(cos(1/2*arctan(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arctan(x*sqrt(b)/sqrt(a)))*EllipticF(sin(1/2*arctan(x*sqrt(b)/sqrt(a))),sqrt(2))*sqrt(a)/((a+b*x^2)^(3/4)*sqrt(b))],
[1/(x^2*(a+b*x^2)^(3/4)),x,3,-(a+b*x^2)^(1/4)/(a*x)-(1+b*x^2/a)^(3/4)*sqrt(cos(1/2*arctan(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arctan(x*sqrt(b)/sqrt(a)))*EllipticF(sin(1/2*arctan(x*sqrt(b)/sqrt(a))),sqrt(2))*sqrt(b)/((a+b*x^2)^(3/4)*sqrt(a))],
[1/(x^4*(a+b*x^2)^(3/4)),x,4,-1/3*(a+b*x^2)^(1/4)/(a*x^3)+5/6*b*(a+b*x^2)^(1/4)/(a^2*x)+5/6*b^(3/2)*(1+b*x^2/a)^(3/4)*sqrt(cos(1/2*arctan(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arctan(x*sqrt(b)/sqrt(a)))*EllipticF(sin(1/2*arctan(x*sqrt(b)/sqrt(a))),sqrt(2))/(a^(3/2)*(a+b*x^2)^(3/4))],
[1/(x^6*(a+b*x^2)^(3/4)),x,5,-1/5*(a+b*x^2)^(1/4)/(a*x^5)+3/10*b*(a+b*x^2)^(1/4)/(a^2*x^3)-3/4*b^2*(a+b*x^2)^(1/4)/(a^3*x)-3/4*b^(5/2)*(1+b*x^2/a)^(3/4)*sqrt(cos(1/2*arctan(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arctan(x*sqrt(b)/sqrt(a)))*EllipticF(sin(1/2*arctan(x*sqrt(b)/sqrt(a))),sqrt(2))/(a^(5/2)*(a+b*x^2)^(3/4))],
[x^6/(a-b*x^2)^(3/4),x,5,-40/77*a^2*x*(a-b*x^2)^(1/4)/b^3-20/77*a*x^3*(a-b*x^2)^(1/4)/b^2-2/11*x^5*(a-b*x^2)^(1/4)/b+80/77*a^(7/2)*(1-b*x^2/a)^(3/4)*sqrt(cos(1/2*arcsin(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arcsin(x*sqrt(b)/sqrt(a)))*EllipticF(sin(1/2*arcsin(x*sqrt(b)/sqrt(a))),sqrt(2))/(b^(7/2)*(a-b*x^2)^(3/4))],
[x^4/(a-b*x^2)^(3/4),x,4,-4/7*a*x*(a-b*x^2)^(1/4)/b^2-2/7*x^3*(a-b*x^2)^(1/4)/b+8/7*a^(5/2)*(1-b*x^2/a)^(3/4)*sqrt(cos(1/2*arcsin(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arcsin(x*sqrt(b)/sqrt(a)))*EllipticF(sin(1/2*arcsin(x*sqrt(b)/sqrt(a))),sqrt(2))/(b^(5/2)*(a-b*x^2)^(3/4))],
[x^2/(a-b*x^2)^(3/4),x,3,-2/3*x*(a-b*x^2)^(1/4)/b+4/3*a^(3/2)*(1-b*x^2/a)^(3/4)*sqrt(cos(1/2*arcsin(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arcsin(x*sqrt(b)/sqrt(a)))*EllipticF(sin(1/2*arcsin(x*sqrt(b)/sqrt(a))),sqrt(2))/(b^(3/2)*(a-b*x^2)^(3/4))],
[1/(a-b*x^2)^(3/4),x,2,2*(1-b*x^2/a)^(3/4)*sqrt(cos(1/2*arcsin(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arcsin(x*sqrt(b)/sqrt(a)))*EllipticF(sin(1/2*arcsin(x*sqrt(b)/sqrt(a))),sqrt(2))*sqrt(a)/((a-b*x^2)^(3/4)*sqrt(b))],
[1/(x^2*(a-b*x^2)^(3/4)),x,3,-(a-b*x^2)^(1/4)/(a*x)+(1-b*x^2/a)^(3/4)*sqrt(cos(1/2*arcsin(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arcsin(x*sqrt(b)/sqrt(a)))*EllipticF(sin(1/2*arcsin(x*sqrt(b)/sqrt(a))),sqrt(2))*sqrt(b)/((a-b*x^2)^(3/4)*sqrt(a))],
[1/(x^4*(a-b*x^2)^(3/4)),x,4,-1/3*(a-b*x^2)^(1/4)/(a*x^3)-5/6*b*(a-b*x^2)^(1/4)/(a^2*x)+5/6*b^(3/2)*(1-b*x^2/a)^(3/4)*sqrt(cos(1/2*arcsin(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arcsin(x*sqrt(b)/sqrt(a)))*EllipticF(sin(1/2*arcsin(x*sqrt(b)/sqrt(a))),sqrt(2))/(a^(3/2)*(a-b*x^2)^(3/4))],
[1/(x^6*(a-b*x^2)^(3/4)),x,5,-1/5*(a-b*x^2)^(1/4)/(a*x^5)-3/10*b*(a-b*x^2)^(1/4)/(a^2*x^3)-3/4*b^2*(a-b*x^2)^(1/4)/(a^3*x)+3/4*b^(5/2)*(1-b*x^2/a)^(3/4)*sqrt(cos(1/2*arcsin(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arcsin(x*sqrt(b)/sqrt(a)))*EllipticF(sin(1/2*arcsin(x*sqrt(b)/sqrt(a))),sqrt(2))/(a^(5/2)*(a-b*x^2)^(3/4))],
[x^6/(a+b*x^2)^(5/4),x,5,8/3*a^2*x/(b^3*(a+b*x^2)^(1/4))-4/9*a*x^3/(b^2*(a+b*x^2)^(1/4))+2/9*x^5/(b*(a+b*x^2)^(1/4))-16/3*a^(5/2)*(1+b*x^2/a)^(1/4)*sqrt(cos(1/2*arctan(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arctan(x*sqrt(b)/sqrt(a)))*EllipticE(sin(1/2*arctan(x*sqrt(b)/sqrt(a))),sqrt(2))/(b^(7/2)*(a+b*x^2)^(1/4))],
[x^4/(a+b*x^2)^(5/4),x,4,-12/5*a*x/(b^2*(a+b*x^2)^(1/4))+2/5*x^3/(b*(a+b*x^2)^(1/4))+24/5*a^(3/2)*(1+b*x^2/a)^(1/4)*sqrt(cos(1/2*arctan(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arctan(x*sqrt(b)/sqrt(a)))*EllipticE(sin(1/2*arctan(x*sqrt(b)/sqrt(a))),sqrt(2))/(b^(5/2)*(a+b*x^2)^(1/4))],
[x^2/(a+b*x^2)^(5/4),x,3,2*x/(b*(a+b*x^2)^(1/4))-4*(1+b*x^2/a)^(1/4)*sqrt(cos(1/2*arctan(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arctan(x*sqrt(b)/sqrt(a)))*EllipticE(sin(1/2*arctan(x*sqrt(b)/sqrt(a))),sqrt(2))*sqrt(a)/(b^(3/2)*(a+b*x^2)^(1/4))],
[1/(a+b*x^2)^(5/4),x,2,2*(1+b*x^2/a)^(1/4)*sqrt(cos(1/2*arctan(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arctan(x*sqrt(b)/sqrt(a)))*EllipticE(sin(1/2*arctan(x*sqrt(b)/sqrt(a))),sqrt(2))/((a+b*x^2)^(1/4)*sqrt(a)*sqrt(b))],
[1/(x^2*(a+b*x^2)^(5/4)),x,3,(-1)/(a*x*(a+b*x^2)^(1/4))-3*(1+b*x^2/a)^(1/4)*sqrt(cos(1/2*arctan(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arctan(x*sqrt(b)/sqrt(a)))*EllipticE(sin(1/2*arctan(x*sqrt(b)/sqrt(a))),sqrt(2))*sqrt(b)/(a^(3/2)*(a+b*x^2)^(1/4))],
[1/(x^4*(a+b*x^2)^(5/4)),x,4,(-1/3)/(a*x^3*(a+b*x^2)^(1/4))+7/6*b/(a^2*x*(a+b*x^2)^(1/4))+7/2*b^(3/2)*(1+b*x^2/a)^(1/4)*sqrt(cos(1/2*arctan(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arctan(x*sqrt(b)/sqrt(a)))*EllipticE(sin(1/2*arctan(x*sqrt(b)/sqrt(a))),sqrt(2))/(a^(5/2)*(a+b*x^2)^(1/4))],
[1/(x^6*(a+b*x^2)^(5/4)),x,5,(-1/5)/(a*x^5*(a+b*x^2)^(1/4))+11/30*b/(a^2*x^3*(a+b*x^2)^(1/4))-77/60*b^2/(a^3*x*(a+b*x^2)^(1/4))-77/20*b^(5/2)*(1+b*x^2/a)^(1/4)*sqrt(cos(1/2*arctan(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arctan(x*sqrt(b)/sqrt(a)))*EllipticE(sin(1/2*arctan(x*sqrt(b)/sqrt(a))),sqrt(2))/(a^(7/2)*(a+b*x^2)^(1/4))],
[x^6/(a-b*x^2)^(5/4),x,5,2*x^5/(b*(a-b*x^2)^(1/4))+8/3*a*x*(a-b*x^2)^(3/4)/b^3+20/9*x^3*(a-b*x^2)^(3/4)/b^2-16/3*a^(5/2)*(1-b*x^2/a)^(1/4)*sqrt(cos(1/2*arcsin(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arcsin(x*sqrt(b)/sqrt(a)))*EllipticE(sin(1/2*arcsin(x*sqrt(b)/sqrt(a))),sqrt(2))/(b^(7/2)*(a-b*x^2)^(1/4))],
[x^4/(a-b*x^2)^(5/4),x,4,2*x^3/(b*(a-b*x^2)^(1/4))+12/5*x*(a-b*x^2)^(3/4)/b^2-24/5*a^(3/2)*(1-b*x^2/a)^(1/4)*sqrt(cos(1/2*arcsin(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arcsin(x*sqrt(b)/sqrt(a)))*EllipticE(sin(1/2*arcsin(x*sqrt(b)/sqrt(a))),sqrt(2))/(b^(5/2)*(a-b*x^2)^(1/4))],
[x^2/(a-b*x^2)^(5/4),x,3,2*x/(b*(a-b*x^2)^(1/4))-4*(1-b*x^2/a)^(1/4)*sqrt(cos(1/2*arcsin(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arcsin(x*sqrt(b)/sqrt(a)))*EllipticE(sin(1/2*arcsin(x*sqrt(b)/sqrt(a))),sqrt(2))*sqrt(a)/(b^(3/2)*(a-b*x^2)^(1/4))],
[1/(a-b*x^2)^(5/4),x,3,2*x/(a*(a-b*x^2)^(1/4))-2*(1-b*x^2/a)^(1/4)*sqrt(cos(1/2*arcsin(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arcsin(x*sqrt(b)/sqrt(a)))*EllipticE(sin(1/2*arcsin(x*sqrt(b)/sqrt(a))),sqrt(2))/((a-b*x^2)^(1/4)*sqrt(a)*sqrt(b))],
[1/(x^2*(a-b*x^2)^(5/4)),x,4,2/(a*x*(a-b*x^2)^(1/4))-3*(a-b*x^2)^(3/4)/(a^2*x)-3*(1-b*x^2/a)^(1/4)*sqrt(cos(1/2*arcsin(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arcsin(x*sqrt(b)/sqrt(a)))*EllipticE(sin(1/2*arcsin(x*sqrt(b)/sqrt(a))),sqrt(2))*sqrt(b)/(a^(3/2)*(a-b*x^2)^(1/4))],
[1/(x^4*(a-b*x^2)^(5/4)),x,5,2/(a*x^3*(a-b*x^2)^(1/4))-7/3*(a-b*x^2)^(3/4)/(a^2*x^3)-7/2*b*(a-b*x^2)^(3/4)/(a^3*x)-7/2*b^(3/2)*(1-b*x^2/a)^(1/4)*sqrt(cos(1/2*arcsin(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arcsin(x*sqrt(b)/sqrt(a)))*EllipticE(sin(1/2*arcsin(x*sqrt(b)/sqrt(a))),sqrt(2))/(a^(5/2)*(a-b*x^2)^(1/4))],
[1/(x^6*(a-b*x^2)^(5/4)),x,6,2/(a*x^5*(a-b*x^2)^(1/4))-11/5*(a-b*x^2)^(3/4)/(a^2*x^5)-77/30*b*(a-b*x^2)^(3/4)/(a^3*x^3)-77/20*b^2*(a-b*x^2)^(3/4)/(a^4*x)-77/20*b^(5/2)*(1-b*x^2/a)^(1/4)*sqrt(cos(1/2*arcsin(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arcsin(x*sqrt(b)/sqrt(a)))*EllipticE(sin(1/2*arcsin(x*sqrt(b)/sqrt(a))),sqrt(2))/(a^(7/2)*(a-b*x^2)^(1/4))],
[1/(a+b*x^2)^(7/4),x,3,2/3*x/(a*(a+b*x^2)^(3/4))+2/3*(1+b*x^2/a)^(3/4)*sqrt(cos(1/2*arctan(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arctan(x*sqrt(b)/sqrt(a)))*EllipticF(sin(1/2*arctan(x*sqrt(b)/sqrt(a))),sqrt(2))/((a+b*x^2)^(3/4)*sqrt(a)*sqrt(b))],
[1/(a+b*x^2)^(9/4),x,3,2/5*x/(a*(a+b*x^2)^(5/4))+6/5*(1+b*x^2/a)^(1/4)*sqrt(cos(1/2*arctan(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arctan(x*sqrt(b)/sqrt(a)))*EllipticE(sin(1/2*arctan(x*sqrt(b)/sqrt(a))),sqrt(2))/(a^(3/2)*(a+b*x^2)^(1/4)*sqrt(b))],
[1/(a+b*x^2)^(11/4),x,4,2/7*x/(a*(a+b*x^2)^(7/4))+10/21*x/(a^2*(a+b*x^2)^(3/4))+10/21*(1+b*x^2/a)^(3/4)*sqrt(cos(1/2*arctan(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arctan(x*sqrt(b)/sqrt(a)))*EllipticF(sin(1/2*arctan(x*sqrt(b)/sqrt(a))),sqrt(2))/(a^(3/2)*(a+b*x^2)^(3/4)*sqrt(b))],
[1/(a-b*x^2)^(7/4),x,3,2/3*x/(a*(a-b*x^2)^(3/4))+2/3*(1-b*x^2/a)^(3/4)*sqrt(cos(1/2*arcsin(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arcsin(x*sqrt(b)/sqrt(a)))*EllipticF(sin(1/2*arcsin(x*sqrt(b)/sqrt(a))),sqrt(2))/((a-b*x^2)^(3/4)*sqrt(a)*sqrt(b))],
[1/(a-b*x^2)^(9/4),x,4,2/5*x/(a*(a-b*x^2)^(5/4))+6/5*x/(a^2*(a-b*x^2)^(1/4))-6/5*(1-b*x^2/a)^(1/4)*sqrt(cos(1/2*arcsin(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arcsin(x*sqrt(b)/sqrt(a)))*EllipticE(sin(1/2*arcsin(x*sqrt(b)/sqrt(a))),sqrt(2))/(a^(3/2)*(a-b*x^2)^(1/4)*sqrt(b))],
[1/(a-b*x^2)^(11/4),x,4,2/7*x/(a*(a-b*x^2)^(7/4))+10/21*x/(a^2*(a-b*x^2)^(3/4))+10/21*(1-b*x^2/a)^(3/4)*sqrt(cos(1/2*arcsin(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arcsin(x*sqrt(b)/sqrt(a)))*EllipticF(sin(1/2*arcsin(x*sqrt(b)/sqrt(a))),sqrt(2))/(a^(3/2)*(a-b*x^2)^(3/4)*sqrt(b))],
[x^6/(2+3*x^2)^(1/4),x,5,-128/1053*x/(2+3*x^2)^(1/4)+32/1053*x*(2+3*x^2)^(3/4)-40/1053*x^3*(2+3*x^2)^(3/4)+2/39*x^5*(2+3*x^2)^(3/4)+128/1053*2^(1/4)*sqrt(cos(1/2*arctan(x*sqrt(3/2)))^2)/cos(1/2*arctan(x*sqrt(3/2)))*EllipticE(sin(1/2*arctan(x*sqrt(3/2))),sqrt(2))/sqrt(3)],
[x^4/(2+3*x^2)^(1/4),x,4,32/135*x/(2+3*x^2)^(1/4)-8/135*x*(2+3*x^2)^(3/4)+2/27*x^3*(2+3*x^2)^(3/4)-32/135*2^(1/4)*sqrt(cos(1/2*arctan(x*sqrt(3/2)))^2)/cos(1/2*arctan(x*sqrt(3/2)))*EllipticE(sin(1/2*arctan(x*sqrt(3/2))),sqrt(2))/sqrt(3)],
[x^2/(2+3*x^2)^(1/4),x,3,-8/15*x/(2+3*x^2)^(1/4)+2/15*x*(2+3*x^2)^(3/4)+8/15*2^(1/4)*sqrt(cos(1/2*arctan(x*sqrt(3/2)))^2)/cos(1/2*arctan(x*sqrt(3/2)))*EllipticE(sin(1/2*arctan(x*sqrt(3/2))),sqrt(2))/sqrt(3)],
[1/(2+3*x^2)^(1/4),x,2,2*x/(2+3*x^2)^(1/4)-2*2^(1/4)*sqrt(cos(1/2*arctan(x*sqrt(3/2)))^2)/cos(1/2*arctan(x*sqrt(3/2)))*EllipticE(sin(1/2*arctan(x*sqrt(3/2))),sqrt(2))/sqrt(3)],
