# Maple integration test file: "1 Algebraic functions\1.1 Binomial products\1.1.1 Linear\1.1.1.2 (a+b x)^m (c+d x)^n.txt"

lst:=[

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

# Integrands of the form (b x)^n

# Integrands of the form b
[0,x,1,0],
[1,x,1,x],
[5,x,1,5*x],
[-2,x,1,-2*x],
[-3/2,x,1,-3/2*x],
[Pi,x,1,Pi*x],
[a,x,1,a*x],
[3*a,x,1,3*a*x],
[Pi/sqrt(16-exp(2)),x,1,Pi*x/sqrt(16-exp(2))],

# Integrands of the form x^n
[x^100,x,1,1/101*x^101],
[x^3,x,1,1/4*x^4],
[x^2,x,1,1/3*x^3],
[x,x,1,1/2*x^2],
[1,x,1,x],
[1/x,x,1,log(x)],
[1/x^2,x,1,(-1)/x],
[1/x^3,x,1,(-1/2)/x^2],
[1/x^4,x,1,(-1/3)/x^3],
[1/x^100,x,1,(-1/99)/x^99],

# Integrands of the form (b x)^(n/2)
[x^(5/2),x,1,2/7*x^(7/2)],
[x^(3/2),x,1,2/5*x^(5/2)],
[x^(1/2),x,1,2/3*x^(3/2)],
[1/x^(1/2),x,1,2*sqrt(x)],
[1/x^(3/2),x,1,(-2)/sqrt(x)],
[1/x^(5/2),x,1,(-2/3)/x^(3/2)],

# Integrands of the form (b x)^(n/3)
[x^(5/3),x,1,3/8*x^(8/3)],
[x^(4/3),x,1,3/7*x^(7/3)],
[x^(2/3),x,1,3/5*x^(5/3)],
[x^(1/3),x,1,3/4*x^(4/3)],
[1/x^(1/3),x,1,3/2*x^(2/3)],
[1/x^(2/3),x,1,3*x^(1/3)],
[1/x^(4/3),x,1,(-3)/x^(1/3)],
[1/x^(5/3),x,1,(-3/2)/x^(2/3)],

# Integrands of the form (b x)^n with n symbolic
[x^n,x,1,x^(1+n)/(1+n)],
[(b*x)^n,x,1,(b*x)^(1+n)/(b*(1+n))],

# Integrands of the form (c+d (a+b x))^n

# Integrands of the form (c+d (a+b x))^n
[1/(e*(c+d*x)+sqrt(-a)),x,2,log(c*e+d*e*x+sqrt(-a))/(d*e)],

# Integrands of the form (c+d (a+b x))^(n/2)
[(c+d*(a+b*x))^(5/2),x,2,2/7*(c+d*(a+b*x))^(7/2)/(b*d)],
[(c+d*(a+b*x))^(3/2),x,2,2/5*(c+d*(a+b*x))^(5/2)/(b*d)],
[(c+d*(a+b*x))^(1/2),x,2,2/3*(c+d*(a+b*x))^(3/2)/(b*d)],
[1/(c+d*(a+b*x))^(1/2),x,2,2*sqrt(c+d*(a+b*x))/(b*d)],
[1/(c+d*(a+b*x))^(3/2),x,2,(-2)/(b*d*sqrt(c+d*(a+b*x)))],
[1/(c+d*(a+b*x))^(5/2),x,2,(-2/3)/(b*d*(c+d*(a+b*x))^(3/2))],

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

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

# n>0
[x^3*(a+b*x),x,2,1/4*a*x^4+1/5*b*x^5],
[x^2*(a+b*x),x,2,1/3*a*x^3+1/4*b*x^4],
[x*(a+b*x),x,2,1/2*a*x^2+1/3*b*x^3],
[a+b*x,x,1,a*x+1/2*b*x^2],
[(a+b*x)/x,x,2,b*x+a*log(x)],
[(a+b*x)/x^2,x,2,-a/x+b*log(x)],
[(a+b*x)/x^3,x,1,-1/2*(a+b*x)^2/(a*x^2)],
[(a+b*x)/x^4,x,2,-1/3*a/x^3-1/2*b/x^2],
[(a+b*x)/x^5,x,2,-1/4*a/x^4-1/3*b/x^3],
[x^3*(a+b*x)^2,x,2,1/4*a^2*x^4+2/5*a*b*x^5+1/6*b^2*x^6],
[x^2*(a+b*x)^2,x,2,1/3*a^2*x^3+1/2*a*b*x^4+1/5*b^2*x^5],
[x*(a+b*x)^2,x,2,1/2*a^2*x^2+2/3*a*b*x^3+1/4*b^2*x^4],
[(a+b*x)^2,x,1,1/3*(a+b*x)^3/b],
[(a+b*x)^2/x,x,2,2*a*b*x+1/2*b^2*x^2+a^2*log(x)],
[(a+b*x)^2/x^2,x,2,-a^2/x+b^2*x+2*a*b*log(x)],
[(a+b*x)^2/x^3,x,2,-1/2*a^2/x^2-2*a*b/x+b^2*log(x)],
[(a+b*x)^2/x^4,x,1,-1/3*(a+b*x)^3/(a*x^3)],
[(a+b*x)^2/x^5,x,2,-1/4*a^2/x^4-2/3*a*b/x^3-1/2*b^2/x^2],
[(a+b*x)^2/x^6,x,2,-1/5*a^2/x^5-1/2*a*b/x^4-1/3*b^2/x^3],
[(a+b*x)^2/x^7,x,2,-1/6*a^2/x^6-2/5*a*b/x^5-1/4*b^2/x^4],
[(a+b*x)^2/x^8,x,2,-1/7*a^2/x^7-1/3*a*b/x^6-1/5*b^2/x^5],
[x^4*(a+b*x)^3,x,2,1/5*a^3*x^5+1/2*a^2*b*x^6+3/7*a*b^2*x^7+1/8*b^3*x^8],
[x^3*(a+b*x)^3,x,2,1/4*a^3*x^4+3/5*a^2*b*x^5+1/2*a*b^2*x^6+1/7*b^3*x^7],
[x^2*(a+b*x)^3,x,2,1/3*a^3*x^3+3/4*a^2*b*x^4+3/5*a*b^2*x^5+1/6*b^3*x^6],
[x*(a+b*x)^3,x,2,-1/4*a*(a+b*x)^4/b^2+1/5*(a+b*x)^5/b^2],
[(a+b*x)^3,x,1,1/4*(a+b*x)^4/b],
[(a+b*x)^3/x,x,2,3*a^2*b*x+3/2*a*b^2*x^2+1/3*b^3*x^3+a^3*log(x)],
[(a+b*x)^3/x^2,x,2,-a^3/x+3*a*b^2*x+1/2*b^3*x^2+3*a^2*b*log(x)],
[(a+b*x)^3/x^3,x,2,-1/2*a^3/x^2-3*a^2*b/x+b^3*x+3*a*b^2*log(x)],
[(a+b*x)^3/x^4,x,2,-1/3*a^3/x^3-3/2*a^2*b/x^2-3*a*b^2/x+b^3*log(x)],
[(a+b*x)^3/x^5,x,1,-1/4*(a+b*x)^4/(a*x^4)],
[(a+b*x)^3/x^6,x,2,-1/5*(a+b*x)^4/(a*x^5)+1/20*b*(a+b*x)^4/(a^2*x^4)],
[(a+b*x)^3/x^7,x,2,-1/6*a^3/x^6-3/5*a^2*b/x^5-3/4*a*b^2/x^4-1/3*b^3/x^3],
[(a+b*x)^3/x^8,x,2,-1/7*a^3/x^7-1/2*a^2*b/x^6-3/5*a*b^2/x^5-1/4*b^3/x^4],
[x^6*(a+b*x)^5,x,2,1/7*a^5*x^7+5/8*a^4*b*x^8+10/9*a^3*b^2*x^9+a^2*b^3*x^10+5/11*a*b^4*x^11+1/12*b^5*x^12],
[x^5*(a+b*x)^5,x,2,1/6*a^5*x^6+5/7*a^4*b*x^7+5/4*a^3*b^2*x^8+10/9*a^2*b^3*x^9+1/2*a*b^4*x^10+1/11*b^5*x^11],
[x^4*(a+b*x)^5,x,2,1/5*a^5*x^5+5/6*a^4*b*x^6+10/7*a^3*b^2*x^7+5/4*a^2*b^3*x^8+5/9*a*b^4*x^9+1/10*b^5*x^10],
[x^3*(a+b*x)^5,x,2,-1/6*a^3*(a+b*x)^6/b^4+3/7*a^2*(a+b*x)^7/b^4-3/8*a*(a+b*x)^8/b^4+1/9*(a+b*x)^9/b^4],
[x^2*(a+b*x)^5,x,2,1/6*a^2*(a+b*x)^6/b^3-2/7*a*(a+b*x)^7/b^3+1/8*(a+b*x)^8/b^3],
[x*(a+b*x)^5,x,2,-1/6*a*(a+b*x)^6/b^2+1/7*(a+b*x)^7/b^2],
[(a+b*x)^5,x,1,1/6*(a+b*x)^6/b],
[(a+b*x)^5/x,x,2,5*a^4*b*x+5*a^3*b^2*x^2+10/3*a^2*b^3*x^3+5/4*a*b^4*x^4+1/5*b^5*x^5+a^5*log(x)],
[(a+b*x)^5/x^2,x,2,-a^5/x+10*a^3*b^2*x+5*a^2*b^3*x^2+5/3*a*b^4*x^3+1/4*b^5*x^4+5*a^4*b*log(x)],
[(a+b*x)^5/x^3,x,2,-1/2*a^5/x^2-5*a^4*b/x+10*a^2*b^3*x+5/2*a*b^4*x^2+1/3*b^5*x^3+10*a^3*b^2*log(x)],
[(a+b*x)^5/x^4,x,2,-1/3*a^5/x^3-5/2*a^4*b/x^2-10*a^3*b^2/x+5*a*b^4*x+1/2*b^5*x^2+10*a^2*b^3*log(x)],
[(a+b*x)^5/x^5,x,2,-1/4*a^5/x^4-5/3*a^4*b/x^3-5*a^3*b^2/x^2-10*a^2*b^3/x+b^5*x+5*a*b^4*log(x)],
[(a+b*x)^5/x^6,x,2,-1/5*a^5/x^5-5/4*a^4*b/x^4-10/3*a^3*b^2/x^3-5*a^2*b^3/x^2-5*a*b^4/x+b^5*log(x)],
[(a+b*x)^5/x^7,x,1,-1/6*(a+b*x)^6/(a*x^6)],
[(a+b*x)^5/x^8,x,2,-1/7*(a+b*x)^6/(a*x^7)+1/42*b*(a+b*x)^6/(a^2*x^6)],
[(a+b*x)^5/x^9,x,3,-1/8*(a+b*x)^6/(a*x^8)+1/28*b*(a+b*x)^6/(a^2*x^7)-1/168*b^2*(a+b*x)^6/(a^3*x^6)],
[(a+b*x)^5/x^10,x,2,-1/9*a^5/x^9-5/8*a^4*b/x^8-10/7*a^3*b^2/x^7-5/3*a^2*b^3/x^6-a*b^4/x^5-1/4*b^5/x^4],
[(a+b*x)^5/x^11,x,2,-1/10*a^5/x^10-5/9*a^4*b/x^9-5/4*a^3*b^2/x^8-10/7*a^2*b^3/x^7-5/6*a*b^4/x^6-1/5*b^5/x^5],
[(a+b*x)^5/x^12,x,2,-1/11*a^5/x^11-1/2*a^4*b/x^10-10/9*a^3*b^2/x^9-5/4*a^2*b^3/x^8-5/7*a*b^4/x^7-1/6*b^5/x^6],
[(a+b*x)^5/x^13,x,2,-1/12*a^5/x^12-5/11*a^4*b/x^11-a^3*b^2/x^10-10/9*a^2*b^3/x^9-5/8*a*b^4/x^8-1/7*b^5/x^7],
[(a+b*x)^5/x^14,x,2,-1/13*a^5/x^13-5/12*a^4*b/x^12-10/11*a^3*b^2/x^11-a^2*b^3/x^10-5/9*a*b^4/x^9-1/8*b^5/x^8],
[x^8*(a+b*x)^7,x,2,1/9*a^7*x^9+7/10*a^6*b*x^10+21/11*a^5*b^2*x^11+35/12*a^4*b^3*x^12+35/13*a^3*b^4*x^13+3/2*a^2*b^5*x^14+7/15*a*b^6*x^15+1/16*b^7*x^16],
[x^7*(a+b*x)^7,x,2,1/8*a^7*x^8+7/9*a^6*b*x^9+21/10*a^5*b^2*x^10+35/11*a^4*b^3*x^11+35/12*a^3*b^4*x^12+21/13*a^2*b^5*x^13+1/2*a*b^6*x^14+1/15*b^7*x^15],
[x^6*(a+b*x)^7,x,2,1/7*a^7*x^7+7/8*a^6*b*x^8+7/3*a^5*b^2*x^9+7/2*a^4*b^3*x^10+35/11*a^3*b^4*x^11+7/4*a^2*b^5*x^12+7/13*a*b^6*x^13+1/14*b^7*x^14],
[x^5*(a+b*x)^7,x,2,-1/8*a^5*(a+b*x)^8/b^6+5/9*a^4*(a+b*x)^9/b^6-a^3*(a+b*x)^10/b^6+10/11*a^2*(a+b*x)^11/b^6-5/12*a*(a+b*x)^12/b^6+1/13*(a+b*x)^13/b^6],
[x^4*(a+b*x)^7,x,2,1/8*a^4*(a+b*x)^8/b^5-4/9*a^3*(a+b*x)^9/b^5+3/5*a^2*(a+b*x)^10/b^5-4/11*a*(a+b*x)^11/b^5+1/12*(a+b*x)^12/b^5],
[x^3*(a+b*x)^7,x,2,-1/8*a^3*(a+b*x)^8/b^4+1/3*a^2*(a+b*x)^9/b^4-3/10*a*(a+b*x)^10/b^4+1/11*(a+b*x)^11/b^4],
[x^2*(a+b*x)^7,x,2,1/8*a^2*(a+b*x)^8/b^3-2/9*a*(a+b*x)^9/b^3+1/10*(a+b*x)^10/b^3],
[x*(a+b*x)^7,x,2,-1/8*a*(a+b*x)^8/b^2+1/9*(a+b*x)^9/b^2],
[(a+b*x)^7,x,1,1/8*(a+b*x)^8/b],
[(a+b*x)^7/x,x,2,7*a^6*b*x+21/2*a^5*b^2*x^2+35/3*a^4*b^3*x^3+35/4*a^3*b^4*x^4+21/5*a^2*b^5*x^5+7/6*a*b^6*x^6+1/7*b^7*x^7+a^7*log(x)],
[(a+b*x)^7/x^2,x,2,-a^7/x+21*a^5*b^2*x+35/2*a^4*b^3*x^2+35/3*a^3*b^4*x^3+21/4*a^2*b^5*x^4+7/5*a*b^6*x^5+1/6*b^7*x^6+7*a^6*b*log(x)],
[(a+b*x)^7/x^3,x,2,-1/2*a^7/x^2-7*a^6*b/x+35*a^4*b^3*x+35/2*a^3*b^4*x^2+7*a^2*b^5*x^3+7/4*a*b^6*x^4+1/5*b^7*x^5+21*a^5*b^2*log(x)],
[(a+b*x)^7/x^4,x,2,-1/3*a^7/x^3-7/2*a^6*b/x^2-21*a^5*b^2/x+35*a^3*b^4*x+21/2*a^2*b^5*x^2+7/3*a*b^6*x^3+1/4*b^7*x^4+35*a^4*b^3*log(x)],
[(a+b*x)^7/x^5,x,2,-1/4*a^7/x^4-7/3*a^6*b/x^3-21/2*a^5*b^2/x^2-35*a^4*b^3/x+21*a^2*b^5*x+7/2*a*b^6*x^2+1/3*b^7*x^3+35*a^3*b^4*log(x)],
[(a+b*x)^7/x^6,x,2,-1/5*a^7/x^5-7/4*a^6*b/x^4-7*a^5*b^2/x^3-35/2*a^4*b^3/x^2-35*a^3*b^4/x+7*a*b^6*x+1/2*b^7*x^2+21*a^2*b^5*log(x)],
[(a+b*x)^7/x^7,x,2,-1/6*a^7/x^6-7/5*a^6*b/x^5-21/4*a^5*b^2/x^4-35/3*a^4*b^3/x^3-35/2*a^3*b^4/x^2-21*a^2*b^5/x+b^7*x+7*a*b^6*log(x)],
[(a+b*x)^7/x^8,x,2,-1/7*a^7/x^7-7/6*a^6*b/x^6-21/5*a^5*b^2/x^5-35/4*a^4*b^3/x^4-35/3*a^3*b^4/x^3-21/2*a^2*b^5/x^2-7*a*b^6/x+b^7*log(x)],
[(a+b*x)^7/x^9,x,1,-1/8*(a+b*x)^8/(a*x^8)],
[(a+b*x)^7/x^10,x,2,-1/9*(a+b*x)^8/(a*x^9)+1/72*b*(a+b*x)^8/(a^2*x^8)],
[(a+b*x)^7/x^11,x,3,-1/10*(a+b*x)^8/(a*x^10)+1/45*b*(a+b*x)^8/(a^2*x^9)-1/360*b^2*(a+b*x)^8/(a^3*x^8)],
[(a+b*x)^7/x^12,x,4,-1/11*(a+b*x)^8/(a*x^11)+3/110*b*(a+b*x)^8/(a^2*x^10)-1/165*b^2*(a+b*x)^8/(a^3*x^9)+1/1320*b^3*(a+b*x)^8/(a^4*x^8)],
[(a+b*x)^7/x^13,x,5,-1/12*(a+b*x)^8/(a*x^12)+1/33*b*(a+b*x)^8/(a^2*x^11)-1/110*b^2*(a+b*x)^8/(a^3*x^10)+1/495*b^3*(a+b*x)^8/(a^4*x^9)-1/3960*b^4*(a+b*x)^8/(a^5*x^8)],
[(a+b*x)^7/x^14,x,2,-1/13*a^7/x^13-7/12*a^6*b/x^12-21/11*a^5*b^2/x^11-7/2*a^4*b^3/x^10-35/9*a^3*b^4/x^9-21/8*a^2*b^5/x^8-a*b^6/x^7-1/6*b^7/x^6],
[(a+b*x)^7/x^15,x,2,-1/14*a^7/x^14-7/13*a^6*b/x^13-7/4*a^5*b^2/x^12-35/11*a^4*b^3/x^11-7/2*a^3*b^4/x^10-7/3*a^2*b^5/x^9-7/8*a*b^6/x^8-1/7*b^7/x^7],
[(a+b*x)^7/x^16,x,2,-1/15*a^7/x^15-1/2*a^6*b/x^14-21/13*a^5*b^2/x^13-35/12*a^4*b^3/x^12-35/11*a^3*b^4/x^11-21/10*a^2*b^5/x^10-7/9*a*b^6/x^9-1/8*b^7/x^8],
[x^11*(a+b*x)^10,x,2,1/12*a^10*x^12+10/13*a^9*b*x^13+45/14*a^8*b^2*x^14+8*a^7*b^3*x^15+105/8*a^6*b^4*x^16+252/17*a^5*b^5*x^17+35/3*a^4*b^6*x^18+120/19*a^3*b^7*x^19+9/4*a^2*b^8*x^20+10/21*a*b^9*x^21+1/22*b^10*x^22],
[x^10*(a+b*x)^10,x,2,1/11*a^10*x^11+5/6*a^9*b*x^12+45/13*a^8*b^2*x^13+60/7*a^7*b^3*x^14+14*a^6*b^4*x^15+63/4*a^5*b^5*x^16+210/17*a^4*b^6*x^17+20/3*a^3*b^7*x^18+45/19*a^2*b^8*x^19+1/2*a*b^9*x^20+1/21*b^10*x^21],
[x^9*(a+b*x)^10,x,2,1/10*a^10*x^10+10/11*a^9*b*x^11+15/4*a^8*b^2*x^12+120/13*a^7*b^3*x^13+15*a^6*b^4*x^14+84/5*a^5*b^5*x^15+105/8*a^4*b^6*x^16+120/17*a^3*b^7*x^17+5/2*a^2*b^8*x^18+10/19*a*b^9*x^19+1/20*b^10*x^20],
[x^8*(a+b*x)^10,x,2,1/11*a^8*(a+b*x)^11/b^9-2/3*a^7*(a+b*x)^12/b^9+28/13*a^6*(a+b*x)^13/b^9-4*a^5*(a+b*x)^14/b^9+14/3*a^4*(a+b*x)^15/b^9-7/2*a^3*(a+b*x)^16/b^9+28/17*a^2*(a+b*x)^17/b^9-4/9*a*(a+b*x)^18/b^9+1/19*(a+b*x)^19/b^9],
[x^7*(a+b*x)^10,x,2,-1/11*a^7*(a+b*x)^11/b^8+7/12*a^6*(a+b*x)^12/b^8-21/13*a^5*(a+b*x)^13/b^8+5/2*a^4*(a+b*x)^14/b^8-7/3*a^3*(a+b*x)^15/b^8+21/16*a^2*(a+b*x)^16/b^8-7/17*a*(a+b*x)^17/b^8+1/18*(a+b*x)^18/b^8],
[x^6*(a+b*x)^10,x,2,1/11*a^6*(a+b*x)^11/b^7-1/2*a^5*(a+b*x)^12/b^7+15/13*a^4*(a+b*x)^13/b^7-10/7*a^3*(a+b*x)^14/b^7+a^2*(a+b*x)^15/b^7-3/8*a*(a+b*x)^16/b^7+1/17*(a+b*x)^17/b^7],
[x^5*(a+b*x)^10,x,2,-1/11*a^5*(a+b*x)^11/b^6+5/12*a^4*(a+b*x)^12/b^6-10/13*a^3*(a+b*x)^13/b^6+5/7*a^2*(a+b*x)^14/b^6-1/3*a*(a+b*x)^15/b^6+1/16*(a+b*x)^16/b^6],
[x^4*(a+b*x)^10,x,2,1/11*a^4*(a+b*x)^11/b^5-1/3*a^3*(a+b*x)^12/b^5+6/13*a^2*(a+b*x)^13/b^5-2/7*a*(a+b*x)^14/b^5+1/15*(a+b*x)^15/b^5],
[x^3*(a+b*x)^10,x,2,-1/11*a^3*(a+b*x)^11/b^4+1/4*a^2*(a+b*x)^12/b^4-3/13*a*(a+b*x)^13/b^4+1/14*(a+b*x)^14/b^4],
[x^2*(a+b*x)^10,x,2,1/11*a^2*(a+b*x)^11/b^3-1/6*a*(a+b*x)^12/b^3+1/13*(a+b*x)^13/b^3],
[x*(a+b*x)^10,x,2,-1/11*a*(a+b*x)^11/b^2+1/12*(a+b*x)^12/b^2],
[(a+b*x)^10,x,1,1/11*(a+b*x)^11/b],
[(a+b*x)^10/x,x,2,10*a^9*b*x+45/2*a^8*b^2*x^2+40*a^7*b^3*x^3+105/2*a^6*b^4*x^4+252/5*a^5*b^5*x^5+35*a^4*b^6*x^6+120/7*a^3*b^7*x^7+45/8*a^2*b^8*x^8+10/9*a*b^9*x^9+1/10*b^10*x^10+a^10*log(x)],
[(a+b*x)^10/x^2,x,2,-a^10/x+45*a^8*b^2*x+60*a^7*b^3*x^2+70*a^6*b^4*x^3+63*a^5*b^5*x^4+42*a^4*b^6*x^5+20*a^3*b^7*x^6+45/7*a^2*b^8*x^7+5/4*a*b^9*x^8+1/9*b^10*x^9+10*a^9*b*log(x)],
[(a+b*x)^10/x^3,x,2,-1/2*a^10/x^2-10*a^9*b/x+120*a^7*b^3*x+105*a^6*b^4*x^2+84*a^5*b^5*x^3+105/2*a^4*b^6*x^4+24*a^3*b^7*x^5+15/2*a^2*b^8*x^6+10/7*a*b^9*x^7+1/8*b^10*x^8+45*a^8*b^2*log(x)],
[(a+b*x)^10/x^4,x,2,-1/3*a^10/x^3-5*a^9*b/x^2-45*a^8*b^2/x+210*a^6*b^4*x+126*a^5*b^5*x^2+70*a^4*b^6*x^3+30*a^3*b^7*x^4+9*a^2*b^8*x^5+5/3*a*b^9*x^6+1/7*b^10*x^7+120*a^7*b^3*log(x)],
[(a+b*x)^10/x^5,x,2,-1/4*a^10/x^4-10/3*a^9*b/x^3-45/2*a^8*b^2/x^2-120*a^7*b^3/x+252*a^5*b^5*x+105*a^4*b^6*x^2+40*a^3*b^7*x^3+45/4*a^2*b^8*x^4+2*a*b^9*x^5+1/6*b^10*x^6+210*a^6*b^4*log(x)],
[(a+b*x)^10/x^6,x,2,-1/5*a^10/x^5-5/2*a^9*b/x^4-15*a^8*b^2/x^3-60*a^7*b^3/x^2-210*a^6*b^4/x+210*a^4*b^6*x+60*a^3*b^7*x^2+15*a^2*b^8*x^3+5/2*a*b^9*x^4+1/5*b^10*x^5+252*a^5*b^5*log(x)],
[(a+b*x)^10/x^7,x,2,-1/6*a^10/x^6-2*a^9*b/x^5-45/4*a^8*b^2/x^4-40*a^7*b^3/x^3-105*a^6*b^4/x^2-252*a^5*b^5/x+120*a^3*b^7*x+45/2*a^2*b^8*x^2+10/3*a*b^9*x^3+1/4*b^10*x^4+210*a^4*b^6*log(x)],
[(a+b*x)^10/x^8,x,2,-1/7*a^10/x^7-5/3*a^9*b/x^6-9*a^8*b^2/x^5-30*a^7*b^3/x^4-70*a^6*b^4/x^3-126*a^5*b^5/x^2-210*a^4*b^6/x+45*a^2*b^8*x+5*a*b^9*x^2+1/3*b^10*x^3+120*a^3*b^7*log(x)],
[(a+b*x)^10/x^9,x,2,-1/8*a^10/x^8-10/7*a^9*b/x^7-15/2*a^8*b^2/x^6-24*a^7*b^3/x^5-105/2*a^6*b^4/x^4-84*a^5*b^5/x^3-105*a^4*b^6/x^2-120*a^3*b^7/x+10*a*b^9*x+1/2*b^10*x^2+45*a^2*b^8*log(x)],
[(a+b*x)^10/x^10,x,2,-1/9*a^10/x^9-5/4*a^9*b/x^8-45/7*a^8*b^2/x^7-20*a^7*b^3/x^6-42*a^6*b^4/x^5-63*a^5*b^5/x^4-70*a^4*b^6/x^3-60*a^3*b^7/x^2-45*a^2*b^8/x+b^10*x+10*a*b^9*log(x)],
[(a+b*x)^10/x^11,x,2,-1/10*a^10/x^10-10/9*a^9*b/x^9-45/8*a^8*b^2/x^8-120/7*a^7*b^3/x^7-35*a^6*b^4/x^6-252/5*a^5*b^5/x^5-105/2*a^4*b^6/x^4-40*a^3*b^7/x^3-45/2*a^2*b^8/x^2-10*a*b^9/x+b^10*log(x)],
[(a+b*x)^10/x^12,x,1,-1/11*(a+b*x)^11/(a*x^11)],
[(a+b*x)^10/x^13,x,2,-1/12*(a+b*x)^11/(a*x^12)+1/132*b*(a+b*x)^11/(a^2*x^11)],
[(a+b*x)^10/x^14,x,3,-1/13*(a+b*x)^11/(a*x^13)+1/78*b*(a+b*x)^11/(a^2*x^12)-1/858*b^2*(a+b*x)^11/(a^3*x^11)],
[(a+b*x)^10/x^15,x,4,-1/14*(a+b*x)^11/(a*x^14)+3/182*b*(a+b*x)^11/(a^2*x^13)-1/364*b^2*(a+b*x)^11/(a^3*x^12)+1/4004*b^3*(a+b*x)^11/(a^4*x^11)],
[(a+b*x)^10/x^16,x,5,-1/15*(a+b*x)^11/(a*x^15)+2/105*b*(a+b*x)^11/(a^2*x^14)-2/455*b^2*(a+b*x)^11/(a^3*x^13)+1/1365*b^3*(a+b*x)^11/(a^4*x^12)-1/15015*b^4*(a+b*x)^11/(a^5*x^11)],
[(a+b*x)^10/x^17,x,6,-1/16*(a+b*x)^11/(a*x^16)+1/48*b*(a+b*x)^11/(a^2*x^15)-1/168*b^2*(a+b*x)^11/(a^3*x^14)+1/728*b^3*(a+b*x)^11/(a^4*x^13)-1/4368*b^4*(a+b*x)^11/(a^5*x^12)+1/48048*b^5*(a+b*x)^11/(a^6*x^11)],
[(a+b*x)^10/x^18,x,7,-1/17*(a+b*x)^11/(a*x^17)+3/136*b*(a+b*x)^11/(a^2*x^16)-1/136*b^2*(a+b*x)^11/(a^3*x^15)+1/476*b^3*(a+b*x)^11/(a^4*x^14)-3/6188*b^4*(a+b*x)^11/(a^5*x^13)+1/12376*b^5*(a+b*x)^11/(a^6*x^12)-1/136136*b^6*(a+b*x)^11/(a^7*x^11)],
[(a+b*x)^10/x^19,x,2,-1/18*a^10/x^18-10/17*a^9*b/x^17-45/16*a^8*b^2/x^16-8*a^7*b^3/x^15-15*a^6*b^4/x^14-252/13*a^5*b^5/x^13-35/2*a^4*b^6/x^12-120/11*a^3*b^7/x^11-9/2*a^2*b^8/x^10-10/9*a*b^9/x^9-1/8*b^10/x^8],
[(a+b*x)^10/x^20,x,2,-1/19*a^10/x^19-5/9*a^9*b/x^18-45/17*a^8*b^2/x^17-15/2*a^7*b^3/x^16-14*a^6*b^4/x^15-18*a^5*b^5/x^14-210/13*a^4*b^6/x^13-10*a^3*b^7/x^12-45/11*a^2*b^8/x^11-a*b^9/x^10-1/9*b^10/x^9],
# 
# {(a + b*x)^20/x^32, x, 11, -((a + b*x)^21/(31*a*x^31)) + (b*(a + b*x)^21)/(93*a^2*x^30) - (3*b^2*(a + b*x)^21)/(899*a^3*x^29) + (6*b^3*(a + b*x)^21)/(6293*a^4*x^28) - (2*b^4*(a + b*x)^21)/(8091*a^5*x^27) + (2*b^5*(a + b*x)^21)/(35061*a^6*x^26) - (2*b^6*(a + b*x)^21)/(175305*a^7*x^25) + (b^7*(a + b*x)^21)/(525915*a^8*x^24) - (b^8*(a + b*x)^21)/(4032015*a^9*x^23) + (b^9*(a + b*x)^21)/(44352165*a^10*x^22) - (b^10*(a + b*x)^21)/(931395465*a^11*x^21)}
# {(a + b*x)^20/x^33, x, 12, -((a + b*x)^21/(32*a*x^32)) + (11*b*(a + b*x)^21)/(992*a^2*x^31) - (11*b^2*(a + b*x)^21)/(2976*a^3*x^30) + (33*b^3*(a + b*x)^21)/(28768*a^4*x^29) - (33*b^4*(a + b*x)^21)/(100688*a^5*x^28) + (11*b^5*(a + b*x)^21)/(129456*a^6*x^27) - (11*b^6*(a + b*x)^21)/(560976*a^7*x^26) + (11*b^7*(a + b*x)^21)/(2804880*a^8*x^25) - (11*b^8*(a + b*x)^21)/(16829280*a^9*x^24) + (11*b^9*(a + b*x)^21)/(129024480*a^10*x^23) - (b^10*(a + b*x)^21)/(129024480*a^11*x^22) + (b^11*(a + b*x)^21)/(2709514080*a^12*x^21)}
# {(a + b*x)^20/x^34, x, 13, -((a + b*x)^21/(33*a*x^33)) + (b*(a + b*x)^21)/(88*a^2*x^32) - (b^2*(a + b*x)^21)/(248*a^3*x^31) + (b^3*(a + b*x)^21)/(744*a^4*x^30) - (3*b^4*(a + b*x)^21)/(7192*a^5*x^29) + (3*b^5*(a + b*x)^21)/(25172*a^6*x^28) - (b^6*(a + b*x)^21)/(32364*a^7*x^27) + (b^7*(a + b*x)^21)/(140244*a^8*x^26) - (b^8*(a + b*x)^21)/(701220*a^9*x^25) + (b^9*(a + b*x)^21)/(4207320*a^10*x^24) - (b^10*(a + b*x)^21)/(32256120*a^11*x^23) + (b^11*(a + b*x)^21)/(354817320*a^12*x^22) - (b^12*(a + b*x)^21)/(7451163720*a^13*x^21)}
# {(a + b*x)^20/x^35, x, 2, -(a^20/(34*x^34)) - (20*a^19*b)/(33*x^33) - (95*a^18*b^2)/(16*x^32) - (1140*a^17*b^3)/(31*x^31) - (323*a^16*b^4)/(2*x^30) - (15504*a^15*b^5)/(29*x^29) - (9690*a^14*b^6)/(7*x^28) - (25840*a^13*b^7)/(9*x^27) - (4845*a^12*b^8)/x^26 - (33592*a^11*b^9)/(5*x^25) - (46189*a^10*b^10)/(6*x^24) - (167960*a^9*b^11)/(23*x^23) - (62985*a^8*b^12)/(11*x^22) - (25840*a^7*b^13)/(7*x^21) - (1938*a^6*b^14)/x^20 - (816*a^5*b^15)/x^19 - (1615*a^4*b^16)/(6*x^18) - (1140*a^3*b^17)/(17*x^17) - (95*a^2*b^18)/(8*x^16) - (4*a*b^19)/(3*x^15) - b^20/(14*x^14)}
# {(a + b*x)^20/x^36, x, 2, -(a^20/(35*x^35)) - (10*a^19*b)/(17*x^34) - (190*a^18*b^2)/(33*x^33) - (285*a^17*b^3)/(8*x^32) - (4845*a^16*b^4)/(31*x^31) - (2584*a^15*b^5)/(5*x^30) - (38760*a^14*b^6)/(29*x^29) - (19380*a^13*b^7)/(7*x^28) - (41990*a^12*b^8)/(9*x^27) - (6460*a^11*b^9)/x^26 - (184756*a^10*b^10)/(25*x^25) - (20995*a^9*b^11)/(3*x^24) - (125970*a^8*b^12)/(23*x^23) - (38760*a^7*b^13)/(11*x^22) - (12920*a^6*b^14)/(7*x^21) - (3876*a^5*b^15)/(5*x^20) - (255*a^4*b^16)/x^19 - (190*a^3*b^17)/(3*x^18) - (190*a^2*b^18)/(17*x^17) - (5*a*b^19)/(4*x^16) - b^20/(15*x^15)}
# {(a + b*x)^20/x^37, x, 2, -(a^20/(36*x^36)) - (4*a^19*b)/(7*x^35) - (95*a^18*b^2)/(17*x^34) - (380*a^17*b^3)/(11*x^33) - (4845*a^16*b^4)/(32*x^32) - (15504*a^15*b^5)/(31*x^31) - (1292*a^14*b^6)/x^30 - (77520*a^13*b^7)/(29*x^29) - (62985*a^12*b^8)/(14*x^28) - (167960*a^11*b^9)/(27*x^27) - (7106*a^10*b^10)/x^26 - (33592*a^9*b^11)/(5*x^25) - (20995*a^8*b^12)/(4*x^24) - (77520*a^7*b^13)/(23*x^23) - (19380*a^6*b^14)/(11*x^22) - (5168*a^5*b^15)/(7*x^21) - (969*a^4*b^16)/(4*x^20) - (60*a^3*b^17)/x^19 - (95*a^2*b^18)/(9*x^18) - (20*a*b^19)/(17*x^17) - b^20/(16*x^16)}
[c*(a+b*x),x,1,1/2*c*(a+b*x)^2/b],
[(c+d)*(a+b*x)/e,x,1,1/2*(c+d)*(a+b*x)^2/(b*e)],

# n<0
[x^5/(a+b*x),x,2,a^4*x/b^5-1/2*a^3*x^2/b^4+1/3*a^2*x^3/b^3-1/4*a*x^4/b^2+1/5*x^5/b-a^5*log(a+b*x)/b^6],
[x^4/(a+b*x),x,2,-a^3*x/b^4+1/2*a^2*x^2/b^3-1/3*a*x^3/b^2+1/4*x^4/b+a^4*log(a+b*x)/b^5],
[x^3/(a+b*x),x,2,a^2*x/b^3-1/2*a*x^2/b^2+1/3*x^3/b-a^3*log(a+b*x)/b^4],
[x^2/(a+b*x),x,2,-a*x/b^2+1/2*x^2/b+a^2*log(a+b*x)/b^3],
[x/(a+b*x),x,2,x/b-a*log(a+b*x)/b^2],
[1/(a+b*x),x,1,log(a+b*x)/b],
[1/(x*(a+b*x)),x,3,log(x)/a-log(a+b*x)/a],
[1/(x^2*(a+b*x)),x,2,(-1)/(a*x)-b*log(x)/a^2+b*log(a+b*x)/a^2],
[1/(x^3*(a+b*x)),x,2,(-1/2)/(a*x^2)+b/(a^2*x)+b^2*log(x)/a^3-b^2*log(a+b*x)/a^3],
[1/(x^4*(a+b*x)),x,2,(-1/3)/(a*x^3)+1/2*b/(a^2*x^2)-b^2/(a^3*x)-b^3*log(x)/a^4+b^3*log(a+b*x)/a^4],
[1/(x^5*(a+b*x)),x,2,(-1/4)/(a*x^4)+1/3*b/(a^2*x^3)-1/2*b^2/(a^3*x^2)+b^3/(a^4*x)+b^4*log(x)/a^5-b^4*log(a+b*x)/a^5],
[x^6/(a+b*x)^2,x,2,5*a^4*x/b^6-2*a^3*x^2/b^5+a^2*x^3/b^4-1/2*a*x^4/b^3+1/5*x^5/b^2-a^6/(b^7*(a+b*x))-6*a^5*log(a+b*x)/b^7],
[x^5/(a+b*x)^2,x,2,-4*a^3*x/b^5+3/2*a^2*x^2/b^4-2/3*a*x^3/b^3+1/4*x^4/b^2+a^5/(b^6*(a+b*x))+5*a^4*log(a+b*x)/b^6],
[x^4/(a+b*x)^2,x,2,3*a^2*x/b^4-a*x^2/b^3+1/3*x^3/b^2-a^4/(b^5*(a+b*x))-4*a^3*log(a+b*x)/b^5],
[x^3/(a+b*x)^2,x,2,-2*a*x/b^3+1/2*x^2/b^2+a^3/(b^4*(a+b*x))+3*a^2*log(a+b*x)/b^4],
[x^2/(a+b*x)^2,x,2,x/b^2-a^2/(b^3*(a+b*x))-2*a*log(a+b*x)/b^3],
[x/(a+b*x)^2,x,2,a/(b^2*(a+b*x))+log(a+b*x)/b^2],
[1/(a+b*x)^2,x,1,(-1)/(b*(a+b*x))],
[1/(x*(a+b*x)^2),x,2,1/(a*(a+b*x))+log(x)/a^2-log(a+b*x)/a^2],
[1/(x^2*(a+b*x)^2),x,2,(-1)/(a^2*x)-b/(a^2*(a+b*x))-2*b*log(x)/a^3+2*b*log(a+b*x)/a^3],
[1/(x^3*(a+b*x)^2),x,2,(-1/2)/(a^2*x^2)+2*b/(a^3*x)+b^2/(a^3*(a+b*x))+3*b^2*log(x)/a^4-3*b^2*log(a+b*x)/a^4],
[1/(x^4*(a+b*x)^2),x,2,(-1/3)/(a^2*x^3)+b/(a^3*x^2)-3*b^2/(a^4*x)-b^3/(a^4*(a+b*x))-4*b^3*log(x)/a^5+4*b^3*log(a+b*x)/a^5],
[1/(x^5*(a+b*x)^2),x,2,(-1/4)/(a^2*x^4)+2/3*b/(a^3*x^3)-3/2*b^2/(a^4*x^2)+4*b^3/(a^5*x)+b^4/(a^5*(a+b*x))+5*b^4*log(x)/a^6-5*b^4*log(a+b*x)/a^6],
[x^7/(a+b*x)^3,x,2,15*a^4*x/b^7-5*a^3*x^2/b^6+2*a^2*x^3/b^5-3/4*a*x^4/b^4+1/5*x^5/b^3+1/2*a^7/(b^8*(a+b*x)^2)-7*a^6/(b^8*(a+b*x))-21*a^5*log(a+b*x)/b^8],
[x^6/(a+b*x)^3,x,2,-10*a^3*x/b^6+3*a^2*x^2/b^5-a*x^3/b^4+1/4*x^4/b^3-1/2*a^6/(b^7*(a+b*x)^2)+6*a^5/(b^7*(a+b*x))+15*a^4*log(a+b*x)/b^7],
[x^5/(a+b*x)^3,x,2,6*a^2*x/b^5-3/2*a*x^2/b^4+1/3*x^3/b^3+1/2*a^5/(b^6*(a+b*x)^2)-5*a^4/(b^6*(a+b*x))-10*a^3*log(a+b*x)/b^6],
[x^4/(a+b*x)^3,x,2,-3*a*x/b^4+1/2*x^2/b^3-1/2*a^4/(b^5*(a+b*x)^2)+4*a^3/(b^5*(a+b*x))+6*a^2*log(a+b*x)/b^5],
[x^3/(a+b*x)^3,x,2,x/b^3+1/2*a^3/(b^4*(a+b*x)^2)-3*a^2/(b^4*(a+b*x))-3*a*log(a+b*x)/b^4],
[x^2/(a+b*x)^3,x,2,-1/2*a^2/(b^3*(a+b*x)^2)+2*a/(b^3*(a+b*x))+log(a+b*x)/b^3],
[x/(a+b*x)^3,x,1,1/2*x^2/(a*(a+b*x)^2)],
[1/(a+b*x)^3,x,1,(-1/2)/(b*(a+b*x)^2)],
[1/(x*(a+b*x)^3),x,2,1/2/(a*(a+b*x)^2)+1/(a^2*(a+b*x))+log(x)/a^3-log(a+b*x)/a^3],
[1/(x^2*(a+b*x)^3),x,2,(-1)/(a^3*x)-1/2*b/(a^2*(a+b*x)^2)-2*b/(a^3*(a+b*x))-3*b*log(x)/a^4+3*b*log(a+b*x)/a^4],
[1/(x^3*(a+b*x)^3),x,2,(-1/2)/(a^3*x^2)+3*b/(a^4*x)+1/2*b^2/(a^3*(a+b*x)^2)+3*b^2/(a^4*(a+b*x))+6*b^2*log(x)/a^5-6*b^2*log(a+b*x)/a^5],
[1/(x^4*(a+b*x)^3),x,2,(-1/3)/(a^3*x^3)+3/2*b/(a^4*x^2)-6*b^2/(a^5*x)-1/2*b^3/(a^4*(a+b*x)^2)-4*b^3/(a^5*(a+b*x))-10*b^3*log(x)/a^6+10*b^3*log(a+b*x)/a^6],
[1/(x^5*(a+b*x)^3),x,2,(-1/4)/(a^3*x^4)+b/(a^4*x^3)-3*b^2/(a^5*x^2)+10*b^3/(a^6*x)+1/2*b^4/(a^5*(a+b*x)^2)+5*b^4/(a^6*(a+b*x))+15*b^4*log(x)/a^7-15*b^4*log(a+b*x)/a^7],
[x^8/(a+b*x)^4,x,2,35*a^4*x/b^8-10*a^3*x^2/b^7+10/3*a^2*x^3/b^6-a*x^4/b^5+1/5*x^5/b^4-1/3*a^8/(b^9*(a+b*x)^3)+4*a^7/(b^9*(a+b*x)^2)-28*a^6/(b^9*(a+b*x))-56*a^5*log(a+b*x)/b^9],
[x^7/(a+b*x)^4,x,2,-20*a^3*x/b^7+5*a^2*x^2/b^6-4/3*a*x^3/b^5+1/4*x^4/b^4+1/3*a^7/(b^8*(a+b*x)^3)-7/2*a^6/(b^8*(a+b*x)^2)+21*a^5/(b^8*(a+b*x))+35*a^4*log(a+b*x)/b^8],
[x^6/(a+b*x)^4,x,2,10*a^2*x/b^6-2*a*x^2/b^5+1/3*x^3/b^4-1/3*a^6/(b^7*(a+b*x)^3)+3*a^5/(b^7*(a+b*x)^2)-15*a^4/(b^7*(a+b*x))-20*a^3*log(a+b*x)/b^7],
[x^5/(a+b*x)^4,x,2,-4*a*x/b^5+1/2*x^2/b^4+1/3*a^5/(b^6*(a+b*x)^3)-5/2*a^4/(b^6*(a+b*x)^2)+10*a^3/(b^6*(a+b*x))+10*a^2*log(a+b*x)/b^6],
[x^4/(a+b*x)^4,x,2,x/b^4-1/3*a^4/(b^5*(a+b*x)^3)+2*a^3/(b^5*(a+b*x)^2)-6*a^2/(b^5*(a+b*x))-4*a*log(a+b*x)/b^5],
[x^3/(a+b*x)^4,x,2,1/3*a^3/(b^4*(a+b*x)^3)-3/2*a^2/(b^4*(a+b*x)^2)+3*a/(b^4*(a+b*x))+log(a+b*x)/b^4],
[x^2/(a+b*x)^4,x,1,1/3*x^3/(a*(a+b*x)^3)],
[x/(a+b*x)^4,x,2,1/3*a/(b^2*(a+b*x)^3)+(-1/2)/(b^2*(a+b*x)^2)],
[1/(a+b*x)^4,x,1,(-1/3)/(b*(a+b*x)^3)],
[1/(x*(a+b*x)^4),x,2,1/3/(a*(a+b*x)^3)+1/2/(a^2*(a+b*x)^2)+1/(a^3*(a+b*x))+log(x)/a^4-log(a+b*x)/a^4],
[1/(x^2*(a+b*x)^4),x,2,(-1)/(a^4*x)-1/3*b/(a^2*(a+b*x)^3)-b/(a^3*(a+b*x)^2)-3*b/(a^4*(a+b*x))-4*b*log(x)/a^5+4*b*log(a+b*x)/a^5],
[1/(x^3*(a+b*x)^4),x,2,(-1/2)/(a^4*x^2)+4*b/(a^5*x)+1/3*b^2/(a^3*(a+b*x)^3)+3/2*b^2/(a^4*(a+b*x)^2)+6*b^2/(a^5*(a+b*x))+10*b^2*log(x)/a^6-10*b^2*log(a+b*x)/a^6],
[1/(x^4*(a+b*x)^4),x,2,(-1/3)/(a^4*x^3)+2*b/(a^5*x^2)-10*b^2/(a^6*x)-1/3*b^3/(a^4*(a+b*x)^3)-2*b^3/(a^5*(a+b*x)^2)-10*b^3/(a^6*(a+b*x))-20*b^3*log(x)/a^7+20*b^3*log(a+b*x)/a^7],
[1/(x^5*(a+b*x)^4),x,2,(-1/4)/(a^4*x^4)+4/3*b/(a^5*x^3)-5*b^2/(a^6*x^2)+20*b^3/(a^7*x)+1/3*b^4/(a^5*(a+b*x)^3)+5/2*b^4/(a^6*(a+b*x)^2)+15*b^4/(a^7*(a+b*x))+35*b^4*log(x)/a^8-35*b^4*log(a+b*x)/a^8],
[x^10/(a+b*x)^7,x,2,-84*a^3*x/b^10+14*a^2*x^2/b^9-7/3*a*x^3/b^8+1/4*x^4/b^7-1/6*a^10/(b^11*(a+b*x)^6)+2*a^9/(b^11*(a+b*x)^5)-45/4*a^8/(b^11*(a+b*x)^4)+40*a^7/(b^11*(a+b*x)^3)-105*a^6/(b^11*(a+b*x)^2)+252*a^5/(b^11*(a+b*x))+210*a^4*log(a+b*x)/b^11],
[x^9/(a+b*x)^7,x,2,28*a^2*x/b^9-7/2*a*x^2/b^8+1/3*x^3/b^7+1/6*a^9/(b^10*(a+b*x)^6)-9/5*a^8/(b^10*(a+b*x)^5)+9*a^7/(b^10*(a+b*x)^4)-28*a^6/(b^10*(a+b*x)^3)+63*a^5/(b^10*(a+b*x)^2)-126*a^4/(b^10*(a+b*x))-84*a^3*log(a+b*x)/b^10],
[x^8/(a+b*x)^7,x,2,-7*a*x/b^8+1/2*x^2/b^7-1/6*a^8/(b^9*(a+b*x)^6)+8/5*a^7/(b^9*(a+b*x)^5)-7*a^6/(b^9*(a+b*x)^4)+56/3*a^5/(b^9*(a+b*x)^3)-35*a^4/(b^9*(a+b*x)^2)+56*a^3/(b^9*(a+b*x))+28*a^2*log(a+b*x)/b^9],
[x^7/(a+b*x)^7,x,2,x/b^7+1/6*a^7/(b^8*(a+b*x)^6)-7/5*a^6/(b^8*(a+b*x)^5)+21/4*a^5/(b^8*(a+b*x)^4)-35/3*a^4/(b^8*(a+b*x)^3)+35/2*a^3/(b^8*(a+b*x)^2)-21*a^2/(b^8*(a+b*x))-7*a*log(a+b*x)/b^8],
[x^6/(a+b*x)^7,x,2,-1/6*a^6/(b^7*(a+b*x)^6)+6/5*a^5/(b^7*(a+b*x)^5)-15/4*a^4/(b^7*(a+b*x)^4)+20/3*a^3/(b^7*(a+b*x)^3)-15/2*a^2/(b^7*(a+b*x)^2)+6*a/(b^7*(a+b*x))+log(a+b*x)/b^7],
[x^5/(a+b*x)^7,x,1,1/6*x^6/(a*(a+b*x)^6)],
[x^4/(a+b*x)^7,x,2,1/6*x^5/(a*(a+b*x)^6)+1/30*x^5/(a^2*(a+b*x)^5)],
[x^3/(a+b*x)^7,x,2,1/6*x^4/(a*(a+b*x)^6)+1/15*x^4/(a^2*(a+b*x)^5)+1/60*x^4/(a^3*(a+b*x)^4),1/6*a^3/(b^4*(a+b*x)^6)-3/5*a^2/(b^4*(a+b*x)^5)+3/4*a/(b^4*(a+b*x)^4)+(-1/3)/(b^4*(a+b*x)^3)],
[x^2/(a+b*x)^7,x,2,-1/6*a^2/(b^3*(a+b*x)^6)+2/5*a/(b^3*(a+b*x)^5)+(-1/4)/(b^3*(a+b*x)^4)],
[x/(a+b*x)^7,x,2,1/6*a/(b^2*(a+b*x)^6)+(-1/5)/(b^2*(a+b*x)^5)],
[1/(a+b*x)^7,x,1,(-1/6)/(b*(a+b*x)^6)],
[1/(x*(a+b*x)^7),x,2,1/6/(a*(a+b*x)^6)+1/5/(a^2*(a+b*x)^5)+1/4/(a^3*(a+b*x)^4)+1/3/(a^4*(a+b*x)^3)+1/2/(a^5*(a+b*x)^2)+1/(a^6*(a+b*x))+log(x)/a^7-log(a+b*x)/a^7],
[1/(x^2*(a+b*x)^7),x,2,(-1)/(a^7*x)-1/6*b/(a^2*(a+b*x)^6)-2/5*b/(a^3*(a+b*x)^5)-3/4*b/(a^4*(a+b*x)^4)-4/3*b/(a^5*(a+b*x)^3)-5/2*b/(a^6*(a+b*x)^2)-6*b/(a^7*(a+b*x))-7*b*log(x)/a^8+7*b*log(a+b*x)/a^8],
[1/(x^3*(a+b*x)^7),x,2,(-1/2)/(a^7*x^2)+7*b/(a^8*x)+1/6*b^2/(a^3*(a+b*x)^6)+3/5*b^2/(a^4*(a+b*x)^5)+3/2*b^2/(a^5*(a+b*x)^4)+10/3*b^2/(a^6*(a+b*x)^3)+15/2*b^2/(a^7*(a+b*x)^2)+21*b^2/(a^8*(a+b*x))+28*b^2*log(x)/a^9-28*b^2*log(a+b*x)/a^9],
[1/(x^4*(a+b*x)^7),x,2,(-1/3)/(a^7*x^3)+7/2*b/(a^8*x^2)-28*b^2/(a^9*x)-1/6*b^3/(a^4*(a+b*x)^6)-4/5*b^3/(a^5*(a+b*x)^5)-5/2*b^3/(a^6*(a+b*x)^4)-20/3*b^3/(a^7*(a+b*x)^3)-35/2*b^3/(a^8*(a+b*x)^2)-56*b^3/(a^9*(a+b*x))-84*b^3*log(x)/a^10+84*b^3*log(a+b*x)/a^10],
[x^12/(a+b*x)^10,x,2,55*a^2*x/b^12-5*a*x^2/b^11+1/3*x^3/b^10-1/9*a^12/(b^13*(a+b*x)^9)+3/2*a^11/(b^13*(a+b*x)^8)-66/7*a^10/(b^13*(a+b*x)^7)+110/3*a^9/(b^13*(a+b*x)^6)-99*a^8/(b^13*(a+b*x)^5)+198*a^7/(b^13*(a+b*x)^4)-308*a^6/(b^13*(a+b*x)^3)+396*a^5/(b^13*(a+b*x)^2)-495*a^4/(b^13*(a+b*x))-220*a^3*log(a+b*x)/b^13],
[x^11/(a+b*x)^10,x,2,-10*a*x/b^11+1/2*x^2/b^10+1/9*a^11/(b^12*(a+b*x)^9)-11/8*a^10/(b^12*(a+b*x)^8)+55/7*a^9/(b^12*(a+b*x)^7)-55/2*a^8/(b^12*(a+b*x)^6)+66*a^7/(b^12*(a+b*x)^5)-231/2*a^6/(b^12*(a+b*x)^4)+154*a^5/(b^12*(a+b*x)^3)-165*a^4/(b^12*(a+b*x)^2)+165*a^3/(b^12*(a+b*x))+55*a^2*log(a+b*x)/b^12],
[x^10/(a+b*x)^10,x,2,x/b^10-1/9*a^10/(b^11*(a+b*x)^9)+5/4*a^9/(b^11*(a+b*x)^8)-45/7*a^8/(b^11*(a+b*x)^7)+20*a^7/(b^11*(a+b*x)^6)-42*a^6/(b^11*(a+b*x)^5)+63*a^5/(b^11*(a+b*x)^4)-70*a^4/(b^11*(a+b*x)^3)+60*a^3/(b^11*(a+b*x)^2)-45*a^2/(b^11*(a+b*x))-10*a*log(a+b*x)/b^11],
[x^9/(a+b*x)^10,x,2,1/9*a^9/(b^10*(a+b*x)^9)-9/8*a^8/(b^10*(a+b*x)^8)+36/7*a^7/(b^10*(a+b*x)^7)-14*a^6/(b^10*(a+b*x)^6)+126/5*a^5/(b^10*(a+b*x)^5)-63/2*a^4/(b^10*(a+b*x)^4)+28*a^3/(b^10*(a+b*x)^3)-18*a^2/(b^10*(a+b*x)^2)+9*a/(b^10*(a+b*x))+log(a+b*x)/b^10],
[x^8/(a+b*x)^10,x,1,1/9*x^9/(a*(a+b*x)^9)],
[x^7/(a+b*x)^10,x,2,1/9*x^8/(a*(a+b*x)^9)+1/72*x^8/(a^2*(a+b*x)^8)],
[x^6/(a+b*x)^10,x,3,1/9*x^7/(a*(a+b*x)^9)+1/36*x^7/(a^2*(a+b*x)^8)+1/252*x^7/(a^3*(a+b*x)^7)],
[x^5/(a+b*x)^10,x,4,1/9*x^6/(a*(a+b*x)^9)+1/24*x^6/(a^2*(a+b*x)^8)+1/84*x^6/(a^3*(a+b*x)^7)+1/504*x^6/(a^4*(a+b*x)^6)],
[x^4/(a+b*x)^10,x,2,-1/9*a^4/(b^5*(a+b*x)^9)+1/2*a^3/(b^5*(a+b*x)^8)-6/7*a^2/(b^5*(a+b*x)^7)+2/3*a/(b^5*(a+b*x)^6)+(-1/5)/(b^5*(a+b*x)^5)],
[x^3/(a+b*x)^10,x,2,1/9*a^3/(b^4*(a+b*x)^9)-3/8*a^2/(b^4*(a+b*x)^8)+3/7*a/(b^4*(a+b*x)^7)+(-1/6)/(b^4*(a+b*x)^6)],
[x^2/(a+b*x)^10,x,2,-1/9*a^2/(b^3*(a+b*x)^9)+1/4*a/(b^3*(a+b*x)^8)+(-1/7)/(b^3*(a+b*x)^7)],
[x/(a+b*x)^10,x,2,1/9*a/(b^2*(a+b*x)^9)+(-1/8)/(b^2*(a+b*x)^8)],
[1/(a+b*x)^10,x,1,(-1/9)/(b*(a+b*x)^9)],
[1/(x*(a+b*x)^10),x,2,1/9/(a*(a+b*x)^9)+1/8/(a^2*(a+b*x)^8)+1/7/(a^3*(a+b*x)^7)+1/6/(a^4*(a+b*x)^6)+1/5/(a^5*(a+b*x)^5)+1/4/(a^6*(a+b*x)^4)+1/3/(a^7*(a+b*x)^3)+1/2/(a^8*(a+b*x)^2)+1/(a^9*(a+b*x))+log(x)/a^10-log(a+b*x)/a^10],
[1/(x^2*(a+b*x)^10),x,2,(-1)/(a^10*x)-1/9*b/(a^2*(a+b*x)^9)-1/4*b/(a^3*(a+b*x)^8)-3/7*b/(a^4*(a+b*x)^7)-2/3*b/(a^5*(a+b*x)^6)-b/(a^6*(a+b*x)^5)-3/2*b/(a^7*(a+b*x)^4)-7/3*b/(a^8*(a+b*x)^3)-4*b/(a^9*(a+b*x)^2)-9*b/(a^10*(a+b*x))-10*b*log(x)/a^11+10*b*log(a+b*x)/a^11],
[1/(x^3*(a+b*x)^10),x,2,(-1/2)/(a^10*x^2)+10*b/(a^11*x)+1/9*b^2/(a^3*(a+b*x)^9)+3/8*b^2/(a^4*(a+b*x)^8)+6/7*b^2/(a^5*(a+b*x)^7)+5/3*b^2/(a^6*(a+b*x)^6)+3*b^2/(a^7*(a+b*x)^5)+21/4*b^2/(a^8*(a+b*x)^4)+28/3*b^2/(a^9*(a+b*x)^3)+18*b^2/(a^10*(a+b*x)^2)+45*b^2/(a^11*(a+b*x))+55*b^2*log(x)/a^12-55*b^2*log(a+b*x)/a^12],
[1/(x^4*(a+b*x)^10),x,2,(-1/3)/(a^10*x^3)+5*b/(a^11*x^2)-55*b^2/(a^12*x)-1/9*b^3/(a^4*(a+b*x)^9)-1/2*b^3/(a^5*(a+b*x)^8)-10/7*b^3/(a^6*(a+b*x)^7)-10/3*b^3/(a^7*(a+b*x)^6)-7*b^3/(a^8*(a+b*x)^5)-14*b^3/(a^9*(a+b*x)^4)-28*b^3/(a^10*(a+b*x)^3)-60*b^3/(a^11*(a+b*x)^2)-165*b^3/(a^12*(a+b*x))-220*b^3*log(x)/a^13+220*b^3*log(a+b*x)/a^13],
[(a+b*x)^12/x^10,x,2,-1/9*a^12/x^9-3/2*a^11*b/x^8-66/7*a^10*b^2/x^7-110/3*a^9*b^3/x^6-99*a^8*b^4/x^5-198*a^7*b^5/x^4-308*a^6*b^6/x^3-396*a^5*b^7/x^2-495*a^4*b^8/x+66*a^2*b^10*x+6*a*b^11*x^2+1/3*b^12*x^3+220*a^3*b^9*log(x)],
[(a+b*x)^11/x^10,x,2,-1/9*a^11/x^9-11/8*a^10*b/x^8-55/7*a^9*b^2/x^7-55/2*a^8*b^3/x^6-66*a^7*b^4/x^5-231/2*a^6*b^5/x^4-154*a^5*b^6/x^3-165*a^4*b^7/x^2-165*a^3*b^8/x+11*a*b^10*x+1/2*b^11*x^2+55*a^2*b^9*log(x)],
[(a+b*x)^10/x^10,x,2,-1/9*a^10/x^9-5/4*a^9*b/x^8-45/7*a^8*b^2/x^7-20*a^7*b^3/x^6-42*a^6*b^4/x^5-63*a^5*b^5/x^4-70*a^4*b^6/x^3-60*a^3*b^7/x^2-45*a^2*b^8/x+b^10*x+10*a*b^9*log(x)],
[(a+b*x)^9/x^10,x,2,-1/9*a^9/x^9-9/8*a^8*b/x^8-36/7*a^7*b^2/x^7-14*a^6*b^3/x^6-126/5*a^5*b^4/x^5-63/2*a^4*b^5/x^4-28*a^3*b^6/x^3-18*a^2*b^7/x^2-9*a*b^8/x+b^9*log(x)],
[(a+b*x)^8/x^10,x,1,-1/9*(a+b*x)^9/(a*x^9)],
[(a+b*x)^7/x^10,x,2,-1/9*(a+b*x)^8/(a*x^9)+1/72*b*(a+b*x)^8/(a^2*x^8)],
[(a+b*x)^6/x^10,x,3,-1/9*(a+b*x)^7/(a*x^9)+1/36*b*(a+b*x)^7/(a^2*x^8)-1/252*b^2*(a+b*x)^7/(a^3*x^7)],
[(a+b*x)^5/x^10,x,2,-1/9*a^5/x^9-5/8*a^4*b/x^8-10/7*a^3*b^2/x^7-5/3*a^2*b^3/x^6-a*b^4/x^5-1/4*b^5/x^4],
[(a+b*x)^4/x^10,x,2,-1/9*a^4/x^9-1/2*a^3*b/x^8-6/7*a^2*b^2/x^7-2/3*a*b^3/x^6-1/5*b^4/x^5],
[(a+b*x)^3/x^10,x,2,-1/9*a^3/x^9-3/8*a^2*b/x^8-3/7*a*b^2/x^7-1/6*b^3/x^6],
[(a+b*x)^2/x^10,x,2,-1/9*a^2/x^9-1/4*a*b/x^8-1/7*b^2/x^7],
[(a+b*x)/x^10,x,2,-1/9*a/x^9-1/8*b/x^8],
[1/x^10,x,1,(-1/9)/x^9],
[1/(x^10*(a+b*x)),x,2,(-1/9)/(a*x^9)+1/8*b/(a^2*x^8)-1/7*b^2/(a^3*x^7)+1/6*b^3/(a^4*x^6)-1/5*b^4/(a^5*x^5)+1/4*b^5/(a^6*x^4)-1/3*b^6/(a^7*x^3)+1/2*b^7/(a^8*x^2)-b^8/(a^9*x)-b^9*log(x)/a^10+b^9*log(a+b*x)/a^10],
[1/(x^10*(a+b*x)^2),x,2,(-1/9)/(a^2*x^9)+1/4*b/(a^3*x^8)-3/7*b^2/(a^4*x^7)+2/3*b^3/(a^5*x^6)-b^4/(a^6*x^5)+3/2*b^5/(a^7*x^4)-7/3*b^6/(a^8*x^3)+4*b^7/(a^9*x^2)-9*b^8/(a^10*x)-b^9/(a^10*(a+b*x))-10*b^9*log(x)/a^11+10*b^9*log(a+b*x)/a^11],
[1/(x^10*(a+b*x)^3),x,2,(-1/9)/(a^3*x^9)+3/8*b/(a^4*x^8)-6/7*b^2/(a^5*x^7)+5/3*b^3/(a^6*x^6)-3*b^4/(a^7*x^5)+21/4*b^5/(a^8*x^4)-28/3*b^6/(a^9*x^3)+18*b^7/(a^10*x^2)-45*b^8/(a^11*x)-1/2*b^9/(a^10*(a+b*x)^2)-10*b^9/(a^11*(a+b*x))-55*b^9*log(x)/a^12+55*b^9*log(a+b*x)/a^12],
[1/(x*(2+3*x)),x,3,1/2*log(x)-1/2*log(2+3*x)],
[1/(x*(4+6*x)),x,3,1/4*log(x)-1/4*log(2+3*x)],
[1/(x^2*(4+6*x)),x,2,(-1/4)/x-3/8*log(x)+3/8*log(2+3*x)],
[1/(x^3*(4+6*x)),x,2,(-1/8)/x^2+3/8/x+9/16*log(x)-9/16*log(2+3*x)],
[1/(x^4*(4+6*x)),x,2,(-1/12)/x^3+3/16/x^2+(-9/16)/x-27/32*log(x)+27/32*log(2+3*x)],
[1/(x^5*(4+6*x)),x,2,(-1/16)/x^4+1/8/x^3+(-9/32)/x^2+27/32/x+81/64*log(x)-81/64*log(2+3*x)],
[1/(x*(4+6*x)^2),x,2,1/8/(2+3*x)+1/16*log(x)-1/16*log(2+3*x)],
[1/(x^2*(4+6*x)^2),x,2,(-1/16)/x+(-3/16)/(2+3*x)-3/16*log(x)+3/16*log(2+3*x)],
[1/(x^3*(4+6*x)^2),x,2,(-1/32)/x^2+3/16/x+9/32/(2+3*x)+27/64*log(x)-27/64*log(2+3*x)],
[1/(x^4*(4+6*x)^2),x,2,(-1/48)/x^3+3/32/x^2+(-27/64)/x+(-27/64)/(2+3*x)-27/32*log(x)+27/32*log(2+3*x)],
[1/(x^5*(4+6*x)^2),x,2,(-1/64)/x^4+1/16/x^3+(-27/128)/x^2+27/32/x+81/128/(2+3*x)+405/256*log(x)-405/256*log(2+3*x)],
[1/(x*(4+6*x)^3),x,2,1/32/(2+3*x)^2+1/32/(2+3*x)+1/64*log(x)-1/64*log(2+3*x)],
[1/(x^2*(4+6*x)^3),x,2,(-1/64)/x+(-3/64)/(2+3*x)^2+(-3/32)/(2+3*x)-9/128*log(x)+9/128*log(2+3*x)],
[1/(x^3*(4+6*x)^3),x,2,(-1/128)/x^2+9/128/x+9/128/(2+3*x)^2+27/128/(2+3*x)+27/128*log(x)-27/128*log(2+3*x)],
[1/(x^4*(4+6*x)^3),x,2,(-1/192)/x^3+9/256/x^2+(-27/128)/x+(-27/256)/(2+3*x)^2+(-27/64)/(2+3*x)-135/256*log(x)+135/256*log(2+3*x)],
[1/(x^5*(4+6*x)^3),x,2,(-1/256)/x^4+3/128/x^3+(-27/256)/x^2+135/256/x+81/512/(2+3*x)^2+405/512/(2+3*x)+1215/1024*log(x)-1215/1024*log(2+3*x)],

#  Factor content out of denominator before including in Log? 
[1/(2+2*x),x,1,1/2*log(1+x)],
[1/(4-6*x),x,1,-1/6*log(2-3*x)],
[1/(a+x*sqrt(a)),x,1,log(x+sqrt(a))/sqrt(a)],
[1/(a+x*sqrt(-a)),x,1,log(a+x*sqrt(-a))/sqrt(-a)],
[1/(a^2+x*sqrt(-a)),x,1,log(a^2+x*sqrt(-a))/sqrt(-a)],
[1/(a^3+x*sqrt(-a)),x,1,log(a^3+x*sqrt(-a))/sqrt(-a)],
[1/(1/a+x*sqrt(-a)),x,1,log(1-(-a)^(3/2)*x)/sqrt(-a)],
[1/(1/a^2+x*sqrt(-a)),x,1,log(1+(-a)^(5/2)*x)/sqrt(-a)],

#  Integrands of the form 1/(x^m*(a+b*x)) where m>0 is an integer and a^2=1 
[1/(x*(1+b*x)),x,3,log(x)-log(1+b*x)],
[1/(x*(-1+b*x)),x,3,-log(x)+log(1-b*x)],
[1/(x^2*(1+b*x)),x,2,(-1)/x-b*log(x)+b*log(1+b*x)],
[1/(x^2*(-1+b*x)),x,2,1/x-b*log(x)+b*log(1-b*x)],

#  The b*Log[x] terms cannot cancel if ArcTanh[1+2*b*x] is returned instead of Logs! 
[b/x+1/(x^2*(1+b*x)),x,3,(-1)/x+b*log(1+b*x)],

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

# n>0
[x^3*sqrt(a+b*x),x,2,-2/3*a^3*(a+b*x)^(3/2)/b^4+6/5*a^2*(a+b*x)^(5/2)/b^4-6/7*a*(a+b*x)^(7/2)/b^4+2/9*(a+b*x)^(9/2)/b^4],
[x^2*sqrt(a+b*x),x,2,2/3*a^2*(a+b*x)^(3/2)/b^3-4/5*a*(a+b*x)^(5/2)/b^3+2/7*(a+b*x)^(7/2)/b^3],
[x*sqrt(a+b*x),x,2,-2/3*a*(a+b*x)^(3/2)/b^2+2/5*(a+b*x)^(5/2)/b^2],
[sqrt(a+b*x),x,1,2/3*(a+b*x)^(3/2)/b],
[sqrt(a+b*x)/x,x,3,-2*arctanh(sqrt(a+b*x)/sqrt(a))*sqrt(a)+2*sqrt(a+b*x)],
[sqrt(a+b*x)/x^2,x,3,-b*arctanh(sqrt(a+b*x)/sqrt(a))/sqrt(a)-sqrt(a+b*x)/x],
[sqrt(a+b*x)/x^3,x,4,1/4*b^2*arctanh(sqrt(a+b*x)/sqrt(a))/a^(3/2)-1/2*sqrt(a+b*x)/x^2-1/4*b*sqrt(a+b*x)/(a*x)],
[sqrt(a+b*x)/x^4,x,5,-1/8*b^3*arctanh(sqrt(a+b*x)/sqrt(a))/a^(5/2)-1/3*sqrt(a+b*x)/x^3-1/12*b*sqrt(a+b*x)/(a*x^2)+1/8*b^2*sqrt(a+b*x)/(a^2*x)],
[x^3*(a+b*x)^(3/2),x,2,-2/5*a^3*(a+b*x)^(5/2)/b^4+6/7*a^2*(a+b*x)^(7/2)/b^4-2/3*a*(a+b*x)^(9/2)/b^4+2/11*(a+b*x)^(11/2)/b^4],
[x^2*(a+b*x)^(3/2),x,2,2/5*a^2*(a+b*x)^(5/2)/b^3-4/7*a*(a+b*x)^(7/2)/b^3+2/9*(a+b*x)^(9/2)/b^3],
[x*(a+b*x)^(3/2),x,2,-2/5*a*(a+b*x)^(5/2)/b^2+2/7*(a+b*x)^(7/2)/b^2],
[(a+b*x)^(3/2),x,1,2/5*(a+b*x)^(5/2)/b],
[(a+b*x)^(3/2)/x,x,4,2/3*(a+b*x)^(3/2)-2*a^(3/2)*arctanh(sqrt(a+b*x)/sqrt(a))+2*a*sqrt(a+b*x)],
[(a+b*x)^(3/2)/x^2,x,4,-(a+b*x)^(3/2)/x-3*b*arctanh(sqrt(a+b*x)/sqrt(a))*sqrt(a)+3*b*sqrt(a+b*x)],
[(a+b*x)^(3/2)/x^3,x,4,-1/2*(a+b*x)^(3/2)/x^2-3/4*b^2*arctanh(sqrt(a+b*x)/sqrt(a))/sqrt(a)-3/4*b*sqrt(a+b*x)/x],
[(a+b*x)^(3/2)/x^4,x,5,-1/3*(a+b*x)^(3/2)/x^3+1/8*b^3*arctanh(sqrt(a+b*x)/sqrt(a))/a^(3/2)-1/4*b*sqrt(a+b*x)/x^2-1/8*b^2*sqrt(a+b*x)/(a*x)],
[x^3*(a+b*x)^(5/2),x,2,-2/7*a^3*(a+b*x)^(7/2)/b^4+2/3*a^2*(a+b*x)^(9/2)/b^4-6/11*a*(a+b*x)^(11/2)/b^4+2/13*(a+b*x)^(13/2)/b^4],
[x^2*(a+b*x)^(5/2),x,2,2/7*a^2*(a+b*x)^(7/2)/b^3-4/9*a*(a+b*x)^(9/2)/b^3+2/11*(a+b*x)^(11/2)/b^3],
[x*(a+b*x)^(5/2),x,2,-2/7*a*(a+b*x)^(7/2)/b^2+2/9*(a+b*x)^(9/2)/b^2],
[(a+b*x)^(5/2),x,1,2/7*(a+b*x)^(7/2)/b],
[(a+b*x)^(5/2)/x,x,5,2/3*a*(a+b*x)^(3/2)+2/5*(a+b*x)^(5/2)-2*a^(5/2)*arctanh(sqrt(a+b*x)/sqrt(a))+2*a^2*sqrt(a+b*x)],
[(a+b*x)^(5/2)/x^2,x,5,5/3*b*(a+b*x)^(3/2)-(a+b*x)^(5/2)/x-5*a^(3/2)*b*arctanh(sqrt(a+b*x)/sqrt(a))+5*a*b*sqrt(a+b*x)],
[(a+b*x)^(5/2)/x^3,x,5,-5/4*b*(a+b*x)^(3/2)/x-1/2*(a+b*x)^(5/2)/x^2-15/4*b^2*arctanh(sqrt(a+b*x)/sqrt(a))*sqrt(a)+15/4*b^2*sqrt(a+b*x)],
[(a+b*x)^(5/2)/x^4,x,5,-5/12*b*(a+b*x)^(3/2)/x^2-1/3*(a+b*x)^(5/2)/x^3-5/8*b^3*arctanh(sqrt(a+b*x)/sqrt(a))/sqrt(a)-5/8*b^2*sqrt(a+b*x)/x],
[(a+b*x)^(5/2)/x^5,x,6,-5/24*b*(a+b*x)^(3/2)/x^3-1/4*(a+b*x)^(5/2)/x^4+5/64*b^4*arctanh(sqrt(a+b*x)/sqrt(a))/a^(3/2)-5/32*b^2*sqrt(a+b*x)/x^2-5/64*b^3*sqrt(a+b*x)/(a*x)],
[x^7*(a+b*x)^(9/2),x,2,-2/11*a^7*(a+b*x)^(11/2)/b^8+14/13*a^6*(a+b*x)^(13/2)/b^8-14/5*a^5*(a+b*x)^(15/2)/b^8+70/17*a^4*(a+b*x)^(17/2)/b^8-70/19*a^3*(a+b*x)^(19/2)/b^8+2*a^2*(a+b*x)^(21/2)/b^8-14/23*a*(a+b*x)^(23/2)/b^8+2/25*(a+b*x)^(25/2)/b^8],
[x^6*(a+b*x)^(9/2),x,2,2/11*a^6*(a+b*x)^(11/2)/b^7-12/13*a^5*(a+b*x)^(13/2)/b^7+2*a^4*(a+b*x)^(15/2)/b^7-40/17*a^3*(a+b*x)^(17/2)/b^7+30/19*a^2*(a+b*x)^(19/2)/b^7-4/7*a*(a+b*x)^(21/2)/b^7+2/23*(a+b*x)^(23/2)/b^7],
[x^5*(a+b*x)^(9/2),x,2,-2/11*a^5*(a+b*x)^(11/2)/b^6+10/13*a^4*(a+b*x)^(13/2)/b^6-4/3*a^3*(a+b*x)^(15/2)/b^6+20/17*a^2*(a+b*x)^(17/2)/b^6-10/19*a*(a+b*x)^(19/2)/b^6+2/21*(a+b*x)^(21/2)/b^6],
[x^4*(a+b*x)^(9/2),x,2,2/11*a^4*(a+b*x)^(11/2)/b^5-8/13*a^3*(a+b*x)^(13/2)/b^5+4/5*a^2*(a+b*x)^(15/2)/b^5-8/17*a*(a+b*x)^(17/2)/b^5+2/19*(a+b*x)^(19/2)/b^5],
[x^3*(a+b*x)^(9/2),x,2,-2/11*a^3*(a+b*x)^(11/2)/b^4+6/13*a^2*(a+b*x)^(13/2)/b^4-2/5*a*(a+b*x)^(15/2)/b^4+2/17*(a+b*x)^(17/2)/b^4],
[x^2*(a+b*x)^(9/2),x,2,2/11*a^2*(a+b*x)^(11/2)/b^3-4/13*a*(a+b*x)^(13/2)/b^3+2/15*(a+b*x)^(15/2)/b^3],
[x*(a+b*x)^(9/2),x,2,-2/11*a*(a+b*x)^(11/2)/b^2+2/13*(a+b*x)^(13/2)/b^2],
[(a+b*x)^(9/2),x,1,2/11*(a+b*x)^(11/2)/b],
[(a+b*x)^(9/2)/x,x,7,2/3*a^3*(a+b*x)^(3/2)+2/5*a^2*(a+b*x)^(5/2)+2/7*a*(a+b*x)^(7/2)+2/9*(a+b*x)^(9/2)-2*a^(9/2)*arctanh(sqrt(a+b*x)/sqrt(a))+2*a^4*sqrt(a+b*x)],
[(a+b*x)^(9/2)/x^2,x,7,3*a^2*b*(a+b*x)^(3/2)+9/5*a*b*(a+b*x)^(5/2)+9/7*b*(a+b*x)^(7/2)-(a+b*x)^(9/2)/x-9*a^(7/2)*b*arctanh(sqrt(a+b*x)/sqrt(a))+9*a^3*b*sqrt(a+b*x)],
[(a+b*x)^(9/2)/x^3,x,7,21/4*a*b^2*(a+b*x)^(3/2)+63/20*b^2*(a+b*x)^(5/2)-9/4*b*(a+b*x)^(7/2)/x-1/2*(a+b*x)^(9/2)/x^2-63/4*a^(5/2)*b^2*arctanh(sqrt(a+b*x)/sqrt(a))+63/4*a^2*b^2*sqrt(a+b*x)],
[(a+b*x)^(9/2)/x^4,x,7,35/8*b^3*(a+b*x)^(3/2)-21/8*b^2*(a+b*x)^(5/2)/x-3/4*b*(a+b*x)^(7/2)/x^2-1/3*(a+b*x)^(9/2)/x^3-105/8*a^(3/2)*b^3*arctanh(sqrt(a+b*x)/sqrt(a))+105/8*a*b^3*sqrt(a+b*x)],
[(a+b*x)^(9/2)/x^5,x,7,-105/64*b^3*(a+b*x)^(3/2)/x-21/32*b^2*(a+b*x)^(5/2)/x^2-3/8*b*(a+b*x)^(7/2)/x^3-1/4*(a+b*x)^(9/2)/x^4-315/64*b^4*arctanh(sqrt(a+b*x)/sqrt(a))*sqrt(a)+315/64*b^4*sqrt(a+b*x)],
[(a+b*x)^(9/2)/x^6,x,7,-21/64*b^3*(a+b*x)^(3/2)/x^2-21/80*b^2*(a+b*x)^(5/2)/x^3-9/40*b*(a+b*x)^(7/2)/x^4-1/5*(a+b*x)^(9/2)/x^5-63/128*b^5*arctanh(sqrt(a+b*x)/sqrt(a))/sqrt(a)-63/128*b^4*sqrt(a+b*x)/x],
[(a+b*x)^(9/2)/x^7,x,8,-7/64*b^3*(a+b*x)^(3/2)/x^3-21/160*b^2*(a+b*x)^(5/2)/x^4-3/20*b*(a+b*x)^(7/2)/x^5-1/6*(a+b*x)^(9/2)/x^6+21/512*b^6*arctanh(sqrt(a+b*x)/sqrt(a))/a^(3/2)-21/256*b^4*sqrt(a+b*x)/x^2-21/512*b^5*sqrt(a+b*x)/(a*x)],
[(a+b*x)^(9/2)/x^8,x,9,-3/64*b^3*(a+b*x)^(3/2)/x^4-3/40*b^2*(a+b*x)^(5/2)/x^5-3/28*b*(a+b*x)^(7/2)/x^6-1/7*(a+b*x)^(9/2)/x^7-9/1024*b^7*arctanh(sqrt(a+b*x)/sqrt(a))/a^(5/2)-3/128*b^4*sqrt(a+b*x)/x^3-3/512*b^5*sqrt(a+b*x)/(a*x^2)+9/1024*b^6*sqrt(a+b*x)/(a^2*x)],
[sqrt(-a+b*x)/x,x,3,-2*arctan(sqrt(-a+b*x)/sqrt(a))*sqrt(a)+2*sqrt(-a+b*x)],
[sqrt(-a+b*x)/x^2,x,3,b*arctan(sqrt(-a+b*x)/sqrt(a))/sqrt(a)-sqrt(-a+b*x)/x],
[sqrt(-a+b*x)/x^3,x,4,1/4*b^2*arctan(sqrt(-a+b*x)/sqrt(a))/a^(3/2)-1/2*sqrt(-a+b*x)/x^2+1/4*b*sqrt(-a+b*x)/(a*x)],
[(-a+b*x)^(3/2)/x,x,4,2/3*(-a+b*x)^(3/2)+2*a^(3/2)*arctan(sqrt(-a+b*x)/sqrt(a))-2*a*sqrt(-a+b*x)],
[(-a+b*x)^(3/2)/x^2,x,4,-(-a+b*x)^(3/2)/x-3*b*arctan(sqrt(-a+b*x)/sqrt(a))*sqrt(a)+3*b*sqrt(-a+b*x)],
[(-a+b*x)^(3/2)/x^3,x,4,-1/2*(-a+b*x)^(3/2)/x^2+3/4*b^2*arctan(sqrt(-a+b*x)/sqrt(a))/sqrt(a)-3/4*b*sqrt(-a+b*x)/x],
[(-a+b*x)^(5/2)/x,x,5,-2/3*a*(-a+b*x)^(3/2)+2/5*(-a+b*x)^(5/2)-2*a^(5/2)*arctan(sqrt(-a+b*x)/sqrt(a))+2*a^2*sqrt(-a+b*x)],
[(-a+b*x)^(5/2)/x^2,x,5,5/3*b*(-a+b*x)^(3/2)-(-a+b*x)^(5/2)/x+5*a^(3/2)*b*arctan(sqrt(-a+b*x)/sqrt(a))-5*a*b*sqrt(-a+b*x)],
[(-a+b*x)^(5/2)/x^3,x,5,-5/4*b*(-a+b*x)^(3/2)/x-1/2*(-a+b*x)^(5/2)/x^2-15/4*b^2*arctan(sqrt(-a+b*x)/sqrt(a))*sqrt(a)+15/4*b^2*sqrt(-a+b*x)],

# n<0
[x^4/sqrt(a+b*x),x,2,-8/3*a^3*(a+b*x)^(3/2)/b^5+12/5*a^2*(a+b*x)^(5/2)/b^5-8/7*a*(a+b*x)^(7/2)/b^5+2/9*(a+b*x)^(9/2)/b^5+2*a^4*sqrt(a+b*x)/b^5],
[x^3/sqrt(a+b*x),x,2,2*a^2*(a+b*x)^(3/2)/b^4-6/5*a*(a+b*x)^(5/2)/b^4+2/7*(a+b*x)^(7/2)/b^4-2*a^3*sqrt(a+b*x)/b^4],
[x^2/sqrt(a+b*x),x,2,-4/3*a*(a+b*x)^(3/2)/b^3+2/5*(a+b*x)^(5/2)/b^3+2*a^2*sqrt(a+b*x)/b^3],
[x/sqrt(a+b*x),x,2,2/3*(a+b*x)^(3/2)/b^2-2*a*sqrt(a+b*x)/b^2],
[1/sqrt(a+b*x),x,1,2*sqrt(a+b*x)/b],
[1/(x*sqrt(a+b*x)),x,2,-2*arctanh(sqrt(a+b*x)/sqrt(a))/sqrt(a)],
[1/(x^2*sqrt(a+b*x)),x,3,b*arctanh(sqrt(a+b*x)/sqrt(a))/a^(3/2)-sqrt(a+b*x)/(a*x)],
[1/(x^3*sqrt(a+b*x)),x,4,-3/4*b^2*arctanh(sqrt(a+b*x)/sqrt(a))/a^(5/2)-1/2*sqrt(a+b*x)/(a*x^2)+3/4*b*sqrt(a+b*x)/(a^2*x)],
[1/(x^4*sqrt(a+b*x)),x,5,5/8*b^3*arctanh(sqrt(a+b*x)/sqrt(a))/a^(7/2)-1/3*sqrt(a+b*x)/(a*x^3)+5/12*b*sqrt(a+b*x)/(a^2*x^2)-5/8*b^2*sqrt(a+b*x)/(a^3*x)],
[x^4/(a+b*x)^(3/2),x,2,4*a^2*(a+b*x)^(3/2)/b^5-8/5*a*(a+b*x)^(5/2)/b^5+2/7*(a+b*x)^(7/2)/b^5-2*a^4/(b^5*sqrt(a+b*x))-8*a^3*sqrt(a+b*x)/b^5],
[x^3/(a+b*x)^(3/2),x,2,-2*a*(a+b*x)^(3/2)/b^4+2/5*(a+b*x)^(5/2)/b^4+2*a^3/(b^4*sqrt(a+b*x))+6*a^2*sqrt(a+b*x)/b^4],
[x^2/(a+b*x)^(3/2),x,2,2/3*(a+b*x)^(3/2)/b^3-2*a^2/(b^3*sqrt(a+b*x))-4*a*sqrt(a+b*x)/b^3],
[x/(a+b*x)^(3/2),x,2,2*a/(b^2*sqrt(a+b*x))+2*sqrt(a+b*x)/b^2],
[1/(a+b*x)^(3/2),x,1,(-2)/(b*sqrt(a+b*x))],
[1/(x*(a+b*x)^(3/2)),x,3,-2*arctanh(sqrt(a+b*x)/sqrt(a))/a^(3/2)+2/(a*sqrt(a+b*x))],
[1/(x^2*(a+b*x)^(3/2)),x,4,3*b*arctanh(sqrt(a+b*x)/sqrt(a))/a^(5/2)-3*b/(a^2*sqrt(a+b*x))+(-1)/(a*x*sqrt(a+b*x))],
[1/(x^3*(a+b*x)^(3/2)),x,5,-15/4*b^2*arctanh(sqrt(a+b*x)/sqrt(a))/a^(7/2)+15/4*b^2/(a^3*sqrt(a+b*x))+(-1/2)/(a*x^2*sqrt(a+b*x))+5/4*b/(a^2*x*sqrt(a+b*x))],
[x^4/(a+b*x)^(5/2),x,2,-2/3*a^4/(b^5*(a+b*x)^(3/2))-8/3*a*(a+b*x)^(3/2)/b^5+2/5*(a+b*x)^(5/2)/b^5+8*a^3/(b^5*sqrt(a+b*x))+12*a^2*sqrt(a+b*x)/b^5],
[x^3/(a+b*x)^(5/2),x,2,2/3*a^3/(b^4*(a+b*x)^(3/2))+2/3*(a+b*x)^(3/2)/b^4-6*a^2/(b^4*sqrt(a+b*x))-6*a*sqrt(a+b*x)/b^4],
[x^2/(a+b*x)^(5/2),x,2,-2/3*a^2/(b^3*(a+b*x)^(3/2))+4*a/(b^3*sqrt(a+b*x))+2*sqrt(a+b*x)/b^3],
[x/(a+b*x)^(5/2),x,2,2/3*a/(b^2*(a+b*x)^(3/2))+(-2)/(b^2*sqrt(a+b*x))],
[1/(a+b*x)^(5/2),x,1,(-2/3)/(b*(a+b*x)^(3/2))],
[1/(x*(a+b*x)^(5/2)),x,4,2/3/(a*(a+b*x)^(3/2))-2*arctanh(sqrt(a+b*x)/sqrt(a))/a^(5/2)+2/(a^2*sqrt(a+b*x))],
[1/(x^2*(a+b*x)^(5/2)),x,5,-5/3*b/(a^2*(a+b*x)^(3/2))+(-1)/(a*x*(a+b*x)^(3/2))+5*b*arctanh(sqrt(a+b*x)/sqrt(a))/a^(7/2)-5*b/(a^3*sqrt(a+b*x))],
[1/(x^3*(a+b*x)^(5/2)),x,6,35/12*b^2/(a^3*(a+b*x)^(3/2))+(-1/2)/(a*x^2*(a+b*x)^(3/2))+7/4*b/(a^2*x*(a+b*x)^(3/2))-35/4*b^2*arctanh(sqrt(a+b*x)/sqrt(a))/a^(9/2)+35/4*b^2/(a^4*sqrt(a+b*x))],
[1/(x*sqrt(-a+b*x)),x,2,2*arctan(sqrt(-a+b*x)/sqrt(a))/sqrt(a)],
[1/(x^2*sqrt(-a+b*x)),x,3,b*arctan(sqrt(-a+b*x)/sqrt(a))/a^(3/2)+sqrt(-a+b*x)/(a*x)],
[1/(x^3*sqrt(-a+b*x)),x,4,3/4*b^2*arctan(sqrt(-a+b*x)/sqrt(a))/a^(5/2)+1/2*sqrt(-a+b*x)/(a*x^2)+3/4*b*sqrt(-a+b*x)/(a^2*x)],
[1/(x*(-a+b*x)^(3/2)),x,3,-2*arctan(sqrt(-a+b*x)/sqrt(a))/a^(3/2)+(-2)/(a*sqrt(-a+b*x))],
[1/(x^2*(-a+b*x)^(3/2)),x,4,-3*b*arctan(sqrt(-a+b*x)/sqrt(a))/a^(5/2)-3*b/(a^2*sqrt(-a+b*x))+1/(a*x*sqrt(-a+b*x))],
[1/(x^3*(-a+b*x)^(3/2)),x,5,-15/4*b^2*arctan(sqrt(-a+b*x)/sqrt(a))/a^(7/2)-15/4*b^2/(a^3*sqrt(-a+b*x))+1/2/(a*x^2*sqrt(-a+b*x))+5/4*b/(a^2*x*sqrt(-a+b*x))],
[1/(x*(-a+b*x)^(5/2)),x,4,(-2/3)/(a*(-a+b*x)^(3/2))+2*arctan(sqrt(-a+b*x)/sqrt(a))/a^(5/2)+2/(a^2*sqrt(-a+b*x))],
[1/(x^2*(-a+b*x)^(5/2)),x,5,-5/3*b/(a^2*(-a+b*x)^(3/2))+1/(a*x*(-a+b*x)^(3/2))+5*b*arctan(sqrt(-a+b*x)/sqrt(a))/a^(7/2)+5*b/(a^3*sqrt(-a+b*x))],
[1/(x^3*(-a+b*x)^(5/2)),x,6,-35/12*b^2/(a^3*(-a+b*x)^(3/2))+1/2/(a*x^2*(-a+b*x)^(3/2))+7/4*b/(a^2*x*(-a+b*x)^(3/2))+35/4*b^2*arctan(sqrt(-a+b*x)/sqrt(a))/a^(9/2)+35/4*b^2/(a^4*sqrt(-a+b*x))],
[1/2*x^(-1+m)*(2*a*m+b*(-1+2*m)*x)/(a+b*x)^(3/2),x,2,x^m/sqrt(a+b*x)],
[-1/2*b*x^m/(a+b*x)^(3/2)+m*x^(-1+m)/sqrt(a+b*x),x,-5,x^m/sqrt(a+b*x)],
[x^(1/2*(1-n)+1/2*(-3+n))/sqrt(a+b*x),x,3,-2*arctanh(sqrt(a+b*x)/sqrt(a))/sqrt(a)],