[1/(x^2*(2+3*x^2)^(1/4)),x,3,3/2*x/(2+3*x^2)^(1/4)-1/2*(2+3*x^2)^(3/4)/x-sqrt(cos(1/2*arctan(x*sqrt(3/2)))^2)/cos(1/2*arctan(x*sqrt(3/2)))*EllipticE(sin(1/2*arctan(x*sqrt(3/2))),sqrt(2))*sqrt(3)/2^(3/4)],
[1/(x^4*(2+3*x^2)^(1/4)),x,4,-9/8*x/(2+3*x^2)^(1/4)-1/6*(2+3*x^2)^(3/4)/x^3+3/8*(2+3*x^2)^(3/4)/x+3/4*sqrt(cos(1/2*arctan(x*sqrt(3/2)))^2)/cos(1/2*arctan(x*sqrt(3/2)))*EllipticE(sin(1/2*arctan(x*sqrt(3/2))),sqrt(2))*sqrt(3)/2^(3/4)],
[1/(x^6*(2+3*x^2)^(1/4)),x,5,189/160*x/(2+3*x^2)^(1/4)-1/10*(2+3*x^2)^(3/4)/x^5+7/40*(2+3*x^2)^(3/4)/x^3-63/160*(2+3*x^2)^(3/4)/x-63/80*sqrt(cos(1/2*arctan(x*sqrt(3/2)))^2)/cos(1/2*arctan(x*sqrt(3/2)))*EllipticE(sin(1/2*arctan(x*sqrt(3/2))),sqrt(2))*sqrt(3)/2^(3/4)],
[x^6/(2-3*x^2)^(1/4),x,4,-32/1053*x*(2-3*x^2)^(3/4)-40/1053*x^3*(2-3*x^2)^(3/4)-2/39*x^5*(2-3*x^2)^(3/4)+128/1053*2^(1/4)*sqrt(cos(1/2*arcsin(x*sqrt(3/2)))^2)/cos(1/2*arcsin(x*sqrt(3/2)))*EllipticE(sin(1/2*arcsin(x*sqrt(3/2))),sqrt(2))/sqrt(3)],
[x^4/(2-3*x^2)^(1/4),x,3,-8/135*x*(2-3*x^2)^(3/4)-2/27*x^3*(2-3*x^2)^(3/4)+32/135*2^(1/4)*sqrt(cos(1/2*arcsin(x*sqrt(3/2)))^2)/cos(1/2*arcsin(x*sqrt(3/2)))*EllipticE(sin(1/2*arcsin(x*sqrt(3/2))),sqrt(2))/sqrt(3)],
[x^2/(2-3*x^2)^(1/4),x,2,-2/15*x*(2-3*x^2)^(3/4)+8/15*2^(1/4)*sqrt(cos(1/2*arcsin(x*sqrt(3/2)))^2)/cos(1/2*arcsin(x*sqrt(3/2)))*EllipticE(sin(1/2*arcsin(x*sqrt(3/2))),sqrt(2))/sqrt(3)],
[1/(2-3*x^2)^(1/4),x,1,2*2^(1/4)*sqrt(cos(1/2*arcsin(x*sqrt(3/2)))^2)/cos(1/2*arcsin(x*sqrt(3/2)))*EllipticE(sin(1/2*arcsin(x*sqrt(3/2))),sqrt(2))/sqrt(3)],
[1/(x^2*(2-3*x^2)^(1/4)),x,2,-1/2*(2-3*x^2)^(3/4)/x-sqrt(cos(1/2*arcsin(x*sqrt(3/2)))^2)/cos(1/2*arcsin(x*sqrt(3/2)))*EllipticE(sin(1/2*arcsin(x*sqrt(3/2))),sqrt(2))*sqrt(3)/2^(3/4)],
[1/(x^4*(2-3*x^2)^(1/4)),x,3,-1/6*(2-3*x^2)^(3/4)/x^3-3/8*(2-3*x^2)^(3/4)/x-3/4*sqrt(cos(1/2*arcsin(x*sqrt(3/2)))^2)/cos(1/2*arcsin(x*sqrt(3/2)))*EllipticE(sin(1/2*arcsin(x*sqrt(3/2))),sqrt(2))*sqrt(3)/2^(3/4)],
[1/(x^6*(2-3*x^2)^(1/4)),x,4,-1/10*(2-3*x^2)^(3/4)/x^5-7/40*(2-3*x^2)^(3/4)/x^3-63/160*(2-3*x^2)^(3/4)/x-63/80*sqrt(cos(1/2*arcsin(x*sqrt(3/2)))^2)/cos(1/2*arcsin(x*sqrt(3/2)))*EllipticE(sin(1/2*arcsin(x*sqrt(3/2))),sqrt(2))*sqrt(3)/2^(3/4)],
[x^6/(2+3*x^2)^(3/4),x,4,160/2079*x*(2+3*x^2)^(1/4)-40/693*x^3*(2+3*x^2)^(1/4)+2/33*x^5*(2+3*x^2)^(1/4)-320/2079*2^(3/4)*sqrt(cos(1/2*arctan(x*sqrt(3/2)))^2)/cos(1/2*arctan(x*sqrt(3/2)))*EllipticF(sin(1/2*arctan(x*sqrt(3/2))),sqrt(2))/sqrt(3)],
[x^4/(2+3*x^2)^(3/4),x,3,-8/63*x*(2+3*x^2)^(1/4)+2/21*x^3*(2+3*x^2)^(1/4)+16/63*2^(3/4)*sqrt(cos(1/2*arctan(x*sqrt(3/2)))^2)/cos(1/2*arctan(x*sqrt(3/2)))*EllipticF(sin(1/2*arctan(x*sqrt(3/2))),sqrt(2))/sqrt(3)],
[x^2/(2+3*x^2)^(3/4),x,2,2/9*x*(2+3*x^2)^(1/4)-4/9*2^(3/4)*sqrt(cos(1/2*arctan(x*sqrt(3/2)))^2)/cos(1/2*arctan(x*sqrt(3/2)))*EllipticF(sin(1/2*arctan(x*sqrt(3/2))),sqrt(2))/sqrt(3)],
[1/(2+3*x^2)^(3/4),x,1,2^(3/4)*sqrt(cos(1/2*arctan(x*sqrt(3/2)))^2)/cos(1/2*arctan(x*sqrt(3/2)))*EllipticF(sin(1/2*arctan(x*sqrt(3/2))),sqrt(2))/sqrt(3)],
[1/(x^2*(2+3*x^2)^(3/4)),x,2,-1/2*(2+3*x^2)^(1/4)/x-1/2*sqrt(cos(1/2*arctan(x*sqrt(3/2)))^2)/cos(1/2*arctan(x*sqrt(3/2)))*EllipticF(sin(1/2*arctan(x*sqrt(3/2))),sqrt(2))*sqrt(3)/2^(1/4)],
[1/(x^4*(2+3*x^2)^(3/4)),x,3,-1/6*(2+3*x^2)^(1/4)/x^3+5/8*(2+3*x^2)^(1/4)/x+5/8*sqrt(cos(1/2*arctan(x*sqrt(3/2)))^2)/cos(1/2*arctan(x*sqrt(3/2)))*EllipticF(sin(1/2*arctan(x*sqrt(3/2))),sqrt(2))*sqrt(3)/2^(1/4)],
[1/(x^6*(2+3*x^2)^(3/4)),x,4,-1/10*(2+3*x^2)^(1/4)/x^5+9/40*(2+3*x^2)^(1/4)/x^3-27/32*(2+3*x^2)^(1/4)/x-27/32*sqrt(cos(1/2*arctan(x*sqrt(3/2)))^2)/cos(1/2*arctan(x*sqrt(3/2)))*EllipticF(sin(1/2*arctan(x*sqrt(3/2))),sqrt(2))*sqrt(3)/2^(1/4)],
[x^6/(2-3*x^2)^(3/4),x,4,-160/2079*x*(2-3*x^2)^(1/4)-40/693*x^3*(2-3*x^2)^(1/4)-2/33*x^5*(2-3*x^2)^(1/4)+320/2079*2^(3/4)*sqrt(cos(1/2*arcsin(x*sqrt(3/2)))^2)/cos(1/2*arcsin(x*sqrt(3/2)))*EllipticF(sin(1/2*arcsin(x*sqrt(3/2))),sqrt(2))/sqrt(3)],
[x^4/(2-3*x^2)^(3/4),x,3,-8/63*x*(2-3*x^2)^(1/4)-2/21*x^3*(2-3*x^2)^(1/4)+16/63*2^(3/4)*sqrt(cos(1/2*arcsin(x*sqrt(3/2)))^2)/cos(1/2*arcsin(x*sqrt(3/2)))*EllipticF(sin(1/2*arcsin(x*sqrt(3/2))),sqrt(2))/sqrt(3)],
[x^2/(2-3*x^2)^(3/4),x,2,-2/9*x*(2-3*x^2)^(1/4)+4/9*2^(3/4)*sqrt(cos(1/2*arcsin(x*sqrt(3/2)))^2)/cos(1/2*arcsin(x*sqrt(3/2)))*EllipticF(sin(1/2*arcsin(x*sqrt(3/2))),sqrt(2))/sqrt(3)],
[1/(2-3*x^2)^(3/4),x,1,2^(3/4)*sqrt(cos(1/2*arcsin(x*sqrt(3/2)))^2)/cos(1/2*arcsin(x*sqrt(3/2)))*EllipticF(sin(1/2*arcsin(x*sqrt(3/2))),sqrt(2))/sqrt(3)],
[1/(x^2*(2-3*x^2)^(3/4)),x,2,-1/2*(2-3*x^2)^(1/4)/x+1/2*sqrt(cos(1/2*arcsin(x*sqrt(3/2)))^2)/cos(1/2*arcsin(x*sqrt(3/2)))*EllipticF(sin(1/2*arcsin(x*sqrt(3/2))),sqrt(2))*sqrt(3)/2^(1/4)],
[1/(x^4*(2-3*x^2)^(3/4)),x,3,-1/6*(2-3*x^2)^(1/4)/x^3-5/8*(2-3*x^2)^(1/4)/x+5/8*sqrt(cos(1/2*arcsin(x*sqrt(3/2)))^2)/cos(1/2*arcsin(x*sqrt(3/2)))*EllipticF(sin(1/2*arcsin(x*sqrt(3/2))),sqrt(2))*sqrt(3)/2^(1/4)],
[1/(x^6*(2-3*x^2)^(3/4)),x,4,-1/10*(2-3*x^2)^(1/4)/x^5-9/40*(2-3*x^2)^(1/4)/x^3-27/32*(2-3*x^2)^(1/4)/x+27/32*sqrt(cos(1/2*arcsin(x*sqrt(3/2)))^2)/cos(1/2*arcsin(x*sqrt(3/2)))*EllipticF(sin(1/2*arcsin(x*sqrt(3/2))),sqrt(2))*sqrt(3)/2^(1/4)],
[x^6/(-2+3*x^2)^(1/4),x,7,32/1053*x*(-2+3*x^2)^(3/4)+40/1053*x^3*(-2+3*x^2)^(3/4)+2/39*x^5*(-2+3*x^2)^(3/4)+128/1053*x*(-2+3*x^2)^(1/4)/(sqrt(2)+sqrt(-2+3*x^2))-128/1053*2^(1/4)*sqrt(cos(2*arctan((-2+3*x^2)^(1/4)/2^(1/4)))^2)/cos(2*arctan((-2+3*x^2)^(1/4)/2^(1/4)))*EllipticE(sin(2*arctan((-2+3*x^2)^(1/4)/2^(1/4))),sqrt(1/2))*(sqrt(2)+sqrt(-2+3*x^2))*sqrt(x^2/(sqrt(2)+sqrt(-2+3*x^2))^2)/(x*sqrt(3))+64/1053*2^(1/4)*sqrt(cos(2*arctan((-2+3*x^2)^(1/4)/2^(1/4)))^2)/cos(2*arctan((-2+3*x^2)^(1/4)/2^(1/4)))*EllipticF(sin(2*arctan((-2+3*x^2)^(1/4)/2^(1/4))),sqrt(1/2))*(sqrt(2)+sqrt(-2+3*x^2))*sqrt(x^2/(sqrt(2)+sqrt(-2+3*x^2))^2)/(x*sqrt(3))],
[x^4/(-2+3*x^2)^(1/4),x,6,8/135*x*(-2+3*x^2)^(3/4)+2/27*x^3*(-2+3*x^2)^(3/4)+32/135*x*(-2+3*x^2)^(1/4)/(sqrt(2)+sqrt(-2+3*x^2))-32/135*2^(1/4)*sqrt(cos(2*arctan((-2+3*x^2)^(1/4)/2^(1/4)))^2)/cos(2*arctan((-2+3*x^2)^(1/4)/2^(1/4)))*EllipticE(sin(2*arctan((-2+3*x^2)^(1/4)/2^(1/4))),sqrt(1/2))*(sqrt(2)+sqrt(-2+3*x^2))*sqrt(x^2/(sqrt(2)+sqrt(-2+3*x^2))^2)/(x*sqrt(3))+16/135*2^(1/4)*sqrt(cos(2*arctan((-2+3*x^2)^(1/4)/2^(1/4)))^2)/cos(2*arctan((-2+3*x^2)^(1/4)/2^(1/4)))*EllipticF(sin(2*arctan((-2+3*x^2)^(1/4)/2^(1/4))),sqrt(1/2))*(sqrt(2)+sqrt(-2+3*x^2))*sqrt(x^2/(sqrt(2)+sqrt(-2+3*x^2))^2)/(x*sqrt(3))],
[x^2/(-2+3*x^2)^(1/4),x,5,2/15*x*(-2+3*x^2)^(3/4)+8/15*x*(-2+3*x^2)^(1/4)/(sqrt(2)+sqrt(-2+3*x^2))-8/15*2^(1/4)*sqrt(cos(2*arctan((-2+3*x^2)^(1/4)/2^(1/4)))^2)/cos(2*arctan((-2+3*x^2)^(1/4)/2^(1/4)))*EllipticE(sin(2*arctan((-2+3*x^2)^(1/4)/2^(1/4))),sqrt(1/2))*(sqrt(2)+sqrt(-2+3*x^2))*sqrt(x^2/(sqrt(2)+sqrt(-2+3*x^2))^2)/(x*sqrt(3))+4/15*2^(1/4)*sqrt(cos(2*arctan((-2+3*x^2)^(1/4)/2^(1/4)))^2)/cos(2*arctan((-2+3*x^2)^(1/4)/2^(1/4)))*EllipticF(sin(2*arctan((-2+3*x^2)^(1/4)/2^(1/4))),sqrt(1/2))*(sqrt(2)+sqrt(-2+3*x^2))*sqrt(x^2/(sqrt(2)+sqrt(-2+3*x^2))^2)/(x*sqrt(3))],
[1/(-2+3*x^2)^(1/4),x,4,2*x*(-2+3*x^2)^(1/4)/(sqrt(2)+sqrt(-2+3*x^2))-2*2^(1/4)*sqrt(cos(2*arctan((-2+3*x^2)^(1/4)/2^(1/4)))^2)/cos(2*arctan((-2+3*x^2)^(1/4)/2^(1/4)))*EllipticE(sin(2*arctan((-2+3*x^2)^(1/4)/2^(1/4))),sqrt(1/2))*(sqrt(2)+sqrt(-2+3*x^2))*sqrt(x^2/(sqrt(2)+sqrt(-2+3*x^2))^2)/(x*sqrt(3))+2^(1/4)*sqrt(cos(2*arctan((-2+3*x^2)^(1/4)/2^(1/4)))^2)/cos(2*arctan((-2+3*x^2)^(1/4)/2^(1/4)))*EllipticF(sin(2*arctan((-2+3*x^2)^(1/4)/2^(1/4))),sqrt(1/2))*(sqrt(2)+sqrt(-2+3*x^2))*sqrt(x^2/(sqrt(2)+sqrt(-2+3*x^2))^2)/(x*sqrt(3))],
[1/(x^2*(-2+3*x^2)^(1/4)),x,5,1/2*(-2+3*x^2)^(3/4)/x-3/2*x*(-2+3*x^2)^(1/4)/(sqrt(2)+sqrt(-2+3*x^2))+sqrt(cos(2*arctan((-2+3*x^2)^(1/4)/2^(1/4)))^2)/cos(2*arctan((-2+3*x^2)^(1/4)/2^(1/4)))*EllipticE(sin(2*arctan((-2+3*x^2)^(1/4)/2^(1/4))),sqrt(1/2))*sqrt(3)*(sqrt(2)+sqrt(-2+3*x^2))*sqrt(x^2/(sqrt(2)+sqrt(-2+3*x^2))^2)/(2^(3/4)*x)-1/2*sqrt(cos(2*arctan((-2+3*x^2)^(1/4)/2^(1/4)))^2)/cos(2*arctan((-2+3*x^2)^(1/4)/2^(1/4)))*EllipticF(sin(2*arctan((-2+3*x^2)^(1/4)/2^(1/4))),sqrt(1/2))*sqrt(3)*(sqrt(2)+sqrt(-2+3*x^2))*sqrt(x^2/(sqrt(2)+sqrt(-2+3*x^2))^2)/(2^(3/4)*x)],
[1/(x^4*(-2+3*x^2)^(1/4)),x,6,1/6*(-2+3*x^2)^(3/4)/x^3+3/8*(-2+3*x^2)^(3/4)/x-9/8*x*(-2+3*x^2)^(1/4)/(sqrt(2)+sqrt(-2+3*x^2))+3/4*sqrt(cos(2*arctan((-2+3*x^2)^(1/4)/2^(1/4)))^2)/cos(2*arctan((-2+3*x^2)^(1/4)/2^(1/4)))*EllipticE(sin(2*arctan((-2+3*x^2)^(1/4)/2^(1/4))),sqrt(1/2))*sqrt(3)*(sqrt(2)+sqrt(-2+3*x^2))*sqrt(x^2/(sqrt(2)+sqrt(-2+3*x^2))^2)/(2^(3/4)*x)-3/8*sqrt(cos(2*arctan((-2+3*x^2)^(1/4)/2^(1/4)))^2)/cos(2*arctan((-2+3*x^2)^(1/4)/2^(1/4)))*EllipticF(sin(2*arctan((-2+3*x^2)^(1/4)/2^(1/4))),sqrt(1/2))*sqrt(3)*(sqrt(2)+sqrt(-2+3*x^2))*sqrt(x^2/(sqrt(2)+sqrt(-2+3*x^2))^2)/(2^(3/4)*x)],
[1/(x^6*(-2+3*x^2)^(1/4)),x,7,1/10*(-2+3*x^2)^(3/4)/x^5+7/40*(-2+3*x^2)^(3/4)/x^3+63/160*(-2+3*x^2)^(3/4)/x-189/160*x*(-2+3*x^2)^(1/4)/(sqrt(2)+sqrt(-2+3*x^2))+63/80*sqrt(cos(2*arctan((-2+3*x^2)^(1/4)/2^(1/4)))^2)/cos(2*arctan((-2+3*x^2)^(1/4)/2^(1/4)))*EllipticE(sin(2*arctan((-2+3*x^2)^(1/4)/2^(1/4))),sqrt(1/2))*sqrt(3)*(sqrt(2)+sqrt(-2+3*x^2))*sqrt(x^2/(sqrt(2)+sqrt(-2+3*x^2))^2)/(2^(3/4)*x)-63/160*sqrt(cos(2*arctan((-2+3*x^2)^(1/4)/2^(1/4)))^2)/cos(2*arctan((-2+3*x^2)^(1/4)/2^(1/4)))*EllipticF(sin(2*arctan((-2+3*x^2)^(1/4)/2^(1/4))),sqrt(1/2))*sqrt(3)*(sqrt(2)+sqrt(-2+3*x^2))*sqrt(x^2/(sqrt(2)+sqrt(-2+3*x^2))^2)/(2^(3/4)*x)],
[x^6/(-2-3*x^2)^(1/4),x,7,-32/1053*x*(-2-3*x^2)^(3/4)+40/1053*x^3*(-2-3*x^2)^(3/4)-2/39*x^5*(-2-3*x^2)^(3/4)-128/1053*x*(-2-3*x^2)^(1/4)/(sqrt(2)+sqrt(-2-3*x^2))-128/1053*2^(1/4)*sqrt(cos(2*arctan((-2-3*x^2)^(1/4)/2^(1/4)))^2)/cos(2*arctan((-2-3*x^2)^(1/4)/2^(1/4)))*EllipticE(sin(2*arctan((-2-3*x^2)^(1/4)/2^(1/4))),sqrt(1/2))*(sqrt(2)+sqrt(-2-3*x^2))*sqrt(-x^2/(sqrt(2)+sqrt(-2-3*x^2))^2)/(x*sqrt(3))+64/1053*2^(1/4)*sqrt(cos(2*arctan((-2-3*x^2)^(1/4)/2^(1/4)))^2)/cos(2*arctan((-2-3*x^2)^(1/4)/2^(1/4)))*EllipticF(sin(2*arctan((-2-3*x^2)^(1/4)/2^(1/4))),sqrt(1/2))*(sqrt(2)+sqrt(-2-3*x^2))*sqrt(-x^2/(sqrt(2)+sqrt(-2-3*x^2))^2)/(x*sqrt(3))],