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

# n>0
[x^3*(a+b*x)^(1/3),x,2,-3/4*a^3*(a+b*x)^(4/3)/b^4+9/7*a^2*(a+b*x)^(7/3)/b^4-9/10*a*(a+b*x)^(10/3)/b^4+3/13*(a+b*x)^(13/3)/b^4],
[x^2*(a+b*x)^(1/3),x,2,3/4*a^2*(a+b*x)^(4/3)/b^3-6/7*a*(a+b*x)^(7/3)/b^3+3/10*(a+b*x)^(10/3)/b^3],
[x*(a+b*x)^(1/3),x,2,-3/4*a*(a+b*x)^(4/3)/b^2+3/7*(a+b*x)^(7/3)/b^2],
[(a+b*x)^(1/3),x,1,3/4*(a+b*x)^(4/3)/b],
[(a+b*x)^(1/3)/x,x,5,3*(a+b*x)^(1/3)-1/2*a^(1/3)*log(x)+3/2*a^(1/3)*log(a^(1/3)-(a+b*x)^(1/3))-a^(1/3)*arctan((a^(1/3)+2*(a+b*x)^(1/3))/(a^(1/3)*sqrt(3)))*sqrt(3)],
[(a+b*x)^(1/3)/x^2,x,5,-(a+b*x)^(1/3)/x-1/6*b*log(x)/a^(2/3)+1/2*b*log(a^(1/3)-(a+b*x)^(1/3))/a^(2/3)-b*arctan((a^(1/3)+2*(a+b*x)^(1/3))/(a^(1/3)*sqrt(3)))/(a^(2/3)*sqrt(3))],
[(a+b*x)^(1/3)/x^3,x,6,-1/2*(a+b*x)^(1/3)/x^2-1/6*b*(a+b*x)^(1/3)/(a*x)+1/18*b^2*log(x)/a^(5/3)-1/6*b^2*log(a^(1/3)-(a+b*x)^(1/3))/a^(5/3)+1/3*b^2*arctan((a^(1/3)+2*(a+b*x)^(1/3))/(a^(1/3)*sqrt(3)))/(a^(5/3)*sqrt(3))],
[x^3*(a+b*x)^(2/3),x,2,-3/5*a^3*(a+b*x)^(5/3)/b^4+9/8*a^2*(a+b*x)^(8/3)/b^4-9/11*a*(a+b*x)^(11/3)/b^4+3/14*(a+b*x)^(14/3)/b^4],
[x^2*(a+b*x)^(2/3),x,2,3/5*a^2*(a+b*x)^(5/3)/b^3-3/4*a*(a+b*x)^(8/3)/b^3+3/11*(a+b*x)^(11/3)/b^3],
[x*(a+b*x)^(2/3),x,2,-3/5*a*(a+b*x)^(5/3)/b^2+3/8*(a+b*x)^(8/3)/b^2],
[(a+b*x)^(2/3),x,1,3/5*(a+b*x)^(5/3)/b],
[(a+b*x)^(2/3)/x,x,5,3/2*(a+b*x)^(2/3)-1/2*a^(2/3)*log(x)+3/2*a^(2/3)*log(a^(1/3)-(a+b*x)^(1/3))+a^(2/3)*arctan((a^(1/3)+2*(a+b*x)^(1/3))/(a^(1/3)*sqrt(3)))*sqrt(3)],
[(a+b*x)^(2/3)/x^2,x,5,-(a+b*x)^(2/3)/x-1/3*b*log(x)/a^(1/3)+b*log(a^(1/3)-(a+b*x)^(1/3))/a^(1/3)+2*b*arctan((a^(1/3)+2*(a+b*x)^(1/3))/(a^(1/3)*sqrt(3)))/(a^(1/3)*sqrt(3))],
[(a+b*x)^(2/3)/x^3,x,6,-1/2*(a+b*x)^(2/3)/x^2-1/3*b*(a+b*x)^(2/3)/(a*x)+1/18*b^2*log(x)/a^(4/3)-1/6*b^2*log(a^(1/3)-(a+b*x)^(1/3))/a^(4/3)-1/3*b^2*arctan((a^(1/3)+2*(a+b*x)^(1/3))/(a^(1/3)*sqrt(3)))/(a^(4/3)*sqrt(3))],
[x^3*(a+b*x)^(4/3),x,2,-3/7*a^3*(a+b*x)^(7/3)/b^4+9/10*a^2*(a+b*x)^(10/3)/b^4-9/13*a*(a+b*x)^(13/3)/b^4+3/16*(a+b*x)^(16/3)/b^4],
[x^2*(a+b*x)^(4/3),x,2,3/7*a^2*(a+b*x)^(7/3)/b^3-3/5*a*(a+b*x)^(10/3)/b^3+3/13*(a+b*x)^(13/3)/b^3],
[x*(a+b*x)^(4/3),x,2,-3/7*a*(a+b*x)^(7/3)/b^2+3/10*(a+b*x)^(10/3)/b^2],
[(a+b*x)^(4/3),x,1,3/7*(a+b*x)^(7/3)/b],
[(a+b*x)^(4/3)/x,x,6,3*a*(a+b*x)^(1/3)+3/4*(a+b*x)^(4/3)-1/2*a^(4/3)*log(x)+3/2*a^(4/3)*log(a^(1/3)-(a+b*x)^(1/3))-a^(4/3)*arctan((a^(1/3)+2*(a+b*x)^(1/3))/(a^(1/3)*sqrt(3)))*sqrt(3)],
[(a+b*x)^(4/3)/x^2,x,6,4*b*(a+b*x)^(1/3)-(a+b*x)^(4/3)/x-2/3*a^(1/3)*b*log(x)+2*a^(1/3)*b*log(a^(1/3)-(a+b*x)^(1/3))-4*a^(1/3)*b*arctan((a^(1/3)+2*(a+b*x)^(1/3))/(a^(1/3)*sqrt(3)))/sqrt(3)],
[(a+b*x)^(4/3)/x^3,x,6,-2/3*b*(a+b*x)^(1/3)/x-1/2*(a+b*x)^(4/3)/x^2-1/9*b^2*log(x)/a^(2/3)+1/3*b^2*log(a^(1/3)-(a+b*x)^(1/3))/a^(2/3)-2/3*b^2*arctan((a^(1/3)+2*(a+b*x)^(1/3))/(a^(1/3)*sqrt(3)))/(a^(2/3)*sqrt(3))],

# n<0
[x^3/(a+b*x)^(1/3),x,2,-3/2*a^3*(a+b*x)^(2/3)/b^4+9/5*a^2*(a+b*x)^(5/3)/b^4-9/8*a*(a+b*x)^(8/3)/b^4+3/11*(a+b*x)^(11/3)/b^4],
[x^2/(a+b*x)^(1/3),x,2,3/2*a^2*(a+b*x)^(2/3)/b^3-6/5*a*(a+b*x)^(5/3)/b^3+3/8*(a+b*x)^(8/3)/b^3],
[x/(a+b*x)^(1/3),x,2,-3/2*a*(a+b*x)^(2/3)/b^2+3/5*(a+b*x)^(5/3)/b^2],
[1/(a+b*x)^(1/3),x,1,3/2*(a+b*x)^(2/3)/b],
[1/(x*(a+b*x)^(1/3)),x,4,-1/2*log(x)/a^(1/3)+3/2*log(a^(1/3)-(a+b*x)^(1/3))/a^(1/3)+arctan((a^(1/3)+2*(a+b*x)^(1/3))/(a^(1/3)*sqrt(3)))*sqrt(3)/a^(1/3)],
[1/(x^2*(a+b*x)^(1/3)),x,5,-(a+b*x)^(2/3)/(a*x)+1/6*b*log(x)/a^(4/3)-1/2*b*log(a^(1/3)-(a+b*x)^(1/3))/a^(4/3)-b*arctan((a^(1/3)+2*(a+b*x)^(1/3))/(a^(1/3)*sqrt(3)))/(a^(4/3)*sqrt(3))],
[1/(x^3*(a+b*x)^(1/3)),x,6,-1/2*(a+b*x)^(2/3)/(a*x^2)+2/3*b*(a+b*x)^(2/3)/(a^2*x)-1/9*b^2*log(x)/a^(7/3)+1/3*b^2*log(a^(1/3)-(a+b*x)^(1/3))/a^(7/3)+2/3*b^2*arctan((a^(1/3)+2*(a+b*x)^(1/3))/(a^(1/3)*sqrt(3)))/(a^(7/3)*sqrt(3))],
[x^3/(-a+b*x)^(1/3),x,2,3/2*a^3*(-a+b*x)^(2/3)/b^4+9/5*a^2*(-a+b*x)^(5/3)/b^4+9/8*a*(-a+b*x)^(8/3)/b^4+3/11*(-a+b*x)^(11/3)/b^4],
[x^2/(-a+b*x)^(1/3),x,2,3/2*a^2*(-a+b*x)^(2/3)/b^3+6/5*a*(-a+b*x)^(5/3)/b^3+3/8*(-a+b*x)^(8/3)/b^3],
[x/(-a+b*x)^(1/3),x,2,3/2*a*(-a+b*x)^(2/3)/b^2+3/5*(-a+b*x)^(5/3)/b^2],
[1/(-a+b*x)^(1/3),x,1,3/2*(-a+b*x)^(2/3)/b],
[1/(x*(-a+b*x)^(1/3)),x,4,1/2*log(x)/a^(1/3)-3/2*log(a^(1/3)+(-a+b*x)^(1/3))/a^(1/3)-arctan((a^(1/3)-2*(-a+b*x)^(1/3))/(a^(1/3)*sqrt(3)))*sqrt(3)/a^(1/3)],
[1/(x^2*(-a+b*x)^(1/3)),x,5,(-a+b*x)^(2/3)/(a*x)+1/6*b*log(x)/a^(4/3)-1/2*b*log(a^(1/3)+(-a+b*x)^(1/3))/a^(4/3)-b*arctan((a^(1/3)-2*(-a+b*x)^(1/3))/(a^(1/3)*sqrt(3)))/(a^(4/3)*sqrt(3))],
[1/(x^3*(-a+b*x)^(1/3)),x,6,1/2*(-a+b*x)^(2/3)/(a*x^2)+2/3*b*(-a+b*x)^(2/3)/(a^2*x)+1/9*b^2*log(x)/a^(7/3)-1/3*b^2*log(a^(1/3)+(-a+b*x)^(1/3))/a^(7/3)-2/3*b^2*arctan((a^(1/3)-2*(-a+b*x)^(1/3))/(a^(1/3)*sqrt(3)))/(a^(7/3)*sqrt(3))],
[x^3/(a+b*x)^(2/3),x,2,-3*a^3*(a+b*x)^(1/3)/b^4+9/4*a^2*(a+b*x)^(4/3)/b^4-9/7*a*(a+b*x)^(7/3)/b^4+3/10*(a+b*x)^(10/3)/b^4],
[x^2/(a+b*x)^(2/3),x,2,3*a^2*(a+b*x)^(1/3)/b^3-3/2*a*(a+b*x)^(4/3)/b^3+3/7*(a+b*x)^(7/3)/b^3],
[x/(a+b*x)^(2/3),x,2,-3*a*(a+b*x)^(1/3)/b^2+3/4*(a+b*x)^(4/3)/b^2],
[1/(a+b*x)^(2/3),x,1,3*(a+b*x)^(1/3)/b],
[1/(x*(a+b*x)^(2/3)),x,4,-1/2*log(x)/a^(2/3)+3/2*log(a^(1/3)-(a+b*x)^(1/3))/a^(2/3)-arctan((a^(1/3)+2*(a+b*x)^(1/3))/(a^(1/3)*sqrt(3)))*sqrt(3)/a^(2/3)],
[1/(x^2*(a+b*x)^(2/3)),x,5,-(a+b*x)^(1/3)/(a*x)+1/3*b*log(x)/a^(5/3)-b*log(a^(1/3)-(a+b*x)^(1/3))/a^(5/3)+2*b*arctan((a^(1/3)+2*(a+b*x)^(1/3))/(a^(1/3)*sqrt(3)))/(a^(5/3)*sqrt(3))],
[1/(x^3*(a+b*x)^(2/3)),x,6,-1/2*(a+b*x)^(1/3)/(a*x^2)+5/6*b*(a+b*x)^(1/3)/(a^2*x)-5/18*b^2*log(x)/a^(8/3)+5/6*b^2*log(a^(1/3)-(a+b*x)^(1/3))/a^(8/3)-5/3*b^2*arctan((a^(1/3)+2*(a+b*x)^(1/3))/(a^(1/3)*sqrt(3)))/(a^(8/3)*sqrt(3))],
[x^3/(a+b*x)^(4/3),x,2,3*a^3/(b^4*(a+b*x)^(1/3))+9/2*a^2*(a+b*x)^(2/3)/b^4-9/5*a*(a+b*x)^(5/3)/b^4+3/8*(a+b*x)^(8/3)/b^4],
[x^2/(a+b*x)^(4/3),x,2,-3*a^2/(b^3*(a+b*x)^(1/3))-3*a*(a+b*x)^(2/3)/b^3+3/5*(a+b*x)^(5/3)/b^3],
[x/(a+b*x)^(4/3),x,2,3*a/(b^2*(a+b*x)^(1/3))+3/2*(a+b*x)^(2/3)/b^2],
[1/(a+b*x)^(4/3),x,1,(-3)/(b*(a+b*x)^(1/3))],
[1/(x*(a+b*x)^(4/3)),x,5,3/(a*(a+b*x)^(1/3))-1/2*log(x)/a^(4/3)+3/2*log(a^(1/3)-(a+b*x)^(1/3))/a^(4/3)+arctan((a^(1/3)+2*(a+b*x)^(1/3))/(a^(1/3)*sqrt(3)))*sqrt(3)/a^(4/3)],
[1/(x^2*(a+b*x)^(4/3)),x,6,-4*b/(a^2*(a+b*x)^(1/3))+(-1)/(a*x*(a+b*x)^(1/3))+2/3*b*log(x)/a^(7/3)-2*b*log(a^(1/3)-(a+b*x)^(1/3))/a^(7/3)-4*b*arctan((a^(1/3)+2*(a+b*x)^(1/3))/(a^(1/3)*sqrt(3)))/(a^(7/3)*sqrt(3))],
[1/(x^3*(a+b*x)^(4/3)),x,7,14/3*b^2/(a^3*(a+b*x)^(1/3))+(-1/2)/(a*x^2*(a+b*x)^(1/3))+7/6*b/(a^2*x*(a+b*x)^(1/3))-7/9*b^2*log(x)/a^(10/3)+7/3*b^2*log(a^(1/3)-(a+b*x)^(1/3))/a^(10/3)+14/3*b^2*arctan((a^(1/3)+2*(a+b*x)^(1/3))/(a^(1/3)*sqrt(3)))/(a^(10/3)*sqrt(3))],
[1/(x*(a^3+b^3*x)^(1/3)),x,4,-1/2*log(x)/a+3/2*log(a-(a^3+b^3*x)^(1/3))/a+arctan((a+2*(a^3+b^3*x)^(1/3))/(a*sqrt(3)))*sqrt(3)/a],
[1/(x*(a^3-b^3*x)^(1/3)),x,4,-1/2*log(x)/a+3/2*log(a-(a^3-b^3*x)^(1/3))/a+arctan((a+2*(a^3-b^3*x)^(1/3))/(a*sqrt(3)))*sqrt(3)/a],
[1/(x*(-a^3+b^3*x)^(1/3)),x,4,1/2*log(x)/a-3/2*log(a+(-a^3+b^3*x)^(1/3))/a-arctan((a-2*(-a^3+b^3*x)^(1/3))/(a*sqrt(3)))*sqrt(3)/a],
[1/(x*(-a^3-b^3*x)^(1/3)),x,4,1/2*log(x)/a-3/2*log(a+(-a^3-b^3*x)^(1/3))/a-arctan((a-2*(-a^3-b^3*x)^(1/3))/(a*sqrt(3)))*sqrt(3)/a],
[1/(x*(a^3+b^3*x)^(2/3)),x,4,-1/2*log(x)/a^2+3/2*log(a-(a^3+b^3*x)^(1/3))/a^2-arctan((a+2*(a^3+b^3*x)^(1/3))/(a*sqrt(3)))*sqrt(3)/a^2],
[1/(x*(a^3-b^3*x)^(2/3)),x,4,-1/2*log(x)/a^2+3/2*log(a-(a^3-b^3*x)^(1/3))/a^2-arctan((a+2*(a^3-b^3*x)^(1/3))/(a*sqrt(3)))*sqrt(3)/a^2],
[1/(x*(-a^3+b^3*x)^(2/3)),x,4,-1/2*log(x)/a^2+3/2*log(a+(-a^3+b^3*x)^(1/3))/a^2-arctan((a-2*(-a^3+b^3*x)^(1/3))/(a*sqrt(3)))*sqrt(3)/a^2],
[1/(x*(-a^3-b^3*x)^(2/3)),x,4,-1/2*log(x)/a^2+3/2*log(a+(-a^3-b^3*x)^(1/3))/a^2-arctan((a-2*(-a^3-b^3*x)^(1/3))/(a*sqrt(3)))*sqrt(3)/a^2],

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

# n>0
[x^m*(a+b*x),x,2,a*x^(1+m)/(1+m)+b*x^(2+m)/(2+m)],
[x^(5/2)*(a+b*x),x,2,2/7*a*x^(7/2)+2/9*b*x^(9/2)],
[x^(3/2)*(a+b*x),x,2,2/5*a*x^(5/2)+2/7*b*x^(7/2)],
[(a+b*x)*sqrt(x),x,2,2/3*a*x^(3/2)+2/5*b*x^(5/2)],
[(a+b*x)/sqrt(x),x,2,2/3*b*x^(3/2)+2*a*sqrt(x)],
[(a+b*x)/x^(3/2),x,2,-2*a/sqrt(x)+2*b*sqrt(x)],
[(a+b*x)/x^(5/2),x,2,-2/3*a/x^(3/2)-2*b/sqrt(x)],
[x^m*(a+b*x)^2,x,2,a^2*x^(1+m)/(1+m)+2*a*b*x^(2+m)/(2+m)+b^2*x^(3+m)/(3+m)],
[x^(5/2)*(a+b*x)^2,x,2,2/7*a^2*x^(7/2)+4/9*a*b*x^(9/2)+2/11*b^2*x^(11/2)],
[x^(3/2)*(a+b*x)^2,x,2,2/5*a^2*x^(5/2)+4/7*a*b*x^(7/2)+2/9*b^2*x^(9/2)],
[(a+b*x)^2*sqrt(x),x,2,2/3*a^2*x^(3/2)+4/5*a*b*x^(5/2)+2/7*b^2*x^(7/2)],
[(a+b*x)^2/sqrt(x),x,2,4/3*a*b*x^(3/2)+2/5*b^2*x^(5/2)+2*a^2*sqrt(x)],
[(a+b*x)^2/x^(3/2),x,2,2/3*b^2*x^(3/2)-2*a^2/sqrt(x)+4*a*b*sqrt(x)],
[(a+b*x)^2/x^(5/2),x,2,-2/3*a^2/x^(3/2)-4*a*b/sqrt(x)+2*b^2*sqrt(x)],
[x^m*(a+b*x)^3,x,2,a^3*x^(1+m)/(1+m)+3*a^2*b*x^(2+m)/(2+m)+3*a*b^2*x^(3+m)/(3+m)+b^3*x^(4+m)/(4+m)],
[x^(5/2)*(a+b*x)^3,x,2,2/7*a^3*x^(7/2)+2/3*a^2*b*x^(9/2)+6/11*a*b^2*x^(11/2)+2/13*b^3*x^(13/2)],
[x^(3/2)*(a+b*x)^3,x,2,2/5*a^3*x^(5/2)+6/7*a^2*b*x^(7/2)+2/3*a*b^2*x^(9/2)+2/11*b^3*x^(11/2)],
[(a+b*x)^3*sqrt(x),x,2,2/3*a^3*x^(3/2)+6/5*a^2*b*x^(5/2)+6/7*a*b^2*x^(7/2)+2/9*b^3*x^(9/2)],
[(a+b*x)^3/sqrt(x),x,2,2*a^2*b*x^(3/2)+6/5*a*b^2*x^(5/2)+2/7*b^3*x^(7/2)+2*a^3*sqrt(x)],
[(a+b*x)^3/x^(3/2),x,2,2*a*b^2*x^(3/2)+2/5*b^3*x^(5/2)-2*a^3/sqrt(x)+6*a^2*b*sqrt(x)],
[(a+b*x)^3/x^(5/2),x,2,-2/3*a^3/x^(3/2)+2/3*b^3*x^(3/2)-6*a^2*b/sqrt(x)+6*a*b^2*sqrt(x)],

# n<0
[x^(5/2)/(a+b*x),x,5,-2/3*a*x^(3/2)/b^2+2/5*x^(5/2)/b-2*a^(5/2)*arctan(sqrt(b)*sqrt(x)/sqrt(a))/b^(7/2)+2*a^2*sqrt(x)/b^3],
[x^(3/2)/(a+b*x),x,4,2/3*x^(3/2)/b+2*a^(3/2)*arctan(sqrt(b)*sqrt(x)/sqrt(a))/b^(5/2)-2*a*sqrt(x)/b^2],
[sqrt(x)/(a+b*x),x,3,-2*arctan(sqrt(b)*sqrt(x)/sqrt(a))*sqrt(a)/b^(3/2)+2*sqrt(x)/b],
[1/((a+b*x)*sqrt(x)),x,2,2*arctan(sqrt(b)*sqrt(x)/sqrt(a))/(sqrt(a)*sqrt(b))],
[1/(x^(3/2)*(a+b*x)),x,3,-2*arctan(sqrt(b)*sqrt(x)/sqrt(a))*sqrt(b)/a^(3/2)+(-2)/(a*sqrt(x))],
[1/(x^(5/2)*(a+b*x)),x,4,(-2/3)/(a*x^(3/2))+2*b^(3/2)*arctan(sqrt(b)*sqrt(x)/sqrt(a))/a^(5/2)+2*b/(a^2*sqrt(x))],
[1/(x^(7/2)*(a+b*x)),x,5,(-2/5)/(a*x^(5/2))+2/3*b/(a^2*x^(3/2))-2*b^(5/2)*arctan(sqrt(b)*sqrt(x)/sqrt(a))/a^(7/2)-2*b^2/(a^3*sqrt(x))],
[x^(5/2)/(a+b*x)^2,x,5,5/3*x^(3/2)/b^2-x^(5/2)/(b*(a+b*x))+5*a^(3/2)*arctan(sqrt(b)*sqrt(x)/sqrt(a))/b^(7/2)-5*a*sqrt(x)/b^3],
[x^(3/2)/(a+b*x)^2,x,4,-x^(3/2)/(b*(a+b*x))-3*arctan(sqrt(b)*sqrt(x)/sqrt(a))*sqrt(a)/b^(5/2)+3*sqrt(x)/b^2],
[sqrt(x)/(a+b*x)^2,x,3,arctan(sqrt(b)*sqrt(x)/sqrt(a))/(b^(3/2)*sqrt(a))-sqrt(x)/(b*(a+b*x))],
[1/((a+b*x)^2*sqrt(x)),x,3,arctan(sqrt(b)*sqrt(x)/sqrt(a))/(a^(3/2)*sqrt(b))+sqrt(x)/(a*(a+b*x))],
[1/(x^(3/2)*(a+b*x)^2),x,4,-3*arctan(sqrt(b)*sqrt(x)/sqrt(a))*sqrt(b)/a^(5/2)+(-3)/(a^2*sqrt(x))+1/(a*(a+b*x)*sqrt(x))],
[1/(x^(5/2)*(a+b*x)^2),x,5,(-5/3)/(a^2*x^(3/2))+1/(a*x^(3/2)*(a+b*x))+5*b^(3/2)*arctan(sqrt(b)*sqrt(x)/sqrt(a))/a^(7/2)+5*b/(a^3*sqrt(x))],
[x^(7/2)/(a+b*x)^3,x,6,35/12*x^(3/2)/b^3-1/2*x^(7/2)/(b*(a+b*x)^2)-7/4*x^(5/2)/(b^2*(a+b*x))+35/4*a^(3/2)*arctan(sqrt(b)*sqrt(x)/sqrt(a))/b^(9/2)-35/4*a*sqrt(x)/b^4],
[x^(5/2)/(a+b*x)^3,x,5,-1/2*x^(5/2)/(b*(a+b*x)^2)-5/4*x^(3/2)/(b^2*(a+b*x))-15/4*arctan(sqrt(b)*sqrt(x)/sqrt(a))*sqrt(a)/b^(7/2)+15/4*sqrt(x)/b^3],
[x^(3/2)/(a+b*x)^3,x,4,-1/2*x^(3/2)/(b*(a+b*x)^2)+3/4*arctan(sqrt(b)*sqrt(x)/sqrt(a))/(b^(5/2)*sqrt(a))-3/4*sqrt(x)/(b^2*(a+b*x))],
[sqrt(x)/(a+b*x)^3,x,4,1/4*arctan(sqrt(b)*sqrt(x)/sqrt(a))/(a^(3/2)*b^(3/2))-1/2*sqrt(x)/(b*(a+b*x)^2)+1/4*sqrt(x)/(a*b*(a+b*x))],
[1/((a+b*x)^3*sqrt(x)),x,4,3/4*arctan(sqrt(b)*sqrt(x)/sqrt(a))/(a^(5/2)*sqrt(b))+1/2*sqrt(x)/(a*(a+b*x)^2)+3/4*sqrt(x)/(a^2*(a+b*x))],
[1/(x^(3/2)*(a+b*x)^3),x,5,-15/4*arctan(sqrt(b)*sqrt(x)/sqrt(a))*sqrt(b)/a^(7/2)+(-15/4)/(a^3*sqrt(x))+1/2/(a*(a+b*x)^2*sqrt(x))+5/4/(a^2*(a+b*x)*sqrt(x))],
[1/(x^(5/2)*(a+b*x)^3),x,6,(-35/12)/(a^3*x^(3/2))+1/2/(a*x^(3/2)*(a+b*x)^2)+7/4/(a^2*x^(3/2)*(a+b*x))+35/4*b^(3/2)*arctan(sqrt(b)*sqrt(x)/sqrt(a))/a^(9/2)+35/4*b/(a^4*sqrt(x))],
[x^(5/2)/(-a+b*x),x,5,2/3*a*x^(3/2)/b^2+2/5*x^(5/2)/b-2*a^(5/2)*arctanh(sqrt(b)*sqrt(x)/sqrt(a))/b^(7/2)+2*a^2*sqrt(x)/b^3],
[x^(3/2)/(-a+b*x),x,4,2/3*x^(3/2)/b-2*a^(3/2)*arctanh(sqrt(b)*sqrt(x)/sqrt(a))/b^(5/2)+2*a*sqrt(x)/b^2],
[sqrt(x)/(-a+b*x),x,3,-2*arctanh(sqrt(b)*sqrt(x)/sqrt(a))*sqrt(a)/b^(3/2)+2*sqrt(x)/b],
[1/((-a+b*x)*sqrt(x)),x,2,-2*arctanh(sqrt(b)*sqrt(x)/sqrt(a))/(sqrt(a)*sqrt(b))],
[1/(x^(3/2)*(-a+b*x)),x,3,-2*arctanh(sqrt(b)*sqrt(x)/sqrt(a))*sqrt(b)/a^(3/2)+2/(a*sqrt(x))],
[1/(x^(5/2)*(-a+b*x)),x,4,2/3/(a*x^(3/2))-2*b^(3/2)*arctanh(sqrt(b)*sqrt(x)/sqrt(a))/a^(5/2)+2*b/(a^2*sqrt(x))],
[1/(x^(7/2)*(-a+b*x)),x,5,2/5/(a*x^(5/2))+2/3*b/(a^2*x^(3/2))-2*b^(5/2)*arctanh(sqrt(b)*sqrt(x)/sqrt(a))/a^(7/2)+2*b^2/(a^3*sqrt(x))],
[x^(5/2)/(-a+b*x)^2,x,5,5/3*x^(3/2)/b^2+x^(5/2)/(b*(a-b*x))-5*a^(3/2)*arctanh(sqrt(b)*sqrt(x)/sqrt(a))/b^(7/2)+5*a*sqrt(x)/b^3],
[x^(3/2)/(-a+b*x)^2,x,4,x^(3/2)/(b*(a-b*x))-3*arctanh(sqrt(b)*sqrt(x)/sqrt(a))*sqrt(a)/b^(5/2)+3*sqrt(x)/b^2],
[sqrt(x)/(-a+b*x)^2,x,3,-arctanh(sqrt(b)*sqrt(x)/sqrt(a))/(b^(3/2)*sqrt(a))+sqrt(x)/(b*(a-b*x))],
[1/((-a+b*x)^2*sqrt(x)),x,3,arctanh(sqrt(b)*sqrt(x)/sqrt(a))/(a^(3/2)*sqrt(b))+sqrt(x)/(a*(a-b*x))],
[1/(x^(3/2)*(-a+b*x)^2),x,4,3*arctanh(sqrt(b)*sqrt(x)/sqrt(a))*sqrt(b)/a^(5/2)+(-3)/(a^2*sqrt(x))+1/(a*(a-b*x)*sqrt(x))],
[1/(x^(5/2)*(-a+b*x)^2),x,5,(-5/3)/(a^2*x^(3/2))+1/(a*x^(3/2)*(a-b*x))+5*b^(3/2)*arctanh(sqrt(b)*sqrt(x)/sqrt(a))/a^(7/2)-5*b/(a^3*sqrt(x))],
[x^(7/2)/(-a+b*x)^3,x,6,35/12*x^(3/2)/b^3-1/2*x^(7/2)/(b*(a-b*x)^2)+7/4*x^(5/2)/(b^2*(a-b*x))-35/4*a^(3/2)*arctanh(sqrt(b)*sqrt(x)/sqrt(a))/b^(9/2)+35/4*a*sqrt(x)/b^4],
[x^(5/2)/(-a+b*x)^3,x,5,-1/2*x^(5/2)/(b*(a-b*x)^2)+5/4*x^(3/2)/(b^2*(a-b*x))-15/4*arctanh(sqrt(b)*sqrt(x)/sqrt(a))*sqrt(a)/b^(7/2)+15/4*sqrt(x)/b^3],
[x^(3/2)/(-a+b*x)^3,x,4,-1/2*x^(3/2)/(b*(a-b*x)^2)-3/4*arctanh(sqrt(b)*sqrt(x)/sqrt(a))/(b^(5/2)*sqrt(a))+3/4*sqrt(x)/(b^2*(a-b*x))],
[sqrt(x)/(-a+b*x)^3,x,4,1/4*arctanh(sqrt(b)*sqrt(x)/sqrt(a))/(a^(3/2)*b^(3/2))-1/2*sqrt(x)/(b*(a-b*x)^2)+1/4*sqrt(x)/(a*b*(a-b*x))],
[1/((-a+b*x)^3*sqrt(x)),x,4,-3/4*arctanh(sqrt(b)*sqrt(x)/sqrt(a))/(a^(5/2)*sqrt(b))-1/2*sqrt(x)/(a*(a-b*x)^2)-3/4*sqrt(x)/(a^2*(a-b*x))],
[1/(x^(3/2)*(-a+b*x)^3),x,5,-15/4*arctanh(sqrt(b)*sqrt(x)/sqrt(a))*sqrt(b)/a^(7/2)+15/4/(a^3*sqrt(x))+(-1/2)/(a*(a-b*x)^2*sqrt(x))+(-5/4)/(a^2*(a-b*x)*sqrt(x))],
[1/(x^(5/2)*(-a+b*x)^3),x,6,35/12/(a^3*x^(3/2))+(-1/2)/(a*x^(3/2)*(a-b*x)^2)+(-7/4)/(a^2*x^(3/2)*(a-b*x))-35/4*b^(3/2)*arctanh(sqrt(b)*sqrt(x)/sqrt(a))/a^(9/2)+35/4*b/(a^4*sqrt(x))],

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

# n>0
[x^(5/2)*sqrt(a+b*x),x,7,-5/64*a^4*arctanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))/b^(7/2)-5/96*a^2*x^(3/2)*sqrt(a+b*x)/b^2+1/24*a*x^(5/2)*sqrt(a+b*x)/b+1/4*x^(7/2)*sqrt(a+b*x)+5/64*a^3*sqrt(x)*sqrt(a+b*x)/b^3],
[x^(3/2)*sqrt(a+b*x),x,6,1/8*a^3*arctanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))/b^(5/2)+1/12*a*x^(3/2)*sqrt(a+b*x)/b+1/3*x^(5/2)*sqrt(a+b*x)-1/8*a^2*sqrt(x)*sqrt(a+b*x)/b^2],
[sqrt(x)*sqrt(a+b*x),x,5,-1/4*a^2*arctanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))/b^(3/2)+1/2*x^(3/2)*sqrt(a+b*x)+1/4*a*sqrt(x)*sqrt(a+b*x)/b],
[sqrt(a+b*x)/sqrt(x),x,4,a*arctanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))/sqrt(b)+sqrt(x)*sqrt(a+b*x)],
[sqrt(a+b*x)/x^(3/2),x,4,2*arctanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))*sqrt(b)-2*sqrt(a+b*x)/sqrt(x)],
[sqrt(a+b*x)/x^(5/2),x,1,-2/3*(a+b*x)^(3/2)/(a*x^(3/2))],
[sqrt(a+b*x)/x^(7/2),x,2,-2/5*(a+b*x)^(3/2)/(a*x^(5/2))+4/15*b*(a+b*x)^(3/2)/(a^2*x^(3/2))],
[sqrt(a+b*x)/x^(9/2),x,3,-2/7*(a+b*x)^(3/2)/(a*x^(7/2))+8/35*b*(a+b*x)^(3/2)/(a^2*x^(5/2))-16/105*b^2*(a+b*x)^(3/2)/(a^3*x^(3/2))],
[x^(5/2)*sqrt(a-b*x),x,7,5/64*a^4*arctan(sqrt(b)*sqrt(x)/sqrt(a-b*x))/b^(7/2)-5/96*a^2*x^(3/2)*sqrt(a-b*x)/b^2-1/24*a*x^(5/2)*sqrt(a-b*x)/b+1/4*x^(7/2)*sqrt(a-b*x)-5/64*a^3*sqrt(x)*sqrt(a-b*x)/b^3],
[x^(3/2)*sqrt(a-b*x),x,6,1/8*a^3*arctan(sqrt(b)*sqrt(x)/sqrt(a-b*x))/b^(5/2)-1/12*a*x^(3/2)*sqrt(a-b*x)/b+1/3*x^(5/2)*sqrt(a-b*x)-1/8*a^2*sqrt(x)*sqrt(a-b*x)/b^2],
[sqrt(x)*sqrt(a-b*x),x,5,1/4*a^2*arctan(sqrt(b)*sqrt(x)/sqrt(a-b*x))/b^(3/2)+1/2*x^(3/2)*sqrt(a-b*x)-1/4*a*sqrt(x)*sqrt(a-b*x)/b],
[sqrt(a-b*x)/sqrt(x),x,4,a*arctan(sqrt(b)*sqrt(x)/sqrt(a-b*x))/sqrt(b)+sqrt(x)*sqrt(a-b*x)],
[sqrt(a-b*x)/x^(3/2),x,4,-2*arctan(sqrt(b)*sqrt(x)/sqrt(a-b*x))*sqrt(b)-2*sqrt(a-b*x)/sqrt(x)],
[sqrt(a-b*x)/x^(5/2),x,1,-2/3*(a-b*x)^(3/2)/(a*x^(3/2))],
[sqrt(a-b*x)/x^(7/2),x,2,-2/5*(a-b*x)^(3/2)/(a*x^(5/2))-4/15*b*(a-b*x)^(3/2)/(a^2*x^(3/2))],
[sqrt(a-b*x)/x^(9/2),x,3,-2/7*(a-b*x)^(3/2)/(a*x^(7/2))-8/35*b*(a-b*x)^(3/2)/(a^2*x^(5/2))-16/105*b^2*(a-b*x)^(3/2)/(a^3*x^(3/2))],
[x^(5/2)*sqrt(2+b*x),x,6,-5/4*arcsinh(sqrt(b)*sqrt(x)/sqrt(2))/b^(7/2)-5/24*x^(3/2)*sqrt(2+b*x)/b^2+1/12*x^(5/2)*sqrt(2+b*x)/b+1/4*x^(7/2)*sqrt(2+b*x)+5/8*sqrt(x)*sqrt(2+b*x)/b^3],
[x^(3/2)*sqrt(2+b*x),x,5,arcsinh(sqrt(b)*sqrt(x)/sqrt(2))/b^(5/2)+1/6*x^(3/2)*sqrt(2+b*x)/b+1/3*x^(5/2)*sqrt(2+b*x)-1/2*sqrt(x)*sqrt(2+b*x)/b^2],
[sqrt(x)*sqrt(2+b*x),x,4,-arcsinh(sqrt(b)*sqrt(x)/sqrt(2))/b^(3/2)+1/2*x^(3/2)*sqrt(2+b*x)+1/2*sqrt(x)*sqrt(2+b*x)/b],
[sqrt(2+b*x)/sqrt(x),x,3,2*arcsinh(sqrt(b)*sqrt(x)/sqrt(2))/sqrt(b)+sqrt(x)*sqrt(2+b*x)],
[sqrt(2+b*x)/x^(3/2),x,3,2*arcsinh(sqrt(b)*sqrt(x)/sqrt(2))*sqrt(b)-2*sqrt(2+b*x)/sqrt(x)],
[sqrt(2+b*x)/x^(5/2),x,1,-1/3*(2+b*x)^(3/2)/x^(3/2)],
[sqrt(2+b*x)/x^(7/2),x,2,-1/5*(2+b*x)^(3/2)/x^(5/2)+1/15*b*(2+b*x)^(3/2)/x^(3/2)],
[sqrt(2+b*x)/x^(9/2),x,3,-1/7*(2+b*x)^(3/2)/x^(7/2)+2/35*b*(2+b*x)^(3/2)/x^(5/2)-2/105*b^2*(2+b*x)^(3/2)/x^(3/2)],
[x^(5/2)*sqrt(2-b*x),x,6,5/4*arcsin(sqrt(b)*sqrt(x)/sqrt(2))/b^(7/2)-5/24*x^(3/2)*sqrt(2-b*x)/b^2-1/12*x^(5/2)*sqrt(2-b*x)/b+1/4*x^(7/2)*sqrt(2-b*x)-5/8*sqrt(x)*sqrt(2-b*x)/b^3],
[x^(3/2)*sqrt(2-b*x),x,5,arcsin(sqrt(b)*sqrt(x)/sqrt(2))/b^(5/2)-1/6*x^(3/2)*sqrt(2-b*x)/b+1/3*x^(5/2)*sqrt(2-b*x)-1/2*sqrt(x)*sqrt(2-b*x)/b^2],
[sqrt(x)*sqrt(2-b*x),x,4,arcsin(sqrt(b)*sqrt(x)/sqrt(2))/b^(3/2)+1/2*x^(3/2)*sqrt(2-b*x)-1/2*sqrt(x)*sqrt(2-b*x)/b],
[sqrt(2-b*x)/sqrt(x),x,3,2*arcsin(sqrt(b)*sqrt(x)/sqrt(2))/sqrt(b)+sqrt(x)*sqrt(2-b*x)],
[sqrt(2-b*x)/x^(3/2),x,3,-2*arcsin(sqrt(b)*sqrt(x)/sqrt(2))*sqrt(b)-2*sqrt(2-b*x)/sqrt(x)],
[sqrt(2-b*x)/x^(5/2),x,1,-1/3*(2-b*x)^(3/2)/x^(3/2)],
[sqrt(2-b*x)/x^(7/2),x,2,-1/5*(2-b*x)^(3/2)/x^(5/2)-1/15*b*(2-b*x)^(3/2)/x^(3/2)],
[sqrt(2-b*x)/x^(9/2),x,3,-1/7*(2-b*x)^(3/2)/x^(7/2)-2/35*b*(2-b*x)^(3/2)/x^(5/2)-2/105*b^2*(2-b*x)^(3/2)/x^(3/2)],
[x^(5/2)*(a+b*x)^(3/2),x,8,1/5*x^(7/2)*(a+b*x)^(3/2)-3/128*a^5*arctanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))/b^(7/2)-1/64*a^3*x^(3/2)*sqrt(a+b*x)/b^2+1/80*a^2*x^(5/2)*sqrt(a+b*x)/b+3/40*a*x^(7/2)*sqrt(a+b*x)+3/128*a^4*sqrt(x)*sqrt(a+b*x)/b^3],
[x^(3/2)*(a+b*x)^(3/2),x,7,1/4*x^(5/2)*(a+b*x)^(3/2)+3/64*a^4*arctanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))/b^(5/2)+1/32*a^2*x^(3/2)*sqrt(a+b*x)/b+1/8*a*x^(5/2)*sqrt(a+b*x)-3/64*a^3*sqrt(x)*sqrt(a+b*x)/b^2],
[(a+b*x)^(3/2)*sqrt(x),x,6,1/3*x^(3/2)*(a+b*x)^(3/2)-1/8*a^3*arctanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))/b^(3/2)+1/4*a*x^(3/2)*sqrt(a+b*x)+1/8*a^2*sqrt(x)*sqrt(a+b*x)/b],
[(a+b*x)^(3/2)/sqrt(x),x,5,3/4*a^2*arctanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))/sqrt(b)+1/2*(a+b*x)^(3/2)*sqrt(x)+3/4*a*sqrt(x)*sqrt(a+b*x)],
[(a+b*x)^(3/2)/x^(3/2),x,5,3*a*arctanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))*sqrt(b)-2*(a+b*x)^(3/2)/sqrt(x)+3*b*sqrt(x)*sqrt(a+b*x)],
[(a+b*x)^(3/2)/x^(5/2),x,5,-2/3*(a+b*x)^(3/2)/x^(3/2)+2*b^(3/2)*arctanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))-2*b*sqrt(a+b*x)/sqrt(x)],
[x^(5/2)*(a-b*x)^(3/2),x,8,1/5*x^(7/2)*(a-b*x)^(3/2)+3/128*a^5*arctan(sqrt(b)*sqrt(x)/sqrt(a-b*x))/b^(7/2)-1/64*a^3*x^(3/2)*sqrt(a-b*x)/b^2-1/80*a^2*x^(5/2)*sqrt(a-b*x)/b+3/40*a*x^(7/2)*sqrt(a-b*x)-3/128*a^4*sqrt(x)*sqrt(a-b*x)/b^3],
[x^(3/2)*(a-b*x)^(3/2),x,7,1/4*x^(5/2)*(a-b*x)^(3/2)+3/64*a^4*arctan(sqrt(b)*sqrt(x)/sqrt(a-b*x))/b^(5/2)-1/32*a^2*x^(3/2)*sqrt(a-b*x)/b+1/8*a*x^(5/2)*sqrt(a-b*x)-3/64*a^3*sqrt(x)*sqrt(a-b*x)/b^2],
[(a-b*x)^(3/2)*sqrt(x),x,6,1/3*x^(3/2)*(a-b*x)^(3/2)+1/8*a^3*arctan(sqrt(b)*sqrt(x)/sqrt(a-b*x))/b^(3/2)+1/4*a*x^(3/2)*sqrt(a-b*x)-1/8*a^2*sqrt(x)*sqrt(a-b*x)/b],
[(a-b*x)^(3/2)/sqrt(x),x,5,3/4*a^2*arctan(sqrt(b)*sqrt(x)/sqrt(a-b*x))/sqrt(b)+1/2*(a-b*x)^(3/2)*sqrt(x)+3/4*a*sqrt(x)*sqrt(a-b*x)],
[(a-b*x)^(3/2)/x^(3/2),x,5,-3*a*arctan(sqrt(b)*sqrt(x)/sqrt(a-b*x))*sqrt(b)-2*(a-b*x)^(3/2)/sqrt(x)-3*b*sqrt(x)*sqrt(a-b*x)],
[(a-b*x)^(3/2)/x^(5/2),x,5,-2/3*(a-b*x)^(3/2)/x^(3/2)+2*b^(3/2)*arctan(sqrt(b)*sqrt(x)/sqrt(a-b*x))+2*b*sqrt(a-b*x)/sqrt(x)],
[x^(5/2)*(2+b*x)^(3/2),x,7,1/5*x^(7/2)*(2+b*x)^(3/2)-3/4*arcsinh(sqrt(b)*sqrt(x)/sqrt(2))/b^(7/2)-1/8*x^(3/2)*sqrt(2+b*x)/b^2+1/20*x^(5/2)*sqrt(2+b*x)/b+3/20*x^(7/2)*sqrt(2+b*x)+3/8*sqrt(x)*sqrt(2+b*x)/b^3],
[x^(3/2)*(2+b*x)^(3/2),x,6,1/4*x^(5/2)*(2+b*x)^(3/2)+3/4*arcsinh(sqrt(b)*sqrt(x)/sqrt(2))/b^(5/2)+1/8*x^(3/2)*sqrt(2+b*x)/b+1/4*x^(5/2)*sqrt(2+b*x)-3/8*sqrt(x)*sqrt(2+b*x)/b^2],
[(2+b*x)^(3/2)*sqrt(x),x,5,1/3*x^(3/2)*(2+b*x)^(3/2)-arcsinh(sqrt(b)*sqrt(x)/sqrt(2))/b^(3/2)+1/2*x^(3/2)*sqrt(2+b*x)+1/2*sqrt(x)*sqrt(2+b*x)/b],
[(2+b*x)^(3/2)/sqrt(x),x,4,3*arcsinh(sqrt(b)*sqrt(x)/sqrt(2))/sqrt(b)+1/2*(2+b*x)^(3/2)*sqrt(x)+3/2*sqrt(x)*sqrt(2+b*x)],
[(2+b*x)^(3/2)/x^(3/2),x,4,6*arcsinh(sqrt(b)*sqrt(x)/sqrt(2))*sqrt(b)-2*(2+b*x)^(3/2)/sqrt(x)+3*b*sqrt(x)*sqrt(2+b*x)],
[(2+b*x)^(3/2)/x^(5/2),x,4,-2/3*(2+b*x)^(3/2)/x^(3/2)+2*b^(3/2)*arcsinh(sqrt(b)*sqrt(x)/sqrt(2))-2*b*sqrt(2+b*x)/sqrt(x)],
[x^(5/2)*(2-b*x)^(3/2),x,7,1/5*x^(7/2)*(2-b*x)^(3/2)+3/4*arcsin(sqrt(b)*sqrt(x)/sqrt(2))/b^(7/2)-1/8*x^(3/2)*sqrt(2-b*x)/b^2-1/20*x^(5/2)*sqrt(2-b*x)/b+3/20*x^(7/2)*sqrt(2-b*x)-3/8*sqrt(x)*sqrt(2-b*x)/b^3],
[x^(3/2)*(2-b*x)^(3/2),x,6,1/4*x^(5/2)*(2-b*x)^(3/2)+3/4*arcsin(sqrt(b)*sqrt(x)/sqrt(2))/b^(5/2)-1/8*x^(3/2)*sqrt(2-b*x)/b+1/4*x^(5/2)*sqrt(2-b*x)-3/8*sqrt(x)*sqrt(2-b*x)/b^2],
[(2-b*x)^(3/2)*sqrt(x),x,5,1/3*x^(3/2)*(2-b*x)^(3/2)+arcsin(sqrt(b)*sqrt(x)/sqrt(2))/b^(3/2)+1/2*x^(3/2)*sqrt(2-b*x)-1/2*sqrt(x)*sqrt(2-b*x)/b],
[(2-b*x)^(3/2)/sqrt(x),x,4,3*arcsin(sqrt(b)*sqrt(x)/sqrt(2))/sqrt(b)+1/2*(2-b*x)^(3/2)*sqrt(x)+3/2*sqrt(x)*sqrt(2-b*x)],
[(2-b*x)^(3/2)/x^(3/2),x,4,-6*arcsin(sqrt(b)*sqrt(x)/sqrt(2))*sqrt(b)-2*(2-b*x)^(3/2)/sqrt(x)-3*b*sqrt(x)*sqrt(2-b*x)],
[(2-b*x)^(3/2)/x^(5/2),x,4,-2/3*(2-b*x)^(3/2)/x^(3/2)+2*b^(3/2)*arcsin(sqrt(b)*sqrt(x)/sqrt(2))+2*b*sqrt(2-b*x)/sqrt(x)],
[x^(5/2)*(a+b*x)^(5/2),x,9,1/12*a*x^(7/2)*(a+b*x)^(3/2)+1/6*x^(7/2)*(a+b*x)^(5/2)-5/512*a^6*arctanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))/b^(7/2)-5/768*a^4*x^(3/2)*sqrt(a+b*x)/b^2+1/192*a^3*x^(5/2)*sqrt(a+b*x)/b+1/32*a^2*x^(7/2)*sqrt(a+b*x)+5/512*a^5*sqrt(x)*sqrt(a+b*x)/b^3],
[x^(3/2)*(a+b*x)^(5/2),x,8,1/8*a*x^(5/2)*(a+b*x)^(3/2)+1/5*x^(5/2)*(a+b*x)^(5/2)+3/128*a^5*arctanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))/b^(5/2)+1/64*a^3*x^(3/2)*sqrt(a+b*x)/b+1/16*a^2*x^(5/2)*sqrt(a+b*x)-3/128*a^4*sqrt(x)*sqrt(a+b*x)/b^2],
[(a+b*x)^(5/2)*sqrt(x),x,7,5/24*a*x^(3/2)*(a+b*x)^(3/2)+1/4*x^(3/2)*(a+b*x)^(5/2)-5/64*a^4*arctanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))/b^(3/2)+5/32*a^2*x^(3/2)*sqrt(a+b*x)+5/64*a^3*sqrt(x)*sqrt(a+b*x)/b],
[(a+b*x)^(5/2)/sqrt(x),x,6,5/8*a^3*arctanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))/sqrt(b)+5/12*a*(a+b*x)^(3/2)*sqrt(x)+1/3*(a+b*x)^(5/2)*sqrt(x)+5/8*a^2*sqrt(x)*sqrt(a+b*x)],
[(a+b*x)^(5/2)/x^(3/2),x,6,15/4*a^2*arctanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))*sqrt(b)-2*(a+b*x)^(5/2)/sqrt(x)+5/2*b*(a+b*x)^(3/2)*sqrt(x)+15/4*a*b*sqrt(x)*sqrt(a+b*x)],
[(a+b*x)^(5/2)/x^(5/2),x,6,-2/3*(a+b*x)^(5/2)/x^(3/2)+5*a*b^(3/2)*arctanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))-10/3*b*(a+b*x)^(3/2)/sqrt(x)+5*b^2*sqrt(x)*sqrt(a+b*x)],
[x^(5/2)*(a-b*x)^(5/2),x,9,1/12*a*x^(7/2)*(a-b*x)^(3/2)+1/6*x^(7/2)*(a-b*x)^(5/2)+5/512*a^6*arctan(sqrt(b)*sqrt(x)/sqrt(a-b*x))/b^(7/2)-5/768*a^4*x^(3/2)*sqrt(a-b*x)/b^2-1/192*a^3*x^(5/2)*sqrt(a-b*x)/b+1/32*a^2*x^(7/2)*sqrt(a-b*x)-5/512*a^5*sqrt(x)*sqrt(a-b*x)/b^3],
[x^(3/2)*(a-b*x)^(5/2),x,8,1/8*a*x^(5/2)*(a-b*x)^(3/2)+1/5*x^(5/2)*(a-b*x)^(5/2)+3/128*a^5*arctan(sqrt(b)*sqrt(x)/sqrt(a-b*x))/b^(5/2)-1/64*a^3*x^(3/2)*sqrt(a-b*x)/b+1/16*a^2*x^(5/2)*sqrt(a-b*x)-3/128*a^4*sqrt(x)*sqrt(a-b*x)/b^2],
[(a-b*x)^(5/2)*sqrt(x),x,7,5/24*a*x^(3/2)*(a-b*x)^(3/2)+1/4*x^(3/2)*(a-b*x)^(5/2)+5/64*a^4*arctan(sqrt(b)*sqrt(x)/sqrt(a-b*x))/b^(3/2)+5/32*a^2*x^(3/2)*sqrt(a-b*x)-5/64*a^3*sqrt(x)*sqrt(a-b*x)/b],
[(a-b*x)^(5/2)/sqrt(x),x,6,5/8*a^3*arctan(sqrt(b)*sqrt(x)/sqrt(a-b*x))/sqrt(b)+5/12*a*(a-b*x)^(3/2)*sqrt(x)+1/3*(a-b*x)^(5/2)*sqrt(x)+5/8*a^2*sqrt(x)*sqrt(a-b*x)],
[(a-b*x)^(5/2)/x^(3/2),x,6,-15/4*a^2*arctan(sqrt(b)*sqrt(x)/sqrt(a-b*x))*sqrt(b)-2*(a-b*x)^(5/2)/sqrt(x)-5/2*b*(a-b*x)^(3/2)*sqrt(x)-15/4*a*b*sqrt(x)*sqrt(a-b*x)],
[(a-b*x)^(5/2)/x^(5/2),x,6,-2/3*(a-b*x)^(5/2)/x^(3/2)+5*a*b^(3/2)*arctan(sqrt(b)*sqrt(x)/sqrt(a-b*x))+10/3*b*(a-b*x)^(3/2)/sqrt(x)+5*b^2*sqrt(x)*sqrt(a-b*x)],
[x^(5/2)*(2+b*x)^(5/2),x,8,1/6*x^(7/2)*(2+b*x)^(3/2)+1/6*x^(7/2)*(2+b*x)^(5/2)-5/8*arcsinh(sqrt(b)*sqrt(x)/sqrt(2))/b^(7/2)-5/48*x^(3/2)*sqrt(2+b*x)/b^2+1/24*x^(5/2)*sqrt(2+b*x)/b+1/8*x^(7/2)*sqrt(2+b*x)+5/16*sqrt(x)*sqrt(2+b*x)/b^3],
[x^(3/2)*(2+b*x)^(5/2),x,7,1/4*x^(5/2)*(2+b*x)^(3/2)+1/5*x^(5/2)*(2+b*x)^(5/2)+3/4*arcsinh(sqrt(b)*sqrt(x)/sqrt(2))/b^(5/2)+1/8*x^(3/2)*sqrt(2+b*x)/b+1/4*x^(5/2)*sqrt(2+b*x)-3/8*sqrt(x)*sqrt(2+b*x)/b^2],
[(2+b*x)^(5/2)*sqrt(x),x,6,5/12*x^(3/2)*(2+b*x)^(3/2)+1/4*x^(3/2)*(2+b*x)^(5/2)-5/4*arcsinh(sqrt(b)*sqrt(x)/sqrt(2))/b^(3/2)+5/8*x^(3/2)*sqrt(2+b*x)+5/8*sqrt(x)*sqrt(2+b*x)/b],
[(2+b*x)^(5/2)/sqrt(x),x,5,5*arcsinh(sqrt(b)*sqrt(x)/sqrt(2))/sqrt(b)+5/6*(2+b*x)^(3/2)*sqrt(x)+1/3*(2+b*x)^(5/2)*sqrt(x)+5/2*sqrt(x)*sqrt(2+b*x)],
[(2+b*x)^(5/2)/x^(3/2),x,5,15*arcsinh(sqrt(b)*sqrt(x)/sqrt(2))*sqrt(b)-2*(2+b*x)^(5/2)/sqrt(x)+5/2*b*(2+b*x)^(3/2)*sqrt(x)+15/2*b*sqrt(x)*sqrt(2+b*x)],
[(2+b*x)^(5/2)/x^(5/2),x,5,-2/3*(2+b*x)^(5/2)/x^(3/2)+10*b^(3/2)*arcsinh(sqrt(b)*sqrt(x)/sqrt(2))-10/3*b*(2+b*x)^(3/2)/sqrt(x)+5*b^2*sqrt(x)*sqrt(2+b*x)],
[x^(5/2)*(2-b*x)^(5/2),x,8,1/6*x^(7/2)*(2-b*x)^(3/2)+1/6*x^(7/2)*(2-b*x)^(5/2)+5/8*arcsin(sqrt(b)*sqrt(x)/sqrt(2))/b^(7/2)-5/48*x^(3/2)*sqrt(2-b*x)/b^2-1/24*x^(5/2)*sqrt(2-b*x)/b+1/8*x^(7/2)*sqrt(2-b*x)-5/16*sqrt(x)*sqrt(2-b*x)/b^3],
[x^(3/2)*(2-b*x)^(5/2),x,7,1/4*x^(5/2)*(2-b*x)^(3/2)+1/5*x^(5/2)*(2-b*x)^(5/2)+3/4*arcsin(sqrt(b)*sqrt(x)/sqrt(2))/b^(5/2)-1/8*x^(3/2)*sqrt(2-b*x)/b+1/4*x^(5/2)*sqrt(2-b*x)-3/8*sqrt(x)*sqrt(2-b*x)/b^2],
[(2-b*x)^(5/2)*sqrt(x),x,6,5/12*x^(3/2)*(2-b*x)^(3/2)+1/4*x^(3/2)*(2-b*x)^(5/2)+5/4*arcsin(sqrt(b)*sqrt(x)/sqrt(2))/b^(3/2)+5/8*x^(3/2)*sqrt(2-b*x)-5/8*sqrt(x)*sqrt(2-b*x)/b],
[(2-b*x)^(5/2)/sqrt(x),x,5,5*arcsin(sqrt(b)*sqrt(x)/sqrt(2))/sqrt(b)+5/6*(2-b*x)^(3/2)*sqrt(x)+1/3*(2-b*x)^(5/2)*sqrt(x)+5/2*sqrt(x)*sqrt(2-b*x)],
[(2-b*x)^(5/2)/x^(3/2),x,5,-15*arcsin(sqrt(b)*sqrt(x)/sqrt(2))*sqrt(b)-2*(2-b*x)^(5/2)/sqrt(x)-5/2*b*(2-b*x)^(3/2)*sqrt(x)-15/2*b*sqrt(x)*sqrt(2-b*x)],
[(2-b*x)^(5/2)/x^(5/2),x,5,-2/3*(2-b*x)^(5/2)/x^(3/2)+10*b^(3/2)*arcsin(sqrt(b)*sqrt(x)/sqrt(2))+10/3*b*(2-b*x)^(3/2)/sqrt(x)+5*b^2*sqrt(x)*sqrt(2-b*x)],

# n<0
[x^(5/2)/sqrt(a+b*x),x,6,-5/8*a^3*arctanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))/b^(7/2)-5/12*a*x^(3/2)*sqrt(a+b*x)/b^2+1/3*x^(5/2)*sqrt(a+b*x)/b+5/8*a^2*sqrt(x)*sqrt(a+b*x)/b^3],
[x^(3/2)/sqrt(a+b*x),x,5,3/4*a^2*arctanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))/b^(5/2)+1/2*x^(3/2)*sqrt(a+b*x)/b-3/4*a*sqrt(x)*sqrt(a+b*x)/b^2],
[sqrt(x)/sqrt(a+b*x),x,4,-a*arctanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))/b^(3/2)+sqrt(x)*sqrt(a+b*x)/b],
[1/(sqrt(x)*sqrt(a+b*x)),x,3,2*arctanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))/sqrt(b)],
[1/(x^(3/2)*sqrt(a+b*x)),x,1,-2*sqrt(a+b*x)/(a*sqrt(x))],
[1/(x^(5/2)*sqrt(a+b*x)),x,2,-2/3*sqrt(a+b*x)/(a*x^(3/2))+4/3*b*sqrt(a+b*x)/(a^2*sqrt(x))],
[1/(x^(7/2)*sqrt(a+b*x)),x,3,-2/5*sqrt(a+b*x)/(a*x^(5/2))+8/15*b*sqrt(a+b*x)/(a^2*x^(3/2))-16/15*b^2*sqrt(a+b*x)/(a^3*sqrt(x))],
[1/(x^(9/2)*sqrt(a+b*x)),x,4,-2/7*sqrt(a+b*x)/(a*x^(7/2))+12/35*b*sqrt(a+b*x)/(a^2*x^(5/2))-16/35*b^2*sqrt(a+b*x)/(a^3*x^(3/2))+32/35*b^3*sqrt(a+b*x)/(a^4*sqrt(x))],
[x^(5/2)/(a+b*x)^(3/2),x,6,15/4*a^2*arctanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))/b^(7/2)-2*x^(5/2)/(b*sqrt(a+b*x))+5/2*x^(3/2)*sqrt(a+b*x)/b^2-15/4*a*sqrt(x)*sqrt(a+b*x)/b^3],
[x^(3/2)/(a+b*x)^(3/2),x,5,-3*a*arctanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))/b^(5/2)-2*x^(3/2)/(b*sqrt(a+b*x))+3*sqrt(x)*sqrt(a+b*x)/b^2],
[sqrt(x)/(a+b*x)^(3/2),x,4,2*arctanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))/b^(3/2)-2*sqrt(x)/(b*sqrt(a+b*x))],
[1/((a+b*x)^(3/2)*sqrt(x)),x,1,2*sqrt(x)/(a*sqrt(a+b*x))],
[1/(x^(3/2)*(a+b*x)^(3/2)),x,2,2/(a*sqrt(x)*sqrt(a+b*x))-4*sqrt(a+b*x)/(a^2*sqrt(x))],
[1/(x^(5/2)*(a+b*x)^(3/2)),x,3,2/(a*x^(3/2)*sqrt(a+b*x))-8/3*sqrt(a+b*x)/(a^2*x^(3/2))+16/3*b*sqrt(a+b*x)/(a^3*sqrt(x))],
[1/(x^(7/2)*(a+b*x)^(3/2)),x,4,2/(a*x^(5/2)*sqrt(a+b*x))-12/5*sqrt(a+b*x)/(a^2*x^(5/2))+16/5*b*sqrt(a+b*x)/(a^3*x^(3/2))-32/5*b^2*sqrt(a+b*x)/(a^4*sqrt(x))],
[x^(5/2)/(a+b*x)^(5/2),x,6,-2/3*x^(5/2)/(b*(a+b*x)^(3/2))-5*a*arctanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))/b^(7/2)-10/3*x^(3/2)/(b^2*sqrt(a+b*x))+5*sqrt(x)*sqrt(a+b*x)/b^3],
[x^(3/2)/(a+b*x)^(5/2),x,5,-2/3*x^(3/2)/(b*(a+b*x)^(3/2))+2*arctanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))/b^(5/2)-2*sqrt(x)/(b^2*sqrt(a+b*x))],
[sqrt(x)/(a+b*x)^(5/2),x,1,2/3*x^(3/2)/(a*(a+b*x)^(3/2))],
[1/((a+b*x)^(5/2)*sqrt(x)),x,2,2/3*sqrt(x)/(a*(a+b*x)^(3/2))+4/3*sqrt(x)/(a^2*sqrt(a+b*x))],
[1/(x^(3/2)*(a+b*x)^(5/2)),x,3,2/3/(a*(a+b*x)^(3/2)*sqrt(x))+8/3/(a^2*sqrt(x)*sqrt(a+b*x))-16/3*sqrt(a+b*x)/(a^3*sqrt(x))],
[1/(x^(5/2)*(a+b*x)^(5/2)),x,4,2/3/(a*x^(3/2)*(a+b*x)^(3/2))+4/(a^2*x^(3/2)*sqrt(a+b*x))-16/3*sqrt(a+b*x)/(a^3*x^(3/2))+32/3*b*sqrt(a+b*x)/(a^4*sqrt(x))],
[x^(5/2)/sqrt(a-b*x),x,6,5/8*a^3*arctan(sqrt(b)*sqrt(x)/sqrt(a-b*x))/b^(7/2)-5/12*a*x^(3/2)*sqrt(a-b*x)/b^2-1/3*x^(5/2)*sqrt(a-b*x)/b-5/8*a^2*sqrt(x)*sqrt(a-b*x)/b^3],
[x^(3/2)/sqrt(a-b*x),x,5,3/4*a^2*arctan(sqrt(b)*sqrt(x)/sqrt(a-b*x))/b^(5/2)-1/2*x^(3/2)*sqrt(a-b*x)/b-3/4*a*sqrt(x)*sqrt(a-b*x)/b^2],
[sqrt(x)/sqrt(a-b*x),x,4,a*arctan(sqrt(b)*sqrt(x)/sqrt(a-b*x))/b^(3/2)-sqrt(x)*sqrt(a-b*x)/b],
[1/(sqrt(x)*sqrt(a-b*x)),x,3,2*arctan(sqrt(b)*sqrt(x)/sqrt(a-b*x))/sqrt(b)],
[1/(x^(3/2)*sqrt(a-b*x)),x,1,-2*sqrt(a-b*x)/(a*sqrt(x))],
[1/(x^(5/2)*sqrt(a-b*x)),x,2,-2/3*sqrt(a-b*x)/(a*x^(3/2))-4/3*b*sqrt(a-b*x)/(a^2*sqrt(x))],
[x^(5/2)/(a-b*x)^(3/2),x,6,-15/4*a^2*arctan(sqrt(b)*sqrt(x)/sqrt(a-b*x))/b^(7/2)+2*x^(5/2)/(b*sqrt(a-b*x))+5/2*x^(3/2)*sqrt(a-b*x)/b^2+15/4*a*sqrt(x)*sqrt(a-b*x)/b^3],
[x^(3/2)/(a-b*x)^(3/2),x,5,-3*a*arctan(sqrt(b)*sqrt(x)/sqrt(a-b*x))/b^(5/2)+2*x^(3/2)/(b*sqrt(a-b*x))+3*sqrt(x)*sqrt(a-b*x)/b^2],
[sqrt(x)/(a-b*x)^(3/2),x,4,-2*arctan(sqrt(b)*sqrt(x)/sqrt(a-b*x))/b^(3/2)+2*sqrt(x)/(b*sqrt(a-b*x))],
[1/((a-b*x)^(3/2)*sqrt(x)),x,1,2*sqrt(x)/(a*sqrt(a-b*x))],
[1/(x^(3/2)*(a-b*x)^(3/2)),x,2,2/(a*sqrt(x)*sqrt(a-b*x))-4*sqrt(a-b*x)/(a^2*sqrt(x))],
[1/(x^(5/2)*(a-b*x)^(3/2)),x,3,2/(a*x^(3/2)*sqrt(a-b*x))-8/3*sqrt(a-b*x)/(a^2*x^(3/2))-16/3*b*sqrt(a-b*x)/(a^3*sqrt(x))],
[x^(5/2)/(a-b*x)^(5/2),x,6,2/3*x^(5/2)/(b*(a-b*x)^(3/2))+5*a*arctan(sqrt(b)*sqrt(x)/sqrt(a-b*x))/b^(7/2)-10/3*x^(3/2)/(b^2*sqrt(a-b*x))-5*sqrt(x)*sqrt(a-b*x)/b^3],
[x^(3/2)/(a-b*x)^(5/2),x,5,2/3*x^(3/2)/(b*(a-b*x)^(3/2))+2*arctan(sqrt(b)*sqrt(x)/sqrt(a-b*x))/b^(5/2)-2*sqrt(x)/(b^2*sqrt(a-b*x))],
[sqrt(x)/(a-b*x)^(5/2),x,1,2/3*x^(3/2)/(a*(a-b*x)^(3/2))],
[1/((a-b*x)^(5/2)*sqrt(x)),x,2,2/3*sqrt(x)/(a*(a-b*x)^(3/2))+4/3*sqrt(x)/(a^2*sqrt(a-b*x))],
[1/(x^(3/2)*(a-b*x)^(5/2)),x,3,2/3/(a*(a-b*x)^(3/2)*sqrt(x))+8/3/(a^2*sqrt(x)*sqrt(a-b*x))-16/3*sqrt(a-b*x)/(a^3*sqrt(x))],
[1/(x^(5/2)*(a-b*x)^(5/2)),x,4,2/3/(a*x^(3/2)*(a-b*x)^(3/2))+4/(a^2*x^(3/2)*sqrt(a-b*x))-16/3*sqrt(a-b*x)/(a^3*x^(3/2))-32/3*b*sqrt(a-b*x)/(a^4*sqrt(x))],
[x^(5/2)/sqrt(2+b*x),x,5,-5*arcsinh(sqrt(b)*sqrt(x)/sqrt(2))/b^(7/2)-5/6*x^(3/2)*sqrt(2+b*x)/b^2+1/3*x^(5/2)*sqrt(2+b*x)/b+5/2*sqrt(x)*sqrt(2+b*x)/b^3],
[x^(3/2)/sqrt(2+b*x),x,4,3*arcsinh(sqrt(b)*sqrt(x)/sqrt(2))/b^(5/2)+1/2*x^(3/2)*sqrt(2+b*x)/b-3/2*sqrt(x)*sqrt(2+b*x)/b^2],
[sqrt(x)/sqrt(2+b*x),x,3,-2*arcsinh(sqrt(b)*sqrt(x)/sqrt(2))/b^(3/2)+sqrt(x)*sqrt(2+b*x)/b],
[1/(sqrt(x)*sqrt(2+b*x)),x,2,2*arcsinh(sqrt(b)*sqrt(x)/sqrt(2))/sqrt(b)],
[1/(x^(3/2)*sqrt(2+b*x)),x,1,-sqrt(2+b*x)/sqrt(x)],
[1/(x^(5/2)*sqrt(2+b*x)),x,2,-1/3*sqrt(2+b*x)/x^(3/2)+1/3*b*sqrt(2+b*x)/sqrt(x)],
[1/(x^(7/2)*sqrt(2+b*x)),x,3,-1/5*sqrt(2+b*x)/x^(5/2)+2/15*b*sqrt(2+b*x)/x^(3/2)-2/15*b^2*sqrt(2+b*x)/sqrt(x)],
[1/(x^(9/2)*sqrt(2+b*x)),x,4,-1/7*sqrt(2+b*x)/x^(7/2)+3/35*b*sqrt(2+b*x)/x^(5/2)-2/35*b^2*sqrt(2+b*x)/x^(3/2)+2/35*b^3*sqrt(2+b*x)/sqrt(x)],
[x^(5/2)/(2+b*x)^(3/2),x,5,15*arcsinh(sqrt(b)*sqrt(x)/sqrt(2))/b^(7/2)-2*x^(5/2)/(b*sqrt(2+b*x))+5/2*x^(3/2)*sqrt(2+b*x)/b^2-15/2*sqrt(x)*sqrt(2+b*x)/b^3],
[x^(3/2)/(2+b*x)^(3/2),x,4,-6*arcsinh(sqrt(b)*sqrt(x)/sqrt(2))/b^(5/2)-2*x^(3/2)/(b*sqrt(2+b*x))+3*sqrt(x)*sqrt(2+b*x)/b^2],
[sqrt(x)/(2+b*x)^(3/2),x,3,2*arcsinh(sqrt(b)*sqrt(x)/sqrt(2))/b^(3/2)-2*sqrt(x)/(b*sqrt(2+b*x))],
[1/((2+b*x)^(3/2)*sqrt(x)),x,1,sqrt(x)/sqrt(2+b*x)],
[1/(x^(3/2)*(2+b*x)^(3/2)),x,2,1/(sqrt(x)*sqrt(2+b*x))-sqrt(2+b*x)/sqrt(x)],
[1/(x^(5/2)*(2+b*x)^(3/2)),x,3,1/(x^(3/2)*sqrt(2+b*x))-2/3*sqrt(2+b*x)/x^(3/2)+2/3*b*sqrt(2+b*x)/sqrt(x)],
[1/(x^(7/2)*(2+b*x)^(3/2)),x,4,1/(x^(5/2)*sqrt(2+b*x))-3/5*sqrt(2+b*x)/x^(5/2)+2/5*b*sqrt(2+b*x)/x^(3/2)-2/5*b^2*sqrt(2+b*x)/sqrt(x)],
[x^(5/2)/(2+b*x)^(5/2),x,5,-2/3*x^(5/2)/(b*(2+b*x)^(3/2))-10*arcsinh(sqrt(b)*sqrt(x)/sqrt(2))/b^(7/2)-10/3*x^(3/2)/(b^2*sqrt(2+b*x))+5*sqrt(x)*sqrt(2+b*x)/b^3],
[x^(3/2)/(2+b*x)^(5/2),x,4,-2/3*x^(3/2)/(b*(2+b*x)^(3/2))+2*arcsinh(sqrt(b)*sqrt(x)/sqrt(2))/b^(5/2)-2*sqrt(x)/(b^2*sqrt(2+b*x))],
[sqrt(x)/(2+b*x)^(5/2),x,1,1/3*x^(3/2)/(2+b*x)^(3/2)],
[1/((2+b*x)^(5/2)*sqrt(x)),x,2,1/3*sqrt(x)/(2+b*x)^(3/2)+1/3*sqrt(x)/sqrt(2+b*x)],
[1/(x^(3/2)*(2+b*x)^(5/2)),x,3,1/3/((2+b*x)^(3/2)*sqrt(x))+2/3/(sqrt(x)*sqrt(2+b*x))-2/3*sqrt(2+b*x)/sqrt(x)],
[1/(x^(5/2)*(2+b*x)^(5/2)),x,4,1/3/(x^(3/2)*(2+b*x)^(3/2))+1/(x^(3/2)*sqrt(2+b*x))-2/3*sqrt(2+b*x)/x^(3/2)+2/3*b*sqrt(2+b*x)/sqrt(x)],
[x^(5/2)/sqrt(2-b*x),x,5,5*arcsin(sqrt(b)*sqrt(x)/sqrt(2))/b^(7/2)-5/6*x^(3/2)*sqrt(2-b*x)/b^2-1/3*x^(5/2)*sqrt(2-b*x)/b-5/2*sqrt(x)*sqrt(2-b*x)/b^3],
[x^(3/2)/sqrt(2-b*x),x,4,3*arcsin(sqrt(b)*sqrt(x)/sqrt(2))/b^(5/2)-1/2*x^(3/2)*sqrt(2-b*x)/b-3/2*sqrt(x)*sqrt(2-b*x)/b^2],
[sqrt(x)/sqrt(2-b*x),x,3,2*arcsin(sqrt(b)*sqrt(x)/sqrt(2))/b^(3/2)-sqrt(x)*sqrt(2-b*x)/b],
[1/(sqrt(x)*sqrt(2-b*x)),x,2,2*arcsin(sqrt(b)*sqrt(x)/sqrt(2))/sqrt(b)],
[1/(x^(3/2)*sqrt(2-b*x)),x,1,-sqrt(2-b*x)/sqrt(x)],
[1/(x^(5/2)*sqrt(2-b*x)),x,2,-1/3*sqrt(2-b*x)/x^(3/2)-1/3*b*sqrt(2-b*x)/sqrt(x)],
[x^(5/2)/(2-b*x)^(3/2),x,5,-15*arcsin(sqrt(b)*sqrt(x)/sqrt(2))/b^(7/2)+2*x^(5/2)/(b*sqrt(2-b*x))+5/2*x^(3/2)*sqrt(2-b*x)/b^2+15/2*sqrt(x)*sqrt(2-b*x)/b^3],
[x^(3/2)/(2-b*x)^(3/2),x,4,-6*arcsin(sqrt(b)*sqrt(x)/sqrt(2))/b^(5/2)+2*x^(3/2)/(b*sqrt(2-b*x))+3*sqrt(x)*sqrt(2-b*x)/b^2],
[sqrt(x)/(2-b*x)^(3/2),x,3,-2*arcsin(sqrt(b)*sqrt(x)/sqrt(2))/b^(3/2)+2*sqrt(x)/(b*sqrt(2-b*x))],
[1/((2-b*x)^(3/2)*sqrt(x)),x,1,sqrt(x)/sqrt(2-b*x)],
[1/(x^(3/2)*(2-b*x)^(3/2)),x,2,1/(sqrt(x)*sqrt(2-b*x))-sqrt(2-b*x)/sqrt(x)],
[1/(x^(5/2)*(2-b*x)^(3/2)),x,3,1/(x^(3/2)*sqrt(2-b*x))-2/3*sqrt(2-b*x)/x^(3/2)-2/3*b*sqrt(2-b*x)/sqrt(x)],
[x^(5/2)/(2-b*x)^(5/2),x,5,2/3*x^(5/2)/(b*(2-b*x)^(3/2))+10*arcsin(sqrt(b)*sqrt(x)/sqrt(2))/b^(7/2)-10/3*x^(3/2)/(b^2*sqrt(2-b*x))-5*sqrt(x)*sqrt(2-b*x)/b^3],
[x^(3/2)/(2-b*x)^(5/2),x,4,2/3*x^(3/2)/(b*(2-b*x)^(3/2))+2*arcsin(sqrt(b)*sqrt(x)/sqrt(2))/b^(5/2)-2*sqrt(x)/(b^2*sqrt(2-b*x))],
[sqrt(x)/(2-b*x)^(5/2),x,1,1/3*x^(3/2)/(2-b*x)^(3/2)],
[1/((2-b*x)^(5/2)*sqrt(x)),x,2,1/3*sqrt(x)/(2-b*x)^(3/2)+1/3*sqrt(x)/sqrt(2-b*x)],
[1/(x^(3/2)*(2-b*x)^(5/2)),x,3,1/3/((2-b*x)^(3/2)*sqrt(x))+2/3/(sqrt(x)*sqrt(2-b*x))-2/3*sqrt(2-b*x)/sqrt(x)],
[1/(x^(5/2)*(2-b*x)^(5/2)),x,4,1/3/(x^(3/2)*(2-b*x)^(3/2))+1/(x^(3/2)*sqrt(2-b*x))-2/3*sqrt(2-b*x)/x^(3/2)-2/3*b*sqrt(2-b*x)/sqrt(x)],
[sqrt(x)/sqrt(1-x),x,4,-1/2*arcsin(1-2*x)-sqrt(1-x)*sqrt(x)],
[1/(sqrt(1-x)*sqrt(x)),x,3,-arcsin(1-2*x)],
[1/(sqrt(x)*sqrt(1-b*x)),x,2,2*arcsin(sqrt(b)*sqrt(x))/sqrt(b)],

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

# n>0
[x^(5/3)*(a+b*x),x,2,3/8*a*x^(8/3)+3/11*b*x^(11/3)],
[x^(4/3)*(a+b*x),x,2,3/7*a*x^(7/3)+3/10*b*x^(10/3)],
[x^(2/3)*(a+b*x),x,2,3/5*a*x^(5/3)+3/8*b*x^(8/3)],
[x^(1/3)*(a+b*x),x,2,3/4*a*x^(4/3)+3/7*b*x^(7/3)],
[(a+b*x)/x^(1/3),x,2,3/2*a*x^(2/3)+3/5*b*x^(5/3)],
[(a+b*x)/x^(2/3),x,2,3*a*x^(1/3)+3/4*b*x^(4/3)],
[(a+b*x)/x^(4/3),x,2,-3*a/x^(1/3)+3/2*b*x^(2/3)],
[(a+b*x)/x^(5/3),x,2,-3/2*a/x^(2/3)+3*b*x^(1/3)],
[x^(5/3)*(a+b*x)^2,x,2,3/8*a^2*x^(8/3)+6/11*a*b*x^(11/3)+3/14*b^2*x^(14/3)],
[x^(4/3)*(a+b*x)^2,x,2,3/7*a^2*x^(7/3)+3/5*a*b*x^(10/3)+3/13*b^2*x^(13/3)],
[x^(2/3)*(a+b*x)^2,x,2,3/5*a^2*x^(5/3)+3/4*a*b*x^(8/3)+3/11*b^2*x^(11/3)],
[x^(1/3)*(a+b*x)^2,x,2,3/4*a^2*x^(4/3)+6/7*a*b*x^(7/3)+3/10*b^2*x^(10/3)],
[(a+b*x)^2/x^(1/3),x,2,3/2*a^2*x^(2/3)+6/5*a*b*x^(5/3)+3/8*b^2*x^(8/3)],
[(a+b*x)^2/x^(2/3),x,2,3*a^2*x^(1/3)+3/2*a*b*x^(4/3)+3/7*b^2*x^(7/3)],
[(a+b*x)^2/x^(4/3),x,2,-3*a^2/x^(1/3)+3*a*b*x^(2/3)+3/5*b^2*x^(5/3)],
[(a+b*x)^2/x^(5/3),x,2,-3/2*a^2/x^(2/3)+6*a*b*x^(1/3)+3/4*b^2*x^(4/3)],
[x^(5/3)*(a+b*x)^3,x,2,3/8*a^3*x^(8/3)+9/11*a^2*b*x^(11/3)+9/14*a*b^2*x^(14/3)+3/17*b^3*x^(17/3)],
[x^(4/3)*(a+b*x)^3,x,2,3/7*a^3*x^(7/3)+9/10*a^2*b*x^(10/3)+9/13*a*b^2*x^(13/3)+3/16*b^3*x^(16/3)],
[x^(2/3)*(a+b*x)^3,x,2,3/5*a^3*x^(5/3)+9/8*a^2*b*x^(8/3)+9/11*a*b^2*x^(11/3)+3/14*b^3*x^(14/3)],
[x^(1/3)*(a+b*x)^3,x,2,3/4*a^3*x^(4/3)+9/7*a^2*b*x^(7/3)+9/10*a*b^2*x^(10/3)+3/13*b^3*x^(13/3)],
[(a+b*x)^3/x^(1/3),x,2,3/2*a^3*x^(2/3)+9/5*a^2*b*x^(5/3)+9/8*a*b^2*x^(8/3)+3/11*b^3*x^(11/3)],
[(a+b*x)^3/x^(2/3),x,2,3*a^3*x^(1/3)+9/4*a^2*b*x^(4/3)+9/7*a*b^2*x^(7/3)+3/10*b^3*x^(10/3)],
[(a+b*x)^3/x^(4/3),x,2,-3*a^3/x^(1/3)+9/2*a^2*b*x^(2/3)+9/5*a*b^2*x^(5/3)+3/8*b^3*x^(8/3)],
[(a+b*x)^3/x^(5/3),x,2,-3/2*a^3/x^(2/3)+9*a^2*b*x^(1/3)+9/4*a*b^2*x^(4/3)+3/7*b^3*x^(7/3)],

# n<0
[x^(5/3)/(a+b*x),x,6,-3/2*a*x^(2/3)/b^2+3/5*x^(5/3)/b-3/2*a^(5/3)*log(a^(1/3)+b^(1/3)*x^(1/3))/b^(8/3)+1/2*a^(5/3)*log(a+b*x)/b^(8/3)-a^(5/3)*arctan((a^(1/3)-2*b^(1/3)*x^(1/3))/(a^(1/3)*sqrt(3)))*sqrt(3)/b^(8/3)],
[x^(4/3)/(a+b*x),x,6,-3*a*x^(1/3)/b^2+3/4*x^(4/3)/b+3/2*a^(4/3)*log(a^(1/3)+b^(1/3)*x^(1/3))/b^(7/3)-1/2*a^(4/3)*log(a+b*x)/b^(7/3)-a^(4/3)*arctan((a^(1/3)-2*b^(1/3)*x^(1/3))/(a^(1/3)*sqrt(3)))*sqrt(3)/b^(7/3)],
[x^(2/3)/(a+b*x),x,5,3/2*x^(2/3)/b+3/2*a^(2/3)*log(a^(1/3)+b^(1/3)*x^(1/3))/b^(5/3)-1/2*a^(2/3)*log(a+b*x)/b^(5/3)+a^(2/3)*arctan((a^(1/3)-2*b^(1/3)*x^(1/3))/(a^(1/3)*sqrt(3)))*sqrt(3)/b^(5/3)],
[x^(1/3)/(a+b*x),x,5,3*x^(1/3)/b-3/2*a^(1/3)*log(a^(1/3)+b^(1/3)*x^(1/3))/b^(4/3)+1/2*a^(1/3)*log(a+b*x)/b^(4/3)+a^(1/3)*arctan((a^(1/3)-2*b^(1/3)*x^(1/3))/(a^(1/3)*sqrt(3)))*sqrt(3)/b^(4/3)],
[1/(x^(1/3)*(a+b*x)),x,4,-3/2*log(a^(1/3)+b^(1/3)*x^(1/3))/(a^(1/3)*b^(2/3))+1/2*log(a+b*x)/(a^(1/3)*b^(2/3))-arctan((a^(1/3)-2*b^(1/3)*x^(1/3))/(a^(1/3)*sqrt(3)))*sqrt(3)/(a^(1/3)*b^(2/3))],
[1/(x^(2/3)*(a+b*x)),x,4,3/2*log(a^(1/3)+b^(1/3)*x^(1/3))/(a^(2/3)*b^(1/3))-1/2*log(a+b*x)/(a^(2/3)*b^(1/3))-arctan((a^(1/3)-2*b^(1/3)*x^(1/3))/(a^(1/3)*sqrt(3)))*sqrt(3)/(a^(2/3)*b^(1/3))],
[1/(x^(4/3)*(a+b*x)),x,5,(-3)/(a*x^(1/3))+3/2*b^(1/3)*log(a^(1/3)+b^(1/3)*x^(1/3))/a^(4/3)-1/2*b^(1/3)*log(a+b*x)/a^(4/3)+b^(1/3)*arctan((a^(1/3)-2*b^(1/3)*x^(1/3))/(a^(1/3)*sqrt(3)))*sqrt(3)/a^(4/3)],
[1/(x^(5/3)*(a+b*x)),x,5,(-3/2)/(a*x^(2/3))-3/2*b^(2/3)*log(a^(1/3)+b^(1/3)*x^(1/3))/a^(5/3)+1/2*b^(2/3)*log(a+b*x)/a^(5/3)+b^(2/3)*arctan((a^(1/3)-2*b^(1/3)*x^(1/3))/(a^(1/3)*sqrt(3)))*sqrt(3)/a^(5/3)],
[x^(5/3)/(a+b*x)^2,x,6,5/2*x^(2/3)/b^2-x^(5/3)/(b*(a+b*x))+5/2*a^(2/3)*log(a^(1/3)+b^(1/3)*x^(1/3))/b^(8/3)-5/6*a^(2/3)*log(a+b*x)/b^(8/3)+5*a^(2/3)*arctan((a^(1/3)-2*b^(1/3)*x^(1/3))/(a^(1/3)*sqrt(3)))/(b^(8/3)*sqrt(3))],
[x^(4/3)/(a+b*x)^2,x,6,4*x^(1/3)/b^2-x^(4/3)/(b*(a+b*x))-2*a^(1/3)*log(a^(1/3)+b^(1/3)*x^(1/3))/b^(7/3)+2/3*a^(1/3)*log(a+b*x)/b^(7/3)+4*a^(1/3)*arctan((a^(1/3)-2*b^(1/3)*x^(1/3))/(a^(1/3)*sqrt(3)))/(b^(7/3)*sqrt(3))],
[x^(2/3)/(a+b*x)^2,x,5,-x^(2/3)/(b*(a+b*x))-log(a^(1/3)+b^(1/3)*x^(1/3))/(a^(1/3)*b^(5/3))+1/3*log(a+b*x)/(a^(1/3)*b^(5/3))-2*arctan((a^(1/3)-2*b^(1/3)*x^(1/3))/(a^(1/3)*sqrt(3)))/(a^(1/3)*b^(5/3)*sqrt(3))],
[x^(1/3)/(a+b*x)^2,x,5,-x^(1/3)/(b*(a+b*x))+1/2*log(a^(1/3)+b^(1/3)*x^(1/3))/(a^(2/3)*b^(4/3))-1/6*log(a+b*x)/(a^(2/3)*b^(4/3))-arctan((a^(1/3)-2*b^(1/3)*x^(1/3))/(a^(1/3)*sqrt(3)))/(a^(2/3)*b^(4/3)*sqrt(3))],
[1/(x^(1/3)*(a+b*x)^2),x,5,x^(2/3)/(a*(a+b*x))-1/2*log(a^(1/3)+b^(1/3)*x^(1/3))/(a^(4/3)*b^(2/3))+1/6*log(a+b*x)/(a^(4/3)*b^(2/3))-arctan((a^(1/3)-2*b^(1/3)*x^(1/3))/(a^(1/3)*sqrt(3)))/(a^(4/3)*b^(2/3)*sqrt(3))],
[1/(x^(2/3)*(a+b*x)^2),x,5,x^(1/3)/(a*(a+b*x))+log(a^(1/3)+b^(1/3)*x^(1/3))/(a^(5/3)*b^(1/3))-1/3*log(a+b*x)/(a^(5/3)*b^(1/3))-2*arctan((a^(1/3)-2*b^(1/3)*x^(1/3))/(a^(1/3)*sqrt(3)))/(a^(5/3)*b^(1/3)*sqrt(3))],
[1/(x^(4/3)*(a+b*x)^2),x,6,(-4)/(a^2*x^(1/3))+1/(a*x^(1/3)*(a+b*x))+2*b^(1/3)*log(a^(1/3)+b^(1/3)*x^(1/3))/a^(7/3)-2/3*b^(1/3)*log(a+b*x)/a^(7/3)+4*b^(1/3)*arctan((a^(1/3)-2*b^(1/3)*x^(1/3))/(a^(1/3)*sqrt(3)))/(a^(7/3)*sqrt(3))],
[1/(x^(5/3)*(a+b*x)^2),x,6,(-5/2)/(a^2*x^(2/3))+1/(a*x^(2/3)*(a+b*x))-5/2*b^(2/3)*log(a^(1/3)+b^(1/3)*x^(1/3))/a^(8/3)+5/6*b^(2/3)*log(a+b*x)/a^(8/3)+5*b^(2/3)*arctan((a^(1/3)-2*b^(1/3)*x^(1/3))/(a^(1/3)*sqrt(3)))/(a^(8/3)*sqrt(3))],
[x^(5/3)/(a+b*x)^3,x,6,-1/2*x^(5/3)/(b*(a+b*x)^2)-5/6*x^(2/3)/(b^2*(a+b*x))-5/6*log(a^(1/3)+b^(1/3)*x^(1/3))/(a^(1/3)*b^(8/3))+5/18*log(a+b*x)/(a^(1/3)*b^(8/3))-5/3*arctan((a^(1/3)-2*b^(1/3)*x^(1/3))/(a^(1/3)*sqrt(3)))/(a^(1/3)*b^(8/3)*sqrt(3))],
[x^(4/3)/(a+b*x)^3,x,6,-1/2*x^(4/3)/(b*(a+b*x)^2)-2/3*x^(1/3)/(b^2*(a+b*x))+1/3*log(a^(1/3)+b^(1/3)*x^(1/3))/(a^(2/3)*b^(7/3))-1/9*log(a+b*x)/(a^(2/3)*b^(7/3))-2/3*arctan((a^(1/3)-2*b^(1/3)*x^(1/3))/(a^(1/3)*sqrt(3)))/(a^(2/3)*b^(7/3)*sqrt(3))],
[x^(2/3)/(a+b*x)^3,x,6,-1/2*x^(2/3)/(b*(a+b*x)^2)+1/3*x^(2/3)/(a*b*(a+b*x))-1/6*log(a^(1/3)+b^(1/3)*x^(1/3))/(a^(4/3)*b^(5/3))+1/18*log(a+b*x)/(a^(4/3)*b^(5/3))-1/3*arctan((a^(1/3)-2*b^(1/3)*x^(1/3))/(a^(1/3)*sqrt(3)))/(a^(4/3)*b^(5/3)*sqrt(3))],
[x^(1/3)/(a+b*x)^3,x,6,-1/2*x^(1/3)/(b*(a+b*x)^2)+1/6*x^(1/3)/(a*b*(a+b*x))+1/6*log(a^(1/3)+b^(1/3)*x^(1/3))/(a^(5/3)*b^(4/3))-1/18*log(a+b*x)/(a^(5/3)*b^(4/3))-1/3*arctan((a^(1/3)-2*b^(1/3)*x^(1/3))/(a^(1/3)*sqrt(3)))/(a^(5/3)*b^(4/3)*sqrt(3))],
[1/(x^(1/3)*(a+b*x)^3),x,6,1/2*x^(2/3)/(a*(a+b*x)^2)+2/3*x^(2/3)/(a^2*(a+b*x))-1/3*log(a^(1/3)+b^(1/3)*x^(1/3))/(a^(7/3)*b^(2/3))+1/9*log(a+b*x)/(a^(7/3)*b^(2/3))-2/3*arctan((a^(1/3)-2*b^(1/3)*x^(1/3))/(a^(1/3)*sqrt(3)))/(a^(7/3)*b^(2/3)*sqrt(3))],
[1/(x^(2/3)*(a+b*x)^3),x,6,1/2*x^(1/3)/(a*(a+b*x)^2)+5/6*x^(1/3)/(a^2*(a+b*x))+5/6*log(a^(1/3)+b^(1/3)*x^(1/3))/(a^(8/3)*b^(1/3))-5/18*log(a+b*x)/(a^(8/3)*b^(1/3))-5/3*arctan((a^(1/3)-2*b^(1/3)*x^(1/3))/(a^(1/3)*sqrt(3)))/(a^(8/3)*b^(1/3)*sqrt(3))],
[1/(x^(4/3)*(a+b*x)^3),x,7,(-14/3)/(a^3*x^(1/3))+1/2/(a*x^(1/3)*(a+b*x)^2)+7/6/(a^2*x^(1/3)*(a+b*x))+7/3*b^(1/3)*log(a^(1/3)+b^(1/3)*x^(1/3))/a^(10/3)-7/9*b^(1/3)*log(a+b*x)/a^(10/3)+14/3*b^(1/3)*arctan((a^(1/3)-2*b^(1/3)*x^(1/3))/(a^(1/3)*sqrt(3)))/(a^(10/3)*sqrt(3))],
[1/(x^(5/3)*(a+b*x)^3),x,7,(-10/3)/(a^3*x^(2/3))+1/2/(a*x^(2/3)*(a+b*x)^2)+4/3/(a^2*x^(2/3)*(a+b*x))-10/3*b^(2/3)*log(a^(1/3)+b^(1/3)*x^(1/3))/a^(11/3)+10/9*b^(2/3)*log(a+b*x)/a^(11/3)+20/3*b^(2/3)*arctan((a^(1/3)-2*b^(1/3)*x^(1/3))/(a^(1/3)*sqrt(3)))/(a^(11/3)*sqrt(3))],