[x^4/(-2-3*x^2)^(1/4),x,6,8/135*x*(-2-3*x^2)^(3/4)-2/27*x^3*(-2-3*x^2)^(3/4)+32/135*x*(-2-3*x^2)^(1/4)/(sqrt(2)+sqrt(-2-3*x^2))+32/135*2^(1/4)*sqrt(cos(2*arctan((-2-3*x^2)^(1/4)/2^(1/4)))^2)/cos(2*arctan((-2-3*x^2)^(1/4)/2^(1/4)))*EllipticE(sin(2*arctan((-2-3*x^2)^(1/4)/2^(1/4))),sqrt(1/2))*(sqrt(2)+sqrt(-2-3*x^2))*sqrt(-x^2/(sqrt(2)+sqrt(-2-3*x^2))^2)/(x*sqrt(3))-16/135*2^(1/4)*sqrt(cos(2*arctan((-2-3*x^2)^(1/4)/2^(1/4)))^2)/cos(2*arctan((-2-3*x^2)^(1/4)/2^(1/4)))*EllipticF(sin(2*arctan((-2-3*x^2)^(1/4)/2^(1/4))),sqrt(1/2))*(sqrt(2)+sqrt(-2-3*x^2))*sqrt(-x^2/(sqrt(2)+sqrt(-2-3*x^2))^2)/(x*sqrt(3))],
[x^2/(-2-3*x^2)^(1/4),x,5,-2/15*x*(-2-3*x^2)^(3/4)-8/15*x*(-2-3*x^2)^(1/4)/(sqrt(2)+sqrt(-2-3*x^2))-8/15*2^(1/4)*sqrt(cos(2*arctan((-2-3*x^2)^(1/4)/2^(1/4)))^2)/cos(2*arctan((-2-3*x^2)^(1/4)/2^(1/4)))*EllipticE(sin(2*arctan((-2-3*x^2)^(1/4)/2^(1/4))),sqrt(1/2))*(sqrt(2)+sqrt(-2-3*x^2))*sqrt(-x^2/(sqrt(2)+sqrt(-2-3*x^2))^2)/(x*sqrt(3))+4/15*2^(1/4)*sqrt(cos(2*arctan((-2-3*x^2)^(1/4)/2^(1/4)))^2)/cos(2*arctan((-2-3*x^2)^(1/4)/2^(1/4)))*EllipticF(sin(2*arctan((-2-3*x^2)^(1/4)/2^(1/4))),sqrt(1/2))*(sqrt(2)+sqrt(-2-3*x^2))*sqrt(-x^2/(sqrt(2)+sqrt(-2-3*x^2))^2)/(x*sqrt(3))],
[1/(-2-3*x^2)^(1/4),x,4,2*x*(-2-3*x^2)^(1/4)/(sqrt(2)+sqrt(-2-3*x^2))+2*2^(1/4)*sqrt(cos(2*arctan((-2-3*x^2)^(1/4)/2^(1/4)))^2)/cos(2*arctan((-2-3*x^2)^(1/4)/2^(1/4)))*EllipticE(sin(2*arctan((-2-3*x^2)^(1/4)/2^(1/4))),sqrt(1/2))*(sqrt(2)+sqrt(-2-3*x^2))*sqrt(-x^2/(sqrt(2)+sqrt(-2-3*x^2))^2)/(x*sqrt(3))-2^(1/4)*sqrt(cos(2*arctan((-2-3*x^2)^(1/4)/2^(1/4)))^2)/cos(2*arctan((-2-3*x^2)^(1/4)/2^(1/4)))*EllipticF(sin(2*arctan((-2-3*x^2)^(1/4)/2^(1/4))),sqrt(1/2))*(sqrt(2)+sqrt(-2-3*x^2))*sqrt(-x^2/(sqrt(2)+sqrt(-2-3*x^2))^2)/(x*sqrt(3))],
[1/(x^2*(-2-3*x^2)^(1/4)),x,5,1/2*(-2-3*x^2)^(3/4)/x+3/2*x*(-2-3*x^2)^(1/4)/(sqrt(2)+sqrt(-2-3*x^2))+sqrt(cos(2*arctan((-2-3*x^2)^(1/4)/2^(1/4)))^2)/cos(2*arctan((-2-3*x^2)^(1/4)/2^(1/4)))*EllipticE(sin(2*arctan((-2-3*x^2)^(1/4)/2^(1/4))),sqrt(1/2))*sqrt(3)*(sqrt(2)+sqrt(-2-3*x^2))*sqrt(-x^2/(sqrt(2)+sqrt(-2-3*x^2))^2)/(2^(3/4)*x)-1/2*sqrt(cos(2*arctan((-2-3*x^2)^(1/4)/2^(1/4)))^2)/cos(2*arctan((-2-3*x^2)^(1/4)/2^(1/4)))*EllipticF(sin(2*arctan((-2-3*x^2)^(1/4)/2^(1/4))),sqrt(1/2))*sqrt(3)*(sqrt(2)+sqrt(-2-3*x^2))*sqrt(-x^2/(sqrt(2)+sqrt(-2-3*x^2))^2)/(2^(3/4)*x)],
[1/(x^4*(-2-3*x^2)^(1/4)),x,6,1/6*(-2-3*x^2)^(3/4)/x^3-3/8*(-2-3*x^2)^(3/4)/x-9/8*x*(-2-3*x^2)^(1/4)/(sqrt(2)+sqrt(-2-3*x^2))-3/4*sqrt(cos(2*arctan((-2-3*x^2)^(1/4)/2^(1/4)))^2)/cos(2*arctan((-2-3*x^2)^(1/4)/2^(1/4)))*EllipticE(sin(2*arctan((-2-3*x^2)^(1/4)/2^(1/4))),sqrt(1/2))*sqrt(3)*(sqrt(2)+sqrt(-2-3*x^2))*sqrt(-x^2/(sqrt(2)+sqrt(-2-3*x^2))^2)/(2^(3/4)*x)+3/8*sqrt(cos(2*arctan((-2-3*x^2)^(1/4)/2^(1/4)))^2)/cos(2*arctan((-2-3*x^2)^(1/4)/2^(1/4)))*EllipticF(sin(2*arctan((-2-3*x^2)^(1/4)/2^(1/4))),sqrt(1/2))*sqrt(3)*(sqrt(2)+sqrt(-2-3*x^2))*sqrt(-x^2/(sqrt(2)+sqrt(-2-3*x^2))^2)/(2^(3/4)*x)],
[1/(x^6*(-2-3*x^2)^(1/4)),x,7,1/10*(-2-3*x^2)^(3/4)/x^5-7/40*(-2-3*x^2)^(3/4)/x^3+63/160*(-2-3*x^2)^(3/4)/x+189/160*x*(-2-3*x^2)^(1/4)/(sqrt(2)+sqrt(-2-3*x^2))+63/80*sqrt(cos(2*arctan((-2-3*x^2)^(1/4)/2^(1/4)))^2)/cos(2*arctan((-2-3*x^2)^(1/4)/2^(1/4)))*EllipticE(sin(2*arctan((-2-3*x^2)^(1/4)/2^(1/4))),sqrt(1/2))*sqrt(3)*(sqrt(2)+sqrt(-2-3*x^2))*sqrt(-x^2/(sqrt(2)+sqrt(-2-3*x^2))^2)/(2^(3/4)*x)-63/160*sqrt(cos(2*arctan((-2-3*x^2)^(1/4)/2^(1/4)))^2)/cos(2*arctan((-2-3*x^2)^(1/4)/2^(1/4)))*EllipticF(sin(2*arctan((-2-3*x^2)^(1/4)/2^(1/4))),sqrt(1/2))*sqrt(3)*(sqrt(2)+sqrt(-2-3*x^2))*sqrt(-x^2/(sqrt(2)+sqrt(-2-3*x^2))^2)/(2^(3/4)*x)],
[x^6/(-2+3*x^2)^(3/4),x,5,160/2079*x*(-2+3*x^2)^(1/4)+40/693*x^3*(-2+3*x^2)^(1/4)+2/33*x^5*(-2+3*x^2)^(1/4)+160/2079*2^(3/4)*sqrt(cos(2*arctan((-2+3*x^2)^(1/4)/2^(1/4)))^2)/cos(2*arctan((-2+3*x^2)^(1/4)/2^(1/4)))*EllipticF(sin(2*arctan((-2+3*x^2)^(1/4)/2^(1/4))),sqrt(1/2))*(sqrt(2)+sqrt(-2+3*x^2))*sqrt(x^2/(sqrt(2)+sqrt(-2+3*x^2))^2)/(x*sqrt(3))],
[x^4/(-2+3*x^2)^(3/4),x,4,8/63*x*(-2+3*x^2)^(1/4)+2/21*x^3*(-2+3*x^2)^(1/4)+8/63*2^(3/4)*sqrt(cos(2*arctan((-2+3*x^2)^(1/4)/2^(1/4)))^2)/cos(2*arctan((-2+3*x^2)^(1/4)/2^(1/4)))*EllipticF(sin(2*arctan((-2+3*x^2)^(1/4)/2^(1/4))),sqrt(1/2))*(sqrt(2)+sqrt(-2+3*x^2))*sqrt(x^2/(sqrt(2)+sqrt(-2+3*x^2))^2)/(x*sqrt(3))],
[x^2/(-2+3*x^2)^(3/4),x,3,2/9*x*(-2+3*x^2)^(1/4)+2/9*2^(3/4)*sqrt(cos(2*arctan((-2+3*x^2)^(1/4)/2^(1/4)))^2)/cos(2*arctan((-2+3*x^2)^(1/4)/2^(1/4)))*EllipticF(sin(2*arctan((-2+3*x^2)^(1/4)/2^(1/4))),sqrt(1/2))*(sqrt(2)+sqrt(-2+3*x^2))*sqrt(x^2/(sqrt(2)+sqrt(-2+3*x^2))^2)/(x*sqrt(3))],
[1/(-2+3*x^2)^(3/4),x,2,sqrt(cos(2*arctan((-2+3*x^2)^(1/4)/2^(1/4)))^2)/cos(2*arctan((-2+3*x^2)^(1/4)/2^(1/4)))*EllipticF(sin(2*arctan((-2+3*x^2)^(1/4)/2^(1/4))),sqrt(1/2))*(sqrt(2)+sqrt(-2+3*x^2))*sqrt(x^2/(sqrt(2)+sqrt(-2+3*x^2))^2)/(2^(1/4)*x*sqrt(3))],
[1/(x^2*(-2+3*x^2)^(3/4)),x,3,1/2*(-2+3*x^2)^(1/4)/x+1/4*sqrt(cos(2*arctan((-2+3*x^2)^(1/4)/2^(1/4)))^2)/cos(2*arctan((-2+3*x^2)^(1/4)/2^(1/4)))*EllipticF(sin(2*arctan((-2+3*x^2)^(1/4)/2^(1/4))),sqrt(1/2))*sqrt(3)*(sqrt(2)+sqrt(-2+3*x^2))*sqrt(x^2/(sqrt(2)+sqrt(-2+3*x^2))^2)/(2^(1/4)*x)],
[1/(x^4*(-2+3*x^2)^(3/4)),x,4,1/6*(-2+3*x^2)^(1/4)/x^3+5/8*(-2+3*x^2)^(1/4)/x+5/16*sqrt(cos(2*arctan((-2+3*x^2)^(1/4)/2^(1/4)))^2)/cos(2*arctan((-2+3*x^2)^(1/4)/2^(1/4)))*EllipticF(sin(2*arctan((-2+3*x^2)^(1/4)/2^(1/4))),sqrt(1/2))*sqrt(3)*(sqrt(2)+sqrt(-2+3*x^2))*sqrt(x^2/(sqrt(2)+sqrt(-2+3*x^2))^2)/(2^(1/4)*x)],
[1/(x^6*(-2+3*x^2)^(3/4)),x,5,1/10*(-2+3*x^2)^(1/4)/x^5+9/40*(-2+3*x^2)^(1/4)/x^3+27/32*(-2+3*x^2)^(1/4)/x+27/64*sqrt(cos(2*arctan((-2+3*x^2)^(1/4)/2^(1/4)))^2)/cos(2*arctan((-2+3*x^2)^(1/4)/2^(1/4)))*EllipticF(sin(2*arctan((-2+3*x^2)^(1/4)/2^(1/4))),sqrt(1/2))*sqrt(3)*(sqrt(2)+sqrt(-2+3*x^2))*sqrt(x^2/(sqrt(2)+sqrt(-2+3*x^2))^2)/(2^(1/4)*x)],
[x^6/(-2-3*x^2)^(3/4),x,5,-160/2079*x*(-2-3*x^2)^(1/4)+40/693*x^3*(-2-3*x^2)^(1/4)-2/33*x^5*(-2-3*x^2)^(1/4)+160/2079*2^(3/4)*sqrt(cos(2*arctan((-2-3*x^2)^(1/4)/2^(1/4)))^2)/cos(2*arctan((-2-3*x^2)^(1/4)/2^(1/4)))*EllipticF(sin(2*arctan((-2-3*x^2)^(1/4)/2^(1/4))),sqrt(1/2))*(sqrt(2)+sqrt(-2-3*x^2))*sqrt(-x^2/(sqrt(2)+sqrt(-2-3*x^2))^2)/(x*sqrt(3))],
[x^4/(-2-3*x^2)^(3/4),x,4,8/63*x*(-2-3*x^2)^(1/4)-2/21*x^3*(-2-3*x^2)^(1/4)-8/63*2^(3/4)*sqrt(cos(2*arctan((-2-3*x^2)^(1/4)/2^(1/4)))^2)/cos(2*arctan((-2-3*x^2)^(1/4)/2^(1/4)))*EllipticF(sin(2*arctan((-2-3*x^2)^(1/4)/2^(1/4))),sqrt(1/2))*(sqrt(2)+sqrt(-2-3*x^2))*sqrt(-x^2/(sqrt(2)+sqrt(-2-3*x^2))^2)/(x*sqrt(3))],
[x^2/(-2-3*x^2)^(3/4),x,3,-2/9*x*(-2-3*x^2)^(1/4)+2/9*2^(3/4)*sqrt(cos(2*arctan((-2-3*x^2)^(1/4)/2^(1/4)))^2)/cos(2*arctan((-2-3*x^2)^(1/4)/2^(1/4)))*EllipticF(sin(2*arctan((-2-3*x^2)^(1/4)/2^(1/4))),sqrt(1/2))*(sqrt(2)+sqrt(-2-3*x^2))*sqrt(-x^2/(sqrt(2)+sqrt(-2-3*x^2))^2)/(x*sqrt(3))],
[1/(-2-3*x^2)^(3/4),x,2,-sqrt(cos(2*arctan((-2-3*x^2)^(1/4)/2^(1/4)))^2)/cos(2*arctan((-2-3*x^2)^(1/4)/2^(1/4)))*EllipticF(sin(2*arctan((-2-3*x^2)^(1/4)/2^(1/4))),sqrt(1/2))*(sqrt(2)+sqrt(-2-3*x^2))*sqrt(-x^2/(sqrt(2)+sqrt(-2-3*x^2))^2)/(2^(1/4)*x*sqrt(3))],
[1/(x^2*(-2-3*x^2)^(3/4)),x,3,1/2*(-2-3*x^2)^(1/4)/x+1/4*sqrt(cos(2*arctan((-2-3*x^2)^(1/4)/2^(1/4)))^2)/cos(2*arctan((-2-3*x^2)^(1/4)/2^(1/4)))*EllipticF(sin(2*arctan((-2-3*x^2)^(1/4)/2^(1/4))),sqrt(1/2))*sqrt(3)*(sqrt(2)+sqrt(-2-3*x^2))*sqrt(-x^2/(sqrt(2)+sqrt(-2-3*x^2))^2)/(2^(1/4)*x)],
[1/(x^4*(-2-3*x^2)^(3/4)),x,4,1/6*(-2-3*x^2)^(1/4)/x^3-5/8*(-2-3*x^2)^(1/4)/x-5/16*sqrt(cos(2*arctan((-2-3*x^2)^(1/4)/2^(1/4)))^2)/cos(2*arctan((-2-3*x^2)^(1/4)/2^(1/4)))*EllipticF(sin(2*arctan((-2-3*x^2)^(1/4)/2^(1/4))),sqrt(1/2))*sqrt(3)*(sqrt(2)+sqrt(-2-3*x^2))*sqrt(-x^2/(sqrt(2)+sqrt(-2-3*x^2))^2)/(2^(1/4)*x)],
[1/(x^6*(-2-3*x^2)^(3/4)),x,5,1/10*(-2-3*x^2)^(1/4)/x^5-9/40*(-2-3*x^2)^(1/4)/x^3+27/32*(-2-3*x^2)^(1/4)/x+27/64*sqrt(cos(2*arctan((-2-3*x^2)^(1/4)/2^(1/4)))^2)/cos(2*arctan((-2-3*x^2)^(1/4)/2^(1/4)))*EllipticF(sin(2*arctan((-2-3*x^2)^(1/4)/2^(1/4))),sqrt(1/2))*sqrt(3)*(sqrt(2)+sqrt(-2-3*x^2))*sqrt(-x^2/(sqrt(2)+sqrt(-2-3*x^2))^2)/(2^(1/4)*x)],

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

# p>0
[(c*x)^(7/2)*(a+b*x^2)^(1/4),x,8,1/30*a*c*(c*x)^(5/2)*(a+b*x^2)^(1/4)/b+1/5*(c*x)^(9/2)*(a+b*x^2)^(1/4)/c-1/12*a^(5/2)*c^2*(1+a/(b*x^2))^(3/4)*(c*x)^(3/2)*sqrt(cos(1/2*arccot(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arccot(x*sqrt(b)/sqrt(a)))*EllipticF(sin(1/2*arccot(x*sqrt(b)/sqrt(a))),sqrt(2))/(b^(3/2)*(a+b*x^2)^(3/4))-1/12*a^2*c^3*(a+b*x^2)^(1/4)*sqrt(c*x)/b^2],
[(c*x)^(3/2)*(a+b*x^2)^(1/4),x,7,1/3*(c*x)^(5/2)*(a+b*x^2)^(1/4)/c+1/6*a^(3/2)*(1+a/(b*x^2))^(3/4)*(c*x)^(3/2)*sqrt(cos(1/2*arccot(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arccot(x*sqrt(b)/sqrt(a)))*EllipticF(sin(1/2*arccot(x*sqrt(b)/sqrt(a))),sqrt(2))/((a+b*x^2)^(3/4)*sqrt(b))+1/6*a*c*(a+b*x^2)^(1/4)*sqrt(c*x)/b],
[(a+b*x^2)^(1/4)/(c*x)^(1/2),x,6,-(1+a/(b*x^2))^(3/4)*(c*x)^(3/2)*sqrt(cos(1/2*arccot(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arccot(x*sqrt(b)/sqrt(a)))*EllipticF(sin(1/2*arccot(x*sqrt(b)/sqrt(a))),sqrt(2))*sqrt(a)*sqrt(b)/(c^2*(a+b*x^2)^(3/4))+(a+b*x^2)^(1/4)*sqrt(c*x)/c],
[(a+b*x^2)^(1/4)/(c*x)^(5/2),x,6,-2/3*(a+b*x^2)^(1/4)/(c*(c*x)^(3/2))-2/3*b^(3/2)*(1+a/(b*x^2))^(3/4)*(c*x)^(3/2)*sqrt(cos(1/2*arccot(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arccot(x*sqrt(b)/sqrt(a)))*EllipticF(sin(1/2*arccot(x*sqrt(b)/sqrt(a))),sqrt(2))/(c^4*(a+b*x^2)^(3/4)*sqrt(a))],
[(a+b*x^2)^(1/4)/(c*x)^(9/2),x,7,-2/7*(a+b*x^2)^(1/4)/(c*(c*x)^(7/2))-2/21*b*(a+b*x^2)^(1/4)/(a*c^3*(c*x)^(3/2))+4/21*b^(5/2)*(1+a/(b*x^2))^(3/4)*(c*x)^(3/2)*sqrt(cos(1/2*arccot(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arccot(x*sqrt(b)/sqrt(a)))*EllipticF(sin(1/2*arccot(x*sqrt(b)/sqrt(a))),sqrt(2))/(a^(3/2)*c^6*(a+b*x^2)^(3/4))],