# Integrands of the form (c x)^(m/4) (a+b x)^n
[(1-x)^(1/4)/(1+x),x,5,4*(1-x)^(1/4)-2*2^(1/4)*arctan((1-x)^(1/4)/2^(1/4))-2*2^(1/4)*arctanh((1-x)^(1/4)/2^(1/4))],

# Integrands of the form (c x)^m (a+b x)^n when m is symbolic
[x^m*(a+b*x)^10,x,2,a^10*x^(1+m)/(1+m)+10*a^9*b*x^(2+m)/(2+m)+45*a^8*b^2*x^(3+m)/(3+m)+120*a^7*b^3*x^(4+m)/(4+m)+210*a^6*b^4*x^(5+m)/(5+m)+252*a^5*b^5*x^(6+m)/(6+m)+210*a^4*b^6*x^(7+m)/(7+m)+120*a^3*b^7*x^(8+m)/(8+m)+45*a^2*b^8*x^(9+m)/(9+m)+10*a*b^9*x^(10+m)/(10+m)+b^10*x^(11+m)/(11+m)],
[x^m*(a+b*x)^7,x,2,a^7*x^(1+m)/(1+m)+7*a^6*b*x^(2+m)/(2+m)+21*a^5*b^2*x^(3+m)/(3+m)+35*a^4*b^3*x^(4+m)/(4+m)+35*a^3*b^4*x^(5+m)/(5+m)+21*a^2*b^5*x^(6+m)/(6+m)+7*a*b^6*x^(7+m)/(7+m)+b^7*x^(8+m)/(8+m)],
[x^m*(a+b*x)^3,x,2,a^3*x^(1+m)/(1+m)+3*a^2*b*x^(2+m)/(2+m)+3*a*b^2*x^(3+m)/(3+m)+b^3*x^(4+m)/(4+m)],
[x^m*(a+b*x)^2,x,2,a^2*x^(1+m)/(1+m)+2*a*b*x^(2+m)/(2+m)+b^2*x^(3+m)/(3+m)],
[x^m*(a+b*x),x,2,a*x^(1+m)/(1+m)+b*x^(2+m)/(2+m)],
[x^m/(a+b*x),x,1,x^(1+m)*hypergeom([1,1+m],[2+m],-b*x/a)/(a*(1+m))],
[x^m/(a+b*x)^2,x,1,x^(1+m)*hypergeom([2,1+m],[2+m],-b*x/a)/(a^2*(1+m))],
[x^m/(a+b*x)^3,x,1,x^(1+m)*hypergeom([3,1+m],[2+m],-b*x/a)/(a^3*(1+m))],
[x^m*(a+b*x)^(5/2),x,2,2/7*x^m*(a+b*x)^(7/2)*hypergeom([7/2,-m],[9/2],1+b*x/a)/(b*(-b*x/a)^m)],
[x^m*(a+b*x)^(3/2),x,2,2/5*x^m*(a+b*x)^(5/2)*hypergeom([5/2,-m],[7/2],1+b*x/a)/(b*(-b*x/a)^m)],
[x^m*(a+b*x)^(1/2),x,2,2/3*x^m*(a+b*x)^(3/2)*hypergeom([3/2,-m],[5/2],1+b*x/a)/(b*(-b*x/a)^m)],
[x^m/(a+b*x)^(1/2),x,2,2*x^m*hypergeom([1/2,-m],[3/2],1+b*x/a)*sqrt(a+b*x)/(b*(-b*x/a)^m)],
[x^m/(a+b*x)^(3/2),x,2,-2*x^m*hypergeom([-1/2,-m],[1/2],1+b*x/a)/(b*(-b*x/a)^m*sqrt(a+b*x))],
[x^m/(a+b*x)^(5/2),x,2,-2/3*x^m*hypergeom([-3/2,-m],[-1/2],1+b*x/a)/(b*(-b*x/a)^m*(a+b*x)^(3/2))],
[x^(2+m)/sqrt(a+b*x),x,2,2*a^2*x^m*hypergeom([1/2,-2-m],[3/2],1+b*x/a)*sqrt(a+b*x)/(b^3*(-b*x/a)^m)],
[x^(1+m)/sqrt(a+b*x),x,2,-2*a*x^m*hypergeom([1/2,-1-m],[3/2],1+b*x/a)*sqrt(a+b*x)/(b^2*(-b*x/a)^m)],
[x^m/sqrt(a+b*x),x,2,2*x^m*hypergeom([1/2,-m],[3/2],1+b*x/a)*sqrt(a+b*x)/(b*(-b*x/a)^m)],
[x^(-1+m)/sqrt(a+b*x),x,2,-2*x^m*hypergeom([1/2,1-m],[3/2],1+b*x/a)*sqrt(a+b*x)/(a*(-b*x/a)^m)],
[x^(-2+m)/sqrt(a+b*x),x,2,2*b*x^m*hypergeom([1/2,2-m],[3/2],1+b*x/a)*sqrt(a+b*x)/(a^2*(-b*x/a)^m)],
[x^(-3+m)/sqrt(a+b*x),x,2,-2*b^2*x^m*hypergeom([1/2,3-m],[3/2],1+b*x/a)*sqrt(a+b*x)/(a^3*(-b*x/a)^m)],
[x^m/sqrt(2+3*x),x,1,x^(1+m)*hypergeom([1/2,1+m],[2+m],-3/2*x)/((1+m)*sqrt(2))],
[x^m/sqrt(2-3*x),x,1,x^(1+m)*hypergeom([1/2,1+m],[2+m],3/2*x)/((1+m)*sqrt(2))],
[x^m/sqrt(-2+3*x),x,1,(3/2)^(-1-m)*hypergeom([1/2,-m],[3/2],1-3/2*x)*sqrt(-2+3*x)],
[x^m/sqrt(-2-3*x),x,3,-2^(1+m)*3^(-1-m)*x^m*hypergeom([1/2,-m],[3/2],1+3/2*x)*sqrt(-2-3*x)/(-x)^m],
[(-x)^m/sqrt(a+b*x),x,2,2*(-x)^m*hypergeom([1/2,-m],[3/2],1+b*x/a)*sqrt(a+b*x)/(b*(-b*x/a)^m)],
[(-x)^m/sqrt(2+3*x),x,1,-(-x)^(1+m)*hypergeom([1/2,1+m],[2+m],-3/2*x)/((1+m)*sqrt(2))],
[(-x)^m/sqrt(2-3*x),x,1,-(-x)^(1+m)*hypergeom([1/2,1+m],[2+m],3/2*x)/((1+m)*sqrt(2))],
[(-x)^m/sqrt(-2+3*x),x,3,2^(1+m)*3^(-1-m)*(-x)^m*hypergeom([1/2,-m],[3/2],1-3/2*x)*sqrt(-2+3*x)/x^m],
[(-x)^m/sqrt(-2-3*x),x,1,-(3/2)^(-1-m)*hypergeom([1/2,-m],[3/2],1+3/2*x)*sqrt(-2-3*x)],
[x^n/sqrt(1-x),x,1,-2*hypergeom([1/2,-n],[3/2],1-x)*sqrt(1-x)],
[x^n/sqrt(a-a*x),x,1,-2*hypergeom([1/2,-n],[3/2],1-x)*sqrt(a-a*x)/a],

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

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

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

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

# p>0
[x^3*(a+b*x)*sqrt(c*x^2),x,3,1/5*a*x^4*sqrt(c*x^2)+1/6*b*x^5*sqrt(c*x^2)],
[x^2*(a+b*x)*sqrt(c*x^2),x,3,1/4*a*x^3*sqrt(c*x^2)+1/5*b*x^4*sqrt(c*x^2)],
[x*(a+b*x)*sqrt(c*x^2),x,3,1/3*a*x^2*sqrt(c*x^2)+1/4*b*x^3*sqrt(c*x^2)],
[(a+b*x)*sqrt(c*x^2),x,3,1/2*a*x*sqrt(c*x^2)+1/3*b*x^2*sqrt(c*x^2)],
[(a+b*x)*sqrt(c*x^2)/x,x,2,a*sqrt(c*x^2)+1/2*b*x*sqrt(c*x^2)],
[(a+b*x)*sqrt(c*x^2)/x^2,x,3,b*sqrt(c*x^2)+a*log(x)*sqrt(c*x^2)/x],
[(a+b*x)*sqrt(c*x^2)/x^3,x,3,-a*sqrt(c*x^2)/x^2+b*log(x)*sqrt(c*x^2)/x],
[(a+b*x)*sqrt(c*x^2)/x^4,x,2,-1/2*(a+b*x)^2*sqrt(c*x^2)/(a*x^3)],
[x^3*(c*x^2)^(3/2)*(a+b*x),x,3,1/7*a*c*x^6*sqrt(c*x^2)+1/8*b*c*x^7*sqrt(c*x^2)],
[x^2*(c*x^2)^(3/2)*(a+b*x),x,3,1/6*a*c*x^5*sqrt(c*x^2)+1/7*b*c*x^6*sqrt(c*x^2)],
[x*(c*x^2)^(3/2)*(a+b*x),x,3,1/5*a*c*x^4*sqrt(c*x^2)+1/6*b*c*x^5*sqrt(c*x^2)],
[(c*x^2)^(3/2)*(a+b*x),x,3,1/4*a*c*x^3*sqrt(c*x^2)+1/5*b*c*x^4*sqrt(c*x^2)],
[(c*x^2)^(3/2)*(a+b*x)/x,x,3,1/3*a*c*x^2*sqrt(c*x^2)+1/4*b*c*x^3*sqrt(c*x^2)],
[(c*x^2)^(3/2)*(a+b*x)/x^2,x,3,1/2*a*c*x*sqrt(c*x^2)+1/3*b*c*x^2*sqrt(c*x^2)],
[(c*x^2)^(3/2)*(a+b*x)/x^3,x,2,a*c*sqrt(c*x^2)+1/2*b*c*x*sqrt(c*x^2)],
[(c*x^2)^(3/2)*(a+b*x)/x^4,x,3,b*c*sqrt(c*x^2)+a*c*log(x)*sqrt(c*x^2)/x],
[x^3*(c*x^2)^(5/2)*(a+b*x),x,3,1/9*a*c^2*x^8*sqrt(c*x^2)+1/10*b*c^2*x^9*sqrt(c*x^2)],
[x^2*(c*x^2)^(5/2)*(a+b*x),x,3,1/8*a*c^2*x^7*sqrt(c*x^2)+1/9*b*c^2*x^8*sqrt(c*x^2)],
[x*(c*x^2)^(5/2)*(a+b*x),x,3,1/7*a*c^2*x^6*sqrt(c*x^2)+1/8*b*c^2*x^7*sqrt(c*x^2)],
[(c*x^2)^(5/2)*(a+b*x),x,3,1/6*a*c^2*x^5*sqrt(c*x^2)+1/7*b*c^2*x^6*sqrt(c*x^2)],
[(c*x^2)^(5/2)*(a+b*x)/x,x,3,1/5*a*c^2*x^4*sqrt(c*x^2)+1/6*b*c^2*x^5*sqrt(c*x^2)],
[(c*x^2)^(5/2)*(a+b*x)/x^2,x,3,1/4*a*c^2*x^3*sqrt(c*x^2)+1/5*b*c^2*x^4*sqrt(c*x^2)],
[(c*x^2)^(5/2)*(a+b*x)/x^3,x,3,1/3*a*c^2*x^2*sqrt(c*x^2)+1/4*b*c^2*x^3*sqrt(c*x^2)],
[(c*x^2)^(5/2)*(a+b*x)/x^4,x,3,1/2*a*c^2*x*sqrt(c*x^2)+1/3*b*c^2*x^2*sqrt(c*x^2)],

# p<0
[x^3*(a+b*x)/sqrt(c*x^2),x,3,1/3*a*x^4/sqrt(c*x^2)+1/4*b*x^5/sqrt(c*x^2)],
[x^2*(a+b*x)/sqrt(c*x^2),x,3,1/2*a*x^3/sqrt(c*x^2)+1/3*b*x^4/sqrt(c*x^2)],
[x*(a+b*x)/sqrt(c*x^2),x,2,a*x^2/sqrt(c*x^2)+1/2*b*x^3/sqrt(c*x^2)],
[(a+b*x)/sqrt(c*x^2),x,3,b*x^2/sqrt(c*x^2)+a*x*log(x)/sqrt(c*x^2)],
[(a+b*x)/(x*sqrt(c*x^2)),x,3,-a/sqrt(c*x^2)+b*x*log(x)/sqrt(c*x^2)],
[(a+b*x)/(x^2*sqrt(c*x^2)),x,2,-1/2*(a+b*x)^2/(a*x*sqrt(c*x^2))],
[(a+b*x)/(x^3*sqrt(c*x^2)),x,3,-1/3*a/(x^2*sqrt(c*x^2))-1/2*b/(x*sqrt(c*x^2))],
[(a+b*x)/(x^4*sqrt(c*x^2)),x,3,-1/4*a/(x^3*sqrt(c*x^2))-1/3*b/(x^2*sqrt(c*x^2))],
[x^3*(a+b*x)/(c*x^2)^(3/2),x,2,a*x^2/(c*sqrt(c*x^2))+1/2*b*x^3/(c*sqrt(c*x^2))],
[x^2*(a+b*x)/(c*x^2)^(3/2),x,3,b*x^2/(c*sqrt(c*x^2))+a*x*log(x)/(c*sqrt(c*x^2))],
[x*(a+b*x)/(c*x^2)^(3/2),x,3,-a/(c*sqrt(c*x^2))+b*x*log(x)/(c*sqrt(c*x^2))],
[(a+b*x)/(c*x^2)^(3/2),x,2,-1/2*(a+b*x)^2/(a*c*x*sqrt(c*x^2))],
[(a+b*x)/(x*(c*x^2)^(3/2)),x,3,-1/3*a/(c*x^2*sqrt(c*x^2))-1/2*b/(c*x*sqrt(c*x^2))],
[(a+b*x)/(x^2*(c*x^2)^(3/2)),x,3,-1/4*a/(c*x^3*sqrt(c*x^2))-1/3*b/(c*x^2*sqrt(c*x^2))],
[(a+b*x)/(x^3*(c*x^2)^(3/2)),x,3,-1/5*a/(c*x^4*sqrt(c*x^2))-1/4*b/(c*x^3*sqrt(c*x^2))],
[(a+b*x)/(x^4*(c*x^2)^(3/2)),x,3,-1/6*a/(c*x^5*sqrt(c*x^2))-1/5*b/(c*x^4*sqrt(c*x^2))],
[x^3*(a+b*x)/(c*x^2)^(5/2),x,3,-a/(c^2*sqrt(c*x^2))+b*x*log(x)/(c^2*sqrt(c*x^2))],
[x^2*(a+b*x)/(c*x^2)^(5/2),x,2,-1/2*(a+b*x)^2/(a*c^2*x*sqrt(c*x^2))],
[x*(a+b*x)/(c*x^2)^(5/2),x,3,-1/3*a/(c^2*x^2*sqrt(c*x^2))-1/2*b/(c^2*x*sqrt(c*x^2))],
[(a+b*x)/(c*x^2)^(5/2),x,3,-1/4*a/(c^2*x^3*sqrt(c*x^2))-1/3*b/(c^2*x^2*sqrt(c*x^2))],
[(a+b*x)/(x*(c*x^2)^(5/2)),x,3,-1/5*a/(c^2*x^4*sqrt(c*x^2))-1/4*b/(c^2*x^3*sqrt(c*x^2))],
[(a+b*x)/(x^2*(c*x^2)^(5/2)),x,3,-1/6*a/(c^2*x^5*sqrt(c*x^2))-1/5*b/(c^2*x^4*sqrt(c*x^2))],
[(a+b*x)/(x^3*(c*x^2)^(5/2)),x,3,-1/7*a/(c^2*x^6*sqrt(c*x^2))-1/6*b/(c^2*x^5*sqrt(c*x^2))],
[(a+b*x)/(x^4*(c*x^2)^(5/2)),x,3,-1/8*a/(c^2*x^7*sqrt(c*x^2))-1/7*b/(c^2*x^6*sqrt(c*x^2))],

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

# p>0
[x^3*(a+b*x)^2*sqrt(c*x^2),x,3,1/5*a^2*x^4*sqrt(c*x^2)+1/3*a*b*x^5*sqrt(c*x^2)+1/7*b^2*x^6*sqrt(c*x^2)],
[x^2*(a+b*x)^2*sqrt(c*x^2),x,3,1/4*a^2*x^3*sqrt(c*x^2)+2/5*a*b*x^4*sqrt(c*x^2)+1/6*b^2*x^5*sqrt(c*x^2)],
[x*(a+b*x)^2*sqrt(c*x^2),x,3,1/3*a^2*x^2*sqrt(c*x^2)+1/2*a*b*x^3*sqrt(c*x^2)+1/5*b^2*x^4*sqrt(c*x^2)],
[(a+b*x)^2*sqrt(c*x^2),x,3,1/2*a^2*x*sqrt(c*x^2)+2/3*a*b*x^2*sqrt(c*x^2)+1/4*b^2*x^3*sqrt(c*x^2)],
[(a+b*x)^2*sqrt(c*x^2)/x,x,2,1/3*(a+b*x)^3*sqrt(c*x^2)/(b*x)],
[(a+b*x)^2*sqrt(c*x^2)/x^2,x,3,2*a*b*sqrt(c*x^2)+1/2*b^2*x*sqrt(c*x^2)+a^2*log(x)*sqrt(c*x^2)/x],
[(a+b*x)^2*sqrt(c*x^2)/x^3,x,3,b^2*sqrt(c*x^2)-a^2*sqrt(c*x^2)/x^2+2*a*b*log(x)*sqrt(c*x^2)/x],
[(a+b*x)^2*sqrt(c*x^2)/x^4,x,3,-1/2*a^2*sqrt(c*x^2)/x^3-2*a*b*sqrt(c*x^2)/x^2+b^2*log(x)*sqrt(c*x^2)/x],
[x^3*(c*x^2)^(3/2)*(a+b*x)^2,x,3,1/7*a^2*c*x^6*sqrt(c*x^2)+1/4*a*b*c*x^7*sqrt(c*x^2)+1/9*b^2*c*x^8*sqrt(c*x^2)],
[x^2*(c*x^2)^(3/2)*(a+b*x)^2,x,3,1/6*a^2*c*x^5*sqrt(c*x^2)+2/7*a*b*c*x^6*sqrt(c*x^2)+1/8*b^2*c*x^7*sqrt(c*x^2)],
[x*(c*x^2)^(3/2)*(a+b*x)^2,x,3,1/5*a^2*c*x^4*sqrt(c*x^2)+1/3*a*b*c*x^5*sqrt(c*x^2)+1/7*b^2*c*x^6*sqrt(c*x^2)],
[(c*x^2)^(3/2)*(a+b*x)^2,x,3,1/4*a^2*c*x^3*sqrt(c*x^2)+2/5*a*b*c*x^4*sqrt(c*x^2)+1/6*b^2*c*x^5*sqrt(c*x^2)],
[(c*x^2)^(3/2)*(a+b*x)^2/x,x,3,1/3*a^2*c*x^2*sqrt(c*x^2)+1/2*a*b*c*x^3*sqrt(c*x^2)+1/5*b^2*c*x^4*sqrt(c*x^2)],
[(c*x^2)^(3/2)*(a+b*x)^2/x^2,x,3,1/2*a^2*c*x*sqrt(c*x^2)+2/3*a*b*c*x^2*sqrt(c*x^2)+1/4*b^2*c*x^3*sqrt(c*x^2)],
[(c*x^2)^(3/2)*(a+b*x)^2/x^3,x,2,1/3*c*(a+b*x)^3*sqrt(c*x^2)/(b*x)],
[(c*x^2)^(3/2)*(a+b*x)^2/x^4,x,3,2*a*b*c*sqrt(c*x^2)+1/2*b^2*c*x*sqrt(c*x^2)+a^2*c*log(x)*sqrt(c*x^2)/x],
[x*(c*x^2)^(5/2)*(a+b*x)^2,x,3,1/7*a^2*c^2*x^6*sqrt(c*x^2)+1/4*a*b*c^2*x^7*sqrt(c*x^2)+1/9*b^2*c^2*x^8*sqrt(c*x^2)],
[(c*x^2)^(5/2)*(a+b*x)^2,x,3,1/6*a^2*c^2*x^5*sqrt(c*x^2)+2/7*a*b*c^2*x^6*sqrt(c*x^2)+1/8*b^2*c^2*x^7*sqrt(c*x^2)],
[(c*x^2)^(5/2)*(a+b*x)^2/x,x,3,1/5*a^2*c^2*x^4*sqrt(c*x^2)+1/3*a*b*c^2*x^5*sqrt(c*x^2)+1/7*b^2*c^2*x^6*sqrt(c*x^2)],
[(c*x^2)^(5/2)*(a+b*x)^2/x^2,x,3,1/4*a^2*c^2*x^3*sqrt(c*x^2)+2/5*a*b*c^2*x^4*sqrt(c*x^2)+1/6*b^2*c^2*x^5*sqrt(c*x^2)],
[(c*x^2)^(5/2)*(a+b*x)^2/x^3,x,3,1/3*a^2*c^2*x^2*sqrt(c*x^2)+1/2*a*b*c^2*x^3*sqrt(c*x^2)+1/5*b^2*c^2*x^4*sqrt(c*x^2)],
[(c*x^2)^(5/2)*(a+b*x)^2/x^4,x,3,1/2*a^2*c^2*x*sqrt(c*x^2)+2/3*a*b*c^2*x^2*sqrt(c*x^2)+1/4*b^2*c^2*x^3*sqrt(c*x^2)],
[(c*x^2)^(5/2)*(a+b*x)^2/x^5,x,2,1/3*c^2*(a+b*x)^3*sqrt(c*x^2)/(b*x)],
[(c*x^2)^(5/2)*(a+b*x)^2/x^6,x,3,2*a*b*c^2*sqrt(c*x^2)+1/2*b^2*c^2*x*sqrt(c*x^2)+a^2*c^2*log(x)*sqrt(c*x^2)/x],

# p<0
[x^3*(a+b*x)^2/sqrt(c*x^2),x,3,1/3*a^2*x^4/sqrt(c*x^2)+1/2*a*b*x^5/sqrt(c*x^2)+1/5*b^2*x^6/sqrt(c*x^2)],
[x^2*(a+b*x)^2/sqrt(c*x^2),x,3,1/2*a^2*x^3/sqrt(c*x^2)+2/3*a*b*x^4/sqrt(c*x^2)+1/4*b^2*x^5/sqrt(c*x^2)],
[x*(a+b*x)^2/sqrt(c*x^2),x,2,1/3*x*(a+b*x)^3/(b*sqrt(c*x^2))],
[(a+b*x)^2/sqrt(c*x^2),x,3,2*a*b*x^2/sqrt(c*x^2)+1/2*b^2*x^3/sqrt(c*x^2)+a^2*x*log(x)/sqrt(c*x^2)],
[(a+b*x)^2/(x*sqrt(c*x^2)),x,3,-a^2/sqrt(c*x^2)+b^2*x^2/sqrt(c*x^2)+2*a*b*x*log(x)/sqrt(c*x^2)],
[(a+b*x)^2/(x^2*sqrt(c*x^2)),x,3,-2*a*b/sqrt(c*x^2)-1/2*a^2/(x*sqrt(c*x^2))+b^2*x*log(x)/sqrt(c*x^2)],
[(a+b*x)^2/(x^3*sqrt(c*x^2)),x,2,-1/3*(a+b*x)^3/(a*x^2*sqrt(c*x^2))],
[(a+b*x)^2/(x^4*sqrt(c*x^2)),x,3,-1/4*a^2/(x^3*sqrt(c*x^2))-2/3*a*b/(x^2*sqrt(c*x^2))-1/2*b^2/(x*sqrt(c*x^2))],
[x^3*(a+b*x)^2/(c*x^2)^(3/2),x,2,1/3*x*(a+b*x)^3/(b*c*sqrt(c*x^2))],
[x^2*(a+b*x)^2/(c*x^2)^(3/2),x,3,2*a*b*x^2/(c*sqrt(c*x^2))+1/2*b^2*x^3/(c*sqrt(c*x^2))+a^2*x*log(x)/(c*sqrt(c*x^2))],
[x*(a+b*x)^2/(c*x^2)^(3/2),x,3,-a^2/(c*sqrt(c*x^2))+b^2*x^2/(c*sqrt(c*x^2))+2*a*b*x*log(x)/(c*sqrt(c*x^2))],
[(a+b*x)^2/(c*x^2)^(3/2),x,3,-2*a*b/(c*sqrt(c*x^2))-1/2*a^2/(c*x*sqrt(c*x^2))+b^2*x*log(x)/(c*sqrt(c*x^2))],
[(a+b*x)^2/(x*(c*x^2)^(3/2)),x,2,-1/3*(a+b*x)^3/(a*c*x^2*sqrt(c*x^2))],
[(a+b*x)^2/(x^2*(c*x^2)^(3/2)),x,3,-1/4*a^2/(c*x^3*sqrt(c*x^2))-2/3*a*b/(c*x^2*sqrt(c*x^2))-1/2*b^2/(c*x*sqrt(c*x^2))],
[(a+b*x)^2/(x^3*(c*x^2)^(3/2)),x,3,-1/5*a^2/(c*x^4*sqrt(c*x^2))-1/2*a*b/(c*x^3*sqrt(c*x^2))-1/3*b^2/(c*x^2*sqrt(c*x^2))],
[(a+b*x)^2/(x^4*(c*x^2)^(3/2)),x,3,-1/6*a^2/(c*x^5*sqrt(c*x^2))-2/5*a*b/(c*x^4*sqrt(c*x^2))-1/4*b^2/(c*x^3*sqrt(c*x^2))],
[x^3*(a+b*x)^2/(c*x^2)^(5/2),x,3,-a^2/(c^2*sqrt(c*x^2))+b^2*x^2/(c^2*sqrt(c*x^2))+2*a*b*x*log(x)/(c^2*sqrt(c*x^2))],
[x^2*(a+b*x)^2/(c*x^2)^(5/2),x,3,-2*a*b/(c^2*sqrt(c*x^2))-1/2*a^2/(c^2*x*sqrt(c*x^2))+b^2*x*log(x)/(c^2*sqrt(c*x^2))],
[x*(a+b*x)^2/(c*x^2)^(5/2),x,2,-1/3*(a+b*x)^3/(a*c^2*x^2*sqrt(c*x^2))],
[(a+b*x)^2/(c*x^2)^(5/2),x,3,-1/4*a^2/(c^2*x^3*sqrt(c*x^2))-2/3*a*b/(c^2*x^2*sqrt(c*x^2))-1/2*b^2/(c^2*x*sqrt(c*x^2))],
[(a+b*x)^2/(x*(c*x^2)^(5/2)),x,3,-1/5*a^2/(c^2*x^4*sqrt(c*x^2))-1/2*a*b/(c^2*x^3*sqrt(c*x^2))-1/3*b^2/(c^2*x^2*sqrt(c*x^2))],
[(a+b*x)^2/(x^2*(c*x^2)^(5/2)),x,3,-1/6*a^2/(c^2*x^5*sqrt(c*x^2))-2/5*a*b/(c^2*x^4*sqrt(c*x^2))-1/4*b^2/(c^2*x^3*sqrt(c*x^2))],
[(a+b*x)^2/(x^3*(c*x^2)^(5/2)),x,3,-1/7*a^2/(c^2*x^6*sqrt(c*x^2))-1/3*a*b/(c^2*x^5*sqrt(c*x^2))-1/5*b^2/(c^2*x^4*sqrt(c*x^2))],
[(a+b*x)^2/(x^4*(c*x^2)^(5/2)),x,3,-1/8*a^2/(c^2*x^7*sqrt(c*x^2))-2/7*a*b/(c^2*x^6*sqrt(c*x^2))-1/6*b^2/(c^2*x^5*sqrt(c*x^2))],

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

# p>0
[x^3*sqrt(c*x^2)/(a+b*x),x,3,-a^3*sqrt(c*x^2)/b^4+1/2*a^2*x*sqrt(c*x^2)/b^3-1/3*a*x^2*sqrt(c*x^2)/b^2+1/4*x^3*sqrt(c*x^2)/b+a^4*log(a+b*x)*sqrt(c*x^2)/(b^5*x)],
[x^2*sqrt(c*x^2)/(a+b*x),x,3,a^2*sqrt(c*x^2)/b^3-1/2*a*x*sqrt(c*x^2)/b^2+1/3*x^2*sqrt(c*x^2)/b-a^3*log(a+b*x)*sqrt(c*x^2)/(b^4*x)],
[x*sqrt(c*x^2)/(a+b*x),x,3,-a*sqrt(c*x^2)/b^2+1/2*x*sqrt(c*x^2)/b+a^2*log(a+b*x)*sqrt(c*x^2)/(b^3*x)],
[sqrt(c*x^2)/(a+b*x),x,3,sqrt(c*x^2)/b-a*log(a+b*x)*sqrt(c*x^2)/(b^2*x)],
[sqrt(c*x^2)/(x*(a+b*x)),x,2,log(a+b*x)*sqrt(c*x^2)/(b*x)],
[sqrt(c*x^2)/(x^2*(a+b*x)),x,4,log(x)*sqrt(c*x^2)/(a*x)-log(a+b*x)*sqrt(c*x^2)/(a*x)],
[sqrt(c*x^2)/(x^3*(a+b*x)),x,3,-sqrt(c*x^2)/(a*x^2)-b*log(x)*sqrt(c*x^2)/(a^2*x)+b*log(a+b*x)*sqrt(c*x^2)/(a^2*x)],
[sqrt(c*x^2)/(x^4*(a+b*x)),x,3,-1/2*sqrt(c*x^2)/(a*x^3)+b*sqrt(c*x^2)/(a^2*x^2)+b^2*log(x)*sqrt(c*x^2)/(a^3*x)-b^2*log(a+b*x)*sqrt(c*x^2)/(a^3*x)],
[x*(c*x^2)^(3/2)/(a+b*x),x,3,-a^3*c*sqrt(c*x^2)/b^4+1/2*a^2*c*x*sqrt(c*x^2)/b^3-1/3*a*c*x^2*sqrt(c*x^2)/b^2+1/4*c*x^3*sqrt(c*x^2)/b+a^4*c*log(a+b*x)*sqrt(c*x^2)/(b^5*x)],
[(c*x^2)^(3/2)/(a+b*x),x,3,a^2*c*sqrt(c*x^2)/b^3-1/2*a*c*x*sqrt(c*x^2)/b^2+1/3*c*x^2*sqrt(c*x^2)/b-a^3*c*log(a+b*x)*sqrt(c*x^2)/(b^4*x)],
[(c*x^2)^(3/2)/(x*(a+b*x)),x,3,-a*c*sqrt(c*x^2)/b^2+1/2*c*x*sqrt(c*x^2)/b+a^2*c*log(a+b*x)*sqrt(c*x^2)/(b^3*x)],
[(c*x^2)^(3/2)/(x^2*(a+b*x)),x,3,c*sqrt(c*x^2)/b-a*c*log(a+b*x)*sqrt(c*x^2)/(b^2*x)],
[(c*x^2)^(3/2)/(x^3*(a+b*x)),x,2,c*log(a+b*x)*sqrt(c*x^2)/(b*x)],
[(c*x^2)^(3/2)/(x^4*(a+b*x)),x,4,c*log(x)*sqrt(c*x^2)/(a*x)-c*log(a+b*x)*sqrt(c*x^2)/(a*x)],
[(c*x^2)^(3/2)/(x^5*(a+b*x)),x,3,-c*sqrt(c*x^2)/(a*x^2)-b*c*log(x)*sqrt(c*x^2)/(a^2*x)+b*c*log(a+b*x)*sqrt(c*x^2)/(a^2*x)],
[(c*x^2)^(3/2)/(x^6*(a+b*x)),x,3,-1/2*c*sqrt(c*x^2)/(a*x^3)+b*c*sqrt(c*x^2)/(a^2*x^2)+b^2*c*log(x)*sqrt(c*x^2)/(a^3*x)-b^2*c*log(a+b*x)*sqrt(c*x^2)/(a^3*x)],
[(c*x^2)^(3/2)/(x^7*(a+b*x)),x,3,-1/3*c*sqrt(c*x^2)/(a*x^4)+1/2*b*c*sqrt(c*x^2)/(a^2*x^3)-b^2*c*sqrt(c*x^2)/(a^3*x^2)-b^3*c*log(x)*sqrt(c*x^2)/(a^4*x)+b^3*c*log(a+b*x)*sqrt(c*x^2)/(a^4*x)],
[(c*x^2)^(5/2)/(a+b*x),x,3,a^4*c^2*sqrt(c*x^2)/b^5-1/2*a^3*c^2*x*sqrt(c*x^2)/b^4+1/3*a^2*c^2*x^2*sqrt(c*x^2)/b^3-1/4*a*c^2*x^3*sqrt(c*x^2)/b^2+1/5*c^2*x^4*sqrt(c*x^2)/b-a^5*c^2*log(a+b*x)*sqrt(c*x^2)/(b^6*x)],
[(c*x^2)^(5/2)/(x*(a+b*x)),x,3,-a^3*c^2*sqrt(c*x^2)/b^4+1/2*a^2*c^2*x*sqrt(c*x^2)/b^3-1/3*a*c^2*x^2*sqrt(c*x^2)/b^2+1/4*c^2*x^3*sqrt(c*x^2)/b+a^4*c^2*log(a+b*x)*sqrt(c*x^2)/(b^5*x)],
[(c*x^2)^(5/2)/(x^2*(a+b*x)),x,3,a^2*c^2*sqrt(c*x^2)/b^3-1/2*a*c^2*x*sqrt(c*x^2)/b^2+1/3*c^2*x^2*sqrt(c*x^2)/b-a^3*c^2*log(a+b*x)*sqrt(c*x^2)/(b^4*x)],
[(c*x^2)^(5/2)/(x^3*(a+b*x)),x,3,-a*c^2*sqrt(c*x^2)/b^2+1/2*c^2*x*sqrt(c*x^2)/b+a^2*c^2*log(a+b*x)*sqrt(c*x^2)/(b^3*x)],
[(c*x^2)^(5/2)/(x^4*(a+b*x)),x,3,c^2*sqrt(c*x^2)/b-a*c^2*log(a+b*x)*sqrt(c*x^2)/(b^2*x)],
[(c*x^2)^(5/2)/(x^5*(a+b*x)),x,2,c^2*log(a+b*x)*sqrt(c*x^2)/(b*x)],
[(c*x^2)^(5/2)/(x^6*(a+b*x)),x,4,c^2*log(x)*sqrt(c*x^2)/(a*x)-c^2*log(a+b*x)*sqrt(c*x^2)/(a*x)],
[(c*x^2)^(5/2)/(x^7*(a+b*x)),x,3,-c^2*sqrt(c*x^2)/(a*x^2)-b*c^2*log(x)*sqrt(c*x^2)/(a^2*x)+b*c^2*log(a+b*x)*sqrt(c*x^2)/(a^2*x)],

# p<0
[x^4/((a+b*x)*sqrt(c*x^2)),x,3,a^2*x^2/(b^3*sqrt(c*x^2))-1/2*a*x^3/(b^2*sqrt(c*x^2))+1/3*x^4/(b*sqrt(c*x^2))-a^3*x*log(a+b*x)/(b^4*sqrt(c*x^2))],
[x^3/((a+b*x)*sqrt(c*x^2)),x,3,-a*x^2/(b^2*sqrt(c*x^2))+1/2*x^3/(b*sqrt(c*x^2))+a^2*x*log(a+b*x)/(b^3*sqrt(c*x^2))],
[x^2/((a+b*x)*sqrt(c*x^2)),x,3,x^2/(b*sqrt(c*x^2))-a*x*log(a+b*x)/(b^2*sqrt(c*x^2))],
[x/((a+b*x)*sqrt(c*x^2)),x,2,x*log(a+b*x)/(b*sqrt(c*x^2))],
[1/((a+b*x)*sqrt(c*x^2)),x,4,x*log(x)/(a*sqrt(c*x^2))-x*log(a+b*x)/(a*sqrt(c*x^2))],
[1/(x*(a+b*x)*sqrt(c*x^2)),x,3,(-1)/(a*sqrt(c*x^2))-b*x*log(x)/(a^2*sqrt(c*x^2))+b*x*log(a+b*x)/(a^2*sqrt(c*x^2))],
[1/(x^2*(a+b*x)*sqrt(c*x^2)),x,3,b/(a^2*sqrt(c*x^2))+(-1/2)/(a*x*sqrt(c*x^2))+b^2*x*log(x)/(a^3*sqrt(c*x^2))-b^2*x*log(a+b*x)/(a^3*sqrt(c*x^2))],
[1/(x^3*(a+b*x)*sqrt(c*x^2)),x,3,-b^2/(a^3*sqrt(c*x^2))+(-1/3)/(a*x^2*sqrt(c*x^2))+1/2*b/(a^2*x*sqrt(c*x^2))-b^3*x*log(x)/(a^4*sqrt(c*x^2))+b^3*x*log(a+b*x)/(a^4*sqrt(c*x^2))],
[x^6/((c*x^2)^(3/2)*(a+b*x)),x,3,a^2*x^2/(b^3*c*sqrt(c*x^2))-1/2*a*x^3/(b^2*c*sqrt(c*x^2))+1/3*x^4/(b*c*sqrt(c*x^2))-a^3*x*log(a+b*x)/(b^4*c*sqrt(c*x^2))],
[x^5/((c*x^2)^(3/2)*(a+b*x)),x,3,-a*x^2/(b^2*c*sqrt(c*x^2))+1/2*x^3/(b*c*sqrt(c*x^2))+a^2*x*log(a+b*x)/(b^3*c*sqrt(c*x^2))],
[x^4/((c*x^2)^(3/2)*(a+b*x)),x,3,x^2/(b*c*sqrt(c*x^2))-a*x*log(a+b*x)/(b^2*c*sqrt(c*x^2))],
[x^3/((c*x^2)^(3/2)*(a+b*x)),x,2,x*log(a+b*x)/(b*c*sqrt(c*x^2))],
[x^2/((c*x^2)^(3/2)*(a+b*x)),x,4,x*log(x)/(a*c*sqrt(c*x^2))-x*log(a+b*x)/(a*c*sqrt(c*x^2))],
[x/((c*x^2)^(3/2)*(a+b*x)),x,3,(-1)/(a*c*sqrt(c*x^2))-b*x*log(x)/(a^2*c*sqrt(c*x^2))+b*x*log(a+b*x)/(a^2*c*sqrt(c*x^2))],
[1/((c*x^2)^(3/2)*(a+b*x)),x,3,b/(a^2*c*sqrt(c*x^2))+(-1/2)/(a*c*x*sqrt(c*x^2))+b^2*x*log(x)/(a^3*c*sqrt(c*x^2))-b^2*x*log(a+b*x)/(a^3*c*sqrt(c*x^2))],
[1/(x*(c*x^2)^(3/2)*(a+b*x)),x,3,-b^2/(a^3*c*sqrt(c*x^2))+(-1/3)/(a*c*x^2*sqrt(c*x^2))+1/2*b/(a^2*c*x*sqrt(c*x^2))-b^3*x*log(x)/(a^4*c*sqrt(c*x^2))+b^3*x*log(a+b*x)/(a^4*c*sqrt(c*x^2))],

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

# p>0
[x^3*sqrt(c*x^2)/(a+b*x)^2,x,3,3*a^2*sqrt(c*x^2)/b^4-a*x*sqrt(c*x^2)/b^3+1/3*x^2*sqrt(c*x^2)/b^2-a^4*sqrt(c*x^2)/(b^5*x*(a+b*x))-4*a^3*log(a+b*x)*sqrt(c*x^2)/(b^5*x)],
[x^2*sqrt(c*x^2)/(a+b*x)^2,x,3,-2*a*sqrt(c*x^2)/b^3+1/2*x*sqrt(c*x^2)/b^2+a^3*sqrt(c*x^2)/(b^4*x*(a+b*x))+3*a^2*log(a+b*x)*sqrt(c*x^2)/(b^4*x)],
[x*sqrt(c*x^2)/(a+b*x)^2,x,3,sqrt(c*x^2)/b^2-a^2*sqrt(c*x^2)/(b^3*x*(a+b*x))-2*a*log(a+b*x)*sqrt(c*x^2)/(b^3*x)],
[sqrt(c*x^2)/(a+b*x)^2,x,3,a*sqrt(c*x^2)/(b^2*x*(a+b*x))+log(a+b*x)*sqrt(c*x^2)/(b^2*x)],
[sqrt(c*x^2)/(x*(a+b*x)^2),x,2,-sqrt(c*x^2)/(b*x*(a+b*x))],
[sqrt(c*x^2)/(x^2*(a+b*x)^2),x,3,sqrt(c*x^2)/(a*x*(a+b*x))+log(x)*sqrt(c*x^2)/(a^2*x)-log(a+b*x)*sqrt(c*x^2)/(a^2*x)],
[sqrt(c*x^2)/(x^3*(a+b*x)^2),x,3,-sqrt(c*x^2)/(a^2*x^2)-b*sqrt(c*x^2)/(a^2*x*(a+b*x))-2*b*log(x)*sqrt(c*x^2)/(a^3*x)+2*b*log(a+b*x)*sqrt(c*x^2)/(a^3*x)],
[sqrt(c*x^2)/(x^4*(a+b*x)^2),x,3,-1/2*sqrt(c*x^2)/(a^2*x^3)+2*b*sqrt(c*x^2)/(a^3*x^2)+b^2*sqrt(c*x^2)/(a^3*x*(a+b*x))+3*b^2*log(x)*sqrt(c*x^2)/(a^4*x)-3*b^2*log(a+b*x)*sqrt(c*x^2)/(a^4*x)],
[x*(c*x^2)^(3/2)/(a+b*x)^2,x,3,3*a^2*c*sqrt(c*x^2)/b^4-a*c*x*sqrt(c*x^2)/b^3+1/3*c*x^2*sqrt(c*x^2)/b^2-a^4*c*sqrt(c*x^2)/(b^5*x*(a+b*x))-4*a^3*c*log(a+b*x)*sqrt(c*x^2)/(b^5*x)],
[(c*x^2)^(3/2)/(a+b*x)^2,x,3,-2*a*c*sqrt(c*x^2)/b^3+1/2*c*x*sqrt(c*x^2)/b^2+a^3*c*sqrt(c*x^2)/(b^4*x*(a+b*x))+3*a^2*c*log(a+b*x)*sqrt(c*x^2)/(b^4*x)],
[(c*x^2)^(3/2)/(x*(a+b*x)^2),x,3,c*sqrt(c*x^2)/b^2-a^2*c*sqrt(c*x^2)/(b^3*x*(a+b*x))-2*a*c*log(a+b*x)*sqrt(c*x^2)/(b^3*x)],
[(c*x^2)^(3/2)/(x^2*(a+b*x)^2),x,3,a*c*sqrt(c*x^2)/(b^2*x*(a+b*x))+c*log(a+b*x)*sqrt(c*x^2)/(b^2*x)],
[(c*x^2)^(3/2)/(x^3*(a+b*x)^2),x,2,-c*sqrt(c*x^2)/(b*x*(a+b*x))],
[(c*x^2)^(3/2)/(x^4*(a+b*x)^2),x,3,c*sqrt(c*x^2)/(a*x*(a+b*x))+c*log(x)*sqrt(c*x^2)/(a^2*x)-c*log(a+b*x)*sqrt(c*x^2)/(a^2*x)],
[(c*x^2)^(3/2)/(x^5*(a+b*x)^2),x,3,-c*sqrt(c*x^2)/(a^2*x^2)-b*c*sqrt(c*x^2)/(a^2*x*(a+b*x))-2*b*c*log(x)*sqrt(c*x^2)/(a^3*x)+2*b*c*log(a+b*x)*sqrt(c*x^2)/(a^3*x)],
[(c*x^2)^(3/2)/(x^6*(a+b*x)^2),x,3,-1/2*c*sqrt(c*x^2)/(a^2*x^3)+2*b*c*sqrt(c*x^2)/(a^3*x^2)+b^2*c*sqrt(c*x^2)/(a^3*x*(a+b*x))+3*b^2*c*log(x)*sqrt(c*x^2)/(a^4*x)-3*b^2*c*log(a+b*x)*sqrt(c*x^2)/(a^4*x)],

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

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

# p>0
[x^2*(a+b*x)^n*sqrt(c*x^2),x,3,-a^3*(a+b*x)^(1+n)*sqrt(c*x^2)/(b^4*(1+n)*x)+3*a^2*(a+b*x)^(2+n)*sqrt(c*x^2)/(b^4*(2+n)*x)-3*a*(a+b*x)^(3+n)*sqrt(c*x^2)/(b^4*(3+n)*x)+(a+b*x)^(4+n)*sqrt(c*x^2)/(b^4*(4+n)*x)],
[x*(a+b*x)^n*sqrt(c*x^2),x,3,a^2*(a+b*x)^(1+n)*sqrt(c*x^2)/(b^3*(1+n)*x)-2*a*(a+b*x)^(2+n)*sqrt(c*x^2)/(b^3*(2+n)*x)+(a+b*x)^(3+n)*sqrt(c*x^2)/(b^3*(3+n)*x)],
[(a+b*x)^n*sqrt(c*x^2),x,3,-a*(a+b*x)^(1+n)*sqrt(c*x^2)/(b^2*(1+n)*x)+(a+b*x)^(2+n)*sqrt(c*x^2)/(b^2*(2+n)*x)],
[(a+b*x)^n*sqrt(c*x^2)/x,x,2,(a+b*x)^(1+n)*sqrt(c*x^2)/(b*(1+n)*x)],
[(a+b*x)^n*sqrt(c*x^2)/x^2,x,2,-(a+b*x)^(1+n)*hypergeom([1,1+n],[2+n],1+b*x/a)*sqrt(c*x^2)/(a*(1+n)*x)],
[(a+b*x)^n*sqrt(c*x^2)/x^3,x,2,b*(a+b*x)^(1+n)*hypergeom([2,1+n],[2+n],1+b*x/a)*sqrt(c*x^2)/(a^2*(1+n)*x)],
[(a+b*x)^n*sqrt(c*x^2)/x^4,x,2,-b^2*(a+b*x)^(1+n)*hypergeom([3,1+n],[2+n],1+b*x/a)*sqrt(c*x^2)/(a^3*(1+n)*x)],
[x*(c*x^2)^(3/2)*(a+b*x)^n,x,3,a^4*c*(a+b*x)^(1+n)*sqrt(c*x^2)/(b^5*(1+n)*x)-4*a^3*c*(a+b*x)^(2+n)*sqrt(c*x^2)/(b^5*(2+n)*x)+6*a^2*c*(a+b*x)^(3+n)*sqrt(c*x^2)/(b^5*(3+n)*x)-4*a*c*(a+b*x)^(4+n)*sqrt(c*x^2)/(b^5*(4+n)*x)+c*(a+b*x)^(5+n)*sqrt(c*x^2)/(b^5*(5+n)*x)],
[(c*x^2)^(3/2)*(a+b*x)^n,x,3,-a^3*c*(a+b*x)^(1+n)*sqrt(c*x^2)/(b^4*(1+n)*x)+3*a^2*c*(a+b*x)^(2+n)*sqrt(c*x^2)/(b^4*(2+n)*x)-3*a*c*(a+b*x)^(3+n)*sqrt(c*x^2)/(b^4*(3+n)*x)+c*(a+b*x)^(4+n)*sqrt(c*x^2)/(b^4*(4+n)*x)],
[(c*x^2)^(3/2)*(a+b*x)^n/x,x,3,a^2*c*(a+b*x)^(1+n)*sqrt(c*x^2)/(b^3*(1+n)*x)-2*a*c*(a+b*x)^(2+n)*sqrt(c*x^2)/(b^3*(2+n)*x)+c*(a+b*x)^(3+n)*sqrt(c*x^2)/(b^3*(3+n)*x)],
[(c*x^2)^(3/2)*(a+b*x)^n/x^2,x,3,-a*c*(a+b*x)^(1+n)*sqrt(c*x^2)/(b^2*(1+n)*x)+c*(a+b*x)^(2+n)*sqrt(c*x^2)/(b^2*(2+n)*x)],
[(c*x^2)^(3/2)*(a+b*x)^n/x^3,x,2,c*(a+b*x)^(1+n)*sqrt(c*x^2)/(b*(1+n)*x)],
[(c*x^2)^(3/2)*(a+b*x)^n/x^4,x,2,-c*(a+b*x)^(1+n)*hypergeom([1,1+n],[2+n],1+b*x/a)*sqrt(c*x^2)/(a*(1+n)*x)],
[(c*x^2)^(3/2)*(a+b*x)^n/x^5,x,2,b*c*(a+b*x)^(1+n)*hypergeom([2,1+n],[2+n],1+b*x/a)*sqrt(c*x^2)/(a^2*(1+n)*x)],
[(c*x^2)^(3/2)*(a+b*x)^n/x^6,x,2,-b^2*c*(a+b*x)^(1+n)*hypergeom([3,1+n],[2+n],1+b*x/a)*sqrt(c*x^2)/(a^3*(1+n)*x)],
[(c*x^2)^(5/2)*(a+b*x)^n,x,3,-a^5*c^2*(a+b*x)^(1+n)*sqrt(c*x^2)/(b^6*(1+n)*x)+5*a^4*c^2*(a+b*x)^(2+n)*sqrt(c*x^2)/(b^6*(2+n)*x)-10*a^3*c^2*(a+b*x)^(3+n)*sqrt(c*x^2)/(b^6*(3+n)*x)+10*a^2*c^2*(a+b*x)^(4+n)*sqrt(c*x^2)/(b^6*(4+n)*x)-5*a*c^2*(a+b*x)^(5+n)*sqrt(c*x^2)/(b^6*(5+n)*x)+c^2*(a+b*x)^(6+n)*sqrt(c*x^2)/(b^6*(6+n)*x)],
[(c*x^2)^(5/2)*(a+b*x)^n/x,x,3,a^4*c^2*(a+b*x)^(1+n)*sqrt(c*x^2)/(b^5*(1+n)*x)-4*a^3*c^2*(a+b*x)^(2+n)*sqrt(c*x^2)/(b^5*(2+n)*x)+6*a^2*c^2*(a+b*x)^(3+n)*sqrt(c*x^2)/(b^5*(3+n)*x)-4*a*c^2*(a+b*x)^(4+n)*sqrt(c*x^2)/(b^5*(4+n)*x)+c^2*(a+b*x)^(5+n)*sqrt(c*x^2)/(b^5*(5+n)*x)],
[(c*x^2)^(5/2)*(a+b*x)^n/x^2,x,3,-a^3*c^2*(a+b*x)^(1+n)*sqrt(c*x^2)/(b^4*(1+n)*x)+3*a^2*c^2*(a+b*x)^(2+n)*sqrt(c*x^2)/(b^4*(2+n)*x)-3*a*c^2*(a+b*x)^(3+n)*sqrt(c*x^2)/(b^4*(3+n)*x)+c^2*(a+b*x)^(4+n)*sqrt(c*x^2)/(b^4*(4+n)*x)],
[(c*x^2)^(5/2)*(a+b*x)^n/x^3,x,3,a^2*c^2*(a+b*x)^(1+n)*sqrt(c*x^2)/(b^3*(1+n)*x)-2*a*c^2*(a+b*x)^(2+n)*sqrt(c*x^2)/(b^3*(2+n)*x)+c^2*(a+b*x)^(3+n)*sqrt(c*x^2)/(b^3*(3+n)*x)],
[(c*x^2)^(5/2)*(a+b*x)^n/x^4,x,3,-a*c^2*(a+b*x)^(1+n)*sqrt(c*x^2)/(b^2*(1+n)*x)+c^2*(a+b*x)^(2+n)*sqrt(c*x^2)/(b^2*(2+n)*x)],
[(c*x^2)^(5/2)*(a+b*x)^n/x^5,x,2,c^2*(a+b*x)^(1+n)*sqrt(c*x^2)/(b*(1+n)*x)],
[(c*x^2)^(5/2)*(a+b*x)^n/x^6,x,2,-c^2*(a+b*x)^(1+n)*hypergeom([1,1+n],[2+n],1+b*x/a)*sqrt(c*x^2)/(a*(1+n)*x)],
[(c*x^2)^(5/2)*(a+b*x)^n/x^7,x,2,b*c^2*(a+b*x)^(1+n)*hypergeom([2,1+n],[2+n],1+b*x/a)*sqrt(c*x^2)/(a^2*(1+n)*x)],

# p<0
[x^4*(a+b*x)^n/sqrt(c*x^2),x,3,-a^3*x*(a+b*x)^(1+n)/(b^4*(1+n)*sqrt(c*x^2))+3*a^2*x*(a+b*x)^(2+n)/(b^4*(2+n)*sqrt(c*x^2))-3*a*x*(a+b*x)^(3+n)/(b^4*(3+n)*sqrt(c*x^2))+x*(a+b*x)^(4+n)/(b^4*(4+n)*sqrt(c*x^2))],
[x^3*(a+b*x)^n/sqrt(c*x^2),x,3,a^2*x*(a+b*x)^(1+n)/(b^3*(1+n)*sqrt(c*x^2))-2*a*x*(a+b*x)^(2+n)/(b^3*(2+n)*sqrt(c*x^2))+x*(a+b*x)^(3+n)/(b^3*(3+n)*sqrt(c*x^2))],
[x^2*(a+b*x)^n/sqrt(c*x^2),x,3,-a*x*(a+b*x)^(1+n)/(b^2*(1+n)*sqrt(c*x^2))+x*(a+b*x)^(2+n)/(b^2*(2+n)*sqrt(c*x^2))],
[x*(a+b*x)^n/sqrt(c*x^2),x,2,x*(a+b*x)^(1+n)/(b*(1+n)*sqrt(c*x^2))],
[(a+b*x)^n/sqrt(c*x^2),x,2,-x*(a+b*x)^(1+n)*hypergeom([1,1+n],[2+n],1+b*x/a)/(a*(1+n)*sqrt(c*x^2))],
[(a+b*x)^n/(x*sqrt(c*x^2)),x,2,b*x*(a+b*x)^(1+n)*hypergeom([2,1+n],[2+n],1+b*x/a)/(a^2*(1+n)*sqrt(c*x^2))],
[(a+b*x)^n/(x^2*sqrt(c*x^2)),x,2,-b^2*x*(a+b*x)^(1+n)*hypergeom([3,1+n],[2+n],1+b*x/a)/(a^3*(1+n)*sqrt(c*x^2))],
[x^6*(a+b*x)^n/(c*x^2)^(3/2),x,3,-a^3*x*(a+b*x)^(1+n)/(b^4*c*(1+n)*sqrt(c*x^2))+3*a^2*x*(a+b*x)^(2+n)/(b^4*c*(2+n)*sqrt(c*x^2))-3*a*x*(a+b*x)^(3+n)/(b^4*c*(3+n)*sqrt(c*x^2))+x*(a+b*x)^(4+n)/(b^4*c*(4+n)*sqrt(c*x^2))],
[x^5*(a+b*x)^n/(c*x^2)^(3/2),x,3,a^2*x*(a+b*x)^(1+n)/(b^3*c*(1+n)*sqrt(c*x^2))-2*a*x*(a+b*x)^(2+n)/(b^3*c*(2+n)*sqrt(c*x^2))+x*(a+b*x)^(3+n)/(b^3*c*(3+n)*sqrt(c*x^2))],
[x^4*(a+b*x)^n/(c*x^2)^(3/2),x,3,-a*x*(a+b*x)^(1+n)/(b^2*c*(1+n)*sqrt(c*x^2))+x*(a+b*x)^(2+n)/(b^2*c*(2+n)*sqrt(c*x^2))],
[x^3*(a+b*x)^n/(c*x^2)^(3/2),x,2,x*(a+b*x)^(1+n)/(b*c*(1+n)*sqrt(c*x^2))],
[x^2*(a+b*x)^n/(c*x^2)^(3/2),x,2,-x*(a+b*x)^(1+n)*hypergeom([1,1+n],[2+n],1+b*x/a)/(a*c*(1+n)*sqrt(c*x^2))],
[x*(a+b*x)^n/(c*x^2)^(3/2),x,2,b*x*(a+b*x)^(1+n)*hypergeom([2,1+n],[2+n],1+b*x/a)/(a^2*c*(1+n)*sqrt(c*x^2))],
[(a+b*x)^n/(c*x^2)^(3/2),x,2,-b^2*x*(a+b*x)^(1+n)*hypergeom([3,1+n],[2+n],1+b*x/a)/(a^3*c*(1+n)*sqrt(c*x^2))],
[(a+b*x)^n/(x*(c*x^2)^(3/2)),x,2,b^3*x*(a+b*x)^(1+n)*hypergeom([4,1+n],[2+n],1+b*x/a)/(a^4*c*(1+n)*sqrt(c*x^2))],
[x^8*(a+b*x)^n/(c*x^2)^(5/2),x,3,-a^3*x*(a+b*x)^(1+n)/(b^4*c^2*(1+n)*sqrt(c*x^2))+3*a^2*x*(a+b*x)^(2+n)/(b^4*c^2*(2+n)*sqrt(c*x^2))-3*a*x*(a+b*x)^(3+n)/(b^4*c^2*(3+n)*sqrt(c*x^2))+x*(a+b*x)^(4+n)/(b^4*c^2*(4+n)*sqrt(c*x^2))],
[x^7*(a+b*x)^n/(c*x^2)^(5/2),x,3,a^2*x*(a+b*x)^(1+n)/(b^3*c^2*(1+n)*sqrt(c*x^2))-2*a*x*(a+b*x)^(2+n)/(b^3*c^2*(2+n)*sqrt(c*x^2))+x*(a+b*x)^(3+n)/(b^3*c^2*(3+n)*sqrt(c*x^2))],
[x^6*(a+b*x)^n/(c*x^2)^(5/2),x,3,-a*x*(a+b*x)^(1+n)/(b^2*c^2*(1+n)*sqrt(c*x^2))+x*(a+b*x)^(2+n)/(b^2*c^2*(2+n)*sqrt(c*x^2))],
[x^5*(a+b*x)^n/(c*x^2)^(5/2),x,2,x*(a+b*x)^(1+n)/(b*c^2*(1+n)*sqrt(c*x^2))],
[x^4*(a+b*x)^n/(c*x^2)^(5/2),x,2,-x*(a+b*x)^(1+n)*hypergeom([1,1+n],[2+n],1+b*x/a)/(a*c^2*(1+n)*sqrt(c*x^2))],
[x^3*(a+b*x)^n/(c*x^2)^(5/2),x,2,b*x*(a+b*x)^(1+n)*hypergeom([2,1+n],[2+n],1+b*x/a)/(a^2*c^2*(1+n)*sqrt(c*x^2))],
[x^2*(a+b*x)^n/(c*x^2)^(5/2),x,2,-b^2*x*(a+b*x)^(1+n)*hypergeom([3,1+n],[2+n],1+b*x/a)/(a^3*c^2*(1+n)*sqrt(c*x^2))],
[x*(a+b*x)^n/(c*x^2)^(5/2),x,2,b^3*x*(a+b*x)^(1+n)*hypergeom([4,1+n],[2+n],1+b*x/a)/(a^4*c^2*(1+n)*sqrt(c*x^2))],

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

# n>0
[(d*x)^m*(c*x^2)^(5/2)*(a+b*x),x,4,a*c^2*(d*x)^(6+m)*sqrt(c*x^2)/(d^6*(6+m)*x)+b*c^2*(d*x)^(7+m)*sqrt(c*x^2)/(d^7*(7+m)*x)],
[(d*x)^m*(c*x^2)^(3/2)*(a+b*x),x,4,a*c*(d*x)^(4+m)*sqrt(c*x^2)/(d^4*(4+m)*x)+b*c*(d*x)^(5+m)*sqrt(c*x^2)/(d^5*(5+m)*x)],
[(d*x)^m*(c*x^2)^(1/2)*(a+b*x),x,4,a*(d*x)^(2+m)*sqrt(c*x^2)/(d^2*(2+m)*x)+b*(d*x)^(3+m)*sqrt(c*x^2)/(d^3*(3+m)*x)],
[(d*x)^m*(a+b*x)/(c*x^2)^(1/2),x,4,a*x*(d*x)^m/(m*sqrt(c*x^2))+b*x*(d*x)^(1+m)/(d*(1+m)*sqrt(c*x^2))],
[(d*x)^m*(a+b*x)/(c*x^2)^(3/2),x,4,-a*d^2*x*(d*x)^(-2+m)/(c*(2-m)*sqrt(c*x^2))-b*d*x*(d*x)^(-1+m)/(c*(1-m)*sqrt(c*x^2))],
[(d*x)^m*(a+b*x)/(c*x^2)^(5/2),x,4,-a*d^4*x*(d*x)^(-4+m)/(c^2*(4-m)*sqrt(c*x^2))-b*d^3*x*(d*x)^(-3+m)/(c^2*(3-m)*sqrt(c*x^2))],
[(d*x)^m*(c*x^2)^(5/2)*(a+b*x)^2,x,4,a^2*c^2*(d*x)^(6+m)*sqrt(c*x^2)/(d^6*(6+m)*x)+2*a*b*c^2*(d*x)^(7+m)*sqrt(c*x^2)/(d^7*(7+m)*x)+b^2*c^2*(d*x)^(8+m)*sqrt(c*x^2)/(d^8*(8+m)*x)],
[(d*x)^m*(c*x^2)^(3/2)*(a+b*x)^2,x,4,a^2*c*(d*x)^(4+m)*sqrt(c*x^2)/(d^4*(4+m)*x)+2*a*b*c*(d*x)^(5+m)*sqrt(c*x^2)/(d^5*(5+m)*x)+b^2*c*(d*x)^(6+m)*sqrt(c*x^2)/(d^6*(6+m)*x)],
[(d*x)^m*(c*x^2)^(1/2)*(a+b*x)^2,x,4,a^2*(d*x)^(2+m)*sqrt(c*x^2)/(d^2*(2+m)*x)+2*a*b*(d*x)^(3+m)*sqrt(c*x^2)/(d^3*(3+m)*x)+b^2*(d*x)^(4+m)*sqrt(c*x^2)/(d^4*(4+m)*x)],
[(d*x)^m*(a+b*x)^2/(c*x^2)^(1/2),x,4,a^2*x*(d*x)^m/(m*sqrt(c*x^2))+2*a*b*x*(d*x)^(1+m)/(d*(1+m)*sqrt(c*x^2))+b^2*x*(d*x)^(2+m)/(d^2*(2+m)*sqrt(c*x^2))],
[(d*x)^m*(a+b*x)^2/(c*x^2)^(3/2),x,4,-a^2*d^2*x*(d*x)^(-2+m)/(c*(2-m)*sqrt(c*x^2))-2*a*b*d*x*(d*x)^(-1+m)/(c*(1-m)*sqrt(c*x^2))+b^2*x*(d*x)^m/(c*m*sqrt(c*x^2))],
[(d*x)^m*(a+b*x)^2/(c*x^2)^(5/2),x,4,-a^2*d^4*x*(d*x)^(-4+m)/(c^2*(4-m)*sqrt(c*x^2))-2*a*b*d^3*x*(d*x)^(-3+m)/(c^2*(3-m)*sqrt(c*x^2))-b^2*d^2*x*(d*x)^(-2+m)/(c^2*(2-m)*sqrt(c*x^2))],

# n<0

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

# Integrands of the form (d x)^m (c x^2)^p (a+b x)^n when -n=2 p+m+2

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

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

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

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

# Integrands of the form (a+b x)^m (c+d x)^n when b c-a d=0

# Integrands of the form (a+b x)^m (a d/b+d x)^n when b c-a d=0
[(a+b*x)^5/(a*d/b+d*x)^3,x,2,1/3*b^2*(a+b*x)^3/d^3],
[(a+b*x)^4/(a*d/b+d*x)^3,x,2,a*b^3*x/d^3+1/2*b^4*x^2/d^3],
[(a+b*x)^3/(a*d/b+d*x)^3,x,2,b^3*x/d^3],
[(a+b*x)^2/(a*d/b+d*x)^3,x,2,b^2*log(a+b*x)/d^3],
[(a+b*x)/(a*d/b+d*x)^3,x,2,-b^2/(d^3*(a+b*x))],
[1/((a+b*x)*(a*d/b+d*x)^3),x,2,-1/3*b^2/(d^3*(a+b*x)^3)],
[1/((a+b*x)^2*(a*d/b+d*x)^3),x,2,-1/4*b^2/(d^3*(a+b*x)^4)],
[1/((a+b*x)^3*(a*d/b+d*x)^3),x,2,-1/5*b^2/(d^3*(a+b*x)^5)],
[(b*c/d+b*x)^5/(c+d*x)^3,x,2,1/3*b^5*(c+d*x)^3/d^6],
[(b*c/d+b*x)^4/(c+d*x)^3,x,2,b^4*c*x/d^4+1/2*b^4*x^2/d^3],
[(b*c/d+b*x)^3/(c+d*x)^3,x,2,b^3*x/d^3],
[(b*c/d+b*x)^2/(c+d*x)^3,x,2,b^2*log(c+d*x)/d^3],
[(b*c/d+b*x)/(c+d*x)^3,x,2,-b/(d^2*(c+d*x))],
[1/((b*c/d+b*x)*(c+d*x)^3),x,2,(-1/3)/(b*(c+d*x)^3)],
[1/((b*c/d+b*x)^2*(c+d*x)^3),x,2,-1/4*d/(b^2*(c+d*x)^4)],
[1/((b*c/d+b*x)^3*(c+d*x)^3),x,2,-1/5*d^2/(b^3*(c+d*x)^5)],
[(a+b*x)^5*(a*c+b*c*x)^n,x,2,(a*c+b*c*x)^(6+n)/(b*c^6*(6+n))],
[(a+b*x)^5*(a*c+b*c*x)^3,x,2,1/9*c^3*(a+b*x)^9/b],
[(a+b*x)^5*(a*c+b*c*x)^2,x,2,1/8*c^2*(a+b*x)^8/b],
[(a+b*x)^5*(a*c+b*c*x),x,2,1/7*c*(a+b*x)^7/b],
[(a+b*x)^5/(a*c+b*c*x),x,2,1/5*(a+b*x)^5/(b*c)],
[(a+b*x)^5/(a*c+b*c*x)^2,x,2,1/4*(a+b*x)^4/(b*c^2)],
[(a+b*x)^5/(a*c+b*c*x)^3,x,2,1/3*(a+b*x)^3/(b*c^3)],
[(a+b*x)^5/(a*c+b*c*x)^4,x,2,a*x/c^4+1/2*b*x^2/c^4],
[(a+b*x)^5/(a*c+b*c*x)^5,x,2,x/c^5],
[(a+b*x)^5/(a*c+b*c*x)^6,x,2,log(a+b*x)/(b*c^6)],
[(a+b*x)^5/(a*c+b*c*x)^7,x,2,(-1)/(b*c^7*(a+b*x))],
[(a+b*x)^5/(a*c+b*c*x)^8,x,2,(-1/2)/(b*c^8*(a+b*x)^2)],
[1/(sqrt(-2-3*x)*sqrt(2+3*x)),x,2,1/3*log(2+3*x)*sqrt(2+3*x)/sqrt(-2-3*x)],

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

# Integrands of the form (a+b x)^m (a c-b c x)^n

# m>0
[(a+b*x)*(a*c-b*c*x)^3,x,2,-1/2*a*c^3*(a-b*x)^4/b+1/5*c^3*(a-b*x)^5/b],
[(a+b*x)*(a*c-b*c*x)^2,x,2,-2/3*a*c^2*(a-b*x)^3/b+1/4*c^2*(a-b*x)^4/b],
[(a+b*x)*(a*c-b*c*x),x,2,a^2*c*x-1/3*b^2*c*x^3],
[a+b*x,x,1,a*x+1/2*b*x^2],
[(a+b*x)/(a*c-b*c*x),x,2,-x/c-2*a*log(a-b*x)/(b*c)],
[(a+b*x)/(a*c-b*c*x)^2,x,2,2*a/(b*c^2*(a-b*x))+log(a-b*x)/(b*c^2)],
[(a+b*x)/(a*c-b*c*x)^3,x,1,x/(c^3*(a-b*x)^2)],
[(a+b*x)/(a*c-b*c*x)^4,x,2,2/3*a/(b*c^4*(a-b*x)^3)+(-1/2)/(b*c^4*(a-b*x)^2)],
[(a+b*x)/(a*c-b*c*x)^5,x,2,1/2*a/(b*c^5*(a-b*x)^4)+(-1/3)/(b*c^5*(a-b*x)^3)],
[(a+b*x)/(a*c-b*c*x)^6,x,2,2/5*a/(b*c^6*(a-b*x)^5)+(-1/4)/(b*c^6*(a-b*x)^4)],
[(a+b*x)^2*(a*c-b*c*x)^3,x,2,-a^2*c^3*(a-b*x)^4/b+4/5*a*c^3*(a-b*x)^5/b-1/6*c^3*(a-b*x)^6/b],
[(a+b*x)^2*(a*c-b*c*x)^2,x,3,a^4*c^2*x-2/3*a^2*b^2*c^2*x^3+1/5*b^4*c^2*x^5],
[(a+b*x)^2*(a*c-b*c*x),x,2,2/3*a*c*(a+b*x)^3/b-1/4*c*(a+b*x)^4/b],
[(a+b*x)^2,x,1,1/3*(a+b*x)^3/b],
[(a+b*x)^2/(a*c-b*c*x),x,2,-2*a*x/c-1/2*(a+b*x)^2/(b*c)-4*a^2*log(a-b*x)/(b*c)],
[(a+b*x)^2/(a*c-b*c*x)^2,x,2,x/c^2+4*a^2/(b*c^2*(a-b*x))+4*a*log(a-b*x)/(b*c^2)],
[(a+b*x)^2/(a*c-b*c*x)^3,x,2,2*a^2/(b*c^3*(a-b*x)^2)-4*a/(b*c^3*(a-b*x))-log(a-b*x)/(b*c^3)],
[(a+b*x)^2/(a*c-b*c*x)^4,x,1,1/6*(a+b*x)^3/(a*b*c^4*(a-b*x)^3)],
[(a+b*x)^2/(a*c-b*c*x)^5,x,2,a^2/(b*c^5*(a-b*x)^4)-4/3*a/(b*c^5*(a-b*x)^3)+1/2/(b*c^5*(a-b*x)^2)],
[(a+b*x)^2/(a*c-b*c*x)^6,x,2,4/5*a^2/(b*c^6*(a-b*x)^5)-a/(b*c^6*(a-b*x)^4)+1/3/(b*c^6*(a-b*x)^3)],
[(a+b*x)^2/(a*c-b*c*x)^7,x,2,2/3*a^2/(b*c^7*(a-b*x)^6)-4/5*a/(b*c^7*(a-b*x)^5)+1/4/(b*c^7*(a-b*x)^4)],

# m<0
[(a*c-b*c*x)^3/(a+b*x),x,2,-4*a^2*c^3*x+a*c^3*(a-b*x)^2/b+1/3*c^3*(a-b*x)^3/b+8*a^3*c^3*log(a+b*x)/b],
[(a*c-b*c*x)^2/(a+b*x),x,2,-2*a*c^2*x+1/2*c^2*(a-b*x)^2/b+4*a^2*c^2*log(a+b*x)/b],
[(a*c-b*c*x)/(a+b*x),x,2,-c*x+2*a*c*log(a+b*x)/b],
[1/(a+b*x),x,1,log(a+b*x)/b],
[1/((a+b*x)*(a*c-b*c*x)),x,2,arctanh(b*x/a)/(a*b*c)],
[1/((a+b*x)*(a*c-b*c*x)^2),x,3,1/2/(a*b*c^2*(a-b*x))+1/2*arctanh(b*x/a)/(a^2*b*c^2)],
[1/((a+b*x)*(a*c-b*c*x)^3),x,3,1/4/(a*b*c^3*(a-b*x)^2)+1/4/(a^2*b*c^3*(a-b*x))+1/4*arctanh(b*x/a)/(a^3*b*c^3)],
[(a*c-b*c*x)^3/(a+b*x)^2,x,2,5*a*c^3*x-1/2*b*c^3*x^2-8*a^3*c^3/(b*(a+b*x))-12*a^2*c^3*log(a+b*x)/b],
[(a*c-b*c*x)^2/(a+b*x)^2,x,2,c^2*x-4*a^2*c^2/(b*(a+b*x))-4*a*c^2*log(a+b*x)/b],
[(a*c-b*c*x)/(a+b*x)^2,x,2,-2*a*c/(b*(a+b*x))-c*log(a+b*x)/b],
[1/(a+b*x)^2,x,1,(-1)/(b*(a+b*x))],
[1/((a+b*x)^2*(a*c-b*c*x)),x,3,(-1/2)/(a*b*c*(a+b*x))+1/2*arctanh(b*x/a)/(a^2*b*c)],
[1/((a+b*x)^2*(a*c-b*c*x)^2),x,3,1/2*x/(a^2*c^2*(a^2-b^2*x^2))+1/2*arctanh(b*x/a)/(a^3*b*c^2)],
[1/((a+b*x)^2*(a*c-b*c*x)^3),x,3,1/8/(a^2*b*c^3*(a-b*x)^2)+1/4/(a^3*b*c^3*(a-b*x))+(-1/8)/(a^3*b*c^3*(a+b*x))+3/8*arctanh(b*x/a)/(a^4*b*c^3)],

# Integrands of the form (1 - x)^(m/2) (1 + x)^(n/2)

# n>0

#  Note: (1-x)^m*(1+x)^m == (1-x^2)^m 
[(1-x)^(9/2)*(1+x)^(1/2),x,7,7/8*(1-x)^(3/2)*(1+x)^(3/2)+21/40*(1-x)^(5/2)*(1+x)^(3/2)+3/10*(1-x)^(7/2)*(1+x)^(3/2)+1/6*(1-x)^(9/2)*(1+x)^(3/2)+21/16*arcsin(x)+21/16*x*sqrt(1-x)*sqrt(1+x)],
[(1-x)^(7/2)*(1+x)^(1/2),x,6,7/12*(1-x)^(3/2)*(1+x)^(3/2)+7/20*(1-x)^(5/2)*(1+x)^(3/2)+1/5*(1-x)^(7/2)*(1+x)^(3/2)+7/8*arcsin(x)+7/8*x*sqrt(1-x)*sqrt(1+x)],
[(1-x)^(5/2)*(1+x)^(1/2),x,5,5/12*(1-x)^(3/2)*(1+x)^(3/2)+1/4*(1-x)^(5/2)*(1+x)^(3/2)+5/8*arcsin(x)+5/8*x*sqrt(1-x)*sqrt(1+x)],
[(1-x)^(3/2)*(1+x)^(1/2),x,4,1/3*(1-x)^(3/2)*(1+x)^(3/2)+1/2*arcsin(x)+1/2*x*sqrt(1-x)*sqrt(1+x)],
[(1-x)^(1/2)*(1+x)^(1/2),x,3,1/2*arcsin(x)+1/2*x*sqrt(1-x)*sqrt(1+x)],
[(1+x)^(1/2)/(1-x)^(1/2),x,3,arcsin(x)-sqrt(1-x)*sqrt(1+x)],
[(1+x)^(1/2)/(1-x)^(3/2),x,3,-arcsin(x)+2*sqrt(1+x)/sqrt(1-x)],
[(1+x)^(1/2)/(1-x)^(5/2),x,1,1/3*(1+x)^(3/2)/(1-x)^(3/2)],
[(1+x)^(1/2)/(1-x)^(7/2),x,2,1/5*(1+x)^(3/2)/(1-x)^(5/2)+1/15*(1+x)^(3/2)/(1-x)^(3/2)],
[(1+x)^(1/2)/(1-x)^(9/2),x,3,1/7*(1+x)^(3/2)/(1-x)^(7/2)+2/35*(1+x)^(3/2)/(1-x)^(5/2)+2/105*(1+x)^(3/2)/(1-x)^(3/2)],
[(1+x)^(1/2)/(1-x)^(11/2),x,4,1/9*(1+x)^(3/2)/(1-x)^(9/2)+1/21*(1+x)^(3/2)/(1-x)^(7/2)+2/105*(1+x)^(3/2)/(1-x)^(5/2)+2/315*(1+x)^(3/2)/(1-x)^(3/2)],
[(1+x)^(1/2)/(1-x)^(13/2),x,5,1/11*(1+x)^(3/2)/(1-x)^(11/2)+4/99*(1+x)^(3/2)/(1-x)^(9/2)+4/231*(1+x)^(3/2)/(1-x)^(7/2)+8/1155*(1+x)^(3/2)/(1-x)^(5/2)+8/3465*(1+x)^(3/2)/(1-x)^(3/2)],
[(1-x)^(9/2)*(1+x)^(3/2),x,7,3/8*(1-x)^(3/2)*x*(1+x)^(3/2)+3/10*(1-x)^(5/2)*(1+x)^(5/2)+3/14*(1-x)^(7/2)*(1+x)^(5/2)+1/7*(1-x)^(9/2)*(1+x)^(5/2)+9/16*arcsin(x)+9/16*x*sqrt(1-x)*sqrt(1+x)],
[(1-x)^(7/2)*(1+x)^(3/2),x,6,7/24*(1-x)^(3/2)*x*(1+x)^(3/2)+7/30*(1-x)^(5/2)*(1+x)^(5/2)+1/6*(1-x)^(7/2)*(1+x)^(5/2)+7/16*arcsin(x)+7/16*x*sqrt(1-x)*sqrt(1+x)],
[(1-x)^(5/2)*(1+x)^(3/2),x,5,1/4*(1-x)^(3/2)*x*(1+x)^(3/2)+1/5*(1-x)^(5/2)*(1+x)^(5/2)+3/8*arcsin(x)+3/8*x*sqrt(1-x)*sqrt(1+x)],
[(1-x)^(3/2)*(1+x)^(3/2),x,4,1/4*(1-x)^(3/2)*x*(1+x)^(3/2)+3/8*arcsin(x)+3/8*x*sqrt(1-x)*sqrt(1+x)],
[(1-x)^(1/2)*(1+x)^(3/2),x,4,-1/3*(1-x)^(3/2)*(1+x)^(3/2)+1/2*arcsin(x)+1/2*x*sqrt(1-x)*sqrt(1+x)],
[(1+x)^(3/2)/(1-x)^(1/2),x,4,3/2*arcsin(x)-1/2*(1+x)^(3/2)*sqrt(1-x)-3/2*sqrt(1-x)*sqrt(1+x)],
[(1+x)^(3/2)/(1-x)^(3/2),x,4,-3*arcsin(x)+2*(1+x)^(3/2)/sqrt(1-x)+3*sqrt(1-x)*sqrt(1+x)],
[(1+x)^(3/2)/(1-x)^(5/2),x,4,2/3*(1+x)^(3/2)/(1-x)^(3/2)+arcsin(x)-2*sqrt(1+x)/sqrt(1-x)],
[(1+x)^(3/2)/(1-x)^(7/2),x,1,1/5*(1+x)^(5/2)/(1-x)^(5/2)],
[(1+x)^(3/2)/(1-x)^(9/2),x,2,1/7*(1+x)^(5/2)/(1-x)^(7/2)+1/35*(1+x)^(5/2)/(1-x)^(5/2)],
[(1+x)^(3/2)/(1-x)^(11/2),x,3,1/9*(1+x)^(5/2)/(1-x)^(9/2)+2/63*(1+x)^(5/2)/(1-x)^(7/2)+2/315*(1+x)^(5/2)/(1-x)^(5/2)],
[(1+x)^(3/2)/(1-x)^(13/2),x,4,1/11*(1+x)^(5/2)/(1-x)^(11/2)+1/33*(1+x)^(5/2)/(1-x)^(9/2)+2/231*(1+x)^(5/2)/(1-x)^(7/2)+2/1155*(1+x)^(5/2)/(1-x)^(5/2)],
[(1+x)^(3/2)/(1-x)^(15/2),x,5,1/13*(1+x)^(5/2)/(1-x)^(13/2)+4/143*(1+x)^(5/2)/(1-x)^(11/2)+4/429*(1+x)^(5/2)/(1-x)^(9/2)+8/3003*(1+x)^(5/2)/(1-x)^(7/2)+8/15015*(1+x)^(5/2)/(1-x)^(5/2)],
[(1-x)^(11/2)*(1+x)^(5/2),x,8,55/192*(1-x)^(3/2)*x*(1+x)^(3/2)+11/48*(1-x)^(5/2)*x*(1+x)^(5/2)+11/56*(1-x)^(7/2)*(1+x)^(7/2)+11/72*(1-x)^(9/2)*(1+x)^(7/2)+1/9*(1-x)^(11/2)*(1+x)^(7/2)+55/128*arcsin(x)+55/128*x*sqrt(1-x)*sqrt(1+x)],
[(1-x)^(9/2)*(1+x)^(5/2),x,7,15/64*(1-x)^(3/2)*x*(1+x)^(3/2)+3/16*(1-x)^(5/2)*x*(1+x)^(5/2)+9/56*(1-x)^(7/2)*(1+x)^(7/2)+1/8*(1-x)^(9/2)*(1+x)^(7/2)+45/128*arcsin(x)+45/128*x*sqrt(1-x)*sqrt(1+x)],
[(1-x)^(7/2)*(1+x)^(5/2),x,6,5/24*(1-x)^(3/2)*x*(1+x)^(3/2)+1/6*(1-x)^(5/2)*x*(1+x)^(5/2)+1/7*(1-x)^(7/2)*(1+x)^(7/2)+5/16*arcsin(x)+5/16*x*sqrt(1-x)*sqrt(1+x)],
[(1-x)^(5/2)*(1+x)^(5/2),x,5,5/24*(1-x)^(3/2)*x*(1+x)^(3/2)+1/6*(1-x)^(5/2)*x*(1+x)^(5/2)+5/16*arcsin(x)+5/16*x*sqrt(1-x)*sqrt(1+x)],
[(1-x)^(3/2)*(1+x)^(5/2),x,5,1/4*(1-x)^(3/2)*x*(1+x)^(3/2)-1/5*(1-x)^(5/2)*(1+x)^(5/2)+3/8*arcsin(x)+3/8*x*sqrt(1-x)*sqrt(1+x)],
[(1-x)^(1/2)*(1+x)^(5/2),x,5,-5/12*(1-x)^(3/2)*(1+x)^(3/2)-1/4*(1-x)^(3/2)*(1+x)^(5/2)+5/8*arcsin(x)+5/8*x*sqrt(1-x)*sqrt(1+x)],
[(1+x)^(5/2)/(1-x)^(1/2),x,5,5/2*arcsin(x)-5/6*(1+x)^(3/2)*sqrt(1-x)-1/3*(1+x)^(5/2)*sqrt(1-x)-5/2*sqrt(1-x)*sqrt(1+x)],
[(1+x)^(5/2)/(1-x)^(3/2),x,5,-15/2*arcsin(x)+2*(1+x)^(5/2)/sqrt(1-x)+5/2*(1+x)^(3/2)*sqrt(1-x)+15/2*sqrt(1-x)*sqrt(1+x)],
[(1+x)^(5/2)/(1-x)^(5/2),x,5,2/3*(1+x)^(5/2)/(1-x)^(3/2)+5*arcsin(x)-10/3*(1+x)^(3/2)/sqrt(1-x)-5*sqrt(1-x)*sqrt(1+x)],
[(1+x)^(5/2)/(1-x)^(7/2),x,5,-2/3*(1+x)^(3/2)/(1-x)^(3/2)+2/5*(1+x)^(5/2)/(1-x)^(5/2)-arcsin(x)+2*sqrt(1+x)/sqrt(1-x)],
[(1+x)^(5/2)/(1-x)^(9/2),x,1,1/7*(1+x)^(7/2)/(1-x)^(7/2)],
[(1+x)^(5/2)/(1-x)^(11/2),x,2,1/9*(1+x)^(7/2)/(1-x)^(9/2)+1/63*(1+x)^(7/2)/(1-x)^(7/2)],
[(1+x)^(5/2)/(1-x)^(13/2),x,3,1/11*(1+x)^(7/2)/(1-x)^(11/2)+2/99*(1+x)^(7/2)/(1-x)^(9/2)+2/693*(1+x)^(7/2)/(1-x)^(7/2)],
[(1+x)^(5/2)/(1-x)^(15/2),x,4,1/13*(1+x)^(7/2)/(1-x)^(13/2)+3/143*(1+x)^(7/2)/(1-x)^(11/2)+2/429*(1+x)^(7/2)/(1-x)^(9/2)+2/3003*(1+x)^(7/2)/(1-x)^(7/2)],
[(1+x)^(5/2)/(1-x)^(17/2),x,5,1/15*(1+x)^(7/2)/(1-x)^(15/2)+4/195*(1+x)^(7/2)/(1-x)^(13/2)+4/715*(1+x)^(7/2)/(1-x)^(11/2)+8/6435*(1+x)^(7/2)/(1-x)^(9/2)+8/45045*(1+x)^(7/2)/(1-x)^(7/2)],
[(1+x)^(5/2)/(1-x)^(19/2),x,6,1/17*(1+x)^(7/2)/(1-x)^(17/2)+1/51*(1+x)^(7/2)/(1-x)^(15/2)+4/663*(1+x)^(7/2)/(1-x)^(13/2)+4/2431*(1+x)^(7/2)/(1-x)^(11/2)+8/21879*(1+x)^(7/2)/(1-x)^(9/2)+8/153153*(1+x)^(7/2)/(1-x)^(7/2)],

#  Note: Following two integrands are equal. 
[(1+a*x)^(3/2)/sqrt(1-a*x),x,4,3/2*arcsin(a*x)/a-1/2*(1+a*x)^(3/2)*sqrt(1-a*x)/a-3/2*sqrt(1-a*x)*sqrt(1+a*x)/a],
[(1+a*x)*sqrt(1-a^2*x^2)/(1-a*x),x,3,-1/2*(1-a^2*x^2)^(3/2)/(a*(1-a*x))+3/2*arcsin(a*x)/a-3/2*sqrt(1-a^2*x^2)/a],