[(a+b*x^2)^(1/4)/(c*x)^(13/2),x,8,-2/11*(a+b*x^2)^(1/4)/(c*(c*x)^(11/2))-2/77*b*(a+b*x^2)^(1/4)/(a*c^3*(c*x)^(7/2))+4/77*b^2*(a+b*x^2)^(1/4)/(a^2*c^5*(c*x)^(3/2))-8/77*b^(7/2)*(1+a/(b*x^2))^(3/4)*(c*x)^(3/2)*sqrt(cos(1/2*arccot(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arccot(x*sqrt(b)/sqrt(a)))*EllipticF(sin(1/2*arccot(x*sqrt(b)/sqrt(a))),sqrt(2))/(a^(5/2)*c^8*(a+b*x^2)^(3/4))],
[(c*x)^(5/2)*(a+b*x^2)^(1/4),x,7,1/16*a*c*(c*x)^(3/2)*(a+b*x^2)^(1/4)/b+1/4*(c*x)^(7/2)*(a+b*x^2)^(1/4)/c+3/32*a^2*c^(5/2)*arctan(b^(1/4)*sqrt(c*x)/((a+b*x^2)^(1/4)*sqrt(c)))/b^(7/4)-3/32*a^2*c^(5/2)*arctanh(b^(1/4)*sqrt(c*x)/((a+b*x^2)^(1/4)*sqrt(c)))/b^(7/4)],
[(c*x)^(1/2)*(a+b*x^2)^(1/4),x,6,1/2*(c*x)^(3/2)*(a+b*x^2)^(1/4)/c-1/4*a*arctan(b^(1/4)*sqrt(c*x)/((a+b*x^2)^(1/4)*sqrt(c)))*sqrt(c)/b^(3/4)+1/4*a*arctanh(b^(1/4)*sqrt(c*x)/((a+b*x^2)^(1/4)*sqrt(c)))*sqrt(c)/b^(3/4)],
[(a+b*x^2)^(1/4)/(c*x)^(3/2),x,6,-b^(1/4)*arctan(b^(1/4)*sqrt(c*x)/((a+b*x^2)^(1/4)*sqrt(c)))/c^(3/2)+b^(1/4)*arctanh(b^(1/4)*sqrt(c*x)/((a+b*x^2)^(1/4)*sqrt(c)))/c^(3/2)-2*(a+b*x^2)^(1/4)/(c*sqrt(c*x))],
[(a+b*x^2)^(1/4)/(c*x)^(7/2),x,1,-2/5*(a+b*x^2)^(5/4)/(a*c*(c*x)^(5/2))],
[(a+b*x^2)^(1/4)/(c*x)^(11/2),x,2,-2/5*(a+b*x^2)^(5/4)/(a*c*(c*x)^(9/2))+8/45*(a+b*x^2)^(9/4)/(a^2*c*(c*x)^(9/2))],
[(a+b*x^2)^(1/4)/(c*x)^(15/2),x,3,-2/5*(a+b*x^2)^(5/4)/(a*c*(c*x)^(13/2))+16/45*(a+b*x^2)^(9/4)/(a^2*c*(c*x)^(13/2))-64/585*(a+b*x^2)^(13/4)/(a^3*c*(c*x)^(13/2))],
[(a+b*x^2)^(1/4)/(c*x)^(19/2),x,4,-2/5*(a+b*x^2)^(5/4)/(a*c*(c*x)^(17/2))+8/15*(a+b*x^2)^(9/4)/(a^2*c*(c*x)^(17/2))-64/195*(a+b*x^2)^(13/4)/(a^3*c*(c*x)^(17/2))+256/3315*(a+b*x^2)^(17/4)/(a^4*c*(c*x)^(17/2))],
[(c*x)^(3/2)*(a-b*x^2)^(1/4),x,7,1/3*(c*x)^(5/2)*(a-b*x^2)^(1/4)/c-1/6*a^(3/2)*(1-a/(b*x^2))^(3/4)*(c*x)^(3/2)*sqrt(cos(1/2*arccsc(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arccsc(x*sqrt(b)/sqrt(a)))*EllipticF(sin(1/2*arccsc(x*sqrt(b)/sqrt(a))),sqrt(2))/((a-b*x^2)^(3/4)*sqrt(b))-1/6*a*c*(a-b*x^2)^(1/4)*sqrt(c*x)/b],
[(a-b*x^2)^(1/4)/(c*x)^(1/2),x,6,-(1-a/(b*x^2))^(3/4)*(c*x)^(3/2)*sqrt(cos(1/2*arccsc(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arccsc(x*sqrt(b)/sqrt(a)))*EllipticF(sin(1/2*arccsc(x*sqrt(b)/sqrt(a))),sqrt(2))*sqrt(a)*sqrt(b)/(c^2*(a-b*x^2)^(3/4))+(a-b*x^2)^(1/4)*sqrt(c*x)/c],
[(a-b*x^2)^(1/4)/(c*x)^(5/2),x,6,-2/3*(a-b*x^2)^(1/4)/(c*(c*x)^(3/2))+2/3*b^(3/2)*(1-a/(b*x^2))^(3/4)*(c*x)^(3/2)*sqrt(cos(1/2*arccsc(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arccsc(x*sqrt(b)/sqrt(a)))*EllipticF(sin(1/2*arccsc(x*sqrt(b)/sqrt(a))),sqrt(2))/(c^4*(a-b*x^2)^(3/4)*sqrt(a))],
[(a-b*x^2)^(1/4)/(c*x)^(9/2),x,7,-2/7*(a-b*x^2)^(1/4)/(c*(c*x)^(7/2))+2/21*b*(a-b*x^2)^(1/4)/(a*c^3*(c*x)^(3/2))+4/21*b^(5/2)*(1-a/(b*x^2))^(3/4)*(c*x)^(3/2)*sqrt(cos(1/2*arccsc(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arccsc(x*sqrt(b)/sqrt(a)))*EllipticF(sin(1/2*arccsc(x*sqrt(b)/sqrt(a))),sqrt(2))/(a^(3/2)*c^6*(a-b*x^2)^(3/4))],
[(a-b*x^2)^(1/4)/(c*x)^(13/2),x,8,-2/11*(a-b*x^2)^(1/4)/(c*(c*x)^(11/2))+2/77*b*(a-b*x^2)^(1/4)/(a*c^3*(c*x)^(7/2))+4/77*b^2*(a-b*x^2)^(1/4)/(a^2*c^5*(c*x)^(3/2))+8/77*b^(7/2)*(1-a/(b*x^2))^(3/4)*(c*x)^(3/2)*sqrt(cos(1/2*arccsc(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arccsc(x*sqrt(b)/sqrt(a)))*EllipticF(sin(1/2*arccsc(x*sqrt(b)/sqrt(a))),sqrt(2))/(a^(5/2)*c^8*(a-b*x^2)^(3/4))],
[(c*x)^(5/2)*(a-b*x^2)^(1/4),x,13,-1/16*a*c*(c*x)^(3/2)*(a-b*x^2)^(1/4)/b+1/4*(c*x)^(7/2)*(a-b*x^2)^(1/4)/c-3/32*a^2*c^(5/2)*arctan(1-b^(1/4)*sqrt(2)*sqrt(c*x)/((a-b*x^2)^(1/4)*sqrt(c)))/(b^(7/4)*sqrt(2))+3/32*a^2*c^(5/2)*arctan(1+b^(1/4)*sqrt(2)*sqrt(c*x)/((a-b*x^2)^(1/4)*sqrt(c)))/(b^(7/4)*sqrt(2))+3/64*a^2*c^(5/2)*log(sqrt(c)-b^(1/4)*sqrt(2)*sqrt(c*x)/(a-b*x^2)^(1/4)+x*sqrt(b)*sqrt(c)/sqrt(a-b*x^2))/(b^(7/4)*sqrt(2))-3/64*a^2*c^(5/2)*log(sqrt(c)+b^(1/4)*sqrt(2)*sqrt(c*x)/(a-b*x^2)^(1/4)+x*sqrt(b)*sqrt(c)/sqrt(a-b*x^2))/(b^(7/4)*sqrt(2))],
[(c*x)^(1/2)*(a-b*x^2)^(1/4),x,12,1/2*(c*x)^(3/2)*(a-b*x^2)^(1/4)/c-1/4*a*arctan(1-b^(1/4)*sqrt(2)*sqrt(c*x)/((a-b*x^2)^(1/4)*sqrt(c)))*sqrt(c)/(b^(3/4)*sqrt(2))+1/4*a*arctan(1+b^(1/4)*sqrt(2)*sqrt(c*x)/((a-b*x^2)^(1/4)*sqrt(c)))*sqrt(c)/(b^(3/4)*sqrt(2))+1/8*a*log(sqrt(c)-b^(1/4)*sqrt(2)*sqrt(c*x)/(a-b*x^2)^(1/4)+x*sqrt(b)*sqrt(c)/sqrt(a-b*x^2))*sqrt(c)/(b^(3/4)*sqrt(2))-1/8*a*log(sqrt(c)+b^(1/4)*sqrt(2)*sqrt(c*x)/(a-b*x^2)^(1/4)+x*sqrt(b)*sqrt(c)/sqrt(a-b*x^2))*sqrt(c)/(b^(3/4)*sqrt(2))],
[(a-b*x^2)^(1/4)/(c*x)^(3/2),x,12,b^(1/4)*arctan(1-b^(1/4)*sqrt(2)*sqrt(c*x)/((a-b*x^2)^(1/4)*sqrt(c)))/(c^(3/2)*sqrt(2))-b^(1/4)*arctan(1+b^(1/4)*sqrt(2)*sqrt(c*x)/((a-b*x^2)^(1/4)*sqrt(c)))/(c^(3/2)*sqrt(2))-1/2*b^(1/4)*log(sqrt(c)-b^(1/4)*sqrt(2)*sqrt(c*x)/(a-b*x^2)^(1/4)+x*sqrt(b)*sqrt(c)/sqrt(a-b*x^2))/(c^(3/2)*sqrt(2))+1/2*b^(1/4)*log(sqrt(c)+b^(1/4)*sqrt(2)*sqrt(c*x)/(a-b*x^2)^(1/4)+x*sqrt(b)*sqrt(c)/sqrt(a-b*x^2))/(c^(3/2)*sqrt(2))-2*(a-b*x^2)^(1/4)/(c*sqrt(c*x))],
[(a-b*x^2)^(1/4)/(c*x)^(7/2),x,1,-2/5*(a-b*x^2)^(5/4)/(a*c*(c*x)^(5/2))],
[(a-b*x^2)^(1/4)/(c*x)^(11/2),x,2,-2/5*(a-b*x^2)^(5/4)/(a*c*(c*x)^(9/2))+8/45*(a-b*x^2)^(9/4)/(a^2*c*(c*x)^(9/2))],
[(a-b*x^2)^(1/4)/(c*x)^(15/2),x,3,-2/5*(a-b*x^2)^(5/4)/(a*c*(c*x)^(13/2))+16/45*(a-b*x^2)^(9/4)/(a^2*c*(c*x)^(13/2))-64/585*(a-b*x^2)^(13/4)/(a^3*c*(c*x)^(13/2))],
[(a-b*x^2)^(1/4)/(c*x)^(19/2),x,4,-2/5*(a-b*x^2)^(5/4)/(a*c*(c*x)^(17/2))+8/15*(a-b*x^2)^(9/4)/(a^2*c*(c*x)^(17/2))-64/195*(a-b*x^2)^(13/4)/(a^3*c*(c*x)^(17/2))+256/3315*(a-b*x^2)^(17/4)/(a^4*c*(c*x)^(17/2))],

# p<0
[(c*x)^(3/2)/(a+b*x^2)^(1/4),x,6,-1/4*a*c^(3/2)*arctan(b^(1/4)*sqrt(c*x)/((a+b*x^2)^(1/4)*sqrt(c)))/b^(5/4)-1/4*a*c^(3/2)*arctanh(b^(1/4)*sqrt(c*x)/((a+b*x^2)^(1/4)*sqrt(c)))/b^(5/4)+1/2*c*(a+b*x^2)^(3/4)*sqrt(c*x)/b],
[1/((c*x)^(1/2)*(a+b*x^2)^(1/4)),x,5,arctan(b^(1/4)*sqrt(c*x)/((a+b*x^2)^(1/4)*sqrt(c)))/(b^(1/4)*sqrt(c))+arctanh(b^(1/4)*sqrt(c*x)/((a+b*x^2)^(1/4)*sqrt(c)))/(b^(1/4)*sqrt(c))],
[1/((c*x)^(5/2)*(a+b*x^2)^(1/4)),x,1,-2/3*(a+b*x^2)^(3/4)/(a*c*(c*x)^(3/2))],
[1/((c*x)^(9/2)*(a+b*x^2)^(1/4)),x,2,-2/3*(a+b*x^2)^(3/4)/(a*c*(c*x)^(7/2))+8/21*(a+b*x^2)^(7/4)/(a^2*c*(c*x)^(7/2))],
[1/((c*x)^(13/2)*(a+b*x^2)^(1/4)),x,3,-2/3*(a+b*x^2)^(3/4)/(a*c*(c*x)^(11/2))+16/21*(a+b*x^2)^(7/4)/(a^2*c*(c*x)^(11/2))-64/231*(a+b*x^2)^(11/4)/(a^3*c*(c*x)^(11/2))],
[(c*x)^(9/2)/(a+b*x^2)^(1/4),x,6,-7/30*a*c^3*(c*x)^(3/2)*(a+b*x^2)^(3/4)/b^2+1/5*c*(c*x)^(7/2)*(a+b*x^2)^(3/4)/b+7/20*a^2*c^4*x*sqrt(c*x)/(b^2*(a+b*x^2)^(1/4))+7/20*a^(5/2)*c^4*(1+a/(b*x^2))^(1/4)*sqrt(cos(1/2*arccot(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arccot(x*sqrt(b)/sqrt(a)))*EllipticE(sin(1/2*arccot(x*sqrt(b)/sqrt(a))),sqrt(2))*sqrt(c*x)/(b^(5/2)*(a+b*x^2)^(1/4))],
[(c*x)^(5/2)/(a+b*x^2)^(1/4),x,5,1/3*c*(c*x)^(3/2)*(a+b*x^2)^(3/4)/b-1/2*a*c^2*x*sqrt(c*x)/(b*(a+b*x^2)^(1/4))-1/2*a^(3/2)*c^2*(1+a/(b*x^2))^(1/4)*sqrt(cos(1/2*arccot(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arccot(x*sqrt(b)/sqrt(a)))*EllipticE(sin(1/2*arccot(x*sqrt(b)/sqrt(a))),sqrt(2))*sqrt(c*x)/(b^(3/2)*(a+b*x^2)^(1/4))],
[(c*x)^(1/2)/(a+b*x^2)^(1/4),x,4,x*sqrt(c*x)/(a+b*x^2)^(1/4)+(1+a/(b*x^2))^(1/4)*sqrt(cos(1/2*arccot(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arccot(x*sqrt(b)/sqrt(a)))*EllipticE(sin(1/2*arccot(x*sqrt(b)/sqrt(a))),sqrt(2))*sqrt(a)*sqrt(c*x)/((a+b*x^2)^(1/4)*sqrt(b))],
[1/((c*x)^(3/2)*(a+b*x^2)^(1/4)),x,4,(-2)/(c*(a+b*x^2)^(1/4)*sqrt(c*x))+2*(1+a/(b*x^2))^(1/4)*sqrt(cos(1/2*arccot(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arccot(x*sqrt(b)/sqrt(a)))*EllipticE(sin(1/2*arccot(x*sqrt(b)/sqrt(a))),sqrt(2))*sqrt(b)*sqrt(c*x)/(c^2*(a+b*x^2)^(1/4)*sqrt(a))],
[1/((c*x)^(7/2)*(a+b*x^2)^(1/4)),x,5,-2/5*(a+b*x^2)^(3/4)/(a*c*(c*x)^(5/2))+4/5*b/(a*c^3*(a+b*x^2)^(1/4)*sqrt(c*x))-4/5*b^(3/2)*(1+a/(b*x^2))^(1/4)*sqrt(cos(1/2*arccot(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arccot(x*sqrt(b)/sqrt(a)))*EllipticE(sin(1/2*arccot(x*sqrt(b)/sqrt(a))),sqrt(2))*sqrt(c*x)/(a^(3/2)*c^4*(a+b*x^2)^(1/4))],
[1/((c*x)^(11/2)*(a+b*x^2)^(1/4)),x,6,-2/9*(a+b*x^2)^(3/4)/(a*c*(c*x)^(9/2))+4/15*b*(a+b*x^2)^(3/4)/(a^2*c^3*(c*x)^(5/2))-8/15*b^2/(a^2*c^5*(a+b*x^2)^(1/4)*sqrt(c*x))+8/15*b^(5/2)*(1+a/(b*x^2))^(1/4)*sqrt(cos(1/2*arccot(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arccot(x*sqrt(b)/sqrt(a)))*EllipticE(sin(1/2*arccot(x*sqrt(b)/sqrt(a))),sqrt(2))*sqrt(c*x)/(a^(5/2)*c^6*(a+b*x^2)^(1/4))],
[(c*x)^(3/2)/(a-b*x^2)^(1/4),x,12,-1/4*a*c^(3/2)*arctan(1-b^(1/4)*sqrt(2)*sqrt(c*x)/((a-b*x^2)^(1/4)*sqrt(c)))/(b^(5/4)*sqrt(2))+1/4*a*c^(3/2)*arctan(1+b^(1/4)*sqrt(2)*sqrt(c*x)/((a-b*x^2)^(1/4)*sqrt(c)))/(b^(5/4)*sqrt(2))-1/8*a*c^(3/2)*log(sqrt(c)-b^(1/4)*sqrt(2)*sqrt(c*x)/(a-b*x^2)^(1/4)+x*sqrt(b)*sqrt(c)/sqrt(a-b*x^2))/(b^(5/4)*sqrt(2))+1/8*a*c^(3/2)*log(sqrt(c)+b^(1/4)*sqrt(2)*sqrt(c*x)/(a-b*x^2)^(1/4)+x*sqrt(b)*sqrt(c)/sqrt(a-b*x^2))/(b^(5/4)*sqrt(2))-1/2*c*(a-b*x^2)^(3/4)*sqrt(c*x)/b],
[1/((c*x)^(1/2)*(a-b*x^2)^(1/4)),x,11,-arctan(1-b^(1/4)*sqrt(2)*sqrt(c*x)/((a-b*x^2)^(1/4)*sqrt(c)))/(b^(1/4)*sqrt(2)*sqrt(c))+arctan(1+b^(1/4)*sqrt(2)*sqrt(c*x)/((a-b*x^2)^(1/4)*sqrt(c)))/(b^(1/4)*sqrt(2)*sqrt(c))-1/2*log(sqrt(c)-b^(1/4)*sqrt(2)*sqrt(c*x)/(a-b*x^2)^(1/4)+x*sqrt(b)*sqrt(c)/sqrt(a-b*x^2))/(b^(1/4)*sqrt(2)*sqrt(c))+1/2*log(sqrt(c)+b^(1/4)*sqrt(2)*sqrt(c*x)/(a-b*x^2)^(1/4)+x*sqrt(b)*sqrt(c)/sqrt(a-b*x^2))/(b^(1/4)*sqrt(2)*sqrt(c))],
[1/((c*x)^(5/2)*(a-b*x^2)^(1/4)),x,1,-2/3*(a-b*x^2)^(3/4)/(a*c*(c*x)^(3/2))],
[1/((c*x)^(9/2)*(a-b*x^2)^(1/4)),x,2,-2/3*(a-b*x^2)^(3/4)/(a*c*(c*x)^(7/2))+8/21*(a-b*x^2)^(7/4)/(a^2*c*(c*x)^(7/2))],
[1/((c*x)^(13/2)*(a-b*x^2)^(1/4)),x,3,-2/3*(a-b*x^2)^(3/4)/(a*c*(c*x)^(11/2))+16/21*(a-b*x^2)^(7/4)/(a^2*c*(c*x)^(11/2))-64/231*(a-b*x^2)^(11/4)/(a^3*c*(c*x)^(11/2))],
[(c*x)^(5/2)/(a-b*x^2)^(1/4),x,5,-1/3*c*(c*x)^(3/2)*(a-b*x^2)^(3/4)/b-1/2*a*c^3*(a-b*x^2)^(3/4)/(b^2*sqrt(c*x))+1/2*a^(3/2)*c^2*(1-a/(b*x^2))^(1/4)*sqrt(cos(1/2*arccsc(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arccsc(x*sqrt(b)/sqrt(a)))*EllipticE(sin(1/2*arccsc(x*sqrt(b)/sqrt(a))),sqrt(2))*sqrt(c*x)/(b^(3/2)*(a-b*x^2)^(1/4))],