# n<0
[(1-x)^(7/2)/(1+x)^(1/2),x,6,35/8*arcsin(x)+35/24*(1-x)^(3/2)*sqrt(1+x)+7/12*(1-x)^(5/2)*sqrt(1+x)+1/4*(1-x)^(7/2)*sqrt(1+x)+35/8*sqrt(1-x)*sqrt(1+x)],
[(1-x)^(5/2)/(1+x)^(1/2),x,5,5/2*arcsin(x)+5/6*(1-x)^(3/2)*sqrt(1+x)+1/3*(1-x)^(5/2)*sqrt(1+x)+5/2*sqrt(1-x)*sqrt(1+x)],
[(1-x)^(3/2)/(1+x)^(1/2),x,4,3/2*arcsin(x)+1/2*(1-x)^(3/2)*sqrt(1+x)+3/2*sqrt(1-x)*sqrt(1+x)],
[(1-x)^(1/2)/(1+x)^(1/2),x,3,arcsin(x)+sqrt(1-x)*sqrt(1+x)],
[1/((1-x)^(1/2)*(1+x)^(1/2)),x,2,arcsin(x)],
[1/((1-x)^(3/2)*(1+x)^(1/2)),x,1,sqrt(1+x)/sqrt(1-x)],
[1/((1-x)^(5/2)*(1+x)^(1/2)),x,2,1/3*sqrt(1+x)/(1-x)^(3/2)+1/3*sqrt(1+x)/sqrt(1-x)],
[1/((1-x)^(7/2)*(1+x)^(1/2)),x,3,1/5*sqrt(1+x)/(1-x)^(5/2)+2/15*sqrt(1+x)/(1-x)^(3/2)+2/15*sqrt(1+x)/sqrt(1-x)],
[1/((1-x)^(9/2)*(1+x)^(1/2)),x,4,1/7*sqrt(1+x)/(1-x)^(7/2)+3/35*sqrt(1+x)/(1-x)^(5/2)+2/35*sqrt(1+x)/(1-x)^(3/2)+2/35*sqrt(1+x)/sqrt(1-x)],
[1/((1-x)^(11/2)*(1+x)^(1/2)),x,5,1/9*sqrt(1+x)/(1-x)^(9/2)+4/63*sqrt(1+x)/(1-x)^(7/2)+4/105*sqrt(1+x)/(1-x)^(5/2)+8/315*sqrt(1+x)/(1-x)^(3/2)+8/315*sqrt(1+x)/sqrt(1-x)],
[(1-x)^(7/2)/(1+x)^(3/2),x,6,-35/2*arcsin(x)-2*(1-x)^(7/2)/sqrt(1+x)-35/6*(1-x)^(3/2)*sqrt(1+x)-7/3*(1-x)^(5/2)*sqrt(1+x)-35/2*sqrt(1-x)*sqrt(1+x)],
[(1-x)^(5/2)/(1+x)^(3/2),x,5,-15/2*arcsin(x)-2*(1-x)^(5/2)/sqrt(1+x)-5/2*(1-x)^(3/2)*sqrt(1+x)-15/2*sqrt(1-x)*sqrt(1+x)],
[(1-x)^(3/2)/(1+x)^(3/2),x,4,-3*arcsin(x)-2*(1-x)^(3/2)/sqrt(1+x)-3*sqrt(1-x)*sqrt(1+x)],
[(1-x)^(1/2)/(1+x)^(3/2),x,3,-arcsin(x)-2*sqrt(1-x)/sqrt(1+x)],
[1/((1-x)^(1/2)*(1+x)^(3/2)),x,1,-sqrt(1-x)/sqrt(1+x)],
[1/((1-x)^(3/2)*(1+x)^(3/2)),x,1,x/(sqrt(1-x)*sqrt(1+x))],
[1/((1-x)^(5/2)*(1+x)^(3/2)),x,2,1/3/((1-x)^(3/2)*sqrt(1+x))+2/3*x/(sqrt(1-x)*sqrt(1+x))],
[1/((1-x)^(7/2)*(1+x)^(3/2)),x,3,1/5/((1-x)^(5/2)*sqrt(1+x))+1/5/((1-x)^(3/2)*sqrt(1+x))+2/5*x/(sqrt(1-x)*sqrt(1+x))],
[1/((1-x)^(9/2)*(1+x)^(3/2)),x,4,1/7/((1-x)^(7/2)*sqrt(1+x))+4/35/((1-x)^(5/2)*sqrt(1+x))+4/35/((1-x)^(3/2)*sqrt(1+x))+8/35*x/(sqrt(1-x)*sqrt(1+x))],
[1/((1-x)^(11/2)*(1+x)^(3/2)),x,5,1/9/((1-x)^(9/2)*sqrt(1+x))+5/63/((1-x)^(7/2)*sqrt(1+x))+4/63/((1-x)^(5/2)*sqrt(1+x))+4/63/((1-x)^(3/2)*sqrt(1+x))+8/63*x/(sqrt(1-x)*sqrt(1+x))],
[(1-x)^(9/2)/(1+x)^(5/2),x,7,-2/3*(1-x)^(9/2)/(1+x)^(3/2)+105/2*arcsin(x)+6*(1-x)^(7/2)/sqrt(1+x)+35/2*(1-x)^(3/2)*sqrt(1+x)+7*(1-x)^(5/2)*sqrt(1+x)+105/2*sqrt(1-x)*sqrt(1+x)],
[(1-x)^(7/2)/(1+x)^(5/2),x,6,-2/3*(1-x)^(7/2)/(1+x)^(3/2)+35/2*arcsin(x)+14/3*(1-x)^(5/2)/sqrt(1+x)+35/6*(1-x)^(3/2)*sqrt(1+x)+35/2*sqrt(1-x)*sqrt(1+x)],
[(1-x)^(5/2)/(1+x)^(5/2),x,5,-2/3*(1-x)^(5/2)/(1+x)^(3/2)+5*arcsin(x)+10/3*(1-x)^(3/2)/sqrt(1+x)+5*sqrt(1-x)*sqrt(1+x)],
[(1-x)^(3/2)/(1+x)^(5/2),x,4,-2/3*(1-x)^(3/2)/(1+x)^(3/2)+arcsin(x)+2*sqrt(1-x)/sqrt(1+x)],
[(1-x)^(1/2)/(1+x)^(5/2),x,1,-1/3*(1-x)^(3/2)/(1+x)^(3/2)],
[1/((1-x)^(1/2)*(1+x)^(5/2)),x,2,-1/3*sqrt(1-x)/(1+x)^(3/2)-1/3*sqrt(1-x)/sqrt(1+x)],
[1/((1-x)^(3/2)*(1+x)^(5/2)),x,3,1/((1+x)^(3/2)*sqrt(1-x))-2/3*sqrt(1-x)/(1+x)^(3/2)-2/3*sqrt(1-x)/sqrt(1+x)],
[1/((1-x)^(5/2)*(1+x)^(5/2)),x,2,1/3*x/((1-x)^(3/2)*(1+x)^(3/2))+2/3*x/(sqrt(1-x)*sqrt(1+x))],
[1/((1-x)^(7/2)*(1+x)^(5/2)),x,3,1/5/((1-x)^(5/2)*(1+x)^(3/2))+4/15*x/((1-x)^(3/2)*(1+x)^(3/2))+8/15*x/(sqrt(1-x)*sqrt(1+x))],
[1/((1-x)^(9/2)*(1+x)^(5/2)),x,4,1/7/((1-x)^(7/2)*(1+x)^(3/2))+1/7/((1-x)^(5/2)*(1+x)^(3/2))+4/21*x/((1-x)^(3/2)*(1+x)^(3/2))+8/21*x/(sqrt(1-x)*sqrt(1+x))],
[1/((1-x)^(11/2)*(1+x)^(5/2)),x,5,1/9/((1-x)^(9/2)*(1+x)^(3/2))+2/21/((1-x)^(7/2)*(1+x)^(3/2))+2/21/((1-x)^(5/2)*(1+x)^(3/2))+8/63*x/((1-x)^(3/2)*(1+x)^(3/2))+16/63*x/(sqrt(1-x)*sqrt(1+x))],

# Integrands of the form (a+b x)^(m/2) (c+d x)^(m/2) when b c+a d=0
[(a+a*x)^(5/2)*(c-c*x)^(5/2),x,6,5/24*a*c*x*(a+a*x)^(3/2)*(c-c*x)^(3/2)+1/6*x*(a+a*x)^(5/2)*(c-c*x)^(5/2)+5/8*a^(5/2)*c^(5/2)*arctan(sqrt(c)*sqrt(a+a*x)/(sqrt(a)*sqrt(c-c*x)))+5/16*a^2*c^2*x*sqrt(a+a*x)*sqrt(c-c*x)],
[(a+a*x)^(3/2)*(c-c*x)^(3/2),x,5,1/4*x*(a+a*x)^(3/2)*(c-c*x)^(3/2)+3/4*a^(3/2)*c^(3/2)*arctan(sqrt(c)*sqrt(a+a*x)/(sqrt(a)*sqrt(c-c*x)))+3/8*a*c*x*sqrt(a+a*x)*sqrt(c-c*x)],
[(a+a*x)^(1/2)*(c-c*x)^(1/2),x,4,arctan(sqrt(c)*sqrt(a+a*x)/(sqrt(a)*sqrt(c-c*x)))*sqrt(a)*sqrt(c)+1/2*x*sqrt(a+a*x)*sqrt(c-c*x)],
[1/((a+a*x)^(1/2)*(c-c*x)^(1/2)),x,3,2*arctan(sqrt(c)*sqrt(a+a*x)/(sqrt(a)*sqrt(c-c*x)))/(sqrt(a)*sqrt(c))],
[1/((a+a*x)^(3/2)*(c-c*x)^(3/2)),x,1,x/(a*c*sqrt(a+a*x)*sqrt(c-c*x))],
[1/((a+a*x)^(5/2)*(c-c*x)^(5/2)),x,2,1/3*x/(a*c*(a+a*x)^(3/2)*(c-c*x)^(3/2))+2/3*x/(a^2*c^2*sqrt(a+a*x)*sqrt(c-c*x))],
[1/((a+a*x)^(7/2)*(c-c*x)^(7/2)),x,3,1/5*x/(a*c*(a+a*x)^(5/2)*(c-c*x)^(5/2))+4/15*x/(a^2*c^2*(a+a*x)^(3/2)*(c-c*x)^(3/2))+8/15*x/(a^3*c^3*sqrt(a+a*x)*sqrt(c-c*x))],
[1/((a+a*x)^(9/2)*(c-c*x)^(9/2)),x,4,1/7*x/(a*c*(a+a*x)^(7/2)*(c-c*x)^(7/2))+6/35*x/(a^2*c^2*(a+a*x)^(5/2)*(c-c*x)^(5/2))+8/35*x/(a^3*c^3*(a+a*x)^(3/2)*(c-c*x)^(3/2))+16/35*x/(a^4*c^4*sqrt(a+a*x)*sqrt(c-c*x))],
[(a+b*x)^(5/2)*(a*c-b*c*x)^(5/2),x,6,5/24*a^2*c*x*(a+b*x)^(3/2)*(a*c-b*c*x)^(3/2)+1/6*x*(a+b*x)^(5/2)*(a*c-b*c*x)^(5/2)+5/8*a^6*c^(5/2)*arctan(sqrt(c)*sqrt(a+b*x)/sqrt(c*(a-b*x)))/b+5/16*a^4*c^2*x*sqrt(a+b*x)*sqrt(a*c-b*c*x)],
[(a+b*x)^(3/2)*(a*c-b*c*x)^(3/2),x,5,1/4*x*(a+b*x)^(3/2)*(a*c-b*c*x)^(3/2)+3/4*a^4*c^(3/2)*arctan(sqrt(c)*sqrt(a+b*x)/sqrt(c*(a-b*x)))/b+3/8*a^2*c*x*sqrt(a+b*x)*sqrt(a*c-b*c*x)],
[(a+b*x)^(1/2)*(a*c-b*c*x)^(1/2),x,4,a^2*arctan(sqrt(c)*sqrt(a+b*x)/sqrt(c*(a-b*x)))*sqrt(c)/b+1/2*x*sqrt(a+b*x)*sqrt(a*c-b*c*x)],
[1/((a+b*x)^(1/2)*(a*c-b*c*x)^(1/2)),x,3,2*arctan(sqrt(c)*sqrt(a+b*x)/sqrt(c*(a-b*x)))/(b*sqrt(c))],
[1/((a+b*x)^(3/2)*(a*c-b*c*x)^(3/2)),x,1,x/(a^2*c*sqrt(a+b*x)*sqrt(a*c-b*c*x))],
[1/((a+b*x)^(5/2)*(a*c-b*c*x)^(5/2)),x,2,1/3*x/(a^2*c*(a+b*x)^(3/2)*(a*c-b*c*x)^(3/2))+2/3*x/(a^4*c^2*sqrt(a+b*x)*sqrt(a*c-b*c*x))],
[1/((a+b*x)^(7/2)*(a*c-b*c*x)^(7/2)),x,3,1/5*x/(a^2*c*(a+b*x)^(5/2)*(a*c-b*c*x)^(5/2))+4/15*x/(a^4*c^2*(a+b*x)^(3/2)*(a*c-b*c*x)^(3/2))+8/15*x/(a^6*c^3*sqrt(a+b*x)*sqrt(a*c-b*c*x))],
[1/((a+b*x)^(9/2)*(a*c-b*c*x)^(9/2)),x,4,1/7*x/(a^2*c*(a+b*x)^(7/2)*(a*c-b*c*x)^(7/2))+6/35*x/(a^4*c^2*(a+b*x)^(5/2)*(a*c-b*c*x)^(5/2))+8/35*x/(a^6*c^3*(a+b*x)^(3/2)*(a*c-b*c*x)^(3/2))+16/35*x/(a^8*c^4*sqrt(a+b*x)*sqrt(a*c-b*c*x))],
[(3-6*x)^(5/2)*(2+4*x)^(5/2),x,5,15*(1-2*x)^(3/2)*x*(1+2*x)^(3/2)*sqrt(3/2)+45/4*arcsin(2*x)*sqrt(3/2)+6*(1-2*x)^(5/2)*x*(1+2*x)^(5/2)*sqrt(6)+45/2*x*sqrt(3/2)*sqrt(1-2*x)*sqrt(1+2*x)],
[(3-6*x)^(3/2)*(2+4*x)^(3/2),x,4,3*(1-2*x)^(3/2)*x*(1+2*x)^(3/2)*sqrt(3/2)+9/4*arcsin(2*x)*sqrt(3/2)+9/2*x*sqrt(3/2)*sqrt(1-2*x)*sqrt(1+2*x)],
[(3-6*x)^(1/2)*(2+4*x)^(1/2),x,3,1/2*arcsin(2*x)*sqrt(3/2)+x*sqrt(3/2)*sqrt(1-2*x)*sqrt(1+2*x)],
[1/((3-6*x)^(1/2)*(2+4*x)^(1/2)),x,2,1/2*arcsin(2*x)/sqrt(6)],
[1/((3-6*x)^(3/2)*(2+4*x)^(3/2)),x,1,1/6*x/(sqrt(6)*sqrt(1-2*x)*sqrt(1+2*x))],
[1/((3-6*x)^(5/2)*(2+4*x)^(5/2)),x,2,1/108*x/((1-2*x)^(3/2)*(1+2*x)^(3/2)*sqrt(6))+1/54*x/(sqrt(6)*sqrt(1-2*x)*sqrt(1+2*x))],
[1/((3-6*x)^(7/2)*(2+4*x)^(7/2)),x,3,1/1080*x/((1-2*x)^(5/2)*(1+2*x)^(5/2)*sqrt(6))+1/810*x/((1-2*x)^(3/2)*(1+2*x)^(3/2)*sqrt(6))+1/405*x/(sqrt(6)*sqrt(1-2*x)*sqrt(1+2*x))],

#  Note: (3-x)^m*(-2+x)^m == (-6+5*x-x^2)^m 
[(3-x)^(3/2)*(-2+x)^(3/2),x,7,-1/4*(3-x)^(5/2)*(-2+x)^(3/2)-3/128*arcsin(5-2*x)+1/32*(3-x)^(3/2)*sqrt(-2+x)-1/8*(3-x)^(5/2)*sqrt(-2+x)+3/64*sqrt(3-x)*sqrt(-2+x)],
[(3-x)^(1/2)*(-2+x)^(1/2),x,5,-1/8*arcsin(5-2*x)-1/2*(3-x)^(3/2)*sqrt(-2+x)+1/4*sqrt(3-x)*sqrt(-2+x)],
[1/((3-x)^(1/2)*(-2+x)^(1/2)),x,3,-arcsin(5-2*x)],
[1/((3-x)^(3/2)*(-2+x)^(3/2)),x,2,2/(sqrt(3-x)*sqrt(-2+x))-4*sqrt(3-x)/sqrt(-2+x)],
[1/((3-x)^(5/2)*(-2+x)^(5/2)),x,4,2/3/((3-x)^(3/2)*(-2+x)^(3/2))+4/((-2+x)^(3/2)*sqrt(3-x))-16/3*sqrt(3-x)/(-2+x)^(3/2)-32/3*sqrt(3-x)/sqrt(-2+x)],
[1/((3-x)^(3/2)*(3+x)^(3/2)),x,1,1/9*x/(sqrt(3-x)*sqrt(3+x))],
[1/((3-b*x)^(3/2)*(3+b*x)^(3/2)),x,1,1/9*x/(sqrt(3-b*x)*sqrt(3+b*x))],
[1/((6-2*x)^(3/2)*(3+x)^(3/2)),x,1,1/18*x/(sqrt(2)*sqrt(3-x)*sqrt(3+x))],
[1/((6-2*b*x)^(3/2)*(3+b*x)^(3/2)),x,1,1/18*x/(sqrt(2)*sqrt(3-b*x)*sqrt(3+b*x))],
[1/(sqrt(a+b*x)*sqrt(-a*d+b*d*x)),x,3,2*arctanh(sqrt(d)*sqrt(a+b*x)/sqrt(-a*d+b*d*x))/(b*sqrt(d))],

# Integrands of the form (a+b x)^(m/4) (c+d x)^(n/4) when b c+a d=0
[1/((6-3*e*x)^(1/4)*(2+e*x)^(3/4)),x,11,-log(sqrt(3)-(2-e*x)^(1/4)*sqrt(6)/(2+e*x)^(1/4)+sqrt(3)*sqrt(2-e*x)/sqrt(2+e*x))/(3^(1/4)*e*sqrt(2))+log(sqrt(3)+(2-e*x)^(1/4)*sqrt(6)/(2+e*x)^(1/4)+sqrt(3)*sqrt(2-e*x)/sqrt(2+e*x))/(3^(1/4)*e*sqrt(2))+arctan(1-(2-e*x)^(1/4)*sqrt(2)/(2+e*x)^(1/4))*sqrt(2)/(3^(1/4)*e)-arctan(1+(2-e*x)^(1/4)*sqrt(2)/(2+e*x)^(1/4))*sqrt(2)/(3^(1/4)*e)],

# n>0

# n<0
[(a-I*a*x)^(7/4)/(a+I*a*x)^(1/4),x,6,14/5*a^2*x/((a-I*a*x)^(1/4)*(a+I*a*x)^(1/4))-14/15*I*(a-I*a*x)^(3/4)*(a+I*a*x)^(3/4)-2/5*I*(a-I*a*x)^(7/4)*(a+I*a*x)^(3/4)/a-14/5*a^2*(1+x^2)^(1/4)*sqrt(cos(1/2*arctan(x))^2)/cos(1/2*arctan(x))*EllipticE(sin(1/2*arctan(x)),sqrt(2))/((a-I*a*x)^(1/4)*(a+I*a*x)^(1/4))],
[(a-I*a*x)^(3/4)/(a+I*a*x)^(1/4),x,5,2*a*x/((a-I*a*x)^(1/4)*(a+I*a*x)^(1/4))-2/3*I*(a-I*a*x)^(3/4)*(a+I*a*x)^(3/4)/a-2*a*(1+x^2)^(1/4)*sqrt(cos(1/2*arctan(x))^2)/cos(1/2*arctan(x))*EllipticE(sin(1/2*arctan(x)),sqrt(2))/((a-I*a*x)^(1/4)*(a+I*a*x)^(1/4))],
[1/((a-I*a*x)^(1/4)*(a+I*a*x)^(1/4)),x,4,2*x/((a-I*a*x)^(1/4)*(a+I*a*x)^(1/4))-2*(1+x^2)^(1/4)*sqrt(cos(1/2*arctan(x))^2)/cos(1/2*arctan(x))*EllipticE(sin(1/2*arctan(x)),sqrt(2))/((a-I*a*x)^(1/4)*(a+I*a*x)^(1/4))],
[1/((a-I*a*x)^(5/4)*(a+I*a*x)^(1/4)),x,4,(-2*I)/(a*(a-I*a*x)^(1/4)*(a+I*a*x)^(1/4))+2*(1+x^2)^(1/4)*sqrt(cos(1/2*arctan(x))^2)/cos(1/2*arctan(x))*EllipticE(sin(1/2*arctan(x)),sqrt(2))/(a*(a-I*a*x)^(1/4)*(a+I*a*x)^(1/4))],
[1/((a-I*a*x)^(9/4)*(a+I*a*x)^(1/4)),x,4,(-4/5*I)/(a*(a-I*a*x)^(5/4)*(a+I*a*x)^(1/4))+2/5*(1+x^2)^(1/4)*sqrt(cos(1/2*arctan(x))^2)/cos(1/2*arctan(x))*EllipticE(sin(1/2*arctan(x)),sqrt(2))/(a^2*(a-I*a*x)^(1/4)*(a+I*a*x)^(1/4))],
[1/((a-I*a*x)^(13/4)*(a+I*a*x)^(1/4)),x,5,(-4/15*I)/(a^2*(a-I*a*x)^(5/4)*(a+I*a*x)^(1/4))-2/9*I*(a+I*a*x)^(3/4)/(a^2*(a-I*a*x)^(9/4))+2/15*(1+x^2)^(1/4)*sqrt(cos(1/2*arctan(x))^2)/cos(1/2*arctan(x))*EllipticE(sin(1/2*arctan(x)),sqrt(2))/(a^3*(a-I*a*x)^(1/4)*(a+I*a*x)^(1/4))],
[1/((a-I*a*x)^(17/4)*(a+I*a*x)^(1/4)),x,6,(-4/39*I)/(a^3*(a-I*a*x)^(5/4)*(a+I*a*x)^(1/4))-2/13*I*(a+I*a*x)^(3/4)/(a^2*(a-I*a*x)^(13/4))-10/117*I*(a+I*a*x)^(3/4)/(a^3*(a-I*a*x)^(9/4))+2/39*(1+x^2)^(1/4)*sqrt(cos(1/2*arctan(x))^2)/cos(1/2*arctan(x))*EllipticE(sin(1/2*arctan(x)),sqrt(2))/(a^4*(a-I*a*x)^(1/4)*(a+I*a*x)^(1/4))],
[(a-I*a*x)^(1/4)/(a+I*a*x)^(1/4),x,12,-I*(a-I*a*x)^(1/4)*(a+I*a*x)^(3/4)/a-I*arctan(1-(a-I*a*x)^(1/4)*sqrt(2)/(a+I*a*x)^(1/4))/sqrt(2)+I*arctan(1+(a-I*a*x)^(1/4)*sqrt(2)/(a+I*a*x)^(1/4))/sqrt(2)-1/2*I*log(1-(a-I*a*x)^(1/4)*sqrt(2)/(a+I*a*x)^(1/4)+sqrt(a-I*a*x)/sqrt(a+I*a*x))/sqrt(2)+1/2*I*log(1+(a-I*a*x)^(1/4)*sqrt(2)/(a+I*a*x)^(1/4)+sqrt(a-I*a*x)/sqrt(a+I*a*x))/sqrt(2)],
[1/((a-I*a*x)^(3/4)*(a+I*a*x)^(1/4)),x,11,-I*log(1-(a-I*a*x)^(1/4)*sqrt(2)/(a+I*a*x)^(1/4)+sqrt(a-I*a*x)/sqrt(a+I*a*x))/(a*sqrt(2))+I*log(1+(a-I*a*x)^(1/4)*sqrt(2)/(a+I*a*x)^(1/4)+sqrt(a-I*a*x)/sqrt(a+I*a*x))/(a*sqrt(2))-I*arctan(1-(a-I*a*x)^(1/4)*sqrt(2)/(a+I*a*x)^(1/4))*sqrt(2)/a+I*arctan(1+(a-I*a*x)^(1/4)*sqrt(2)/(a+I*a*x)^(1/4))*sqrt(2)/a],
[1/((a-I*a*x)^(7/4)*(a+I*a*x)^(1/4)),x,1,-2/3*I*(a+I*a*x)^(3/4)/(a^2*(a-I*a*x)^(3/4))],
[1/((a-I*a*x)^(11/4)*(a+I*a*x)^(1/4)),x,2,-2/7*I*(a+I*a*x)^(3/4)/(a^2*(a-I*a*x)^(7/4))-4/21*I*(a+I*a*x)^(3/4)/(a^3*(a-I*a*x)^(3/4))],
[1/((a-I*a*x)^(15/4)*(a+I*a*x)^(1/4)),x,3,-2/11*I*(a+I*a*x)^(3/4)/(a^2*(a-I*a*x)^(11/4))-8/77*I*(a+I*a*x)^(3/4)/(a^3*(a-I*a*x)^(7/4))-16/231*I*(a+I*a*x)^(3/4)/(a^4*(a-I*a*x)^(3/4))],
[1/((a-I*a*x)^(19/4)*(a+I*a*x)^(1/4)),x,4,-2/15*I*(a+I*a*x)^(3/4)/(a^2*(a-I*a*x)^(15/4))-4/55*I*(a+I*a*x)^(3/4)/(a^3*(a-I*a*x)^(11/4))-16/385*I*(a+I*a*x)^(3/4)/(a^4*(a-I*a*x)^(7/4))-32/1155*I*(a+I*a*x)^(3/4)/(a^5*(a-I*a*x)^(3/4))],
[(a-I*a*x)^(3/4)/(a+I*a*x)^(3/4),x,12,-I*(a-I*a*x)^(3/4)*(a+I*a*x)^(1/4)/a-3*I*arctan(1-(a-I*a*x)^(1/4)*sqrt(2)/(a+I*a*x)^(1/4))/sqrt(2)+3*I*arctan(1+(a-I*a*x)^(1/4)*sqrt(2)/(a+I*a*x)^(1/4))/sqrt(2)+3/2*I*log(1-(a-I*a*x)^(1/4)*sqrt(2)/(a+I*a*x)^(1/4)+sqrt(a-I*a*x)/sqrt(a+I*a*x))/sqrt(2)-3/2*I*log(1+(a-I*a*x)^(1/4)*sqrt(2)/(a+I*a*x)^(1/4)+sqrt(a-I*a*x)/sqrt(a+I*a*x))/sqrt(2)],
[1/((a-I*a*x)^(1/4)*(a+I*a*x)^(3/4)),x,11,I*log(1-(a-I*a*x)^(1/4)*sqrt(2)/(a+I*a*x)^(1/4)+sqrt(a-I*a*x)/sqrt(a+I*a*x))/(a*sqrt(2))-I*log(1+(a-I*a*x)^(1/4)*sqrt(2)/(a+I*a*x)^(1/4)+sqrt(a-I*a*x)/sqrt(a+I*a*x))/(a*sqrt(2))-I*arctan(1-(a-I*a*x)^(1/4)*sqrt(2)/(a+I*a*x)^(1/4))*sqrt(2)/a+I*arctan(1+(a-I*a*x)^(1/4)*sqrt(2)/(a+I*a*x)^(1/4))*sqrt(2)/a],
[1/((a-I*a*x)^(5/4)*(a+I*a*x)^(3/4)),x,1,-2*I*(a+I*a*x)^(1/4)/(a^2*(a-I*a*x)^(1/4))],
[1/((a-I*a*x)^(9/4)*(a+I*a*x)^(3/4)),x,2,-2/5*I*(a+I*a*x)^(1/4)/(a^2*(a-I*a*x)^(5/4))-4/5*I*(a+I*a*x)^(1/4)/(a^3*(a-I*a*x)^(1/4))],
[1/((a-I*a*x)^(13/4)*(a+I*a*x)^(3/4)),x,3,-2/9*I*(a+I*a*x)^(1/4)/(a^2*(a-I*a*x)^(9/4))-8/45*I*(a+I*a*x)^(1/4)/(a^3*(a-I*a*x)^(5/4))-16/45*I*(a+I*a*x)^(1/4)/(a^4*(a-I*a*x)^(1/4))],
[(a-I*a*x)^(5/4)/(a+I*a*x)^(3/4),x,5,-10/3*I*(a-I*a*x)^(1/4)*(a+I*a*x)^(1/4)-2/3*I*(a-I*a*x)^(5/4)*(a+I*a*x)^(1/4)/a+10/3*a^2*(1+x^2)^(3/4)*sqrt(cos(1/2*arctan(x))^2)/cos(1/2*arctan(x))*EllipticF(sin(1/2*arctan(x)),sqrt(2))/((a-I*a*x)^(3/4)*(a+I*a*x)^(3/4))],
[(a-I*a*x)^(1/4)/(a+I*a*x)^(3/4),x,4,-2*I*(a-I*a*x)^(1/4)*(a+I*a*x)^(1/4)/a+2*a*(1+x^2)^(3/4)*sqrt(cos(1/2*arctan(x))^2)/cos(1/2*arctan(x))*EllipticF(sin(1/2*arctan(x)),sqrt(2))/((a-I*a*x)^(3/4)*(a+I*a*x)^(3/4))],
[1/((a-I*a*x)^(3/4)*(a+I*a*x)^(3/4)),x,3,2*(1+x^2)^(3/4)*sqrt(cos(1/2*arctan(x))^2)/cos(1/2*arctan(x))*EllipticF(sin(1/2*arctan(x)),sqrt(2))/((a-I*a*x)^(3/4)*(a+I*a*x)^(3/4))],
[1/((a-I*a*x)^(7/4)*(a+I*a*x)^(3/4)),x,4,-2/3*I*(a+I*a*x)^(1/4)/(a^2*(a-I*a*x)^(3/4))+2/3*(1+x^2)^(3/4)*sqrt(cos(1/2*arctan(x))^2)/cos(1/2*arctan(x))*EllipticF(sin(1/2*arctan(x)),sqrt(2))/(a*(a-I*a*x)^(3/4)*(a+I*a*x)^(3/4))],
[1/((a-I*a*x)^(11/4)*(a+I*a*x)^(3/4)),x,5,-2/7*I*(a+I*a*x)^(1/4)/(a^2*(a-I*a*x)^(7/4))-2/7*I*(a+I*a*x)^(1/4)/(a^3*(a-I*a*x)^(3/4))+2/7*(1+x^2)^(3/4)*sqrt(cos(1/2*arctan(x))^2)/cos(1/2*arctan(x))*EllipticF(sin(1/2*arctan(x)),sqrt(2))/(a^2*(a-I*a*x)^(3/4)*(a+I*a*x)^(3/4))],
[(a-I*a*x)^(7/4)/(a+I*a*x)^(7/4),x,13,4/3*I*(a-I*a*x)^(7/4)/(a*(a+I*a*x)^(3/4))+7/3*I*(a-I*a*x)^(3/4)*(a+I*a*x)^(1/4)/a+7*I*arctan(1-(a-I*a*x)^(1/4)*sqrt(2)/(a+I*a*x)^(1/4))/sqrt(2)-7*I*arctan(1+(a-I*a*x)^(1/4)*sqrt(2)/(a+I*a*x)^(1/4))/sqrt(2)-7/2*I*log(1-(a-I*a*x)^(1/4)*sqrt(2)/(a+I*a*x)^(1/4)+sqrt(a-I*a*x)/sqrt(a+I*a*x))/sqrt(2)+7/2*I*log(1+(a-I*a*x)^(1/4)*sqrt(2)/(a+I*a*x)^(1/4)+sqrt(a-I*a*x)/sqrt(a+I*a*x))/sqrt(2)],
[(a-I*a*x)^(3/4)/(a+I*a*x)^(7/4),x,12,4/3*I*(a-I*a*x)^(3/4)/(a*(a+I*a*x)^(3/4))-I*log(1-(a-I*a*x)^(1/4)*sqrt(2)/(a+I*a*x)^(1/4)+sqrt(a-I*a*x)/sqrt(a+I*a*x))/(a*sqrt(2))+I*log(1+(a-I*a*x)^(1/4)*sqrt(2)/(a+I*a*x)^(1/4)+sqrt(a-I*a*x)/sqrt(a+I*a*x))/(a*sqrt(2))+I*arctan(1-(a-I*a*x)^(1/4)*sqrt(2)/(a+I*a*x)^(1/4))*sqrt(2)/a-I*arctan(1+(a-I*a*x)^(1/4)*sqrt(2)/(a+I*a*x)^(1/4))*sqrt(2)/a],
[1/((a-I*a*x)^(1/4)*(a+I*a*x)^(7/4)),x,1,2/3*I*(a-I*a*x)^(3/4)/(a^2*(a+I*a*x)^(3/4))],
[1/((a-I*a*x)^(5/4)*(a+I*a*x)^(7/4)),x,2,(-2*I)/(a^2*(a-I*a*x)^(1/4)*(a+I*a*x)^(3/4))+4/3*I*(a-I*a*x)^(3/4)/(a^3*(a+I*a*x)^(3/4))],
[1/((a-I*a*x)^(9/4)*(a+I*a*x)^(7/4)),x,3,(-2/5*I)/(a^2*(a-I*a*x)^(5/4)*(a+I*a*x)^(3/4))+(-8/5*I)/(a^3*(a-I*a*x)^(1/4)*(a+I*a*x)^(3/4))+16/15*I*(a-I*a*x)^(3/4)/(a^4*(a+I*a*x)^(3/4))],
[(a-I*a*x)^(9/4)/(a+I*a*x)^(7/4),x,6,4/3*I*(a-I*a*x)^(9/4)/(a*(a+I*a*x)^(3/4))+10*I*(a-I*a*x)^(1/4)*(a+I*a*x)^(1/4)+2*I*(a-I*a*x)^(5/4)*(a+I*a*x)^(1/4)/a-10*a^2*(1+x^2)^(3/4)*sqrt(cos(1/2*arctan(x))^2)/cos(1/2*arctan(x))*EllipticF(sin(1/2*arctan(x)),sqrt(2))/((a-I*a*x)^(3/4)*(a+I*a*x)^(3/4))],
[(a-I*a*x)^(5/4)/(a+I*a*x)^(7/4),x,5,4/3*I*(a-I*a*x)^(5/4)/(a*(a+I*a*x)^(3/4))+10/3*I*(a-I*a*x)^(1/4)*(a+I*a*x)^(1/4)/a-10/3*a*(1+x^2)^(3/4)*sqrt(cos(1/2*arctan(x))^2)/cos(1/2*arctan(x))*EllipticF(sin(1/2*arctan(x)),sqrt(2))/((a-I*a*x)^(3/4)*(a+I*a*x)^(3/4))],
[(a-I*a*x)^(1/4)/(a+I*a*x)^(7/4),x,4,4/3*I*(a-I*a*x)^(1/4)/(a*(a+I*a*x)^(3/4))-2/3*(1+x^2)^(3/4)*sqrt(cos(1/2*arctan(x))^2)/cos(1/2*arctan(x))*EllipticF(sin(1/2*arctan(x)),sqrt(2))/((a-I*a*x)^(3/4)*(a+I*a*x)^(3/4))],
[1/((a-I*a*x)^(3/4)*(a+I*a*x)^(7/4)),x,4,2/3*I*(a-I*a*x)^(1/4)/(a^2*(a+I*a*x)^(3/4))+2/3*(1+x^2)^(3/4)*sqrt(cos(1/2*arctan(x))^2)/cos(1/2*arctan(x))*EllipticF(sin(1/2*arctan(x)),sqrt(2))/(a*(a-I*a*x)^(3/4)*(a+I*a*x)^(3/4))],
[1/((a-I*a*x)^(7/4)*(a+I*a*x)^(7/4)),x,4,2/3*x/(a^2*(a-I*a*x)^(3/4)*(a+I*a*x)^(3/4))+2/3*(1+x^2)^(3/4)*sqrt(cos(1/2*arctan(x))^2)/cos(1/2*arctan(x))*EllipticF(sin(1/2*arctan(x)),sqrt(2))/(a^2*(a-I*a*x)^(3/4)*(a+I*a*x)^(3/4))],
[1/((a-I*a*x)^(11/4)*(a+I*a*x)^(7/4)),x,5,(-2/7*I)/(a^2*(a-I*a*x)^(7/4)*(a+I*a*x)^(3/4))+10/21*x/(a^3*(a-I*a*x)^(3/4)*(a+I*a*x)^(3/4))+10/21*(1+x^2)^(3/4)*sqrt(cos(1/2*arctan(x))^2)/cos(1/2*arctan(x))*EllipticF(sin(1/2*arctan(x)),sqrt(2))/(a^3*(a-I*a*x)^(3/4)*(a+I*a*x)^(3/4))],
[1/((a-I*a*x)^(15/4)*(a+I*a*x)^(7/4)),x,6,(-2/11*I)/(a^2*(a-I*a*x)^(11/4)*(a+I*a*x)^(3/4))+(-2/11*I)/(a^3*(a-I*a*x)^(7/4)*(a+I*a*x)^(3/4))+10/33*x/(a^4*(a-I*a*x)^(3/4)*(a+I*a*x)^(3/4))+10/33*(1+x^2)^(3/4)*sqrt(cos(1/2*arctan(x))^2)/cos(1/2*arctan(x))*EllipticF(sin(1/2*arctan(x)),sqrt(2))/(a^4*(a-I*a*x)^(3/4)*(a+I*a*x)^(3/4))],
[(a-I*a*x)^(7/4)/(a+I*a*x)^(5/4),x,6,-14*a*x/((a-I*a*x)^(1/4)*(a+I*a*x)^(1/4))+4*I*(a-I*a*x)^(7/4)/(a*(a+I*a*x)^(1/4))+14/3*I*(a-I*a*x)^(3/4)*(a+I*a*x)^(3/4)/a+14*a*(1+x^2)^(1/4)*sqrt(cos(1/2*arctan(x))^2)/cos(1/2*arctan(x))*EllipticE(sin(1/2*arctan(x)),sqrt(2))/((a-I*a*x)^(1/4)*(a+I*a*x)^(1/4))],
[(a-I*a*x)^(3/4)/(a+I*a*x)^(5/4),x,5,-6*x/((a-I*a*x)^(1/4)*(a+I*a*x)^(1/4))+4*I*(a-I*a*x)^(3/4)/(a*(a+I*a*x)^(1/4))+6*(1+x^2)^(1/4)*sqrt(cos(1/2*arctan(x))^2)/cos(1/2*arctan(x))*EllipticE(sin(1/2*arctan(x)),sqrt(2))/((a-I*a*x)^(1/4)*(a+I*a*x)^(1/4))],
[1/((a-I*a*x)^(1/4)*(a+I*a*x)^(5/4)),x,4,2*I/(a*(a-I*a*x)^(1/4)*(a+I*a*x)^(1/4))+2*(1+x^2)^(1/4)*sqrt(cos(1/2*arctan(x))^2)/cos(1/2*arctan(x))*EllipticE(sin(1/2*arctan(x)),sqrt(2))/(a*(a-I*a*x)^(1/4)*(a+I*a*x)^(1/4))],
[1/((a-I*a*x)^(5/4)*(a+I*a*x)^(5/4)),x,3,2*(1+x^2)^(1/4)*sqrt(cos(1/2*arctan(x))^2)/cos(1/2*arctan(x))*EllipticE(sin(1/2*arctan(x)),sqrt(2))/(a^2*(a-I*a*x)^(1/4)*(a+I*a*x)^(1/4))],
[1/((a-I*a*x)^(9/4)*(a+I*a*x)^(5/4)),x,4,(-2/5*I)/(a^2*(a-I*a*x)^(5/4)*(a+I*a*x)^(1/4))+6/5*(1+x^2)^(1/4)*sqrt(cos(1/2*arctan(x))^2)/cos(1/2*arctan(x))*EllipticE(sin(1/2*arctan(x)),sqrt(2))/(a^3*(a-I*a*x)^(1/4)*(a+I*a*x)^(1/4))],
[1/((a-I*a*x)^(13/4)*(a+I*a*x)^(5/4)),x,5,(-2/9*I)/(a^2*(a-I*a*x)^(9/4)*(a+I*a*x)^(1/4))+(-2/9*I)/(a^3*(a-I*a*x)^(5/4)*(a+I*a*x)^(1/4))+2/3*(1+x^2)^(1/4)*sqrt(cos(1/2*arctan(x))^2)/cos(1/2*arctan(x))*EllipticE(sin(1/2*arctan(x)),sqrt(2))/(a^4*(a-I*a*x)^(1/4)*(a+I*a*x)^(1/4))],
[(a-I*a*x)^(5/4)/(a+I*a*x)^(5/4),x,13,4*I*(a-I*a*x)^(5/4)/(a*(a+I*a*x)^(1/4))+5*I*(a-I*a*x)^(1/4)*(a+I*a*x)^(3/4)/a+5*I*arctan(1-(a-I*a*x)^(1/4)*sqrt(2)/(a+I*a*x)^(1/4))/sqrt(2)-5*I*arctan(1+(a-I*a*x)^(1/4)*sqrt(2)/(a+I*a*x)^(1/4))/sqrt(2)+5/2*I*log(1-(a-I*a*x)^(1/4)*sqrt(2)/(a+I*a*x)^(1/4)+sqrt(a-I*a*x)/sqrt(a+I*a*x))/sqrt(2)-5/2*I*log(1+(a-I*a*x)^(1/4)*sqrt(2)/(a+I*a*x)^(1/4)+sqrt(a-I*a*x)/sqrt(a+I*a*x))/sqrt(2)],
[(a-I*a*x)^(1/4)/(a+I*a*x)^(5/4),x,12,4*I*(a-I*a*x)^(1/4)/(a*(a+I*a*x)^(1/4))+I*log(1-(a-I*a*x)^(1/4)*sqrt(2)/(a+I*a*x)^(1/4)+sqrt(a-I*a*x)/sqrt(a+I*a*x))/(a*sqrt(2))-I*log(1+(a-I*a*x)^(1/4)*sqrt(2)/(a+I*a*x)^(1/4)+sqrt(a-I*a*x)/sqrt(a+I*a*x))/(a*sqrt(2))+I*arctan(1-(a-I*a*x)^(1/4)*sqrt(2)/(a+I*a*x)^(1/4))*sqrt(2)/a-I*arctan(1+(a-I*a*x)^(1/4)*sqrt(2)/(a+I*a*x)^(1/4))*sqrt(2)/a],
[1/((a-I*a*x)^(3/4)*(a+I*a*x)^(5/4)),x,1,2*I*(a-I*a*x)^(1/4)/(a^2*(a+I*a*x)^(1/4))],
[1/((a-I*a*x)^(7/4)*(a+I*a*x)^(5/4)),x,2,(-2/3*I)/(a^2*(a-I*a*x)^(3/4)*(a+I*a*x)^(1/4))+4/3*I*(a-I*a*x)^(1/4)/(a^3*(a+I*a*x)^(1/4))],
[1/((a-I*a*x)^(11/4)*(a+I*a*x)^(5/4)),x,3,(-2/7*I)/(a^2*(a-I*a*x)^(7/4)*(a+I*a*x)^(1/4))+(-8/21*I)/(a^3*(a-I*a*x)^(3/4)*(a+I*a*x)^(1/4))+16/21*I*(a-I*a*x)^(1/4)/(a^4*(a+I*a*x)^(1/4))],
[(a-I*a*x)^(7/4)/(a+I*a*x)^(9/4),x,6,4/5*I*(a-I*a*x)^(7/4)/(a*(a+I*a*x)^(5/4))+42/5*x/((a-I*a*x)^(1/4)*(a+I*a*x)^(1/4))-28/5*I*(a-I*a*x)^(3/4)/(a*(a+I*a*x)^(1/4))-42/5*(1+x^2)^(1/4)*sqrt(cos(1/2*arctan(x))^2)/cos(1/2*arctan(x))*EllipticE(sin(1/2*arctan(x)),sqrt(2))/((a-I*a*x)^(1/4)*(a+I*a*x)^(1/4))],
[(a-I*a*x)^(3/4)/(a+I*a*x)^(9/4),x,5,4/5*I*(a-I*a*x)^(3/4)/(a*(a+I*a*x)^(5/4))+(-6/5*I)/(a*(a-I*a*x)^(1/4)*(a+I*a*x)^(1/4))-6/5*(1+x^2)^(1/4)*sqrt(cos(1/2*arctan(x))^2)/cos(1/2*arctan(x))*EllipticE(sin(1/2*arctan(x)),sqrt(2))/(a*(a-I*a*x)^(1/4)*(a+I*a*x)^(1/4))],
[1/((a-I*a*x)^(1/4)*(a+I*a*x)^(9/4)),x,4,4/5*I/(a*(a-I*a*x)^(1/4)*(a+I*a*x)^(5/4))+2/5*(1+x^2)^(1/4)*sqrt(cos(1/2*arctan(x))^2)/cos(1/2*arctan(x))*EllipticE(sin(1/2*arctan(x)),sqrt(2))/(a^2*(a-I*a*x)^(1/4)*(a+I*a*x)^(1/4))],
[1/((a-I*a*x)^(5/4)*(a+I*a*x)^(9/4)),x,5,2/5*I/(a^2*(a-I*a*x)^(1/4)*(a+I*a*x)^(5/4))+6/5*(1+x^2)^(1/4)*sqrt(cos(1/2*arctan(x))^2)/cos(1/2*arctan(x))*EllipticE(sin(1/2*arctan(x)),sqrt(2))/(a^3*(a-I*a*x)^(1/4)*(a+I*a*x)^(1/4))],
[1/((a-I*a*x)^(9/4)*(a+I*a*x)^(9/4)),x,4,2/5*x/(a^4*(a-I*a*x)^(1/4)*(a+I*a*x)^(1/4)*(1+x^2))+6/5*(1+x^2)^(1/4)*sqrt(cos(1/2*arctan(x))^2)/cos(1/2*arctan(x))*EllipticE(sin(1/2*arctan(x)),sqrt(2))/(a^4*(a-I*a*x)^(1/4)*(a+I*a*x)^(1/4))],
[1/((a-I*a*x)^(13/4)*(a+I*a*x)^(9/4)),x,5,(-2/9*I)/(a^2*(a-I*a*x)^(9/4)*(a+I*a*x)^(5/4))+14/45*x/(a^5*(a-I*a*x)^(1/4)*(a+I*a*x)^(1/4)*(1+x^2))+14/15*(1+x^2)^(1/4)*sqrt(cos(1/2*arctan(x))^2)/cos(1/2*arctan(x))*EllipticE(sin(1/2*arctan(x)),sqrt(2))/(a^5*(a-I*a*x)^(1/4)*(a+I*a*x)^(1/4))],
[1/((a-I*a*x)^(17/4)*(a+I*a*x)^(9/4)),x,6,(-2/13*I)/(a^2*(a-I*a*x)^(13/4)*(a+I*a*x)^(5/4))+(-2/13*I)/(a^3*(a-I*a*x)^(9/4)*(a+I*a*x)^(5/4))+14/65*x/(a^6*(a-I*a*x)^(1/4)*(a+I*a*x)^(1/4)*(1+x^2))+42/65*(1+x^2)^(1/4)*sqrt(cos(1/2*arctan(x))^2)/cos(1/2*arctan(x))*EllipticE(sin(1/2*arctan(x)),sqrt(2))/(a^6*(a-I*a*x)^(1/4)*(a+I*a*x)^(1/4))],
[(a-I*a*x)^(5/4)/(a+I*a*x)^(9/4),x,13,4/5*I*(a-I*a*x)^(5/4)/(a*(a+I*a*x)^(5/4))-4*I*(a-I*a*x)^(1/4)/(a*(a+I*a*x)^(1/4))-I*log(1-(a-I*a*x)^(1/4)*sqrt(2)/(a+I*a*x)^(1/4)+sqrt(a-I*a*x)/sqrt(a+I*a*x))/(a*sqrt(2))+I*log(1+(a-I*a*x)^(1/4)*sqrt(2)/(a+I*a*x)^(1/4)+sqrt(a-I*a*x)/sqrt(a+I*a*x))/(a*sqrt(2))-I*arctan(1-(a-I*a*x)^(1/4)*sqrt(2)/(a+I*a*x)^(1/4))*sqrt(2)/a+I*arctan(1+(a-I*a*x)^(1/4)*sqrt(2)/(a+I*a*x)^(1/4))*sqrt(2)/a],
[(a-I*a*x)^(1/4)/(a+I*a*x)^(9/4),x,1,2/5*I*(a-I*a*x)^(5/4)/(a^2*(a+I*a*x)^(5/4))],
[1/((a-I*a*x)^(3/4)*(a+I*a*x)^(9/4)),x,2,2/5*I*(a-I*a*x)^(1/4)/(a^2*(a+I*a*x)^(5/4))+4/5*I*(a-I*a*x)^(1/4)/(a^3*(a+I*a*x)^(1/4))],
[1/((a-I*a*x)^(7/4)*(a+I*a*x)^(9/4)),x,3,(-2/3*I)/(a^2*(a-I*a*x)^(3/4)*(a+I*a*x)^(5/4))+8/15*I*(a-I*a*x)^(1/4)/(a^3*(a+I*a*x)^(5/4))+16/15*I*(a-I*a*x)^(1/4)/(a^4*(a+I*a*x)^(1/4))],
[1/((a-I*a*x)^(11/4)*(a+I*a*x)^(9/4)),x,4,(-2/7*I)/(a^2*(a-I*a*x)^(7/4)*(a+I*a*x)^(5/4))+(-4/7*I)/(a^3*(a-I*a*x)^(3/4)*(a+I*a*x)^(5/4))+16/35*I*(a-I*a*x)^(1/4)/(a^4*(a+I*a*x)^(5/4))+32/35*I*(a-I*a*x)^(1/4)/(a^5*(a+I*a*x)^(1/4))],

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

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

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

# n>0
[(a+b*x)^4*(c+d*x),x,2,1/5*(b*c-a*d)*(a+b*x)^5/b^2+1/6*d*(a+b*x)^6/b^2],
[(a+b*x)^3*(c+d*x),x,2,1/4*(b*c-a*d)*(a+b*x)^4/b^2+1/5*d*(a+b*x)^5/b^2],
[(a+b*x)^2*(c+d*x),x,2,1/3*(b*c-a*d)*(a+b*x)^3/b^2+1/4*d*(a+b*x)^4/b^2],
[(a+b*x)*(c+d*x),x,2,a*c*x+1/2*(b*c+a*d)*x^2+1/3*b*d*x^3],
[c+d*x,x,1,c*x+1/2*d*x^2],
[(c+d*x)/(a+b*x),x,2,d*x/b+(b*c-a*d)*log(a+b*x)/b^2],
[(c+d*x)/(a+b*x)^2,x,2,(-b*c+a*d)/(b^2*(a+b*x))+d*log(a+b*x)/b^2],
[(c+d*x)/(a+b*x)^3,x,1,-1/2*(c+d*x)^2/((b*c-a*d)*(a+b*x)^2)],
[(c+d*x)/(a+b*x)^4,x,2,1/3*(-b*c+a*d)/(b^2*(a+b*x)^3)-1/2*d/(b^2*(a+b*x)^2)],
[(c+d*x)/(a+b*x)^5,x,2,1/4*(-b*c+a*d)/(b^2*(a+b*x)^4)-1/3*d/(b^2*(a+b*x)^3)],
[(a+b*x)^4*(c+d*x)^2,x,2,1/5*(b*c-a*d)^2*(a+b*x)^5/b^3+1/3*d*(b*c-a*d)*(a+b*x)^6/b^3+1/7*d^2*(a+b*x)^7/b^3],
[(a+b*x)^3*(c+d*x)^2,x,2,1/4*(b*c-a*d)^2*(a+b*x)^4/b^3+2/5*d*(b*c-a*d)*(a+b*x)^5/b^3+1/6*d^2*(a+b*x)^6/b^3],
[(a+b*x)^2*(c+d*x)^2,x,2,1/3*(b*c-a*d)^2*(a+b*x)^3/b^3+1/2*d*(b*c-a*d)*(a+b*x)^4/b^3+1/5*d^2*(a+b*x)^5/b^3],
[(a+b*x)*(c+d*x)^2,x,2,-1/3*(b*c-a*d)*(c+d*x)^3/d^2+1/4*b*(c+d*x)^4/d^2],
[(c+d*x)^2,x,1,1/3*(c+d*x)^3/d],
[(c+d*x)^2/(a+b*x),x,2,d*(b*c-a*d)*x/b^2+1/2*(c+d*x)^2/b+(b*c-a*d)^2*log(a+b*x)/b^3],
[(c+d*x)^2/(a+b*x)^2,x,2,d^2*x/b^2-(b*c-a*d)^2/(b^3*(a+b*x))+2*d*(b*c-a*d)*log(a+b*x)/b^3],
[(c+d*x)^2/(a+b*x)^3,x,2,-1/2*(b*c-a*d)^2/(b^3*(a+b*x)^2)-2*d*(b*c-a*d)/(b^3*(a+b*x))+d^2*log(a+b*x)/b^3],
[(c+d*x)^2/(a+b*x)^4,x,1,-1/3*(c+d*x)^3/((b*c-a*d)*(a+b*x)^3)],
[(c+d*x)^2/(a+b*x)^5,x,2,-1/4*(b*c-a*d)^2/(b^3*(a+b*x)^4)-2/3*d*(b*c-a*d)/(b^3*(a+b*x)^3)-1/2*d^2/(b^3*(a+b*x)^2)],
[(c+d*x)^2/(a+b*x)^6,x,2,-1/5*(b*c-a*d)^2/(b^3*(a+b*x)^5)-1/2*d*(b*c-a*d)/(b^3*(a+b*x)^4)-1/3*d^2/(b^3*(a+b*x)^3)],
[(c+d*x)^2/(a+b*x)^7,x,2,-1/6*(b*c-a*d)^2/(b^3*(a+b*x)^6)-2/5*d*(b*c-a*d)/(b^3*(a+b*x)^5)-1/4*d^2/(b^3*(a+b*x)^4)],
[(a+b*x)^5*(c+d*x)^3,x,2,1/6*(b*c-a*d)^3*(a+b*x)^6/b^4+3/7*d*(b*c-a*d)^2*(a+b*x)^7/b^4+3/8*d^2*(b*c-a*d)*(a+b*x)^8/b^4+1/9*d^3*(a+b*x)^9/b^4],
[(a+b*x)^4*(c+d*x)^3,x,2,1/5*(b*c-a*d)^3*(a+b*x)^5/b^4+1/2*d*(b*c-a*d)^2*(a+b*x)^6/b^4+3/7*d^2*(b*c-a*d)*(a+b*x)^7/b^4+1/8*d^3*(a+b*x)^8/b^4],
[(a+b*x)^3*(c+d*x)^3,x,2,1/4*(b*c-a*d)^3*(a+b*x)^4/b^4+3/5*d*(b*c-a*d)^2*(a+b*x)^5/b^4+1/2*d^2*(b*c-a*d)*(a+b*x)^6/b^4+1/7*d^3*(a+b*x)^7/b^4],
[(a+b*x)^2*(c+d*x)^3,x,2,1/4*(b*c-a*d)^2*(c+d*x)^4/d^3-2/5*b*(b*c-a*d)*(c+d*x)^5/d^3+1/6*b^2*(c+d*x)^6/d^3],
[(a+b*x)*(c+d*x)^3,x,2,-1/4*(b*c-a*d)*(c+d*x)^4/d^2+1/5*b*(c+d*x)^5/d^2],
[(c+d*x)^3,x,1,1/4*(c+d*x)^4/d],
[(c+d*x)^3/(a+b*x),x,2,d*(b*c-a*d)^2*x/b^3+1/2*(b*c-a*d)*(c+d*x)^2/b^2+1/3*(c+d*x)^3/b+(b*c-a*d)^3*log(a+b*x)/b^4],
[(c+d*x)^3/(a+b*x)^2,x,2,d^2*(3*b*c-2*a*d)*x/b^3+1/2*d^3*x^2/b^2-(b*c-a*d)^3/(b^4*(a+b*x))+3*d*(b*c-a*d)^2*log(a+b*x)/b^4],
[(c+d*x)^3/(a+b*x)^3,x,2,d^3*x/b^3-1/2*(b*c-a*d)^3/(b^4*(a+b*x)^2)-3*d*(b*c-a*d)^2/(b^4*(a+b*x))+3*d^2*(b*c-a*d)*log(a+b*x)/b^4],
[(c+d*x)^3/(a+b*x)^4,x,2,-1/3*(b*c-a*d)^3/(b^4*(a+b*x)^3)-3/2*d*(b*c-a*d)^2/(b^4*(a+b*x)^2)-3*d^2*(b*c-a*d)/(b^4*(a+b*x))+d^3*log(a+b*x)/b^4],
[(c+d*x)^3/(a+b*x)^5,x,1,-1/4*(c+d*x)^4/((b*c-a*d)*(a+b*x)^4)],
[(c+d*x)^3/(a+b*x)^6,x,2,-1/5*(c+d*x)^4/((b*c-a*d)*(a+b*x)^5)+1/20*d*(c+d*x)^4/((b*c-a*d)^2*(a+b*x)^4)],
[(c+d*x)^3/(a+b*x)^7,x,2,-1/6*(b*c-a*d)^3/(b^4*(a+b*x)^6)-3/5*d*(b*c-a*d)^2/(b^4*(a+b*x)^5)-3/4*d^2*(b*c-a*d)/(b^4*(a+b*x)^4)-1/3*d^3/(b^4*(a+b*x)^3)],
[(c+d*x)^3/(a+b*x)^8,x,2,-1/7*(b*c-a*d)^3/(b^4*(a+b*x)^7)-1/2*d*(b*c-a*d)^2/(b^4*(a+b*x)^6)-3/5*d^2*(b*c-a*d)/(b^4*(a+b*x)^5)-1/4*d^3/(b^4*(a+b*x)^4)],
[(c+d*x)^3/(a+b*x)^9,x,2,-1/8*(b*c-a*d)^3/(b^4*(a+b*x)^8)-3/7*d*(b*c-a*d)^2/(b^4*(a+b*x)^7)-1/2*d^2*(b*c-a*d)/(b^4*(a+b*x)^6)-1/5*d^3/(b^4*(a+b*x)^5)],
[(a+b*x)^9*(c+d*x)^7,x,2,1/10*(b*c-a*d)^7*(a+b*x)^10/b^8+7/11*d*(b*c-a*d)^6*(a+b*x)^11/b^8+7/4*d^2*(b*c-a*d)^5*(a+b*x)^12/b^8+35/13*d^3*(b*c-a*d)^4*(a+b*x)^13/b^8+5/2*d^4*(b*c-a*d)^3*(a+b*x)^14/b^8+7/5*d^5*(b*c-a*d)^2*(a+b*x)^15/b^8+7/16*d^6*(b*c-a*d)*(a+b*x)^16/b^8+1/17*d^7*(a+b*x)^17/b^8],
[(a+b*x)^8*(c+d*x)^7,x,2,1/9*(b*c-a*d)^7*(a+b*x)^9/b^8+7/10*d*(b*c-a*d)^6*(a+b*x)^10/b^8+21/11*d^2*(b*c-a*d)^5*(a+b*x)^11/b^8+35/12*d^3*(b*c-a*d)^4*(a+b*x)^12/b^8+35/13*d^4*(b*c-a*d)^3*(a+b*x)^13/b^8+3/2*d^5*(b*c-a*d)^2*(a+b*x)^14/b^8+7/15*d^6*(b*c-a*d)*(a+b*x)^15/b^8+1/16*d^7*(a+b*x)^16/b^8],
[(a+b*x)^7*(c+d*x)^7,x,2,1/8*(b*c-a*d)^7*(a+b*x)^8/b^8+7/9*d*(b*c-a*d)^6*(a+b*x)^9/b^8+21/10*d^2*(b*c-a*d)^5*(a+b*x)^10/b^8+35/11*d^3*(b*c-a*d)^4*(a+b*x)^11/b^8+35/12*d^4*(b*c-a*d)^3*(a+b*x)^12/b^8+21/13*d^5*(b*c-a*d)^2*(a+b*x)^13/b^8+1/2*d^6*(b*c-a*d)*(a+b*x)^14/b^8+1/15*d^7*(a+b*x)^15/b^8],
[(a+b*x)^6*(c+d*x)^7,x,2,1/8*(b*c-a*d)^6*(c+d*x)^8/d^7-2/3*b*(b*c-a*d)^5*(c+d*x)^9/d^7+3/2*b^2*(b*c-a*d)^4*(c+d*x)^10/d^7-20/11*b^3*(b*c-a*d)^3*(c+d*x)^11/d^7+5/4*b^4*(b*c-a*d)^2*(c+d*x)^12/d^7-6/13*b^5*(b*c-a*d)*(c+d*x)^13/d^7+1/14*b^6*(c+d*x)^14/d^7],
[(a+b*x)^5*(c+d*x)^7,x,2,-1/8*(b*c-a*d)^5*(c+d*x)^8/d^6+5/9*b*(b*c-a*d)^4*(c+d*x)^9/d^6-b^2*(b*c-a*d)^3*(c+d*x)^10/d^6+10/11*b^3*(b*c-a*d)^2*(c+d*x)^11/d^6-5/12*b^4*(b*c-a*d)*(c+d*x)^12/d^6+1/13*b^5*(c+d*x)^13/d^6],
[(a+b*x)^4*(c+d*x)^7,x,2,1/8*(b*c-a*d)^4*(c+d*x)^8/d^5-4/9*b*(b*c-a*d)^3*(c+d*x)^9/d^5+3/5*b^2*(b*c-a*d)^2*(c+d*x)^10/d^5-4/11*b^3*(b*c-a*d)*(c+d*x)^11/d^5+1/12*b^4*(c+d*x)^12/d^5],
[(a+b*x)^3*(c+d*x)^7,x,2,-1/8*(b*c-a*d)^3*(c+d*x)^8/d^4+1/3*b*(b*c-a*d)^2*(c+d*x)^9/d^4-3/10*b^2*(b*c-a*d)*(c+d*x)^10/d^4+1/11*b^3*(c+d*x)^11/d^4],
[(a+b*x)^2*(c+d*x)^7,x,2,1/8*(b*c-a*d)^2*(c+d*x)^8/d^3-2/9*b*(b*c-a*d)*(c+d*x)^9/d^3+1/10*b^2*(c+d*x)^10/d^3],
[(a+b*x)*(c+d*x)^7,x,2,-1/8*(b*c-a*d)*(c+d*x)^8/d^2+1/9*b*(c+d*x)^9/d^2],
[(c+d*x)^7,x,1,1/8*(c+d*x)^8/d],
[(c+d*x)^7/(a+b*x),x,2,d*(b*c-a*d)^6*x/b^7+1/2*(b*c-a*d)^5*(c+d*x)^2/b^6+1/3*(b*c-a*d)^4*(c+d*x)^3/b^5+1/4*(b*c-a*d)^3*(c+d*x)^4/b^4+1/5*(b*c-a*d)^2*(c+d*x)^5/b^3+1/6*(b*c-a*d)*(c+d*x)^6/b^2+1/7*(c+d*x)^7/b+(b*c-a*d)^7*log(a+b*x)/b^8],
[(c+d*x)^7/(a+b*x)^2,x,2,21*d^2*(b*c-a*d)^5*x/b^7-(b*c-a*d)^7/(b^8*(a+b*x))+35/2*d^3*(b*c-a*d)^4*(a+b*x)^2/b^8+35/3*d^4*(b*c-a*d)^3*(a+b*x)^3/b^8+21/4*d^5*(b*c-a*d)^2*(a+b*x)^4/b^8+7/5*d^6*(b*c-a*d)*(a+b*x)^5/b^8+1/6*d^7*(a+b*x)^6/b^8+7*d*(b*c-a*d)^6*log(a+b*x)/b^8],
[(c+d*x)^7/(a+b*x)^3,x,2,35*d^3*(b*c-a*d)^4*x/b^7-1/2*(b*c-a*d)^7/(b^8*(a+b*x)^2)-7*d*(b*c-a*d)^6/(b^8*(a+b*x))+35/2*d^4*(b*c-a*d)^3*(a+b*x)^2/b^8+7*d^5*(b*c-a*d)^2*(a+b*x)^3/b^8+7/4*d^6*(b*c-a*d)*(a+b*x)^4/b^8+1/5*d^7*(a+b*x)^5/b^8+21*d^2*(b*c-a*d)^5*log(a+b*x)/b^8],
[(c+d*x)^7/(a+b*x)^4,x,2,35*d^4*(b*c-a*d)^3*x/b^7-1/3*(b*c-a*d)^7/(b^8*(a+b*x)^3)-7/2*d*(b*c-a*d)^6/(b^8*(a+b*x)^2)-21*d^2*(b*c-a*d)^5/(b^8*(a+b*x))+21/2*d^5*(b*c-a*d)^2*(a+b*x)^2/b^8+7/3*d^6*(b*c-a*d)*(a+b*x)^3/b^8+1/4*d^7*(a+b*x)^4/b^8+35*d^3*(b*c-a*d)^4*log(a+b*x)/b^8],
[(c+d*x)^7/(a+b*x)^5,x,2,21*d^5*(b*c-a*d)^2*x/b^7-1/4*(b*c-a*d)^7/(b^8*(a+b*x)^4)-7/3*d*(b*c-a*d)^6/(b^8*(a+b*x)^3)-21/2*d^2*(b*c-a*d)^5/(b^8*(a+b*x)^2)-35*d^3*(b*c-a*d)^4/(b^8*(a+b*x))+7/2*d^6*(b*c-a*d)*(a+b*x)^2/b^8+1/3*d^7*(a+b*x)^3/b^8+35*d^4*(b*c-a*d)^3*log(a+b*x)/b^8],
[(c+d*x)^7/(a+b*x)^6,x,2,d^6*(7*b*c-6*a*d)*x/b^7+1/2*d^7*x^2/b^6-1/5*(b*c-a*d)^7/(b^8*(a+b*x)^5)-7/4*d*(b*c-a*d)^6/(b^8*(a+b*x)^4)-7*d^2*(b*c-a*d)^5/(b^8*(a+b*x)^3)-35/2*d^3*(b*c-a*d)^4/(b^8*(a+b*x)^2)-35*d^4*(b*c-a*d)^3/(b^8*(a+b*x))+21*d^5*(b*c-a*d)^2*log(a+b*x)/b^8],
[(c+d*x)^7/(a+b*x)^7,x,2,d^7*x/b^7-1/6*(b*c-a*d)^7/(b^8*(a+b*x)^6)-7/5*d*(b*c-a*d)^6/(b^8*(a+b*x)^5)-21/4*d^2*(b*c-a*d)^5/(b^8*(a+b*x)^4)-35/3*d^3*(b*c-a*d)^4/(b^8*(a+b*x)^3)-35/2*d^4*(b*c-a*d)^3/(b^8*(a+b*x)^2)-21*d^5*(b*c-a*d)^2/(b^8*(a+b*x))+7*d^6*(b*c-a*d)*log(a+b*x)/b^8],
[(c+d*x)^7/(a+b*x)^8,x,2,-1/7*(b*c-a*d)^7/(b^8*(a+b*x)^7)-7/6*d*(b*c-a*d)^6/(b^8*(a+b*x)^6)-21/5*d^2*(b*c-a*d)^5/(b^8*(a+b*x)^5)-35/4*d^3*(b*c-a*d)^4/(b^8*(a+b*x)^4)-35/3*d^4*(b*c-a*d)^3/(b^8*(a+b*x)^3)-21/2*d^5*(b*c-a*d)^2/(b^8*(a+b*x)^2)-7*d^6*(b*c-a*d)/(b^8*(a+b*x))+d^7*log(a+b*x)/b^8],
[(c+d*x)^7/(a+b*x)^9,x,1,-1/8*(c+d*x)^8/((b*c-a*d)*(a+b*x)^8)],
[(c+d*x)^7/(a+b*x)^10,x,2,-1/9*(c+d*x)^8/((b*c-a*d)*(a+b*x)^9)+1/72*d*(c+d*x)^8/((b*c-a*d)^2*(a+b*x)^8)],
[(c+d*x)^7/(a+b*x)^11,x,3,-1/10*(c+d*x)^8/((b*c-a*d)*(a+b*x)^10)+1/45*d*(c+d*x)^8/((b*c-a*d)^2*(a+b*x)^9)-1/360*d^2*(c+d*x)^8/((b*c-a*d)^3*(a+b*x)^8)],
[(c+d*x)^7/(a+b*x)^12,x,4,-1/11*(c+d*x)^8/((b*c-a*d)*(a+b*x)^11)+3/110*d*(c+d*x)^8/((b*c-a*d)^2*(a+b*x)^10)-1/165*d^2*(c+d*x)^8/((b*c-a*d)^3*(a+b*x)^9)+1/1320*d^3*(c+d*x)^8/((b*c-a*d)^4*(a+b*x)^8)],
[(c+d*x)^7/(a+b*x)^13,x,5,-1/12*(c+d*x)^8/((b*c-a*d)*(a+b*x)^12)+1/33*d*(c+d*x)^8/((b*c-a*d)^2*(a+b*x)^11)-1/110*d^2*(c+d*x)^8/((b*c-a*d)^3*(a+b*x)^10)+1/495*d^3*(c+d*x)^8/((b*c-a*d)^4*(a+b*x)^9)-1/3960*d^4*(c+d*x)^8/((b*c-a*d)^5*(a+b*x)^8)],
[(c+d*x)^7/(a+b*x)^14,x,2,-1/13*(b*c-a*d)^7/(b^8*(a+b*x)^13)-7/12*d*(b*c-a*d)^6/(b^8*(a+b*x)^12)-21/11*d^2*(b*c-a*d)^5/(b^8*(a+b*x)^11)-7/2*d^3*(b*c-a*d)^4/(b^8*(a+b*x)^10)-35/9*d^4*(b*c-a*d)^3/(b^8*(a+b*x)^9)-21/8*d^5*(b*c-a*d)^2/(b^8*(a+b*x)^8)-d^6*(b*c-a*d)/(b^8*(a+b*x)^7)-1/6*d^7/(b^8*(a+b*x)^6)],
[(c+d*x)^7/(a+b*x)^15,x,2,-1/14*(b*c-a*d)^7/(b^8*(a+b*x)^14)-7/13*d*(b*c-a*d)^6/(b^8*(a+b*x)^13)-7/4*d^2*(b*c-a*d)^5/(b^8*(a+b*x)^12)-35/11*d^3*(b*c-a*d)^4/(b^8*(a+b*x)^11)-7/2*d^4*(b*c-a*d)^3/(b^8*(a+b*x)^10)-7/3*d^5*(b*c-a*d)^2/(b^8*(a+b*x)^9)-7/8*d^6*(b*c-a*d)/(b^8*(a+b*x)^8)-1/7*d^7/(b^8*(a+b*x)^7)],
[(c+d*x)^7/(a+b*x)^16,x,2,-1/15*(b*c-a*d)^7/(b^8*(a+b*x)^15)-1/2*d*(b*c-a*d)^6/(b^8*(a+b*x)^14)-21/13*d^2*(b*c-a*d)^5/(b^8*(a+b*x)^13)-35/12*d^3*(b*c-a*d)^4/(b^8*(a+b*x)^12)-35/11*d^4*(b*c-a*d)^3/(b^8*(a+b*x)^11)-21/10*d^5*(b*c-a*d)^2/(b^8*(a+b*x)^10)-7/9*d^6*(b*c-a*d)/(b^8*(a+b*x)^9)-1/8*d^7/(b^8*(a+b*x)^8)],
[(a+b*x)^12*(c+d*x)^10,x,2,1/13*(b*c-a*d)^10*(a+b*x)^13/b^11+5/7*d*(b*c-a*d)^9*(a+b*x)^14/b^11+3*d^2*(b*c-a*d)^8*(a+b*x)^15/b^11+15/2*d^3*(b*c-a*d)^7*(a+b*x)^16/b^11+210/17*d^4*(b*c-a*d)^6*(a+b*x)^17/b^11+14*d^5*(b*c-a*d)^5*(a+b*x)^18/b^11+210/19*d^6*(b*c-a*d)^4*(a+b*x)^19/b^11+6*d^7*(b*c-a*d)^3*(a+b*x)^20/b^11+15/7*d^8*(b*c-a*d)^2*(a+b*x)^21/b^11+5/11*d^9*(b*c-a*d)*(a+b*x)^22/b^11+1/23*d^10*(a+b*x)^23/b^11],
[(a+b*x)^11*(c+d*x)^10,x,2,1/12*(b*c-a*d)^10*(a+b*x)^12/b^11+10/13*d*(b*c-a*d)^9*(a+b*x)^13/b^11+45/14*d^2*(b*c-a*d)^8*(a+b*x)^14/b^11+8*d^3*(b*c-a*d)^7*(a+b*x)^15/b^11+105/8*d^4*(b*c-a*d)^6*(a+b*x)^16/b^11+252/17*d^5*(b*c-a*d)^5*(a+b*x)^17/b^11+35/3*d^6*(b*c-a*d)^4*(a+b*x)^18/b^11+120/19*d^7*(b*c-a*d)^3*(a+b*x)^19/b^11+9/4*d^8*(b*c-a*d)^2*(a+b*x)^20/b^11+10/21*d^9*(b*c-a*d)*(a+b*x)^21/b^11+1/22*d^10*(a+b*x)^22/b^11],
[(a+b*x)^10*(c+d*x)^10,x,2,1/11*(b*c-a*d)^10*(a+b*x)^11/b^11+5/6*d*(b*c-a*d)^9*(a+b*x)^12/b^11+45/13*d^2*(b*c-a*d)^8*(a+b*x)^13/b^11+60/7*d^3*(b*c-a*d)^7*(a+b*x)^14/b^11+14*d^4*(b*c-a*d)^6*(a+b*x)^15/b^11+63/4*d^5*(b*c-a*d)^5*(a+b*x)^16/b^11+210/17*d^6*(b*c-a*d)^4*(a+b*x)^17/b^11+20/3*d^7*(b*c-a*d)^3*(a+b*x)^18/b^11+45/19*d^8*(b*c-a*d)^2*(a+b*x)^19/b^11+1/2*d^9*(b*c-a*d)*(a+b*x)^20/b^11+1/21*d^10*(a+b*x)^21/b^11],
[(a+b*x)^9*(c+d*x)^10,x,2,-1/11*(b*c-a*d)^9*(c+d*x)^11/d^10+3/4*b*(b*c-a*d)^8*(c+d*x)^12/d^10-36/13*b^2*(b*c-a*d)^7*(c+d*x)^13/d^10+6*b^3*(b*c-a*d)^6*(c+d*x)^14/d^10-42/5*b^4*(b*c-a*d)^5*(c+d*x)^15/d^10+63/8*b^5*(b*c-a*d)^4*(c+d*x)^16/d^10-84/17*b^6*(b*c-a*d)^3*(c+d*x)^17/d^10+2*b^7*(b*c-a*d)^2*(c+d*x)^18/d^10-9/19*b^8*(b*c-a*d)*(c+d*x)^19/d^10+1/20*b^9*(c+d*x)^20/d^10],
[(a+b*x)^8*(c+d*x)^10,x,2,1/11*(b*c-a*d)^8*(c+d*x)^11/d^9-2/3*b*(b*c-a*d)^7*(c+d*x)^12/d^9+28/13*b^2*(b*c-a*d)^6*(c+d*x)^13/d^9-4*b^3*(b*c-a*d)^5*(c+d*x)^14/d^9+14/3*b^4*(b*c-a*d)^4*(c+d*x)^15/d^9-7/2*b^5*(b*c-a*d)^3*(c+d*x)^16/d^9+28/17*b^6*(b*c-a*d)^2*(c+d*x)^17/d^9-4/9*b^7*(b*c-a*d)*(c+d*x)^18/d^9+1/19*b^8*(c+d*x)^19/d^9],
[(a+b*x)^7*(c+d*x)^10,x,2,-1/11*(b*c-a*d)^7*(c+d*x)^11/d^8+7/12*b*(b*c-a*d)^6*(c+d*x)^12/d^8-21/13*b^2*(b*c-a*d)^5*(c+d*x)^13/d^8+5/2*b^3*(b*c-a*d)^4*(c+d*x)^14/d^8-7/3*b^4*(b*c-a*d)^3*(c+d*x)^15/d^8+21/16*b^5*(b*c-a*d)^2*(c+d*x)^16/d^8-7/17*b^6*(b*c-a*d)*(c+d*x)^17/d^8+1/18*b^7*(c+d*x)^18/d^8],
[(a+b*x)^6*(c+d*x)^10,x,2,1/11*(b*c-a*d)^6*(c+d*x)^11/d^7-1/2*b*(b*c-a*d)^5*(c+d*x)^12/d^7+15/13*b^2*(b*c-a*d)^4*(c+d*x)^13/d^7-10/7*b^3*(b*c-a*d)^3*(c+d*x)^14/d^7+b^4*(b*c-a*d)^2*(c+d*x)^15/d^7-3/8*b^5*(b*c-a*d)*(c+d*x)^16/d^7+1/17*b^6*(c+d*x)^17/d^7],
[(a+b*x)^5*(c+d*x)^10,x,2,-1/11*(b*c-a*d)^5*(c+d*x)^11/d^6+5/12*b*(b*c-a*d)^4*(c+d*x)^12/d^6-10/13*b^2*(b*c-a*d)^3*(c+d*x)^13/d^6+5/7*b^3*(b*c-a*d)^2*(c+d*x)^14/d^6-1/3*b^4*(b*c-a*d)*(c+d*x)^15/d^6+1/16*b^5*(c+d*x)^16/d^6],
[(a+b*x)^4*(c+d*x)^10,x,2,1/11*(b*c-a*d)^4*(c+d*x)^11/d^5-1/3*b*(b*c-a*d)^3*(c+d*x)^12/d^5+6/13*b^2*(b*c-a*d)^2*(c+d*x)^13/d^5-2/7*b^3*(b*c-a*d)*(c+d*x)^14/d^5+1/15*b^4*(c+d*x)^15/d^5],
[(a+b*x)^3*(c+d*x)^10,x,2,-1/11*(b*c-a*d)^3*(c+d*x)^11/d^4+1/4*b*(b*c-a*d)^2*(c+d*x)^12/d^4-3/13*b^2*(b*c-a*d)*(c+d*x)^13/d^4+1/14*b^3*(c+d*x)^14/d^4],
[(a+b*x)^2*(c+d*x)^10,x,2,1/11*(b*c-a*d)^2*(c+d*x)^11/d^3-1/6*b*(b*c-a*d)*(c+d*x)^12/d^3+1/13*b^2*(c+d*x)^13/d^3],
[(a+b*x)*(c+d*x)^10,x,2,-1/11*(b*c-a*d)*(c+d*x)^11/d^2+1/12*b*(c+d*x)^12/d^2],
[(c+d*x)^10,x,1,1/11*(c+d*x)^11/d],
[(c+d*x)^10/(a+b*x),x,2,d*(b*c-a*d)^9*x/b^10+1/2*(b*c-a*d)^8*(c+d*x)^2/b^9+1/3*(b*c-a*d)^7*(c+d*x)^3/b^8+1/4*(b*c-a*d)^6*(c+d*x)^4/b^7+1/5*(b*c-a*d)^5*(c+d*x)^5/b^6+1/6*(b*c-a*d)^4*(c+d*x)^6/b^5+1/7*(b*c-a*d)^3*(c+d*x)^7/b^4+1/8*(b*c-a*d)^2*(c+d*x)^8/b^3+1/9*(b*c-a*d)*(c+d*x)^9/b^2+1/10*(c+d*x)^10/b+(b*c-a*d)^10*log(a+b*x)/b^11],
[(c+d*x)^10/(a+b*x)^2,x,2,45*d^2*(b*c-a*d)^8*x/b^10-(b*c-a*d)^10/(b^11*(a+b*x))+60*d^3*(b*c-a*d)^7*(a+b*x)^2/b^11+70*d^4*(b*c-a*d)^6*(a+b*x)^3/b^11+63*d^5*(b*c-a*d)^5*(a+b*x)^4/b^11+42*d^6*(b*c-a*d)^4*(a+b*x)^5/b^11+20*d^7*(b*c-a*d)^3*(a+b*x)^6/b^11+45/7*d^8*(b*c-a*d)^2*(a+b*x)^7/b^11+5/4*d^9*(b*c-a*d)*(a+b*x)^8/b^11+1/9*d^10*(a+b*x)^9/b^11+10*d*(b*c-a*d)^9*log(a+b*x)/b^11],
[(c+d*x)^10/(a+b*x)^3,x,2,120*d^3*(b*c-a*d)^7*x/b^10-1/2*(b*c-a*d)^10/(b^11*(a+b*x)^2)-10*d*(b*c-a*d)^9/(b^11*(a+b*x))+105*d^4*(b*c-a*d)^6*(a+b*x)^2/b^11+84*d^5*(b*c-a*d)^5*(a+b*x)^3/b^11+105/2*d^6*(b*c-a*d)^4*(a+b*x)^4/b^11+24*d^7*(b*c-a*d)^3*(a+b*x)^5/b^11+15/2*d^8*(b*c-a*d)^2*(a+b*x)^6/b^11+10/7*d^9*(b*c-a*d)*(a+b*x)^7/b^11+1/8*d^10*(a+b*x)^8/b^11+45*d^2*(b*c-a*d)^8*log(a+b*x)/b^11],
[(c+d*x)^10/(a+b*x)^4,x,2,210*d^4*(b*c-a*d)^6*x/b^10-1/3*(b*c-a*d)^10/(b^11*(a+b*x)^3)-5*d*(b*c-a*d)^9/(b^11*(a+b*x)^2)-45*d^2*(b*c-a*d)^8/(b^11*(a+b*x))+126*d^5*(b*c-a*d)^5*(a+b*x)^2/b^11+70*d^6*(b*c-a*d)^4*(a+b*x)^3/b^11+30*d^7*(b*c-a*d)^3*(a+b*x)^4/b^11+9*d^8*(b*c-a*d)^2*(a+b*x)^5/b^11+5/3*d^9*(b*c-a*d)*(a+b*x)^6/b^11+1/7*d^10*(a+b*x)^7/b^11+120*d^3*(b*c-a*d)^7*log(a+b*x)/b^11],
[(c+d*x)^10/(a+b*x)^5,x,2,252*d^5*(b*c-a*d)^5*x/b^10-1/4*(b*c-a*d)^10/(b^11*(a+b*x)^4)-10/3*d*(b*c-a*d)^9/(b^11*(a+b*x)^3)-45/2*d^2*(b*c-a*d)^8/(b^11*(a+b*x)^2)-120*d^3*(b*c-a*d)^7/(b^11*(a+b*x))+105*d^6*(b*c-a*d)^4*(a+b*x)^2/b^11+40*d^7*(b*c-a*d)^3*(a+b*x)^3/b^11+45/4*d^8*(b*c-a*d)^2*(a+b*x)^4/b^11+2*d^9*(b*c-a*d)*(a+b*x)^5/b^11+1/6*d^10*(a+b*x)^6/b^11+210*d^4*(b*c-a*d)^6*log(a+b*x)/b^11],
[(c+d*x)^10/(a+b*x)^6,x,2,210*d^6*(b*c-a*d)^4*x/b^10-1/5*(b*c-a*d)^10/(b^11*(a+b*x)^5)-5/2*d*(b*c-a*d)^9/(b^11*(a+b*x)^4)-15*d^2*(b*c-a*d)^8/(b^11*(a+b*x)^3)-60*d^3*(b*c-a*d)^7/(b^11*(a+b*x)^2)-210*d^4*(b*c-a*d)^6/(b^11*(a+b*x))+60*d^7*(b*c-a*d)^3*(a+b*x)^2/b^11+15*d^8*(b*c-a*d)^2*(a+b*x)^3/b^11+5/2*d^9*(b*c-a*d)*(a+b*x)^4/b^11+1/5*d^10*(a+b*x)^5/b^11+252*d^5*(b*c-a*d)^5*log(a+b*x)/b^11],
[(c+d*x)^10/(a+b*x)^7,x,2,120*d^7*(b*c-a*d)^3*x/b^10-1/6*(b*c-a*d)^10/(b^11*(a+b*x)^6)-2*d*(b*c-a*d)^9/(b^11*(a+b*x)^5)-45/4*d^2*(b*c-a*d)^8/(b^11*(a+b*x)^4)-40*d^3*(b*c-a*d)^7/(b^11*(a+b*x)^3)-105*d^4*(b*c-a*d)^6/(b^11*(a+b*x)^2)-252*d^5*(b*c-a*d)^5/(b^11*(a+b*x))+45/2*d^8*(b*c-a*d)^2*(a+b*x)^2/b^11+10/3*d^9*(b*c-a*d)*(a+b*x)^3/b^11+1/4*d^10*(a+b*x)^4/b^11+210*d^6*(b*c-a*d)^4*log(a+b*x)/b^11],
[(c+d*x)^10/(a+b*x)^8,x,2,45*d^8*(b*c-a*d)^2*x/b^10-1/7*(b*c-a*d)^10/(b^11*(a+b*x)^7)-5/3*d*(b*c-a*d)^9/(b^11*(a+b*x)^6)-9*d^2*(b*c-a*d)^8/(b^11*(a+b*x)^5)-30*d^3*(b*c-a*d)^7/(b^11*(a+b*x)^4)-70*d^4*(b*c-a*d)^6/(b^11*(a+b*x)^3)-126*d^5*(b*c-a*d)^5/(b^11*(a+b*x)^2)-210*d^6*(b*c-a*d)^4/(b^11*(a+b*x))+5*d^9*(b*c-a*d)*(a+b*x)^2/b^11+1/3*d^10*(a+b*x)^3/b^11+120*d^7*(b*c-a*d)^3*log(a+b*x)/b^11],
[(c+d*x)^10/(a+b*x)^9,x,2,d^9*(10*b*c-9*a*d)*x/b^10+1/2*d^10*x^2/b^9-1/8*(b*c-a*d)^10/(b^11*(a+b*x)^8)-10/7*d*(b*c-a*d)^9/(b^11*(a+b*x)^7)-15/2*d^2*(b*c-a*d)^8/(b^11*(a+b*x)^6)-24*d^3*(b*c-a*d)^7/(b^11*(a+b*x)^5)-105/2*d^4*(b*c-a*d)^6/(b^11*(a+b*x)^4)-84*d^5*(b*c-a*d)^5/(b^11*(a+b*x)^3)-105*d^6*(b*c-a*d)^4/(b^11*(a+b*x)^2)-120*d^7*(b*c-a*d)^3/(b^11*(a+b*x))+45*d^8*(b*c-a*d)^2*log(a+b*x)/b^11],
[(c+d*x)^10/(a+b*x)^10,x,2,d^10*x/b^10-1/9*(b*c-a*d)^10/(b^11*(a+b*x)^9)-5/4*d*(b*c-a*d)^9/(b^11*(a+b*x)^8)-45/7*d^2*(b*c-a*d)^8/(b^11*(a+b*x)^7)-20*d^3*(b*c-a*d)^7/(b^11*(a+b*x)^6)-42*d^4*(b*c-a*d)^6/(b^11*(a+b*x)^5)-63*d^5*(b*c-a*d)^5/(b^11*(a+b*x)^4)-70*d^6*(b*c-a*d)^4/(b^11*(a+b*x)^3)-60*d^7*(b*c-a*d)^3/(b^11*(a+b*x)^2)-45*d^8*(b*c-a*d)^2/(b^11*(a+b*x))+10*d^9*(b*c-a*d)*log(a+b*x)/b^11],
[(c+d*x)^10/(a+b*x)^11,x,2,-1/10*(b*c-a*d)^10/(b^11*(a+b*x)^10)-10/9*d*(b*c-a*d)^9/(b^11*(a+b*x)^9)-45/8*d^2*(b*c-a*d)^8/(b^11*(a+b*x)^8)-120/7*d^3*(b*c-a*d)^7/(b^11*(a+b*x)^7)-35*d^4*(b*c-a*d)^6/(b^11*(a+b*x)^6)-252/5*d^5*(b*c-a*d)^5/(b^11*(a+b*x)^5)-105/2*d^6*(b*c-a*d)^4/(b^11*(a+b*x)^4)-40*d^7*(b*c-a*d)^3/(b^11*(a+b*x)^3)-45/2*d^8*(b*c-a*d)^2/(b^11*(a+b*x)^2)-10*d^9*(b*c-a*d)/(b^11*(a+b*x))+d^10*log(a+b*x)/b^11],
[(c+d*x)^10/(a+b*x)^12,x,1,-1/11*(c+d*x)^11/((b*c-a*d)*(a+b*x)^11)],
[(c+d*x)^10/(a+b*x)^13,x,2,-1/12*(c+d*x)^11/((b*c-a*d)*(a+b*x)^12)+1/132*d*(c+d*x)^11/((b*c-a*d)^2*(a+b*x)^11)],
[(c+d*x)^10/(a+b*x)^14,x,3,-1/13*(c+d*x)^11/((b*c-a*d)*(a+b*x)^13)+1/78*d*(c+d*x)^11/((b*c-a*d)^2*(a+b*x)^12)-1/858*d^2*(c+d*x)^11/((b*c-a*d)^3*(a+b*x)^11)],
[(c+d*x)^10/(a+b*x)^15,x,4,-1/14*(c+d*x)^11/((b*c-a*d)*(a+b*x)^14)+3/182*d*(c+d*x)^11/((b*c-a*d)^2*(a+b*x)^13)-1/364*d^2*(c+d*x)^11/((b*c-a*d)^3*(a+b*x)^12)+1/4004*d^3*(c+d*x)^11/((b*c-a*d)^4*(a+b*x)^11)],
[(c+d*x)^10/(a+b*x)^16,x,5,-1/15*(c+d*x)^11/((b*c-a*d)*(a+b*x)^15)+2/105*d*(c+d*x)^11/((b*c-a*d)^2*(a+b*x)^14)-2/455*d^2*(c+d*x)^11/((b*c-a*d)^3*(a+b*x)^13)+1/1365*d^3*(c+d*x)^11/((b*c-a*d)^4*(a+b*x)^12)-1/15015*d^4*(c+d*x)^11/((b*c-a*d)^5*(a+b*x)^11)],
[(c+d*x)^10/(a+b*x)^17,x,6,-1/16*(c+d*x)^11/((b*c-a*d)*(a+b*x)^16)+1/48*d*(c+d*x)^11/((b*c-a*d)^2*(a+b*x)^15)-1/168*d^2*(c+d*x)^11/((b*c-a*d)^3*(a+b*x)^14)+1/728*d^3*(c+d*x)^11/((b*c-a*d)^4*(a+b*x)^13)-1/4368*d^4*(c+d*x)^11/((b*c-a*d)^5*(a+b*x)^12)+1/48048*d^5*(c+d*x)^11/((b*c-a*d)^6*(a+b*x)^11)],
[(c+d*x)^10/(a+b*x)^18,x,7,-1/17*(c+d*x)^11/((b*c-a*d)*(a+b*x)^17)+3/136*d*(c+d*x)^11/((b*c-a*d)^2*(a+b*x)^16)-1/136*d^2*(c+d*x)^11/((b*c-a*d)^3*(a+b*x)^15)+1/476*d^3*(c+d*x)^11/((b*c-a*d)^4*(a+b*x)^14)-3/6188*d^4*(c+d*x)^11/((b*c-a*d)^5*(a+b*x)^13)+1/12376*d^5*(c+d*x)^11/((b*c-a*d)^6*(a+b*x)^12)-1/136136*d^6*(c+d*x)^11/((b*c-a*d)^7*(a+b*x)^11)],
[(c+d*x)^10/(a+b*x)^19,x,8,-1/18*(c+d*x)^11/((b*c-a*d)*(a+b*x)^18)+7/306*d*(c+d*x)^11/((b*c-a*d)^2*(a+b*x)^17)-7/816*d^2*(c+d*x)^11/((b*c-a*d)^3*(a+b*x)^16)+7/2448*d^3*(c+d*x)^11/((b*c-a*d)^4*(a+b*x)^15)-1/1224*d^4*(c+d*x)^11/((b*c-a*d)^5*(a+b*x)^14)+1/5304*d^5*(c+d*x)^11/((b*c-a*d)^6*(a+b*x)^13)-1/31824*d^6*(c+d*x)^11/((b*c-a*d)^7*(a+b*x)^12)+1/350064*d^7*(c+d*x)^11/((b*c-a*d)^8*(a+b*x)^11)],
[(c+d*x)^10/(a+b*x)^20,x,2,-1/19*(b*c-a*d)^10/(b^11*(a+b*x)^19)-5/9*d*(b*c-a*d)^9/(b^11*(a+b*x)^18)-45/17*d^2*(b*c-a*d)^8/(b^11*(a+b*x)^17)-15/2*d^3*(b*c-a*d)^7/(b^11*(a+b*x)^16)-14*d^4*(b*c-a*d)^6/(b^11*(a+b*x)^15)-18*d^5*(b*c-a*d)^5/(b^11*(a+b*x)^14)-210/13*d^6*(b*c-a*d)^4/(b^11*(a+b*x)^13)-10*d^7*(b*c-a*d)^3/(b^11*(a+b*x)^12)-45/11*d^8*(b*c-a*d)^2/(b^11*(a+b*x)^11)-d^9*(b*c-a*d)/(b^11*(a+b*x)^10)-1/9*d^10/(b^11*(a+b*x)^9)],
[(c+d*x)^10/(a+b*x)^21,x,2,-1/20*(b*c-a*d)^10/(b^11*(a+b*x)^20)-10/19*d*(b*c-a*d)^9/(b^11*(a+b*x)^19)-5/2*d^2*(b*c-a*d)^8/(b^11*(a+b*x)^18)-120/17*d^3*(b*c-a*d)^7/(b^11*(a+b*x)^17)-105/8*d^4*(b*c-a*d)^6/(b^11*(a+b*x)^16)-84/5*d^5*(b*c-a*d)^5/(b^11*(a+b*x)^15)-15*d^6*(b*c-a*d)^4/(b^11*(a+b*x)^14)-120/13*d^7*(b*c-a*d)^3/(b^11*(a+b*x)^13)-15/4*d^8*(b*c-a*d)^2/(b^11*(a+b*x)^12)-10/11*d^9*(b*c-a*d)/(b^11*(a+b*x)^11)-1/10*d^10/(b^11*(a+b*x)^10)],
[(c+d*x)^10/(a+b*x)^22,x,2,-1/21*(b*c-a*d)^10/(b^11*(a+b*x)^21)-1/2*d*(b*c-a*d)^9/(b^11*(a+b*x)^20)-45/19*d^2*(b*c-a*d)^8/(b^11*(a+b*x)^19)-20/3*d^3*(b*c-a*d)^7/(b^11*(a+b*x)^18)-210/17*d^4*(b*c-a*d)^6/(b^11*(a+b*x)^17)-63/4*d^5*(b*c-a*d)^5/(b^11*(a+b*x)^16)-14*d^6*(b*c-a*d)^4/(b^11*(a+b*x)^15)-60/7*d^7*(b*c-a*d)^3/(b^11*(a+b*x)^14)-45/13*d^8*(b*c-a*d)^2/(b^11*(a+b*x)^13)-5/6*d^9*(b*c-a*d)/(b^11*(a+b*x)^12)-1/11*d^10/(b^11*(a+b*x)^11)],
#  {(a + b*x)^m*(c + d*x)^15, x, 2, ((b*c - a*d)^15*(a + b*x)^(1 + m))/(b^16*(1 + m)) + (15*d*(b*c - a*d)^14*(a + b*x)^(2 + m))/(b^16*(2 + m)) + (105*d^2*(b*c - a*d)^13*(a + b*x)^(3 + m))/(b^16*(3 + m)) + (455*d^3*(b*c - a*d)^12*(a + b*x)^(4 + m))/(b^16*(4 + m)) + (1365*d^4*(b*c - a*d)^11*(a + b*x)^(5 + m))/(b^16*(5 + m)) + (3003*d^5*(b*c - a*d)^10*(a + b*x)^(6 + m))/(b^16*(6 + m)) + (5005*d^6*(b*c - a*d)^9*(a + b*x)^(7 + m))/(b^16*(7 + m)) + (6435*d^7*(b*c - a*d)^8*(a + b*x)^(8 + m))/(b^16*(8 + m)) + (6435*d^8*(b*c - a*d)^7*(a + b*x)^(9 + m))/(b^16*(9 + m)) + (5005*d^9*(b*c - a*d)^6*(a + b*x)^(10 + m))/(b^16*(10 + m)) + (3003*d^10*(b*c - a*d)^5*(a + b*x)^(11 + m))/(b^16*(11 + m)) + (1365*d^11*(b*c - a*d)^4*(a + b*x)^(12 + m))/(b^16*(12 + m)) + (455*d^12*(b*c - a*d)^3*(a + b*x)^(13 + m))/(b^16*(13 + m)) + (105*d^13*(b*c - a*d)^2*(a + b*x)^(14 + m))/(b^16*(14 + m)) + (15*d^14*(b*c - a*d)*(a + b*x)^(15 + m))/(b^16*(15 + m)) + (d^15*(a + b*x)^(16 + m))/(b^16*(16 + m))}
# {(a + b*x)^17*(c + d*x)^15, x, 2, ((b*c - a*d)^15*(a + b*x)^18)/(18*b^16) + (15*d*(b*c - a*d)^14*(a + b*x)^19)/(19*b^16) + (21*d^2*(b*c - a*d)^13*(a + b*x)^20)/(4*b^16) + (65*d^3*(b*c - a*d)^12*(a + b*x)^21)/(3*b^16) + (1365*d^4*(b*c - a*d)^11*(a + b*x)^22)/(22*b^16) + (3003*d^5*(b*c - a*d)^10*(a + b*x)^23)/(23*b^16) + (5005*d^6*(b*c - a*d)^9*(a + b*x)^24)/(24*b^16) + (1287*d^7*(b*c - a*d)^8*(a + b*x)^25)/(5*b^16) + (495*d^8*(b*c - a*d)^7*(a + b*x)^26)/(2*b^16) + (5005*d^9*(b*c - a*d)^6*(a + b*x)^27)/(27*b^16) + (429*d^10*(b*c - a*d)^5*(a + b*x)^28)/(4*b^16) + (1365*d^11*(b*c - a*d)^4*(a + b*x)^29)/(29*b^16) + (91*d^12*(b*c - a*d)^3*(a + b*x)^30)/(6*b^16) + (105*d^13*(b*c - a*d)^2*(a + b*x)^31)/(31*b^16) + (15*d^14*(b*c - a*d)*(a + b*x)^32)/(32*b^16) + (d^15*(a + b*x)^33)/(33*b^16)}
# {(a + b*x)^16*(c + d*x)^15, x, 2, ((b*c - a*d)^15*(a + b*x)^17)/(17*b^16) + (5*d*(b*c - a*d)^14*(a + b*x)^18)/(6*b^16) + (105*d^2*(b*c - a*d)^13*(a + b*x)^19)/(19*b^16) + (91*d^3*(b*c - a*d)^12*(a + b*x)^20)/(4*b^16) + (65*d^4*(b*c - a*d)^11*(a + b*x)^21)/b^16 + (273*d^5*(b*c - a*d)^10*(a + b*x)^22)/(2*b^16) + (5005*d^6*(b*c - a*d)^9*(a + b*x)^23)/(23*b^16) + (2145*d^7*(b*c - a*d)^8*(a + b*x)^24)/(8*b^16) + (1287*d^8*(b*c - a*d)^7*(a + b*x)^25)/(5*b^16) + (385*d^9*(b*c - a*d)^6*(a + b*x)^26)/(2*b^16) + (1001*d^10*(b*c - a*d)^5*(a + b*x)^27)/(9*b^16) + (195*d^11*(b*c - a*d)^4*(a + b*x)^28)/(4*b^16) + (455*d^12*(b*c - a*d)^3*(a + b*x)^29)/(29*b^16) + (7*d^13*(b*c - a*d)^2*(a + b*x)^30)/(2*b^16) + (15*d^14*(b*c - a*d)*(a + b*x)^31)/(31*b^16) + (d^15*(a + b*x)^32)/(32*b^16)}
# {(a + b*x)^15*(c + d*x)^15, x, 2, ((b*c - a*d)^15*(a + b*x)^16)/(16*b^16) + (15*d*(b*c - a*d)^14*(a + b*x)^17)/(17*b^16) + (35*d^2*(b*c - a*d)^13*(a + b*x)^18)/(6*b^16) + (455*d^3*(b*c - a*d)^12*(a + b*x)^19)/(19*b^16) + (273*d^4*(b*c - a*d)^11*(a + b*x)^20)/(4*b^16) + (143*d^5*(b*c - a*d)^10*(a + b*x)^21)/b^16 + (455*d^6*(b*c - a*d)^9*(a + b*x)^22)/(2*b^16) + (6435*d^7*(b*c - a*d)^8*(a + b*x)^23)/(23*b^16) + (2145*d^8*(b*c - a*d)^7*(a + b*x)^24)/(8*b^16) + (1001*d^9*(b*c - a*d)^6*(a + b*x)^25)/(5*b^16) + (231*d^10*(b*c - a*d)^5*(a + b*x)^26)/(2*b^16) + (455*d^11*(b*c - a*d)^4*(a + b*x)^27)/(9*b^16) + (65*d^12*(b*c - a*d)^3*(a + b*x)^28)/(4*b^16) + (105*d^13*(b*c - a*d)^2*(a + b*x)^29)/(29*b^16) + (d^14*(b*c - a*d)*(a + b*x)^30)/(2*b^16) + (d^15*(a + b*x)^31)/(31*b^16)}
# {(a + b*x)^14*(c + d*x)^15, x, 2, ((b*c - a*d)^14*(c + d*x)^16)/(16*d^15) - (14*b*(b*c - a*d)^13*(c + d*x)^17)/(17*d^15) + (91*b^2*(b*c - a*d)^12*(c + d*x)^18)/(18*d^15) - (364*b^3*(b*c - a*d)^11*(c + d*x)^19)/(19*d^15) + (1001*b^4*(b*c - a*d)^10*(c + d*x)^20)/(20*d^15) - (286*b^5*(b*c - a*d)^9*(c + d*x)^21)/(3*d^15) + (273*b^6*(b*c - a*d)^8*(c + d*x)^22)/(2*d^15) - (3432*b^7*(b*c - a*d)^7*(c + d*x)^23)/(23*d^15) + (1001*b^8*(b*c - a*d)^6*(c + d*x)^24)/(8*d^15) - (2002*b^9*(b*c - a*d)^5*(c + d*x)^25)/(25*d^15) + (77*b^10*(b*c - a*d)^4*(c + d*x)^26)/(2*d^15) - (364*b^11*(b*c - a*d)^3*(c + d*x)^27)/(27*d^15) + (13*b^12*(b*c - a*d)^2*(c + d*x)^28)/(4*d^15) - (14*b^13*(b*c - a*d)*(c + d*x)^29)/(29*d^15) + (b^14*(c + d*x)^30)/(30*d^15)}
# {(a + b*x)^13*(c + d*x)^15, x, 2, -(((b*c - a*d)^13*(c + d*x)^16)/(16*d^14)) + (13*b*(b*c - a*d)^12*(c + d*x)^17)/(17*d^14) - (13*b^2*(b*c - a*d)^11*(c + d*x)^18)/(3*d^14) + (286*b^3*(b*c - a*d)^10*(c + d*x)^19)/(19*d^14) - (143*b^4*(b*c - a*d)^9*(c + d*x)^20)/(4*d^14) + (429*b^5*(b*c - a*d)^8*(c + d*x)^21)/(7*d^14) - (78*b^6*(b*c - a*d)^7*(c + d*x)^22)/d^14 + (1716*b^7*(b*c - a*d)^6*(c + d*x)^23)/(23*d^14) - (429*b^8*(b*c - a*d)^5*(c + d*x)^24)/(8*d^14) + (143*b^9*(b*c - a*d)^4*(c + d*x)^25)/(5*d^14) - (11*b^10*(b*c - a*d)^3*(c + d*x)^26)/d^14 + (26*b^11*(b*c - a*d)^2*(c + d*x)^27)/(9*d^14) - (13*b^12*(b*c - a*d)*(c + d*x)^28)/(28*d^14) + (b^13*(c + d*x)^29)/(29*d^14)}
# {(a + b*x)^12*(c + d*x)^15, x, 2, ((b*c - a*d)^12*(c + d*x)^16)/(16*d^13) - (12*b*(b*c - a*d)^11*(c + d*x)^17)/(17*d^13) + (11*b^2*(b*c - a*d)^10*(c + d*x)^18)/(3*d^13) - (220*b^3*(b*c - a*d)^9*(c + d*x)^19)/(19*d^13) + (99*b^4*(b*c - a*d)^8*(c + d*x)^20)/(4*d^13) - (264*b^5*(b*c - a*d)^7*(c + d*x)^21)/(7*d^13) + (42*b^6*(b*c - a*d)^6*(c + d*x)^22)/d^13 - (792*b^7*(b*c - a*d)^5*(c + d*x)^23)/(23*d^13) + (165*b^8*(b*c - a*d)^4*(c + d*x)^24)/(8*d^13) - (44*b^9*(b*c - a*d)^3*(c + d*x)^25)/(5*d^13) + (33*b^10*(b*c - a*d)^2*(c + d*x)^26)/(13*d^13) - (4*b^11*(b*c - a*d)*(c + d*x)^27)/(9*d^13) + (b^12*(c + d*x)^28)/(28*d^13)}
# {(a + b*x)^11*(c + d*x)^15, x, 2, -((b*c - a*d)^11*(c + d*x)^16)/(16*d^12) + (11*b*(b*c - a*d)^10*(c + d*x)^17)/(17*d^12) - (55*b^2*(b*c - a*d)^9*(c + d*x)^18)/(18*d^12) + (165*b^3*(b*c - a*d)^8*(c + d*x)^19)/(19*d^12) - (33*b^4*(b*c - a*d)^7*(c + d*x)^20)/(2*d^12) + (22*b^5*(b*c - a*d)^6*(c + d*x)^21)/d^12 - (21*b^6*(b*c - a*d)^5*(c + d*x)^22)/d^12 + (330*b^7*(b*c - a*d)^4*(c + d*x)^23)/(23*d^12) - (55*b^8*(b*c - a*d)^3*(c + d*x)^24)/(8*d^12) + (11*b^9*(b*c - a*d)^2*(c + d*x)^25)/(5*d^12) - (11*b^10*(b*c - a*d)*(c + d*x)^26)/(26*d^12) + (b^11*(c + d*x)^27)/(27*d^12)}
# {(a + b*x)^10*(c + d*x)^15, x, 2, ((b*c - a*d)^10*(c + d*x)^16)/(16*d^11) - (10*b*(b*c - a*d)^9*(c + d*x)^17)/(17*d^11) + (5*b^2*(b*c - a*d)^8*(c + d*x)^18)/(2*d^11) - (120*b^3*(b*c - a*d)^7*(c + d*x)^19)/(19*d^11) + (21*b^4*(b*c - a*d)^6*(c + d*x)^20)/(2*d^11) - (12*b^5*(b*c - a*d)^5*(c + d*x)^21)/d^11 + (105*b^6*(b*c - a*d)^4*(c + d*x)^22)/(11*d^11) - (120*b^7*(b*c - a*d)^3*(c + d*x)^23)/(23*d^11) + (15*b^8*(b*c - a*d)^2*(c + d*x)^24)/(8*d^11) - (2*b^9*(b*c - a*d)*(c + d*x)^25)/(5*d^11) + (b^10*(c + d*x)^26)/(26*d^11)}
# {(a + b*x)^9*(c + d*x)^15, x, 2, -((b*c - a*d)^9*(c + d*x)^16)/(16*d^10) + (9*b*(b*c - a*d)^8*(c + d*x)^17)/(17*d^10) - (2*b^2*(b*c - a*d)^7*(c + d*x)^18)/d^10 + (84*b^3*(b*c - a*d)^6*(c + d*x)^19)/(19*d^10) - (63*b^4*(b*c - a*d)^5*(c + d*x)^20)/(10*d^10) + (6*b^5*(b*c - a*d)^4*(c + d*x)^21)/d^10 - (42*b^6*(b*c - a*d)^3*(c + d*x)^22)/(11*d^10) + (36*b^7*(b*c - a*d)^2*(c + d*x)^23)/(23*d^10) - (3*b^8*(b*c - a*d)*(c + d*x)^24)/(8*d^10) + (b^9*(c + d*x)^25)/(25*d^10)}
# {(a + b*x)^8*(c + d*x)^15, x, 2, ((b*c - a*d)^8*(c + d*x)^16)/(16*d^9) - (8*b*(b*c - a*d)^7*(c + d*x)^17)/(17*d^9) + (14*b^2*(b*c - a*d)^6*(c + d*x)^18)/(9*d^9) - (56*b^3*(b*c - a*d)^5*(c + d*x)^19)/(19*d^9) + (7*b^4*(b*c - a*d)^4*(c + d*x)^20)/(2*d^9) - (8*b^5*(b*c - a*d)^3*(c + d*x)^21)/(3*d^9) + (14*b^6*(b*c - a*d)^2*(c + d*x)^22)/(11*d^9) - (8*b^7*(b*c - a*d)*(c + d*x)^23)/(23*d^9) + (b^8*(c + d*x)^24)/(24*d^9)}
# {(a + b*x)^7*(c + d*x)^15, x, 2, -((b*c - a*d)^7*(c + d*x)^16)/(16*d^8) + (7*b*(b*c - a*d)^6*(c + d*x)^17)/(17*d^8) - (7*b^2*(b*c - a*d)^5*(c + d*x)^18)/(6*d^8) + (35*b^3*(b*c - a*d)^4*(c + d*x)^19)/(19*d^8) - (7*b^4*(b*c - a*d)^3*(c + d*x)^20)/(4*d^8) + (b^5*(b*c - a*d)^2*(c + d*x)^21)/d^8 - (7*b^6*(b*c - a*d)*(c + d*x)^22)/(22*d^8) + (b^7*(c + d*x)^23)/(23*d^8)}
# {(a + b*x)^6*(c + d*x)^15, x, 2, ((b*c - a*d)^6*(c + d*x)^16)/(16*d^7) - (6*b*(b*c - a*d)^5*(c + d*x)^17)/(17*d^7) + (5*b^2*(b*c - a*d)^4*(c + d*x)^18)/(6*d^7) - (20*b^3*(b*c - a*d)^3*(c + d*x)^19)/(19*d^7) + (3*b^4*(b*c - a*d)^2*(c + d*x)^20)/(4*d^7) - (2*b^5*(b*c - a*d)*(c + d*x)^21)/(7*d^7) + (b^6*(c + d*x)^22)/(22*d^7)}
# {(a + b*x)^5*(c + d*x)^15, x, 2, -((b*c - a*d)^5*(c + d*x)^16)/(16*d^6) + (5*b*(b*c - a*d)^4*(c + d*x)^17)/(17*d^6) - (5*b^2*(b*c - a*d)^3*(c + d*x)^18)/(9*d^6) + (10*b^3*(b*c - a*d)^2*(c + d*x)^19)/(19*d^6) - (b^4*(b*c - a*d)*(c + d*x)^20)/(4*d^6) + (b^5*(c + d*x)^21)/(21*d^6)}
# {(a + b*x)^4*(c + d*x)^15, x, 2, ((b*c - a*d)^4*(c + d*x)^16)/(16*d^5) - (4*b*(b*c - a*d)^3*(c + d*x)^17)/(17*d^5) + (b^2*(b*c - a*d)^2*(c + d*x)^18)/(3*d^5) - (4*b^3*(b*c - a*d)*(c + d*x)^19)/(19*d^5) + (b^4*(c + d*x)^20)/(20*d^5)}
# {(a + b*x)^3*(c + d*x)^15, x, 2, -((b*c - a*d)^3*(c + d*x)^16)/(16*d^4) + (3*b*(b*c - a*d)^2*(c + d*x)^17)/(17*d^4) - (b^2*(b*c - a*d)*(c + d*x)^18)/(6*d^4) + (b^3*(c + d*x)^19)/(19*d^4)}
# {(a + b*x)^2*(c + d*x)^15, x, 2, ((b*c - a*d)^2*(c + d*x)^16)/(16*d^3) - (2*b*(b*c - a*d)*(c + d*x)^17)/(17*d^3) + (b^2*(c + d*x)^18)/(18*d^3)}
# {(a + b*x)*(c + d*x)^15, x, 2, -((b*c - a*d)*(c + d*x)^16)/(16*d^2) + (b*(c + d*x)^17)/(17*d^2)}
# {(c + d*x)^15, x, 1, (c + d*x)^16/(16*d)}
# {(c + d*x)^15/(a + b*x), x, 2, (d*(b*c - a*d)^14*x)/b^15 + ((b*c - a*d)^13*(c + d*x)^2)/(2*b^14) + ((b*c - a*d)^12*(c + d*x)^3)/(3*b^13) + ((b*c - a*d)^11*(c + d*x)^4)/(4*b^12) + ((b*c - a*d)^10*(c + d*x)^5)/(5*b^11) + ((b*c - a*d)^9*(c + d*x)^6)/(6*b^10) + ((b*c - a*d)^8*(c + d*x)^7)/(7*b^9) + ((b*c - a*d)^7*(c + d*x)^8)/(8*b^8) + ((b*c - a*d)^6*(c + d*x)^9)/(9*b^7) + ((b*c - a*d)^5*(c + d*x)^10)/(10*b^6) + ((b*c - a*d)^4*(c + d*x)^11)/(11*b^5) + ((b*c - a*d)^3*(c + d*x)^12)/(12*b^4) + ((b*c - a*d)^2*(c + d*x)^13)/(13*b^3) + ((b*c - a*d)*(c + d*x)^14)/(14*b^2) + (c + d*x)^15/(15*b) + ((b*c - a*d)^15*Log[a + b*x])/b^16}
# {(c + d*x)^15/(a + b*x)^2, x, 2, (105*d^2*(b*c - a*d)^13*x)/b^15 - (b*c - a*d)^15/(b^16*(a + b*x)) + (455*d^3*(b*c - a*d)^12*(a + b*x)^2)/(2*b^16) + (455*d^4*(b*c - a*d)^11*(a + b*x)^3)/b^16 + (3003*d^5*(b*c - a*d)^10*(a + b*x)^4)/(4*b^16) + (1001*d^6*(b*c - a*d)^9*(a + b*x)^5)/b^16 + (2145*d^7*(b*c - a*d)^8*(a + b*x)^6)/(2*b^16) + (6435*d^8*(b*c - a*d)^7*(a + b*x)^7)/(7*b^16) + (5005*d^9*(b*c - a*d)^6*(a + b*x)^8)/(8*b^16) + (1001*d^10*(b*c - a*d)^5*(a + b*x)^9)/(3*b^16) + (273*d^11*(b*c - a*d)^4*(a + b*x)^10)/(2*b^16) + (455*d^12*(b*c - a*d)^3*(a + b*x)^11)/(11*b^16) + (35*d^13*(b*c - a*d)^2*(a + b*x)^12)/(4*b^16) + (15*d^14*(b*c - a*d)*(a + b*x)^13)/(13*b^16) + (d^15*(a + b*x)^14)/(14*b^16) + (15*d*(b*c - a*d)^14*Log[a + b*x])/b^16}
# {(c + d*x)^15/(a + b*x)^3, x, 2, (455*d^3*(b*c - a*d)^12*x)/b^15 - (b*c - a*d)^15/(2*b^16*(a + b*x)^2) - (15*d*(b*c - a*d)^14)/(b^16*(a + b*x)) + (1365*d^4*(b*c - a*d)^11*(a + b*x)^2)/(2*b^16) + (1001*d^5*(b*c - a*d)^10*(a + b*x)^3)/b^16 + (5005*d^6*(b*c - a*d)^9*(a + b*x)^4)/(4*b^16) + (1287*d^7*(b*c - a*d)^8*(a + b*x)^5)/b^16 + (2145*d^8*(b*c - a*d)^7*(a + b*x)^6)/(2*b^16) + (715*d^9*(b*c - a*d)^6*(a + b*x)^7)/b^16 + (3003*d^10*(b*c - a*d)^5*(a + b*x)^8)/(8*b^16) + (455*d^11*(b*c - a*d)^4*(a + b*x)^9)/(3*b^16) + (91*d^12*(b*c - a*d)^3*(a + b*x)^10)/(2*b^16) + (105*d^13*(b*c - a*d)^2*(a + b*x)^11)/(11*b^16) + (5*d^14*(b*c - a*d)*(a + b*x)^12)/(4*b^16) + (d^15*(a + b*x)^13)/(13*b^16) + (105*d^2*(b*c - a*d)^13*Log[a + b*x])/b^16}
# {(c + d*x)^15/(a + b*x)^4, x, 2, (1365*d^4*(b*c - a*d)^11*x)/b^15 - (b*c - a*d)^15/(3*b^16*(a + b*x)^3) - (15*d*(b*c - a*d)^14)/(2*b^16*(a + b*x)^2) - (105*d^2*(b*c - a*d)^13)/(b^16*(a + b*x)) + (3003*d^5*(b*c - a*d)^10*(a + b*x)^2)/(2*b^16) + (5005*d^6*(b*c - a*d)^9*(a + b*x)^3)/(3*b^16) + (6435*d^7*(b*c - a*d)^8*(a + b*x)^4)/(4*b^16) + (1287*d^8*(b*c - a*d)^7*(a + b*x)^5)/b^16 + (5005*d^9*(b*c - a*d)^6*(a + b*x)^6)/(6*b^16) + (429*d^10*(b*c - a*d)^5*(a + b*x)^7)/b^16 + (1365*d^11*(b*c - a*d)^4*(a + b*x)^8)/(8*b^16) + (455*d^12*(b*c - a*d)^3*(a + b*x)^9)/(9*b^16) + (21*d^13*(b*c - a*d)^2*(a + b*x)^10)/(2*b^16) + (15*d^14*(b*c - a*d)*(a + b*x)^11)/(11*b^16) + (d^15*(a + b*x)^12)/(12*b^16) + (455*d^3*(b*c - a*d)^12*Log[a + b*x])/b^16}
# {(c + d*x)^15/(a + b*x)^5, x, 2, (3003*d^5*(b*c - a*d)^10*x)/b^15 - (b*c - a*d)^15/(4*b^16*(a + b*x)^4) - (5*d*(b*c - a*d)^14)/(b^16*(a + b*x)^3) - (105*d^2*(b*c - a*d)^13)/(2*b^16*(a + b*x)^2) - (455*d^3*(b*c - a*d)^12)/(b^16*(a + b*x)) + (5005*d^6*(b*c - a*d)^9*(a + b*x)^2)/(2*b^16) + (2145*d^7*(b*c - a*d)^8*(a + b*x)^3)/b^16 + (6435*d^8*(b*c - a*d)^7*(a + b*x)^4)/(4*b^16) + (1001*d^9*(b*c - a*d)^6*(a + b*x)^5)/b^16 + (1001*d^10*(b*c - a*d)^5*(a + b*x)^6)/(2*b^16) + (195*d^11*(b*c - a*d)^4*(a + b*x)^7)/b^16 + (455*d^12*(b*c - a*d)^3*(a + b*x)^8)/(8*b^16) + (35*d^13*(b*c - a*d)^2*(a + b*x)^9)/(3*b^16) + (3*d^14*(b*c - a*d)*(a + b*x)^10)/(2*b^16) + (d^15*(a + b*x)^11)/(11*b^16) + (1365*d^4*(b*c - a*d)^11*Log[a + b*x])/b^16}
# {(c + d*x)^15/(a + b*x)^6, x, 2, (5005*d^6*(b*c - a*d)^9*x)/b^15 - (b*c - a*d)^15/(5*b^16*(a + b*x)^5) - (15*d*(b*c - a*d)^14)/(4*b^16*(a + b*x)^4) - (35*d^2*(b*c - a*d)^13)/(b^16*(a + b*x)^3) - (455*d^3*(b*c - a*d)^12)/(2*b^16*(a + b*x)^2) - (1365*d^4*(b*c - a*d)^11)/(b^16*(a + b*x)) + (6435*d^7*(b*c - a*d)^8*(a + b*x)^2)/(2*b^16) + (2145*d^8*(b*c - a*d)^7*(a + b*x)^3)/b^16 + (5005*d^9*(b*c - a*d)^6*(a + b*x)^4)/(4*b^16) + (3003*d^10*(b*c - a*d)^5*(a + b*x)^5)/(5*b^16) + (455*d^11*(b*c - a*d)^4*(a + b*x)^6)/(2*b^16) + (65*d^12*(b*c - a*d)^3*(a + b*x)^7)/b^16 + (105*d^13*(b*c - a*d)^2*(a + b*x)^8)/(8*b^16) + (5*d^14*(b*c - a*d)*(a + b*x)^9)/(3*b^16) + (d^15*(a + b*x)^10)/(10*b^16) + (3003*d^5*(b*c - a*d)^10*Log[a + b*x])/b^16}
# {(c + d*x)^15/(a + b*x)^7, x, 2, (6435*d^7*(b*c - a*d)^8*x)/b^15 - (b*c - a*d)^15/(6*b^16*(a + b*x)^6) - (3*d*(b*c - a*d)^14)/(b^16*(a + b*x)^5) - (105*d^2*(b*c - a*d)^13)/(4*b^16*(a + b*x)^4) - (455*d^3*(b*c - a*d)^12)/(3*b^16*(a + b*x)^3) - (1365*d^4*(b*c - a*d)^11)/(2*b^16*(a + b*x)^2) - (3003*d^5*(b*c - a*d)^10)/(b^16*(a + b*x)) + (6435*d^8*(b*c - a*d)^7*(a + b*x)^2)/(2*b^16) + (5005*d^9*(b*c - a*d)^6*(a + b*x)^3)/(3*b^16) + (3003*d^10*(b*c - a*d)^5*(a + b*x)^4)/(4*b^16) + (273*d^11*(b*c - a*d)^4*(a + b*x)^5)/b^16 + (455*d^12*(b*c - a*d)^3*(a + b*x)^6)/(6*b^16) + (15*d^13*(b*c - a*d)^2*(a + b*x)^7)/b^16 + (15*d^14*(b*c - a*d)*(a + b*x)^8)/(8*b^16) + (d^15*(a + b*x)^9)/(9*b^16) + (5005*d^6*(b*c - a*d)^9*Log[a + b*x])/b^16}
# {(c + d*x)^15/(a + b*x)^8, x, 2, (6435*d^8*(b*c - a*d)^7*x)/b^15 - (b*c - a*d)^15/(7*b^16*(a + b*x)^7) - (5*d*(b*c - a*d)^14)/(2*b^16*(a + b*x)^6) - (21*d^2*(b*c - a*d)^13)/(b^16*(a + b*x)^5) - (455*d^3*(b*c - a*d)^12)/(4*b^16*(a + b*x)^4) - (455*d^4*(b*c - a*d)^11)/(b^16*(a + b*x)^3) - (3003*d^5*(b*c - a*d)^10)/(2*b^16*(a + b*x)^2) - (5005*d^6*(b*c - a*d)^9)/(b^16*(a + b*x)) + (5005*d^9*(b*c - a*d)^6*(a + b*x)^2)/(2*b^16) + (1001*d^10*(b*c - a*d)^5*(a + b*x)^3)/b^16 + (1365*d^11*(b*c - a*d)^4*(a + b*x)^4)/(4*b^16) + (91*d^12*(b*c - a*d)^3*(a + b*x)^5)/b^16 + (35*d^13*(b*c - a*d)^2*(a + b*x)^6)/(2*b^16) + (15*d^14*(b*c - a*d)*(a + b*x)^7)/(7*b^16) + (d^15*(a + b*x)^8)/(8*b^16) + (6435*d^7*(b*c - a*d)^8*Log[a + b*x])/b^16}
# {(c + d*x)^15/(a + b*x)^9, x, 2, (5005*d^9*(b*c - a*d)^6*x)/b^15 - (b*c - a*d)^15/(8*b^16*(a + b*x)^8) - (15*d*(b*c - a*d)^14)/(7*b^16*(a + b*x)^7) - (35*d^2*(b*c - a*d)^13)/(2*b^16*(a + b*x)^6) - (91*d^3*(b*c - a*d)^12)/(b^16*(a + b*x)^5) - (1365*d^4*(b*c - a*d)^11)/(4*b^16*(a + b*x)^4) - (1001*d^5*(b*c - a*d)^10)/(b^16*(a + b*x)^3) - (5005*d^6*(b*c - a*d)^9)/(2*b^16*(a + b*x)^2) - (6435*d^7*(b*c - a*d)^8)/(b^16*(a + b*x)) + (3003*d^10*(b*c - a*d)^5*(a + b*x)^2)/(2*b^16) + (455*d^11*(b*c - a*d)^4*(a + b*x)^3)/b^16 + (455*d^12*(b*c - a*d)^3*(a + b*x)^4)/(4*b^16) + (21*d^13*(b*c - a*d)^2*(a + b*x)^5)/b^16 + (5*d^14*(b*c - a*d)*(a + b*x)^6)/(2*b^16) + (d^15*(a + b*x)^7)/(7*b^16) + (6435*d^8*(b*c - a*d)^7*Log[a + b*x])/b^16}
# {(c + d*x)^15/(a + b*x)^10, x, 2, (3003*d^10*(b*c - a*d)^5*x)/b^15 - (b*c - a*d)^15/(9*b^16*(a + b*x)^9) - (15*d*(b*c - a*d)^14)/(8*b^16*(a + b*x)^8) - (15*d^2*(b*c - a*d)^13)/(b^16*(a + b*x)^7) - (455*d^3*(b*c - a*d)^12)/(6*b^16*(a + b*x)^6) - (273*d^4*(b*c - a*d)^11)/(b^16*(a + b*x)^5) - (3003*d^5*(b*c - a*d)^10)/(4*b^16*(a + b*x)^4) - (5005*d^6*(b*c - a*d)^9)/(3*b^16*(a + b*x)^3) - (6435*d^7*(b*c - a*d)^8)/(2*b^16*(a + b*x)^2) - (6435*d^8*(b*c - a*d)^7)/(b^16*(a + b*x)) + (1365*d^11*(b*c - a*d)^4*(a + b*x)^2)/(2*b^16) + (455*d^12*(b*c - a*d)^3*(a + b*x)^3)/(3*b^16) + (105*d^13*(b*c - a*d)^2*(a + b*x)^4)/(4*b^16) + (3*d^14*(b*c - a*d)*(a + b*x)^5)/b^16 + (d^15*(a + b*x)^6)/(6*b^16) + (5005*d^9*(b*c - a*d)^6*Log[a + b*x])/b^16}
# {(c + d*x)^15/(a + b*x)^11, x, 2, (1365*d^11*(b*c - a*d)^4*x)/b^15 - (b*c - a*d)^15/(10*b^16*(a + b*x)^10) - (5*d*(b*c - a*d)^14)/(3*b^16*(a + b*x)^9) - (105*d^2*(b*c - a*d)^13)/(8*b^16*(a + b*x)^8) - (65*d^3*(b*c - a*d)^12)/(b^16*(a + b*x)^7) - (455*d^4*(b*c - a*d)^11)/(2*b^16*(a + b*x)^6) - (3003*d^5*(b*c - a*d)^10)/(5*b^16*(a + b*x)^5) - (5005*d^6*(b*c - a*d)^9)/(4*b^16*(a + b*x)^4) - (2145*d^7*(b*c - a*d)^8)/(b^16*(a + b*x)^3) - (6435*d^8*(b*c - a*d)^7)/(2*b^16*(a + b*x)^2) - (5005*d^9*(b*c - a*d)^6)/(b^16*(a + b*x)) + (455*d^12*(b*c - a*d)^3*(a + b*x)^2)/(2*b^16) + (35*d^13*(b*c - a*d)^2*(a + b*x)^3)/b^16 + (15*d^14*(b*c - a*d)*(a + b*x)^4)/(4*b^16) + (d^15*(a + b*x)^5)/(5*b^16) + (3003*d^10*(b*c - a*d)^5*Log[a + b*x])/b^16}
# {(c + d*x)^15/(a + b*x)^12, x, 2, (455*d^12*(b*c - a*d)^3*x)/b^15 - (b*c - a*d)^15/(11*b^16*(a + b*x)^11) - (3*d*(b*c - a*d)^14)/(2*b^16*(a + b*x)^10) - (35*d^2*(b*c - a*d)^13)/(3*b^16*(a + b*x)^9) - (455*d^3*(b*c - a*d)^12)/(8*b^16*(a + b*x)^8) - (195*d^4*(b*c - a*d)^11)/(b^16*(a + b*x)^7) - (1001*d^5*(b*c - a*d)^10)/(2*b^16*(a + b*x)^6) - (1001*d^6*(b*c - a*d)^9)/(b^16*(a + b*x)^5) - (6435*d^7*(b*c - a*d)^8)/(4*b^16*(a + b*x)^4) - (2145*d^8*(b*c - a*d)^7)/(b^16*(a + b*x)^3) - (5005*d^9*(b*c - a*d)^6)/(2*b^16*(a + b*x)^2) - (3003*d^10*(b*c - a*d)^5)/(b^16*(a + b*x)) + (105*d^13*(b*c - a*d)^2*(a + b*x)^2)/(2*b^16) + (5*d^14*(b*c - a*d)*(a + b*x)^3)/b^16 + (d^15*(a + b*x)^4)/(4*b^16) + (1365*d^11*(b*c - a*d)^4*Log[a + b*x])/b^16}
# {(c + d*x)^15/(a + b*x)^13, x, 2, (105*d^13*(b*c - a*d)^2*x)/b^15 - (b*c - a*d)^15/(12*b^16*(a + b*x)^12) - (15*d*(b*c - a*d)^14)/(11*b^16*(a + b*x)^11) - (21*d^2*(b*c - a*d)^13)/(2*b^16*(a + b*x)^10) - (455*d^3*(b*c - a*d)^12)/(9*b^16*(a + b*x)^9) - (1365*d^4*(b*c - a*d)^11)/(8*b^16*(a + b*x)^8) - (429*d^5*(b*c - a*d)^10)/(b^16*(a + b*x)^7) - (5005*d^6*(b*c - a*d)^9)/(6*b^16*(a + b*x)^6) - (1287*d^7*(b*c - a*d)^8)/(b^16*(a + b*x)^5) - (6435*d^8*(b*c - a*d)^7)/(4*b^16*(a + b*x)^4) - (5005*d^9*(b*c - a*d)^6)/(3*b^16*(a + b*x)^3) - (3003*d^10*(b*c - a*d)^5)/(2*b^16*(a + b*x)^2) - (1365*d^11*(b*c - a*d)^4)/(b^16*(a + b*x)) + (15*d^14*(b*c - a*d)*(a + b*x)^2)/(2*b^16) + (d^15*(a + b*x)^3)/(3*b^16) + (455*d^12*(b*c - a*d)^3*Log[a + b*x])/b^16}
# {(c + d*x)^15/(a + b*x)^14, x, 2, (d^14*(15*b*c - 14*a*d)*x)/b^15 + (d^15*x^2)/(2*b^14) - (b*c - a*d)^15/(13*b^16*(a + b*x)^13) - (5*d*(b*c - a*d)^14)/(4*b^16*(a + b*x)^12) - (105*d^2*(b*c - a*d)^13)/(11*b^16*(a + b*x)^11) - (91*d^3*(b*c - a*d)^12)/(2*b^16*(a + b*x)^10) - (455*d^4*(b*c - a*d)^11)/(3*b^16*(a + b*x)^9) - (3003*d^5*(b*c - a*d)^10)/(8*b^16*(a + b*x)^8) - (715*d^6*(b*c - a*d)^9)/(b^16*(a + b*x)^7) - (2145*d^7*(b*c - a*d)^8)/(2*b^16*(a + b*x)^6) - (1287*d^8*(b*c - a*d)^7)/(b^16*(a + b*x)^5) - (5005*d^9*(b*c - a*d)^6)/(4*b^16*(a + b*x)^4) - (1001*d^10*(b*c - a*d)^5)/(b^16*(a + b*x)^3) - (1365*d^11*(b*c - a*d)^4)/(2*b^16*(a + b*x)^2) - (455*d^12*(b*c - a*d)^3)/(b^16*(a + b*x)) + (105*d^13*(b*c - a*d)^2*Log[a + b*x])/b^16}
# {(c + d*x)^15/(a + b*x)^15, x, 2, (d^15*x)/b^15 - (b*c - a*d)^15/(14*b^16*(a + b*x)^14) - (15*d*(b*c - a*d)^14)/(13*b^16*(a + b*x)^13) - (35*d^2*(b*c - a*d)^13)/(4*b^16*(a + b*x)^12) - (455*d^3*(b*c - a*d)^12)/(11*b^16*(a + b*x)^11) - (273*d^4*(b*c - a*d)^11)/(2*b^16*(a + b*x)^10) - (1001*d^5*(b*c - a*d)^10)/(3*b^16*(a + b*x)^9) - (5005*d^6*(b*c - a*d)^9)/(8*b^16*(a + b*x)^8) - (6435*d^7*(b*c - a*d)^8)/(7*b^16*(a + b*x)^7) - (2145*d^8*(b*c - a*d)^7)/(2*b^16*(a + b*x)^6) - (1001*d^9*(b*c - a*d)^6)/(b^16*(a + b*x)^5) - (3003*d^10*(b*c - a*d)^5)/(4*b^16*(a + b*x)^4) - (455*d^11*(b*c - a*d)^4)/(b^16*(a + b*x)^3) - (455*d^12*(b*c - a*d)^3)/(2*b^16*(a + b*x)^2) - (105*d^13*(b*c - a*d)^2)/(b^16*(a + b*x)) + (15*d^14*(b*c - a*d)*Log[a + b*x])/b^16}
# {(c + d*x)^15/(a + b*x)^16, x, 2, -(b*c - a*d)^15/(15*b^16*(a + b*x)^15) - (15*d*(b*c - a*d)^14)/(14*b^16*(a + b*x)^14) - (105*d^2*(b*c - a*d)^13)/(13*b^16*(a + b*x)^13) - (455*d^3*(b*c - a*d)^12)/(12*b^16*(a + b*x)^12) - (1365*d^4*(b*c - a*d)^11)/(11*b^16*(a + b*x)^11) - (3003*d^5*(b*c - a*d)^10)/(10*b^16*(a + b*x)^10) - (5005*d^6*(b*c - a*d)^9)/(9*b^16*(a + b*x)^9) - (6435*d^7*(b*c - a*d)^8)/(8*b^16*(a + b*x)^8) - (6435*d^8*(b*c - a*d)^7)/(7*b^16*(a + b*x)^7) - (5005*d^9*(b*c - a*d)^6)/(6*b^16*(a + b*x)^6) - (3003*d^10*(b*c - a*d)^5)/(5*b^16*(a + b*x)^5) - (1365*d^11*(b*c - a*d)^4)/(4*b^16*(a + b*x)^4) - (455*d^12*(b*c - a*d)^3)/(3*b^16*(a + b*x)^3) - (105*d^13*(b*c - a*d)^2)/(2*b^16*(a + b*x)^2) - (15*d^14*(b*c - a*d))/(b^16*(a + b*x)) + (d^15*Log[a + b*x])/b^16}
# {(c + d*x)^15/(a + b*x)^17, x, 1, -(c + d*x)^16/(16*(b*c - a*d)*(a + b*x)^16)}
# {(c + d*x)^15/(a + b*x)^18, x, 2, -(c + d*x)^16/(17*(b*c - a*d)*(a + b*x)^17) + (d*(c + d*x)^16)/(272*(b*c - a*d)^2*(a + b*x)^16)}
# {(c + d*x)^15/(a + b*x)^19, x, 3, -(c + d*x)^16/(18*(b*c - a*d)*(a + b*x)^18) + (d*(c + d*x)^16)/(153*(b*c - a*d)^2*(a + b*x)^17) - (d^2*(c + d*x)^16)/(2448*(b*c - a*d)^3*(a + b*x)^16)}
# {(c + d*x)^15/(a + b*x)^20, x, 4, -(c + d*x)^16/(19*(b*c - a*d)*(a + b*x)^19) + (d*(c + d*x)^16)/(114*(b*c - a*d)^2*(a + b*x)^18) - (d^2*(c + d*x)^16)/(969*(b*c - a*d)^3*(a + b*x)^17) + (d^3*(c + d*x)^16)/(15504*(b*c - a*d)^4*(a + b*x)^16)}
# {(c + d*x)^15/(a + b*x)^21, x, 5, -(c + d*x)^16/(20*(b*c - a*d)*(a + b*x)^20) + (d*(c + d*x)^16)/(95*(b*c - a*d)^2*(a + b*x)^19) - (d^2*(c + d*x)^16)/(570*(b*c - a*d)^3*(a + b*x)^18) + (d^3*(c + d*x)^16)/(4845*(b*c - a*d)^4*(a + b*x)^17) - (d^4*(c + d*x)^16)/(77520*(b*c - a*d)^5*(a + b*x)^16)}
# {(c + d*x)^15/(a + b*x)^22, x, 6, -(c + d*x)^16/(21*(b*c - a*d)*(a + b*x)^21) + (d*(c + d*x)^16)/(84*(b*c - a*d)^2*(a + b*x)^20) - (d^2*(c + d*x)^16)/(399*(b*c - a*d)^3*(a + b*x)^19) + (d^3*(c + d*x)^16)/(2394*(b*c - a*d)^4*(a + b*x)^18) - (d^4*(c + d*x)^16)/(20349*(b*c - a*d)^5*(a + b*x)^17) + (d^5*(c + d*x)^16)/(325584*(b*c - a*d)^6*(a + b*x)^16)}
# {(c + d*x)^15/(a + b*x)^23, x, 7, -(c + d*x)^16/(22*(b*c - a*d)*(a + b*x)^22) + (d*(c + d*x)^16)/(77*(b*c - a*d)^2*(a + b*x)^21) - (d^2*(c + d*x)^16)/(308*(b*c - a*d)^3*(a + b*x)^20) + (d^3*(c + d*x)^16)/(1463*(b*c - a*d)^4*(a + b*x)^19) - (d^4*(c + d*x)^16)/(8778*(b*c - a*d)^5*(a + b*x)^18) + (d^5*(c + d*x)^16)/(74613*(b*c - a*d)^6*(a + b*x)^17) - (d^6*(c + d*x)^16)/(1193808*(b*c - a*d)^7*(a + b*x)^16)}
# {(c + d*x)^15/(a + b*x)^24, x, 8, -(c + d*x)^16/(23*(b*c - a*d)*(a + b*x)^23) + (7*d*(c + d*x)^16)/(506*(b*c - a*d)^2*(a + b*x)^22) - (d^2*(c + d*x)^16)/(253*(b*c - a*d)^3*(a + b*x)^21) + (d^3*(c + d*x)^16)/(1012*(b*c - a*d)^4*(a + b*x)^20) - (d^4*(c + d*x)^16)/(4807*(b*c - a*d)^5*(a + b*x)^19) + (d^5*(c + d*x)^16)/(28842*(b*c - a*d)^6*(a + b*x)^18) - (d^6*(c + d*x)^16)/(245157*(b*c - a*d)^7*(a + b*x)^17) + (d^7*(c + d*x)^16)/(3922512*(b*c - a*d)^8*(a + b*x)^16)}
# {(c + d*x)^15/(a + b*x)^25, x, 9, -(c + d*x)^16/(24*(b*c - a*d)*(a + b*x)^24) + (d*(c + d*x)^16)/(69*(b*c - a*d)^2*(a + b*x)^23) - (7*d^2*(c + d*x)^16)/(1518*(b*c - a*d)^3*(a + b*x)^22) + (d^3*(c + d*x)^16)/(759*(b*c - a*d)^4*(a + b*x)^21) - (d^4*(c + d*x)^16)/(3036*(b*c - a*d)^5*(a + b*x)^20) + (d^5*(c + d*x)^16)/(14421*(b*c - a*d)^6*(a + b*x)^19) - (d^6*(c + d*x)^16)/(86526*(b*c - a*d)^7*(a + b*x)^18) + (d^7*(c + d*x)^16)/(735471*(b*c - a*d)^8*(a + b*x)^17) - (d^8*(c + d*x)^16)/(11767536*(b*c - a*d)^9*(a + b*x)^16)}
# {(c + d*x)^15/(a + b*x)^26, x, 10, -(c + d*x)^16/(25*(b*c - a*d)*(a + b*x)^25) + (3*d*(c + d*x)^16)/(200*(b*c - a*d)^2*(a + b*x)^24) - (3*d^2*(c + d*x)^16)/(575*(b*c - a*d)^3*(a + b*x)^23) + (21*d^3*(c + d*x)^16)/(12650*(b*c - a*d)^4*(a + b*x)^22) - (3*d^4*(c + d*x)^16)/(6325*(b*c - a*d)^5*(a + b*x)^21) + (3*d^5*(c + d*x)^16)/(25300*(b*c - a*d)^6*(a + b*x)^20) - (3*d^6*(c + d*x)^16)/(120175*(b*c - a*d)^7*(a + b*x)^19) + (d^7*(c + d*x)^16)/(240350*(b*c - a*d)^8*(a + b*x)^18) - (d^8*(c + d*x)^16)/(2042975*(b*c - a*d)^9*(a + b*x)^17) + (d^9*(c + d*x)^16)/(32687600*(b*c - a*d)^10*(a + b*x)^16)}
# {(c + d*x)^15/(a + b*x)^27, x, 11, -(c + d*x)^16/(26*(b*c - a*d)*(a + b*x)^26) + (d*(c + d*x)^16)/(65*(b*c - a*d)^2*(a + b*x)^25) - (3*d^2*(c + d*x)^16)/(520*(b*c - a*d)^3*(a + b*x)^24) + (3*d^3*(c + d*x)^16)/(1495*(b*c - a*d)^4*(a + b*x)^23) - (21*d^4*(c + d*x)^16)/(32890*(b*c - a*d)^5*(a + b*x)^22) + (3*d^5*(c + d*x)^16)/(16445*(b*c - a*d)^6*(a + b*x)^21) - (3*d^6*(c + d*x)^16)/(65780*(b*c - a*d)^7*(a + b*x)^20) + (3*d^7*(c + d*x)^16)/(312455*(b*c - a*d)^8*(a + b*x)^19) - (d^8*(c + d*x)^16)/(624910*(b*c - a*d)^9*(a + b*x)^18) + (d^9*(c + d*x)^16)/(5311735*(b*c - a*d)^10*(a + b*x)^17) - (d^10*(c + d*x)^16)/(84987760*(b*c - a*d)^11*(a + b*x)^16)}
# {(c + d*x)^15/(a + b*x)^28, x, 12, -((c + d*x)^16/(27*(b*c - a*d)*(a + b*x)^27)) + (11*d*(c + d*x)^16)/(702*(b*c - a*d)^2*(a + b*x)^26) - (11*d^2*(c + d*x)^16)/(1755*(b*c - a*d)^3*(a + b*x)^25) + (11*d^3*(c + d*x)^16)/(4680*(b*c - a*d)^4*(a + b*x)^24) - (11*d^4*(c + d*x)^16)/(13455*(b*c - a*d)^5*(a + b*x)^23) + (7*d^5*(c + d*x)^16)/(26910*(b*c - a*d)^6*(a + b*x)^22) - (d^6*(c + d*x)^16)/(13455*(b*c - a*d)^7*(a + b*x)^21) + (d^7*(c + d*x)^16)/(53820*(b*c - a*d)^8*(a + b*x)^20) - (d^8*(c + d*x)^16)/(255645*(b*c - a*d)^9*(a + b*x)^19) + (d^9*(c + d*x)^16)/(1533870*(b*c - a*d)^10*(a + b*x)^18) - (d^10*(c + d*x)^16)/(13037895*(b*c - a*d)^11*(a + b*x)^17) + (d^11*(c + d*x)^16)/(208606320*(b*c - a*d)^12*(a + b*x)^16)}
# {(c + d*x)^15/(a + b*x)^29, x, 2, -(b*c - a*d)^15/(28*b^16*(a + b*x)^28) - (5*d*(b*c - a*d)^14)/(9*b^16*(a + b*x)^27) - (105*d^2*(b*c - a*d)^13)/(26*b^16*(a + b*x)^26) - (91*d^3*(b*c - a*d)^12)/(5*b^16*(a + b*x)^25) - (455*d^4*(b*c - a*d)^11)/(8*b^16*(a + b*x)^24) - (3003*d^5*(b*c - a*d)^10)/(23*b^16*(a + b*x)^23) - (455*d^6*(b*c - a*d)^9)/(2*b^16*(a + b*x)^22) - (2145*d^7*(b*c - a*d)^8)/(7*b^16*(a + b*x)^21) - (1287*d^8*(b*c - a*d)^7)/(4*b^16*(a + b*x)^20) - (5005*d^9*(b*c - a*d)^6)/(19*b^16*(a + b*x)^19) - (1001*d^10*(b*c - a*d)^5)/(6*b^16*(a + b*x)^18) - (1365*d^11*(b*c - a*d)^4)/(17*b^16*(a + b*x)^17) - (455*d^12*(b*c - a*d)^3)/(16*b^16*(a + b*x)^16) - (7*d^13*(b*c - a*d)^2)/(b^16*(a + b*x)^15) - (15*d^14*(b*c - a*d))/(14*b^16*(a + b*x)^14) - d^15/(13*b^16*(a + b*x)^13)}
# {(c + d*x)^15/(a + b*x)^30, x, 2, -(b*c - a*d)^15/(29*b^16*(a + b*x)^29) - (15*d*(b*c - a*d)^14)/(28*b^16*(a + b*x)^28) - (35*d^2*(b*c - a*d)^13)/(9*b^16*(a + b*x)^27) - (35*d^3*(b*c - a*d)^12)/(2*b^16*(a + b*x)^26) - (273*d^4*(b*c - a*d)^11)/(5*b^16*(a + b*x)^25) - (1001*d^5*(b*c - a*d)^10)/(8*b^16*(a + b*x)^24) - (5005*d^6*(b*c - a*d)^9)/(23*b^16*(a + b*x)^23) - (585*d^7*(b*c - a*d)^8)/(2*b^16*(a + b*x)^22) - (2145*d^8*(b*c - a*d)^7)/(7*b^16*(a + b*x)^21) - (1001*d^9*(b*c - a*d)^6)/(4*b^16*(a + b*x)^20) - (3003*d^10*(b*c - a*d)^5)/(19*b^16*(a + b*x)^19) - (455*d^11*(b*c - a*d)^4)/(6*b^16*(a + b*x)^18) - (455*d^12*(b*c - a*d)^3)/(17*b^16*(a + b*x)^17) - (105*d^13*(b*c - a*d)^2)/(16*b^16*(a + b*x)^16) - (d^14*(b*c - a*d))/(b^16*(a + b*x)^15) - d^15/(14*b^16*(a + b*x)^14)}

# {(c + d*x)^15/(a + b*x)^31, x, 2, -(b*c - a*d)^15/(30*b^16*(a + b*x)^30) - (15*d*(b*c - a*d)^14)/(29*b^16*(a + b*x)^29) - (15*d^2*(b*c - a*d)^13)/(4*b^16*(a + b*x)^28) - (455*d^3*(b*c - a*d)^12)/(27*b^16*(a + b*x)^27) - (105*d^4*(b*c - a*d)^11)/(2*b^16*(a + b*x)^26) - (3003*d^5*(b*c - a*d)^10)/(25*b^16*(a + b*x)^25) - (5005*d^6*(b*c - a*d)^9)/(24*b^16*(a + b*x)^24) - (6435*d^7*(b*c - a*d)^8)/(23*b^16*(a + b*x)^23) - (585*d^8*(b*c - a*d)^7)/(2*b^16*(a + b*x)^22) - (715*d^9*(b*c - a*d)^6)/(3*b^16*(a + b*x)^21) - (3003*d^10*(b*c - a*d)^5)/(20*b^16*(a + b*x)^20) - (1365*d^11*(b*c - a*d)^4)/(19*b^16*(a + b*x)^19) - (455*d^12*(b*c - a*d)^3)/(18*b^16*(a + b*x)^18) - (105*d^13*(b*c - a*d)^2)/(17*b^16*(a + b*x)^17) - (15*d^14*(b*c - a*d))/(16*b^16*(a + b*x)^16) - d^15/(15*b^16*(a + b*x)^15)} 

# n<0
[(a+b*x)^5/(c+d*x),x,2,b*(b*c-a*d)^4*x/d^5-1/2*(b*c-a*d)^3*(a+b*x)^2/d^4+1/3*(b*c-a*d)^2*(a+b*x)^3/d^3-1/4*(b*c-a*d)*(a+b*x)^4/d^2+1/5*(a+b*x)^5/d-(b*c-a*d)^5*log(c+d*x)/d^6],
[(a+b*x)^4/(c+d*x),x,2,-b*(b*c-a*d)^3*x/d^4+1/2*(b*c-a*d)^2*(a+b*x)^2/d^3-1/3*(b*c-a*d)*(a+b*x)^3/d^2+1/4*(a+b*x)^4/d+(b*c-a*d)^4*log(c+d*x)/d^5],
[(a+b*x)^3/(c+d*x),x,2,b*(b*c-a*d)^2*x/d^3-1/2*(b*c-a*d)*(a+b*x)^2/d^2+1/3*(a+b*x)^3/d-(b*c-a*d)^3*log(c+d*x)/d^4],
[(a+b*x)^2/(c+d*x),x,2,-b*(b*c-a*d)*x/d^2+1/2*(a+b*x)^2/d+(b*c-a*d)^2*log(c+d*x)/d^3],
[(a+b*x)/(c+d*x),x,2,b*x/d-(b*c-a*d)*log(c+d*x)/d^2],
[1/(c+d*x),x,1,log(c+d*x)/d],
[1/((a+b*x)*(c+d*x)),x,3,log(a+b*x)/(b*c-a*d)-log(c+d*x)/(b*c-a*d)],
[1/((a+b*x)^2*(c+d*x)),x,2,(-1)/((b*c-a*d)*(a+b*x))-d*log(a+b*x)/(b*c-a*d)^2+d*log(c+d*x)/(b*c-a*d)^2],
[1/((a+b*x)^3*(c+d*x)),x,2,(-1/2)/((b*c-a*d)*(a+b*x)^2)+d/((b*c-a*d)^2*(a+b*x))+d^2*log(a+b*x)/(b*c-a*d)^3-d^2*log(c+d*x)/(b*c-a*d)^3],
[(a+b*x)^5/(c+d*x)^2,x,2,-10*b^2*(b*c-a*d)^3*x/d^5+(b*c-a*d)^5/(d^6*(c+d*x))+5*b^3*(b*c-a*d)^2*(c+d*x)^2/d^6-5/3*b^4*(b*c-a*d)*(c+d*x)^3/d^6+1/4*b^5*(c+d*x)^4/d^6+5*b*(b*c-a*d)^4*log(c+d*x)/d^6],
[(a+b*x)^4/(c+d*x)^2,x,2,6*b^2*(b*c-a*d)^2*x/d^4-(b*c-a*d)^4/(d^5*(c+d*x))-2*b^3*(b*c-a*d)*(c+d*x)^2/d^5+1/3*b^4*(c+d*x)^3/d^5-4*b*(b*c-a*d)^3*log(c+d*x)/d^5],
[(a+b*x)^3/(c+d*x)^2,x,2,-b^2*(2*b*c-3*a*d)*x/d^3+1/2*b^3*x^2/d^2+(b*c-a*d)^3/(d^4*(c+d*x))+3*b*(b*c-a*d)^2*log(c+d*x)/d^4],
[(a+b*x)^2/(c+d*x)^2,x,2,b^2*x/d^2-(b*c-a*d)^2/(d^3*(c+d*x))-2*b*(b*c-a*d)*log(c+d*x)/d^3],
[(a+b*x)/(c+d*x)^2,x,2,(b*c-a*d)/(d^2*(c+d*x))+b*log(c+d*x)/d^2],
[1/(c+d*x)^2,x,1,(-1)/(d*(c+d*x))],
[1/((a+b*x)*(c+d*x)^2),x,2,1/((b*c-a*d)*(c+d*x))+b*log(a+b*x)/(b*c-a*d)^2-b*log(c+d*x)/(b*c-a*d)^2],
[1/((a+b*x)^2*(c+d*x)^2),x,2,-b/((b*c-a*d)^2*(a+b*x))-d/((b*c-a*d)^2*(c+d*x))-2*b*d*log(a+b*x)/(b*c-a*d)^3+2*b*d*log(c+d*x)/(b*c-a*d)^3],
[1/((a+b*x)^3*(c+d*x)^2),x,2,-1/2*b/((b*c-a*d)^2*(a+b*x)^2)+2*b*d/((b*c-a*d)^3*(a+b*x))+d^2/((b*c-a*d)^3*(c+d*x))+3*b*d^2*log(a+b*x)/(b*c-a*d)^4-3*b*d^2*log(c+d*x)/(b*c-a*d)^4],
[(a+b*x)^6/(c+d*x)^3,x,2,-20*b^3*(b*c-a*d)^3*x/d^6-1/2*(b*c-a*d)^6/(d^7*(c+d*x)^2)+6*b*(b*c-a*d)^5/(d^7*(c+d*x))+15/2*b^4*(b*c-a*d)^2*(c+d*x)^2/d^7-2*b^5*(b*c-a*d)*(c+d*x)^3/d^7+1/4*b^6*(c+d*x)^4/d^7+15*b^2*(b*c-a*d)^4*log(c+d*x)/d^7],
[(a+b*x)^5/(c+d*x)^3,x,2,10*b^3*(b*c-a*d)^2*x/d^5+1/2*(b*c-a*d)^5/(d^6*(c+d*x)^2)-5*b*(b*c-a*d)^4/(d^6*(c+d*x))-5/2*b^4*(b*c-a*d)*(c+d*x)^2/d^6+1/3*b^5*(c+d*x)^3/d^6-10*b^2*(b*c-a*d)^3*log(c+d*x)/d^6],
[(a+b*x)^4/(c+d*x)^3,x,2,-b^3*(3*b*c-4*a*d)*x/d^4+1/2*b^4*x^2/d^3-1/2*(b*c-a*d)^4/(d^5*(c+d*x)^2)+4*b*(b*c-a*d)^3/(d^5*(c+d*x))+6*b^2*(b*c-a*d)^2*log(c+d*x)/d^5],
[(a+b*x)^3/(c+d*x)^3,x,2,b^3*x/d^3+1/2*(b*c-a*d)^3/(d^4*(c+d*x)^2)-3*b*(b*c-a*d)^2/(d^4*(c+d*x))-3*b^2*(b*c-a*d)*log(c+d*x)/d^4],
[(a+b*x)^2/(c+d*x)^3,x,2,-1/2*(b*c-a*d)^2/(d^3*(c+d*x)^2)+2*b*(b*c-a*d)/(d^3*(c+d*x))+b^2*log(c+d*x)/d^3],
[(a+b*x)/(c+d*x)^3,x,1,1/2*(a+b*x)^2/((b*c-a*d)*(c+d*x)^2)],
[1/(c+d*x)^3,x,1,(-1/2)/(d*(c+d*x)^2)],
[1/((a+b*x)*(c+d*x)^3),x,2,1/2/((b*c-a*d)*(c+d*x)^2)+b/((b*c-a*d)^2*(c+d*x))+b^2*log(a+b*x)/(b*c-a*d)^3-b^2*log(c+d*x)/(b*c-a*d)^3],
[1/((a+b*x)^2*(c+d*x)^3),x,2,-b^2/((b*c-a*d)^3*(a+b*x))-1/2*d/((b*c-a*d)^2*(c+d*x)^2)-2*b*d/((b*c-a*d)^3*(c+d*x))-3*b^2*d*log(a+b*x)/(b*c-a*d)^4+3*b^2*d*log(c+d*x)/(b*c-a*d)^4],
[1/((a+b*x)^3*(c+d*x)^3),x,2,-1/2*b^2/((b*c-a*d)^3*(a+b*x)^2)+3*b^2*d/((b*c-a*d)^4*(a+b*x))+1/2*d^2/((b*c-a*d)^3*(c+d*x)^2)+3*b*d^2/((b*c-a*d)^4*(c+d*x))+6*b^2*d^2*log(a+b*x)/(b*c-a*d)^5-6*b^2*d^2*log(c+d*x)/(b*c-a*d)^5],
[(a+b*x)^9/(c+d*x)^8,x,2,-b^8*(8*b*c-9*a*d)*x/d^9+1/2*b^9*x^2/d^8+1/7*(b*c-a*d)^9/(d^10*(c+d*x)^7)-3/2*b*(b*c-a*d)^8/(d^10*(c+d*x)^6)+36/5*b^2*(b*c-a*d)^7/(d^10*(c+d*x)^5)-21*b^3*(b*c-a*d)^6/(d^10*(c+d*x)^4)+42*b^4*(b*c-a*d)^5/(d^10*(c+d*x)^3)-63*b^5*(b*c-a*d)^4/(d^10*(c+d*x)^2)+84*b^6*(b*c-a*d)^3/(d^10*(c+d*x))+36*b^7*(b*c-a*d)^2*log(c+d*x)/d^10],
[(a+b*x)^8/(c+d*x)^8,x,2,b^8*x/d^8-1/7*(b*c-a*d)^8/(d^9*(c+d*x)^7)+4/3*b*(b*c-a*d)^7/(d^9*(c+d*x)^6)-28/5*b^2*(b*c-a*d)^6/(d^9*(c+d*x)^5)+14*b^3*(b*c-a*d)^5/(d^9*(c+d*x)^4)-70/3*b^4*(b*c-a*d)^4/(d^9*(c+d*x)^3)+28*b^5*(b*c-a*d)^3/(d^9*(c+d*x)^2)-28*b^6*(b*c-a*d)^2/(d^9*(c+d*x))-8*b^7*(b*c-a*d)*log(c+d*x)/d^9],
[(a+b*x)^7/(c+d*x)^8,x,2,1/7*(b*c-a*d)^7/(d^8*(c+d*x)^7)-7/6*b*(b*c-a*d)^6/(d^8*(c+d*x)^6)+21/5*b^2*(b*c-a*d)^5/(d^8*(c+d*x)^5)-35/4*b^3*(b*c-a*d)^4/(d^8*(c+d*x)^4)+35/3*b^4*(b*c-a*d)^3/(d^8*(c+d*x)^3)-21/2*b^5*(b*c-a*d)^2/(d^8*(c+d*x)^2)+7*b^6*(b*c-a*d)/(d^8*(c+d*x))+b^7*log(c+d*x)/d^8],
[(a+b*x)^6/(c+d*x)^8,x,1,1/7*(a+b*x)^7/((b*c-a*d)*(c+d*x)^7)],
[(a+b*x)^5/(c+d*x)^8,x,2,1/7*(a+b*x)^6/((b*c-a*d)*(c+d*x)^7)+1/42*b*(a+b*x)^6/((b*c-a*d)^2*(c+d*x)^6)],
[(a+b*x)^4/(c+d*x)^8,x,3,1/7*(a+b*x)^5/((b*c-a*d)*(c+d*x)^7)+1/21*b*(a+b*x)^5/((b*c-a*d)^2*(c+d*x)^6)+1/105*b^2*(a+b*x)^5/((b*c-a*d)^3*(c+d*x)^5)],
[(a+b*x)^3/(c+d*x)^8,x,2,1/7*(b*c-a*d)^3/(d^4*(c+d*x)^7)-1/2*b*(b*c-a*d)^2/(d^4*(c+d*x)^6)+3/5*b^2*(b*c-a*d)/(d^4*(c+d*x)^5)-1/4*b^3/(d^4*(c+d*x)^4)],
[(a+b*x)^2/(c+d*x)^8,x,2,-1/7*(b*c-a*d)^2/(d^3*(c+d*x)^7)+1/3*b*(b*c-a*d)/(d^3*(c+d*x)^6)-1/5*b^2/(d^3*(c+d*x)^5)],
[(a+b*x)/(c+d*x)^8,x,2,1/7*(b*c-a*d)/(d^2*(c+d*x)^7)-1/6*b/(d^2*(c+d*x)^6)],
[1/(c+d*x)^8,x,1,(-1/7)/(d*(c+d*x)^7)],
[1/((a+b*x)*(c+d*x)^8),x,2,1/7/((b*c-a*d)*(c+d*x)^7)+1/6*b/((b*c-a*d)^2*(c+d*x)^6)+1/5*b^2/((b*c-a*d)^3*(c+d*x)^5)+1/4*b^3/((b*c-a*d)^4*(c+d*x)^4)+1/3*b^4/((b*c-a*d)^5*(c+d*x)^3)+1/2*b^5/((b*c-a*d)^6*(c+d*x)^2)+b^6/((b*c-a*d)^7*(c+d*x))+b^7*log(a+b*x)/(b*c-a*d)^8-b^7*log(c+d*x)/(b*c-a*d)^8],
[1/((a+b*x)^2*(c+d*x)^8),x,2,-b^7/((b*c-a*d)^8*(a+b*x))-1/7*d/((b*c-a*d)^2*(c+d*x)^7)-1/3*b*d/((b*c-a*d)^3*(c+d*x)^6)-3/5*b^2*d/((b*c-a*d)^4*(c+d*x)^5)-b^3*d/((b*c-a*d)^5*(c+d*x)^4)-5/3*b^4*d/((b*c-a*d)^6*(c+d*x)^3)-3*b^5*d/((b*c-a*d)^7*(c+d*x)^2)-7*b^6*d/((b*c-a*d)^8*(c+d*x))-8*b^7*d*log(a+b*x)/(b*c-a*d)^9+8*b^7*d*log(c+d*x)/(b*c-a*d)^9],
[1/((a+b*x)^3*(c+d*x)^8),x,2,-1/2*b^7/((b*c-a*d)^8*(a+b*x)^2)+8*b^7*d/((b*c-a*d)^9*(a+b*x))+1/7*d^2/((b*c-a*d)^3*(c+d*x)^7)+1/2*b*d^2/((b*c-a*d)^4*(c+d*x)^6)+6/5*b^2*d^2/((b*c-a*d)^5*(c+d*x)^5)+5/2*b^3*d^2/((b*c-a*d)^6*(c+d*x)^4)+5*b^4*d^2/((b*c-a*d)^7*(c+d*x)^3)+21/2*b^5*d^2/((b*c-a*d)^8*(c+d*x)^2)+28*b^6*d^2/((b*c-a*d)^9*(c+d*x))+36*b^7*d^2*log(a+b*x)/(b*c-a*d)^10-36*b^7*d^2*log(c+d*x)/(b*c-a*d)^10],

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

# n>0
[(a+b*x)^5*(c+d*x)^(1/2),x,2,-2/3*(b*c-a*d)^5*(c+d*x)^(3/2)/d^6+2*b*(b*c-a*d)^4*(c+d*x)^(5/2)/d^6-20/7*b^2*(b*c-a*d)^3*(c+d*x)^(7/2)/d^6+20/9*b^3*(b*c-a*d)^2*(c+d*x)^(9/2)/d^6-10/11*b^4*(b*c-a*d)*(c+d*x)^(11/2)/d^6+2/13*b^5*(c+d*x)^(13/2)/d^6],
[(a+b*x)^4*(c+d*x)^(1/2),x,2,2/3*(b*c-a*d)^4*(c+d*x)^(3/2)/d^5-8/5*b*(b*c-a*d)^3*(c+d*x)^(5/2)/d^5+12/7*b^2*(b*c-a*d)^2*(c+d*x)^(7/2)/d^5-8/9*b^3*(b*c-a*d)*(c+d*x)^(9/2)/d^5+2/11*b^4*(c+d*x)^(11/2)/d^5],
[(a+b*x)^3*(c+d*x)^(1/2),x,2,-2/3*(b*c-a*d)^3*(c+d*x)^(3/2)/d^4+6/5*b*(b*c-a*d)^2*(c+d*x)^(5/2)/d^4-6/7*b^2*(b*c-a*d)*(c+d*x)^(7/2)/d^4+2/9*b^3*(c+d*x)^(9/2)/d^4],
[(a+b*x)^2*(c+d*x)^(1/2),x,2,2/3*(b*c-a*d)^2*(c+d*x)^(3/2)/d^3-4/5*b*(b*c-a*d)*(c+d*x)^(5/2)/d^3+2/7*b^2*(c+d*x)^(7/2)/d^3],
[(a+b*x)*(c+d*x)^(1/2),x,2,-2/3*(b*c-a*d)*(c+d*x)^(3/2)/d^2+2/5*b*(c+d*x)^(5/2)/d^2],
[(c+d*x)^(1/2),x,1,2/3*(c+d*x)^(3/2)/d],
[(c+d*x)^(1/2)/(a+b*x),x,3,-2*arctanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))*sqrt(b*c-a*d)/b^(3/2)+2*sqrt(c+d*x)/b],
[(c+d*x)^(1/2)/(a+b*x)^2,x,3,-d*arctanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/(b^(3/2)*sqrt(b*c-a*d))-sqrt(c+d*x)/(b*(a+b*x))],
[(c+d*x)^(1/2)/(a+b*x)^3,x,4,1/4*d^2*arctanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/(b^(3/2)*(b*c-a*d)^(3/2))-1/2*sqrt(c+d*x)/(b*(a+b*x)^2)-1/4*d*sqrt(c+d*x)/(b*(b*c-a*d)*(a+b*x))],
[(c+d*x)^(1/2)/(a+b*x)^4,x,5,-1/8*d^3*arctanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/(b^(3/2)*(b*c-a*d)^(5/2))-1/3*sqrt(c+d*x)/(b*(a+b*x)^3)-1/12*d*sqrt(c+d*x)/(b*(b*c-a*d)*(a+b*x)^2)+1/8*d^2*sqrt(c+d*x)/(b*(b*c-a*d)^2*(a+b*x))],
[(c+d*x)^(1/2)/(a+b*x)^5,x,6,5/64*d^4*arctanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/(b^(3/2)*(b*c-a*d)^(7/2))-1/4*sqrt(c+d*x)/(b*(a+b*x)^4)-1/24*d*sqrt(c+d*x)/(b*(b*c-a*d)*(a+b*x)^3)+5/96*d^2*sqrt(c+d*x)/(b*(b*c-a*d)^2*(a+b*x)^2)-5/64*d^3*sqrt(c+d*x)/(b*(b*c-a*d)^3*(a+b*x))],
[(c+d*x)^(1/2)/(a+b*x)^6,x,7,-7/128*d^5*arctanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/(b^(3/2)*(b*c-a*d)^(9/2))-1/5*sqrt(c+d*x)/(b*(a+b*x)^5)-1/40*d*sqrt(c+d*x)/(b*(b*c-a*d)*(a+b*x)^4)+7/240*d^2*sqrt(c+d*x)/(b*(b*c-a*d)^2*(a+b*x)^3)-7/192*d^3*sqrt(c+d*x)/(b*(b*c-a*d)^3*(a+b*x)^2)+7/128*d^4*sqrt(c+d*x)/(b*(b*c-a*d)^4*(a+b*x))],
[(a+b*x)^5*(c+d*x)^(3/2),x,2,-2/5*(b*c-a*d)^5*(c+d*x)^(5/2)/d^6+10/7*b*(b*c-a*d)^4*(c+d*x)^(7/2)/d^6-20/9*b^2*(b*c-a*d)^3*(c+d*x)^(9/2)/d^6+20/11*b^3*(b*c-a*d)^2*(c+d*x)^(11/2)/d^6-10/13*b^4*(b*c-a*d)*(c+d*x)^(13/2)/d^6+2/15*b^5*(c+d*x)^(15/2)/d^6],
[(a+b*x)^4*(c+d*x)^(3/2),x,2,2/5*(b*c-a*d)^4*(c+d*x)^(5/2)/d^5-8/7*b*(b*c-a*d)^3*(c+d*x)^(7/2)/d^5+4/3*b^2*(b*c-a*d)^2*(c+d*x)^(9/2)/d^5-8/11*b^3*(b*c-a*d)*(c+d*x)^(11/2)/d^5+2/13*b^4*(c+d*x)^(13/2)/d^5],
[(a+b*x)^3*(c+d*x)^(3/2),x,2,-2/5*(b*c-a*d)^3*(c+d*x)^(5/2)/d^4+6/7*b*(b*c-a*d)^2*(c+d*x)^(7/2)/d^4-2/3*b^2*(b*c-a*d)*(c+d*x)^(9/2)/d^4+2/11*b^3*(c+d*x)^(11/2)/d^4],
[(a+b*x)^2*(c+d*x)^(3/2),x,2,2/5*(b*c-a*d)^2*(c+d*x)^(5/2)/d^3-4/7*b*(b*c-a*d)*(c+d*x)^(7/2)/d^3+2/9*b^2*(c+d*x)^(9/2)/d^3],
[(a+b*x)*(c+d*x)^(3/2),x,2,-2/5*(b*c-a*d)*(c+d*x)^(5/2)/d^2+2/7*b*(c+d*x)^(7/2)/d^2],
[(c+d*x)^(3/2),x,1,2/5*(c+d*x)^(5/2)/d],
[(c+d*x)^(3/2)/(a+b*x),x,4,2/3*(c+d*x)^(3/2)/b-2*(b*c-a*d)^(3/2)*arctanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/b^(5/2)+2*(b*c-a*d)*sqrt(c+d*x)/b^2],
[(c+d*x)^(3/2)/(a+b*x)^2,x,4,-(c+d*x)^(3/2)/(b*(a+b*x))-3*d*arctanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))*sqrt(b*c-a*d)/b^(5/2)+3*d*sqrt(c+d*x)/b^2],
[(c+d*x)^(3/2)/(a+b*x)^3,x,4,-1/2*(c+d*x)^(3/2)/(b*(a+b*x)^2)-3/4*d^2*arctanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/(b^(5/2)*sqrt(b*c-a*d))-3/4*d*sqrt(c+d*x)/(b^2*(a+b*x))],
[(c+d*x)^(3/2)/(a+b*x)^4,x,5,-1/3*(c+d*x)^(3/2)/(b*(a+b*x)^3)+1/8*d^3*arctanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/(b^(5/2)*(b*c-a*d)^(3/2))-1/4*d*sqrt(c+d*x)/(b^2*(a+b*x)^2)-1/8*d^2*sqrt(c+d*x)/(b^2*(b*c-a*d)*(a+b*x))],
[(c+d*x)^(3/2)/(a+b*x)^5,x,6,-1/4*(c+d*x)^(3/2)/(b*(a+b*x)^4)-3/64*d^4*arctanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/(b^(5/2)*(b*c-a*d)^(5/2))-1/8*d*sqrt(c+d*x)/(b^2*(a+b*x)^3)-1/32*d^2*sqrt(c+d*x)/(b^2*(b*c-a*d)*(a+b*x)^2)+3/64*d^3*sqrt(c+d*x)/(b^2*(b*c-a*d)^2*(a+b*x))],
[(c+d*x)^(3/2)/(a+b*x)^6,x,7,-1/5*(c+d*x)^(3/2)/(b*(a+b*x)^5)+3/128*d^5*arctanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/(b^(5/2)*(b*c-a*d)^(7/2))-3/40*d*sqrt(c+d*x)/(b^2*(a+b*x)^4)-1/80*d^2*sqrt(c+d*x)/(b^2*(b*c-a*d)*(a+b*x)^3)+1/64*d^3*sqrt(c+d*x)/(b^2*(b*c-a*d)^2*(a+b*x)^2)-3/128*d^4*sqrt(c+d*x)/(b^2*(b*c-a*d)^3*(a+b*x))],
[(a+b*x)^5*(c+d*x)^(5/2),x,2,-2/7*(b*c-a*d)^5*(c+d*x)^(7/2)/d^6+10/9*b*(b*c-a*d)^4*(c+d*x)^(9/2)/d^6-20/11*b^2*(b*c-a*d)^3*(c+d*x)^(11/2)/d^6+20/13*b^3*(b*c-a*d)^2*(c+d*x)^(13/2)/d^6-2/3*b^4*(b*c-a*d)*(c+d*x)^(15/2)/d^6+2/17*b^5*(c+d*x)^(17/2)/d^6],
[(a+b*x)^4*(c+d*x)^(5/2),x,2,2/7*(b*c-a*d)^4*(c+d*x)^(7/2)/d^5-8/9*b*(b*c-a*d)^3*(c+d*x)^(9/2)/d^5+12/11*b^2*(b*c-a*d)^2*(c+d*x)^(11/2)/d^5-8/13*b^3*(b*c-a*d)*(c+d*x)^(13/2)/d^5+2/15*b^4*(c+d*x)^(15/2)/d^5],
[(a+b*x)^3*(c+d*x)^(5/2),x,2,-2/7*(b*c-a*d)^3*(c+d*x)^(7/2)/d^4+2/3*b*(b*c-a*d)^2*(c+d*x)^(9/2)/d^4-6/11*b^2*(b*c-a*d)*(c+d*x)^(11/2)/d^4+2/13*b^3*(c+d*x)^(13/2)/d^4],
[(a+b*x)^2*(c+d*x)^(5/2),x,2,2/7*(b*c-a*d)^2*(c+d*x)^(7/2)/d^3-4/9*b*(b*c-a*d)*(c+d*x)^(9/2)/d^3+2/11*b^2*(c+d*x)^(11/2)/d^3],
[(a+b*x)*(c+d*x)^(5/2),x,2,-2/7*(b*c-a*d)*(c+d*x)^(7/2)/d^2+2/9*b*(c+d*x)^(9/2)/d^2],
[(c+d*x)^(5/2),x,1,2/7*(c+d*x)^(7/2)/d],
[(c+d*x)^(5/2)/(a+b*x),x,5,2/3*(b*c-a*d)*(c+d*x)^(3/2)/b^2+2/5*(c+d*x)^(5/2)/b-2*(b*c-a*d)^(5/2)*arctanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/b^(7/2)+2*(b*c-a*d)^2*sqrt(c+d*x)/b^3],
[(c+d*x)^(5/2)/(a+b*x)^2,x,5,5/3*d*(c+d*x)^(3/2)/b^2-(c+d*x)^(5/2)/(b*(a+b*x))-5*d*(b*c-a*d)^(3/2)*arctanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/b^(7/2)+5*d*(b*c-a*d)*sqrt(c+d*x)/b^3],
[(c+d*x)^(5/2)/(a+b*x)^3,x,5,-5/4*d*(c+d*x)^(3/2)/(b^2*(a+b*x))-1/2*(c+d*x)^(5/2)/(b*(a+b*x)^2)-15/4*d^2*arctanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))*sqrt(b*c-a*d)/b^(7/2)+15/4*d^2*sqrt(c+d*x)/b^3],
[(c+d*x)^(5/2)/(a+b*x)^4,x,5,-5/12*d*(c+d*x)^(3/2)/(b^2*(a+b*x)^2)-1/3*(c+d*x)^(5/2)/(b*(a+b*x)^3)-5/8*d^3*arctanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/(b^(7/2)*sqrt(b*c-a*d))-5/8*d^2*sqrt(c+d*x)/(b^3*(a+b*x))],
[(c+d*x)^(5/2)/(a+b*x)^5,x,6,-5/24*d*(c+d*x)^(3/2)/(b^2*(a+b*x)^3)-1/4*(c+d*x)^(5/2)/(b*(a+b*x)^4)+5/64*d^4*arctanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/(b^(7/2)*(b*c-a*d)^(3/2))-5/32*d^2*sqrt(c+d*x)/(b^3*(a+b*x)^2)-5/64*d^3*sqrt(c+d*x)/(b^3*(b*c-a*d)*(a+b*x))],
[(c+d*x)^(5/2)/(a+b*x)^6,x,7,-1/8*d*(c+d*x)^(3/2)/(b^2*(a+b*x)^4)-1/5*(c+d*x)^(5/2)/(b*(a+b*x)^5)-3/128*d^5*arctanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/(b^(7/2)*(b*c-a*d)^(5/2))-1/16*d^2*sqrt(c+d*x)/(b^3*(a+b*x)^3)-1/64*d^3*sqrt(c+d*x)/(b^3*(b*c-a*d)*(a+b*x)^2)+3/128*d^4*sqrt(c+d*x)/(b^3*(b*c-a*d)^2*(a+b*x))],
[sqrt(-1+x)/(1+x)^2,x,3,arctan(sqrt(-1+x)/sqrt(2))/sqrt(2)-sqrt(-1+x)/(1+x)],
[sqrt(-1+x)/(1+x)^3,x,4,1/8*arctan(sqrt(-1+x)/sqrt(2))/sqrt(2)-1/2*sqrt(-1+x)/(1+x)^2+1/8*sqrt(-1+x)/(1+x)],

# n<0
[(a+b*x)^5/(c+d*x)^(1/2),x,2,10/3*b*(b*c-a*d)^4*(c+d*x)^(3/2)/d^6-4*b^2*(b*c-a*d)^3*(c+d*x)^(5/2)/d^6+20/7*b^3*(b*c-a*d)^2*(c+d*x)^(7/2)/d^6-10/9*b^4*(b*c-a*d)*(c+d*x)^(9/2)/d^6+2/11*b^5*(c+d*x)^(11/2)/d^6-2*(b*c-a*d)^5*sqrt(c+d*x)/d^6],
[(a+b*x)^4/(c+d*x)^(1/2),x,2,-8/3*b*(b*c-a*d)^3*(c+d*x)^(3/2)/d^5+12/5*b^2*(b*c-a*d)^2*(c+d*x)^(5/2)/d^5-8/7*b^3*(b*c-a*d)*(c+d*x)^(7/2)/d^5+2/9*b^4*(c+d*x)^(9/2)/d^5+2*(b*c-a*d)^4*sqrt(c+d*x)/d^5],
[(a+b*x)^3/(c+d*x)^(1/2),x,2,2*b*(b*c-a*d)^2*(c+d*x)^(3/2)/d^4-6/5*b^2*(b*c-a*d)*(c+d*x)^(5/2)/d^4+2/7*b^3*(c+d*x)^(7/2)/d^4-2*(b*c-a*d)^3*sqrt(c+d*x)/d^4],
[(a+b*x)^2/(c+d*x)^(1/2),x,2,-4/3*b*(b*c-a*d)*(c+d*x)^(3/2)/d^3+2/5*b^2*(c+d*x)^(5/2)/d^3+2*(b*c-a*d)^2*sqrt(c+d*x)/d^3],
[(a+b*x)/(c+d*x)^(1/2),x,2,2/3*b*(c+d*x)^(3/2)/d^2-2*(b*c-a*d)*sqrt(c+d*x)/d^2],
[1/(c+d*x)^(1/2),x,1,2*sqrt(c+d*x)/d],
[1/((a+b*x)*(c+d*x)^(1/2)),x,2,-2*arctanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/(sqrt(b)*sqrt(b*c-a*d))],
[1/((a+b*x)^2*(c+d*x)^(1/2)),x,3,d*arctanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/((b*c-a*d)^(3/2)*sqrt(b))-sqrt(c+d*x)/((b*c-a*d)*(a+b*x))],
[1/((a+b*x)^3*(c+d*x)^(1/2)),x,4,-3/4*d^2*arctanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/((b*c-a*d)^(5/2)*sqrt(b))-1/2*sqrt(c+d*x)/((b*c-a*d)*(a+b*x)^2)+3/4*d*sqrt(c+d*x)/((b*c-a*d)^2*(a+b*x))],
[1/((a+b*x)^4*(c+d*x)^(1/2)),x,5,5/8*d^3*arctanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/((b*c-a*d)^(7/2)*sqrt(b))-1/3*sqrt(c+d*x)/((b*c-a*d)*(a+b*x)^3)+5/12*d*sqrt(c+d*x)/((b*c-a*d)^2*(a+b*x)^2)-5/8*d^2*sqrt(c+d*x)/((b*c-a*d)^3*(a+b*x))],
[1/((a+b*x)^5*(c+d*x)^(1/2)),x,6,-35/64*d^4*arctanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/((b*c-a*d)^(9/2)*sqrt(b))-1/4*sqrt(c+d*x)/((b*c-a*d)*(a+b*x)^4)+7/24*d*sqrt(c+d*x)/((b*c-a*d)^2*(a+b*x)^3)-35/96*d^2*sqrt(c+d*x)/((b*c-a*d)^3*(a+b*x)^2)+35/64*d^3*sqrt(c+d*x)/((b*c-a*d)^4*(a+b*x))],
[(a+b*x)^5/(c+d*x)^(3/2),x,2,-20/3*b^2*(b*c-a*d)^3*(c+d*x)^(3/2)/d^6+4*b^3*(b*c-a*d)^2*(c+d*x)^(5/2)/d^6-10/7*b^4*(b*c-a*d)*(c+d*x)^(7/2)/d^6+2/9*b^5*(c+d*x)^(9/2)/d^6+2*(b*c-a*d)^5/(d^6*sqrt(c+d*x))+10*b*(b*c-a*d)^4*sqrt(c+d*x)/d^6],
[(a+b*x)^4/(c+d*x)^(3/2),x,2,4*b^2*(b*c-a*d)^2*(c+d*x)^(3/2)/d^5-8/5*b^3*(b*c-a*d)*(c+d*x)^(5/2)/d^5+2/7*b^4*(c+d*x)^(7/2)/d^5-2*(b*c-a*d)^4/(d^5*sqrt(c+d*x))-8*b*(b*c-a*d)^3*sqrt(c+d*x)/d^5],
[(a+b*x)^3/(c+d*x)^(3/2),x,2,-2*b^2*(b*c-a*d)*(c+d*x)^(3/2)/d^4+2/5*b^3*(c+d*x)^(5/2)/d^4+2*(b*c-a*d)^3/(d^4*sqrt(c+d*x))+6*b*(b*c-a*d)^2*sqrt(c+d*x)/d^4],
[(a+b*x)^2/(c+d*x)^(3/2),x,2,2/3*b^2*(c+d*x)^(3/2)/d^3-2*(b*c-a*d)^2/(d^3*sqrt(c+d*x))-4*b*(b*c-a*d)*sqrt(c+d*x)/d^3],
[(a+b*x)/(c+d*x)^(3/2),x,2,2*(b*c-a*d)/(d^2*sqrt(c+d*x))+2*b*sqrt(c+d*x)/d^2],
[1/(c+d*x)^(3/2),x,1,(-2)/(d*sqrt(c+d*x))],
[1/((a+b*x)*(c+d*x)^(3/2)),x,3,-2*arctanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))*sqrt(b)/(b*c-a*d)^(3/2)+2/((b*c-a*d)*sqrt(c+d*x))],
[1/((a+b*x)^2*(c+d*x)^(3/2)),x,4,3*d*arctanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))*sqrt(b)/(b*c-a*d)^(5/2)-3*d/((b*c-a*d)^2*sqrt(c+d*x))+(-1)/((b*c-a*d)*(a+b*x)*sqrt(c+d*x))],
[1/((a+b*x)^3*(c+d*x)^(3/2)),x,5,-15/4*d^2*arctanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))*sqrt(b)/(b*c-a*d)^(7/2)+15/4*d^2/((b*c-a*d)^3*sqrt(c+d*x))+(-1/2)/((b*c-a*d)*(a+b*x)^2*sqrt(c+d*x))+5/4*d/((b*c-a*d)^2*(a+b*x)*sqrt(c+d*x))],
[1/((a+b*x)^4*(c+d*x)^(3/2)),x,6,35/8*d^3*arctanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))*sqrt(b)/(b*c-a*d)^(9/2)-35/8*d^3/((b*c-a*d)^4*sqrt(c+d*x))+(-1/3)/((b*c-a*d)*(a+b*x)^3*sqrt(c+d*x))+7/12*d/((b*c-a*d)^2*(a+b*x)^2*sqrt(c+d*x))-35/24*d^2/((b*c-a*d)^3*(a+b*x)*sqrt(c+d*x))],
[(a+b*x)^5/(c+d*x)^(5/2),x,2,2/3*(b*c-a*d)^5/(d^6*(c+d*x)^(3/2))+20/3*b^3*(b*c-a*d)^2*(c+d*x)^(3/2)/d^6-2*b^4*(b*c-a*d)*(c+d*x)^(5/2)/d^6+2/7*b^5*(c+d*x)^(7/2)/d^6-10*b*(b*c-a*d)^4/(d^6*sqrt(c+d*x))-20*b^2*(b*c-a*d)^3*sqrt(c+d*x)/d^6],
[(a+b*x)^4/(c+d*x)^(5/2),x,2,-2/3*(b*c-a*d)^4/(d^5*(c+d*x)^(3/2))-8/3*b^3*(b*c-a*d)*(c+d*x)^(3/2)/d^5+2/5*b^4*(c+d*x)^(5/2)/d^5+8*b*(b*c-a*d)^3/(d^5*sqrt(c+d*x))+12*b^2*(b*c-a*d)^2*sqrt(c+d*x)/d^5],
[(a+b*x)^3/(c+d*x)^(5/2),x,2,2/3*(b*c-a*d)^3/(d^4*(c+d*x)^(3/2))+2/3*b^3*(c+d*x)^(3/2)/d^4-6*b*(b*c-a*d)^2/(d^4*sqrt(c+d*x))-6*b^2*(b*c-a*d)*sqrt(c+d*x)/d^4],
[(a+b*x)^2/(c+d*x)^(5/2),x,2,-2/3*(b*c-a*d)^2/(d^3*(c+d*x)^(3/2))+4*b*(b*c-a*d)/(d^3*sqrt(c+d*x))+2*b^2*sqrt(c+d*x)/d^3],
[(a+b*x)/(c+d*x)^(5/2),x,2,2/3*(b*c-a*d)/(d^2*(c+d*x)^(3/2))-2*b/(d^2*sqrt(c+d*x))],
[1/(c+d*x)^(5/2),x,1,(-2/3)/(d*(c+d*x)^(3/2))],
[1/((a+b*x)*(c+d*x)^(5/2)),x,4,2/3/((b*c-a*d)*(c+d*x)^(3/2))-2*b^(3/2)*arctanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/(b*c-a*d)^(5/2)+2*b/((b*c-a*d)^2*sqrt(c+d*x))],
[1/((a+b*x)^2*(c+d*x)^(5/2)),x,5,-5/3*d/((b*c-a*d)^2*(c+d*x)^(3/2))+(-1)/((b*c-a*d)*(a+b*x)*(c+d*x)^(3/2))+5*b^(3/2)*d*arctanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/(b*c-a*d)^(7/2)-5*b*d/((b*c-a*d)^3*sqrt(c+d*x))],
[1/((a+b*x)^3*(c+d*x)^(5/2)),x,6,35/12*d^2/((b*c-a*d)^3*(c+d*x)^(3/2))+(-1/2)/((b*c-a*d)*(a+b*x)^2*(c+d*x)^(3/2))+7/4*d/((b*c-a*d)^2*(a+b*x)*(c+d*x)^(3/2))-35/4*b^(3/2)*d^2*arctanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/(b*c-a*d)^(9/2)+35/4*b*d^2/((b*c-a*d)^4*sqrt(c+d*x))],
[1/((a+b*x)^4*(c+d*x)^(5/2)),x,7,-35/8*d^3/((b*c-a*d)^4*(c+d*x)^(3/2))+(-1/3)/((b*c-a*d)*(a+b*x)^3*(c+d*x)^(3/2))+3/4*d/((b*c-a*d)^2*(a+b*x)^2*(c+d*x)^(3/2))-21/8*d^2/((b*c-a*d)^3*(a+b*x)*(c+d*x)^(3/2))+105/8*b^(3/2)*d^3*arctanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/(b*c-a*d)^(11/2)-105/8*b*d^3/((b*c-a*d)^5*sqrt(c+d*x))],
[(a+b*x)^5*(a*c+b*c*x)^(3/2),x,2,2/15*(a*c+b*c*x)^(15/2)/(b*c^6)],
[(a+b*x)^5*(a*c+b*c*x)^(1/2),x,2,2/13*(a*c+b*c*x)^(13/2)/(b*c^6)],
[(a+b*x)^5/(a*c+b*c*x)^(1/2),x,2,2/11*(a*c+b*c*x)^(11/2)/(b*c^6)],
[(a+b*x)^5/(a*c+b*c*x)^(3/2),x,2,2/9*(a*c+b*c*x)^(9/2)/(b*c^6)],
[(a+b*x)^5/(a*c+b*c*x)^(5/2),x,2,2/7*(a*c+b*c*x)^(7/2)/(b*c^6)],
[(a+b*x)^5/(a*c+b*c*x)^(7/2),x,2,2/5*(a*c+b*c*x)^(5/2)/(b*c^6)],
[(a+b*x)^5/(a*c+b*c*x)^(9/2),x,2,2/3*(a*c+b*c*x)^(3/2)/(b*c^6)],
[(a+b*x)^5/(a*c+b*c*x)^(11/2),x,2,2*sqrt(a*c+b*c*x)/(b*c^6)],
[(a+b*x)^5/(a*c+b*c*x)^(13/2),x,2,(-2)/(b*c^6*sqrt(a*c+b*c*x))],
[1/((-2+x)*sqrt(2+x)),x,2,-arctanh(1/2*sqrt(2+x))],
[1/((2+3*x)*sqrt(1+5*x)),x,2,2*arctan(sqrt(3/7)*sqrt(1+5*x))/sqrt(21)],