[(c*x)^(1/2)/(a-b*x^2)^(1/4),x,4,-c*(a-b*x^2)^(3/4)/(b*sqrt(c*x))+(1-a/(b*x^2))^(1/4)*sqrt(cos(1/2*arccsc(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arccsc(x*sqrt(b)/sqrt(a)))*EllipticE(sin(1/2*arccsc(x*sqrt(b)/sqrt(a))),sqrt(2))*sqrt(a)*sqrt(c*x)/((a-b*x^2)^(1/4)*sqrt(b))],
[1/((c*x)^(3/2)*(a-b*x^2)^(1/4)),x,3,-2*(1-a/(b*x^2))^(1/4)*sqrt(cos(1/2*arccsc(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arccsc(x*sqrt(b)/sqrt(a)))*EllipticE(sin(1/2*arccsc(x*sqrt(b)/sqrt(a))),sqrt(2))*sqrt(b)*sqrt(c*x)/(c^2*(a-b*x^2)^(1/4)*sqrt(a))],
[1/((c*x)^(7/2)*(a-b*x^2)^(1/4)),x,4,-2/5*(a-b*x^2)^(3/4)/(a*c*(c*x)^(5/2))-4/5*b^(3/2)*(1-a/(b*x^2))^(1/4)*sqrt(cos(1/2*arccsc(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arccsc(x*sqrt(b)/sqrt(a)))*EllipticE(sin(1/2*arccsc(x*sqrt(b)/sqrt(a))),sqrt(2))*sqrt(c*x)/(a^(3/2)*c^4*(a-b*x^2)^(1/4))],
[1/((c*x)^(11/2)*(a-b*x^2)^(1/4)),x,5,-2/9*(a-b*x^2)^(3/4)/(a*c*(c*x)^(9/2))-4/15*b*(a-b*x^2)^(3/4)/(a^2*c^3*(c*x)^(5/2))-8/15*b^(5/2)*(1-a/(b*x^2))^(1/4)*sqrt(cos(1/2*arccsc(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arccsc(x*sqrt(b)/sqrt(a)))*EllipticE(sin(1/2*arccsc(x*sqrt(b)/sqrt(a))),sqrt(2))*sqrt(c*x)/(a^(5/2)*c^6*(a-b*x^2)^(1/4))],
[(c*x)^(3/2)/(a+b*x^2)^(3/4),x,6,(1+a/(b*x^2))^(3/4)*(c*x)^(3/2)*sqrt(cos(1/2*arccot(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arccot(x*sqrt(b)/sqrt(a)))*EllipticF(sin(1/2*arccot(x*sqrt(b)/sqrt(a))),sqrt(2))*sqrt(a)/((a+b*x^2)^(3/4)*sqrt(b))+c*(a+b*x^2)^(1/4)*sqrt(c*x)/b],
[1/((c*x)^(1/2)*(a+b*x^2)^(3/4)),x,5,-2*(1+a/(b*x^2))^(3/4)*(c*x)^(3/2)*sqrt(cos(1/2*arccot(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arccot(x*sqrt(b)/sqrt(a)))*EllipticF(sin(1/2*arccot(x*sqrt(b)/sqrt(a))),sqrt(2))*sqrt(b)/(c^2*(a+b*x^2)^(3/4)*sqrt(a))],
[1/((c*x)^(5/2)*(a+b*x^2)^(3/4)),x,6,-2/3*(a+b*x^2)^(1/4)/(a*c*(c*x)^(3/2))+4/3*b^(3/2)*(1+a/(b*x^2))^(3/4)*(c*x)^(3/2)*sqrt(cos(1/2*arccot(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arccot(x*sqrt(b)/sqrt(a)))*EllipticF(sin(1/2*arccot(x*sqrt(b)/sqrt(a))),sqrt(2))/(a^(3/2)*c^4*(a+b*x^2)^(3/4))],
[1/((c*x)^(9/2)*(a+b*x^2)^(3/4)),x,7,-2/7*(a+b*x^2)^(1/4)/(a*c*(c*x)^(7/2))+4/7*b*(a+b*x^2)^(1/4)/(a^2*c^3*(c*x)^(3/2))-8/7*b^(5/2)*(1+a/(b*x^2))^(3/4)*(c*x)^(3/2)*sqrt(cos(1/2*arccot(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arccot(x*sqrt(b)/sqrt(a)))*EllipticF(sin(1/2*arccot(x*sqrt(b)/sqrt(a))),sqrt(2))/(a^(5/2)*c^6*(a+b*x^2)^(3/4))],
[1/((c*x)^(13/2)*(a+b*x^2)^(3/4)),x,8,-2/11*(a+b*x^2)^(1/4)/(a*c*(c*x)^(11/2))+20/77*b*(a+b*x^2)^(1/4)/(a^2*c^3*(c*x)^(7/2))-40/77*b^2*(a+b*x^2)^(1/4)/(a^3*c^5*(c*x)^(3/2))+80/77*b^(7/2)*(1+a/(b*x^2))^(3/4)*(c*x)^(3/2)*sqrt(cos(1/2*arccot(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arccot(x*sqrt(b)/sqrt(a)))*EllipticF(sin(1/2*arccot(x*sqrt(b)/sqrt(a))),sqrt(2))/(a^(7/2)*c^8*(a+b*x^2)^(3/4))],
[(c*x)^(5/2)/(a+b*x^2)^(3/4),x,6,1/2*c*(c*x)^(3/2)*(a+b*x^2)^(1/4)/b+3/4*a*c^(5/2)*arctan(b^(1/4)*sqrt(c*x)/((a+b*x^2)^(1/4)*sqrt(c)))/b^(7/4)-3/4*a*c^(5/2)*arctanh(b^(1/4)*sqrt(c*x)/((a+b*x^2)^(1/4)*sqrt(c)))/b^(7/4)],
[(c*x)^(1/2)/(a+b*x^2)^(3/4),x,5,-arctan(b^(1/4)*sqrt(c*x)/((a+b*x^2)^(1/4)*sqrt(c)))*sqrt(c)/b^(3/4)+arctanh(b^(1/4)*sqrt(c*x)/((a+b*x^2)^(1/4)*sqrt(c)))*sqrt(c)/b^(3/4)],
[1/((c*x)^(3/2)*(a+b*x^2)^(3/4)),x,1,-2*(a+b*x^2)^(1/4)/(a*c*sqrt(c*x))],
[1/((c*x)^(7/2)*(a+b*x^2)^(3/4)),x,2,-2*(a+b*x^2)^(1/4)/(a*c*(c*x)^(5/2))+8/5*(a+b*x^2)^(5/4)/(a^2*c*(c*x)^(5/2))],
[1/((c*x)^(11/2)*(a+b*x^2)^(3/4)),x,3,-2*(a+b*x^2)^(1/4)/(a*c*(c*x)^(9/2))+16/5*(a+b*x^2)^(5/4)/(a^2*c*(c*x)^(9/2))-64/45*(a+b*x^2)^(9/4)/(a^3*c*(c*x)^(9/2))],
[(c*x)^(3/2)/(a-b*x^2)^(3/4),x,6,-(1-a/(b*x^2))^(3/4)*(c*x)^(3/2)*sqrt(cos(1/2*arccsc(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arccsc(x*sqrt(b)/sqrt(a)))*EllipticF(sin(1/2*arccsc(x*sqrt(b)/sqrt(a))),sqrt(2))*sqrt(a)/((a-b*x^2)^(3/4)*sqrt(b))-c*(a-b*x^2)^(1/4)*sqrt(c*x)/b],
[1/((c*x)^(1/2)*(a-b*x^2)^(3/4)),x,5,-2*(1-a/(b*x^2))^(3/4)*(c*x)^(3/2)*sqrt(cos(1/2*arccsc(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arccsc(x*sqrt(b)/sqrt(a)))*EllipticF(sin(1/2*arccsc(x*sqrt(b)/sqrt(a))),sqrt(2))*sqrt(b)/(c^2*(a-b*x^2)^(3/4)*sqrt(a))],
[1/((c*x)^(5/2)*(a-b*x^2)^(3/4)),x,6,-2/3*(a-b*x^2)^(1/4)/(a*c*(c*x)^(3/2))-4/3*b^(3/2)*(1-a/(b*x^2))^(3/4)*(c*x)^(3/2)*sqrt(cos(1/2*arccsc(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arccsc(x*sqrt(b)/sqrt(a)))*EllipticF(sin(1/2*arccsc(x*sqrt(b)/sqrt(a))),sqrt(2))/(a^(3/2)*c^4*(a-b*x^2)^(3/4))],
[1/((c*x)^(9/2)*(a-b*x^2)^(3/4)),x,7,-2/7*(a-b*x^2)^(1/4)/(a*c*(c*x)^(7/2))-4/7*b*(a-b*x^2)^(1/4)/(a^2*c^3*(c*x)^(3/2))-8/7*b^(5/2)*(1-a/(b*x^2))^(3/4)*(c*x)^(3/2)*sqrt(cos(1/2*arccsc(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arccsc(x*sqrt(b)/sqrt(a)))*EllipticF(sin(1/2*arccsc(x*sqrt(b)/sqrt(a))),sqrt(2))/(a^(5/2)*c^6*(a-b*x^2)^(3/4))],
[1/((c*x)^(13/2)*(a-b*x^2)^(3/4)),x,8,-2/11*(a-b*x^2)^(1/4)/(a*c*(c*x)^(11/2))-20/77*b*(a-b*x^2)^(1/4)/(a^2*c^3*(c*x)^(7/2))-40/77*b^2*(a-b*x^2)^(1/4)/(a^3*c^5*(c*x)^(3/2))-80/77*b^(7/2)*(1-a/(b*x^2))^(3/4)*(c*x)^(3/2)*sqrt(cos(1/2*arccsc(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arccsc(x*sqrt(b)/sqrt(a)))*EllipticF(sin(1/2*arccsc(x*sqrt(b)/sqrt(a))),sqrt(2))/(a^(7/2)*c^8*(a-b*x^2)^(3/4))],
[(c*x)^(5/2)/(a-b*x^2)^(3/4),x,12,-1/2*c*(c*x)^(3/2)*(a-b*x^2)^(1/4)/b-3/4*a*c^(5/2)*arctan(1-b^(1/4)*sqrt(2)*sqrt(c*x)/((a-b*x^2)^(1/4)*sqrt(c)))/(b^(7/4)*sqrt(2))+3/4*a*c^(5/2)*arctan(1+b^(1/4)*sqrt(2)*sqrt(c*x)/((a-b*x^2)^(1/4)*sqrt(c)))/(b^(7/4)*sqrt(2))+3/8*a*c^(5/2)*log(sqrt(c)-b^(1/4)*sqrt(2)*sqrt(c*x)/(a-b*x^2)^(1/4)+x*sqrt(b)*sqrt(c)/sqrt(a-b*x^2))/(b^(7/4)*sqrt(2))-3/8*a*c^(5/2)*log(sqrt(c)+b^(1/4)*sqrt(2)*sqrt(c*x)/(a-b*x^2)^(1/4)+x*sqrt(b)*sqrt(c)/sqrt(a-b*x^2))/(b^(7/4)*sqrt(2))],
[(c*x)^(1/2)/(a-b*x^2)^(3/4),x,11,-arctan(1-b^(1/4)*sqrt(2)*sqrt(c*x)/((a-b*x^2)^(1/4)*sqrt(c)))*sqrt(c)/(b^(3/4)*sqrt(2))+arctan(1+b^(1/4)*sqrt(2)*sqrt(c*x)/((a-b*x^2)^(1/4)*sqrt(c)))*sqrt(c)/(b^(3/4)*sqrt(2))+1/2*log(sqrt(c)-b^(1/4)*sqrt(2)*sqrt(c*x)/(a-b*x^2)^(1/4)+x*sqrt(b)*sqrt(c)/sqrt(a-b*x^2))*sqrt(c)/(b^(3/4)*sqrt(2))-1/2*log(sqrt(c)+b^(1/4)*sqrt(2)*sqrt(c*x)/(a-b*x^2)^(1/4)+x*sqrt(b)*sqrt(c)/sqrt(a-b*x^2))*sqrt(c)/(b^(3/4)*sqrt(2))],
[1/((c*x)^(3/2)*(a-b*x^2)^(3/4)),x,1,-2*(a-b*x^2)^(1/4)/(a*c*sqrt(c*x))],
[1/((c*x)^(7/2)*(a-b*x^2)^(3/4)),x,2,-2*(a-b*x^2)^(1/4)/(a*c*(c*x)^(5/2))+8/5*(a-b*x^2)^(5/4)/(a^2*c*(c*x)^(5/2))],
[1/((c*x)^(11/2)*(a-b*x^2)^(3/4)),x,3,-2*(a-b*x^2)^(1/4)/(a*c*(c*x)^(9/2))+16/5*(a-b*x^2)^(5/4)/(a^2*c*(c*x)^(9/2))-64/45*(a-b*x^2)^(9/4)/(a^3*c*(c*x)^(9/2))],
[(c*x)^(7/2)/(a+b*x^2)^(5/4),x,7,1/2*c*(c*x)^(5/2)/(b*(a+b*x^2)^(1/4))-5/4*a*c^(7/2)*arctan(b^(1/4)*sqrt(c*x)/((a+b*x^2)^(1/4)*sqrt(c)))/b^(9/4)-5/4*a*c^(7/2)*arctanh(b^(1/4)*sqrt(c*x)/((a+b*x^2)^(1/4)*sqrt(c)))/b^(9/4)+5/2*a*c^3*sqrt(c*x)/(b^2*(a+b*x^2)^(1/4))],
[(c*x)^(3/2)/(a+b*x^2)^(5/4),x,6,c^(3/2)*arctan(b^(1/4)*sqrt(c*x)/((a+b*x^2)^(1/4)*sqrt(c)))/b^(5/4)+c^(3/2)*arctanh(b^(1/4)*sqrt(c*x)/((a+b*x^2)^(1/4)*sqrt(c)))/b^(5/4)-2*c*sqrt(c*x)/(b*(a+b*x^2)^(1/4))],
[1/((c*x)^(1/2)*(a+b*x^2)^(5/4)),x,1,2*sqrt(c*x)/(a*c*(a+b*x^2)^(1/4))],
[1/((c*x)^(5/2)*(a+b*x^2)^(5/4)),x,2,2/(a*c*(c*x)^(3/2)*(a+b*x^2)^(1/4))-8/3*(a+b*x^2)^(3/4)/(a^2*c*(c*x)^(3/2))],
[1/((c*x)^(9/2)*(a+b*x^2)^(5/4)),x,3,2/(a*c*(c*x)^(7/2)*(a+b*x^2)^(1/4))-16/3*(a+b*x^2)^(3/4)/(a^2*c*(c*x)^(7/2))+64/21*(a+b*x^2)^(7/4)/(a^3*c*(c*x)^(7/2))],
[1/((c*x)^(13/2)*(a+b*x^2)^(5/4)),x,4,2/(a*c*(c*x)^(11/2)*(a+b*x^2)^(1/4))-8*(a+b*x^2)^(3/4)/(a^2*c*(c*x)^(11/2))+64/7*(a+b*x^2)^(7/4)/(a^3*c*(c*x)^(11/2))-256/77*(a+b*x^2)^(11/4)/(a^4*c*(c*x)^(11/2))],
[(c*x)^(13/2)/(a+b*x^2)^(5/4),x,6,77/60*a^2*c^5*(c*x)^(3/2)/(b^3*(a+b*x^2)^(1/4))-11/30*a*c^3*(c*x)^(7/2)/(b^2*(a+b*x^2)^(1/4))+1/5*c*(c*x)^(11/2)/(b*(a+b*x^2)^(1/4))+77/20*a^(5/2)*c^6*(1+a/(b*x^2))^(1/4)*sqrt(cos(1/2*arccot(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arccot(x*sqrt(b)/sqrt(a)))*EllipticE(sin(1/2*arccot(x*sqrt(b)/sqrt(a))),sqrt(2))*sqrt(c*x)/(b^(7/2)*(a+b*x^2)^(1/4))],
[(c*x)^(9/2)/(a+b*x^2)^(5/4),x,5,-7/6*a*c^3*(c*x)^(3/2)/(b^2*(a+b*x^2)^(1/4))+1/3*c*(c*x)^(7/2)/(b*(a+b*x^2)^(1/4))-7/2*a^(3/2)*c^4*(1+a/(b*x^2))^(1/4)*sqrt(cos(1/2*arccot(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arccot(x*sqrt(b)/sqrt(a)))*EllipticE(sin(1/2*arccot(x*sqrt(b)/sqrt(a))),sqrt(2))*sqrt(c*x)/(b^(5/2)*(a+b*x^2)^(1/4))],
[(c*x)^(5/2)/(a+b*x^2)^(5/4),x,4,c*(c*x)^(3/2)/(b*(a+b*x^2)^(1/4))+3*c^2*(1+a/(b*x^2))^(1/4)*sqrt(cos(1/2*arccot(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arccot(x*sqrt(b)/sqrt(a)))*EllipticE(sin(1/2*arccot(x*sqrt(b)/sqrt(a))),sqrt(2))*sqrt(a)*sqrt(c*x)/(b^(3/2)*(a+b*x^2)^(1/4))],
[(c*x)^(1/2)/(a+b*x^2)^(5/4),x,3,-2*(1+a/(b*x^2))^(1/4)*sqrt(cos(1/2*arccot(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arccot(x*sqrt(b)/sqrt(a)))*EllipticE(sin(1/2*arccot(x*sqrt(b)/sqrt(a))),sqrt(2))*sqrt(c*x)/((a+b*x^2)^(1/4)*sqrt(a)*sqrt(b))],
[1/((c*x)^(3/2)*(a+b*x^2)^(5/4)),x,4,(-2)/(a*c*(a+b*x^2)^(1/4)*sqrt(c*x))+4*(1+a/(b*x^2))^(1/4)*sqrt(cos(1/2*arccot(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arccot(x*sqrt(b)/sqrt(a)))*EllipticE(sin(1/2*arccot(x*sqrt(b)/sqrt(a))),sqrt(2))*sqrt(b)*sqrt(c*x)/(a^(3/2)*c^2*(a+b*x^2)^(1/4))],
[1/((c*x)^(7/2)*(a+b*x^2)^(5/4)),x,5,(-2/5)/(a*c*(c*x)^(5/2)*(a+b*x^2)^(1/4))+12/5*b/(a^2*c^3*(a+b*x^2)^(1/4)*sqrt(c*x))-24/5*b^(3/2)*(1+a/(b*x^2))^(1/4)*sqrt(cos(1/2*arccot(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arccot(x*sqrt(b)/sqrt(a)))*EllipticE(sin(1/2*arccot(x*sqrt(b)/sqrt(a))),sqrt(2))*sqrt(c*x)/(a^(5/2)*c^4*(a+b*x^2)^(1/4))],