# Integrands of the form (a+b x)^m (c+d x)^(n/3)
[(1-x)^(1/3)/(1+x),x,5,3*(1-x)^(1/3)+3*log(2^(1/3)-(1-x)^(1/3))/2^(2/3)-log(1+x)/2^(2/3)-2^(1/3)*arctan((1+2^(2/3)*(1-x)^(1/3))/sqrt(3))*sqrt(3)],
[(3-2*x)^(1/3)*(7+x),x,2,-51/16*(3-2*x)^(4/3)+3/28*(3-2*x)^(7/3)],
[(1-x)^(1/3)*(1+x)^2,x,2,-3*(1-x)^(4/3)+12/7*(1-x)^(7/3)-3/10*(1-x)^(10/3)],
[1/((a+b*x)*(c+d*x)^(1/3)),x,4,-1/2*log(a+b*x)/(b^(2/3)*(b*c-a*d)^(1/3))+3/2*log((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))/(b^(2/3)*(b*c-a*d)^(1/3))+arctan((1+2*b^(1/3)*(c+d*x)^(1/3)/(b*c-a*d)^(1/3))/sqrt(3))*sqrt(3)/(b^(2/3)*(b*c-a*d)^(1/3))],
[1/((a+b*x)*(c+d*x)^(2/3)),x,4,-1/2*log(a+b*x)/(b^(1/3)*(b*c-a*d)^(2/3))+3/2*log((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))/(b^(1/3)*(b*c-a*d)^(2/3))-arctan((1+2*b^(1/3)*(c+d*x)^(1/3)/(b*c-a*d)^(1/3))/sqrt(3))*sqrt(3)/(b^(1/3)*(b*c-a*d)^(2/3))],

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

# n>0
[(a+b*x)^(7/2)*(c+d*x)^(1/2),x,8,7/128*(b*c-a*d)^5*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(3/2)*d^(9/2))+7/192*(b*c-a*d)^3*(a+b*x)^(3/2)*sqrt(c+d*x)/(b*d^3)-7/240*(b*c-a*d)^2*(a+b*x)^(5/2)*sqrt(c+d*x)/(b*d^2)+1/40*(b*c-a*d)*(a+b*x)^(7/2)*sqrt(c+d*x)/(b*d)+1/5*(a+b*x)^(9/2)*sqrt(c+d*x)/b-7/128*(b*c-a*d)^4*sqrt(a+b*x)*sqrt(c+d*x)/(b*d^4)],
[(a+b*x)^(5/2)*(c+d*x)^(1/2),x,7,-5/64*(b*c-a*d)^4*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(3/2)*d^(7/2))-5/96*(b*c-a*d)^2*(a+b*x)^(3/2)*sqrt(c+d*x)/(b*d^2)+1/24*(b*c-a*d)*(a+b*x)^(5/2)*sqrt(c+d*x)/(b*d)+1/4*(a+b*x)^(7/2)*sqrt(c+d*x)/b+5/64*(b*c-a*d)^3*sqrt(a+b*x)*sqrt(c+d*x)/(b*d^3)],
[(a+b*x)^(3/2)*(c+d*x)^(1/2),x,6,1/8*(b*c-a*d)^3*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(3/2)*d^(5/2))+1/12*(b*c-a*d)*(a+b*x)^(3/2)*sqrt(c+d*x)/(b*d)+1/3*(a+b*x)^(5/2)*sqrt(c+d*x)/b-1/8*(b*c-a*d)^2*sqrt(a+b*x)*sqrt(c+d*x)/(b*d^2)],
[(a+b*x)^(1/2)*(c+d*x)^(1/2),x,5,-1/4*(b*c-a*d)^2*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(3/2)*d^(3/2))+1/2*(a+b*x)^(3/2)*sqrt(c+d*x)/b+1/4*(b*c-a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(b*d)],
[(c+d*x)^(1/2)/(a+b*x)^(1/2),x,4,(b*c-a*d)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(3/2)*sqrt(d))+sqrt(a+b*x)*sqrt(c+d*x)/b],
[(c+d*x)^(1/2)/(a+b*x)^(3/2),x,4,2*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))*sqrt(d)/b^(3/2)-2*sqrt(c+d*x)/(b*sqrt(a+b*x))],
[(c+d*x)^(1/2)/(a+b*x)^(5/2),x,1,-2/3*(c+d*x)^(3/2)/((b*c-a*d)*(a+b*x)^(3/2))],
[(c+d*x)^(1/2)/(a+b*x)^(7/2),x,2,-2/5*(c+d*x)^(3/2)/((b*c-a*d)*(a+b*x)^(5/2))+4/15*d*(c+d*x)^(3/2)/((b*c-a*d)^2*(a+b*x)^(3/2))],
[(c+d*x)^(1/2)/(a+b*x)^(9/2),x,3,-2/7*(c+d*x)^(3/2)/((b*c-a*d)*(a+b*x)^(7/2))+8/35*d*(c+d*x)^(3/2)/((b*c-a*d)^2*(a+b*x)^(5/2))-16/105*d^2*(c+d*x)^(3/2)/((b*c-a*d)^3*(a+b*x)^(3/2))],
[(c+d*x)^(1/2)/(a+b*x)^(11/2),x,4,-2/9*(c+d*x)^(3/2)/((b*c-a*d)*(a+b*x)^(9/2))+4/21*d*(c+d*x)^(3/2)/((b*c-a*d)^2*(a+b*x)^(7/2))-16/105*d^2*(c+d*x)^(3/2)/((b*c-a*d)^3*(a+b*x)^(5/2))+32/315*d^3*(c+d*x)^(3/2)/((b*c-a*d)^4*(a+b*x)^(3/2))],
[(c+d*x)^(1/2)/(a+b*x)^(13/2),x,5,-2/11*(c+d*x)^(3/2)/((b*c-a*d)*(a+b*x)^(11/2))+16/99*d*(c+d*x)^(3/2)/((b*c-a*d)^2*(a+b*x)^(9/2))-32/231*d^2*(c+d*x)^(3/2)/((b*c-a*d)^3*(a+b*x)^(7/2))+128/1155*d^3*(c+d*x)^(3/2)/((b*c-a*d)^4*(a+b*x)^(5/2))-256/3465*d^4*(c+d*x)^(3/2)/((b*c-a*d)^5*(a+b*x)^(3/2))],
[(a+b*x)^(5/2)*(c+d*x)^(3/2),x,8,1/5*(a+b*x)^(7/2)*(c+d*x)^(3/2)/b-3/128*(b*c-a*d)^5*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(5/2)*d^(7/2))-1/64*(b*c-a*d)^3*(a+b*x)^(3/2)*sqrt(c+d*x)/(b^2*d^2)+1/80*(b*c-a*d)^2*(a+b*x)^(5/2)*sqrt(c+d*x)/(b^2*d)+3/40*(b*c-a*d)*(a+b*x)^(7/2)*sqrt(c+d*x)/b^2+3/128*(b*c-a*d)^4*sqrt(a+b*x)*sqrt(c+d*x)/(b^2*d^3)],
[(a+b*x)^(3/2)*(c+d*x)^(3/2),x,7,1/4*(a+b*x)^(5/2)*(c+d*x)^(3/2)/b+3/64*(b*c-a*d)^4*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(5/2)*d^(5/2))+1/32*(b*c-a*d)^2*(a+b*x)^(3/2)*sqrt(c+d*x)/(b^2*d)+1/8*(b*c-a*d)*(a+b*x)^(5/2)*sqrt(c+d*x)/b^2-3/64*(b*c-a*d)^3*sqrt(a+b*x)*sqrt(c+d*x)/(b^2*d^2)],
[(a+b*x)^(1/2)*(c+d*x)^(3/2),x,6,1/3*(a+b*x)^(3/2)*(c+d*x)^(3/2)/b-1/8*(b*c-a*d)^3*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(5/2)*d^(3/2))+1/4*(b*c-a*d)*(a+b*x)^(3/2)*sqrt(c+d*x)/b^2+1/8*(b*c-a*d)^2*sqrt(a+b*x)*sqrt(c+d*x)/(b^2*d)],
[(c+d*x)^(3/2)/(a+b*x)^(1/2),x,5,3/4*(b*c-a*d)^2*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(5/2)*sqrt(d))+1/2*(c+d*x)^(3/2)*sqrt(a+b*x)/b+3/4*(b*c-a*d)*sqrt(a+b*x)*sqrt(c+d*x)/b^2],
[(c+d*x)^(3/2)/(a+b*x)^(3/2),x,5,3*(b*c-a*d)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))*sqrt(d)/b^(5/2)-2*(c+d*x)^(3/2)/(b*sqrt(a+b*x))+3*d*sqrt(a+b*x)*sqrt(c+d*x)/b^2],
[(c+d*x)^(3/2)/(a+b*x)^(5/2),x,5,-2/3*(c+d*x)^(3/2)/(b*(a+b*x)^(3/2))+2*d^(3/2)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/b^(5/2)-2*d*sqrt(c+d*x)/(b^2*sqrt(a+b*x))],
[(c+d*x)^(3/2)/(a+b*x)^(7/2),x,1,-2/5*(c+d*x)^(5/2)/((b*c-a*d)*(a+b*x)^(5/2))],
[(c+d*x)^(3/2)/(a+b*x)^(9/2),x,2,-2/7*(c+d*x)^(5/2)/((b*c-a*d)*(a+b*x)^(7/2))+4/35*d*(c+d*x)^(5/2)/((b*c-a*d)^2*(a+b*x)^(5/2))],
[(c+d*x)^(3/2)/(a+b*x)^(11/2),x,3,-2/9*(c+d*x)^(5/2)/((b*c-a*d)*(a+b*x)^(9/2))+8/63*d*(c+d*x)^(5/2)/((b*c-a*d)^2*(a+b*x)^(7/2))-16/315*d^2*(c+d*x)^(5/2)/((b*c-a*d)^3*(a+b*x)^(5/2))],
[(c+d*x)^(3/2)/(a+b*x)^(13/2),x,4,-2/11*(c+d*x)^(5/2)/((b*c-a*d)*(a+b*x)^(11/2))+4/33*d*(c+d*x)^(5/2)/((b*c-a*d)^2*(a+b*x)^(9/2))-16/231*d^2*(c+d*x)^(5/2)/((b*c-a*d)^3*(a+b*x)^(7/2))+32/1155*d^3*(c+d*x)^(5/2)/((b*c-a*d)^4*(a+b*x)^(5/2))],
[(a+b*x)^(5/2)*(c+d*x)^(5/2),x,9,1/12*(b*c-a*d)*(a+b*x)^(7/2)*(c+d*x)^(3/2)/b^2+1/6*(a+b*x)^(7/2)*(c+d*x)^(5/2)/b-5/512*(b*c-a*d)^6*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(7/2)*d^(7/2))-5/768*(b*c-a*d)^4*(a+b*x)^(3/2)*sqrt(c+d*x)/(b^3*d^2)+1/192*(b*c-a*d)^3*(a+b*x)^(5/2)*sqrt(c+d*x)/(b^3*d)+1/32*(b*c-a*d)^2*(a+b*x)^(7/2)*sqrt(c+d*x)/b^3+5/512*(b*c-a*d)^5*sqrt(a+b*x)*sqrt(c+d*x)/(b^3*d^3)],
[(a+b*x)^(3/2)*(c+d*x)^(5/2),x,8,1/8*(b*c-a*d)*(a+b*x)^(5/2)*(c+d*x)^(3/2)/b^2+1/5*(a+b*x)^(5/2)*(c+d*x)^(5/2)/b+3/128*(b*c-a*d)^5*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(7/2)*d^(5/2))+1/64*(b*c-a*d)^3*(a+b*x)^(3/2)*sqrt(c+d*x)/(b^3*d)+1/16*(b*c-a*d)^2*(a+b*x)^(5/2)*sqrt(c+d*x)/b^3-3/128*(b*c-a*d)^4*sqrt(a+b*x)*sqrt(c+d*x)/(b^3*d^2)],
[(a+b*x)^(1/2)*(c+d*x)^(5/2),x,7,5/24*(b*c-a*d)*(a+b*x)^(3/2)*(c+d*x)^(3/2)/b^2+1/4*(a+b*x)^(3/2)*(c+d*x)^(5/2)/b-5/64*(b*c-a*d)^4*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(7/2)*d^(3/2))+5/32*(b*c-a*d)^2*(a+b*x)^(3/2)*sqrt(c+d*x)/b^3+5/64*(b*c-a*d)^3*sqrt(a+b*x)*sqrt(c+d*x)/(b^3*d)],
[(c+d*x)^(5/2)/(a+b*x)^(1/2),x,6,5/8*(b*c-a*d)^3*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(7/2)*sqrt(d))+5/12*(b*c-a*d)*(c+d*x)^(3/2)*sqrt(a+b*x)/b^2+1/3*(c+d*x)^(5/2)*sqrt(a+b*x)/b+5/8*(b*c-a*d)^2*sqrt(a+b*x)*sqrt(c+d*x)/b^3],
[(c+d*x)^(5/2)/(a+b*x)^(3/2),x,6,15/4*(b*c-a*d)^2*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))*sqrt(d)/b^(7/2)-2*(c+d*x)^(5/2)/(b*sqrt(a+b*x))+5/2*d*(c+d*x)^(3/2)*sqrt(a+b*x)/b^2+15/4*d*(b*c-a*d)*sqrt(a+b*x)*sqrt(c+d*x)/b^3],
[(c+d*x)^(5/2)/(a+b*x)^(5/2),x,6,-2/3*(c+d*x)^(5/2)/(b*(a+b*x)^(3/2))+5*d^(3/2)*(b*c-a*d)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/b^(7/2)-10/3*d*(c+d*x)^(3/2)/(b^2*sqrt(a+b*x))+5*d^2*sqrt(a+b*x)*sqrt(c+d*x)/b^3],
[(c+d*x)^(5/2)/(a+b*x)^(7/2),x,6,-2/3*d*(c+d*x)^(3/2)/(b^2*(a+b*x)^(3/2))-2/5*(c+d*x)^(5/2)/(b*(a+b*x)^(5/2))+2*d^(5/2)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/b^(7/2)-2*d^2*sqrt(c+d*x)/(b^3*sqrt(a+b*x))],
[(c+d*x)^(5/2)/(a+b*x)^(9/2),x,1,-2/7*(c+d*x)^(7/2)/((b*c-a*d)*(a+b*x)^(7/2))],
[(c+d*x)^(5/2)/(a+b*x)^(11/2),x,2,-2/9*(c+d*x)^(7/2)/((b*c-a*d)*(a+b*x)^(9/2))+4/63*d*(c+d*x)^(7/2)/((b*c-a*d)^2*(a+b*x)^(7/2))],
[(c+d*x)^(5/2)/(a+b*x)^(13/2),x,3,-2/11*(c+d*x)^(7/2)/((b*c-a*d)*(a+b*x)^(11/2))+8/99*d*(c+d*x)^(7/2)/((b*c-a*d)^2*(a+b*x)^(9/2))-16/693*d^2*(c+d*x)^(7/2)/((b*c-a*d)^3*(a+b*x)^(7/2))],
[(c+d*x)^(5/2)/(a+b*x)^(15/2),x,4,-2/13*(c+d*x)^(7/2)/((b*c-a*d)*(a+b*x)^(13/2))+12/143*d*(c+d*x)^(7/2)/((b*c-a*d)^2*(a+b*x)^(11/2))-16/429*d^2*(c+d*x)^(7/2)/((b*c-a*d)^3*(a+b*x)^(9/2))+32/3003*d^3*(c+d*x)^(7/2)/((b*c-a*d)^4*(a+b*x)^(7/2))],

# n<0
[(a+b*x)^(7/2)/(c+d*x)^(1/2),x,7,35/64*(b*c-a*d)^4*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(d^(9/2)*sqrt(b))+35/96*(b*c-a*d)^2*(a+b*x)^(3/2)*sqrt(c+d*x)/d^3-7/24*(b*c-a*d)*(a+b*x)^(5/2)*sqrt(c+d*x)/d^2+1/4*(a+b*x)^(7/2)*sqrt(c+d*x)/d-35/64*(b*c-a*d)^3*sqrt(a+b*x)*sqrt(c+d*x)/d^4],
[(a+b*x)^(5/2)/(c+d*x)^(1/2),x,6,-5/8*(b*c-a*d)^3*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(d^(7/2)*sqrt(b))-5/12*(b*c-a*d)*(a+b*x)^(3/2)*sqrt(c+d*x)/d^2+1/3*(a+b*x)^(5/2)*sqrt(c+d*x)/d+5/8*(b*c-a*d)^2*sqrt(a+b*x)*sqrt(c+d*x)/d^3],
[(a+b*x)^(3/2)/(c+d*x)^(1/2),x,5,3/4*(b*c-a*d)^2*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(d^(5/2)*sqrt(b))+1/2*(a+b*x)^(3/2)*sqrt(c+d*x)/d-3/4*(b*c-a*d)*sqrt(a+b*x)*sqrt(c+d*x)/d^2],
[(a+b*x)^(1/2)/(c+d*x)^(1/2),x,4,-(b*c-a*d)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(d^(3/2)*sqrt(b))+sqrt(a+b*x)*sqrt(c+d*x)/d],
[1/((a+b*x)^(1/2)*(c+d*x)^(1/2)),x,3,2*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(sqrt(b)*sqrt(d))],
[1/((a+b*x)^(3/2)*(c+d*x)^(1/2)),x,1,-2*sqrt(c+d*x)/((b*c-a*d)*sqrt(a+b*x))],
[1/((a+b*x)^(5/2)*(c+d*x)^(1/2)),x,2,-2/3*sqrt(c+d*x)/((b*c-a*d)*(a+b*x)^(3/2))+4/3*d*sqrt(c+d*x)/((b*c-a*d)^2*sqrt(a+b*x))],
[1/((a+b*x)^(7/2)*(c+d*x)^(1/2)),x,3,-2/5*sqrt(c+d*x)/((b*c-a*d)*(a+b*x)^(5/2))+8/15*d*sqrt(c+d*x)/((b*c-a*d)^2*(a+b*x)^(3/2))-16/15*d^2*sqrt(c+d*x)/((b*c-a*d)^3*sqrt(a+b*x))],
[1/((a+b*x)^(9/2)*(c+d*x)^(1/2)),x,4,-2/7*sqrt(c+d*x)/((b*c-a*d)*(a+b*x)^(7/2))+12/35*d*sqrt(c+d*x)/((b*c-a*d)^2*(a+b*x)^(5/2))-16/35*d^2*sqrt(c+d*x)/((b*c-a*d)^3*(a+b*x)^(3/2))+32/35*d^3*sqrt(c+d*x)/((b*c-a*d)^4*sqrt(a+b*x))],
[1/((a+b*x)^(11/2)*(c+d*x)^(1/2)),x,5,-2/9*sqrt(c+d*x)/((b*c-a*d)*(a+b*x)^(9/2))+16/63*d*sqrt(c+d*x)/((b*c-a*d)^2*(a+b*x)^(7/2))-32/105*d^2*sqrt(c+d*x)/((b*c-a*d)^3*(a+b*x)^(5/2))+128/315*d^3*sqrt(c+d*x)/((b*c-a*d)^4*(a+b*x)^(3/2))-256/315*d^4*sqrt(c+d*x)/((b*c-a*d)^5*sqrt(a+b*x))],
[(a+b*x)^(7/2)/(c+d*x)^(3/2),x,7,-35/8*(b*c-a*d)^3*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))*sqrt(b)/d^(9/2)-2*(a+b*x)^(7/2)/(d*sqrt(c+d*x))-35/12*b*(b*c-a*d)*(a+b*x)^(3/2)*sqrt(c+d*x)/d^3+7/3*b*(a+b*x)^(5/2)*sqrt(c+d*x)/d^2+35/8*b*(b*c-a*d)^2*sqrt(a+b*x)*sqrt(c+d*x)/d^4],
[(a+b*x)^(5/2)/(c+d*x)^(3/2),x,6,15/4*(b*c-a*d)^2*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))*sqrt(b)/d^(7/2)-2*(a+b*x)^(5/2)/(d*sqrt(c+d*x))+5/2*b*(a+b*x)^(3/2)*sqrt(c+d*x)/d^2-15/4*b*(b*c-a*d)*sqrt(a+b*x)*sqrt(c+d*x)/d^3],
[(a+b*x)^(3/2)/(c+d*x)^(3/2),x,5,-3*(b*c-a*d)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))*sqrt(b)/d^(5/2)-2*(a+b*x)^(3/2)/(d*sqrt(c+d*x))+3*b*sqrt(a+b*x)*sqrt(c+d*x)/d^2],
[(a+b*x)^(1/2)/(c+d*x)^(3/2),x,4,2*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))*sqrt(b)/d^(3/2)-2*sqrt(a+b*x)/(d*sqrt(c+d*x))],
[1/((a+b*x)^(1/2)*(c+d*x)^(3/2)),x,1,2*sqrt(a+b*x)/((b*c-a*d)*sqrt(c+d*x))],
[1/((a+b*x)^(3/2)*(c+d*x)^(3/2)),x,2,(-2)/((b*c-a*d)*sqrt(a+b*x)*sqrt(c+d*x))-4*d*sqrt(a+b*x)/((b*c-a*d)^2*sqrt(c+d*x))],
[1/((a+b*x)^(5/2)*(c+d*x)^(3/2)),x,3,(-2/3)/((b*c-a*d)*(a+b*x)^(3/2)*sqrt(c+d*x))+8/3*d/((b*c-a*d)^2*sqrt(a+b*x)*sqrt(c+d*x))+16/3*d^2*sqrt(a+b*x)/((b*c-a*d)^3*sqrt(c+d*x))],
[1/((a+b*x)^(7/2)*(c+d*x)^(3/2)),x,4,(-2/5)/((b*c-a*d)*(a+b*x)^(5/2)*sqrt(c+d*x))+4/5*d/((b*c-a*d)^2*(a+b*x)^(3/2)*sqrt(c+d*x))-16/5*d^2/((b*c-a*d)^3*sqrt(a+b*x)*sqrt(c+d*x))-32/5*d^3*sqrt(a+b*x)/((b*c-a*d)^4*sqrt(c+d*x))],
[1/((a+b*x)^(9/2)*(c+d*x)^(3/2)),x,5,(-2/7)/((b*c-a*d)*(a+b*x)^(7/2)*sqrt(c+d*x))+16/35*d/((b*c-a*d)^2*(a+b*x)^(5/2)*sqrt(c+d*x))-32/35*d^2/((b*c-a*d)^3*(a+b*x)^(3/2)*sqrt(c+d*x))+128/35*d^3/((b*c-a*d)^4*sqrt(a+b*x)*sqrt(c+d*x))+256/35*d^4*sqrt(a+b*x)/((b*c-a*d)^5*sqrt(c+d*x))],
[1/((a+b*x)^(11/2)*(c+d*x)^(3/2)),x,6,(-2/9)/((b*c-a*d)*(a+b*x)^(9/2)*sqrt(c+d*x))+20/63*d/((b*c-a*d)^2*(a+b*x)^(7/2)*sqrt(c+d*x))-32/63*d^2/((b*c-a*d)^3*(a+b*x)^(5/2)*sqrt(c+d*x))+64/63*d^3/((b*c-a*d)^4*(a+b*x)^(3/2)*sqrt(c+d*x))-256/63*d^4/((b*c-a*d)^5*sqrt(a+b*x)*sqrt(c+d*x))-512/63*d^5*sqrt(a+b*x)/((b*c-a*d)^6*sqrt(c+d*x))],
[(a+b*x)^(9/2)/(c+d*x)^(5/2),x,8,-2/3*(a+b*x)^(9/2)/(d*(c+d*x)^(3/2))-105/8*b^(3/2)*(b*c-a*d)^3*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/d^(11/2)-6*b*(a+b*x)^(7/2)/(d^2*sqrt(c+d*x))-35/4*b^2*(b*c-a*d)*(a+b*x)^(3/2)*sqrt(c+d*x)/d^4+7*b^2*(a+b*x)^(5/2)*sqrt(c+d*x)/d^3+105/8*b^2*(b*c-a*d)^2*sqrt(a+b*x)*sqrt(c+d*x)/d^5],
[(a+b*x)^(7/2)/(c+d*x)^(5/2),x,7,-2/3*(a+b*x)^(7/2)/(d*(c+d*x)^(3/2))+35/4*b^(3/2)*(b*c-a*d)^2*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/d^(9/2)-14/3*b*(a+b*x)^(5/2)/(d^2*sqrt(c+d*x))+35/6*b^2*(a+b*x)^(3/2)*sqrt(c+d*x)/d^3-35/4*b^2*(b*c-a*d)*sqrt(a+b*x)*sqrt(c+d*x)/d^4],
[(a+b*x)^(5/2)/(c+d*x)^(5/2),x,6,-2/3*(a+b*x)^(5/2)/(d*(c+d*x)^(3/2))-5*b^(3/2)*(b*c-a*d)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/d^(7/2)-10/3*b*(a+b*x)^(3/2)/(d^2*sqrt(c+d*x))+5*b^2*sqrt(a+b*x)*sqrt(c+d*x)/d^3],
[(a+b*x)^(3/2)/(c+d*x)^(5/2),x,5,-2/3*(a+b*x)^(3/2)/(d*(c+d*x)^(3/2))+2*b^(3/2)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/d^(5/2)-2*b*sqrt(a+b*x)/(d^2*sqrt(c+d*x))],
[(a+b*x)^(1/2)/(c+d*x)^(5/2),x,1,2/3*(a+b*x)^(3/2)/((b*c-a*d)*(c+d*x)^(3/2))],
[1/((a+b*x)^(1/2)*(c+d*x)^(5/2)),x,2,2/3*sqrt(a+b*x)/((b*c-a*d)*(c+d*x)^(3/2))+4/3*b*sqrt(a+b*x)/((b*c-a*d)^2*sqrt(c+d*x))],
[1/((a+b*x)^(3/2)*(c+d*x)^(5/2)),x,3,(-2)/((b*c-a*d)*(c+d*x)^(3/2)*sqrt(a+b*x))-8/3*d*sqrt(a+b*x)/((b*c-a*d)^2*(c+d*x)^(3/2))-16/3*b*d*sqrt(a+b*x)/((b*c-a*d)^3*sqrt(c+d*x))],
[1/((a+b*x)^(5/2)*(c+d*x)^(5/2)),x,4,(-2/3)/((b*c-a*d)*(a+b*x)^(3/2)*(c+d*x)^(3/2))+4*d/((b*c-a*d)^2*(c+d*x)^(3/2)*sqrt(a+b*x))+16/3*d^2*sqrt(a+b*x)/((b*c-a*d)^3*(c+d*x)^(3/2))+32/3*b*d^2*sqrt(a+b*x)/((b*c-a*d)^4*sqrt(c+d*x))],
[1/((a+b*x)^(7/2)*(c+d*x)^(5/2)),x,5,(-2/5)/((b*c-a*d)*(a+b*x)^(5/2)*(c+d*x)^(3/2))+16/15*d/((b*c-a*d)^2*(a+b*x)^(3/2)*(c+d*x)^(3/2))-32/5*d^2/((b*c-a*d)^3*(c+d*x)^(3/2)*sqrt(a+b*x))-128/15*d^3*sqrt(a+b*x)/((b*c-a*d)^4*(c+d*x)^(3/2))-256/15*b*d^3*sqrt(a+b*x)/((b*c-a*d)^5*sqrt(c+d*x))],
[1/((a+b*x)^(9/2)*(c+d*x)^(5/2)),x,6,(-2/7)/((b*c-a*d)*(a+b*x)^(7/2)*(c+d*x)^(3/2))+4/7*d/((b*c-a*d)^2*(a+b*x)^(5/2)*(c+d*x)^(3/2))-32/21*d^2/((b*c-a*d)^3*(a+b*x)^(3/2)*(c+d*x)^(3/2))+64/7*d^3/((b*c-a*d)^4*(c+d*x)^(3/2)*sqrt(a+b*x))+256/21*d^4*sqrt(a+b*x)/((b*c-a*d)^5*(c+d*x)^(3/2))+512/21*b*d^4*sqrt(a+b*x)/((b*c-a*d)^6*sqrt(c+d*x))],
[1/(sqrt(a+b*x)*sqrt(4+a+b*x)),x,2,2*arcsinh(1/2*sqrt(a+b*x))/b],
[1/(sqrt(2+b*x)*sqrt(6+b*x)),x,2,2*arcsinh(1/2*sqrt(2+b*x))/b],
[1/(sqrt(1+b*x)*sqrt(5+b*x)),x,2,2*arcsinh(1/2*sqrt(1+b*x))/b],
[1/(sqrt(b*x)*sqrt(4+b*x)),x,2,2*arcsinh(1/2*sqrt(b*x))/b],
[1/(sqrt(-1+b*x)*sqrt(3+b*x)),x,2,2*arcsinh(1/2*sqrt(-1+b*x))/b],
[1/(sqrt(-2+b*x)*sqrt(2+b*x)),x,1,arccosh(1/2*b*x)/b],
[1/(sqrt(-3+b*x)*sqrt(1+b*x)),x,2,2*arcsinh(1/2*sqrt(-3+b*x))/b],
[1/(sqrt(2+b*x)*sqrt(3+b*x)),x,2,2*arcsinh(sqrt(2+b*x))/b],
[1/sqrt(2+b*x)^2,x,1,log(2+b*x)/b],
[1/(sqrt(1+b*x)*sqrt(2+b*x)),x,2,2*arcsinh(sqrt(1+b*x))/b],
[1/(sqrt(b*x)*sqrt(2+b*x)),x,2,2*arcsinh(sqrt(b*x)/sqrt(2))/b],
[1/(sqrt(-1+b*x)*sqrt(2+b*x)),x,2,2*arcsinh(sqrt(-1+b*x)/sqrt(3))/b],
[1/(sqrt(-2+b*x)*sqrt(2+b*x)),x,1,arccosh(1/2*b*x)/b],
[1/(sqrt(-3+b*x)*sqrt(2+b*x)),x,2,2*arcsinh(sqrt(-3+b*x)/sqrt(5))/b],
[1/(sqrt(3-b*x)*sqrt(2+b*x)),x,3,-arcsin(1/5*(1-2*b*x))/b],
[1/(sqrt(2-b*x)*sqrt(2+b*x)),x,2,arcsin(1/2*b*x)/b],
[1/(sqrt(1-b*x)*sqrt(2+b*x)),x,3,-arcsin(1/3*(-1-2*b*x))/b],
[1/(sqrt(-b*x)*sqrt(2+b*x)),x,3,arcsin(1+b*x)/b],
[1/(sqrt(-1-b*x)*sqrt(2+b*x)),x,3,arcsin(3+2*b*x)/b],
[1/(sqrt(-2-b*x)*sqrt(2+b*x)),x,2,log(2+b*x)*sqrt(2+b*x)/(b*sqrt(-2-b*x))],
[1/(sqrt(-3-b*x)*sqrt(2+b*x)),x,3,-2*arctan(sqrt(-3-b*x)/sqrt(2+b*x))/b],
[1/(sqrt(2-b*x)*sqrt(3-b*x)),x,2,-2*arcsinh(sqrt(2-b*x))/b],
[1/sqrt(2-b*x)^2,x,1,-log(2-b*x)/b],
[1/(sqrt(1-b*x)*sqrt(2-b*x)),x,2,-2*arcsinh(sqrt(1-b*x))/b],
[1/(sqrt(-b*x)*sqrt(2-b*x)),x,2,-2*arcsinh(sqrt(-b*x)/sqrt(2))/b],
[1/(sqrt(-1-b*x)*sqrt(2-b*x)),x,2,-2*arcsinh(sqrt(-1-b*x)/sqrt(3))/b],
[1/(sqrt(-2-b*x)*sqrt(2-b*x)),x,1,-arccosh(-1/2*b*x)/b],
[1/(sqrt(-3-b*x)*sqrt(2-b*x)),x,2,-2*arcsinh(sqrt(-3-b*x)/sqrt(5))/b],
[1/(sqrt(-4+b*x)*sqrt(4+b*x)),x,1,arccosh(1/4*b*x)/b],
[1/(sqrt((-b+b*c)/d+b*x)*sqrt(c+d*x)),x,2,2*arcsinh(sqrt(d)*sqrt(-b*(1-c)/d+b*x)/sqrt(b))/(sqrt(b)*sqrt(d))],
[1/(sqrt(x)*sqrt(-3+2*x)),x,2,arcsinh(sqrt(-3+2*x)/sqrt(3))*sqrt(2)],
[1/(sqrt(-3+2*x)*sqrt(2+3*x)),x,2,arcsinh(sqrt(3/13)*sqrt(-3+2*x))*sqrt(2/3)],
[1/(sqrt((b-b*c)/d+b*x)*sqrt(c-d*x)),x,2,2*arcsin(sqrt(d)*sqrt(b*(1-c)/d+b*x)/sqrt(b))/(sqrt(b)*sqrt(d))],
[1/(sqrt(4-x)*sqrt(x)),x,3,-arcsin(1-1/2*x)],
[1/(sqrt(3-2*x)*sqrt(x)),x,2,arcsin(sqrt(2/3)*sqrt(x))*sqrt(2)],
[1/(sqrt(3-2*x)*sqrt(3+5*x)),x,2,arcsin(sqrt(2/21)*sqrt(3+5*x))*sqrt(2/5)],
[1/(sqrt(a-b*x)*sqrt(c+d*x)),x,3,-2*arctan(sqrt(d)*sqrt(a-b*x)/(sqrt(b)*sqrt(c+d*x)))/(sqrt(b)*sqrt(d))],

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

# n>0
[(a+b*x)^(3/2)*(c+d*x)^(1/3),x,5,12/187*(b*c-a*d)*(a+b*x)^(3/2)*(c+d*x)^(1/3)/(b*d)+6/17*(a+b*x)^(5/2)*(c+d*x)^(1/3)/b-108/935*(b*c-a*d)^2*(c+d*x)^(1/3)*sqrt(a+b*x)/(b*d^2)-108/935*3^(3/4)*(b*c-a*d)^3*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))*EllipticF((-b^(1/3)*(c+d*x)^(1/3)+(b*c-a*d)^(1/3)*(1+sqrt(3)))/(-b^(1/3)*(c+d*x)^(1/3)+(b*c-a*d)^(1/3)*(1-sqrt(3))),sqrt(-7+4*sqrt(3)))*sqrt(((b*c-a*d)^(2/3)+b^(1/3)*(b*c-a*d)^(1/3)*(c+d*x)^(1/3)+b^(2/3)*(c+d*x)^(2/3))/(-b^(1/3)*(c+d*x)^(1/3)+(b*c-a*d)^(1/3)*(1-sqrt(3)))^2)*sqrt(2-sqrt(3))/(b^(4/3)*d^3*sqrt(a+b*x)*sqrt(-(b*c-a*d)^(1/3)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))/(-b^(1/3)*(c+d*x)^(1/3)+(b*c-a*d)^(1/3)*(1-sqrt(3)))^2))],
[(a+b*x)^(1/2)*(c+d*x)^(1/3),x,4,6/11*(a+b*x)^(3/2)*(c+d*x)^(1/3)/b+12/55*(b*c-a*d)*(c+d*x)^(1/3)*sqrt(a+b*x)/(b*d)+12/55*3^(3/4)*(b*c-a*d)^2*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))*EllipticF((-b^(1/3)*(c+d*x)^(1/3)+(b*c-a*d)^(1/3)*(1+sqrt(3)))/(-b^(1/3)*(c+d*x)^(1/3)+(b*c-a*d)^(1/3)*(1-sqrt(3))),sqrt(-7+4*sqrt(3)))*sqrt(((b*c-a*d)^(2/3)+b^(1/3)*(b*c-a*d)^(1/3)*(c+d*x)^(1/3)+b^(2/3)*(c+d*x)^(2/3))/(-b^(1/3)*(c+d*x)^(1/3)+(b*c-a*d)^(1/3)*(1-sqrt(3)))^2)*sqrt(2-sqrt(3))/(b^(4/3)*d^2*sqrt(a+b*x)*sqrt(-(b*c-a*d)^(1/3)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))/(-b^(1/3)*(c+d*x)^(1/3)+(b*c-a*d)^(1/3)*(1-sqrt(3)))^2))],
[(c+d*x)^(1/3)/(a+b*x)^(1/2),x,3,6/5*(c+d*x)^(1/3)*sqrt(a+b*x)/b-4/5*3^(3/4)*(b*c-a*d)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))*EllipticF((-b^(1/3)*(c+d*x)^(1/3)+(b*c-a*d)^(1/3)*(1+sqrt(3)))/(-b^(1/3)*(c+d*x)^(1/3)+(b*c-a*d)^(1/3)*(1-sqrt(3))),sqrt(-7+4*sqrt(3)))*sqrt(((b*c-a*d)^(2/3)+b^(1/3)*(b*c-a*d)^(1/3)*(c+d*x)^(1/3)+b^(2/3)*(c+d*x)^(2/3))/(-b^(1/3)*(c+d*x)^(1/3)+(b*c-a*d)^(1/3)*(1-sqrt(3)))^2)*sqrt(2-sqrt(3))/(b^(4/3)*d*sqrt(a+b*x)*sqrt(-(b*c-a*d)^(1/3)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))/(-b^(1/3)*(c+d*x)^(1/3)+(b*c-a*d)^(1/3)*(1-sqrt(3)))^2))],
[(c+d*x)^(1/3)/(a+b*x)^(3/2),x,3,-2*(c+d*x)^(1/3)/(b*sqrt(a+b*x))-4*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))*EllipticF((-b^(1/3)*(c+d*x)^(1/3)+(b*c-a*d)^(1/3)*(1+sqrt(3)))/(-b^(1/3)*(c+d*x)^(1/3)+(b*c-a*d)^(1/3)*(1-sqrt(3))),sqrt(-7+4*sqrt(3)))*sqrt(((b*c-a*d)^(2/3)+b^(1/3)*(b*c-a*d)^(1/3)*(c+d*x)^(1/3)+b^(2/3)*(c+d*x)^(2/3))/(-b^(1/3)*(c+d*x)^(1/3)+(b*c-a*d)^(1/3)*(1-sqrt(3)))^2)*sqrt(2-sqrt(3))/(3^(1/4)*b^(4/3)*sqrt(a+b*x)*sqrt(-(b*c-a*d)^(1/3)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))/(-b^(1/3)*(c+d*x)^(1/3)+(b*c-a*d)^(1/3)*(1-sqrt(3)))^2))],
[(c+d*x)^(1/3)/(a+b*x)^(5/2),x,4,-2/3*(c+d*x)^(1/3)/(b*(a+b*x)^(3/2))-4/9*d*(c+d*x)^(1/3)/(b*(b*c-a*d)*sqrt(a+b*x))+4/9*d*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))*EllipticF((-b^(1/3)*(c+d*x)^(1/3)+(b*c-a*d)^(1/3)*(1+sqrt(3)))/(-b^(1/3)*(c+d*x)^(1/3)+(b*c-a*d)^(1/3)*(1-sqrt(3))),sqrt(-7+4*sqrt(3)))*sqrt(((b*c-a*d)^(2/3)+b^(1/3)*(b*c-a*d)^(1/3)*(c+d*x)^(1/3)+b^(2/3)*(c+d*x)^(2/3))/(-b^(1/3)*(c+d*x)^(1/3)+(b*c-a*d)^(1/3)*(1-sqrt(3)))^2)*sqrt(2-sqrt(3))/(3^(1/4)*b^(4/3)*(b*c-a*d)*sqrt(a+b*x)*sqrt(-(b*c-a*d)^(1/3)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))/(-b^(1/3)*(c+d*x)^(1/3)+(b*c-a*d)^(1/3)*(1-sqrt(3)))^2))],
[(c+d*x)^(1/3)/(a+b*x)^(7/2),x,5,-2/5*(c+d*x)^(1/3)/(b*(a+b*x)^(5/2))-4/45*d*(c+d*x)^(1/3)/(b*(b*c-a*d)*(a+b*x)^(3/2))+28/135*d^2*(c+d*x)^(1/3)/(b*(b*c-a*d)^2*sqrt(a+b*x))-28/135*d^2*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))*EllipticF((-b^(1/3)*(c+d*x)^(1/3)+(b*c-a*d)^(1/3)*(1+sqrt(3)))/(-b^(1/3)*(c+d*x)^(1/3)+(b*c-a*d)^(1/3)*(1-sqrt(3))),sqrt(-7+4*sqrt(3)))*sqrt(((b*c-a*d)^(2/3)+b^(1/3)*(b*c-a*d)^(1/3)*(c+d*x)^(1/3)+b^(2/3)*(c+d*x)^(2/3))/(-b^(1/3)*(c+d*x)^(1/3)+(b*c-a*d)^(1/3)*(1-sqrt(3)))^2)*sqrt(2-sqrt(3))/(3^(1/4)*b^(4/3)*(b*c-a*d)^2*sqrt(a+b*x)*sqrt(-(b*c-a*d)^(1/3)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))/(-b^(1/3)*(c+d*x)^(1/3)+(b*c-a*d)^(1/3)*(1-sqrt(3)))^2))],

# n<0
[(a+b*x)^(3/2)/(c+d*x)^(1/3),x,6,6/13*(a+b*x)^(3/2)*(c+d*x)^(2/3)/d-54/91*(b*c-a*d)*(c+d*x)^(2/3)*sqrt(a+b*x)/d^2-162/91*(b*c-a*d)^2*sqrt(a+b*x)/(b^(2/3)*d^2*(-b^(1/3)*(c+d*x)^(1/3)+(b*c-a*d)^(1/3)*(1-sqrt(3))))-54/91*3^(3/4)*(b*c-a*d)^(7/3)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))*EllipticF((-b^(1/3)*(c+d*x)^(1/3)+(b*c-a*d)^(1/3)*(1+sqrt(3)))/(-b^(1/3)*(c+d*x)^(1/3)+(b*c-a*d)^(1/3)*(1-sqrt(3))),sqrt(-7+4*sqrt(3)))*sqrt(2)*sqrt(((b*c-a*d)^(2/3)+b^(1/3)*(b*c-a*d)^(1/3)*(c+d*x)^(1/3)+b^(2/3)*(c+d*x)^(2/3))/(-b^(1/3)*(c+d*x)^(1/3)+(b*c-a*d)^(1/3)*(1-sqrt(3)))^2)/(b^(2/3)*d^3*sqrt(a+b*x)*sqrt(-(b*c-a*d)^(1/3)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))/(-b^(1/3)*(c+d*x)^(1/3)+(b*c-a*d)^(1/3)*(1-sqrt(3)))^2))+81/91*3^(1/4)*(b*c-a*d)^(7/3)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))*EllipticE((-b^(1/3)*(c+d*x)^(1/3)+(b*c-a*d)^(1/3)*(1+sqrt(3)))/(-b^(1/3)*(c+d*x)^(1/3)+(b*c-a*d)^(1/3)*(1-sqrt(3))),sqrt(-7+4*sqrt(3)))*sqrt(((b*c-a*d)^(2/3)+b^(1/3)*(b*c-a*d)^(1/3)*(c+d*x)^(1/3)+b^(2/3)*(c+d*x)^(2/3))/(-b^(1/3)*(c+d*x)^(1/3)+(b*c-a*d)^(1/3)*(1-sqrt(3)))^2)*sqrt(2+sqrt(3))/(b^(2/3)*d^3*sqrt(a+b*x)*sqrt(-(b*c-a*d)^(1/3)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))/(-b^(1/3)*(c+d*x)^(1/3)+(b*c-a*d)^(1/3)*(1-sqrt(3)))^2))],
[(a+b*x)^(1/2)/(c+d*x)^(1/3),x,5,6/7*(c+d*x)^(2/3)*sqrt(a+b*x)/d+18/7*(b*c-a*d)*sqrt(a+b*x)/(b^(2/3)*d*(-b^(1/3)*(c+d*x)^(1/3)+(b*c-a*d)^(1/3)*(1-sqrt(3))))+6/7*3^(3/4)*(b*c-a*d)^(4/3)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))*EllipticF((-b^(1/3)*(c+d*x)^(1/3)+(b*c-a*d)^(1/3)*(1+sqrt(3)))/(-b^(1/3)*(c+d*x)^(1/3)+(b*c-a*d)^(1/3)*(1-sqrt(3))),sqrt(-7+4*sqrt(3)))*sqrt(2)*sqrt(((b*c-a*d)^(2/3)+b^(1/3)*(b*c-a*d)^(1/3)*(c+d*x)^(1/3)+b^(2/3)*(c+d*x)^(2/3))/(-b^(1/3)*(c+d*x)^(1/3)+(b*c-a*d)^(1/3)*(1-sqrt(3)))^2)/(b^(2/3)*d^2*sqrt(a+b*x)*sqrt(-(b*c-a*d)^(1/3)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))/(-b^(1/3)*(c+d*x)^(1/3)+(b*c-a*d)^(1/3)*(1-sqrt(3)))^2))-9/7*3^(1/4)*(b*c-a*d)^(4/3)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))*EllipticE((-b^(1/3)*(c+d*x)^(1/3)+(b*c-a*d)^(1/3)*(1+sqrt(3)))/(-b^(1/3)*(c+d*x)^(1/3)+(b*c-a*d)^(1/3)*(1-sqrt(3))),sqrt(-7+4*sqrt(3)))*sqrt(((b*c-a*d)^(2/3)+b^(1/3)*(b*c-a*d)^(1/3)*(c+d*x)^(1/3)+b^(2/3)*(c+d*x)^(2/3))/(-b^(1/3)*(c+d*x)^(1/3)+(b*c-a*d)^(1/3)*(1-sqrt(3)))^2)*sqrt(2+sqrt(3))/(b^(2/3)*d^2*sqrt(a+b*x)*sqrt(-(b*c-a*d)^(1/3)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))/(-b^(1/3)*(c+d*x)^(1/3)+(b*c-a*d)^(1/3)*(1-sqrt(3)))^2))],
[1/((a+b*x)^(1/2)*(c+d*x)^(1/3)),x,4,-6*sqrt(a+b*x)/(b^(2/3)*(-b^(1/3)*(c+d*x)^(1/3)+(b*c-a*d)^(1/3)*(1-sqrt(3))))-2*3^(3/4)*(b*c-a*d)^(1/3)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))*EllipticF((-b^(1/3)*(c+d*x)^(1/3)+(b*c-a*d)^(1/3)*(1+sqrt(3)))/(-b^(1/3)*(c+d*x)^(1/3)+(b*c-a*d)^(1/3)*(1-sqrt(3))),sqrt(-7+4*sqrt(3)))*sqrt(2)*sqrt(((b*c-a*d)^(2/3)+b^(1/3)*(b*c-a*d)^(1/3)*(c+d*x)^(1/3)+b^(2/3)*(c+d*x)^(2/3))/(-b^(1/3)*(c+d*x)^(1/3)+(b*c-a*d)^(1/3)*(1-sqrt(3)))^2)/(b^(2/3)*d*sqrt(a+b*x)*sqrt(-(b*c-a*d)^(1/3)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))/(-b^(1/3)*(c+d*x)^(1/3)+(b*c-a*d)^(1/3)*(1-sqrt(3)))^2))+3*3^(1/4)*(b*c-a*d)^(1/3)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))*EllipticE((-b^(1/3)*(c+d*x)^(1/3)+(b*c-a*d)^(1/3)*(1+sqrt(3)))/(-b^(1/3)*(c+d*x)^(1/3)+(b*c-a*d)^(1/3)*(1-sqrt(3))),sqrt(-7+4*sqrt(3)))*sqrt(((b*c-a*d)^(2/3)+b^(1/3)*(b*c-a*d)^(1/3)*(c+d*x)^(1/3)+b^(2/3)*(c+d*x)^(2/3))/(-b^(1/3)*(c+d*x)^(1/3)+(b*c-a*d)^(1/3)*(1-sqrt(3)))^2)*sqrt(2+sqrt(3))/(b^(2/3)*d*sqrt(a+b*x)*sqrt(-(b*c-a*d)^(1/3)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))/(-b^(1/3)*(c+d*x)^(1/3)+(b*c-a*d)^(1/3)*(1-sqrt(3)))^2))],
[1/((a+b*x)^(3/2)*(c+d*x)^(1/3)),x,5,-2*(c+d*x)^(2/3)/((b*c-a*d)*sqrt(a+b*x))-2*d*sqrt(a+b*x)/(b^(2/3)*(b*c-a*d)*(-b^(1/3)*(c+d*x)^(1/3)+(b*c-a*d)^(1/3)*(1-sqrt(3))))-2*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))*EllipticF((-b^(1/3)*(c+d*x)^(1/3)+(b*c-a*d)^(1/3)*(1+sqrt(3)))/(-b^(1/3)*(c+d*x)^(1/3)+(b*c-a*d)^(1/3)*(1-sqrt(3))),sqrt(-7+4*sqrt(3)))*sqrt(2)*sqrt(((b*c-a*d)^(2/3)+b^(1/3)*(b*c-a*d)^(1/3)*(c+d*x)^(1/3)+b^(2/3)*(c+d*x)^(2/3))/(-b^(1/3)*(c+d*x)^(1/3)+(b*c-a*d)^(1/3)*(1-sqrt(3)))^2)/(3^(1/4)*b^(2/3)*(b*c-a*d)^(2/3)*sqrt(a+b*x)*sqrt(-(b*c-a*d)^(1/3)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))/(-b^(1/3)*(c+d*x)^(1/3)+(b*c-a*d)^(1/3)*(1-sqrt(3)))^2))+3^(1/4)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))*EllipticE((-b^(1/3)*(c+d*x)^(1/3)+(b*c-a*d)^(1/3)*(1+sqrt(3)))/(-b^(1/3)*(c+d*x)^(1/3)+(b*c-a*d)^(1/3)*(1-sqrt(3))),sqrt(-7+4*sqrt(3)))*sqrt(((b*c-a*d)^(2/3)+b^(1/3)*(b*c-a*d)^(1/3)*(c+d*x)^(1/3)+b^(2/3)*(c+d*x)^(2/3))/(-b^(1/3)*(c+d*x)^(1/3)+(b*c-a*d)^(1/3)*(1-sqrt(3)))^2)*sqrt(2+sqrt(3))/(b^(2/3)*(b*c-a*d)^(2/3)*sqrt(a+b*x)*sqrt(-(b*c-a*d)^(1/3)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))/(-b^(1/3)*(c+d*x)^(1/3)+(b*c-a*d)^(1/3)*(1-sqrt(3)))^2))],
[1/((a+b*x)^(5/2)*(c+d*x)^(1/3)),x,6,-2/3*(c+d*x)^(2/3)/((b*c-a*d)*(a+b*x)^(3/2))+10/9*d*(c+d*x)^(2/3)/((b*c-a*d)^2*sqrt(a+b*x))+10/9*d^2*sqrt(a+b*x)/(b^(2/3)*(b*c-a*d)^2*(-b^(1/3)*(c+d*x)^(1/3)+(b*c-a*d)^(1/3)*(1-sqrt(3))))+10/9*d*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))*EllipticF((-b^(1/3)*(c+d*x)^(1/3)+(b*c-a*d)^(1/3)*(1+sqrt(3)))/(-b^(1/3)*(c+d*x)^(1/3)+(b*c-a*d)^(1/3)*(1-sqrt(3))),sqrt(-7+4*sqrt(3)))*sqrt(2)*sqrt(((b*c-a*d)^(2/3)+b^(1/3)*(b*c-a*d)^(1/3)*(c+d*x)^(1/3)+b^(2/3)*(c+d*x)^(2/3))/(-b^(1/3)*(c+d*x)^(1/3)+(b*c-a*d)^(1/3)*(1-sqrt(3)))^2)/(3^(1/4)*b^(2/3)*(b*c-a*d)^(5/3)*sqrt(a+b*x)*sqrt(-(b*c-a*d)^(1/3)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))/(-b^(1/3)*(c+d*x)^(1/3)+(b*c-a*d)^(1/3)*(1-sqrt(3)))^2))-5/3*d*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))*EllipticE((-b^(1/3)*(c+d*x)^(1/3)+(b*c-a*d)^(1/3)*(1+sqrt(3)))/(-b^(1/3)*(c+d*x)^(1/3)+(b*c-a*d)^(1/3)*(1-sqrt(3))),sqrt(-7+4*sqrt(3)))*sqrt(((b*c-a*d)^(2/3)+b^(1/3)*(b*c-a*d)^(1/3)*(c+d*x)^(1/3)+b^(2/3)*(c+d*x)^(2/3))/(-b^(1/3)*(c+d*x)^(1/3)+(b*c-a*d)^(1/3)*(1-sqrt(3)))^2)*sqrt(2+sqrt(3))/(3^(3/4)*b^(2/3)*(b*c-a*d)^(5/3)*sqrt(a+b*x)*sqrt(-(b*c-a*d)^(1/3)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))/(-b^(1/3)*(c+d*x)^(1/3)+(b*c-a*d)^(1/3)*(1-sqrt(3)))^2))],
[(a+b*x)^(3/2)/(c+d*x)^(2/3),x,4,6/11*(a+b*x)^(3/2)*(c+d*x)^(1/3)/d-54/55*(b*c-a*d)*(c+d*x)^(1/3)*sqrt(a+b*x)/d^2-54/55*3^(3/4)*(b*c-a*d)^2*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))*EllipticF((-b^(1/3)*(c+d*x)^(1/3)+(b*c-a*d)^(1/3)*(1+sqrt(3)))/(-b^(1/3)*(c+d*x)^(1/3)+(b*c-a*d)^(1/3)*(1-sqrt(3))),sqrt(-7+4*sqrt(3)))*sqrt(((b*c-a*d)^(2/3)+b^(1/3)*(b*c-a*d)^(1/3)*(c+d*x)^(1/3)+b^(2/3)*(c+d*x)^(2/3))/(-b^(1/3)*(c+d*x)^(1/3)+(b*c-a*d)^(1/3)*(1-sqrt(3)))^2)*sqrt(2-sqrt(3))/(b^(1/3)*d^3*sqrt(a+b*x)*sqrt(-(b*c-a*d)^(1/3)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))/(-b^(1/3)*(c+d*x)^(1/3)+(b*c-a*d)^(1/3)*(1-sqrt(3)))^2))],
[(a+b*x)^(1/2)/(c+d*x)^(2/3),x,3,6/5*(c+d*x)^(1/3)*sqrt(a+b*x)/d+6/5*3^(3/4)*(b*c-a*d)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))*EllipticF((-b^(1/3)*(c+d*x)^(1/3)+(b*c-a*d)^(1/3)*(1+sqrt(3)))/(-b^(1/3)*(c+d*x)^(1/3)+(b*c-a*d)^(1/3)*(1-sqrt(3))),sqrt(-7+4*sqrt(3)))*sqrt(((b*c-a*d)^(2/3)+b^(1/3)*(b*c-a*d)^(1/3)*(c+d*x)^(1/3)+b^(2/3)*(c+d*x)^(2/3))/(-b^(1/3)*(c+d*x)^(1/3)+(b*c-a*d)^(1/3)*(1-sqrt(3)))^2)*sqrt(2-sqrt(3))/(b^(1/3)*d^2*sqrt(a+b*x)*sqrt(-(b*c-a*d)^(1/3)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))/(-b^(1/3)*(c+d*x)^(1/3)+(b*c-a*d)^(1/3)*(1-sqrt(3)))^2))],
[1/((a+b*x)^(1/2)*(c+d*x)^(2/3)),x,2,-2*3^(3/4)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))*EllipticF((-b^(1/3)*(c+d*x)^(1/3)+(b*c-a*d)^(1/3)*(1+sqrt(3)))/(-b^(1/3)*(c+d*x)^(1/3)+(b*c-a*d)^(1/3)*(1-sqrt(3))),sqrt(-7+4*sqrt(3)))*sqrt(((b*c-a*d)^(2/3)+b^(1/3)*(b*c-a*d)^(1/3)*(c+d*x)^(1/3)+b^(2/3)*(c+d*x)^(2/3))/(-b^(1/3)*(c+d*x)^(1/3)+(b*c-a*d)^(1/3)*(1-sqrt(3)))^2)*sqrt(2-sqrt(3))/(b^(1/3)*d*sqrt(a+b*x)*sqrt(-(b*c-a*d)^(1/3)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))/(-b^(1/3)*(c+d*x)^(1/3)+(b*c-a*d)^(1/3)*(1-sqrt(3)))^2))],
[1/((a+b*x)^(3/2)*(c+d*x)^(2/3)),x,3,-2*(c+d*x)^(1/3)/((b*c-a*d)*sqrt(a+b*x))+2*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))*EllipticF((-b^(1/3)*(c+d*x)^(1/3)+(b*c-a*d)^(1/3)*(1+sqrt(3)))/(-b^(1/3)*(c+d*x)^(1/3)+(b*c-a*d)^(1/3)*(1-sqrt(3))),sqrt(-7+4*sqrt(3)))*sqrt(((b*c-a*d)^(2/3)+b^(1/3)*(b*c-a*d)^(1/3)*(c+d*x)^(1/3)+b^(2/3)*(c+d*x)^(2/3))/(-b^(1/3)*(c+d*x)^(1/3)+(b*c-a*d)^(1/3)*(1-sqrt(3)))^2)*sqrt(2-sqrt(3))/(3^(1/4)*b^(1/3)*(b*c-a*d)*sqrt(a+b*x)*sqrt(-(b*c-a*d)^(1/3)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))/(-b^(1/3)*(c+d*x)^(1/3)+(b*c-a*d)^(1/3)*(1-sqrt(3)))^2))],
[1/((a+b*x)^(5/2)*(c+d*x)^(2/3)),x,4,-2/3*(c+d*x)^(1/3)/((b*c-a*d)*(a+b*x)^(3/2))+14/9*d*(c+d*x)^(1/3)/((b*c-a*d)^2*sqrt(a+b*x))-14/9*d*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))*EllipticF((-b^(1/3)*(c+d*x)^(1/3)+(b*c-a*d)^(1/3)*(1+sqrt(3)))/(-b^(1/3)*(c+d*x)^(1/3)+(b*c-a*d)^(1/3)*(1-sqrt(3))),sqrt(-7+4*sqrt(3)))*sqrt(((b*c-a*d)^(2/3)+b^(1/3)*(b*c-a*d)^(1/3)*(c+d*x)^(1/3)+b^(2/3)*(c+d*x)^(2/3))/(-b^(1/3)*(c+d*x)^(1/3)+(b*c-a*d)^(1/3)*(1-sqrt(3)))^2)*sqrt(2-sqrt(3))/(3^(1/4)*b^(1/3)*(b*c-a*d)^2*sqrt(a+b*x)*sqrt(-(b*c-a*d)^(1/3)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))/(-b^(1/3)*(c+d*x)^(1/3)+(b*c-a*d)^(1/3)*(1-sqrt(3)))^2))],

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

# n>0
[(a+b*x)^(2/3)*(c+d*x)^(1/3),x,3,1/6*(b*c-a*d)*(a+b*x)^(2/3)*(c+d*x)^(1/3)/(b*d)+1/2*(a+b*x)^(5/3)*(c+d*x)^(1/3)/b+1/18*(b*c-a*d)^2*log(c+d*x)/(b^(4/3)*d^(5/3))+1/6*(b*c-a*d)^2*log(-1+d^(1/3)*(a+b*x)^(1/3)/(b^(1/3)*(c+d*x)^(1/3)))/(b^(4/3)*d^(5/3))+1/3*(b*c-a*d)^2*arctan(1/sqrt(3)+2*d^(1/3)*(a+b*x)^(1/3)/(b^(1/3)*(c+d*x)^(1/3)*sqrt(3)))/(b^(4/3)*d^(5/3)*sqrt(3))],
[(c+d*x)^(1/3)/(a+b*x)^(1/3),x,2,(a+b*x)^(2/3)*(c+d*x)^(1/3)/b-1/6*(b*c-a*d)*log(c+d*x)/(b^(4/3)*d^(2/3))-1/2*(b*c-a*d)*log(-1+d^(1/3)*(a+b*x)^(1/3)/(b^(1/3)*(c+d*x)^(1/3)))/(b^(4/3)*d^(2/3))-(b*c-a*d)*arctan(1/sqrt(3)+2*d^(1/3)*(a+b*x)^(1/3)/(b^(1/3)*(c+d*x)^(1/3)*sqrt(3)))/(b^(4/3)*d^(2/3)*sqrt(3))],
[(c+d*x)^(1/3)/(a+b*x)^(4/3),x,2,-3*(c+d*x)^(1/3)/(b*(a+b*x)^(1/3))-1/2*d^(1/3)*log(c+d*x)/b^(4/3)-3/2*d^(1/3)*log(-1+d^(1/3)*(a+b*x)^(1/3)/(b^(1/3)*(c+d*x)^(1/3)))/b^(4/3)-d^(1/3)*arctan(1/sqrt(3)+2*d^(1/3)*(a+b*x)^(1/3)/(b^(1/3)*(c+d*x)^(1/3)*sqrt(3)))*sqrt(3)/b^(4/3)],
[(c+d*x)^(1/3)/(a+b*x)^(7/3),x,1,-3/4*(c+d*x)^(4/3)/((b*c-a*d)*(a+b*x)^(4/3))],
[(c+d*x)^(1/3)/(a+b*x)^(10/3),x,2,-3/7*(c+d*x)^(4/3)/((b*c-a*d)*(a+b*x)^(7/3))+9/28*d*(c+d*x)^(4/3)/((b*c-a*d)^2*(a+b*x)^(4/3))],
[(c+d*x)^(1/3)/(a+b*x)^(13/3),x,3,-3/10*(c+d*x)^(4/3)/((b*c-a*d)*(a+b*x)^(10/3))+9/35*d*(c+d*x)^(4/3)/((b*c-a*d)^2*(a+b*x)^(7/3))-27/140*d^2*(c+d*x)^(4/3)/((b*c-a*d)^3*(a+b*x)^(4/3))],
[(c+d*x)^(1/3)/(a+b*x)^(16/3),x,4,-3/13*(c+d*x)^(4/3)/((b*c-a*d)*(a+b*x)^(13/3))+27/130*d*(c+d*x)^(4/3)/((b*c-a*d)^2*(a+b*x)^(10/3))-81/455*d^2*(c+d*x)^(4/3)/((b*c-a*d)^3*(a+b*x)^(7/3))+243/1820*d^3*(c+d*x)^(4/3)/((b*c-a*d)^4*(a+b*x)^(4/3))],
[(a+b*x)^(4/3)*(c+d*x)^(1/3),x,6,-3/20*(b*c-a*d)^2*(a+b*x)^(1/3)*(c+d*x)^(1/3)/(b*d^2)+3/40*(b*c-a*d)*(a+b*x)^(4/3)*(c+d*x)^(1/3)/(b*d)+3/8*(a+b*x)^(7/3)*(c+d*x)^(1/3)/b+1/10*3^(3/4)*(b*c-a*d)^3*((a+b*x)*(c+d*x))^(2/3)*((b*c-a*d)^(2/3)+2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3))*EllipticF((2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1-sqrt(3)))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt(2+sqrt(3))*sqrt(((b*c-a*d)^(4/3)-2^(2/3)*b^(1/3)*d^(1/3)*(b*c-a*d)^(2/3)*((a+b*x)*(c+d*x))^(1/3)+2*2^(1/3)*b^(2/3)*d^(2/3)*((a+b*x)*(c+d*x))^(2/3))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2)/(2^(2/3)*b^(4/3)*d^(7/3)*(a+b*x)^(2/3)*(c+d*x)^(2/3)*(b*c+a*d+2*b*d*x)*sqrt((a*d+b*(c+2*d*x))^2)*sqrt((b*c-a*d)^(2/3)*((b*c-a*d)^(2/3)+2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2))],
[(a+b*x)^(1/3)*(c+d*x)^(1/3),x,5,3/10*(b*c-a*d)*(a+b*x)^(1/3)*(c+d*x)^(1/3)/(b*d)+3/5*(a+b*x)^(4/3)*(c+d*x)^(1/3)/b-1/5*3^(3/4)*(b*c-a*d)^2*((a+b*x)*(c+d*x))^(2/3)*((b*c-a*d)^(2/3)+2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3))*EllipticF((2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1-sqrt(3)))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt(2+sqrt(3))*sqrt(((b*c-a*d)^(4/3)-2^(2/3)*b^(1/3)*d^(1/3)*(b*c-a*d)^(2/3)*((a+b*x)*(c+d*x))^(1/3)+2*2^(1/3)*b^(2/3)*d^(2/3)*((a+b*x)*(c+d*x))^(2/3))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2)/(2^(2/3)*b^(4/3)*d^(4/3)*(a+b*x)^(2/3)*(c+d*x)^(2/3)*(b*c+a*d+2*b*d*x)*sqrt((a*d+b*(c+2*d*x))^2)*sqrt((b*c-a*d)^(2/3)*((b*c-a*d)^(2/3)+2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2))],
[(c+d*x)^(1/3)/(a+b*x)^(2/3),x,4,3/2*(a+b*x)^(1/3)*(c+d*x)^(1/3)/b+3^(3/4)*(b*c-a*d)*((a+b*x)*(c+d*x))^(2/3)*((b*c-a*d)^(2/3)+2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3))*EllipticF((2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1-sqrt(3)))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt(2+sqrt(3))*sqrt(((b*c-a*d)^(4/3)-2^(2/3)*b^(1/3)*d^(1/3)*(b*c-a*d)^(2/3)*((a+b*x)*(c+d*x))^(1/3)+2*2^(1/3)*b^(2/3)*d^(2/3)*((a+b*x)*(c+d*x))^(2/3))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2)/(2^(2/3)*b^(4/3)*d^(1/3)*(a+b*x)^(2/3)*(c+d*x)^(2/3)*(b*c+a*d+2*b*d*x)*sqrt((a*d+b*(c+2*d*x))^2)*sqrt((b*c-a*d)^(2/3)*((b*c-a*d)^(2/3)+2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2))],
[(c+d*x)^(1/3)/(a+b*x)^(5/3),x,4,-3/2*(c+d*x)^(1/3)/(b*(a+b*x)^(2/3))+3^(3/4)*d^(2/3)*((a+b*x)*(c+d*x))^(2/3)*((b*c-a*d)^(2/3)+2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3))*EllipticF((2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1-sqrt(3)))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt(2+sqrt(3))*sqrt(((b*c-a*d)^(4/3)-2^(2/3)*b^(1/3)*d^(1/3)*(b*c-a*d)^(2/3)*((a+b*x)*(c+d*x))^(1/3)+2*2^(1/3)*b^(2/3)*d^(2/3)*((a+b*x)*(c+d*x))^(2/3))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2)/(2^(2/3)*b^(4/3)*(a+b*x)^(2/3)*(c+d*x)^(2/3)*(b*c+a*d+2*b*d*x)*sqrt((a*d+b*(c+2*d*x))^2)*sqrt((b*c-a*d)^(2/3)*((b*c-a*d)^(2/3)+2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2))],
[(c+d*x)^(1/3)/(a+b*x)^(8/3),x,5,-3/5*(c+d*x)^(1/3)/(b*(a+b*x)^(5/3))-3/10*d*(c+d*x)^(1/3)/(b*(b*c-a*d)*(a+b*x)^(2/3))-1/5*3^(3/4)*d^(5/3)*((a+b*x)*(c+d*x))^(2/3)*((b*c-a*d)^(2/3)+2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3))*EllipticF((2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1-sqrt(3)))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt(2+sqrt(3))*sqrt(((b*c-a*d)^(4/3)-2^(2/3)*b^(1/3)*d^(1/3)*(b*c-a*d)^(2/3)*((a+b*x)*(c+d*x))^(1/3)+2*2^(1/3)*b^(2/3)*d^(2/3)*((a+b*x)*(c+d*x))^(2/3))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2)/(2^(2/3)*b^(4/3)*(b*c-a*d)*(a+b*x)^(2/3)*(c+d*x)^(2/3)*(b*c+a*d+2*b*d*x)*sqrt((a*d+b*(c+2*d*x))^2)*sqrt((b*c-a*d)^(2/3)*((b*c-a*d)^(2/3)+2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2))],

# n<0
[(a+b*x)^(4/3)/(c+d*x)^(1/3),x,3,-2/3*(b*c-a*d)*(a+b*x)^(1/3)*(c+d*x)^(2/3)/d^2+1/2*(a+b*x)^(4/3)*(c+d*x)^(2/3)/d-1/9*(b*c-a*d)^2*log(a+b*x)/(b^(2/3)*d^(7/3))-1/3*(b*c-a*d)^2*log(-1+b^(1/3)*(c+d*x)^(1/3)/(d^(1/3)*(a+b*x)^(1/3)))/(b^(2/3)*d^(7/3))-2/3*(b*c-a*d)^2*arctan(1/sqrt(3)+2*b^(1/3)*(c+d*x)^(1/3)/(d^(1/3)*(a+b*x)^(1/3)*sqrt(3)))/(b^(2/3)*d^(7/3)*sqrt(3))],
[(a+b*x)^(1/3)/(c+d*x)^(1/3),x,2,(a+b*x)^(1/3)*(c+d*x)^(2/3)/d+1/6*(b*c-a*d)*log(a+b*x)/(b^(2/3)*d^(4/3))+1/2*(b*c-a*d)*log(-1+b^(1/3)*(c+d*x)^(1/3)/(d^(1/3)*(a+b*x)^(1/3)))/(b^(2/3)*d^(4/3))+(b*c-a*d)*arctan(1/sqrt(3)+2*b^(1/3)*(c+d*x)^(1/3)/(d^(1/3)*(a+b*x)^(1/3)*sqrt(3)))/(b^(2/3)*d^(4/3)*sqrt(3))],
[1/((a+b*x)^(2/3)*(c+d*x)^(1/3)),x,1,-1/2*log(a+b*x)/(b^(2/3)*d^(1/3))-3/2*log(-1+b^(1/3)*(c+d*x)^(1/3)/(d^(1/3)*(a+b*x)^(1/3)))/(b^(2/3)*d^(1/3))-arctan(1/sqrt(3)+2*b^(1/3)*(c+d*x)^(1/3)/(d^(1/3)*(a+b*x)^(1/3)*sqrt(3)))*sqrt(3)/(b^(2/3)*d^(1/3))],
[1/((a+b*x)^(5/3)*(c+d*x)^(1/3)),x,1,-3/2*(c+d*x)^(2/3)/((b*c-a*d)*(a+b*x)^(2/3))],
[1/((a+b*x)^(8/3)*(c+d*x)^(1/3)),x,2,-3/5*(c+d*x)^(2/3)/((b*c-a*d)*(a+b*x)^(5/3))+9/10*d*(c+d*x)^(2/3)/((b*c-a*d)^2*(a+b*x)^(2/3))],
[1/((a+b*x)^(11/3)*(c+d*x)^(1/3)),x,3,-3/8*(c+d*x)^(2/3)/((b*c-a*d)*(a+b*x)^(8/3))+9/20*d*(c+d*x)^(2/3)/((b*c-a*d)^2*(a+b*x)^(5/3))-27/40*d^2*(c+d*x)^(2/3)/((b*c-a*d)^3*(a+b*x)^(2/3))],
[1/((a+b*x)^(14/3)*(c+d*x)^(1/3)),x,4,-3/11*(c+d*x)^(2/3)/((b*c-a*d)*(a+b*x)^(11/3))+27/88*d*(c+d*x)^(2/3)/((b*c-a*d)^2*(a+b*x)^(8/3))-81/220*d^2*(c+d*x)^(2/3)/((b*c-a*d)^3*(a+b*x)^(5/3))+243/440*d^3*(c+d*x)^(2/3)/((b*c-a*d)^4*(a+b*x)^(2/3))],
[(a+b*x)^(8/3)/(c+d*x)^(1/3),x,8,3/7*(b*c-a*d)^2*(a+b*x)^(2/3)*(c+d*x)^(2/3)/d^3-12/35*(b*c-a*d)*(a+b*x)^(5/3)*(c+d*x)^(2/3)/d^2+3/10*(a+b*x)^(8/3)*(c+d*x)^(2/3)/d-3/7*2^(2/3)*(b*c-a*d)^3*((a+b*x)*(c+d*x))^(1/3)*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt((a*d+b*(c+2*d*x))^2)/(b^(2/3)*d^(11/3)*(a+b*x)^(1/3)*(c+d*x)^(1/3)*(b*c+a*d+2*b*d*x)*(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3))))-2/7*2^(1/6)*3^(3/4)*(b*c-a*d)^(11/3)*((a+b*x)*(c+d*x))^(1/3)*((b*c-a*d)^(2/3)+2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3))*EllipticF((2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1-sqrt(3)))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt(((b*c-a*d)^(4/3)-2^(2/3)*b^(1/3)*d^(1/3)*(b*c-a*d)^(2/3)*((a+b*x)*(c+d*x))^(1/3)+2*2^(1/3)*b^(2/3)*d^(2/3)*((a+b*x)*(c+d*x))^(2/3))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2)/(b^(2/3)*d^(11/3)*(a+b*x)^(1/3)*(c+d*x)^(1/3)*(b*c+a*d+2*b*d*x)*sqrt((a*d+b*(c+2*d*x))^2)*sqrt((b*c-a*d)^(2/3)*((b*c-a*d)^(2/3)+2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2))+3/7*3^(1/4)*(b*c-a*d)^(11/3)*((a+b*x)*(c+d*x))^(1/3)*((b*c-a*d)^(2/3)+2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3))*EllipticE((2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1-sqrt(3)))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt(2-sqrt(3))*sqrt(((b*c-a*d)^(4/3)-2^(2/3)*b^(1/3)*d^(1/3)*(b*c-a*d)^(2/3)*((a+b*x)*(c+d*x))^(1/3)+2*2^(1/3)*b^(2/3)*d^(2/3)*((a+b*x)*(c+d*x))^(2/3))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2)/(2^(1/3)*b^(2/3)*d^(11/3)*(a+b*x)^(1/3)*(c+d*x)^(1/3)*(b*c+a*d+2*b*d*x)*sqrt((a*d+b*(c+2*d*x))^2)*sqrt((b*c-a*d)^(2/3)*((b*c-a*d)^(2/3)+2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2))],
[(a+b*x)^(5/3)/(c+d*x)^(1/3),x,7,-15/28*(b*c-a*d)*(a+b*x)^(2/3)*(c+d*x)^(2/3)/d^2+3/7*(a+b*x)^(5/3)*(c+d*x)^(2/3)/d+15/14*(b*c-a*d)^2*((a+b*x)*(c+d*x))^(1/3)*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt((a*d+b*(c+2*d*x))^2)/(2^(1/3)*b^(2/3)*d^(8/3)*(a+b*x)^(1/3)*(c+d*x)^(1/3)*(b*c+a*d+2*b*d*x)*(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3))))+5/7*3^(3/4)*(b*c-a*d)^(8/3)*((a+b*x)*(c+d*x))^(1/3)*((b*c-a*d)^(2/3)+2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3))*EllipticF((2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1-sqrt(3)))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt(((b*c-a*d)^(4/3)-2^(2/3)*b^(1/3)*d^(1/3)*(b*c-a*d)^(2/3)*((a+b*x)*(c+d*x))^(1/3)+2*2^(1/3)*b^(2/3)*d^(2/3)*((a+b*x)*(c+d*x))^(2/3))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2)/(2^(5/6)*b^(2/3)*d^(8/3)*(a+b*x)^(1/3)*(c+d*x)^(1/3)*(b*c+a*d+2*b*d*x)*sqrt((a*d+b*(c+2*d*x))^2)*sqrt((b*c-a*d)^(2/3)*((b*c-a*d)^(2/3)+2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2))-15/28*3^(1/4)*(b*c-a*d)^(8/3)*((a+b*x)*(c+d*x))^(1/3)*((b*c-a*d)^(2/3)+2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3))*EllipticE((2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1-sqrt(3)))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt(2-sqrt(3))*sqrt(((b*c-a*d)^(4/3)-2^(2/3)*b^(1/3)*d^(1/3)*(b*c-a*d)^(2/3)*((a+b*x)*(c+d*x))^(1/3)+2*2^(1/3)*b^(2/3)*d^(2/3)*((a+b*x)*(c+d*x))^(2/3))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2)/(2^(1/3)*b^(2/3)*d^(8/3)*(a+b*x)^(1/3)*(c+d*x)^(1/3)*(b*c+a*d+2*b*d*x)*sqrt((a*d+b*(c+2*d*x))^2)*sqrt((b*c-a*d)^(2/3)*((b*c-a*d)^(2/3)+2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2))],
[(a+b*x)^(2/3)/(c+d*x)^(1/3),x,6,3/4*(a+b*x)^(2/3)*(c+d*x)^(2/3)/d-3/2*(b*c-a*d)*((a+b*x)*(c+d*x))^(1/3)*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt((a*d+b*(c+2*d*x))^2)/(2^(1/3)*b^(2/3)*d^(5/3)*(a+b*x)^(1/3)*(c+d*x)^(1/3)*(b*c+a*d+2*b*d*x)*(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3))))-3^(3/4)*(b*c-a*d)^(5/3)*((a+b*x)*(c+d*x))^(1/3)*((b*c-a*d)^(2/3)+2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3))*EllipticF((2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1-sqrt(3)))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt(((b*c-a*d)^(4/3)-2^(2/3)*b^(1/3)*d^(1/3)*(b*c-a*d)^(2/3)*((a+b*x)*(c+d*x))^(1/3)+2*2^(1/3)*b^(2/3)*d^(2/3)*((a+b*x)*(c+d*x))^(2/3))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2)/(2^(5/6)*b^(2/3)*d^(5/3)*(a+b*x)^(1/3)*(c+d*x)^(1/3)*(b*c+a*d+2*b*d*x)*sqrt((a*d+b*(c+2*d*x))^2)*sqrt((b*c-a*d)^(2/3)*((b*c-a*d)^(2/3)+2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2))+3/4*3^(1/4)*(b*c-a*d)^(5/3)*((a+b*x)*(c+d*x))^(1/3)*((b*c-a*d)^(2/3)+2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3))*EllipticE((2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1-sqrt(3)))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt(2-sqrt(3))*sqrt(((b*c-a*d)^(4/3)-2^(2/3)*b^(1/3)*d^(1/3)*(b*c-a*d)^(2/3)*((a+b*x)*(c+d*x))^(1/3)+2*2^(1/3)*b^(2/3)*d^(2/3)*((a+b*x)*(c+d*x))^(2/3))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2)/(2^(1/3)*b^(2/3)*d^(5/3)*(a+b*x)^(1/3)*(c+d*x)^(1/3)*(b*c+a*d+2*b*d*x)*sqrt((a*d+b*(c+2*d*x))^2)*sqrt((b*c-a*d)^(2/3)*((b*c-a*d)^(2/3)+2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2))],
[1/((a+b*x)^(1/3)*(c+d*x)^(1/3)),x,5,3*((a+b*x)*(c+d*x))^(1/3)*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt((a*d+b*(c+2*d*x))^2)/(2^(1/3)*b^(2/3)*d^(2/3)*(a+b*x)^(1/3)*(c+d*x)^(1/3)*(b*c+a*d+2*b*d*x)*(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3))))+2^(1/6)*3^(3/4)*(b*c-a*d)^(2/3)*((a+b*x)*(c+d*x))^(1/3)*((b*c-a*d)^(2/3)+2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3))*EllipticF((2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1-sqrt(3)))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt(((b*c-a*d)^(4/3)-2^(2/3)*b^(1/3)*d^(1/3)*(b*c-a*d)^(2/3)*((a+b*x)*(c+d*x))^(1/3)+2*2^(1/3)*b^(2/3)*d^(2/3)*((a+b*x)*(c+d*x))^(2/3))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2)/(b^(2/3)*d^(2/3)*(a+b*x)^(1/3)*(c+d*x)^(1/3)*(b*c+a*d+2*b*d*x)*sqrt((a*d+b*(c+2*d*x))^2)*sqrt((b*c-a*d)^(2/3)*((b*c-a*d)^(2/3)+2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2))-3/2*3^(1/4)*(b*c-a*d)^(2/3)*((a+b*x)*(c+d*x))^(1/3)*((b*c-a*d)^(2/3)+2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3))*EllipticE((2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1-sqrt(3)))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt(2-sqrt(3))*sqrt(((b*c-a*d)^(4/3)-2^(2/3)*b^(1/3)*d^(1/3)*(b*c-a*d)^(2/3)*((a+b*x)*(c+d*x))^(1/3)+2*2^(1/3)*b^(2/3)*d^(2/3)*((a+b*x)*(c+d*x))^(2/3))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2)/(2^(1/3)*b^(2/3)*d^(2/3)*(a+b*x)^(1/3)*(c+d*x)^(1/3)*(b*c+a*d+2*b*d*x)*sqrt((a*d+b*(c+2*d*x))^2)*sqrt((b*c-a*d)^(2/3)*((b*c-a*d)^(2/3)+2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2))],
[1/((a+b*x)^(4/3)*(c+d*x)^(1/3)),x,6,-3*(c+d*x)^(2/3)/((b*c-a*d)*(a+b*x)^(1/3))+3*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt((a*d+b*(c+2*d*x))^2)/(2^(1/3)*b^(2/3)*(b*c-a*d)*(a+b*x)^(1/3)*(c+d*x)^(1/3)*(b*c+a*d+2*b*d*x)*(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3))))+2^(1/6)*3^(3/4)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)*((b*c-a*d)^(2/3)+2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3))*EllipticF((2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1-sqrt(3)))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt(((b*c-a*d)^(4/3)-2^(2/3)*b^(1/3)*d^(1/3)*(b*c-a*d)^(2/3)*((a+b*x)*(c+d*x))^(1/3)+2*2^(1/3)*b^(2/3)*d^(2/3)*((a+b*x)*(c+d*x))^(2/3))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2)/(b^(2/3)*(b*c-a*d)^(1/3)*(a+b*x)^(1/3)*(c+d*x)^(1/3)*(b*c+a*d+2*b*d*x)*sqrt((a*d+b*(c+2*d*x))^2)*sqrt((b*c-a*d)^(2/3)*((b*c-a*d)^(2/3)+2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2))-3/2*3^(1/4)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)*((b*c-a*d)^(2/3)+2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3))*EllipticE((2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1-sqrt(3)))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt(2-sqrt(3))*sqrt(((b*c-a*d)^(4/3)-2^(2/3)*b^(1/3)*d^(1/3)*(b*c-a*d)^(2/3)*((a+b*x)*(c+d*x))^(1/3)+2*2^(1/3)*b^(2/3)*d^(2/3)*((a+b*x)*(c+d*x))^(2/3))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2)/(2^(1/3)*b^(2/3)*(b*c-a*d)^(1/3)*(a+b*x)^(1/3)*(c+d*x)^(1/3)*(b*c+a*d+2*b*d*x)*sqrt((a*d+b*(c+2*d*x))^2)*sqrt((b*c-a*d)^(2/3)*((b*c-a*d)^(2/3)+2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2))],
[1/((a+b*x)^(7/3)*(c+d*x)^(1/3)),x,7,-3/4*(c+d*x)^(2/3)/((b*c-a*d)*(a+b*x)^(4/3))+3/2*d*(c+d*x)^(2/3)/((b*c-a*d)^2*(a+b*x)^(1/3))-3/2*d^(4/3)*((a+b*x)*(c+d*x))^(1/3)*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt((a*d+b*(c+2*d*x))^2)/(2^(1/3)*b^(2/3)*(b*c-a*d)^2*(a+b*x)^(1/3)*(c+d*x)^(1/3)*(b*c+a*d+2*b*d*x)*(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3))))-3^(3/4)*d^(4/3)*((a+b*x)*(c+d*x))^(1/3)*((b*c-a*d)^(2/3)+2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3))*EllipticF((2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1-sqrt(3)))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt(((b*c-a*d)^(4/3)-2^(2/3)*b^(1/3)*d^(1/3)*(b*c-a*d)^(2/3)*((a+b*x)*(c+d*x))^(1/3)+2*2^(1/3)*b^(2/3)*d^(2/3)*((a+b*x)*(c+d*x))^(2/3))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2)/(2^(5/6)*b^(2/3)*(b*c-a*d)^(4/3)*(a+b*x)^(1/3)*(c+d*x)^(1/3)*(b*c+a*d+2*b*d*x)*sqrt((a*d+b*(c+2*d*x))^2)*sqrt((b*c-a*d)^(2/3)*((b*c-a*d)^(2/3)+2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2))+3/4*3^(1/4)*d^(4/3)*((a+b*x)*(c+d*x))^(1/3)*((b*c-a*d)^(2/3)+2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3))*EllipticE((2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1-sqrt(3)))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt(2-sqrt(3))*sqrt(((b*c-a*d)^(4/3)-2^(2/3)*b^(1/3)*d^(1/3)*(b*c-a*d)^(2/3)*((a+b*x)*(c+d*x))^(1/3)+2*2^(1/3)*b^(2/3)*d^(2/3)*((a+b*x)*(c+d*x))^(2/3))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2)/(2^(1/3)*b^(2/3)*(b*c-a*d)^(4/3)*(a+b*x)^(1/3)*(c+d*x)^(1/3)*(b*c+a*d+2*b*d*x)*sqrt((a*d+b*(c+2*d*x))^2)*sqrt((b*c-a*d)^(2/3)*((b*c-a*d)^(2/3)+2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2))],
[1/((a+b*x)^(10/3)*(c+d*x)^(1/3)),x,8,-3/7*(c+d*x)^(2/3)/((b*c-a*d)*(a+b*x)^(7/3))+15/28*d*(c+d*x)^(2/3)/((b*c-a*d)^2*(a+b*x)^(4/3))-15/14*d^2*(c+d*x)^(2/3)/((b*c-a*d)^3*(a+b*x)^(1/3))+15/14*d^(7/3)*((a+b*x)*(c+d*x))^(1/3)*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt((a*d+b*(c+2*d*x))^2)/(2^(1/3)*b^(2/3)*(b*c-a*d)^3*(a+b*x)^(1/3)*(c+d*x)^(1/3)*(b*c+a*d+2*b*d*x)*(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3))))+5/7*3^(3/4)*d^(7/3)*((a+b*x)*(c+d*x))^(1/3)*((b*c-a*d)^(2/3)+2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3))*EllipticF((2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1-sqrt(3)))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt(((b*c-a*d)^(4/3)-2^(2/3)*b^(1/3)*d^(1/3)*(b*c-a*d)^(2/3)*((a+b*x)*(c+d*x))^(1/3)+2*2^(1/3)*b^(2/3)*d^(2/3)*((a+b*x)*(c+d*x))^(2/3))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2)/(2^(5/6)*b^(2/3)*(b*c-a*d)^(7/3)*(a+b*x)^(1/3)*(c+d*x)^(1/3)*(b*c+a*d+2*b*d*x)*sqrt((a*d+b*(c+2*d*x))^2)*sqrt((b*c-a*d)^(2/3)*((b*c-a*d)^(2/3)+2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2))-15/28*3^(1/4)*d^(7/3)*((a+b*x)*(c+d*x))^(1/3)*((b*c-a*d)^(2/3)+2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3))*EllipticE((2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1-sqrt(3)))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt(2-sqrt(3))*sqrt(((b*c-a*d)^(4/3)-2^(2/3)*b^(1/3)*d^(1/3)*(b*c-a*d)^(2/3)*((a+b*x)*(c+d*x))^(1/3)+2*2^(1/3)*b^(2/3)*d^(2/3)*((a+b*x)*(c+d*x))^(2/3))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2)/(2^(1/3)*b^(2/3)*(b*c-a*d)^(7/3)*(a+b*x)^(1/3)*(c+d*x)^(1/3)*(b*c+a*d+2*b*d*x)*sqrt((a*d+b*(c+2*d*x))^2)*sqrt((b*c-a*d)^(2/3)*((b*c-a*d)^(2/3)+2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2))],
[(a+b*x)^(5/3)/(c+d*x)^(2/3),x,3,-5/6*(b*c-a*d)*(a+b*x)^(2/3)*(c+d*x)^(1/3)/d^2+1/2*(a+b*x)^(5/3)*(c+d*x)^(1/3)/d-5/18*(b*c-a*d)^2*log(c+d*x)/(b^(1/3)*d^(8/3))-5/6*(b*c-a*d)^2*log(-1+d^(1/3)*(a+b*x)^(1/3)/(b^(1/3)*(c+d*x)^(1/3)))/(b^(1/3)*d^(8/3))-5/3*(b*c-a*d)^2*arctan(1/sqrt(3)+2*d^(1/3)*(a+b*x)^(1/3)/(b^(1/3)*(c+d*x)^(1/3)*sqrt(3)))/(b^(1/3)*d^(8/3)*sqrt(3))],
[(a+b*x)^(2/3)/(c+d*x)^(2/3),x,2,(a+b*x)^(2/3)*(c+d*x)^(1/3)/d+1/3*(b*c-a*d)*log(c+d*x)/(b^(1/3)*d^(5/3))+(b*c-a*d)*log(-1+d^(1/3)*(a+b*x)^(1/3)/(b^(1/3)*(c+d*x)^(1/3)))/(b^(1/3)*d^(5/3))+2*(b*c-a*d)*arctan(1/sqrt(3)+2*d^(1/3)*(a+b*x)^(1/3)/(b^(1/3)*(c+d*x)^(1/3)*sqrt(3)))/(b^(1/3)*d^(5/3)*sqrt(3))],
[1/((a+b*x)^(1/3)*(c+d*x)^(2/3)),x,1,-1/2*log(c+d*x)/(b^(1/3)*d^(2/3))-3/2*log(-1+d^(1/3)*(a+b*x)^(1/3)/(b^(1/3)*(c+d*x)^(1/3)))/(b^(1/3)*d^(2/3))-arctan(1/sqrt(3)+2*d^(1/3)*(a+b*x)^(1/3)/(b^(1/3)*(c+d*x)^(1/3)*sqrt(3)))*sqrt(3)/(b^(1/3)*d^(2/3))],
[1/((a+b*x)^(4/3)*(c+d*x)^(2/3)),x,1,-3*(c+d*x)^(1/3)/((b*c-a*d)*(a+b*x)^(1/3))],
[1/((a+b*x)^(7/3)*(c+d*x)^(2/3)),x,2,-3/4*(c+d*x)^(1/3)/((b*c-a*d)*(a+b*x)^(4/3))+9/4*d*(c+d*x)^(1/3)/((b*c-a*d)^2*(a+b*x)^(1/3))],
[1/((a+b*x)^(10/3)*(c+d*x)^(2/3)),x,3,-3/7*(c+d*x)^(1/3)/((b*c-a*d)*(a+b*x)^(7/3))+9/14*d*(c+d*x)^(1/3)/((b*c-a*d)^2*(a+b*x)^(4/3))-27/14*d^2*(c+d*x)^(1/3)/((b*c-a*d)^3*(a+b*x)^(1/3))],
[1/((a+b*x)^(13/3)*(c+d*x)^(2/3)),x,4,-3/10*(c+d*x)^(1/3)/((b*c-a*d)*(a+b*x)^(10/3))+27/70*d*(c+d*x)^(1/3)/((b*c-a*d)^2*(a+b*x)^(7/3))-81/140*d^2*(c+d*x)^(1/3)/((b*c-a*d)^3*(a+b*x)^(4/3))+243/140*d^3*(c+d*x)^(1/3)/((b*c-a*d)^4*(a+b*x)^(1/3))],
[(a+b*x)^(7/3)/(c+d*x)^(2/3),x,6,21/20*(b*c-a*d)^2*(a+b*x)^(1/3)*(c+d*x)^(1/3)/d^3-21/40*(b*c-a*d)*(a+b*x)^(4/3)*(c+d*x)^(1/3)/d^2+3/8*(a+b*x)^(7/3)*(c+d*x)^(1/3)/d-7/10*3^(3/4)*(b*c-a*d)^3*((a+b*x)*(c+d*x))^(2/3)*((b*c-a*d)^(2/3)+2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3))*EllipticF((2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1-sqrt(3)))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt(2+sqrt(3))*sqrt(((b*c-a*d)^(4/3)-2^(2/3)*b^(1/3)*d^(1/3)*(b*c-a*d)^(2/3)*((a+b*x)*(c+d*x))^(1/3)+2*2^(1/3)*b^(2/3)*d^(2/3)*((a+b*x)*(c+d*x))^(2/3))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2)/(2^(2/3)*b^(1/3)*d^(10/3)*(a+b*x)^(2/3)*(c+d*x)^(2/3)*(b*c+a*d+2*b*d*x)*sqrt((a*d+b*(c+2*d*x))^2)*sqrt((b*c-a*d)^(2/3)*((b*c-a*d)^(2/3)+2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2))],
[(a+b*x)^(4/3)/(c+d*x)^(2/3),x,5,-6/5*(b*c-a*d)*(a+b*x)^(1/3)*(c+d*x)^(1/3)/d^2+3/5*(a+b*x)^(4/3)*(c+d*x)^(1/3)/d+2/5*2^(1/3)*3^(3/4)*(b*c-a*d)^2*((a+b*x)*(c+d*x))^(2/3)*((b*c-a*d)^(2/3)+2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3))*EllipticF((2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1-sqrt(3)))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt(2+sqrt(3))*sqrt(((b*c-a*d)^(4/3)-2^(2/3)*b^(1/3)*d^(1/3)*(b*c-a*d)^(2/3)*((a+b*x)*(c+d*x))^(1/3)+2*2^(1/3)*b^(2/3)*d^(2/3)*((a+b*x)*(c+d*x))^(2/3))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2)/(b^(1/3)*d^(7/3)*(a+b*x)^(2/3)*(c+d*x)^(2/3)*(b*c+a*d+2*b*d*x)*sqrt((a*d+b*(c+2*d*x))^2)*sqrt((b*c-a*d)^(2/3)*((b*c-a*d)^(2/3)+2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2))],
[(a+b*x)^(1/3)/(c+d*x)^(2/3),x,4,3/2*(a+b*x)^(1/3)*(c+d*x)^(1/3)/d-3^(3/4)*(b*c-a*d)*((a+b*x)*(c+d*x))^(2/3)*((b*c-a*d)^(2/3)+2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3))*EllipticF((2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1-sqrt(3)))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt(2+sqrt(3))*sqrt(((b*c-a*d)^(4/3)-2^(2/3)*b^(1/3)*d^(1/3)*(b*c-a*d)^(2/3)*((a+b*x)*(c+d*x))^(1/3)+2*2^(1/3)*b^(2/3)*d^(2/3)*((a+b*x)*(c+d*x))^(2/3))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2)/(2^(2/3)*b^(1/3)*d^(4/3)*(a+b*x)^(2/3)*(c+d*x)^(2/3)*(b*c+a*d+2*b*d*x)*sqrt((a*d+b*(c+2*d*x))^2)*sqrt((b*c-a*d)^(2/3)*((b*c-a*d)^(2/3)+2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2))],
[1/((a+b*x)^(2/3)*(c+d*x)^(2/3)),x,3,2^(1/3)*3^(3/4)*((a+b*x)*(c+d*x))^(2/3)*((b*c-a*d)^(2/3)+2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3))*EllipticF((2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1-sqrt(3)))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt(2+sqrt(3))*sqrt(((b*c-a*d)^(4/3)-2^(2/3)*b^(1/3)*d^(1/3)*(b*c-a*d)^(2/3)*((a+b*x)*(c+d*x))^(1/3)+2*2^(1/3)*b^(2/3)*d^(2/3)*((a+b*x)*(c+d*x))^(2/3))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2)/(b^(1/3)*d^(1/3)*(a+b*x)^(2/3)*(c+d*x)^(2/3)*(b*c+a*d+2*b*d*x)*sqrt((a*d+b*(c+2*d*x))^2)*sqrt((b*c-a*d)^(2/3)*((b*c-a*d)^(2/3)+2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2))],
[1/((a+b*x)^(5/3)*(c+d*x)^(2/3)),x,4,-3/2*(c+d*x)^(1/3)/((b*c-a*d)*(a+b*x)^(2/3))-3^(3/4)*d^(2/3)*((a+b*x)*(c+d*x))^(2/3)*((b*c-a*d)^(2/3)+2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3))*EllipticF((2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1-sqrt(3)))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt(2+sqrt(3))*sqrt(((b*c-a*d)^(4/3)-2^(2/3)*b^(1/3)*d^(1/3)*(b*c-a*d)^(2/3)*((a+b*x)*(c+d*x))^(1/3)+2*2^(1/3)*b^(2/3)*d^(2/3)*((a+b*x)*(c+d*x))^(2/3))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2)/(2^(2/3)*b^(1/3)*(b*c-a*d)*(a+b*x)^(2/3)*(c+d*x)^(2/3)*(b*c+a*d+2*b*d*x)*sqrt((a*d+b*(c+2*d*x))^2)*sqrt((b*c-a*d)^(2/3)*((b*c-a*d)^(2/3)+2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2))],
[1/((a+b*x)^(8/3)*(c+d*x)^(2/3)),x,5,-3/5*(c+d*x)^(1/3)/((b*c-a*d)*(a+b*x)^(5/3))+6/5*d*(c+d*x)^(1/3)/((b*c-a*d)^2*(a+b*x)^(2/3))+2/5*2^(1/3)*3^(3/4)*d^(5/3)*((a+b*x)*(c+d*x))^(2/3)*((b*c-a*d)^(2/3)+2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3))*EllipticF((2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1-sqrt(3)))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt(2+sqrt(3))*sqrt(((b*c-a*d)^(4/3)-2^(2/3)*b^(1/3)*d^(1/3)*(b*c-a*d)^(2/3)*((a+b*x)*(c+d*x))^(1/3)+2*2^(1/3)*b^(2/3)*d^(2/3)*((a+b*x)*(c+d*x))^(2/3))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2)/(b^(1/3)*(b*c-a*d)^2*(a+b*x)^(2/3)*(c+d*x)^(2/3)*(b*c+a*d+2*b*d*x)*sqrt((a*d+b*(c+2*d*x))^2)*sqrt((b*c-a*d)^(2/3)*((b*c-a*d)^(2/3)+2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2))],
[1/((a+b*x)^(11/3)*(c+d*x)^(2/3)),x,6,-3/8*(c+d*x)^(1/3)/((b*c-a*d)*(a+b*x)^(8/3))+21/40*d*(c+d*x)^(1/3)/((b*c-a*d)^2*(a+b*x)^(5/3))-21/20*d^2*(c+d*x)^(1/3)/((b*c-a*d)^3*(a+b*x)^(2/3))-7/10*3^(3/4)*d^(8/3)*((a+b*x)*(c+d*x))^(2/3)*((b*c-a*d)^(2/3)+2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3))*EllipticF((2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1-sqrt(3)))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt(2+sqrt(3))*sqrt(((b*c-a*d)^(4/3)-2^(2/3)*b^(1/3)*d^(1/3)*(b*c-a*d)^(2/3)*((a+b*x)*(c+d*x))^(1/3)+2*2^(1/3)*b^(2/3)*d^(2/3)*((a+b*x)*(c+d*x))^(2/3))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2)/(2^(2/3)*b^(1/3)*(b*c-a*d)^3*(a+b*x)^(2/3)*(c+d*x)^(2/3)*(b*c+a*d+2*b*d*x)*sqrt((a*d+b*(c+2*d*x))^2)*sqrt((b*c-a*d)^(2/3)*((b*c-a*d)^(2/3)+2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2))],
[(a+b*x)^(7/3)/(c+d*x)^(4/3),x,4,-3*(a+b*x)^(7/3)/(d*(c+d*x)^(1/3))-14/3*b*(b*c-a*d)*(a+b*x)^(1/3)*(c+d*x)^(2/3)/d^3+7/2*b*(a+b*x)^(4/3)*(c+d*x)^(2/3)/d^2-7/9*b^(1/3)*(b*c-a*d)^2*log(a+b*x)/d^(10/3)-7/3*b^(1/3)*(b*c-a*d)^2*log(-1+b^(1/3)*(c+d*x)^(1/3)/(d^(1/3)*(a+b*x)^(1/3)))/d^(10/3)-14/3*b^(1/3)*(b*c-a*d)^2*arctan(1/sqrt(3)+2*b^(1/3)*(c+d*x)^(1/3)/(d^(1/3)*(a+b*x)^(1/3)*sqrt(3)))/(d^(10/3)*sqrt(3))],
[(a+b*x)^(4/3)/(c+d*x)^(4/3),x,3,-3*(a+b*x)^(4/3)/(d*(c+d*x)^(1/3))+4*b*(a+b*x)^(1/3)*(c+d*x)^(2/3)/d^2+2/3*b^(1/3)*(b*c-a*d)*log(a+b*x)/d^(7/3)+2*b^(1/3)*(b*c-a*d)*log(-1+b^(1/3)*(c+d*x)^(1/3)/(d^(1/3)*(a+b*x)^(1/3)))/d^(7/3)+4*b^(1/3)*(b*c-a*d)*arctan(1/sqrt(3)+2*b^(1/3)*(c+d*x)^(1/3)/(d^(1/3)*(a+b*x)^(1/3)*sqrt(3)))/(d^(7/3)*sqrt(3))],
[(a+b*x)^(1/3)/(c+d*x)^(4/3),x,2,-3*(a+b*x)^(1/3)/(d*(c+d*x)^(1/3))-1/2*b^(1/3)*log(a+b*x)/d^(4/3)-3/2*b^(1/3)*log(-1+b^(1/3)*(c+d*x)^(1/3)/(d^(1/3)*(a+b*x)^(1/3)))/d^(4/3)-b^(1/3)*arctan(1/sqrt(3)+2*b^(1/3)*(c+d*x)^(1/3)/(d^(1/3)*(a+b*x)^(1/3)*sqrt(3)))*sqrt(3)/d^(4/3)],
[1/((a+b*x)^(2/3)*(c+d*x)^(4/3)),x,1,3*(a+b*x)^(1/3)/((b*c-a*d)*(c+d*x)^(1/3))],
[1/((a+b*x)^(5/3)*(c+d*x)^(4/3)),x,2,(-3/2)/((b*c-a*d)*(a+b*x)^(2/3)*(c+d*x)^(1/3))-9/2*d*(a+b*x)^(1/3)/((b*c-a*d)^2*(c+d*x)^(1/3))],
[1/((a+b*x)^(8/3)*(c+d*x)^(4/3)),x,3,(-3/5)/((b*c-a*d)*(a+b*x)^(5/3)*(c+d*x)^(1/3))+9/5*d/((b*c-a*d)^2*(a+b*x)^(2/3)*(c+d*x)^(1/3))+27/5*d^2*(a+b*x)^(1/3)/((b*c-a*d)^3*(c+d*x)^(1/3))],
[1/((a+b*x)^(11/3)*(c+d*x)^(4/3)),x,4,(-3/8)/((b*c-a*d)*(a+b*x)^(8/3)*(c+d*x)^(1/3))+27/40*d/((b*c-a*d)^2*(a+b*x)^(5/3)*(c+d*x)^(1/3))-81/40*d^2/((b*c-a*d)^3*(a+b*x)^(2/3)*(c+d*x)^(1/3))-243/40*d^3*(a+b*x)^(1/3)/((b*c-a*d)^4*(c+d*x)^(1/3))],
[(a+b*x)^(8/3)/(c+d*x)^(4/3),x,8,-3*(a+b*x)^(8/3)/(d*(c+d*x)^(1/3))-30/7*b*(b*c-a*d)*(a+b*x)^(2/3)*(c+d*x)^(2/3)/d^3+24/7*b*(a+b*x)^(5/3)*(c+d*x)^(2/3)/d^2+30/7*2^(2/3)*b^(1/3)*(b*c-a*d)^2*((a+b*x)*(c+d*x))^(1/3)*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt((a*d+b*(c+2*d*x))^2)/(d^(11/3)*(a+b*x)^(1/3)*(c+d*x)^(1/3)*(b*c+a*d+2*b*d*x)*(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3))))+20/7*2^(1/6)*3^(3/4)*b^(1/3)*(b*c-a*d)^(8/3)*((a+b*x)*(c+d*x))^(1/3)*((b*c-a*d)^(2/3)+2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3))*EllipticF((2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1-sqrt(3)))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt(((b*c-a*d)^(4/3)-2^(2/3)*b^(1/3)*d^(1/3)*(b*c-a*d)^(2/3)*((a+b*x)*(c+d*x))^(1/3)+2*2^(1/3)*b^(2/3)*d^(2/3)*((a+b*x)*(c+d*x))^(2/3))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2)/(d^(11/3)*(a+b*x)^(1/3)*(c+d*x)^(1/3)*(b*c+a*d+2*b*d*x)*sqrt((a*d+b*(c+2*d*x))^2)*sqrt((b*c-a*d)^(2/3)*((b*c-a*d)^(2/3)+2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2))-15/7*2^(2/3)*3^(1/4)*b^(1/3)*(b*c-a*d)^(8/3)*((a+b*x)*(c+d*x))^(1/3)*((b*c-a*d)^(2/3)+2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3))*EllipticE((2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1-sqrt(3)))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt(2-sqrt(3))*sqrt(((b*c-a*d)^(4/3)-2^(2/3)*b^(1/3)*d^(1/3)*(b*c-a*d)^(2/3)*((a+b*x)*(c+d*x))^(1/3)+2*2^(1/3)*b^(2/3)*d^(2/3)*((a+b*x)*(c+d*x))^(2/3))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2)/(d^(11/3)*(a+b*x)^(1/3)*(c+d*x)^(1/3)*(b*c+a*d+2*b*d*x)*sqrt((a*d+b*(c+2*d*x))^2)*sqrt((b*c-a*d)^(2/3)*((b*c-a*d)^(2/3)+2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2))],
[(a+b*x)^(5/3)/(c+d*x)^(4/3),x,7,-3*(a+b*x)^(5/3)/(d*(c+d*x)^(1/3))+15/4*b*(a+b*x)^(2/3)*(c+d*x)^(2/3)/d^2-15/2*b^(1/3)*(b*c-a*d)*((a+b*x)*(c+d*x))^(1/3)*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt((a*d+b*(c+2*d*x))^2)/(2^(1/3)*d^(8/3)*(a+b*x)^(1/3)*(c+d*x)^(1/3)*(b*c+a*d+2*b*d*x)*(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3))))-5*3^(3/4)*b^(1/3)*(b*c-a*d)^(5/3)*((a+b*x)*(c+d*x))^(1/3)*((b*c-a*d)^(2/3)+2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3))*EllipticF((2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1-sqrt(3)))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt(((b*c-a*d)^(4/3)-2^(2/3)*b^(1/3)*d^(1/3)*(b*c-a*d)^(2/3)*((a+b*x)*(c+d*x))^(1/3)+2*2^(1/3)*b^(2/3)*d^(2/3)*((a+b*x)*(c+d*x))^(2/3))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2)/(2^(5/6)*d^(8/3)*(a+b*x)^(1/3)*(c+d*x)^(1/3)*(b*c+a*d+2*b*d*x)*sqrt((a*d+b*(c+2*d*x))^2)*sqrt((b*c-a*d)^(2/3)*((b*c-a*d)^(2/3)+2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2))+15/4*3^(1/4)*b^(1/3)*(b*c-a*d)^(5/3)*((a+b*x)*(c+d*x))^(1/3)*((b*c-a*d)^(2/3)+2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3))*EllipticE((2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1-sqrt(3)))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt(2-sqrt(3))*sqrt(((b*c-a*d)^(4/3)-2^(2/3)*b^(1/3)*d^(1/3)*(b*c-a*d)^(2/3)*((a+b*x)*(c+d*x))^(1/3)+2*2^(1/3)*b^(2/3)*d^(2/3)*((a+b*x)*(c+d*x))^(2/3))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2)/(2^(1/3)*d^(8/3)*(a+b*x)^(1/3)*(c+d*x)^(1/3)*(b*c+a*d+2*b*d*x)*sqrt((a*d+b*(c+2*d*x))^2)*sqrt((b*c-a*d)^(2/3)*((b*c-a*d)^(2/3)+2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2))],
[(a+b*x)^(2/3)/(c+d*x)^(4/3),x,6,-3*(a+b*x)^(2/3)/(d*(c+d*x)^(1/3))+3*2^(2/3)*b^(1/3)*((a+b*x)*(c+d*x))^(1/3)*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt((a*d+b*(c+2*d*x))^2)/(d^(5/3)*(a+b*x)^(1/3)*(c+d*x)^(1/3)*(b*c+a*d+2*b*d*x)*(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3))))+2*2^(1/6)*3^(3/4)*b^(1/3)*(b*c-a*d)^(2/3)*((a+b*x)*(c+d*x))^(1/3)*((b*c-a*d)^(2/3)+2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3))*EllipticF((2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1-sqrt(3)))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt(((b*c-a*d)^(4/3)-2^(2/3)*b^(1/3)*d^(1/3)*(b*c-a*d)^(2/3)*((a+b*x)*(c+d*x))^(1/3)+2*2^(1/3)*b^(2/3)*d^(2/3)*((a+b*x)*(c+d*x))^(2/3))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2)/(d^(5/3)*(a+b*x)^(1/3)*(c+d*x)^(1/3)*(b*c+a*d+2*b*d*x)*sqrt((a*d+b*(c+2*d*x))^2)*sqrt((b*c-a*d)^(2/3)*((b*c-a*d)^(2/3)+2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2))-3*3^(1/4)*b^(1/3)*(b*c-a*d)^(2/3)*((a+b*x)*(c+d*x))^(1/3)*((b*c-a*d)^(2/3)+2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3))*EllipticE((2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1-sqrt(3)))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt(2-sqrt(3))*sqrt(((b*c-a*d)^(4/3)-2^(2/3)*b^(1/3)*d^(1/3)*(b*c-a*d)^(2/3)*((a+b*x)*(c+d*x))^(1/3)+2*2^(1/3)*b^(2/3)*d^(2/3)*((a+b*x)*(c+d*x))^(2/3))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2)/(2^(1/3)*d^(5/3)*(a+b*x)^(1/3)*(c+d*x)^(1/3)*(b*c+a*d+2*b*d*x)*sqrt((a*d+b*(c+2*d*x))^2)*sqrt((b*c-a*d)^(2/3)*((b*c-a*d)^(2/3)+2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2))],
[1/((a+b*x)^(1/3)*(c+d*x)^(4/3)),x,6,3*(a+b*x)^(2/3)/((b*c-a*d)*(c+d*x)^(1/3))-3*b^(1/3)*((a+b*x)*(c+d*x))^(1/3)*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt((a*d+b*(c+2*d*x))^2)/(2^(1/3)*d^(2/3)*(b*c-a*d)*(a+b*x)^(1/3)*(c+d*x)^(1/3)*(b*c+a*d+2*b*d*x)*(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3))))-2^(1/6)*3^(3/4)*b^(1/3)*((a+b*x)*(c+d*x))^(1/3)*((b*c-a*d)^(2/3)+2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3))*EllipticF((2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1-sqrt(3)))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt(((b*c-a*d)^(4/3)-2^(2/3)*b^(1/3)*d^(1/3)*(b*c-a*d)^(2/3)*((a+b*x)*(c+d*x))^(1/3)+2*2^(1/3)*b^(2/3)*d^(2/3)*((a+b*x)*(c+d*x))^(2/3))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2)/(d^(2/3)*(b*c-a*d)^(1/3)*(a+b*x)^(1/3)*(c+d*x)^(1/3)*(b*c+a*d+2*b*d*x)*sqrt((a*d+b*(c+2*d*x))^2)*sqrt((b*c-a*d)^(2/3)*((b*c-a*d)^(2/3)+2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2))+3/2*3^(1/4)*b^(1/3)*((a+b*x)*(c+d*x))^(1/3)*((b*c-a*d)^(2/3)+2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3))*EllipticE((2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1-sqrt(3)))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt(2-sqrt(3))*sqrt(((b*c-a*d)^(4/3)-2^(2/3)*b^(1/3)*d^(1/3)*(b*c-a*d)^(2/3)*((a+b*x)*(c+d*x))^(1/3)+2*2^(1/3)*b^(2/3)*d^(2/3)*((a+b*x)*(c+d*x))^(2/3))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2)/(2^(1/3)*d^(2/3)*(b*c-a*d)^(1/3)*(a+b*x)^(1/3)*(c+d*x)^(1/3)*(b*c+a*d+2*b*d*x)*sqrt((a*d+b*(c+2*d*x))^2)*sqrt((b*c-a*d)^(2/3)*((b*c-a*d)^(2/3)+2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2))],
[1/((a+b*x)^(4/3)*(c+d*x)^(4/3)),x,7,(-3)/((b*c-a*d)*(a+b*x)^(1/3)*(c+d*x)^(1/3))-6*d*(a+b*x)^(2/3)/((b*c-a*d)^2*(c+d*x)^(1/3))+3*2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt((a*d+b*(c+2*d*x))^2)/((b*c-a*d)^2*(a+b*x)^(1/3)*(c+d*x)^(1/3)*(b*c+a*d+2*b*d*x)*(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3))))+2*2^(1/6)*3^(3/4)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)*((b*c-a*d)^(2/3)+2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3))*EllipticF((2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1-sqrt(3)))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt(((b*c-a*d)^(4/3)-2^(2/3)*b^(1/3)*d^(1/3)*(b*c-a*d)^(2/3)*((a+b*x)*(c+d*x))^(1/3)+2*2^(1/3)*b^(2/3)*d^(2/3)*((a+b*x)*(c+d*x))^(2/3))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2)/((b*c-a*d)^(4/3)*(a+b*x)^(1/3)*(c+d*x)^(1/3)*(b*c+a*d+2*b*d*x)*sqrt((a*d+b*(c+2*d*x))^2)*sqrt((b*c-a*d)^(2/3)*((b*c-a*d)^(2/3)+2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2))-3*3^(1/4)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)*((b*c-a*d)^(2/3)+2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3))*EllipticE((2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1-sqrt(3)))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt(2-sqrt(3))*sqrt(((b*c-a*d)^(4/3)-2^(2/3)*b^(1/3)*d^(1/3)*(b*c-a*d)^(2/3)*((a+b*x)*(c+d*x))^(1/3)+2*2^(1/3)*b^(2/3)*d^(2/3)*((a+b*x)*(c+d*x))^(2/3))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2)/(2^(1/3)*(b*c-a*d)^(4/3)*(a+b*x)^(1/3)*(c+d*x)^(1/3)*(b*c+a*d+2*b*d*x)*sqrt((a*d+b*(c+2*d*x))^2)*sqrt((b*c-a*d)^(2/3)*((b*c-a*d)^(2/3)+2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2))],
[1/((a+b*x)^(7/3)*(c+d*x)^(4/3)),x,8,(-3/4)/((b*c-a*d)*(a+b*x)^(4/3)*(c+d*x)^(1/3))+15/4*d/((b*c-a*d)^2*(a+b*x)^(1/3)*(c+d*x)^(1/3))+15/2*d^2*(a+b*x)^(2/3)/((b*c-a*d)^3*(c+d*x)^(1/3))-15/2*b^(1/3)*d^(4/3)*((a+b*x)*(c+d*x))^(1/3)*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt((a*d+b*(c+2*d*x))^2)/(2^(1/3)*(b*c-a*d)^3*(a+b*x)^(1/3)*(c+d*x)^(1/3)*(b*c+a*d+2*b*d*x)*(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3))))-5*3^(3/4)*b^(1/3)*d^(4/3)*((a+b*x)*(c+d*x))^(1/3)*((b*c-a*d)^(2/3)+2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3))*EllipticF((2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1-sqrt(3)))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt(((b*c-a*d)^(4/3)-2^(2/3)*b^(1/3)*d^(1/3)*(b*c-a*d)^(2/3)*((a+b*x)*(c+d*x))^(1/3)+2*2^(1/3)*b^(2/3)*d^(2/3)*((a+b*x)*(c+d*x))^(2/3))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2)/(2^(5/6)*(b*c-a*d)^(7/3)*(a+b*x)^(1/3)*(c+d*x)^(1/3)*(b*c+a*d+2*b*d*x)*sqrt((a*d+b*(c+2*d*x))^2)*sqrt((b*c-a*d)^(2/3)*((b*c-a*d)^(2/3)+2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2))+15/4*3^(1/4)*b^(1/3)*d^(4/3)*((a+b*x)*(c+d*x))^(1/3)*((b*c-a*d)^(2/3)+2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3))*EllipticE((2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1-sqrt(3)))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt(2-sqrt(3))*sqrt(((b*c-a*d)^(4/3)-2^(2/3)*b^(1/3)*d^(1/3)*(b*c-a*d)^(2/3)*((a+b*x)*(c+d*x))^(1/3)+2*2^(1/3)*b^(2/3)*d^(2/3)*((a+b*x)*(c+d*x))^(2/3))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2)/(2^(1/3)*(b*c-a*d)^(7/3)*(a+b*x)^(1/3)*(c+d*x)^(1/3)*(b*c+a*d+2*b*d*x)*sqrt((a*d+b*(c+2*d*x))^2)*sqrt((b*c-a*d)^(2/3)*((b*c-a*d)^(2/3)+2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3))/(2^(2/3)*b^(1/3)*d^(1/3)*((a+b*x)*(c+d*x))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2))],
[(-1+x)^(1/3)/(1+x)^(1/3),x,2,(-1+x)^(1/3)*(1+x)^(2/3)+1/3*log(-1+x)+log(-1+(1+x)^(1/3)/(-1+x)^(1/3))+2*arctan(1/sqrt(3)+2*(1+x)^(1/3)/((-1+x)^(1/3)*sqrt(3)))/sqrt(3)],

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

# n>0
[(a+b*x)^(3/2)*(c+d*x)^(1/4),x,6,4/77*(b*c-a*d)*(a+b*x)^(3/2)*(c+d*x)^(1/4)/(b*d)+4/11*(a+b*x)^(5/2)*(c+d*x)^(1/4)/b-8/77*(b*c-a*d)^2*(c+d*x)^(1/4)*sqrt(a+b*x)/(b*d^2)+16/77*(b*c-a*d)^(13/4)*EllipticF(b^(1/4)*(c+d*x)^(1/4)/(b*c-a*d)^(1/4),I)*sqrt(-d*(a+b*x)/(b*c-a*d))/(b^(5/4)*d^3*sqrt(a+b*x))],
[(a+b*x)^(1/2)*(c+d*x)^(1/4),x,5,4/7*(a+b*x)^(3/2)*(c+d*x)^(1/4)/b+4/21*(b*c-a*d)*(c+d*x)^(1/4)*sqrt(a+b*x)/(b*d)-8/21*(b*c-a*d)^(9/4)*EllipticF(b^(1/4)*(c+d*x)^(1/4)/(b*c-a*d)^(1/4),I)*sqrt(-d*(a+b*x)/(b*c-a*d))/(b^(5/4)*d^2*sqrt(a+b*x))],
[(c+d*x)^(1/4)/(a+b*x)^(1/2),x,4,4/3*(c+d*x)^(1/4)*sqrt(a+b*x)/b+4/3*(b*c-a*d)^(5/4)*EllipticF(b^(1/4)*(c+d*x)^(1/4)/(b*c-a*d)^(1/4),I)*sqrt(-d*(a+b*x)/(b*c-a*d))/(b^(5/4)*d*sqrt(a+b*x))],
[(c+d*x)^(1/4)/(a+b*x)^(3/2),x,4,-2*(c+d*x)^(1/4)/(b*sqrt(a+b*x))+2*(b*c-a*d)^(1/4)*EllipticF(b^(1/4)*(c+d*x)^(1/4)/(b*c-a*d)^(1/4),I)*sqrt(-d*(a+b*x)/(b*c-a*d))/(b^(5/4)*sqrt(a+b*x))],
[(c+d*x)^(1/4)/(a+b*x)^(5/2),x,5,-2/3*(c+d*x)^(1/4)/(b*(a+b*x)^(3/2))-1/3*d*(c+d*x)^(1/4)/(b*(b*c-a*d)*sqrt(a+b*x))-1/3*d*EllipticF(b^(1/4)*(c+d*x)^(1/4)/(b*c-a*d)^(1/4),I)*sqrt(-d*(a+b*x)/(b*c-a*d))/(b^(5/4)*(b*c-a*d)^(3/4)*sqrt(a+b*x))],
[(c+d*x)^(1/4)/(a+b*x)^(7/2),x,6,-2/5*(c+d*x)^(1/4)/(b*(a+b*x)^(5/2))-1/15*d*(c+d*x)^(1/4)/(b*(b*c-a*d)*(a+b*x)^(3/2))+1/6*d^2*(c+d*x)^(1/4)/(b*(b*c-a*d)^2*sqrt(a+b*x))+1/6*d^2*EllipticF(b^(1/4)*(c+d*x)^(1/4)/(b*c-a*d)^(1/4),I)*sqrt(-d*(a+b*x)/(b*c-a*d))/(b^(5/4)*(b*c-a*d)^(7/4)*sqrt(a+b*x))],
[(a+b*x)^(3/2)*(c+d*x)^(3/4),x,10,4/39*(b*c-a*d)*(a+b*x)^(3/2)*(c+d*x)^(3/4)/(b*d)+4/13*(a+b*x)^(5/2)*(c+d*x)^(3/4)/b-8/65*(b*c-a*d)^2*(c+d*x)^(3/4)*sqrt(a+b*x)/(b*d^2)+16/65*(b*c-a*d)^(15/4)*EllipticE(b^(1/4)*(c+d*x)^(1/4)/(b*c-a*d)^(1/4),I)*sqrt(-d*(a+b*x)/(b*c-a*d))/(b^(7/4)*d^3*sqrt(a+b*x))-16/65*(b*c-a*d)^(15/4)*EllipticF(b^(1/4)*(c+d*x)^(1/4)/(b*c-a*d)^(1/4),I)*sqrt(-d*(a+b*x)/(b*c-a*d))/(b^(7/4)*d^3*sqrt(a+b*x))],
[(a+b*x)^(1/2)*(c+d*x)^(3/4),x,9,4/9*(a+b*x)^(3/2)*(c+d*x)^(3/4)/b+4/15*(b*c-a*d)*(c+d*x)^(3/4)*sqrt(a+b*x)/(b*d)-8/15*(b*c-a*d)^(11/4)*EllipticE(b^(1/4)*(c+d*x)^(1/4)/(b*c-a*d)^(1/4),I)*sqrt(-d*(a+b*x)/(b*c-a*d))/(b^(7/4)*d^2*sqrt(a+b*x))+8/15*(b*c-a*d)^(11/4)*EllipticF(b^(1/4)*(c+d*x)^(1/4)/(b*c-a*d)^(1/4),I)*sqrt(-d*(a+b*x)/(b*c-a*d))/(b^(7/4)*d^2*sqrt(a+b*x))],
[(c+d*x)^(3/4)/(a+b*x)^(1/2),x,8,4/5*(c+d*x)^(3/4)*sqrt(a+b*x)/b+12/5*(b*c-a*d)^(7/4)*EllipticE(b^(1/4)*(c+d*x)^(1/4)/(b*c-a*d)^(1/4),I)*sqrt(-d*(a+b*x)/(b*c-a*d))/(b^(7/4)*d*sqrt(a+b*x))-12/5*(b*c-a*d)^(7/4)*EllipticF(b^(1/4)*(c+d*x)^(1/4)/(b*c-a*d)^(1/4),I)*sqrt(-d*(a+b*x)/(b*c-a*d))/(b^(7/4)*d*sqrt(a+b*x))],
[(c+d*x)^(3/4)/(a+b*x)^(3/2),x,8,-2*(c+d*x)^(3/4)/(b*sqrt(a+b*x))+6*(b*c-a*d)^(3/4)*EllipticE(b^(1/4)*(c+d*x)^(1/4)/(b*c-a*d)^(1/4),I)*sqrt(-d*(a+b*x)/(b*c-a*d))/(b^(7/4)*sqrt(a+b*x))-6*(b*c-a*d)^(3/4)*EllipticF(b^(1/4)*(c+d*x)^(1/4)/(b*c-a*d)^(1/4),I)*sqrt(-d*(a+b*x)/(b*c-a*d))/(b^(7/4)*sqrt(a+b*x))],
[(c+d*x)^(3/4)/(a+b*x)^(5/2),x,9,-2/3*(c+d*x)^(3/4)/(b*(a+b*x)^(3/2))-d*(c+d*x)^(3/4)/(b*(b*c-a*d)*sqrt(a+b*x))+d*EllipticE(b^(1/4)*(c+d*x)^(1/4)/(b*c-a*d)^(1/4),I)*sqrt(-d*(a+b*x)/(b*c-a*d))/(b^(7/4)*(b*c-a*d)^(1/4)*sqrt(a+b*x))-d*EllipticF(b^(1/4)*(c+d*x)^(1/4)/(b*c-a*d)^(1/4),I)*sqrt(-d*(a+b*x)/(b*c-a*d))/(b^(7/4)*(b*c-a*d)^(1/4)*sqrt(a+b*x))],
[(c+d*x)^(3/4)/(a+b*x)^(7/2),x,10,-2/5*(c+d*x)^(3/4)/(b*(a+b*x)^(5/2))-1/5*d*(c+d*x)^(3/4)/(b*(b*c-a*d)*(a+b*x)^(3/2))+3/10*d^2*(c+d*x)^(3/4)/(b*(b*c-a*d)^2*sqrt(a+b*x))-3/10*d^2*EllipticE(b^(1/4)*(c+d*x)^(1/4)/(b*c-a*d)^(1/4),I)*sqrt(-d*(a+b*x)/(b*c-a*d))/(b^(7/4)*(b*c-a*d)^(5/4)*sqrt(a+b*x))+3/10*d^2*EllipticF(b^(1/4)*(c+d*x)^(1/4)/(b*c-a*d)^(1/4),I)*sqrt(-d*(a+b*x)/(b*c-a*d))/(b^(7/4)*(b*c-a*d)^(5/4)*sqrt(a+b*x))],
[(a+b*x)^(3/2)*(c+d*x)^(5/4),x,7,4/231*(b*c-a*d)^2*(a+b*x)^(3/2)*(c+d*x)^(1/4)/(b^2*d)+4/33*(b*c-a*d)*(a+b*x)^(5/2)*(c+d*x)^(1/4)/b^2+4/15*(a+b*x)^(5/2)*(c+d*x)^(5/4)/b-8/231*(b*c-a*d)^3*(c+d*x)^(1/4)*sqrt(a+b*x)/(b^2*d^2)+16/231*(b*c-a*d)^(17/4)*EllipticF(b^(1/4)*(c+d*x)^(1/4)/(b*c-a*d)^(1/4),I)*sqrt(-d*(a+b*x)/(b*c-a*d))/(b^(9/4)*d^3*sqrt(a+b*x))],
[(a+b*x)^(1/2)*(c+d*x)^(5/4),x,6,20/77*(b*c-a*d)*(a+b*x)^(3/2)*(c+d*x)^(1/4)/b^2+4/11*(a+b*x)^(3/2)*(c+d*x)^(5/4)/b+20/231*(b*c-a*d)^2*(c+d*x)^(1/4)*sqrt(a+b*x)/(b^2*d)-40/231*(b*c-a*d)^(13/4)*EllipticF(b^(1/4)*(c+d*x)^(1/4)/(b*c-a*d)^(1/4),I)*sqrt(-d*(a+b*x)/(b*c-a*d))/(b^(9/4)*d^2*sqrt(a+b*x))],
[(c+d*x)^(5/4)/(a+b*x)^(1/2),x,5,20/21*(b*c-a*d)*(c+d*x)^(1/4)*sqrt(a+b*x)/b^2+4/7*(c+d*x)^(5/4)*sqrt(a+b*x)/b+20/21*(b*c-a*d)^(9/4)*EllipticF(b^(1/4)*(c+d*x)^(1/4)/(b*c-a*d)^(1/4),I)*sqrt(-d*(a+b*x)/(b*c-a*d))/(b^(9/4)*d*sqrt(a+b*x))],
[(c+d*x)^(5/4)/(a+b*x)^(3/2),x,5,-2*(c+d*x)^(5/4)/(b*sqrt(a+b*x))+10/3*d*(c+d*x)^(1/4)*sqrt(a+b*x)/b^2+10/3*(b*c-a*d)^(5/4)*EllipticF(b^(1/4)*(c+d*x)^(1/4)/(b*c-a*d)^(1/4),I)*sqrt(-d*(a+b*x)/(b*c-a*d))/(b^(9/4)*sqrt(a+b*x))],
[(c+d*x)^(5/4)/(a+b*x)^(5/2),x,5,-2/3*(c+d*x)^(5/4)/(b*(a+b*x)^(3/2))-5/3*d*(c+d*x)^(1/4)/(b^2*sqrt(a+b*x))+5/3*d*(b*c-a*d)^(1/4)*EllipticF(b^(1/4)*(c+d*x)^(1/4)/(b*c-a*d)^(1/4),I)*sqrt(-d*(a+b*x)/(b*c-a*d))/(b^(9/4)*sqrt(a+b*x))],
[(c+d*x)^(5/4)/(a+b*x)^(7/2),x,6,-1/3*d*(c+d*x)^(1/4)/(b^2*(a+b*x)^(3/2))-2/5*(c+d*x)^(5/4)/(b*(a+b*x)^(5/2))-1/6*d^2*(c+d*x)^(1/4)/(b^2*(b*c-a*d)*sqrt(a+b*x))-1/6*d^2*EllipticF(b^(1/4)*(c+d*x)^(1/4)/(b*c-a*d)^(1/4),I)*sqrt(-d*(a+b*x)/(b*c-a*d))/(b^(9/4)*(b*c-a*d)^(3/4)*sqrt(a+b*x))],
[(c+d*x)^(5/4)/(a+b*x)^(9/2),x,7,-1/7*d*(c+d*x)^(1/4)/(b^2*(a+b*x)^(5/2))-1/42*d^2*(c+d*x)^(1/4)/(b^2*(b*c-a*d)*(a+b*x)^(3/2))-2/7*(c+d*x)^(5/4)/(b*(a+b*x)^(7/2))+5/84*d^3*(c+d*x)^(1/4)/(b^2*(b*c-a*d)^2*sqrt(a+b*x))+5/84*d^3*EllipticF(b^(1/4)*(c+d*x)^(1/4)/(b*c-a*d)^(1/4),I)*sqrt(-d*(a+b*x)/(b*c-a*d))/(b^(9/4)*(b*c-a*d)^(7/4)*sqrt(a+b*x))],

# n<0
[(a+b*x)^(5/2)/(c+d*x)^(1/4),x,10,-40/117*(b*c-a*d)*(a+b*x)^(3/2)*(c+d*x)^(3/4)/d^2+4/13*(a+b*x)^(5/2)*(c+d*x)^(3/4)/d+16/39*(b*c-a*d)^2*(c+d*x)^(3/4)*sqrt(a+b*x)/d^3-32/39*(b*c-a*d)^(15/4)*EllipticE(b^(1/4)*(c+d*x)^(1/4)/(b*c-a*d)^(1/4),I)*sqrt(-d*(a+b*x)/(b*c-a*d))/(b^(3/4)*d^4*sqrt(a+b*x))+32/39*(b*c-a*d)^(15/4)*EllipticF(b^(1/4)*(c+d*x)^(1/4)/(b*c-a*d)^(1/4),I)*sqrt(-d*(a+b*x)/(b*c-a*d))/(b^(3/4)*d^4*sqrt(a+b*x))],
[(a+b*x)^(3/2)/(c+d*x)^(1/4),x,9,4/9*(a+b*x)^(3/2)*(c+d*x)^(3/4)/d-8/15*(b*c-a*d)*(c+d*x)^(3/4)*sqrt(a+b*x)/d^2+16/15*(b*c-a*d)^(11/4)*EllipticE(b^(1/4)*(c+d*x)^(1/4)/(b*c-a*d)^(1/4),I)*sqrt(-d*(a+b*x)/(b*c-a*d))/(b^(3/4)*d^3*sqrt(a+b*x))-16/15*(b*c-a*d)^(11/4)*EllipticF(b^(1/4)*(c+d*x)^(1/4)/(b*c-a*d)^(1/4),I)*sqrt(-d*(a+b*x)/(b*c-a*d))/(b^(3/4)*d^3*sqrt(a+b*x))],
[(a+b*x)^(1/2)/(c+d*x)^(1/4),x,8,4/5*(c+d*x)^(3/4)*sqrt(a+b*x)/d-8/5*(b*c-a*d)^(7/4)*EllipticE(b^(1/4)*(c+d*x)^(1/4)/(b*c-a*d)^(1/4),I)*sqrt(-d*(a+b*x)/(b*c-a*d))/(b^(3/4)*d^2*sqrt(a+b*x))+8/5*(b*c-a*d)^(7/4)*EllipticF(b^(1/4)*(c+d*x)^(1/4)/(b*c-a*d)^(1/4),I)*sqrt(-d*(a+b*x)/(b*c-a*d))/(b^(3/4)*d^2*sqrt(a+b*x))],
[1/((a+b*x)^(1/2)*(c+d*x)^(1/4)),x,7,4*(b*c-a*d)^(3/4)*EllipticE(b^(1/4)*(c+d*x)^(1/4)/(b*c-a*d)^(1/4),I)*sqrt(-d*(a+b*x)/(b*c-a*d))/(b^(3/4)*d*sqrt(a+b*x))-4*(b*c-a*d)^(3/4)*EllipticF(b^(1/4)*(c+d*x)^(1/4)/(b*c-a*d)^(1/4),I)*sqrt(-d*(a+b*x)/(b*c-a*d))/(b^(3/4)*d*sqrt(a+b*x))],
[1/((a+b*x)^(3/2)*(c+d*x)^(1/4)),x,8,-2*(c+d*x)^(3/4)/((b*c-a*d)*sqrt(a+b*x))+2*EllipticE(b^(1/4)*(c+d*x)^(1/4)/(b*c-a*d)^(1/4),I)*sqrt(-d*(a+b*x)/(b*c-a*d))/(b^(3/4)*(b*c-a*d)^(1/4)*sqrt(a+b*x))-2*EllipticF(b^(1/4)*(c+d*x)^(1/4)/(b*c-a*d)^(1/4),I)*sqrt(-d*(a+b*x)/(b*c-a*d))/(b^(3/4)*(b*c-a*d)^(1/4)*sqrt(a+b*x))],
[1/((a+b*x)^(5/2)*(c+d*x)^(1/4)),x,9,-2/3*(c+d*x)^(3/4)/((b*c-a*d)*(a+b*x)^(3/2))+d*(c+d*x)^(3/4)/((b*c-a*d)^2*sqrt(a+b*x))-d*EllipticE(b^(1/4)*(c+d*x)^(1/4)/(b*c-a*d)^(1/4),I)*sqrt(-d*(a+b*x)/(b*c-a*d))/(b^(3/4)*(b*c-a*d)^(5/4)*sqrt(a+b*x))+d*EllipticF(b^(1/4)*(c+d*x)^(1/4)/(b*c-a*d)^(1/4),I)*sqrt(-d*(a+b*x)/(b*c-a*d))/(b^(3/4)*(b*c-a*d)^(5/4)*sqrt(a+b*x))],
[(a+b*x)^(3/2)/(c+d*x)^(3/4),x,5,4/7*(a+b*x)^(3/2)*(c+d*x)^(1/4)/d-8/7*(b*c-a*d)*(c+d*x)^(1/4)*sqrt(a+b*x)/d^2+16/7*(b*c-a*d)^(9/4)*EllipticF(b^(1/4)*(c+d*x)^(1/4)/(b*c-a*d)^(1/4),I)*sqrt(-d*(a+b*x)/(b*c-a*d))/(b^(1/4)*d^3*sqrt(a+b*x))],
[(a+b*x)^(1/2)/(c+d*x)^(3/4),x,4,4/3*(c+d*x)^(1/4)*sqrt(a+b*x)/d-8/3*(b*c-a*d)^(5/4)*EllipticF(b^(1/4)*(c+d*x)^(1/4)/(b*c-a*d)^(1/4),I)*sqrt(-d*(a+b*x)/(b*c-a*d))/(b^(1/4)*d^2*sqrt(a+b*x))],
[1/((a+b*x)^(1/2)*(c+d*x)^(3/4)),x,3,4*(b*c-a*d)^(1/4)*EllipticF(b^(1/4)*(c+d*x)^(1/4)/(b*c-a*d)^(1/4),I)*sqrt(-d*(a+b*x)/(b*c-a*d))/(b^(1/4)*d*sqrt(a+b*x))],
[1/((a+b*x)^(3/2)*(c+d*x)^(3/4)),x,4,-2*(c+d*x)^(1/4)/((b*c-a*d)*sqrt(a+b*x))-2*EllipticF(b^(1/4)*(c+d*x)^(1/4)/(b*c-a*d)^(1/4),I)*sqrt(-d*(a+b*x)/(b*c-a*d))/(b^(1/4)*(b*c-a*d)^(3/4)*sqrt(a+b*x))],
[1/((a+b*x)^(5/2)*(c+d*x)^(3/4)),x,5,-2/3*(c+d*x)^(1/4)/((b*c-a*d)*(a+b*x)^(3/2))+5/3*d*(c+d*x)^(1/4)/((b*c-a*d)^2*sqrt(a+b*x))+5/3*d*EllipticF(b^(1/4)*(c+d*x)^(1/4)/(b*c-a*d)^(1/4),I)*sqrt(-d*(a+b*x)/(b*c-a*d))/(b^(1/4)*(b*c-a*d)^(7/4)*sqrt(a+b*x))],
[(a+b*x)^(5/2)/(c+d*x)^(5/4),x,10,-4*(a+b*x)^(5/2)/(d*(c+d*x)^(1/4))+40/9*b*(a+b*x)^(3/2)*(c+d*x)^(3/4)/d^2-16/3*b*(b*c-a*d)*(c+d*x)^(3/4)*sqrt(a+b*x)/d^3+32/3*b^(1/4)*(b*c-a*d)^(11/4)*EllipticE(b^(1/4)*(c+d*x)^(1/4)/(b*c-a*d)^(1/4),I)*sqrt(-d*(a+b*x)/(b*c-a*d))/(d^4*sqrt(a+b*x))-32/3*b^(1/4)*(b*c-a*d)^(11/4)*EllipticF(b^(1/4)*(c+d*x)^(1/4)/(b*c-a*d)^(1/4),I)*sqrt(-d*(a+b*x)/(b*c-a*d))/(d^4*sqrt(a+b*x))],
[(a+b*x)^(3/2)/(c+d*x)^(5/4),x,9,-4*(a+b*x)^(3/2)/(d*(c+d*x)^(1/4))+24/5*b*(c+d*x)^(3/4)*sqrt(a+b*x)/d^2-48/5*b^(1/4)*(b*c-a*d)^(7/4)*EllipticE(b^(1/4)*(c+d*x)^(1/4)/(b*c-a*d)^(1/4),I)*sqrt(-d*(a+b*x)/(b*c-a*d))/(d^3*sqrt(a+b*x))+48/5*b^(1/4)*(b*c-a*d)^(7/4)*EllipticF(b^(1/4)*(c+d*x)^(1/4)/(b*c-a*d)^(1/4),I)*sqrt(-d*(a+b*x)/(b*c-a*d))/(d^3*sqrt(a+b*x))],
[(a+b*x)^(1/2)/(c+d*x)^(5/4),x,8,-4*sqrt(a+b*x)/(d*(c+d*x)^(1/4))+8*b^(1/4)*(b*c-a*d)^(3/4)*EllipticE(b^(1/4)*(c+d*x)^(1/4)/(b*c-a*d)^(1/4),I)*sqrt(-d*(a+b*x)/(b*c-a*d))/(d^2*sqrt(a+b*x))-8*b^(1/4)*(b*c-a*d)^(3/4)*EllipticF(b^(1/4)*(c+d*x)^(1/4)/(b*c-a*d)^(1/4),I)*sqrt(-d*(a+b*x)/(b*c-a*d))/(d^2*sqrt(a+b*x))],
[1/((a+b*x)^(1/2)*(c+d*x)^(5/4)),x,8,4*sqrt(a+b*x)/((b*c-a*d)*(c+d*x)^(1/4))-4*b^(1/4)*EllipticE(b^(1/4)*(c+d*x)^(1/4)/(b*c-a*d)^(1/4),I)*sqrt(-d*(a+b*x)/(b*c-a*d))/(d*(b*c-a*d)^(1/4)*sqrt(a+b*x))+4*b^(1/4)*EllipticF(b^(1/4)*(c+d*x)^(1/4)/(b*c-a*d)^(1/4),I)*sqrt(-d*(a+b*x)/(b*c-a*d))/(d*(b*c-a*d)^(1/4)*sqrt(a+b*x))],
[1/((a+b*x)^(3/2)*(c+d*x)^(5/4)),x,9,(-2)/((b*c-a*d)*(c+d*x)^(1/4)*sqrt(a+b*x))-6*d*sqrt(a+b*x)/((b*c-a*d)^2*(c+d*x)^(1/4))+6*b^(1/4)*EllipticE(b^(1/4)*(c+d*x)^(1/4)/(b*c-a*d)^(1/4),I)*sqrt(-d*(a+b*x)/(b*c-a*d))/((b*c-a*d)^(5/4)*sqrt(a+b*x))-6*b^(1/4)*EllipticF(b^(1/4)*(c+d*x)^(1/4)/(b*c-a*d)^(1/4),I)*sqrt(-d*(a+b*x)/(b*c-a*d))/((b*c-a*d)^(5/4)*sqrt(a+b*x))],
[1/((a+b*x)^(5/2)*(c+d*x)^(5/4)),x,10,(-2/3)/((b*c-a*d)*(a+b*x)^(3/2)*(c+d*x)^(1/4))+7/3*d/((b*c-a*d)^2*(c+d*x)^(1/4)*sqrt(a+b*x))+7*d^2*sqrt(a+b*x)/((b*c-a*d)^3*(c+d*x)^(1/4))-7*b^(1/4)*d*EllipticE(b^(1/4)*(c+d*x)^(1/4)/(b*c-a*d)^(1/4),I)*sqrt(-d*(a+b*x)/(b*c-a*d))/((b*c-a*d)^(9/4)*sqrt(a+b*x))+7*b^(1/4)*d*EllipticF(b^(1/4)*(c+d*x)^(1/4)/(b*c-a*d)^(1/4),I)*sqrt(-d*(a+b*x)/(b*c-a*d))/((b*c-a*d)^(9/4)*sqrt(a+b*x))],
[(a+b*x)^(7/2)/(c+d*x)^(7/4),x,7,-4/3*(a+b*x)^(7/2)/(d*(c+d*x)^(3/4))-80/33*b*(b*c-a*d)*(a+b*x)^(3/2)*(c+d*x)^(1/4)/d^3+56/33*b*(a+b*x)^(5/2)*(c+d*x)^(1/4)/d^2+160/33*b*(b*c-a*d)^2*(c+d*x)^(1/4)*sqrt(a+b*x)/d^4-320/33*b^(3/4)*(b*c-a*d)^(13/4)*EllipticF(b^(1/4)*(c+d*x)^(1/4)/(b*c-a*d)^(1/4),I)*sqrt(-d*(a+b*x)/(b*c-a*d))/(d^5*sqrt(a+b*x))],
[(a+b*x)^(3/2)/(c+d*x)^(7/4),x,5,-4/3*(a+b*x)^(3/2)/(d*(c+d*x)^(3/4))+8/3*b*(c+d*x)^(1/4)*sqrt(a+b*x)/d^2-16/3*b^(3/4)*(b*c-a*d)^(5/4)*EllipticF(b^(1/4)*(c+d*x)^(1/4)/(b*c-a*d)^(1/4),I)*sqrt(-d*(a+b*x)/(b*c-a*d))/(d^3*sqrt(a+b*x))],
[(a+b*x)^(1/2)/(c+d*x)^(7/4),x,4,-4/3*sqrt(a+b*x)/(d*(c+d*x)^(3/4))+8/3*b^(3/4)*(b*c-a*d)^(1/4)*EllipticF(b^(1/4)*(c+d*x)^(1/4)/(b*c-a*d)^(1/4),I)*sqrt(-d*(a+b*x)/(b*c-a*d))/(d^2*sqrt(a+b*x))],
[1/((a+b*x)^(1/2)*(c+d*x)^(7/4)),x,4,4/3*sqrt(a+b*x)/((b*c-a*d)*(c+d*x)^(3/4))+4/3*b^(3/4)*EllipticF(b^(1/4)*(c+d*x)^(1/4)/(b*c-a*d)^(1/4),I)*sqrt(-d*(a+b*x)/(b*c-a*d))/(d*(b*c-a*d)^(3/4)*sqrt(a+b*x))],
[1/((a+b*x)^(3/2)*(c+d*x)^(7/4)),x,5,(-2)/((b*c-a*d)*(c+d*x)^(3/4)*sqrt(a+b*x))-10/3*d*sqrt(a+b*x)/((b*c-a*d)^2*(c+d*x)^(3/4))-10/3*b^(3/4)*EllipticF(b^(1/4)*(c+d*x)^(1/4)/(b*c-a*d)^(1/4),I)*sqrt(-d*(a+b*x)/(b*c-a*d))/((b*c-a*d)^(7/4)*sqrt(a+b*x))],
[1/((a+b*x)^(5/2)*(c+d*x)^(7/4)),x,6,(-2/3)/((b*c-a*d)*(a+b*x)^(3/2)*(c+d*x)^(3/4))+3*d/((b*c-a*d)^2*(c+d*x)^(3/4)*sqrt(a+b*x))+5*d^2*sqrt(a+b*x)/((b*c-a*d)^3*(c+d*x)^(3/4))+5*b^(3/4)*d*EllipticF(b^(1/4)*(c+d*x)^(1/4)/(b*c-a*d)^(1/4),I)*sqrt(-d*(a+b*x)/(b*c-a*d))/((b*c-a*d)^(11/4)*sqrt(a+b*x))],
[(a+b*x)^(7/2)/(c+d*x)^(9/4),x,11,-4/5*(a+b*x)^(7/2)/(d*(c+d*x)^(5/4))-56/5*b*(a+b*x)^(5/2)/(d^2*(c+d*x)^(1/4))+112/9*b^2*(a+b*x)^(3/2)*(c+d*x)^(3/4)/d^3-224/15*b^2*(b*c-a*d)*(c+d*x)^(3/4)*sqrt(a+b*x)/d^4+448/15*b^(5/4)*(b*c-a*d)^(11/4)*EllipticE(b^(1/4)*(c+d*x)^(1/4)/(b*c-a*d)^(1/4),I)*sqrt(-d*(a+b*x)/(b*c-a*d))/(d^5*sqrt(a+b*x))-448/15*b^(5/4)*(b*c-a*d)^(11/4)*EllipticF(b^(1/4)*(c+d*x)^(1/4)/(b*c-a*d)^(1/4),I)*sqrt(-d*(a+b*x)/(b*c-a*d))/(d^5*sqrt(a+b*x))],
[(a+b*x)^(5/2)/(c+d*x)^(9/4),x,10,-4/5*(a+b*x)^(5/2)/(d*(c+d*x)^(5/4))-8*b*(a+b*x)^(3/2)/(d^2*(c+d*x)^(1/4))+48/5*b^2*(c+d*x)^(3/4)*sqrt(a+b*x)/d^3-96/5*b^(5/4)*(b*c-a*d)^(7/4)*EllipticE(b^(1/4)*(c+d*x)^(1/4)/(b*c-a*d)^(1/4),I)*sqrt(-d*(a+b*x)/(b*c-a*d))/(d^4*sqrt(a+b*x))+96/5*b^(5/4)*(b*c-a*d)^(7/4)*EllipticF(b^(1/4)*(c+d*x)^(1/4)/(b*c-a*d)^(1/4),I)*sqrt(-d*(a+b*x)/(b*c-a*d))/(d^4*sqrt(a+b*x))],
[(a+b*x)^(3/2)/(c+d*x)^(9/4),x,9,-4/5*(a+b*x)^(3/2)/(d*(c+d*x)^(5/4))-24/5*b*sqrt(a+b*x)/(d^2*(c+d*x)^(1/4))+48/5*b^(5/4)*(b*c-a*d)^(3/4)*EllipticE(b^(1/4)*(c+d*x)^(1/4)/(b*c-a*d)^(1/4),I)*sqrt(-d*(a+b*x)/(b*c-a*d))/(d^3*sqrt(a+b*x))-48/5*b^(5/4)*(b*c-a*d)^(3/4)*EllipticF(b^(1/4)*(c+d*x)^(1/4)/(b*c-a*d)^(1/4),I)*sqrt(-d*(a+b*x)/(b*c-a*d))/(d^3*sqrt(a+b*x))],
[(a+b*x)^(1/2)/(c+d*x)^(9/4),x,9,-4/5*sqrt(a+b*x)/(d*(c+d*x)^(5/4))+8/5*b*sqrt(a+b*x)/(d*(b*c-a*d)*(c+d*x)^(1/4))-8/5*b^(5/4)*EllipticE(b^(1/4)*(c+d*x)^(1/4)/(b*c-a*d)^(1/4),I)*sqrt(-d*(a+b*x)/(b*c-a*d))/(d^2*(b*c-a*d)^(1/4)*sqrt(a+b*x))+8/5*b^(5/4)*EllipticF(b^(1/4)*(c+d*x)^(1/4)/(b*c-a*d)^(1/4),I)*sqrt(-d*(a+b*x)/(b*c-a*d))/(d^2*(b*c-a*d)^(1/4)*sqrt(a+b*x))],
[1/((a+b*x)^(1/2)*(c+d*x)^(9/4)),x,9,4/5*sqrt(a+b*x)/((b*c-a*d)*(c+d*x)^(5/4))+12/5*b*sqrt(a+b*x)/((b*c-a*d)^2*(c+d*x)^(1/4))-12/5*b^(5/4)*EllipticE(b^(1/4)*(c+d*x)^(1/4)/(b*c-a*d)^(1/4),I)*sqrt(-d*(a+b*x)/(b*c-a*d))/(d*(b*c-a*d)^(5/4)*sqrt(a+b*x))+12/5*b^(5/4)*EllipticF(b^(1/4)*(c+d*x)^(1/4)/(b*c-a*d)^(1/4),I)*sqrt(-d*(a+b*x)/(b*c-a*d))/(d*(b*c-a*d)^(5/4)*sqrt(a+b*x))],
[1/((a+b*x)^(3/2)*(c+d*x)^(9/4)),x,10,(-2)/((b*c-a*d)*(c+d*x)^(5/4)*sqrt(a+b*x))-14/5*d*sqrt(a+b*x)/((b*c-a*d)^2*(c+d*x)^(5/4))-42/5*b*d*sqrt(a+b*x)/((b*c-a*d)^3*(c+d*x)^(1/4))+42/5*b^(5/4)*EllipticE(b^(1/4)*(c+d*x)^(1/4)/(b*c-a*d)^(1/4),I)*sqrt(-d*(a+b*x)/(b*c-a*d))/((b*c-a*d)^(9/4)*sqrt(a+b*x))-42/5*b^(5/4)*EllipticF(b^(1/4)*(c+d*x)^(1/4)/(b*c-a*d)^(1/4),I)*sqrt(-d*(a+b*x)/(b*c-a*d))/((b*c-a*d)^(9/4)*sqrt(a+b*x))],
[1/((a+b*x)^(5/2)*(c+d*x)^(9/4)),x,11,(-2/3)/((b*c-a*d)*(a+b*x)^(3/2)*(c+d*x)^(5/4))+11/3*d/((b*c-a*d)^2*(c+d*x)^(5/4)*sqrt(a+b*x))+77/15*d^2*sqrt(a+b*x)/((b*c-a*d)^3*(c+d*x)^(5/4))+77/5*b*d^2*sqrt(a+b*x)/((b*c-a*d)^4*(c+d*x)^(1/4))-77/5*b^(5/4)*d*EllipticE(b^(1/4)*(c+d*x)^(1/4)/(b*c-a*d)^(1/4),I)*sqrt(-d*(a+b*x)/(b*c-a*d))/((b*c-a*d)^(13/4)*sqrt(a+b*x))+77/5*b^(5/4)*d*EllipticF(b^(1/4)*(c+d*x)^(1/4)/(b*c-a*d)^(1/4),I)*sqrt(-d*(a+b*x)/(b*c-a*d))/((b*c-a*d)^(13/4)*sqrt(a+b*x))],

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

# n>0
[(a+b*x)^(3/4)*(c+d*x)^(5/4),x,8,5/96*(b*c-a*d)^2*(a+b*x)^(3/4)*(c+d*x)^(1/4)/(b^2*d)+5/24*(b*c-a*d)*(a+b*x)^(7/4)*(c+d*x)^(1/4)/b^2+1/3*(a+b*x)^(7/4)*(c+d*x)^(5/4)/b+5/64*(b*c-a*d)^3*arctan(d^(1/4)*(a+b*x)^(1/4)/(b^(1/4)*(c+d*x)^(1/4)))/(b^(9/4)*d^(7/4))-5/64*(b*c-a*d)^3*arctanh(d^(1/4)*(a+b*x)^(1/4)/(b^(1/4)*(c+d*x)^(1/4)))/(b^(9/4)*d^(7/4))],
[(c+d*x)^(5/4)/(a+b*x)^(1/4),x,7,5/8*(b*c-a*d)*(a+b*x)^(3/4)*(c+d*x)^(1/4)/b^2+1/2*(a+b*x)^(3/4)*(c+d*x)^(5/4)/b-5/16*(b*c-a*d)^2*arctan(d^(1/4)*(a+b*x)^(1/4)/(b^(1/4)*(c+d*x)^(1/4)))/(b^(9/4)*d^(3/4))+5/16*(b*c-a*d)^2*arctanh(d^(1/4)*(a+b*x)^(1/4)/(b^(1/4)*(c+d*x)^(1/4)))/(b^(9/4)*d^(3/4))],
[(c+d*x)^(5/4)/(a+b*x)^(5/4),x,7,5*d*(a+b*x)^(3/4)*(c+d*x)^(1/4)/b^2-4*(c+d*x)^(5/4)/(b*(a+b*x)^(1/4))-5/2*d^(1/4)*(b*c-a*d)*arctan(d^(1/4)*(a+b*x)^(1/4)/(b^(1/4)*(c+d*x)^(1/4)))/b^(9/4)+5/2*d^(1/4)*(b*c-a*d)*arctanh(d^(1/4)*(a+b*x)^(1/4)/(b^(1/4)*(c+d*x)^(1/4)))/b^(9/4)],
[(c+d*x)^(5/4)/(a+b*x)^(9/4),x,7,-4*d*(c+d*x)^(1/4)/(b^2*(a+b*x)^(1/4))-4/5*(c+d*x)^(5/4)/(b*(a+b*x)^(5/4))-2*d^(5/4)*arctan(d^(1/4)*(a+b*x)^(1/4)/(b^(1/4)*(c+d*x)^(1/4)))/b^(9/4)+2*d^(5/4)*arctanh(d^(1/4)*(a+b*x)^(1/4)/(b^(1/4)*(c+d*x)^(1/4)))/b^(9/4)],
[(c+d*x)^(5/4)/(a+b*x)^(13/4),x,1,-4/9*(c+d*x)^(9/4)/((b*c-a*d)*(a+b*x)^(9/4))],
[(c+d*x)^(5/4)/(a+b*x)^(17/4),x,2,-4/13*(c+d*x)^(9/4)/((b*c-a*d)*(a+b*x)^(13/4))+16/117*d*(c+d*x)^(9/4)/((b*c-a*d)^2*(a+b*x)^(9/4))],
[(c+d*x)^(5/4)/(a+b*x)^(21/4),x,3,-4/17*(c+d*x)^(9/4)/((b*c-a*d)*(a+b*x)^(17/4))+32/221*d*(c+d*x)^(9/4)/((b*c-a*d)^2*(a+b*x)^(13/4))-128/1989*d^2*(c+d*x)^(9/4)/((b*c-a*d)^3*(a+b*x)^(9/4))],
[(c+d*x)^(5/4)/(a+b*x)^(25/4),x,4,-4/21*(c+d*x)^(9/4)/((b*c-a*d)*(a+b*x)^(21/4))+16/119*d*(c+d*x)^(9/4)/((b*c-a*d)^2*(a+b*x)^(17/4))-128/1547*d^2*(c+d*x)^(9/4)/((b*c-a*d)^3*(a+b*x)^(13/4))+512/13923*d^3*(c+d*x)^(9/4)/((b*c-a*d)^4*(a+b*x)^(9/4))],
[(a+b*x)^(5/4)*(c+d*x)^(5/4),x,7,-5/84*(b*c-a*d)^3*(a+b*x)^(1/4)*(c+d*x)^(1/4)/(b^2*d^2)+1/42*(b*c-a*d)^2*(a+b*x)^(5/4)*(c+d*x)^(1/4)/(b^2*d)+1/7*(b*c-a*d)*(a+b*x)^(9/4)*(c+d*x)^(1/4)/b^2+2/7*(a+b*x)^(9/4)*(c+d*x)^(5/4)/b+5/168*(b*c-a*d)^(9/2)*((a+b*x)*(c+d*x))^(3/4)*sqrt(cos(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d)))^2)/cos(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d)))*EllipticF(sin(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d))),sqrt(1/2))*(1+2*sqrt(b)*sqrt(d)*sqrt((a+b*x)*(c+d*x))/(b*c-a*d))*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt((a*d+b*(c+2*d*x))^2/((b*c-a*d)^2*(1+2*sqrt(b)*sqrt(d)*sqrt((a+b*x)*(c+d*x))/(b*c-a*d))^2))/(b^(9/4)*d^(9/4)*(a+b*x)^(3/4)*(c+d*x)^(3/4)*(b*c+a*d+2*b*d*x)*sqrt(2)*sqrt((a*d+b*(c+2*d*x))^2))],
[(a+b*x)^(1/4)*(c+d*x)^(5/4),x,6,1/6*(b*c-a*d)^2*(a+b*x)^(1/4)*(c+d*x)^(1/4)/(b^2*d)+1/3*(b*c-a*d)*(a+b*x)^(5/4)*(c+d*x)^(1/4)/b^2+2/5*(a+b*x)^(5/4)*(c+d*x)^(5/4)/b-1/12*(b*c-a*d)^(7/2)*((a+b*x)*(c+d*x))^(3/4)*sqrt(cos(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d)))^2)/cos(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d)))*EllipticF(sin(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d))),sqrt(1/2))*(1+2*sqrt(b)*sqrt(d)*sqrt((a+b*x)*(c+d*x))/(b*c-a*d))*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt((a*d+b*(c+2*d*x))^2/((b*c-a*d)^2*(1+2*sqrt(b)*sqrt(d)*sqrt((a+b*x)*(c+d*x))/(b*c-a*d))^2))/(b^(9/4)*d^(5/4)*(a+b*x)^(3/4)*(c+d*x)^(3/4)*(b*c+a*d+2*b*d*x)*sqrt(2)*sqrt((a*d+b*(c+2*d*x))^2))],
[(c+d*x)^(5/4)/(a+b*x)^(3/4),x,5,5/3*(b*c-a*d)*(a+b*x)^(1/4)*(c+d*x)^(1/4)/b^2+2/3*(a+b*x)^(1/4)*(c+d*x)^(5/4)/b+5/6*(b*c-a*d)^(5/2)*((a+b*x)*(c+d*x))^(3/4)*sqrt(cos(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d)))^2)/cos(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d)))*EllipticF(sin(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d))),sqrt(1/2))*(1+2*sqrt(b)*sqrt(d)*sqrt((a+b*x)*(c+d*x))/(b*c-a*d))*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt((a*d+b*(c+2*d*x))^2/((b*c-a*d)^2*(1+2*sqrt(b)*sqrt(d)*sqrt((a+b*x)*(c+d*x))/(b*c-a*d))^2))/(b^(9/4)*d^(1/4)*(a+b*x)^(3/4)*(c+d*x)^(3/4)*(b*c+a*d+2*b*d*x)*sqrt(2)*sqrt((a*d+b*(c+2*d*x))^2))],
[(c+d*x)^(5/4)/(a+b*x)^(7/4),x,5,10/3*d*(a+b*x)^(1/4)*(c+d*x)^(1/4)/b^2-4/3*(c+d*x)^(5/4)/(b*(a+b*x)^(3/4))+5/3*d^(3/4)*(b*c-a*d)^(3/2)*((a+b*x)*(c+d*x))^(3/4)*sqrt(cos(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d)))^2)/cos(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d)))*EllipticF(sin(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d))),sqrt(1/2))*(1+2*sqrt(b)*sqrt(d)*sqrt((a+b*x)*(c+d*x))/(b*c-a*d))*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt((a*d+b*(c+2*d*x))^2/((b*c-a*d)^2*(1+2*sqrt(b)*sqrt(d)*sqrt((a+b*x)*(c+d*x))/(b*c-a*d))^2))/(b^(9/4)*(a+b*x)^(3/4)*(c+d*x)^(3/4)*(b*c+a*d+2*b*d*x)*sqrt(2)*sqrt((a*d+b*(c+2*d*x))^2))],
[(c+d*x)^(5/4)/(a+b*x)^(11/4),x,5,-20/21*d*(c+d*x)^(1/4)/(b^2*(a+b*x)^(3/4))-4/7*(c+d*x)^(5/4)/(b*(a+b*x)^(7/4))+5/21*d^(7/4)*((a+b*x)*(c+d*x))^(3/4)*sqrt(cos(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d)))^2)/cos(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d)))*EllipticF(sin(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d))),sqrt(1/2))*sqrt(2)*sqrt(b*c-a*d)*(1+2*sqrt(b)*sqrt(d)*sqrt((a+b*x)*(c+d*x))/(b*c-a*d))*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt((a*d+b*(c+2*d*x))^2/((b*c-a*d)^2*(1+2*sqrt(b)*sqrt(d)*sqrt((a+b*x)*(c+d*x))/(b*c-a*d))^2))/(b^(9/4)*(a+b*x)^(3/4)*(c+d*x)^(3/4)*(b*c+a*d+2*b*d*x)*sqrt((a*d+b*(c+2*d*x))^2))],
[(c+d*x)^(5/4)/(a+b*x)^(15/4),x,6,-20/77*d*(c+d*x)^(1/4)/(b^2*(a+b*x)^(7/4))-20/231*d^2*(c+d*x)^(1/4)/(b^2*(b*c-a*d)*(a+b*x)^(3/4))-4/11*(c+d*x)^(5/4)/(b*(a+b*x)^(11/4))-10/231*d^(11/4)*((a+b*x)*(c+d*x))^(3/4)*sqrt(cos(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d)))^2)/cos(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d)))*EllipticF(sin(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d))),sqrt(1/2))*sqrt(2)*(1+2*sqrt(b)*sqrt(d)*sqrt((a+b*x)*(c+d*x))/(b*c-a*d))*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt((a*d+b*(c+2*d*x))^2/((b*c-a*d)^2*(1+2*sqrt(b)*sqrt(d)*sqrt((a+b*x)*(c+d*x))/(b*c-a*d))^2))/(b^(9/4)*(a+b*x)^(3/4)*(c+d*x)^(3/4)*(b*c+a*d+2*b*d*x)*sqrt(b*c-a*d)*sqrt((a*d+b*(c+2*d*x))^2))],
[(c+d*x)^(5/4)/(a+b*x)^(19/4),x,7,-4/33*d*(c+d*x)^(1/4)/(b^2*(a+b*x)^(11/4))-4/231*d^2*(c+d*x)^(1/4)/(b^2*(b*c-a*d)*(a+b*x)^(7/4))+8/231*d^3*(c+d*x)^(1/4)/(b^2*(b*c-a*d)^2*(a+b*x)^(3/4))-4/15*(c+d*x)^(5/4)/(b*(a+b*x)^(15/4))+4/231*d^(15/4)*((a+b*x)*(c+d*x))^(3/4)*sqrt(cos(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d)))^2)/cos(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d)))*EllipticF(sin(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d))),sqrt(1/2))*sqrt(2)*(1+2*sqrt(b)*sqrt(d)*sqrt((a+b*x)*(c+d*x))/(b*c-a*d))*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt((a*d+b*(c+2*d*x))^2/((b*c-a*d)^2*(1+2*sqrt(b)*sqrt(d)*sqrt((a+b*x)*(c+d*x))/(b*c-a*d))^2))/(b^(9/4)*(b*c-a*d)^(3/2)*(a+b*x)^(3/4)*(c+d*x)^(3/4)*(b*c+a*d+2*b*d*x)*sqrt((a*d+b*(c+2*d*x))^2))],

# n<0
[(a+b*x)^(5/4)/(c+d*x)^(1/4),x,7,-5/8*(b*c-a*d)*(a+b*x)^(1/4)*(c+d*x)^(3/4)/d^2+1/2*(a+b*x)^(5/4)*(c+d*x)^(3/4)/d+5/16*(b*c-a*d)^2*arctan(d^(1/4)*(a+b*x)^(1/4)/(b^(1/4)*(c+d*x)^(1/4)))/(b^(3/4)*d^(9/4))+5/16*(b*c-a*d)^2*arctanh(d^(1/4)*(a+b*x)^(1/4)/(b^(1/4)*(c+d*x)^(1/4)))/(b^(3/4)*d^(9/4))],
[(a+b*x)^(1/4)/(c+d*x)^(1/4),x,6,(a+b*x)^(1/4)*(c+d*x)^(3/4)/d-1/2*(b*c-a*d)*arctan(d^(1/4)*(a+b*x)^(1/4)/(b^(1/4)*(c+d*x)^(1/4)))/(b^(3/4)*d^(5/4))-1/2*(b*c-a*d)*arctanh(d^(1/4)*(a+b*x)^(1/4)/(b^(1/4)*(c+d*x)^(1/4)))/(b^(3/4)*d^(5/4))],
[1/((a+b*x)^(3/4)*(c+d*x)^(1/4)),x,5,2*arctan(d^(1/4)*(a+b*x)^(1/4)/(b^(1/4)*(c+d*x)^(1/4)))/(b^(3/4)*d^(1/4))+2*arctanh(d^(1/4)*(a+b*x)^(1/4)/(b^(1/4)*(c+d*x)^(1/4)))/(b^(3/4)*d^(1/4))],
[1/((a+b*x)^(7/4)*(c+d*x)^(1/4)),x,1,-4/3*(c+d*x)^(3/4)/((b*c-a*d)*(a+b*x)^(3/4))],
[1/((a+b*x)^(11/4)*(c+d*x)^(1/4)),x,2,-4/7*(c+d*x)^(3/4)/((b*c-a*d)*(a+b*x)^(7/4))+16/21*d*(c+d*x)^(3/4)/((b*c-a*d)^2*(a+b*x)^(3/4))],
[1/((a+b*x)^(15/4)*(c+d*x)^(1/4)),x,3,-4/11*(c+d*x)^(3/4)/((b*c-a*d)*(a+b*x)^(11/4))+32/77*d*(c+d*x)^(3/4)/((b*c-a*d)^2*(a+b*x)^(7/4))-128/231*d^2*(c+d*x)^(3/4)/((b*c-a*d)^3*(a+b*x)^(3/4))],
[1/((a+b*x)^(19/4)*(c+d*x)^(1/4)),x,4,-4/15*(c+d*x)^(3/4)/((b*c-a*d)*(a+b*x)^(15/4))+16/55*d*(c+d*x)^(3/4)/((b*c-a*d)^2*(a+b*x)^(11/4))-128/385*d^2*(c+d*x)^(3/4)/((b*c-a*d)^3*(a+b*x)^(7/4))+512/1155*d^3*(c+d*x)^(3/4)/((b*c-a*d)^4*(a+b*x)^(3/4))],
[(a+b*x)^(7/4)/(c+d*x)^(1/4),x,7,-7/15*(b*c-a*d)*(a+b*x)^(3/4)*(c+d*x)^(3/4)/d^2+2/5*(a+b*x)^(7/4)*(c+d*x)^(3/4)/d+7/10*(b*c-a*d)*sqrt((a+b*x)*(c+d*x))*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt((a*d+b*(c+2*d*x))^2)/(d^(5/2)*(a+b*x)^(1/4)*(c+d*x)^(1/4)*(b*c+a*d+2*b*d*x)*sqrt(b)*(1+2*sqrt(b)*sqrt(d)*sqrt((a+b*x)*(c+d*x))/(b*c-a*d)))-7/10*(b*c-a*d)^(7/2)*((a+b*x)*(c+d*x))^(1/4)*sqrt(cos(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d)))^2)/cos(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d)))*EllipticE(sin(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d))),sqrt(1/2))*(1+2*sqrt(b)*sqrt(d)*sqrt((a+b*x)*(c+d*x))/(b*c-a*d))*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt((a*d+b*(c+2*d*x))^2/((b*c-a*d)^2*(1+2*sqrt(b)*sqrt(d)*sqrt((a+b*x)*(c+d*x))/(b*c-a*d))^2))/(b^(3/4)*d^(11/4)*(a+b*x)^(1/4)*(c+d*x)^(1/4)*(b*c+a*d+2*b*d*x)*sqrt(2)*sqrt((a*d+b*(c+2*d*x))^2))+7/20*(b*c-a*d)^(7/2)*((a+b*x)*(c+d*x))^(1/4)*sqrt(cos(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d)))^2)/cos(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d)))*EllipticF(sin(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d))),sqrt(1/2))*(1+2*sqrt(b)*sqrt(d)*sqrt((a+b*x)*(c+d*x))/(b*c-a*d))*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt((a*d+b*(c+2*d*x))^2/((b*c-a*d)^2*(1+2*sqrt(b)*sqrt(d)*sqrt((a+b*x)*(c+d*x))/(b*c-a*d))^2))/(b^(3/4)*d^(11/4)*(a+b*x)^(1/4)*(c+d*x)^(1/4)*(b*c+a*d+2*b*d*x)*sqrt(2)*sqrt((a*d+b*(c+2*d*x))^2))],
[(a+b*x)^(3/4)/(c+d*x)^(1/4),x,6,2/3*(a+b*x)^(3/4)*(c+d*x)^(3/4)/d-sqrt((a+b*x)*(c+d*x))*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt((a*d+b*(c+2*d*x))^2)/(d^(3/2)*(a+b*x)^(1/4)*(c+d*x)^(1/4)*(b*c+a*d+2*b*d*x)*sqrt(b)*(1+2*sqrt(b)*sqrt(d)*sqrt((a+b*x)*(c+d*x))/(b*c-a*d)))+(b*c-a*d)^(5/2)*((a+b*x)*(c+d*x))^(1/4)*sqrt(cos(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d)))^2)/cos(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d)))*EllipticE(sin(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d))),sqrt(1/2))*(1+2*sqrt(b)*sqrt(d)*sqrt((a+b*x)*(c+d*x))/(b*c-a*d))*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt((a*d+b*(c+2*d*x))^2/((b*c-a*d)^2*(1+2*sqrt(b)*sqrt(d)*sqrt((a+b*x)*(c+d*x))/(b*c-a*d))^2))/(b^(3/4)*d^(7/4)*(a+b*x)^(1/4)*(c+d*x)^(1/4)*(b*c+a*d+2*b*d*x)*sqrt(2)*sqrt((a*d+b*(c+2*d*x))^2))-1/2*(b*c-a*d)^(5/2)*((a+b*x)*(c+d*x))^(1/4)*sqrt(cos(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d)))^2)/cos(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d)))*EllipticF(sin(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d))),sqrt(1/2))*(1+2*sqrt(b)*sqrt(d)*sqrt((a+b*x)*(c+d*x))/(b*c-a*d))*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt((a*d+b*(c+2*d*x))^2/((b*c-a*d)^2*(1+2*sqrt(b)*sqrt(d)*sqrt((a+b*x)*(c+d*x))/(b*c-a*d))^2))/(b^(3/4)*d^(7/4)*(a+b*x)^(1/4)*(c+d*x)^(1/4)*(b*c+a*d+2*b*d*x)*sqrt(2)*sqrt((a*d+b*(c+2*d*x))^2))],
[1/((a+b*x)^(1/4)*(c+d*x)^(1/4)),x,5,2*sqrt((a+b*x)*(c+d*x))*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt((a*d+b*(c+2*d*x))^2)/((b*c-a*d)*(a+b*x)^(1/4)*(c+d*x)^(1/4)*(b*c+a*d+2*b*d*x)*sqrt(b)*sqrt(d)*(1+2*sqrt(b)*sqrt(d)*sqrt((a+b*x)*(c+d*x))/(b*c-a*d)))+(b*c-a*d)^(3/2)*((a+b*x)*(c+d*x))^(1/4)*sqrt(cos(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d)))^2)/cos(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d)))*EllipticF(sin(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d))),sqrt(1/2))*(1+2*sqrt(b)*sqrt(d)*sqrt((a+b*x)*(c+d*x))/(b*c-a*d))*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt((a*d+b*(c+2*d*x))^2/((b*c-a*d)^2*(1+2*sqrt(b)*sqrt(d)*sqrt((a+b*x)*(c+d*x))/(b*c-a*d))^2))/(b^(3/4)*d^(3/4)*(a+b*x)^(1/4)*(c+d*x)^(1/4)*(b*c+a*d+2*b*d*x)*sqrt(2)*sqrt((a*d+b*(c+2*d*x))^2))-(b*c-a*d)^(3/2)*((a+b*x)*(c+d*x))^(1/4)*sqrt(cos(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d)))^2)/cos(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d)))*EllipticE(sin(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d))),sqrt(1/2))*sqrt(2)*(1+2*sqrt(b)*sqrt(d)*sqrt((a+b*x)*(c+d*x))/(b*c-a*d))*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt((a*d+b*(c+2*d*x))^2/((b*c-a*d)^2*(1+2*sqrt(b)*sqrt(d)*sqrt((a+b*x)*(c+d*x))/(b*c-a*d))^2))/(b^(3/4)*d^(3/4)*(a+b*x)^(1/4)*(c+d*x)^(1/4)*(b*c+a*d+2*b*d*x)*sqrt((a*d+b*(c+2*d*x))^2))],
[1/((a+b*x)^(5/4)*(c+d*x)^(1/4)),x,6,-4*(c+d*x)^(3/4)/((b*c-a*d)*(a+b*x)^(1/4))+4*sqrt(d)*sqrt((a+b*x)*(c+d*x))*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt((a*d+b*(c+2*d*x))^2)/((b*c-a*d)^2*(a+b*x)^(1/4)*(c+d*x)^(1/4)*(b*c+a*d+2*b*d*x)*sqrt(b)*(1+2*sqrt(b)*sqrt(d)*sqrt((a+b*x)*(c+d*x))/(b*c-a*d)))-2*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(cos(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d)))^2)/cos(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d)))*EllipticE(sin(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d))),sqrt(1/2))*sqrt(2)*sqrt(b*c-a*d)*(1+2*sqrt(b)*sqrt(d)*sqrt((a+b*x)*(c+d*x))/(b*c-a*d))*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt((a*d+b*(c+2*d*x))^2/((b*c-a*d)^2*(1+2*sqrt(b)*sqrt(d)*sqrt((a+b*x)*(c+d*x))/(b*c-a*d))^2))/(b^(3/4)*(a+b*x)^(1/4)*(c+d*x)^(1/4)*(b*c+a*d+2*b*d*x)*sqrt((a*d+b*(c+2*d*x))^2))+d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(cos(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d)))^2)/cos(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d)))*EllipticF(sin(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d))),sqrt(1/2))*sqrt(2)*sqrt(b*c-a*d)*(1+2*sqrt(b)*sqrt(d)*sqrt((a+b*x)*(c+d*x))/(b*c-a*d))*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt((a*d+b*(c+2*d*x))^2/((b*c-a*d)^2*(1+2*sqrt(b)*sqrt(d)*sqrt((a+b*x)*(c+d*x))/(b*c-a*d))^2))/(b^(3/4)*(a+b*x)^(1/4)*(c+d*x)^(1/4)*(b*c+a*d+2*b*d*x)*sqrt((a*d+b*(c+2*d*x))^2))],
[1/((a+b*x)^(9/4)*(c+d*x)^(1/4)),x,7,-4/5*(c+d*x)^(3/4)/((b*c-a*d)*(a+b*x)^(5/4))+8/5*d*(c+d*x)^(3/4)/((b*c-a*d)^2*(a+b*x)^(1/4))-8/5*d^(3/2)*sqrt((a+b*x)*(c+d*x))*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt((a*d+b*(c+2*d*x))^2)/((b*c-a*d)^3*(a+b*x)^(1/4)*(c+d*x)^(1/4)*(b*c+a*d+2*b*d*x)*sqrt(b)*(1+2*sqrt(b)*sqrt(d)*sqrt((a+b*x)*(c+d*x))/(b*c-a*d)))+4/5*d^(5/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(cos(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d)))^2)/cos(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d)))*EllipticE(sin(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d))),sqrt(1/2))*sqrt(2)*(1+2*sqrt(b)*sqrt(d)*sqrt((a+b*x)*(c+d*x))/(b*c-a*d))*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt((a*d+b*(c+2*d*x))^2/((b*c-a*d)^2*(1+2*sqrt(b)*sqrt(d)*sqrt((a+b*x)*(c+d*x))/(b*c-a*d))^2))/(b^(3/4)*(a+b*x)^(1/4)*(c+d*x)^(1/4)*(b*c+a*d+2*b*d*x)*sqrt(b*c-a*d)*sqrt((a*d+b*(c+2*d*x))^2))-2/5*d^(5/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(cos(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d)))^2)/cos(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d)))*EllipticF(sin(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d))),sqrt(1/2))*sqrt(2)*(1+2*sqrt(b)*sqrt(d)*sqrt((a+b*x)*(c+d*x))/(b*c-a*d))*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt((a*d+b*(c+2*d*x))^2/((b*c-a*d)^2*(1+2*sqrt(b)*sqrt(d)*sqrt((a+b*x)*(c+d*x))/(b*c-a*d))^2))/(b^(3/4)*(a+b*x)^(1/4)*(c+d*x)^(1/4)*(b*c+a*d+2*b*d*x)*sqrt(b*c-a*d)*sqrt((a*d+b*(c+2*d*x))^2))],
[(a+b*x)^(7/4)/(c+d*x)^(3/4),x,7,-7/8*(b*c-a*d)*(a+b*x)^(3/4)*(c+d*x)^(1/4)/d^2+1/2*(a+b*x)^(7/4)*(c+d*x)^(1/4)/d-21/16*(b*c-a*d)^2*arctan(d^(1/4)*(a+b*x)^(1/4)/(b^(1/4)*(c+d*x)^(1/4)))/(b^(1/4)*d^(11/4))+21/16*(b*c-a*d)^2*arctanh(d^(1/4)*(a+b*x)^(1/4)/(b^(1/4)*(c+d*x)^(1/4)))/(b^(1/4)*d^(11/4))],
[(a+b*x)^(3/4)/(c+d*x)^(3/4),x,6,(a+b*x)^(3/4)*(c+d*x)^(1/4)/d+3/2*(b*c-a*d)*arctan(d^(1/4)*(a+b*x)^(1/4)/(b^(1/4)*(c+d*x)^(1/4)))/(b^(1/4)*d^(7/4))-3/2*(b*c-a*d)*arctanh(d^(1/4)*(a+b*x)^(1/4)/(b^(1/4)*(c+d*x)^(1/4)))/(b^(1/4)*d^(7/4))],
[1/((a+b*x)^(1/4)*(c+d*x)^(3/4)),x,5,-2*arctan(d^(1/4)*(a+b*x)^(1/4)/(b^(1/4)*(c+d*x)^(1/4)))/(b^(1/4)*d^(3/4))+2*arctanh(d^(1/4)*(a+b*x)^(1/4)/(b^(1/4)*(c+d*x)^(1/4)))/(b^(1/4)*d^(3/4))],
[1/((a+b*x)^(5/4)*(c+d*x)^(3/4)),x,1,-4*(c+d*x)^(1/4)/((b*c-a*d)*(a+b*x)^(1/4))],
[1/((a+b*x)^(9/4)*(c+d*x)^(3/4)),x,2,-4/5*(c+d*x)^(1/4)/((b*c-a*d)*(a+b*x)^(5/4))+16/5*d*(c+d*x)^(1/4)/((b*c-a*d)^2*(a+b*x)^(1/4))],
[1/((a+b*x)^(13/4)*(c+d*x)^(3/4)),x,3,-4/9*(c+d*x)^(1/4)/((b*c-a*d)*(a+b*x)^(9/4))+32/45*d*(c+d*x)^(1/4)/((b*c-a*d)^2*(a+b*x)^(5/4))-128/45*d^2*(c+d*x)^(1/4)/((b*c-a*d)^3*(a+b*x)^(1/4))],
[1/((a+b*x)^(17/4)*(c+d*x)^(3/4)),x,4,-4/13*(c+d*x)^(1/4)/((b*c-a*d)*(a+b*x)^(13/4))+16/39*d*(c+d*x)^(1/4)/((b*c-a*d)^2*(a+b*x)^(9/4))-128/195*d^2*(c+d*x)^(1/4)/((b*c-a*d)^3*(a+b*x)^(5/4))+512/195*d^3*(c+d*x)^(1/4)/((b*c-a*d)^4*(a+b*x)^(1/4))],
[(a+b*x)^(5/4)/(c+d*x)^(3/4),x,5,-5/3*(b*c-a*d)*(a+b*x)^(1/4)*(c+d*x)^(1/4)/d^2+2/3*(a+b*x)^(5/4)*(c+d*x)^(1/4)/d+5/6*(b*c-a*d)^(5/2)*((a+b*x)*(c+d*x))^(3/4)*sqrt(cos(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d)))^2)/cos(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d)))*EllipticF(sin(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d))),sqrt(1/2))*(1+2*sqrt(b)*sqrt(d)*sqrt((a+b*x)*(c+d*x))/(b*c-a*d))*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt((a*d+b*(c+2*d*x))^2/((b*c-a*d)^2*(1+2*sqrt(b)*sqrt(d)*sqrt((a+b*x)*(c+d*x))/(b*c-a*d))^2))/(b^(1/4)*d^(9/4)*(a+b*x)^(3/4)*(c+d*x)^(3/4)*(b*c+a*d+2*b*d*x)*sqrt(2)*sqrt((a*d+b*(c+2*d*x))^2))],
[(a+b*x)^(1/4)/(c+d*x)^(3/4),x,4,2*(a+b*x)^(1/4)*(c+d*x)^(1/4)/d-(b*c-a*d)^(3/2)*((a+b*x)*(c+d*x))^(3/4)*sqrt(cos(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d)))^2)/cos(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d)))*EllipticF(sin(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d))),sqrt(1/2))*(1+2*sqrt(b)*sqrt(d)*sqrt((a+b*x)*(c+d*x))/(b*c-a*d))*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt((a*d+b*(c+2*d*x))^2/((b*c-a*d)^2*(1+2*sqrt(b)*sqrt(d)*sqrt((a+b*x)*(c+d*x))/(b*c-a*d))^2))/(b^(1/4)*d^(5/4)*(a+b*x)^(3/4)*(c+d*x)^(3/4)*(b*c+a*d+2*b*d*x)*sqrt(2)*sqrt((a*d+b*(c+2*d*x))^2))],
[1/((a+b*x)^(3/4)*(c+d*x)^(3/4)),x,3,((a+b*x)*(c+d*x))^(3/4)*sqrt(cos(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d)))^2)/cos(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d)))*EllipticF(sin(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d))),sqrt(1/2))*sqrt(2)*sqrt(b*c-a*d)*(1+2*sqrt(b)*sqrt(d)*sqrt((a+b*x)*(c+d*x))/(b*c-a*d))*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt((a*d+b*(c+2*d*x))^2/((b*c-a*d)^2*(1+2*sqrt(b)*sqrt(d)*sqrt((a+b*x)*(c+d*x))/(b*c-a*d))^2))/(b^(1/4)*d^(1/4)*(a+b*x)^(3/4)*(c+d*x)^(3/4)*(b*c+a*d+2*b*d*x)*sqrt((a*d+b*(c+2*d*x))^2))],
[1/((a+b*x)^(7/4)*(c+d*x)^(3/4)),x,4,-4/3*(c+d*x)^(1/4)/((b*c-a*d)*(a+b*x)^(3/4))-2/3*d^(3/4)*((a+b*x)*(c+d*x))^(3/4)*sqrt(cos(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d)))^2)/cos(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d)))*EllipticF(sin(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d))),sqrt(1/2))*sqrt(2)*(1+2*sqrt(b)*sqrt(d)*sqrt((a+b*x)*(c+d*x))/(b*c-a*d))*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt((a*d+b*(c+2*d*x))^2/((b*c-a*d)^2*(1+2*sqrt(b)*sqrt(d)*sqrt((a+b*x)*(c+d*x))/(b*c-a*d))^2))/(b^(1/4)*(a+b*x)^(3/4)*(c+d*x)^(3/4)*(b*c+a*d+2*b*d*x)*sqrt(b*c-a*d)*sqrt((a*d+b*(c+2*d*x))^2))],
[1/((a+b*x)^(11/4)*(c+d*x)^(3/4)),x,5,-4/7*(c+d*x)^(1/4)/((b*c-a*d)*(a+b*x)^(7/4))+8/7*d*(c+d*x)^(1/4)/((b*c-a*d)^2*(a+b*x)^(3/4))+4/7*d^(7/4)*((a+b*x)*(c+d*x))^(3/4)*sqrt(cos(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d)))^2)/cos(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d)))*EllipticF(sin(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d))),sqrt(1/2))*sqrt(2)*(1+2*sqrt(b)*sqrt(d)*sqrt((a+b*x)*(c+d*x))/(b*c-a*d))*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt((a*d+b*(c+2*d*x))^2/((b*c-a*d)^2*(1+2*sqrt(b)*sqrt(d)*sqrt((a+b*x)*(c+d*x))/(b*c-a*d))^2))/(b^(1/4)*(b*c-a*d)^(3/2)*(a+b*x)^(3/4)*(c+d*x)^(3/4)*(b*c+a*d+2*b*d*x)*sqrt((a*d+b*(c+2*d*x))^2))],
[(a+b*x)^(5/4)/(c+d*x)^(5/4),x,7,-4*(a+b*x)^(5/4)/(d*(c+d*x)^(1/4))+5*b*(a+b*x)^(1/4)*(c+d*x)^(3/4)/d^2-5/2*b^(1/4)*(b*c-a*d)*arctan(d^(1/4)*(a+b*x)^(1/4)/(b^(1/4)*(c+d*x)^(1/4)))/d^(9/4)-5/2*b^(1/4)*(b*c-a*d)*arctanh(d^(1/4)*(a+b*x)^(1/4)/(b^(1/4)*(c+d*x)^(1/4)))/d^(9/4)],
[(a+b*x)^(1/4)/(c+d*x)^(5/4),x,6,-4*(a+b*x)^(1/4)/(d*(c+d*x)^(1/4))+2*b^(1/4)*arctan(d^(1/4)*(a+b*x)^(1/4)/(b^(1/4)*(c+d*x)^(1/4)))/d^(5/4)+2*b^(1/4)*arctanh(d^(1/4)*(a+b*x)^(1/4)/(b^(1/4)*(c+d*x)^(1/4)))/d^(5/4)],
[1/((a+b*x)^(3/4)*(c+d*x)^(5/4)),x,1,4*(a+b*x)^(1/4)/((b*c-a*d)*(c+d*x)^(1/4))],
[1/((a+b*x)^(7/4)*(c+d*x)^(5/4)),x,2,(-4/3)/((b*c-a*d)*(a+b*x)^(3/4)*(c+d*x)^(1/4))-16/3*d*(a+b*x)^(1/4)/((b*c-a*d)^2*(c+d*x)^(1/4))],
[1/((a+b*x)^(11/4)*(c+d*x)^(5/4)),x,3,(-4/7)/((b*c-a*d)*(a+b*x)^(7/4)*(c+d*x)^(1/4))+32/21*d/((b*c-a*d)^2*(a+b*x)^(3/4)*(c+d*x)^(1/4))+128/21*d^2*(a+b*x)^(1/4)/((b*c-a*d)^3*(c+d*x)^(1/4))],
[1/((a+b*x)^(15/4)*(c+d*x)^(5/4)),x,4,(-4/11)/((b*c-a*d)*(a+b*x)^(11/4)*(c+d*x)^(1/4))+48/77*d/((b*c-a*d)^2*(a+b*x)^(7/4)*(c+d*x)^(1/4))-128/77*d^2/((b*c-a*d)^3*(a+b*x)^(3/4)*(c+d*x)^(1/4))-512/77*d^3*(a+b*x)^(1/4)/((b*c-a*d)^4*(c+d*x)^(1/4))],
[(a+b*x)^(11/4)/(c+d*x)^(5/4),x,8,-4*(a+b*x)^(11/4)/(d*(c+d*x)^(1/4))-77/15*b*(b*c-a*d)*(a+b*x)^(3/4)*(c+d*x)^(3/4)/d^3+22/5*b*(a+b*x)^(7/4)*(c+d*x)^(3/4)/d^2+77/10*(b*c-a*d)*sqrt(b)*sqrt((a+b*x)*(c+d*x))*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt((a*d+b*(c+2*d*x))^2)/(d^(7/2)*(a+b*x)^(1/4)*(c+d*x)^(1/4)*(b*c+a*d+2*b*d*x)*(1+2*sqrt(b)*sqrt(d)*sqrt((a+b*x)*(c+d*x))/(b*c-a*d)))-77/10*b^(1/4)*(b*c-a*d)^(7/2)*((a+b*x)*(c+d*x))^(1/4)*sqrt(cos(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d)))^2)/cos(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d)))*EllipticE(sin(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d))),sqrt(1/2))*(1+2*sqrt(b)*sqrt(d)*sqrt((a+b*x)*(c+d*x))/(b*c-a*d))*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt((a*d+b*(c+2*d*x))^2/((b*c-a*d)^2*(1+2*sqrt(b)*sqrt(d)*sqrt((a+b*x)*(c+d*x))/(b*c-a*d))^2))/(d^(15/4)*(a+b*x)^(1/4)*(c+d*x)^(1/4)*(b*c+a*d+2*b*d*x)*sqrt(2)*sqrt((a*d+b*(c+2*d*x))^2))+77/20*b^(1/4)*(b*c-a*d)^(7/2)*((a+b*x)*(c+d*x))^(1/4)*sqrt(cos(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d)))^2)/cos(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d)))*EllipticF(sin(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d))),sqrt(1/2))*(1+2*sqrt(b)*sqrt(d)*sqrt((a+b*x)*(c+d*x))/(b*c-a*d))*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt((a*d+b*(c+2*d*x))^2/((b*c-a*d)^2*(1+2*sqrt(b)*sqrt(d)*sqrt((a+b*x)*(c+d*x))/(b*c-a*d))^2))/(d^(15/4)*(a+b*x)^(1/4)*(c+d*x)^(1/4)*(b*c+a*d+2*b*d*x)*sqrt(2)*sqrt((a*d+b*(c+2*d*x))^2))],
[(a+b*x)^(7/4)/(c+d*x)^(5/4),x,7,-4*(a+b*x)^(7/4)/(d*(c+d*x)^(1/4))+14/3*b*(a+b*x)^(3/4)*(c+d*x)^(3/4)/d^2-7*sqrt(b)*sqrt((a+b*x)*(c+d*x))*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt((a*d+b*(c+2*d*x))^2)/(d^(5/2)*(a+b*x)^(1/4)*(c+d*x)^(1/4)*(b*c+a*d+2*b*d*x)*(1+2*sqrt(b)*sqrt(d)*sqrt((a+b*x)*(c+d*x))/(b*c-a*d)))+7*b^(1/4)*(b*c-a*d)^(5/2)*((a+b*x)*(c+d*x))^(1/4)*sqrt(cos(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d)))^2)/cos(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d)))*EllipticE(sin(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d))),sqrt(1/2))*(1+2*sqrt(b)*sqrt(d)*sqrt((a+b*x)*(c+d*x))/(b*c-a*d))*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt((a*d+b*(c+2*d*x))^2/((b*c-a*d)^2*(1+2*sqrt(b)*sqrt(d)*sqrt((a+b*x)*(c+d*x))/(b*c-a*d))^2))/(d^(11/4)*(a+b*x)^(1/4)*(c+d*x)^(1/4)*(b*c+a*d+2*b*d*x)*sqrt(2)*sqrt((a*d+b*(c+2*d*x))^2))-7/2*b^(1/4)*(b*c-a*d)^(5/2)*((a+b*x)*(c+d*x))^(1/4)*sqrt(cos(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d)))^2)/cos(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d)))*EllipticF(sin(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d))),sqrt(1/2))*(1+2*sqrt(b)*sqrt(d)*sqrt((a+b*x)*(c+d*x))/(b*c-a*d))*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt((a*d+b*(c+2*d*x))^2/((b*c-a*d)^2*(1+2*sqrt(b)*sqrt(d)*sqrt((a+b*x)*(c+d*x))/(b*c-a*d))^2))/(d^(11/4)*(a+b*x)^(1/4)*(c+d*x)^(1/4)*(b*c+a*d+2*b*d*x)*sqrt(2)*sqrt((a*d+b*(c+2*d*x))^2))],
[(a+b*x)^(3/4)/(c+d*x)^(5/4),x,6,-4*(a+b*x)^(3/4)/(d*(c+d*x)^(1/4))+6*sqrt(b)*sqrt((a+b*x)*(c+d*x))*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt((a*d+b*(c+2*d*x))^2)/(d^(3/2)*(b*c-a*d)*(a+b*x)^(1/4)*(c+d*x)^(1/4)*(b*c+a*d+2*b*d*x)*(1+2*sqrt(b)*sqrt(d)*sqrt((a+b*x)*(c+d*x))/(b*c-a*d)))+3*b^(1/4)*(b*c-a*d)^(3/2)*((a+b*x)*(c+d*x))^(1/4)*sqrt(cos(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d)))^2)/cos(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d)))*EllipticF(sin(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d))),sqrt(1/2))*(1+2*sqrt(b)*sqrt(d)*sqrt((a+b*x)*(c+d*x))/(b*c-a*d))*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt((a*d+b*(c+2*d*x))^2/((b*c-a*d)^2*(1+2*sqrt(b)*sqrt(d)*sqrt((a+b*x)*(c+d*x))/(b*c-a*d))^2))/(d^(7/4)*(a+b*x)^(1/4)*(c+d*x)^(1/4)*(b*c+a*d+2*b*d*x)*sqrt(2)*sqrt((a*d+b*(c+2*d*x))^2))-3*b^(1/4)*(b*c-a*d)^(3/2)*((a+b*x)*(c+d*x))^(1/4)*sqrt(cos(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d)))^2)/cos(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d)))*EllipticE(sin(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d))),sqrt(1/2))*sqrt(2)*(1+2*sqrt(b)*sqrt(d)*sqrt((a+b*x)*(c+d*x))/(b*c-a*d))*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt((a*d+b*(c+2*d*x))^2/((b*c-a*d)^2*(1+2*sqrt(b)*sqrt(d)*sqrt((a+b*x)*(c+d*x))/(b*c-a*d))^2))/(d^(7/4)*(a+b*x)^(1/4)*(c+d*x)^(1/4)*(b*c+a*d+2*b*d*x)*sqrt((a*d+b*(c+2*d*x))^2))],
[1/((a+b*x)^(1/4)*(c+d*x)^(5/4)),x,6,4*(a+b*x)^(3/4)/((b*c-a*d)*(c+d*x)^(1/4))-4*sqrt(b)*sqrt((a+b*x)*(c+d*x))*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt((a*d+b*(c+2*d*x))^2)/((b*c-a*d)^2*(a+b*x)^(1/4)*(c+d*x)^(1/4)*(b*c+a*d+2*b*d*x)*sqrt(d)*(1+2*sqrt(b)*sqrt(d)*sqrt((a+b*x)*(c+d*x))/(b*c-a*d)))+2*b^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(cos(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d)))^2)/cos(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d)))*EllipticE(sin(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d))),sqrt(1/2))*sqrt(2)*sqrt(b*c-a*d)*(1+2*sqrt(b)*sqrt(d)*sqrt((a+b*x)*(c+d*x))/(b*c-a*d))*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt((a*d+b*(c+2*d*x))^2/((b*c-a*d)^2*(1+2*sqrt(b)*sqrt(d)*sqrt((a+b*x)*(c+d*x))/(b*c-a*d))^2))/(d^(3/4)*(a+b*x)^(1/4)*(c+d*x)^(1/4)*(b*c+a*d+2*b*d*x)*sqrt((a*d+b*(c+2*d*x))^2))-b^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(cos(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d)))^2)/cos(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d)))*EllipticF(sin(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d))),sqrt(1/2))*sqrt(2)*sqrt(b*c-a*d)*(1+2*sqrt(b)*sqrt(d)*sqrt((a+b*x)*(c+d*x))/(b*c-a*d))*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt((a*d+b*(c+2*d*x))^2/((b*c-a*d)^2*(1+2*sqrt(b)*sqrt(d)*sqrt((a+b*x)*(c+d*x))/(b*c-a*d))^2))/(d^(3/4)*(a+b*x)^(1/4)*(c+d*x)^(1/4)*(b*c+a*d+2*b*d*x)*sqrt((a*d+b*(c+2*d*x))^2))],
[1/((a+b*x)^(5/4)*(c+d*x)^(5/4)),x,7,(-4)/((b*c-a*d)*(a+b*x)^(1/4)*(c+d*x)^(1/4))-8*d*(a+b*x)^(3/4)/((b*c-a*d)^2*(c+d*x)^(1/4))+8*sqrt(b)*sqrt(d)*sqrt((a+b*x)*(c+d*x))*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt((a*d+b*(c+2*d*x))^2)/((b*c-a*d)^3*(a+b*x)^(1/4)*(c+d*x)^(1/4)*(b*c+a*d+2*b*d*x)*(1+2*sqrt(b)*sqrt(d)*sqrt((a+b*x)*(c+d*x))/(b*c-a*d)))-4*b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(cos(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d)))^2)/cos(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d)))*EllipticE(sin(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d))),sqrt(1/2))*sqrt(2)*(1+2*sqrt(b)*sqrt(d)*sqrt((a+b*x)*(c+d*x))/(b*c-a*d))*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt((a*d+b*(c+2*d*x))^2/((b*c-a*d)^2*(1+2*sqrt(b)*sqrt(d)*sqrt((a+b*x)*(c+d*x))/(b*c-a*d))^2))/((a+b*x)^(1/4)*(c+d*x)^(1/4)*(b*c+a*d+2*b*d*x)*sqrt(b*c-a*d)*sqrt((a*d+b*(c+2*d*x))^2))+2*b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(cos(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d)))^2)/cos(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d)))*EllipticF(sin(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d))),sqrt(1/2))*sqrt(2)*(1+2*sqrt(b)*sqrt(d)*sqrt((a+b*x)*(c+d*x))/(b*c-a*d))*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt((a*d+b*(c+2*d*x))^2/((b*c-a*d)^2*(1+2*sqrt(b)*sqrt(d)*sqrt((a+b*x)*(c+d*x))/(b*c-a*d))^2))/((a+b*x)^(1/4)*(c+d*x)^(1/4)*(b*c+a*d+2*b*d*x)*sqrt(b*c-a*d)*sqrt((a*d+b*(c+2*d*x))^2))],
[1/((a+b*x)^(9/4)*(c+d*x)^(5/4)),x,8,(-4/5)/((b*c-a*d)*(a+b*x)^(5/4)*(c+d*x)^(1/4))+24/5*d/((b*c-a*d)^2*(a+b*x)^(1/4)*(c+d*x)^(1/4))+48/5*d^2*(a+b*x)^(3/4)/((b*c-a*d)^3*(c+d*x)^(1/4))-48/5*d^(3/2)*sqrt(b)*sqrt((a+b*x)*(c+d*x))*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt((a*d+b*(c+2*d*x))^2)/((b*c-a*d)^4*(a+b*x)^(1/4)*(c+d*x)^(1/4)*(b*c+a*d+2*b*d*x)*(1+2*sqrt(b)*sqrt(d)*sqrt((a+b*x)*(c+d*x))/(b*c-a*d)))+24/5*b^(1/4)*d^(5/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(cos(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d)))^2)/cos(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d)))*EllipticE(sin(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d))),sqrt(1/2))*sqrt(2)*(1+2*sqrt(b)*sqrt(d)*sqrt((a+b*x)*(c+d*x))/(b*c-a*d))*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt((a*d+b*(c+2*d*x))^2/((b*c-a*d)^2*(1+2*sqrt(b)*sqrt(d)*sqrt((a+b*x)*(c+d*x))/(b*c-a*d))^2))/((b*c-a*d)^(3/2)*(a+b*x)^(1/4)*(c+d*x)^(1/4)*(b*c+a*d+2*b*d*x)*sqrt((a*d+b*(c+2*d*x))^2))-12/5*b^(1/4)*d^(5/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(cos(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d)))^2)/cos(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d)))*EllipticF(sin(2*arctan(b^(1/4)*d^(1/4)*((a+b*x)*(c+d*x))^(1/4)*sqrt(2)/sqrt(b*c-a*d))),sqrt(1/2))*sqrt(2)*(1+2*sqrt(b)*sqrt(d)*sqrt((a+b*x)*(c+d*x))/(b*c-a*d))*sqrt((b*c+a*d+2*b*d*x)^2)*sqrt((a*d+b*(c+2*d*x))^2/((b*c-a*d)^2*(1+2*sqrt(b)*sqrt(d)*sqrt((a+b*x)*(c+d*x))/(b*c-a*d))^2))/((b*c-a*d)^(3/2)*(a+b*x)^(1/4)*(c+d*x)^(1/4)*(b*c+a*d+2*b*d*x)*sqrt((a*d+b*(c+2*d*x))^2))],
[1/((1-a*x)^(1/4)*(1+b*x)^(3/4)),x,11,-log(-a^(1/4)*b^(1/4)*(1-a*x)^(1/4)*sqrt(2)/(1+b*x)^(1/4)+sqrt(a)+sqrt(b)*sqrt(1-a*x)/sqrt(1+b*x))/(a^(1/4)*b^(3/4)*sqrt(2))+log(a^(1/4)*b^(1/4)*(1-a*x)^(1/4)*sqrt(2)/(1+b*x)^(1/4)+sqrt(a)+sqrt(b)*sqrt(1-a*x)/sqrt(1+b*x))/(a^(1/4)*b^(3/4)*sqrt(2))+arctan(1-b^(1/4)*(1-a*x)^(1/4)*sqrt(2)/(a^(1/4)*(1+b*x)^(1/4)))*sqrt(2)/(a^(1/4)*b^(3/4))-arctan(1+b^(1/4)*(1-a*x)^(1/4)*sqrt(2)/(a^(1/4)*(1+b*x)^(1/4)))*sqrt(2)/(a^(1/4)*b^(3/4))],
[1/((1-a*x)^(1/4)*(1+a*x)^(3/4)),x,11,-log(1-(1-a*x)^(1/4)*sqrt(2)/(1+a*x)^(1/4)+sqrt(1-a*x)/sqrt(1+a*x))/(a*sqrt(2))+log(1+(1-a*x)^(1/4)*sqrt(2)/(1+a*x)^(1/4)+sqrt(1-a*x)/sqrt(1+a*x))/(a*sqrt(2))+arctan(1-(1-a*x)^(1/4)*sqrt(2)/(1+a*x)^(1/4))*sqrt(2)/a-arctan(1+(1-a*x)^(1/4)*sqrt(2)/(1+a*x)^(1/4))*sqrt(2)/a],

# Integrands of the form (a+b x)^(m/2) (c+d x)^(n/5)
[(a+b*x)^(3/2)/(c+d*x)^(1/5),x,2,2/5*(a+b*x)^(5/2)*(b*(c+d*x)/(b*c-a*d))^(1/5)*hypergeom([1/5,5/2],[7/2],-d*(a+b*x)/(b*c-a*d))/(b*(c+d*x)^(1/5))],
[(a+b*x)^(1/2)/(c+d*x)^(1/5),x,2,2/3*(a+b*x)^(3/2)*(b*(c+d*x)/(b*c-a*d))^(1/5)*hypergeom([1/5,3/2],[5/2],-d*(a+b*x)/(b*c-a*d))/(b*(c+d*x)^(1/5))],
[1/((a+b*x)^(1/2)*(c+d*x)^(1/5)),x,2,2*(b*(c+d*x)/(b*c-a*d))^(1/5)*hypergeom([1/5,1/2],[3/2],-d*(a+b*x)/(b*c-a*d))*sqrt(a+b*x)/(b*(c+d*x)^(1/5))],
[1/((a+b*x)^(3/2)*(c+d*x)^(1/5)),x,2,-2*(b*(c+d*x)/(b*c-a*d))^(1/5)*hypergeom([-1/2,1/5],[1/2],-d*(a+b*x)/(b*c-a*d))/(b*(c+d*x)^(1/5)*sqrt(a+b*x))],
[1/((a+b*x)^(5/2)*(c+d*x)^(1/5)),x,2,-2/3*(b*(c+d*x)/(b*c-a*d))^(1/5)*hypergeom([-3/2,1/5],[-1/2],-d*(a+b*x)/(b*c-a*d))/(b*(a+b*x)^(3/2)*(c+d*x)^(1/5))],

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

# n>0
[(a+b*x)^(5/2)*(c+d*x)^(1/6),x,6,-9/352*(b*c-a*d)^2*(a+b*x)^(3/2)*(c+d*x)^(1/6)/(b*d^2)+3/176*(b*c-a*d)*(a+b*x)^(5/2)*(c+d*x)^(1/6)/(b*d)+3/11*(a+b*x)^(7/2)*(c+d*x)^(1/6)/b+81/1408*(b*c-a*d)^3*(c+d*x)^(1/6)*sqrt(a+b*x)/(b*d^3)-81/2816*3^(3/4)*(b*c-a*d)^(11/3)*(c+d*x)^(1/6)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))*sqrt(cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))^2)/cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))*EllipticF(sin(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3))))),sqrt(1/4*(2+sqrt(3))))*sqrt(((b*c-a*d)^(2/3)+b^(1/3)*(b*c-a*d)^(1/3)*(c+d*x)^(1/3)+b^(2/3)*(c+d*x)^(2/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2)/(b*d^4*sqrt(a+b*x)*sqrt(-b^(1/3)*(c+d*x)^(1/3)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2))],
[(a+b*x)^(3/2)*(c+d*x)^(1/6),x,5,3/80*(b*c-a*d)*(a+b*x)^(3/2)*(c+d*x)^(1/6)/(b*d)+3/8*(a+b*x)^(5/2)*(c+d*x)^(1/6)/b-27/320*(b*c-a*d)^2*(c+d*x)^(1/6)*sqrt(a+b*x)/(b*d^2)+27/640*3^(3/4)*(b*c-a*d)^(8/3)*(c+d*x)^(1/6)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))*sqrt(cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))^2)/cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))*EllipticF(sin(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3))))),sqrt(1/4*(2+sqrt(3))))*sqrt(((b*c-a*d)^(2/3)+b^(1/3)*(b*c-a*d)^(1/3)*(c+d*x)^(1/3)+b^(2/3)*(c+d*x)^(2/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2)/(b*d^3*sqrt(a+b*x)*sqrt(-b^(1/3)*(c+d*x)^(1/3)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2))],
[(a+b*x)^(1/2)*(c+d*x)^(1/6),x,4,3/5*(a+b*x)^(3/2)*(c+d*x)^(1/6)/b+3/20*(b*c-a*d)*(c+d*x)^(1/6)*sqrt(a+b*x)/(b*d)-3/40*3^(3/4)*(b*c-a*d)^(5/3)*(c+d*x)^(1/6)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))*sqrt(cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))^2)/cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))*EllipticF(sin(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3))))),sqrt(1/4*(2+sqrt(3))))*sqrt(((b*c-a*d)^(2/3)+b^(1/3)*(b*c-a*d)^(1/3)*(c+d*x)^(1/3)+b^(2/3)*(c+d*x)^(2/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2)/(b*d^2*sqrt(a+b*x)*sqrt(-b^(1/3)*(c+d*x)^(1/3)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2))],
[(c+d*x)^(1/6)/(a+b*x)^(1/2),x,3,3/2*(c+d*x)^(1/6)*sqrt(a+b*x)/b+1/4*3^(3/4)*(b*c-a*d)^(2/3)*(c+d*x)^(1/6)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))*sqrt(cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))^2)/cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))*EllipticF(sin(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3))))),sqrt(1/4*(2+sqrt(3))))*sqrt(((b*c-a*d)^(2/3)+b^(1/3)*(b*c-a*d)^(1/3)*(c+d*x)^(1/3)+b^(2/3)*(c+d*x)^(2/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2)/(b*d*sqrt(a+b*x)*sqrt(-b^(1/3)*(c+d*x)^(1/3)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2))],
[(c+d*x)^(1/6)/(a+b*x)^(3/2),x,3,-2*(c+d*x)^(1/6)/(b*sqrt(a+b*x))+(c+d*x)^(1/6)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))*sqrt(cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))^2)/cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))*EllipticF(sin(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3))))),sqrt(1/4*(2+sqrt(3))))*sqrt(((b*c-a*d)^(2/3)+b^(1/3)*(b*c-a*d)^(1/3)*(c+d*x)^(1/3)+b^(2/3)*(c+d*x)^(2/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2)/(3^(1/4)*b*(b*c-a*d)^(1/3)*sqrt(a+b*x)*sqrt(-b^(1/3)*(c+d*x)^(1/3)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2))],
[(c+d*x)^(1/6)/(a+b*x)^(5/2),x,4,-2/3*(c+d*x)^(1/6)/(b*(a+b*x)^(3/2))-2/9*d*(c+d*x)^(1/6)/(b*(b*c-a*d)*sqrt(a+b*x))-2/9*d*(c+d*x)^(1/6)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))*sqrt(cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))^2)/cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))*EllipticF(sin(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3))))),sqrt(1/4*(2+sqrt(3))))*sqrt(((b*c-a*d)^(2/3)+b^(1/3)*(b*c-a*d)^(1/3)*(c+d*x)^(1/3)+b^(2/3)*(c+d*x)^(2/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2)/(3^(1/4)*b*(b*c-a*d)^(4/3)*sqrt(a+b*x)*sqrt(-b^(1/3)*(c+d*x)^(1/3)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2))],
[(a+b*x)^(3/2)*(c+d*x)^(5/6),x,7,3/28*(b*c-a*d)*(a+b*x)^(3/2)*(c+d*x)^(5/6)/(b*d)+3/10*(a+b*x)^(5/2)*(c+d*x)^(5/6)/b-27/224*(b*c-a*d)^2*(c+d*x)^(5/6)*sqrt(a+b*x)/(b*d^2)-81/448*(b*c-a*d)^3*(c+d*x)^(1/6)*(1+sqrt(3))*sqrt(a+b*x)/(b^(5/3)*d^2*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3))))-81/448*3^(1/4)*(b*c-a*d)^(10/3)*(c+d*x)^(1/6)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))*sqrt(cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))^2)/cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))*EllipticE(sin(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3))))),sqrt(1/4*(2+sqrt(3))))*sqrt(((b*c-a*d)^(2/3)+b^(1/3)*(b*c-a*d)^(1/3)*(c+d*x)^(1/3)+b^(2/3)*(c+d*x)^(2/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2)/(b^(5/3)*d^3*sqrt(a+b*x)*sqrt(-b^(1/3)*(c+d*x)^(1/3)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2))-27/896*3^(3/4)*(b*c-a*d)^(10/3)*(c+d*x)^(1/6)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))*sqrt(cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))^2)/cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))*EllipticF(sin(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3))))),sqrt(1/4*(2+sqrt(3))))*(1-sqrt(3))*sqrt(((b*c-a*d)^(2/3)+b^(1/3)*(b*c-a*d)^(1/3)*(c+d*x)^(1/3)+b^(2/3)*(c+d*x)^(2/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2)/(b^(5/3)*d^3*sqrt(a+b*x)*sqrt(-b^(1/3)*(c+d*x)^(1/3)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2))],
[(a+b*x)^(1/2)*(c+d*x)^(5/6),x,6,3/7*(a+b*x)^(3/2)*(c+d*x)^(5/6)/b+15/56*(b*c-a*d)*(c+d*x)^(5/6)*sqrt(a+b*x)/(b*d)+45/112*(b*c-a*d)^2*(c+d*x)^(1/6)*(1+sqrt(3))*sqrt(a+b*x)/(b^(5/3)*d*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3))))+45/112*3^(1/4)*(b*c-a*d)^(7/3)*(c+d*x)^(1/6)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))*sqrt(cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))^2)/cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))*EllipticE(sin(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3))))),sqrt(1/4*(2+sqrt(3))))*sqrt(((b*c-a*d)^(2/3)+b^(1/3)*(b*c-a*d)^(1/3)*(c+d*x)^(1/3)+b^(2/3)*(c+d*x)^(2/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2)/(b^(5/3)*d^2*sqrt(a+b*x)*sqrt(-b^(1/3)*(c+d*x)^(1/3)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2))+15/224*3^(3/4)*(b*c-a*d)^(7/3)*(c+d*x)^(1/6)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))*sqrt(cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))^2)/cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))*EllipticF(sin(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3))))),sqrt(1/4*(2+sqrt(3))))*(1-sqrt(3))*sqrt(((b*c-a*d)^(2/3)+b^(1/3)*(b*c-a*d)^(1/3)*(c+d*x)^(1/3)+b^(2/3)*(c+d*x)^(2/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2)/(b^(5/3)*d^2*sqrt(a+b*x)*sqrt(-b^(1/3)*(c+d*x)^(1/3)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2))],
[(c+d*x)^(5/6)/(a+b*x)^(1/2),x,5,3/4*(c+d*x)^(5/6)*sqrt(a+b*x)/b-15/8*(b*c-a*d)*(c+d*x)^(1/6)*(1+sqrt(3))*sqrt(a+b*x)/(b^(5/3)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3))))-15/8*3^(1/4)*(b*c-a*d)^(4/3)*(c+d*x)^(1/6)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))*sqrt(cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))^2)/cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))*EllipticE(sin(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3))))),sqrt(1/4*(2+sqrt(3))))*sqrt(((b*c-a*d)^(2/3)+b^(1/3)*(b*c-a*d)^(1/3)*(c+d*x)^(1/3)+b^(2/3)*(c+d*x)^(2/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2)/(b^(5/3)*d*sqrt(a+b*x)*sqrt(-b^(1/3)*(c+d*x)^(1/3)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2))-5/16*3^(3/4)*(b*c-a*d)^(4/3)*(c+d*x)^(1/6)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))*sqrt(cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))^2)/cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))*EllipticF(sin(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3))))),sqrt(1/4*(2+sqrt(3))))*(1-sqrt(3))*sqrt(((b*c-a*d)^(2/3)+b^(1/3)*(b*c-a*d)^(1/3)*(c+d*x)^(1/3)+b^(2/3)*(c+d*x)^(2/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2)/(b^(5/3)*d*sqrt(a+b*x)*sqrt(-b^(1/3)*(c+d*x)^(1/3)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2))],
[(c+d*x)^(5/6)/(a+b*x)^(3/2),x,5,-2*(c+d*x)^(5/6)/(b*sqrt(a+b*x))-5*d*(c+d*x)^(1/6)*(1+sqrt(3))*sqrt(a+b*x)/(b^(5/3)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3))))-5*3^(1/4)*(b*c-a*d)^(1/3)*(c+d*x)^(1/6)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))*sqrt(cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))^2)/cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))*EllipticE(sin(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3))))),sqrt(1/4*(2+sqrt(3))))*sqrt(((b*c-a*d)^(2/3)+b^(1/3)*(b*c-a*d)^(1/3)*(c+d*x)^(1/3)+b^(2/3)*(c+d*x)^(2/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2)/(b^(5/3)*sqrt(a+b*x)*sqrt(-b^(1/3)*(c+d*x)^(1/3)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2))-5/2*(b*c-a*d)^(1/3)*(c+d*x)^(1/6)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))*sqrt(cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))^2)/cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))*EllipticF(sin(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3))))),sqrt(1/4*(2+sqrt(3))))*(1-sqrt(3))*sqrt(((b*c-a*d)^(2/3)+b^(1/3)*(b*c-a*d)^(1/3)*(c+d*x)^(1/3)+b^(2/3)*(c+d*x)^(2/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2)/(3^(1/4)*b^(5/3)*sqrt(a+b*x)*sqrt(-b^(1/3)*(c+d*x)^(1/3)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2))],
[(c+d*x)^(5/6)/(a+b*x)^(5/2),x,6,-2/3*(c+d*x)^(5/6)/(b*(a+b*x)^(3/2))-10/9*d*(c+d*x)^(5/6)/(b*(b*c-a*d)*sqrt(a+b*x))-10/9*d^2*(c+d*x)^(1/6)*(1+sqrt(3))*sqrt(a+b*x)/(b^(5/3)*(b*c-a*d)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3))))-10/3*d*(c+d*x)^(1/6)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))*sqrt(cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))^2)/cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))*EllipticE(sin(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3))))),sqrt(1/4*(2+sqrt(3))))*sqrt(((b*c-a*d)^(2/3)+b^(1/3)*(b*c-a*d)^(1/3)*(c+d*x)^(1/3)+b^(2/3)*(c+d*x)^(2/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2)/(3^(3/4)*b^(5/3)*(b*c-a*d)^(2/3)*sqrt(a+b*x)*sqrt(-b^(1/3)*(c+d*x)^(1/3)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2))-5/9*d*(c+d*x)^(1/6)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))*sqrt(cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))^2)/cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))*EllipticF(sin(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3))))),sqrt(1/4*(2+sqrt(3))))*(1-sqrt(3))*sqrt(((b*c-a*d)^(2/3)+b^(1/3)*(b*c-a*d)^(1/3)*(c+d*x)^(1/3)+b^(2/3)*(c+d*x)^(2/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2)/(3^(1/4)*b^(5/3)*(b*c-a*d)^(2/3)*sqrt(a+b*x)*sqrt(-b^(1/3)*(c+d*x)^(1/3)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2))],
[(c+d*x)^(5/6)/(a+b*x)^(7/2),x,7,-2/5*(c+d*x)^(5/6)/(b*(a+b*x)^(5/2))-2/9*d*(c+d*x)^(5/6)/(b*(b*c-a*d)*(a+b*x)^(3/2))+8/27*d^2*(c+d*x)^(5/6)/(b*(b*c-a*d)^2*sqrt(a+b*x))+8/27*d^3*(c+d*x)^(1/6)*(1+sqrt(3))*sqrt(a+b*x)/(b^(5/3)*(b*c-a*d)^2*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3))))+8/9*d^2*(c+d*x)^(1/6)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))*sqrt(cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))^2)/cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))*EllipticE(sin(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3))))),sqrt(1/4*(2+sqrt(3))))*sqrt(((b*c-a*d)^(2/3)+b^(1/3)*(b*c-a*d)^(1/3)*(c+d*x)^(1/3)+b^(2/3)*(c+d*x)^(2/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2)/(3^(3/4)*b^(5/3)*(b*c-a*d)^(5/3)*sqrt(a+b*x)*sqrt(-b^(1/3)*(c+d*x)^(1/3)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2))+4/27*d^2*(c+d*x)^(1/6)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))*sqrt(cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))^2)/cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))*EllipticF(sin(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3))))),sqrt(1/4*(2+sqrt(3))))*(1-sqrt(3))*sqrt(((b*c-a*d)^(2/3)+b^(1/3)*(b*c-a*d)^(1/3)*(c+d*x)^(1/3)+b^(2/3)*(c+d*x)^(2/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2)/(3^(1/4)*b^(5/3)*(b*c-a*d)^(5/3)*sqrt(a+b*x)*sqrt(-b^(1/3)*(c+d*x)^(1/3)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2))],

# n<0
[(a+b*x)^(5/2)/(c+d*x)^(1/6),x,7,-9/28*(b*c-a*d)*(a+b*x)^(3/2)*(c+d*x)^(5/6)/d^2+3/10*(a+b*x)^(5/2)*(c+d*x)^(5/6)/d+81/224*(b*c-a*d)^2*(c+d*x)^(5/6)*sqrt(a+b*x)/d^3+243/448*(b*c-a*d)^3*(c+d*x)^(1/6)*(1+sqrt(3))*sqrt(a+b*x)/(b^(2/3)*d^3*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3))))+243/448*3^(1/4)*(b*c-a*d)^(10/3)*(c+d*x)^(1/6)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))*sqrt(cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))^2)/cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))*EllipticE(sin(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3))))),sqrt(1/4*(2+sqrt(3))))*sqrt(((b*c-a*d)^(2/3)+b^(1/3)*(b*c-a*d)^(1/3)*(c+d*x)^(1/3)+b^(2/3)*(c+d*x)^(2/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2)/(b^(2/3)*d^4*sqrt(a+b*x)*sqrt(-b^(1/3)*(c+d*x)^(1/3)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2))+81/896*3^(3/4)*(b*c-a*d)^(10/3)*(c+d*x)^(1/6)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))*sqrt(cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))^2)/cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))*EllipticF(sin(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3))))),sqrt(1/4*(2+sqrt(3))))*(1-sqrt(3))*sqrt(((b*c-a*d)^(2/3)+b^(1/3)*(b*c-a*d)^(1/3)*(c+d*x)^(1/3)+b^(2/3)*(c+d*x)^(2/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2)/(b^(2/3)*d^4*sqrt(a+b*x)*sqrt(-b^(1/3)*(c+d*x)^(1/3)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2))],
[(a+b*x)^(3/2)/(c+d*x)^(1/6),x,6,3/7*(a+b*x)^(3/2)*(c+d*x)^(5/6)/d-27/56*(b*c-a*d)*(c+d*x)^(5/6)*sqrt(a+b*x)/d^2-81/112*(b*c-a*d)^2*(c+d*x)^(1/6)*(1+sqrt(3))*sqrt(a+b*x)/(b^(2/3)*d^2*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3))))-81/112*3^(1/4)*(b*c-a*d)^(7/3)*(c+d*x)^(1/6)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))*sqrt(cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))^2)/cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))*EllipticE(sin(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3))))),sqrt(1/4*(2+sqrt(3))))*sqrt(((b*c-a*d)^(2/3)+b^(1/3)*(b*c-a*d)^(1/3)*(c+d*x)^(1/3)+b^(2/3)*(c+d*x)^(2/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2)/(b^(2/3)*d^3*sqrt(a+b*x)*sqrt(-b^(1/3)*(c+d*x)^(1/3)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2))-27/224*3^(3/4)*(b*c-a*d)^(7/3)*(c+d*x)^(1/6)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))*sqrt(cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))^2)/cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))*EllipticF(sin(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3))))),sqrt(1/4*(2+sqrt(3))))*(1-sqrt(3))*sqrt(((b*c-a*d)^(2/3)+b^(1/3)*(b*c-a*d)^(1/3)*(c+d*x)^(1/3)+b^(2/3)*(c+d*x)^(2/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2)/(b^(2/3)*d^3*sqrt(a+b*x)*sqrt(-b^(1/3)*(c+d*x)^(1/3)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2))],
[(a+b*x)^(1/2)/(c+d*x)^(1/6),x,5,3/4*(c+d*x)^(5/6)*sqrt(a+b*x)/d+9/8*(b*c-a*d)*(c+d*x)^(1/6)*(1+sqrt(3))*sqrt(a+b*x)/(b^(2/3)*d*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3))))+9/8*3^(1/4)*(b*c-a*d)^(4/3)*(c+d*x)^(1/6)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))*sqrt(cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))^2)/cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))*EllipticE(sin(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3))))),sqrt(1/4*(2+sqrt(3))))*sqrt(((b*c-a*d)^(2/3)+b^(1/3)*(b*c-a*d)^(1/3)*(c+d*x)^(1/3)+b^(2/3)*(c+d*x)^(2/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2)/(b^(2/3)*d^2*sqrt(a+b*x)*sqrt(-b^(1/3)*(c+d*x)^(1/3)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2))+3/16*3^(3/4)*(b*c-a*d)^(4/3)*(c+d*x)^(1/6)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))*sqrt(cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))^2)/cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))*EllipticF(sin(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3))))),sqrt(1/4*(2+sqrt(3))))*(1-sqrt(3))*sqrt(((b*c-a*d)^(2/3)+b^(1/3)*(b*c-a*d)^(1/3)*(c+d*x)^(1/3)+b^(2/3)*(c+d*x)^(2/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2)/(b^(2/3)*d^2*sqrt(a+b*x)*sqrt(-b^(1/3)*(c+d*x)^(1/3)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2))],
[1/((a+b*x)^(1/2)*(c+d*x)^(1/6)),x,4,-3*(c+d*x)^(1/6)*(1+sqrt(3))*sqrt(a+b*x)/(b^(2/3)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3))))-3*3^(1/4)*(b*c-a*d)^(1/3)*(c+d*x)^(1/6)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))*sqrt(cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))^2)/cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))*EllipticE(sin(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3))))),sqrt(1/4*(2+sqrt(3))))*sqrt(((b*c-a*d)^(2/3)+b^(1/3)*(b*c-a*d)^(1/3)*(c+d*x)^(1/3)+b^(2/3)*(c+d*x)^(2/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2)/(b^(2/3)*d*sqrt(a+b*x)*sqrt(-b^(1/3)*(c+d*x)^(1/3)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2))-1/2*3^(3/4)*(b*c-a*d)^(1/3)*(c+d*x)^(1/6)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))*sqrt(cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))^2)/cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))*EllipticF(sin(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3))))),sqrt(1/4*(2+sqrt(3))))*(1-sqrt(3))*sqrt(((b*c-a*d)^(2/3)+b^(1/3)*(b*c-a*d)^(1/3)*(c+d*x)^(1/3)+b^(2/3)*(c+d*x)^(2/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2)/(b^(2/3)*d*sqrt(a+b*x)*sqrt(-b^(1/3)*(c+d*x)^(1/3)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2))],
[1/((a+b*x)^(3/2)*(c+d*x)^(1/6)),x,5,-2*(c+d*x)^(5/6)/((b*c-a*d)*sqrt(a+b*x))-2*d*(c+d*x)^(1/6)*(1+sqrt(3))*sqrt(a+b*x)/(b^(2/3)*(b*c-a*d)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3))))-2*3^(1/4)*(c+d*x)^(1/6)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))*sqrt(cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))^2)/cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))*EllipticE(sin(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3))))),sqrt(1/4*(2+sqrt(3))))*sqrt(((b*c-a*d)^(2/3)+b^(1/3)*(b*c-a*d)^(1/3)*(c+d*x)^(1/3)+b^(2/3)*(c+d*x)^(2/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2)/(b^(2/3)*(b*c-a*d)^(2/3)*sqrt(a+b*x)*sqrt(-b^(1/3)*(c+d*x)^(1/3)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2))-(c+d*x)^(1/6)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))*sqrt(cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))^2)/cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))*EllipticF(sin(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3))))),sqrt(1/4*(2+sqrt(3))))*(1-sqrt(3))*sqrt(((b*c-a*d)^(2/3)+b^(1/3)*(b*c-a*d)^(1/3)*(c+d*x)^(1/3)+b^(2/3)*(c+d*x)^(2/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2)/(3^(1/4)*b^(2/3)*(b*c-a*d)^(2/3)*sqrt(a+b*x)*sqrt(-b^(1/3)*(c+d*x)^(1/3)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2))],
[1/((a+b*x)^(5/2)*(c+d*x)^(1/6)),x,6,-2/3*(c+d*x)^(5/6)/((b*c-a*d)*(a+b*x)^(3/2))+8/9*d*(c+d*x)^(5/6)/((b*c-a*d)^2*sqrt(a+b*x))+8/9*d^2*(c+d*x)^(1/6)*(1+sqrt(3))*sqrt(a+b*x)/(b^(2/3)*(b*c-a*d)^2*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3))))+8/3*d*(c+d*x)^(1/6)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))*sqrt(cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))^2)/cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))*EllipticE(sin(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3))))),sqrt(1/4*(2+sqrt(3))))*sqrt(((b*c-a*d)^(2/3)+b^(1/3)*(b*c-a*d)^(1/3)*(c+d*x)^(1/3)+b^(2/3)*(c+d*x)^(2/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2)/(3^(3/4)*b^(2/3)*(b*c-a*d)^(5/3)*sqrt(a+b*x)*sqrt(-b^(1/3)*(c+d*x)^(1/3)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2))+4/9*d*(c+d*x)^(1/6)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))*sqrt(cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))^2)/cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))*EllipticF(sin(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3))))),sqrt(1/4*(2+sqrt(3))))*(1-sqrt(3))*sqrt(((b*c-a*d)^(2/3)+b^(1/3)*(b*c-a*d)^(1/3)*(c+d*x)^(1/3)+b^(2/3)*(c+d*x)^(2/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2)/(3^(1/4)*b^(2/3)*(b*c-a*d)^(5/3)*sqrt(a+b*x)*sqrt(-b^(1/3)*(c+d*x)^(1/3)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2))],
[(a+b*x)^(5/2)/(c+d*x)^(5/6),x,5,-9/16*(b*c-a*d)*(a+b*x)^(3/2)*(c+d*x)^(1/6)/d^2+3/8*(a+b*x)^(5/2)*(c+d*x)^(1/6)/d+81/64*(b*c-a*d)^2*(c+d*x)^(1/6)*sqrt(a+b*x)/d^3-81/128*3^(3/4)*(b*c-a*d)^(8/3)*(c+d*x)^(1/6)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))*sqrt(cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))^2)/cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))*EllipticF(sin(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3))))),sqrt(1/4*(2+sqrt(3))))*sqrt(((b*c-a*d)^(2/3)+b^(1/3)*(b*c-a*d)^(1/3)*(c+d*x)^(1/3)+b^(2/3)*(c+d*x)^(2/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2)/(d^4*sqrt(a+b*x)*sqrt(-b^(1/3)*(c+d*x)^(1/3)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2))],
[(a+b*x)^(3/2)/(c+d*x)^(5/6),x,4,3/5*(a+b*x)^(3/2)*(c+d*x)^(1/6)/d-27/20*(b*c-a*d)*(c+d*x)^(1/6)*sqrt(a+b*x)/d^2+27/40*3^(3/4)*(b*c-a*d)^(5/3)*(c+d*x)^(1/6)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))*sqrt(cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))^2)/cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))*EllipticF(sin(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3))))),sqrt(1/4*(2+sqrt(3))))*sqrt(((b*c-a*d)^(2/3)+b^(1/3)*(b*c-a*d)^(1/3)*(c+d*x)^(1/3)+b^(2/3)*(c+d*x)^(2/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2)/(d^3*sqrt(a+b*x)*sqrt(-b^(1/3)*(c+d*x)^(1/3)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2))],
[(a+b*x)^(1/2)/(c+d*x)^(5/6),x,3,3/2*(c+d*x)^(1/6)*sqrt(a+b*x)/d-3/4*3^(3/4)*(b*c-a*d)^(2/3)*(c+d*x)^(1/6)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))*sqrt(cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))^2)/cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))*EllipticF(sin(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3))))),sqrt(1/4*(2+sqrt(3))))*sqrt(((b*c-a*d)^(2/3)+b^(1/3)*(b*c-a*d)^(1/3)*(c+d*x)^(1/3)+b^(2/3)*(c+d*x)^(2/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2)/(d^2*sqrt(a+b*x)*sqrt(-b^(1/3)*(c+d*x)^(1/3)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2))],
[1/((a+b*x)^(1/2)*(c+d*x)^(5/6)),x,2,3^(3/4)*(c+d*x)^(1/6)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))*sqrt(cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))^2)/cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))*EllipticF(sin(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3))))),sqrt(1/4*(2+sqrt(3))))*sqrt(((b*c-a*d)^(2/3)+b^(1/3)*(b*c-a*d)^(1/3)*(c+d*x)^(1/3)+b^(2/3)*(c+d*x)^(2/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2)/(d*(b*c-a*d)^(1/3)*sqrt(a+b*x)*sqrt(-b^(1/3)*(c+d*x)^(1/3)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2))],
[1/((a+b*x)^(3/2)*(c+d*x)^(5/6)),x,3,-2*(c+d*x)^(1/6)/((b*c-a*d)*sqrt(a+b*x))-2*(c+d*x)^(1/6)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))*sqrt(cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))^2)/cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))*EllipticF(sin(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3))))),sqrt(1/4*(2+sqrt(3))))*sqrt(((b*c-a*d)^(2/3)+b^(1/3)*(b*c-a*d)^(1/3)*(c+d*x)^(1/3)+b^(2/3)*(c+d*x)^(2/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2)/(3^(1/4)*(b*c-a*d)^(4/3)*sqrt(a+b*x)*sqrt(-b^(1/3)*(c+d*x)^(1/3)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2))],
[1/((a+b*x)^(5/2)*(c+d*x)^(5/6)),x,4,-2/3*(c+d*x)^(1/6)/((b*c-a*d)*(a+b*x)^(3/2))+16/9*d*(c+d*x)^(1/6)/((b*c-a*d)^2*sqrt(a+b*x))+16/9*d*(c+d*x)^(1/6)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))*sqrt(cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))^2)/cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))*EllipticF(sin(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3))))),sqrt(1/4*(2+sqrt(3))))*sqrt(((b*c-a*d)^(2/3)+b^(1/3)*(b*c-a*d)^(1/3)*(c+d*x)^(1/3)+b^(2/3)*(c+d*x)^(2/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2)/(3^(1/4)*(b*c-a*d)^(7/3)*sqrt(a+b*x)*sqrt(-b^(1/3)*(c+d*x)^(1/3)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2))],
[(a+b*x)^(5/2)/(c+d*x)^(7/6),x,7,-6*(a+b*x)^(5/2)/(d*(c+d*x)^(1/6))+45/7*b*(a+b*x)^(3/2)*(c+d*x)^(5/6)/d^2-405/56*b*(b*c-a*d)*(c+d*x)^(5/6)*sqrt(a+b*x)/d^3-1215/112*b^(1/3)*(b*c-a*d)^2*(c+d*x)^(1/6)*(1+sqrt(3))*sqrt(a+b*x)/(d^3*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3))))-1215/112*3^(1/4)*b^(1/3)*(b*c-a*d)^(7/3)*(c+d*x)^(1/6)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))*sqrt(cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))^2)/cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))*EllipticE(sin(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3))))),sqrt(1/4*(2+sqrt(3))))*sqrt(((b*c-a*d)^(2/3)+b^(1/3)*(b*c-a*d)^(1/3)*(c+d*x)^(1/3)+b^(2/3)*(c+d*x)^(2/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2)/(d^4*sqrt(a+b*x)*sqrt(-b^(1/3)*(c+d*x)^(1/3)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2))-405/224*3^(3/4)*b^(1/3)*(b*c-a*d)^(7/3)*(c+d*x)^(1/6)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))*sqrt(cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))^2)/cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))*EllipticF(sin(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3))))),sqrt(1/4*(2+sqrt(3))))*(1-sqrt(3))*sqrt(((b*c-a*d)^(2/3)+b^(1/3)*(b*c-a*d)^(1/3)*(c+d*x)^(1/3)+b^(2/3)*(c+d*x)^(2/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2)/(d^4*sqrt(a+b*x)*sqrt(-b^(1/3)*(c+d*x)^(1/3)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2))],
[(a+b*x)^(3/2)/(c+d*x)^(7/6),x,6,-6*(a+b*x)^(3/2)/(d*(c+d*x)^(1/6))+27/4*b*(c+d*x)^(5/6)*sqrt(a+b*x)/d^2+81/8*b^(1/3)*(b*c-a*d)*(c+d*x)^(1/6)*(1+sqrt(3))*sqrt(a+b*x)/(d^2*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3))))+81/8*3^(1/4)*b^(1/3)*(b*c-a*d)^(4/3)*(c+d*x)^(1/6)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))*sqrt(cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))^2)/cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))*EllipticE(sin(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3))))),sqrt(1/4*(2+sqrt(3))))*sqrt(((b*c-a*d)^(2/3)+b^(1/3)*(b*c-a*d)^(1/3)*(c+d*x)^(1/3)+b^(2/3)*(c+d*x)^(2/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2)/(d^3*sqrt(a+b*x)*sqrt(-b^(1/3)*(c+d*x)^(1/3)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2))+27/16*3^(3/4)*b^(1/3)*(b*c-a*d)^(4/3)*(c+d*x)^(1/6)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))*sqrt(cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))^2)/cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))*EllipticF(sin(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3))))),sqrt(1/4*(2+sqrt(3))))*(1-sqrt(3))*sqrt(((b*c-a*d)^(2/3)+b^(1/3)*(b*c-a*d)^(1/3)*(c+d*x)^(1/3)+b^(2/3)*(c+d*x)^(2/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2)/(d^3*sqrt(a+b*x)*sqrt(-b^(1/3)*(c+d*x)^(1/3)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2))],
[(a+b*x)^(1/2)/(c+d*x)^(7/6),x,5,-6*sqrt(a+b*x)/(d*(c+d*x)^(1/6))-9*b^(1/3)*(c+d*x)^(1/6)*(1+sqrt(3))*sqrt(a+b*x)/(d*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3))))-9*3^(1/4)*b^(1/3)*(b*c-a*d)^(1/3)*(c+d*x)^(1/6)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))*sqrt(cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))^2)/cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))*EllipticE(sin(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3))))),sqrt(1/4*(2+sqrt(3))))*sqrt(((b*c-a*d)^(2/3)+b^(1/3)*(b*c-a*d)^(1/3)*(c+d*x)^(1/3)+b^(2/3)*(c+d*x)^(2/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2)/(d^2*sqrt(a+b*x)*sqrt(-b^(1/3)*(c+d*x)^(1/3)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2))-3/2*3^(3/4)*b^(1/3)*(b*c-a*d)^(1/3)*(c+d*x)^(1/6)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))*sqrt(cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))^2)/cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))*EllipticF(sin(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3))))),sqrt(1/4*(2+sqrt(3))))*(1-sqrt(3))*sqrt(((b*c-a*d)^(2/3)+b^(1/3)*(b*c-a*d)^(1/3)*(c+d*x)^(1/3)+b^(2/3)*(c+d*x)^(2/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2)/(d^2*sqrt(a+b*x)*sqrt(-b^(1/3)*(c+d*x)^(1/3)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2))],
[1/((a+b*x)^(1/2)*(c+d*x)^(7/6)),x,5,6*sqrt(a+b*x)/((b*c-a*d)*(c+d*x)^(1/6))+6*b^(1/3)*(c+d*x)^(1/6)*(1+sqrt(3))*sqrt(a+b*x)/((b*c-a*d)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3))))+6*3^(1/4)*b^(1/3)*(c+d*x)^(1/6)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))*sqrt(cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))^2)/cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))*EllipticE(sin(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3))))),sqrt(1/4*(2+sqrt(3))))*sqrt(((b*c-a*d)^(2/3)+b^(1/3)*(b*c-a*d)^(1/3)*(c+d*x)^(1/3)+b^(2/3)*(c+d*x)^(2/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2)/(d*(b*c-a*d)^(2/3)*sqrt(a+b*x)*sqrt(-b^(1/3)*(c+d*x)^(1/3)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2))+3^(3/4)*b^(1/3)*(c+d*x)^(1/6)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))*sqrt(cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))^2)/cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))*EllipticF(sin(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3))))),sqrt(1/4*(2+sqrt(3))))*(1-sqrt(3))*sqrt(((b*c-a*d)^(2/3)+b^(1/3)*(b*c-a*d)^(1/3)*(c+d*x)^(1/3)+b^(2/3)*(c+d*x)^(2/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2)/(d*(b*c-a*d)^(2/3)*sqrt(a+b*x)*sqrt(-b^(1/3)*(c+d*x)^(1/3)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2))],
[1/((a+b*x)^(3/2)*(c+d*x)^(7/6)),x,6,(-2)/((b*c-a*d)*(c+d*x)^(1/6)*sqrt(a+b*x))-8*d*sqrt(a+b*x)/((b*c-a*d)^2*(c+d*x)^(1/6))-8*b^(1/3)*d*(c+d*x)^(1/6)*(1+sqrt(3))*sqrt(a+b*x)/((b*c-a*d)^2*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3))))-8*3^(1/4)*b^(1/3)*(c+d*x)^(1/6)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))*sqrt(cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))^2)/cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))*EllipticE(sin(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3))))),sqrt(1/4*(2+sqrt(3))))*sqrt(((b*c-a*d)^(2/3)+b^(1/3)*(b*c-a*d)^(1/3)*(c+d*x)^(1/3)+b^(2/3)*(c+d*x)^(2/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2)/((b*c-a*d)^(5/3)*sqrt(a+b*x)*sqrt(-b^(1/3)*(c+d*x)^(1/3)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2))-4*b^(1/3)*(c+d*x)^(1/6)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))*sqrt(cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))^2)/cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))*EllipticF(sin(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3))))),sqrt(1/4*(2+sqrt(3))))*(1-sqrt(3))*sqrt(((b*c-a*d)^(2/3)+b^(1/3)*(b*c-a*d)^(1/3)*(c+d*x)^(1/3)+b^(2/3)*(c+d*x)^(2/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2)/(3^(1/4)*(b*c-a*d)^(5/3)*sqrt(a+b*x)*sqrt(-b^(1/3)*(c+d*x)^(1/3)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2))],
[1/((a+b*x)^(5/2)*(c+d*x)^(7/6)),x,7,(-2/3)/((b*c-a*d)*(a+b*x)^(3/2)*(c+d*x)^(1/6))+20/9*d/((b*c-a*d)^2*(c+d*x)^(1/6)*sqrt(a+b*x))+80/9*d^2*sqrt(a+b*x)/((b*c-a*d)^3*(c+d*x)^(1/6))+80/9*b^(1/3)*d^2*(c+d*x)^(1/6)*(1+sqrt(3))*sqrt(a+b*x)/((b*c-a*d)^3*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3))))+80/3*b^(1/3)*d*(c+d*x)^(1/6)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))*sqrt(cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))^2)/cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))*EllipticE(sin(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3))))),sqrt(1/4*(2+sqrt(3))))*sqrt(((b*c-a*d)^(2/3)+b^(1/3)*(b*c-a*d)^(1/3)*(c+d*x)^(1/3)+b^(2/3)*(c+d*x)^(2/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2)/(3^(3/4)*(b*c-a*d)^(8/3)*sqrt(a+b*x)*sqrt(-b^(1/3)*(c+d*x)^(1/3)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2))+40/9*b^(1/3)*d*(c+d*x)^(1/6)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))*sqrt(cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))^2)/cos(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))))*EllipticF(sin(arccos(((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1-sqrt(3)))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3))))),sqrt(1/4*(2+sqrt(3))))*(1-sqrt(3))*sqrt(((b*c-a*d)^(2/3)+b^(1/3)*(b*c-a*d)^(1/3)*(c+d*x)^(1/3)+b^(2/3)*(c+d*x)^(2/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2)/(3^(1/4)*(b*c-a*d)^(8/3)*sqrt(a+b*x)*sqrt(-b^(1/3)*(c+d*x)^(1/3)*((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3))/((b*c-a*d)^(1/3)-b^(1/3)*(c+d*x)^(1/3)*(1+sqrt(3)))^2))],

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

# m>0
[(a+b*x)^(1/6)*(c+d*x)^(13/6),x,2,6/7*(b*c-a*d)^2*(a+b*x)^(7/6)*(c+d*x)^(1/6)*hypergeom([-13/6,7/6],[13/6],-d*(a+b*x)/(b*c-a*d))/(b^3*(b*(c+d*x)/(b*c-a*d))^(1/6))],
[(a+b*x)^(1/6)*(c+d*x)^(7/6),x,2,6/7*(b*c-a*d)*(a+b*x)^(7/6)*(c+d*x)^(1/6)*hypergeom([-7/6,7/6],[13/6],-d*(a+b*x)/(b*c-a*d))/(b^2*(b*(c+d*x)/(b*c-a*d))^(1/6))],
[(a+b*x)^(1/6)*(c+d*x)^(1/6),x,2,6/7*(a+b*x)^(7/6)*(c+d*x)^(1/6)*hypergeom([-1/6,7/6],[13/6],-d*(a+b*x)/(b*c-a*d))/(b*(b*(c+d*x)/(b*c-a*d))^(1/6))],
[(a+b*x)^(1/6)/(c+d*x)^(5/6),x,2,6/7*(a+b*x)^(7/6)*(b*(c+d*x)/(b*c-a*d))^(5/6)*hypergeom([5/6,7/6],[13/6],-d*(a+b*x)/(b*c-a*d))/(b*(c+d*x)^(5/6))],
[(a+b*x)^(1/6)/(c+d*x)^(11/6),x,2,6/7*(a+b*x)^(7/6)*(b*(c+d*x)/(b*c-a*d))^(5/6)*hypergeom([7/6,11/6],[13/6],-d*(a+b*x)/(b*c-a*d))/((b*c-a*d)*(c+d*x)^(5/6))],
[(a+b*x)^(1/6)/(c+d*x)^(17/6),x,2,6/7*b*(a+b*x)^(7/6)*(b*(c+d*x)/(b*c-a*d))^(5/6)*hypergeom([7/6,17/6],[13/6],-d*(a+b*x)/(b*c-a*d))/((b*c-a*d)^2*(c+d*x)^(5/6))],
[(a+b*x)^(1/6)*(c+d*x)^(5/6),x,14,5/12*(b*c-a*d)*(a+b*x)^(1/6)*(c+d*x)^(5/6)/(b*d)+1/2*(a+b*x)^(7/6)*(c+d*x)^(5/6)/b-5/36*(b*c-a*d)^2*arctanh(d^(1/6)*(a+b*x)^(1/6)/(b^(1/6)*(c+d*x)^(1/6)))/(b^(11/6)*d^(7/6))+5/144*(b*c-a*d)^2*log(b^(1/3)+d^(1/3)*(a+b*x)^(1/3)/(c+d*x)^(1/3)-b^(1/6)*d^(1/6)*(a+b*x)^(1/6)/(c+d*x)^(1/6))/(b^(11/6)*d^(7/6))-5/144*(b*c-a*d)^2*log(b^(1/3)+d^(1/3)*(a+b*x)^(1/3)/(c+d*x)^(1/3)+b^(1/6)*d^(1/6)*(a+b*x)^(1/6)/(c+d*x)^(1/6))/(b^(11/6)*d^(7/6))+5/24*(b*c-a*d)^2*arctan(1/sqrt(3)-2*d^(1/6)*(a+b*x)^(1/6)/(b^(1/6)*(c+d*x)^(1/6)*sqrt(3)))/(b^(11/6)*d^(7/6)*sqrt(3))-5/24*(b*c-a*d)^2*arctan(1/sqrt(3)+2*d^(1/6)*(a+b*x)^(1/6)/(b^(1/6)*(c+d*x)^(1/6)*sqrt(3)))/(b^(11/6)*d^(7/6)*sqrt(3))],
[(a+b*x)^(1/6)/(c+d*x)^(1/6),x,13,(a+b*x)^(1/6)*(c+d*x)^(5/6)/d-1/3*(b*c-a*d)*arctanh(d^(1/6)*(a+b*x)^(1/6)/(b^(1/6)*(c+d*x)^(1/6)))/(b^(5/6)*d^(7/6))+1/12*(b*c-a*d)*log(b^(1/3)+d^(1/3)*(a+b*x)^(1/3)/(c+d*x)^(1/3)-b^(1/6)*d^(1/6)*(a+b*x)^(1/6)/(c+d*x)^(1/6))/(b^(5/6)*d^(7/6))-1/12*(b*c-a*d)*log(b^(1/3)+d^(1/3)*(a+b*x)^(1/3)/(c+d*x)^(1/3)+b^(1/6)*d^(1/6)*(a+b*x)^(1/6)/(c+d*x)^(1/6))/(b^(5/6)*d^(7/6))+1/2*(b*c-a*d)*arctan(1/sqrt(3)-2*d^(1/6)*(a+b*x)^(1/6)/(b^(1/6)*(c+d*x)^(1/6)*sqrt(3)))/(b^(5/6)*d^(7/6)*sqrt(3))-1/2*(b*c-a*d)*arctan(1/sqrt(3)+2*d^(1/6)*(a+b*x)^(1/6)/(b^(1/6)*(c+d*x)^(1/6)*sqrt(3)))/(b^(5/6)*d^(7/6)*sqrt(3))],
[(a+b*x)^(1/6)/(c+d*x)^(7/6),x,13,-6*(a+b*x)^(1/6)/(d*(c+d*x)^(1/6))+2*b^(1/6)*arctanh(d^(1/6)*(a+b*x)^(1/6)/(b^(1/6)*(c+d*x)^(1/6)))/d^(7/6)-1/2*b^(1/6)*log(b^(1/3)+d^(1/3)*(a+b*x)^(1/3)/(c+d*x)^(1/3)-b^(1/6)*d^(1/6)*(a+b*x)^(1/6)/(c+d*x)^(1/6))/d^(7/6)+1/2*b^(1/6)*log(b^(1/3)+d^(1/3)*(a+b*x)^(1/3)/(c+d*x)^(1/3)+b^(1/6)*d^(1/6)*(a+b*x)^(1/6)/(c+d*x)^(1/6))/d^(7/6)-b^(1/6)*arctan(1/sqrt(3)-2*d^(1/6)*(a+b*x)^(1/6)/(b^(1/6)*(c+d*x)^(1/6)*sqrt(3)))*sqrt(3)/d^(7/6)+b^(1/6)*arctan(1/sqrt(3)+2*d^(1/6)*(a+b*x)^(1/6)/(b^(1/6)*(c+d*x)^(1/6)*sqrt(3)))*sqrt(3)/d^(7/6)],
[(a+b*x)^(1/6)/(c+d*x)^(13/6),x,1,6/7*(a+b*x)^(7/6)/((b*c-a*d)*(c+d*x)^(7/6))],
[(a+b*x)^(1/6)/(c+d*x)^(19/6),x,2,6/13*(a+b*x)^(7/6)/((b*c-a*d)*(c+d*x)^(13/6))+36/91*b*(a+b*x)^(7/6)/((b*c-a*d)^2*(c+d*x)^(7/6))],
[(a+b*x)^(1/6)/(c+d*x)^(25/6),x,3,6/19*(a+b*x)^(7/6)/((b*c-a*d)*(c+d*x)^(19/6))+72/247*b*(a+b*x)^(7/6)/((b*c-a*d)^2*(c+d*x)^(13/6))+432/1729*b^2*(a+b*x)^(7/6)/((b*c-a*d)^3*(c+d*x)^(7/6))],
[(a+b*x)^(1/6)/(c+d*x)^(31/6),x,4,6/25*(a+b*x)^(7/6)/((b*c-a*d)*(c+d*x)^(25/6))+108/475*b*(a+b*x)^(7/6)/((b*c-a*d)^2*(c+d*x)^(19/6))+1296/6175*b^2*(a+b*x)^(7/6)/((b*c-a*d)^3*(c+d*x)^(13/6))+7776/43225*b^3*(a+b*x)^(7/6)/((b*c-a*d)^4*(c+d*x)^(7/6))],
[(a+b*x)^(5/6)*(c+d*x)^(1/6),x,14,1/12*(b*c-a*d)*(a+b*x)^(5/6)*(c+d*x)^(1/6)/(b*d)+1/2*(a+b*x)^(11/6)*(c+d*x)^(1/6)/b-5/36*(b*c-a*d)^2*arctanh(d^(1/6)*(a+b*x)^(1/6)/(b^(1/6)*(c+d*x)^(1/6)))/(b^(7/6)*d^(11/6))+5/144*(b*c-a*d)^2*log(b^(1/3)+d^(1/3)*(a+b*x)^(1/3)/(c+d*x)^(1/3)-b^(1/6)*d^(1/6)*(a+b*x)^(1/6)/(c+d*x)^(1/6))/(b^(7/6)*d^(11/6))-5/144*(b*c-a*d)^2*log(b^(1/3)+d^(1/3)*(a+b*x)^(1/3)/(c+d*x)^(1/3)+b^(1/6)*d^(1/6)*(a+b*x)^(1/6)/(c+d*x)^(1/6))/(b^(7/6)*d^(11/6))-5/24*(b*c-a*d)^2*arctan(1/sqrt(3)-2*d^(1/6)*(a+b*x)^(1/6)/(b^(1/6)*(c+d*x)^(1/6)*sqrt(3)))/(b^(7/6)*d^(11/6)*sqrt(3))+5/24*(b*c-a*d)^2*arctan(1/sqrt(3)+2*d^(1/6)*(a+b*x)^(1/6)/(b^(1/6)*(c+d*x)^(1/6)*sqrt(3)))/(b^(7/6)*d^(11/6)*sqrt(3))],
[(a+b*x)^(5/6)/(c+d*x)^(5/6),x,13,(a+b*x)^(5/6)*(c+d*x)^(1/6)/d-5/3*(b*c-a*d)*arctanh(d^(1/6)*(a+b*x)^(1/6)/(b^(1/6)*(c+d*x)^(1/6)))/(b^(1/6)*d^(11/6))+5/12*(b*c-a*d)*log(b^(1/3)+d^(1/3)*(a+b*x)^(1/3)/(c+d*x)^(1/3)-b^(1/6)*d^(1/6)*(a+b*x)^(1/6)/(c+d*x)^(1/6))/(b^(1/6)*d^(11/6))-5/12*(b*c-a*d)*log(b^(1/3)+d^(1/3)*(a+b*x)^(1/3)/(c+d*x)^(1/3)+b^(1/6)*d^(1/6)*(a+b*x)^(1/6)/(c+d*x)^(1/6))/(b^(1/6)*d^(11/6))-5/2*(b*c-a*d)*arctan(1/sqrt(3)-2*d^(1/6)*(a+b*x)^(1/6)/(b^(1/6)*(c+d*x)^(1/6)*sqrt(3)))/(b^(1/6)*d^(11/6)*sqrt(3))+5/2*(b*c-a*d)*arctan(1/sqrt(3)+2*d^(1/6)*(a+b*x)^(1/6)/(b^(1/6)*(c+d*x)^(1/6)*sqrt(3)))/(b^(1/6)*d^(11/6)*sqrt(3))],
[(a+b*x)^(5/6)/(c+d*x)^(11/6),x,13,-6/5*(a+b*x)^(5/6)/(d*(c+d*x)^(5/6))+2*b^(5/6)*arctanh(d^(1/6)*(a+b*x)^(1/6)/(b^(1/6)*(c+d*x)^(1/6)))/d^(11/6)-1/2*b^(5/6)*log(b^(1/3)+d^(1/3)*(a+b*x)^(1/3)/(c+d*x)^(1/3)-b^(1/6)*d^(1/6)*(a+b*x)^(1/6)/(c+d*x)^(1/6))/d^(11/6)+1/2*b^(5/6)*log(b^(1/3)+d^(1/3)*(a+b*x)^(1/3)/(c+d*x)^(1/3)+b^(1/6)*d^(1/6)*(a+b*x)^(1/6)/(c+d*x)^(1/6))/d^(11/6)+b^(5/6)*arctan(1/sqrt(3)-2*d^(1/6)*(a+b*x)^(1/6)/(b^(1/6)*(c+d*x)^(1/6)*sqrt(3)))*sqrt(3)/d^(11/6)-b^(5/6)*arctan(1/sqrt(3)+2*d^(1/6)*(a+b*x)^(1/6)/(b^(1/6)*(c+d*x)^(1/6)*sqrt(3)))*sqrt(3)/d^(11/6)],
[(a+b*x)^(5/6)/(c+d*x)^(17/6),x,1,6/11*(a+b*x)^(11/6)/((b*c-a*d)*(c+d*x)^(11/6))],
[(a+b*x)^(5/6)/(c+d*x)^(23/6),x,2,6/17*(a+b*x)^(11/6)/((b*c-a*d)*(c+d*x)^(17/6))+36/187*b*(a+b*x)^(11/6)/((b*c-a*d)^2*(c+d*x)^(11/6))],
[(a+b*x)^(5/6)/(c+d*x)^(29/6),x,3,6/23*(a+b*x)^(11/6)/((b*c-a*d)*(c+d*x)^(23/6))+72/391*b*(a+b*x)^(11/6)/((b*c-a*d)^2*(c+d*x)^(17/6))+432/4301*b^2*(a+b*x)^(11/6)/((b*c-a*d)^3*(c+d*x)^(11/6))],
[(a+b*x)^(5/6)/(c+d*x)^(35/6),x,4,6/29*(a+b*x)^(11/6)/((b*c-a*d)*(c+d*x)^(29/6))+108/667*b*(a+b*x)^(11/6)/((b*c-a*d)^2*(c+d*x)^(23/6))+1296/11339*b^2*(a+b*x)^(11/6)/((b*c-a*d)^3*(c+d*x)^(17/6))+7776/124729*b^3*(a+b*x)^(11/6)/((b*c-a*d)^4*(c+d*x)^(11/6))],
[(a+b*x)^(5/6)*(c+d*x)^(11/6),x,2,6/11*(b*c-a*d)*(a+b*x)^(11/6)*(c+d*x)^(5/6)*hypergeom([-11/6,11/6],[17/6],-d*(a+b*x)/(b*c-a*d))/(b^2*(b*(c+d*x)/(b*c-a*d))^(5/6))],
[(a+b*x)^(5/6)*(c+d*x)^(5/6),x,2,6/11*(a+b*x)^(11/6)*(c+d*x)^(5/6)*hypergeom([-5/6,11/6],[17/6],-d*(a+b*x)/(b*c-a*d))/(b*(b*(c+d*x)/(b*c-a*d))^(5/6))],
[(a+b*x)^(5/6)/(c+d*x)^(1/6),x,2,6/11*(a+b*x)^(11/6)*(b*(c+d*x)/(b*c-a*d))^(1/6)*hypergeom([1/6,11/6],[17/6],-d*(a+b*x)/(b*c-a*d))/(b*(c+d*x)^(1/6))],
[(a+b*x)^(5/6)/(c+d*x)^(7/6),x,2,6/11*(a+b*x)^(11/6)*(b*(c+d*x)/(b*c-a*d))^(1/6)*hypergeom([7/6,11/6],[17/6],-d*(a+b*x)/(b*c-a*d))/((b*c-a*d)*(c+d*x)^(1/6))],
[(a+b*x)^(5/6)/(c+d*x)^(13/6),x,2,6/11*b*(a+b*x)^(11/6)*(b*(c+d*x)/(b*c-a*d))^(1/6)*hypergeom([11/6,13/6],[17/6],-d*(a+b*x)/(b*c-a*d))/((b*c-a*d)^2*(c+d*x)^(1/6))],
[(a+b*x)^(5/6)/(c+d*x)^(19/6),x,2,6/11*b^2*(a+b*x)^(11/6)*(b*(c+d*x)/(b*c-a*d))^(1/6)*hypergeom([11/6,19/6],[17/6],-d*(a+b*x)/(b*c-a*d))/((b*c-a*d)^3*(c+d*x)^(1/6))],
[(a+b*x)^(7/6)*(c+d*x)^(13/6),x,2,6/13*(b*c-a*d)^2*(a+b*x)^(13/6)*(c+d*x)^(1/6)*hypergeom([-13/6,13/6],[19/6],-d*(a+b*x)/(b*c-a*d))/(b^3*(b*(c+d*x)/(b*c-a*d))^(1/6))],
[(a+b*x)^(7/6)*(c+d*x)^(7/6),x,2,6/13*(b*c-a*d)*(a+b*x)^(13/6)*(c+d*x)^(1/6)*hypergeom([-7/6,13/6],[19/6],-d*(a+b*x)/(b*c-a*d))/(b^2*(b*(c+d*x)/(b*c-a*d))^(1/6))],
[(a+b*x)^(7/6)*(c+d*x)^(1/6),x,2,6/13*(a+b*x)^(13/6)*(c+d*x)^(1/6)*hypergeom([-1/6,13/6],[19/6],-d*(a+b*x)/(b*c-a*d))/(b*(b*(c+d*x)/(b*c-a*d))^(1/6))],
[(a+b*x)^(7/6)/(c+d*x)^(5/6),x,2,6/13*(a+b*x)^(13/6)*(b*(c+d*x)/(b*c-a*d))^(5/6)*hypergeom([5/6,13/6],[19/6],-d*(a+b*x)/(b*c-a*d))/(b*(c+d*x)^(5/6))],
[(a+b*x)^(7/6)/(c+d*x)^(11/6),x,2,6/13*(a+b*x)^(13/6)*(b*(c+d*x)/(b*c-a*d))^(5/6)*hypergeom([11/6,13/6],[19/6],-d*(a+b*x)/(b*c-a*d))/((b*c-a*d)*(c+d*x)^(5/6))],
[(a+b*x)^(7/6)/(c+d*x)^(17/6),x,2,6/13*b*(a+b*x)^(13/6)*(b*(c+d*x)/(b*c-a*d))^(5/6)*hypergeom([13/6,17/6],[19/6],-d*(a+b*x)/(b*c-a*d))/((b*c-a*d)^2*(c+d*x)^(5/6))],
[(a+b*x)^(7/6)/(c+d*x)^(1/6),x,14,-7/12*(b*c-a*d)*(a+b*x)^(1/6)*(c+d*x)^(5/6)/d^2+1/2*(a+b*x)^(7/6)*(c+d*x)^(5/6)/d+7/36*(b*c-a*d)^2*arctanh(d^(1/6)*(a+b*x)^(1/6)/(b^(1/6)*(c+d*x)^(1/6)))/(b^(5/6)*d^(13/6))-7/144*(b*c-a*d)^2*log(b^(1/3)+d^(1/3)*(a+b*x)^(1/3)/(c+d*x)^(1/3)-b^(1/6)*d^(1/6)*(a+b*x)^(1/6)/(c+d*x)^(1/6))/(b^(5/6)*d^(13/6))+7/144*(b*c-a*d)^2*log(b^(1/3)+d^(1/3)*(a+b*x)^(1/3)/(c+d*x)^(1/3)+b^(1/6)*d^(1/6)*(a+b*x)^(1/6)/(c+d*x)^(1/6))/(b^(5/6)*d^(13/6))-7/24*(b*c-a*d)^2*arctan(1/sqrt(3)-2*d^(1/6)*(a+b*x)^(1/6)/(b^(1/6)*(c+d*x)^(1/6)*sqrt(3)))/(b^(5/6)*d^(13/6)*sqrt(3))+7/24*(b*c-a*d)^2*arctan(1/sqrt(3)+2*d^(1/6)*(a+b*x)^(1/6)/(b^(1/6)*(c+d*x)^(1/6)*sqrt(3)))/(b^(5/6)*d^(13/6)*sqrt(3))],
[(a+b*x)^(7/6)/(c+d*x)^(7/6),x,14,-6*(a+b*x)^(7/6)/(d*(c+d*x)^(1/6))+7*b*(a+b*x)^(1/6)*(c+d*x)^(5/6)/d^2-7/3*b^(1/6)*(b*c-a*d)*arctanh(d^(1/6)*(a+b*x)^(1/6)/(b^(1/6)*(c+d*x)^(1/6)))/d^(13/6)+7/12*b^(1/6)*(b*c-a*d)*log(b^(1/3)+d^(1/3)*(a+b*x)^(1/3)/(c+d*x)^(1/3)-b^(1/6)*d^(1/6)*(a+b*x)^(1/6)/(c+d*x)^(1/6))/d^(13/6)-7/12*b^(1/6)*(b*c-a*d)*log(b^(1/3)+d^(1/3)*(a+b*x)^(1/3)/(c+d*x)^(1/3)+b^(1/6)*d^(1/6)*(a+b*x)^(1/6)/(c+d*x)^(1/6))/d^(13/6)+7/2*b^(1/6)*(b*c-a*d)*arctan(1/sqrt(3)-2*d^(1/6)*(a+b*x)^(1/6)/(b^(1/6)*(c+d*x)^(1/6)*sqrt(3)))/(d^(13/6)*sqrt(3))-7/2*b^(1/6)*(b*c-a*d)*arctan(1/sqrt(3)+2*d^(1/6)*(a+b*x)^(1/6)/(b^(1/6)*(c+d*x)^(1/6)*sqrt(3)))/(d^(13/6)*sqrt(3))],
[(a+b*x)^(7/6)/(c+d*x)^(13/6),x,14,-6/7*(a+b*x)^(7/6)/(d*(c+d*x)^(7/6))-6*b*(a+b*x)^(1/6)/(d^2*(c+d*x)^(1/6))+2*b^(7/6)*arctanh(d^(1/6)*(a+b*x)^(1/6)/(b^(1/6)*(c+d*x)^(1/6)))/d^(13/6)-1/2*b^(7/6)*log(b^(1/3)+d^(1/3)*(a+b*x)^(1/3)/(c+d*x)^(1/3)-b^(1/6)*d^(1/6)*(a+b*x)^(1/6)/(c+d*x)^(1/6))/d^(13/6)+1/2*b^(7/6)*log(b^(1/3)+d^(1/3)*(a+b*x)^(1/3)/(c+d*x)^(1/3)+b^(1/6)*d^(1/6)*(a+b*x)^(1/6)/(c+d*x)^(1/6))/d^(13/6)-b^(7/6)*arctan(1/sqrt(3)-2*d^(1/6)*(a+b*x)^(1/6)/(b^(1/6)*(c+d*x)^(1/6)*sqrt(3)))*sqrt(3)/d^(13/6)+b^(7/6)*arctan(1/sqrt(3)+2*d^(1/6)*(a+b*x)^(1/6)/(b^(1/6)*(c+d*x)^(1/6)*sqrt(3)))*sqrt(3)/d^(13/6)],
[(a+b*x)^(7/6)/(c+d*x)^(19/6),x,1,6/13*(a+b*x)^(13/6)/((b*c-a*d)*(c+d*x)^(13/6))],
[(a+b*x)^(7/6)/(c+d*x)^(25/6),x,2,6/19*(a+b*x)^(13/6)/((b*c-a*d)*(c+d*x)^(19/6))+36/247*b*(a+b*x)^(13/6)/((b*c-a*d)^2*(c+d*x)^(13/6))],
[(a+b*x)^(7/6)/(c+d*x)^(31/6),x,3,6/25*(a+b*x)^(13/6)/((b*c-a*d)*(c+d*x)^(25/6))+72/475*b*(a+b*x)^(13/6)/((b*c-a*d)^2*(c+d*x)^(19/6))+432/6175*b^2*(a+b*x)^(13/6)/((b*c-a*d)^3*(c+d*x)^(13/6))],
[(a+b*x)^(7/6)/(c+d*x)^(37/6),x,4,6/31*(a+b*x)^(13/6)/((b*c-a*d)*(c+d*x)^(31/6))+108/775*b*(a+b*x)^(13/6)/((b*c-a*d)^2*(c+d*x)^(25/6))+1296/14725*b^2*(a+b*x)^(13/6)/((b*c-a*d)^3*(c+d*x)^(19/6))+7776/191425*b^3*(a+b*x)^(13/6)/((b*c-a*d)^4*(c+d*x)^(13/6))],
[(c+d*x)^(7/6)/(a+b*x)^(1/6),x,14,7/12*(b*c-a*d)*(a+b*x)^(5/6)*(c+d*x)^(1/6)/b^2+1/2*(a+b*x)^(5/6)*(c+d*x)^(7/6)/b+7/36*(b*c-a*d)^2*arctanh(d^(1/6)*(a+b*x)^(1/6)/(b^(1/6)*(c+d*x)^(1/6)))/(b^(13/6)*d^(5/6))-7/144*(b*c-a*d)^2*log(b^(1/3)+d^(1/3)*(a+b*x)^(1/3)/(c+d*x)^(1/3)-b^(1/6)*d^(1/6)*(a+b*x)^(1/6)/(c+d*x)^(1/6))/(b^(13/6)*d^(5/6))+7/144*(b*c-a*d)^2*log(b^(1/3)+d^(1/3)*(a+b*x)^(1/3)/(c+d*x)^(1/3)+b^(1/6)*d^(1/6)*(a+b*x)^(1/6)/(c+d*x)^(1/6))/(b^(13/6)*d^(5/6))+7/24*(b*c-a*d)^2*arctan(1/sqrt(3)-2*d^(1/6)*(a+b*x)^(1/6)/(b^(1/6)*(c+d*x)^(1/6)*sqrt(3)))/(b^(13/6)*d^(5/6)*sqrt(3))-7/24*(b*c-a*d)^2*arctan(1/sqrt(3)+2*d^(1/6)*(a+b*x)^(1/6)/(b^(1/6)*(c+d*x)^(1/6)*sqrt(3)))/(b^(13/6)*d^(5/6)*sqrt(3))],

# m<0
[(c+d*x)^(1/6)/(a+b*x)^(1/6),x,13,(a+b*x)^(5/6)*(c+d*x)^(1/6)/b+1/3*(b*c-a*d)*arctanh(d^(1/6)*(a+b*x)^(1/6)/(b^(1/6)*(c+d*x)^(1/6)))/(b^(7/6)*d^(5/6))-1/12*(b*c-a*d)*log(b^(1/3)+d^(1/3)*(a+b*x)^(1/3)/(c+d*x)^(1/3)-b^(1/6)*d^(1/6)*(a+b*x)^(1/6)/(c+d*x)^(1/6))/(b^(7/6)*d^(5/6))+1/12*(b*c-a*d)*log(b^(1/3)+d^(1/3)*(a+b*x)^(1/3)/(c+d*x)^(1/3)+b^(1/6)*d^(1/6)*(a+b*x)^(1/6)/(c+d*x)^(1/6))/(b^(7/6)*d^(5/6))+1/2*(b*c-a*d)*arctan(1/sqrt(3)-2*d^(1/6)*(a+b*x)^(1/6)/(b^(1/6)*(c+d*x)^(1/6)*sqrt(3)))/(b^(7/6)*d^(5/6)*sqrt(3))-1/2*(b*c-a*d)*arctan(1/sqrt(3)+2*d^(1/6)*(a+b*x)^(1/6)/(b^(1/6)*(c+d*x)^(1/6)*sqrt(3)))/(b^(7/6)*d^(5/6)*sqrt(3))],
[1/((a+b*x)^(1/6)*(c+d*x)^(5/6)),x,12,2*arctanh(d^(1/6)*(a+b*x)^(1/6)/(b^(1/6)*(c+d*x)^(1/6)))/(b^(1/6)*d^(5/6))-1/2*log(b^(1/3)+d^(1/3)*(a+b*x)^(1/3)/(c+d*x)^(1/3)-b^(1/6)*d^(1/6)*(a+b*x)^(1/6)/(c+d*x)^(1/6))/(b^(1/6)*d^(5/6))+1/2*log(b^(1/3)+d^(1/3)*(a+b*x)^(1/3)/(c+d*x)^(1/3)+b^(1/6)*d^(1/6)*(a+b*x)^(1/6)/(c+d*x)^(1/6))/(b^(1/6)*d^(5/6))+arctan(1/sqrt(3)-2*d^(1/6)*(a+b*x)^(1/6)/(b^(1/6)*(c+d*x)^(1/6)*sqrt(3)))*sqrt(3)/(b^(1/6)*d^(5/6))-arctan(1/sqrt(3)+2*d^(1/6)*(a+b*x)^(1/6)/(b^(1/6)*(c+d*x)^(1/6)*sqrt(3)))*sqrt(3)/(b^(1/6)*d^(5/6))],
[1/((a+b*x)^(1/6)*(c+d*x)^(11/6)),x,1,6/5*(a+b*x)^(5/6)/((b*c-a*d)*(c+d*x)^(5/6))],
[1/((a+b*x)^(1/6)*(c+d*x)^(17/6)),x,2,6/11*(a+b*x)^(5/6)/((b*c-a*d)*(c+d*x)^(11/6))+36/55*b*(a+b*x)^(5/6)/((b*c-a*d)^2*(c+d*x)^(5/6))],
[1/((a+b*x)^(1/6)*(c+d*x)^(23/6)),x,3,6/17*(a+b*x)^(5/6)/((b*c-a*d)*(c+d*x)^(17/6))+72/187*b*(a+b*x)^(5/6)/((b*c-a*d)^2*(c+d*x)^(11/6))+432/935*b^2*(a+b*x)^(5/6)/((b*c-a*d)^3*(c+d*x)^(5/6))],
[1/((a+b*x)^(1/6)*(c+d*x)^(29/6)),x,4,6/23*(a+b*x)^(5/6)/((b*c-a*d)*(c+d*x)^(23/6))+108/391*b*(a+b*x)^(5/6)/((b*c-a*d)^2*(c+d*x)^(17/6))+1296/4301*b^2*(a+b*x)^(5/6)/((b*c-a*d)^3*(c+d*x)^(11/6))+7776/21505*b^3*(a+b*x)^(5/6)/((b*c-a*d)^4*(c+d*x)^(5/6))],
[(c+d*x)^(11/6)/(a+b*x)^(1/6),x,2,6/5*(b*c-a*d)*(a+b*x)^(5/6)*(c+d*x)^(5/6)*hypergeom([-11/6,5/6],[11/6],-d*(a+b*x)/(b*c-a*d))/(b^2*(b*(c+d*x)/(b*c-a*d))^(5/6))],
[(c+d*x)^(5/6)/(a+b*x)^(1/6),x,2,6/5*(a+b*x)^(5/6)*(c+d*x)^(5/6)*hypergeom([-5/6,5/6],[11/6],-d*(a+b*x)/(b*c-a*d))/(b*(b*(c+d*x)/(b*c-a*d))^(5/6))],
[1/((a+b*x)^(1/6)*(c+d*x)^(1/6)),x,2,6/5*(a+b*x)^(5/6)*(b*(c+d*x)/(b*c-a*d))^(1/6)*hypergeom([1/6,5/6],[11/6],-d*(a+b*x)/(b*c-a*d))/(b*(c+d*x)^(1/6))],
[1/((a+b*x)^(1/6)*(c+d*x)^(7/6)),x,2,6/5*(a+b*x)^(5/6)*(b*(c+d*x)/(b*c-a*d))^(1/6)*hypergeom([5/6,7/6],[11/6],-d*(a+b*x)/(b*c-a*d))/((b*c-a*d)*(c+d*x)^(1/6))],
[1/((a+b*x)^(1/6)*(c+d*x)^(13/6)),x,2,6/5*b*(a+b*x)^(5/6)*(b*(c+d*x)/(b*c-a*d))^(1/6)*hypergeom([5/6,13/6],[11/6],-d*(a+b*x)/(b*c-a*d))/((b*c-a*d)^2*(c+d*x)^(1/6))],
[1/((a+b*x)^(1/6)*(c+d*x)^(19/6)),x,2,6/5*b^2*(a+b*x)^(5/6)*(b*(c+d*x)/(b*c-a*d))^(1/6)*hypergeom([5/6,19/6],[11/6],-d*(a+b*x)/(b*c-a*d))/((b*c-a*d)^3*(c+d*x)^(1/6))],
[(c+d*x)^(13/6)/(a+b*x)^(5/6),x,2,6*(b*c-a*d)^2*(a+b*x)^(1/6)*(c+d*x)^(1/6)*hypergeom([-13/6,1/6],[7/6],-d*(a+b*x)/(b*c-a*d))/(b^3*(b*(c+d*x)/(b*c-a*d))^(1/6))],
[(c+d*x)^(7/6)/(a+b*x)^(5/6),x,2,6*(b*c-a*d)*(a+b*x)^(1/6)*(c+d*x)^(1/6)*hypergeom([-7/6,1/6],[7/6],-d*(a+