[1/((c*x)^(11/2)*(a+b*x^2)^(5/4)),x,6,(-2/9)/(a*c*(c*x)^(9/2)*(a+b*x^2)^(1/4))+4/9*b/(a^2*c^3*(c*x)^(5/2)*(a+b*x^2)^(1/4))-8/3*b^2/(a^3*c^5*(a+b*x^2)^(1/4)*sqrt(c*x))+16/3*b^(5/2)*(1+a/(b*x^2))^(1/4)*sqrt(cos(1/2*arccot(x*sqrt(b)/sqrt(a)))^2)/cos(1/2*arccot(x*sqrt(b)/sqrt(a)))*EllipticE(sin(1/2*arccot(x*sqrt(b)/sqrt(a))),sqrt(2))*sqrt(c*x)/(a^(7/2)*c^6*(a+b*x^2)^(1/4))],

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

# p>0

# p<0
[(c*x)^(5/4)/(a+b*x^2)^(1/4),x,2,4/9*(c*x)^(9/4)*(1+b*x^2/a)^(1/4)*hypergeom([1/4,9/8],[17/8],-b*x^2/a)/(c*(a+b*x^2)^(1/4))],
[(c*x)^(3/4)/(a+b*x^2)^(1/4),x,2,4/7*(c*x)^(7/4)*(1+b*x^2/a)^(1/4)*hypergeom([1/4,7/8],[15/8],-b*x^2/a)/(c*(a+b*x^2)^(1/4))],
[(c*x)^(1/4)/(a+b*x^2)^(1/4),x,2,4/5*(c*x)^(5/4)*(1+b*x^2/a)^(1/4)*hypergeom([1/4,5/8],[13/8],-b*x^2/a)/(c*(a+b*x^2)^(1/4))],
[1/((c*x)^(1/4)*(a+b*x^2)^(1/4)),x,2,4/3*(c*x)^(3/4)*(1+b*x^2/a)^(1/4)*hypergeom([1/4,3/8],[11/8],-b*x^2/a)/(c*(a+b*x^2)^(1/4))],
[1/((c*x)^(3/4)*(a+b*x^2)^(1/4)),x,2,4*(c*x)^(1/4)*(1+b*x^2/a)^(1/4)*hypergeom([1/8,1/4],[9/8],-b*x^2/a)/(c*(a+b*x^2)^(1/4))],
[1/((c*x)^(5/4)*(a+b*x^2)^(1/4)),x,2,-4*(1+b*x^2/a)^(1/4)*hypergeom([-1/8,1/4],[7/8],-b*x^2/a)/(c*(c*x)^(1/4)*(a+b*x^2)^(1/4))],
[(c*x)^(5/4)/(a+b*x^2)^(7/4),x,2,4/9*(c*x)^(9/4)*(1+b*x^2/a)^(3/4)*hypergeom([9/8,7/4],[17/8],-b*x^2/a)/(a*c*(a+b*x^2)^(3/4))],
[(c*x)^(3/4)/(a+b*x^2)^(7/4),x,2,4/7*(c*x)^(7/4)*(1+b*x^2/a)^(3/4)*hypergeom([7/8,7/4],[15/8],-b*x^2/a)/(a*c*(a+b*x^2)^(3/4))],
[(c*x)^(1/4)/(a+b*x^2)^(7/4),x,2,4/5*(c*x)^(5/4)*(1+b*x^2/a)^(3/4)*hypergeom([5/8,7/4],[13/8],-b*x^2/a)/(a*c*(a+b*x^2)^(3/4))],
[1/((c*x)^(1/4)*(a+b*x^2)^(7/4)),x,2,4/3*(c*x)^(3/4)*(1+b*x^2/a)^(3/4)*hypergeom([3/8,7/4],[11/8],-b*x^2/a)/(a*c*(a+b*x^2)^(3/4))],
[1/((c*x)^(3/4)*(a+b*x^2)^(7/4)),x,2,4*(c*x)^(1/4)*(1+b*x^2/a)^(3/4)*hypergeom([1/8,7/4],[9/8],-b*x^2/a)/(a*c*(a+b*x^2)^(3/4))],
[1/((c*x)^(5/4)*(a+b*x^2)^(7/4)),x,2,-4*(1+b*x^2/a)^(3/4)*hypergeom([-1/8,7/4],[7/8],-b*x^2/a)/(a*c*(c*x)^(1/4)*(a+b*x^2)^(3/4))],

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

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

# p>0
[x^6*(a+b*x^2)^(1/6),x,7,81/2816*a^3*x*(a+b*x^2)^(1/6)/b^3-9/704*a^2*x^3*(a+b*x^2)^(1/6)/b^2+3/352*a*x^5*(a+b*x^2)^(1/6)/b+3/22*x^7*(a+b*x^2)^(1/6)-81/2816*3^(3/4)*a^4*(a+b*x^2)^(1/6)*(1-(a/(a+b*x^2))^(1/3))*EllipticF((1-(a/(a+b*x^2))^(1/3)+sqrt(3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3)),sqrt(-7+4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((1+(a/(a+b*x^2))^(1/3)+(a/(a+b*x^2))^(2/3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3))^2)/(b^4*x*(a/(a+b*x^2))^(1/3)*sqrt((-1+(a/(a+b*x^2))^(1/3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3))^2))],
[x^4*(a+b*x^2)^(1/6),x,6,-27/640*a^2*x*(a+b*x^2)^(1/6)/b^2+3/160*a*x^3*(a+b*x^2)^(1/6)/b+3/16*x^5*(a+b*x^2)^(1/6)+27/640*3^(3/4)*a^3*(a+b*x^2)^(1/6)*(1-(a/(a+b*x^2))^(1/3))*EllipticF((1-(a/(a+b*x^2))^(1/3)+sqrt(3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3)),sqrt(-7+4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((1+(a/(a+b*x^2))^(1/3)+(a/(a+b*x^2))^(2/3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3))^2)/(b^3*x*(a/(a+b*x^2))^(1/3)*sqrt((-1+(a/(a+b*x^2))^(1/3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3))^2))],
[x^2*(a+b*x^2)^(1/6),x,5,3/40*a*x*(a+b*x^2)^(1/6)/b+3/10*x^3*(a+b*x^2)^(1/6)-3/40*3^(3/4)*a^2*(a+b*x^2)^(1/6)*(1-(a/(a+b*x^2))^(1/3))*EllipticF((1-(a/(a+b*x^2))^(1/3)+sqrt(3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3)),sqrt(-7+4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((1+(a/(a+b*x^2))^(1/3)+(a/(a+b*x^2))^(2/3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3))^2)/(b^2*x*(a/(a+b*x^2))^(1/3)*sqrt((-1+(a/(a+b*x^2))^(1/3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3))^2))],
[(a+b*x^2)^(1/6),x,4,3/4*x*(a+b*x^2)^(1/6)+1/4*3^(3/4)*a*(a+b*x^2)^(1/6)*(1-(a/(a+b*x^2))^(1/3))*EllipticF((1-(a/(a+b*x^2))^(1/3)+sqrt(3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3)),sqrt(-7+4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((1+(a/(a+b*x^2))^(1/3)+(a/(a+b*x^2))^(2/3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3))^2)/(b*x*(a/(a+b*x^2))^(1/3)*sqrt((-1+(a/(a+b*x^2))^(1/3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3))^2))],
[(a+b*x^2)^(1/6)/x^2,x,4,-(a+b*x^2)^(1/6)/x+(a+b*x^2)^(1/6)*(1-(a/(a+b*x^2))^(1/3))*EllipticF((1-(a/(a+b*x^2))^(1/3)+sqrt(3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3)),sqrt(-7+4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((1+(a/(a+b*x^2))^(1/3)+(a/(a+b*x^2))^(2/3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3))^2)/(3^(1/4)*x*(a/(a+b*x^2))^(1/3)*sqrt((-1+(a/(a+b*x^2))^(1/3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3))^2))],
[(a+b*x^2)^(1/6)/x^4,x,5,-1/3*(a+b*x^2)^(1/6)/x^3-1/9*b*(a+b*x^2)^(1/6)/(a*x)-2/9*b*(a+b*x^2)^(1/6)*(1-(a/(a+b*x^2))^(1/3))*EllipticF((1-(a/(a+b*x^2))^(1/3)+sqrt(3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3)),sqrt(-7+4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((1+(a/(a+b*x^2))^(1/3)+(a/(a+b*x^2))^(2/3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3))^2)/(3^(1/4)*a*x*(a/(a+b*x^2))^(1/3)*sqrt((-1+(a/(a+b*x^2))^(1/3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3))^2))],
[(a+b*x^2)^(1/6)/x^6,x,6,-1/5*(a+b*x^2)^(1/6)/x^5-1/45*b*(a+b*x^2)^(1/6)/(a*x^3)+8/135*b^2*(a+b*x^2)^(1/6)/(a^2*x)+16/135*b^2*(a+b*x^2)^(1/6)*(1-(a/(a+b*x^2))^(1/3))*EllipticF((1-(a/(a+b*x^2))^(1/3)+sqrt(3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3)),sqrt(-7+4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((1+(a/(a+b*x^2))^(1/3)+(a/(a+b*x^2))^(2/3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3))^2)/(3^(1/4)*a^2*x*(a/(a+b*x^2))^(1/3)*sqrt((-1+(a/(a+b*x^2))^(1/3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3))^2))],
[(a+b*x^2)^(1/6)/x^8,x,7,-1/7*(a+b*x^2)^(1/6)/x^7-1/105*b*(a+b*x^2)^(1/6)/(a*x^5)+2/135*b^2*(a+b*x^2)^(1/6)/(a^2*x^3)-16/405*b^3*(a+b*x^2)^(1/6)/(a^3*x)-32/405*b^3*(a+b*x^2)^(1/6)*(1-(a/(a+b*x^2))^(1/3))*EllipticF((1-(a/(a+b*x^2))^(1/3)+sqrt(3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3)),sqrt(-7+4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((1+(a/(a+b*x^2))^(1/3)+(a/(a+b*x^2))^(2/3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3))^2)/(3^(1/4)*a^3*x*(a/(a+b*x^2))^(1/3)*sqrt((-1+(a/(a+b*x^2))^(1/3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3))^2))],

# p<0
[x^6/(a+b*x^2)^(1/6),x,9,-243/896*a^3*x/(b^3*(a+b*x^2)^(1/6))+81/448*a^2*x*(a+b*x^2)^(5/6)/b^3-9/56*a*x^3*(a+b*x^2)^(5/6)/b^2+3/20*x^5*(a+b*x^2)^(5/6)/b-243/896*a^4*x/(b^3*(a/(a+b*x^2))^(2/3)*(a+b*x^2)^(7/6)*(1-(a/(a+b*x^2))^(1/3)-sqrt(3)))+81/448*3^(3/4)*a^4*(1-(a/(a+b*x^2))^(1/3))*EllipticF((1-(a/(a+b*x^2))^(1/3)+sqrt(3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3)),sqrt(-7+4*sqrt(3)))*sqrt((1+(a/(a+b*x^2))^(1/3)+(a/(a+b*x^2))^(2/3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3))^2)/(b^4*x*(a/(a+b*x^2))^(2/3)*(a+b*x^2)^(1/6)*sqrt(2)*sqrt((-1+(a/(a+b*x^2))^(1/3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3))^2))-243/1792*3^(1/4)*a^4*(1-(a/(a+b*x^2))^(1/3))*EllipticE((1-(a/(a+b*x^2))^(1/3)+sqrt(3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3)),sqrt(-7+4*sqrt(3)))*sqrt((1+(a/(a+b*x^2))^(1/3)+(a/(a+b*x^2))^(2/3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3))^2)*sqrt(2+sqrt(3))/(b^4*x*(a/(a+b*x^2))^(2/3)*(a+b*x^2)^(1/6)*sqrt((-1+(a/(a+b*x^2))^(1/3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3))^2))],
[x^4/(a+b*x^2)^(1/6),x,8,81/224*a^2*x/(b^2*(a+b*x^2)^(1/6))-27/112*a*x*(a+b*x^2)^(5/6)/b^2+3/14*x^3*(a+b*x^2)^(5/6)/b+81/224*a^3*x/(b^2*(a/(a+b*x^2))^(2/3)*(a+b*x^2)^(7/6)*(1-(a/(a+b*x^2))^(1/3)-sqrt(3)))-27/112*3^(3/4)*a^3*(1-(a/(a+b*x^2))^(1/3))*EllipticF((1-(a/(a+b*x^2))^(1/3)+sqrt(3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3)),sqrt(-7+4*sqrt(3)))*sqrt((1+(a/(a+b*x^2))^(1/3)+(a/(a+b*x^2))^(2/3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3))^2)/(b^3*x*(a/(a+b*x^2))^(2/3)*(a+b*x^2)^(1/6)*sqrt(2)*sqrt((-1+(a/(a+b*x^2))^(1/3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3))^2))+81/448*3^(1/4)*a^3*(1-(a/(a+b*x^2))^(1/3))*EllipticE((1-(a/(a+b*x^2))^(1/3)+sqrt(3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3)),sqrt(-7+4*sqrt(3)))*sqrt((1+(a/(a+b*x^2))^(1/3)+(a/(a+b*x^2))^(2/3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3))^2)*sqrt(2+sqrt(3))/(b^3*x*(a/(a+b*x^2))^(2/3)*(a+b*x^2)^(1/6)*sqrt((-1+(a/(a+b*x^2))^(1/3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3))^2))],
[x^2/(a+b*x^2)^(1/6),x,7,-9/16*a*x/(b*(a+b*x^2)^(1/6))+3/8*x*(a+b*x^2)^(5/6)/b-9/16*a^2*x/(b*(a/(a+b*x^2))^(2/3)*(a+b*x^2)^(7/6)*(1-(a/(a+b*x^2))^(1/3)-sqrt(3)))+3/8*3^(3/4)*a^2*(1-(a/(a+b*x^2))^(1/3))*EllipticF((1-(a/(a+b*x^2))^(1/3)+sqrt(3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3)),sqrt(-7+4*sqrt(3)))*sqrt((1+(a/(a+b*x^2))^(1/3)+(a/(a+b*x^2))^(2/3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3))^2)/(b^2*x*(a/(a+b*x^2))^(2/3)*(a+b*x^2)^(1/6)*sqrt(2)*sqrt((-1+(a/(a+b*x^2))^(1/3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3))^2))-9/32*3^(1/4)*a^2*(1-(a/(a+b*x^2))^(1/3))*EllipticE((1-(a/(a+b*x^2))^(1/3)+sqrt(3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3)),sqrt(-7+4*sqrt(3)))*sqrt((1+(a/(a+b*x^2))^(1/3)+(a/(a+b*x^2))^(2/3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3))^2)*sqrt(2+sqrt(3))/(b^2*x*(a/(a+b*x^2))^(2/3)*(a+b*x^2)^(1/6)*sqrt((-1+(a/(a+b*x^2))^(1/3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3))^2))],
[1/(a+b*x^2)^(1/6),x,6,3/2*x/(a+b*x^2)^(1/6)+3/2*a*x/((a/(a+b*x^2))^(2/3)*(a+b*x^2)^(7/6)*(1-(a/(a+b*x^2))^(1/3)-sqrt(3)))-3^(3/4)*a*(1-(a/(a+b*x^2))^(1/3))*EllipticF((1-(a/(a+b*x^2))^(1/3)+sqrt(3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3)),sqrt(-7+4*sqrt(3)))*sqrt((1+(a/(a+b*x^2))^(1/3)+(a/(a+b*x^2))^(2/3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3))^2)/(b*x*(a/(a+b*x^2))^(2/3)*(a+b*x^2)^(1/6)*sqrt(2)*sqrt((-1+(a/(a+b*x^2))^(1/3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3))^2))+3/4*3^(1/4)*a*(1-(a/(a+b*x^2))^(1/3))*EllipticE((1-(a/(a+b*x^2))^(1/3)+sqrt(3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3)),sqrt(-7+4*sqrt(3)))*sqrt((1+(a/(a+b*x^2))^(1/3)+(a/(a+b*x^2))^(2/3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3))^2)*sqrt(2+sqrt(3))/(b*x*(a/(a+b*x^2))^(2/3)*(a+b*x^2)^(1/6)*sqrt((-1+(a/(a+b*x^2))^(1/3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3))^2))],
[1/(x^2*(a+b*x^2)^(1/6)),x,7,b*x/(a*(a+b*x^2)^(1/6))-(a+b*x^2)^(5/6)/(a*x)+b*x/((a/(a+b*x^2))^(2/3)*(a+b*x^2)^(7/6)*(1-(a/(a+b*x^2))^(1/3)-sqrt(3)))-(1-(a/(a+b*x^2))^(1/3))*EllipticF((1-(a/(a+b*x^2))^(1/3)+sqrt(3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3)),sqrt(-7+4*sqrt(3)))*sqrt(2)*sqrt((1+(a/(a+b*x^2))^(1/3)+(a/(a+b*x^2))^(2/3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3))^2)/(3^(1/4)*x*(a/(a+b*x^2))^(2/3)*(a+b*x^2)^(1/6)*sqrt((-1+(a/(a+b*x^2))^(1/3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3))^2))+1/2*3^(1/4)*(1-(a/(a+b*x^2))^(1/3))*EllipticE((1-(a/(a+b*x^2))^(1/3)+sqrt(3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3)),sqrt(-7+4*sqrt(3)))*sqrt((1+(a/(a+b*x^2))^(1/3)+(a/(a+b*x^2))^(2/3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3))^2)*sqrt(2+sqrt(3))/(x*(a/(a+b*x^2))^(2/3)*(a+b*x^2)^(1/6)*sqrt((-1+(a/(a+b*x^2))^(1/3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3))^2))],
[1/(x^4*(a+b*x^2)^(1/6)),x,8,-4/9*b^2*x/(a^2*(a+b*x^2)^(1/6))-1/3*(a+b*x^2)^(5/6)/(a*x^3)+4/9*b*(a+b*x^2)^(5/6)/(a^2*x)-4/9*b^2*x/(a*(a/(a+b*x^2))^(2/3)*(a+b*x^2)^(7/6)*(1-(a/(a+b*x^2))^(1/3)-sqrt(3)))+4/9*b*(1-(a/(a+b*x^2))^(1/3))*EllipticF((1-(a/(a+b*x^2))^(1/3)+sqrt(3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3)),sqrt(-7+4*sqrt(3)))*sqrt(2)*sqrt((1+(a/(a+b*x^2))^(1/3)+(a/(a+b*x^2))^(2/3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3))^2)/(3^(1/4)*a*x*(a/(a+b*x^2))^(2/3)*(a+b*x^2)^(1/6)*sqrt((-1+(a/(a+b*x^2))^(1/3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3))^2))-2/3*b*(1-(a/(a+b*x^2))^(1/3))*EllipticE((1-(a/(a+b*x^2))^(1/3)+sqrt(3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3)),sqrt(-7+4*sqrt(3)))*sqrt((1+(a/(a+b*x^2))^(1/3)+(a/(a+b*x^2))^(2/3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3))^2)*sqrt(2+sqrt(3))/(3^(3/4)*a*x*(a/(a+b*x^2))^(2/3)*(a+b*x^2)^(1/6)*sqrt((-1+(a/(a+b*x^2))^(1/3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3))^2))],
[1/(x^6*(a+b*x^2)^(1/6)),x,9,8/27*b^3*x/(a^3*(a+b*x^2)^(1/6))-1/5*(a+b*x^2)^(5/6)/(a*x^5)+2/9*b*(a+b*x^2)^(5/6)/(a^2*x^3)-8/27*b^2*(a+b*x^2)^(5/6)/(a^3*x)+8/27*b^3*x/(a^2*(a/(a+b*x^2))^(2/3)*(a+b*x^2)^(7/6)*(1-(a/(a+b*x^2))^(1/3)-sqrt(3)))-8/27*b^2*(1-(a/(a+b*x^2))^(1/3))*EllipticF((1-(a/(a+b*x^2))^(1/3)+sqrt(3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3)),sqrt(-7+4*sqrt(3)))*sqrt(2)*sqrt((1+(a/(a+b*x^2))^(1/3)+(a/(a+b*x^2))^(2/3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3))^2)/(3^(1/4)*a^2*x*(a/(a+b*x^2))^(2/3)*(a+b*x^2)^(1/6)*sqrt((-1+(a/(a+b*x^2))^(1/3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3))^2))+4/9*b^2*(1-(a/(a+b*x^2))^(1/3))*EllipticE((1-(a/(a+b*x^2))^(1/3)+sqrt(3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3)),sqrt(-7+4*sqrt(3)))*sqrt((1+(a/(a+b*x^2))^(1/3)+(a/(a+b*x^2))^(2/3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3))^2)*sqrt(2+sqrt(3))/(3^(3/4)*a^2*x*(a/(a+b*x^2))^(2/3)*(a+b*x^2)^(1/6)*sqrt((-1+(a/(a+b*x^2))^(1/3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3))^2))],
[x^6/(a+b*x^2)^(5/6),x,6,81/128*a^2*x*(a+b*x^2)^(1/6)/b^3-9/32*a*x^3*(a+b*x^2)^(1/6)/b^2+3/16*x^5*(a+b*x^2)^(1/6)/b-81/128*3^(3/4)*a^3*(a+b*x^2)^(1/6)*(1-(a/(a+b*x^2))^(1/3))*EllipticF((1-(a/(a+b*x^2))^(1/3)+sqrt(3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3)),sqrt(-7+4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((1+(a/(a+b*x^2))^(1/3)+(a/(a+b*x^2))^(2/3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3))^2)/(b^4*x*(a/(a+b*x^2))^(1/3)*sqrt((-1+(a/(a+b*x^2))^(1/3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3))^2))],
[x^4/(a+b*x^2)^(5/6),x,5,-27/40*a*x*(a+b*x^2)^(1/6)/b^2+3/10*x^3*(a+b*x^2)^(1/6)/b+27/40*3^(3/4)*a^2*(a+b*x^2)^(1/6)*(1-(a/(a+b*x^2))^(1/3))*EllipticF((1-(a/(a+b*x^2))^(1/3)+sqrt(3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3)),sqrt(-7+4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((1+(a/(a+b*x^2))^(1/3)+(a/(a+b*x^2))^(2/3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3))^2)/(b^3*x*(a/(a+b*x^2))^(1/3)*sqrt((-1+(a/(a+b*x^2))^(1/3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3))^2))],
[x^2/(a+b*x^2)^(5/6),x,4,3/4*x*(a+b*x^2)^(1/6)/b-3/4*3^(3/4)*a*(a+b*x^2)^(1/6)*(1-(a/(a+b*x^2))^(1/3))*EllipticF((1-(a/(a+b*x^2))^(1/3)+sqrt(3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3)),sqrt(-7+4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((1+(a/(a+b*x^2))^(1/3)+(a/(a+b*x^2))^(2/3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3))^2)/(b^2*x*(a/(a+b*x^2))^(1/3)*sqrt((-1+(a/(a+b*x^2))^(1/3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3))^2))],
[1/(a+b*x^2)^(5/6),x,3,3^(3/4)*(a+b*x^2)^(1/6)*(1-(a/(a+b*x^2))^(1/3))*EllipticF((1-(a/(a+b*x^2))^(1/3)+sqrt(3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3)),sqrt(-7+4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((1+(a/(a+b*x^2))^(1/3)+(a/(a+b*x^2))^(2/3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3))^2)/(b*x*(a/(a+b*x^2))^(1/3)*sqrt((-1+(a/(a+b*x^2))^(1/3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3))^2))],
[1/(x^2*(a+b*x^2)^(5/6)),x,4,-(a+b*x^2)^(1/6)/(a*x)-2*(a+b*x^2)^(1/6)*(1-(a/(a+b*x^2))^(1/3))*EllipticF((1-(a/(a+b*x^2))^(1/3)+sqrt(3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3)),sqrt(-7+4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((1+(a/(a+b*x^2))^(1/3)+(a/(a+b*x^2))^(2/3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3))^2)/(3^(1/4)*a*x*(a/(a+b*x^2))^(1/3)*sqrt((-1+(a/(a+b*x^2))^(1/3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3))^2))],
[1/(x^4*(a+b*x^2)^(5/6)),x,5,-1/3*(a+b*x^2)^(1/6)/(a*x^3)+8/9*b*(a+b*x^2)^(1/6)/(a^2*x)+16/9*b*(a+b*x^2)^(1/6)*(1-(a/(a+b*x^2))^(1/3))*EllipticF((1-(a/(a+b*x^2))^(1/3)+sqrt(3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3)),sqrt(-7+4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((1+(a/(a+b*x^2))^(1/3)+(a/(a+b*x^2))^(2/3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3))^2)/(3^(1/4)*a^2*x*(a/(a+b*x^2))^(1/3)*sqrt((-1+(a/(a+b*x^2))^(1/3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3))^2))],
[1/(x^6*(a+b*x^2)^(5/6)),x,6,-1/5*(a+b*x^2)^(1/6)/(a*x^5)+14/45*b*(a+b*x^2)^(1/6)/(a^2*x^3)-112/135*b^2*(a+b*x^2)^(1/6)/(a^3*x)-224/135*b^2*(a+b*x^2)^(1/6)*(1-(a/(a+b*x^2))^(1/3))*EllipticF((1-(a/(a+b*x^2))^(1/3)+sqrt(3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3)),sqrt(-7+4*sqrt(3)))*sqrt(2-sqrt(3))*sqrt((1+(a/(a+b*x^2))^(1/3)+(a/(a+b*x^2))^(2/3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3))^2)/(3^(1/4)*a^3*x*(a/(a+b*x^2))^(1/3)*sqrt((-1+(a/(a+b*x^2))^(1/3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3))^2))],
[x^6/(a+b*x^2)^(7/6),x,9,1215/224*a^2*x/(b^3*(a+b*x^2)^(1/6))-3*x^5/(b*(a+b*x^2)^(1/6))-405/112*a*x*(a+b*x^2)^(5/6)/b^3+45/14*x^3*(a+b*x^2)^(5/6)/b^2+1215/224*a^3*x/(b^3*(a/(a+b*x^2))^(2/3)*(a+b*x^2)^(7/6)*(1-(a/(a+b*x^2))^(1/3)-sqrt(3)))-405/112*3^(3/4)*a^3*(1-(a/(a+b*x^2))^(1/3))*EllipticF((1-(a/(a+b*x^2))^(1/3)+sqrt(3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3)),sqrt(-7+4*sqrt(3)))*sqrt((1+(a/(a+b*x^2))^(1/3)+(a/(a+b*x^2))^(2/3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3))^2)/(b^4*x*(a/(a+b*x^2))^(2/3)*(a+b*x^2)^(1/6)*sqrt(2)*sqrt((-1+(a/(a+b*x^2))^(1/3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3))^2))+1215/448*3^(1/4)*a^3*(1-(a/(a+b*x^2))^(1/3))*EllipticE((1-(a/(a+b*x^2))^(1/3)+sqrt(3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3)),sqrt(-7+4*sqrt(3)))*sqrt((1+(a/(a+b*x^2))^(1/3)+(a/(a+b*x^2))^(2/3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3))^2)*sqrt(2+sqrt(3))/(b^4*x*(a/(a+b*x^2))^(2/3)*(a+b*x^2)^(1/6)*sqrt((-1+(a/(a+b*x^2))^(1/3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3))^2))],
[x^4/(a+b*x^2)^(7/6),x,8,-81/16*a*x/(b^2*(a+b*x^2)^(1/6))-3*x^3/(b*(a+b*x^2)^(1/6))+27/8*x*(a+b*x^2)^(5/6)/b^2-81/16*a^2*x/(b^2*(a/(a+b*x^2))^(2/3)*(a+b*x^2)^(7/6)*(1-(a/(a+b*x^2))^(1/3)-sqrt(3)))+27/8*3^(3/4)*a^2*(1-(a/(a+b*x^2))^(1/3))*EllipticF((1-(a/(a+b*x^2))^(1/3)+sqrt(3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3)),sqrt(-7+4*sqrt(3)))*sqrt((1+(a/(a+b*x^2))^(1/3)+(a/(a+b*x^2))^(2/3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3))^2)/(b^3*x*(a/(a+b*x^2))^(2/3)*(a+b*x^2)^(1/6)*sqrt(2)*sqrt((-1+(a/(a+b*x^2))^(1/3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3))^2))-81/32*3^(1/4)*a^2*(1-(a/(a+b*x^2))^(1/3))*EllipticE((1-(a/(a+b*x^2))^(1/3)+sqrt(3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3)),sqrt(-7+4*sqrt(3)))*sqrt((1+(a/(a+b*x^2))^(1/3)+(a/(a+b*x^2))^(2/3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3))^2)*sqrt(2+sqrt(3))/(b^3*x*(a/(a+b*x^2))^(2/3)*(a+b*x^2)^(1/6)*sqrt((-1+(a/(a+b*x^2))^(1/3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3))^2))],
[x^2/(a+b*x^2)^(7/6),x,7,3/2*x/(b*(a+b*x^2)^(1/6))+9/2*a*x/(b*(a/(a+b*x^2))^(2/3)*(a+b*x^2)^(7/6)*(1-(a/(a+b*x^2))^(1/3)-sqrt(3)))-3*3^(3/4)*a*(1-(a/(a+b*x^2))^(1/3))*EllipticF((1-(a/(a+b*x^2))^(1/3)+sqrt(3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3)),sqrt(-7+4*sqrt(3)))*sqrt((1+(a/(a+b*x^2))^(1/3)+(a/(a+b*x^2))^(2/3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3))^2)/(b^2*x*(a/(a+b*x^2))^(2/3)*(a+b*x^2)^(1/6)*sqrt(2)*sqrt((-1+(a/(a+b*x^2))^(1/3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3))^2))+9/4*3^(1/4)*a*(1-(a/(a+b*x^2))^(1/3))*EllipticE((1-(a/(a+b*x^2))^(1/3)+sqrt(3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3)),sqrt(-7+4*sqrt(3)))*sqrt((1+(a/(a+b*x^2))^(1/3)+(a/(a+b*x^2))^(2/3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3))^2)*sqrt(2+sqrt(3))/(b^2*x*(a/(a+b*x^2))^(2/3)*(a+b*x^2)^(1/6)*sqrt((-1+(a/(a+b*x^2))^(1/3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3))^2))],
[1/(a+b*x^2)^(7/6),x,5,-3*x/((a/(a+b*x^2))^(2/3)*(a+b*x^2)^(7/6)*(1-(a/(a+b*x^2))^(1/3)-sqrt(3)))+3^(3/4)*(1-(a/(a+b*x^2))^(1/3))*EllipticF((1-(a/(a+b*x^2))^(1/3)+sqrt(3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3)),sqrt(-7+4*sqrt(3)))*sqrt(2)*sqrt((1+(a/(a+b*x^2))^(1/3)+(a/(a+b*x^2))^(2/3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3))^2)/(b*x*(a/(a+b*x^2))^(2/3)*(a+b*x^2)^(1/6)*sqrt((-1+(a/(a+b*x^2))^(1/3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3))^2))-3/2*3^(1/4)*(1-(a/(a+b*x^2))^(1/3))*EllipticE((1-(a/(a+b*x^2))^(1/3)+sqrt(3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3)),sqrt(-7+4*sqrt(3)))*sqrt((1+(a/(a+b*x^2))^(1/3)+(a/(a+b*x^2))^(2/3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3))^2)*sqrt(2+sqrt(3))/(b*x*(a/(a+b*x^2))^(2/3)*(a+b*x^2)^(1/6)*sqrt((-1+(a/(a+b*x^2))^(1/3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3))^2))],
[1/(x^2*(a+b*x^2)^(7/6)),x,8,3/(a*x*(a+b*x^2)^(1/6))+4*b*x/(a^2*(a+b*x^2)^(1/6))-4*(a+b*x^2)^(5/6)/(a^2*x)+4*b*x/(a*(a/(a+b*x^2))^(2/3)*(a+b*x^2)^(7/6)*(1-(a/(a+b*x^2))^(1/3)-sqrt(3)))-4*(1-(a/(a+b*x^2))^(1/3))*EllipticF((1-(a/(a+b*x^2))^(1/3)+sqrt(3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3)),sqrt(-7+4*sqrt(3)))*sqrt(2)*sqrt((1+(a/(a+b*x^2))^(1/3)+(a/(a+b*x^2))^(2/3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3))^2)/(3^(1/4)*a*x*(a/(a+b*x^2))^(2/3)*(a+b*x^2)^(1/6)*sqrt((-1+(a/(a+b*x^2))^(1/3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3))^2))+2*3^(1/4)*(1-(a/(a+b*x^2))^(1/3))*EllipticE((1-(a/(a+b*x^2))^(1/3)+sqrt(3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3)),sqrt(-7+4*sqrt(3)))*sqrt((1+(a/(a+b*x^2))^(1/3)+(a/(a+b*x^2))^(2/3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3))^2)*sqrt(2+sqrt(3))/(a*x*(a/(a+b*x^2))^(2/3)*(a+b*x^2)^(1/6)*sqrt((-1+(a/(a+b*x^2))^(1/3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3))^2))],
[1/(x^4*(a+b*x^2)^(7/6)),x,9,3/(a*x^3*(a+b*x^2)^(1/6))-40/9*b^2*x/(a^3*(a+b*x^2)^(1/6))-10/3*(a+b*x^2)^(5/6)/(a^2*x^3)+40/9*b*(a+b*x^2)^(5/6)/(a^3*x)-40/9*b^2*x/(a^2*(a/(a+b*x^2))^(2/3)*(a+b*x^2)^(7/6)*(1-(a/(a+b*x^2))^(1/3)-sqrt(3)))+40/9*b*(1-(a/(a+b*x^2))^(1/3))*EllipticF((1-(a/(a+b*x^2))^(1/3)+sqrt(3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3)),sqrt(-7+4*sqrt(3)))*sqrt(2)*sqrt((1+(a/(a+b*x^2))^(1/3)+(a/(a+b*x^2))^(2/3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3))^2)/(3^(1/4)*a^2*x*(a/(a+b*x^2))^(2/3)*(a+b*x^2)^(1/6)*sqrt((-1+(a/(a+b*x^2))^(1/3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3))^2))-20/3*b*(1-(a/(a+b*x^2))^(1/3))*EllipticE((1-(a/(a+b*x^2))^(1/3)+sqrt(3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3)),sqrt(-7+4*sqrt(3)))*sqrt((1+(a/(a+b*x^2))^(1/3)+(a/(a+b*x^2))^(2/3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3))^2)*sqrt(2+sqrt(3))/(3^(3/4)*a^2*x*(a/(a+b*x^2))^(2/3)*(a+b*x^2)^(1/6)*sqrt((-1+(a/(a+b*x^2))^(1/3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3))^2))],
[1/(x^6*(a+b*x^2)^(7/6)),x,10,3/(a*x^5*(a+b*x^2)^(1/6))+128/27*b^3*x/(a^4*(a+b*x^2)^(1/6))-16/5*(a+b*x^2)^(5/6)/(a^2*x^5)+32/9*b*(a+b*x^2)^(5/6)/(a^3*x^3)-128/27*b^2*(a+b*x^2)^(5/6)/(a^4*x)+128/27*b^3*x/(a^3*(a/(a+b*x^2))^(2/3)*(a+b*x^2)^(7/6)*(1-(a/(a+b*x^2))^(1/3)-sqrt(3)))-128/27*b^2*(1-(a/(a+b*x^2))^(1/3))*EllipticF((1-(a/(a+b*x^2))^(1/3)+sqrt(3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3)),sqrt(-7+4*sqrt(3)))*sqrt(2)*sqrt((1+(a/(a+b*x^2))^(1/3)+(a/(a+b*x^2))^(2/3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3))^2)/(3^(1/4)*a^3*x*(a/(a+b*x^2))^(2/3)*(a+b*x^2)^(1/6)*sqrt((-1+(a/(a+b*x^2))^(1/3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3))^2))+64/9*b^2*(1-(a/(a+b*x^2))^(1/3))*EllipticE((1-(a/(a+b*x^2))^(1/3)+sqrt(3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3)),sqrt(-7+4*sqrt(3)))*sqrt((1+(a/(a+b*x^2))^(1/3)+(a/(a+b*x^2))^(2/3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3))^2)*sqrt(2+sqrt(3))/(3^(3/4)*a^3*x*(a/(a+b*x^2))^(2/3)*(a+b*x^2)^(1/6)*sqrt((-1+(a/(a+b*x^2))^(1/3))/(1-(a/(a+b*x^2))^(1/3)-sqrt(3))^2))],

# Integrands of the form (c x)^m (a+b x^2)^p when p symbolic

# Integrands of the form x^m (a+b x^2)^p when p symbolic
[x^7*(a+b*x^2)^p,x,3,-1/2*a^3*(a+b*x^2)^(1+p)/(b^4*(1+p))+3/2*a^2*(a+b*x^2)^(2+p)/(b^4*(2+p))-3/2*a*(a+b*x^2)^(3+p)/(b^4*(3+p))+1/2*(a+b*x^2)^(4+p)/(b^4*(4+p))],
[x^5*(a+b*x^2)^p,x,3,1/2*a^2*(a+b*x^2)^(1+p)/(b^3*(1+p))-a*(a+b*x^2)^(2+p)/(b^3*(2+p))+1/2*(a+b*x^2)^(3+p)/(b^3*(3+p))],
[x^3*(a+b*x^2)^p,x,3,-1/2*a*(a+b*x^2)^(1+p)/(b^2*(1+p))+1/2*(a+b*x^2)^(2+p)/(b^2*(2+p))],
[x*(a+b*x^2)^p,x,1,1/2*(a+b*x^2)^(1+p)/(b*(1+p))],
[(a+b*x^2)^p/x,x,2,-1/2*(a+b*x^2)^(1+p)*hypergeom([1,1+p],[2+p],1+b*x^2/a)/(a*(1+p))],
[(a+b*x^2)^p/x^3,x,2,1/2*b*(a+b*x^2)^(1+p)*hypergeom([2,1+p],[2+p],1+b*x^2/a)/(a^2*(1+p))],
[x^6*(a+b*x^2)^p,x,2,1/7*x^7*(a+b*x^2)^(1+p)*hypergeom([1,9/2+p],[9/2],-b*x^2/a)/a,1/7*x^7*(a+b*x^2)^p*hypergeom([7/2,-p],[9/2],-b*x^2/a)/(1+b*x^2/a)^p],
[x^4*(a+b*x^2)^p,x,2,1/5*x^5*(a+b*x^2)^(1+p)*hypergeom([1,7/2+p],[7/2],-b*x^2/a)/a,1/5*x^5*(a+b*x^2)^p*hypergeom([5/2,-p],[7/2],-b*x^2/a)/(1+b*x^2/a)^p],
[x^2*(a+b*x^2)^p,x,2,1/3*x^3*(a+b*x^2)^(1+p)*hypergeom([1,5/2+p],[5/2],-b*x^2/a)/a,1/3*x^3*(a+b*x^2)^p*hypergeom([3/2,-p],[5/2],-b*x^2/a)/(1+b*x^2/a)^p],
[(a+b*x^2)^p,x,2,x*(a+b*x^2)^(1+p)*hypergeom([1,3/2+p],[3/2],-b*x^2/a)/a,x*(a+b*x^2)^p*hypergeom([1/2,-p],[3/2],-b*x^2/a)/(1+b*x^2/a)^p],
[(a+b*x^2)^p/x^2,x,2,-(a+b*x^2)^(1+p)*hypergeom([1,1/2+p],[1/2],-b*x^2/a)/(a*x),-(a+b*x^2)^p*hypergeom([-1/2,-p],[1/2],-b*x^2/a)/(x*(1+b*x^2/a)^p)],

# Integrands of the form (c x)^(m/2) (a+b x^2)^p when p symbolic
[x^(7/2)*(a+b*x^2)^p,x,2,2/9*x^(9/2)*(a+b*x^2)^(1+p)*hypergeom([1,13/4+p],[13/4],-b*x^2/a)/a,2/9*x^(9/2)*(a+b*x^2)^p*hypergeom([9/4,-p],[13/4],-b*x^2/a)/(1+b*x^2/a)^p],
[x^(5/2)*(a+b*x^2)^p,x,2,2/7*x^(7/2)*(a+b*x^2)^(1+p)*hypergeom([1,11/4+p],[11/4],-b*x^2/a)/a,2/7*x^(7/2)*(a+b*x^2)^p*hypergeom([7/4,-p],[11/4],-b*x^2/a)/(1+b*x^2/a)^p],
[x^(3/2)*(a+b*x^2)^p,x,2,2/5*x^(5/2)*(a+b*x^2)^(1+p)*hypergeom([1,9/4+p],[9/4],-b*x^2/a)/a,2/5*x^(5/2)*(a+b*x^2)^p*hypergeom([5/4,-p],[9/4],-b*x^2/a)/(1+b*x^2/a)^p],
[x^(1/2)*(a+b*x^2)^p,x,2,2/3*x^(3/2)*(a+b*x^2)^(1+p)*hypergeom([1,7/4+p],[7/4],-b*x^2/a)/a,2/3*x^(3/2)*(a+b*x^2)^p*hypergeom([3/4,-p],[7/4],-b*x^2/a)/(1+b*x^2/a)^p],
[(a+b*x^2)^p/x^(1/2),x,2,2*(a+b*x^2)^(1+p)*hypergeom([1,5/4+p],[5/4],-b*x^2/a)*sqrt(x)/a,2*(a+b*x^2)^p*hypergeom([1/4,-p],[5/4],-b*x^2/a)*sqrt(x)/(1+b*x^2/a)^p],
[(a+b*x^2)^p/x^(3/2),x,2,-2*(a+b*x^2)^(1+p)*hypergeom([1,3/4+p],[3/4],-b*x^2/a)/(a*sqrt(x)),-2*(a+b*x^2)^p*hypergeom([-1/4,-p],[3/4],-b*x^2/a)/((1+b*x^2/a)^p*sqrt(x))],
[(a+b*x^2)^p/x^(5/2),x,2,-2/3*(a+b*x^2)^(1+p)*hypergeom([1,1/4+p],[1/4],-b*x^2/a)/(a*x^(3/2)),-2/3*(a+b*x^2)^p*hypergeom([-3/4,-p],[1/4],-b*x^2/a)/(x^(3/2)*(1+b*x^2/a)^p)],
[(a+b*x^2)^p/x^(7/2),x,2,-2/5*(a+b*x^2)^(1+p)*hypergeom([1,-1/4+p],[-1/4],-b*x^2/a)/(a*x^(5/2)),-2/5*(a+b*x^2)^p*hypergeom([-5/4,-p],[-1/4],-b*x^2/a)/(x^(5/2)*(1+b*x^2/a)^p)],

# Integrands of the form (c x)^m (a+b x^2)^p when m and p symbolic
[x^m*(a+b*x^2)^p,x,2,x^(1+m)*(a+b*x^2)^(1+p)*hypergeom([1,1/2*(3+m+2*p)],[1/2*(3+m)],-b*x^2/a)/(a*(1+m)),x^(1+m)*(a+b*x^2)^p*hypergeom([1/2*(1+m),-p],[1/2*(3+m)],-b*x^2/a)/((1+m)*(1+b*x^2/a)^p)],
[(c*x)^m*(a+b*x^2)^p,x,2,(c*x)^(1+m)*(a+b*x^2)^p*hypergeom([1/2*(1+m),-p],[1/2*(3+m)],-b*x^2/a)/(c*(1+m)*(1+b*x^2/a)^p)],
[x^(-8-2*p)*(a+b*x^2)^p,x,2,-x^(-7-2*p)*(a+b*x^2)^(1+p)*hypergeom([-5/2,1],[1/2*(-5-2*p)],-b*x^2/a)/(a*(7+2*p)),-x^(-7-2*p)*(a+b*x^2)^p*hypergeom([1/2*(-7-2*p),-p],[1/2*(-5-2*p)],-b*x^2/a)/((7+2*p)*(1+b*x^2/a)^p)],
[x^(-7-2*p)*(a+b*x^2)^p,x,3,-b^2*(a+b*x^2)^(1+p)/(a^3*(2+p)*(3+4*p+p^2)*x^(2*(1+p)))+b*(a+b*x^2)^(1+p)/(a^2*(2+p)*(3+p)*x^(2*(2+p)))-1/2*(a+b*x^2)^(1+p)/(a*(3+p)*x^(2*(3+p)))],
[x^(-6-2*p)*(a+b*x^2)^p,x,2,-x^(-5-2*p)*(a+b*x^2)^(1+p)*hypergeom([-3/2,1],[1/2*(-3-2*p)],-b*x^2/a)/(a*(5+2*p)),-x^(-5-2*p)*(a+b*x^2)^p*hypergeom([1/2*(-5-2*p),-p],[1/2*(-3-2*p)],-b*x^2/a)/((5+2*p)*(1+b*x^2/a)^p)],
[x^(-5-2*p)*(a+b*x^2)^p,x,2,1/2*b*(a+b*x^2)^(1+p)/(a^2*(1+p)*(2+p)*x^(2*(1+p)))-1/2*(a+b*x^2)^(1+p)/(a*(2+p)*x^(2*(2+p)))],
[x^(-4-2*p)*(a+b*x^2)^p,x,2,-x^(-3-2*p)*(a+b*x^2)^(1+p)*hypergeom([-1/2,1],[1/2*(-1-2*p)],-b*x^2/a)/(a*(3+2*p)),-x^(-3-2*p)*(a+b*x^2)^p*hypergeom([1/2*(-3-2*p),-p],[1/2*(-1-2*p)],-b*x^2/a)/((3+2*p)*(1+b*x^2/a)^p)],
[x^(-3-2*p)*(a+b*x^2)^p,x,1,-1/2*(a+b*x^2)^(1+p)/(a*(1+p)*x^(2*(1+p)))],
[x^(-2-2*p)*(a+b*x^2)^p,x,2,-x^(-1-2*p)*(a+b*x^2)^(1+p)*hypergeom([1/2,1],[1/2*(1-2*p)],-b*x^2/a)/(a*(1+2*p)),-x^(-1-2*p)*(a+b*x^2)^p*hypergeom([1/2*(-1-2*p),-p],[1/2*(1-2*p)],-b*x^2/a)/((1+2*p)*(1+b*x^2/a)^p)],
[x^(-1-2*p)*(a+b*x^2)^p,x,2,-1/2*(a+b*x^2)^(1+p)*hypergeom([1,1],[1-p],-b*x^2/a)/(a*p*x^(2*p)),-1/2*(a+b*x^2)^p*hypergeom([-p,-p],[1-p],-b*x^2/a)/(p*x^(2*p)*(1+b*x^2/a)^p)],
[(a+b*x^2)^p/x^(2*p),x,2,x^(1-2*p)*(a+b*x^2)^(1+p)*hypergeom([1,3/2],[1/2*(3-2*p)],-b*x^2/a)/(a*(1-2*p)),x^(1-2*p)*(a+b*x^2)^p*hypergeom([1/2*(1-2*p),-p],[1/2*(3-2*p)],-b*x^2/a)/((1-2*p)*(1+b*x^2/a)^p)],
[x^(1-2*p)*(a+b*x^2)^p,x,2,1/2*x^(2-2*p)*(a+b*x^2)^(1+p)*hypergeom([1,2],[2-p],-b*x^2/a)/(a*(1-p)),1/2*x^(2-2*p)*(a+b*x^2)^p*hypergeom([1-p,-p],[2-p],-b*x^2/a)/((1-p)*(1+b*x^2/a)^p)],
[x^(2-2*p)*(a+b*x^2)^p,x,2,x^(3-2*p)*(a+b*x^2)^(1+p)*hypergeom([1,5/2],[1/2*(5-2*p)],-b*x^2/a)/(a*(3-2*p)),x^(3-2*p)*(a+b*x^2)^p*hypergeom([1/2*(3-2*p),-p],[1/2*(5-2*p)],-b*x^2/a)/((3-2*p)*(1+b*x^2/a)^p)],
[x^(3-2*p)*(a+b*x^2)^p,x,2,1/2*x^(4-2*p)*(a+b*x^2)^(1+p)*hypergeom([1,3],[3-p],-b*x^2/a)/(a*(2-p)),1/2*x^(4-2*p)*(a+b*x^2)^p*hypergeom([2-p,-p],[3-p],-b*x^2/a)/((2-p)*(1+b*x^2/a)^p)]]:
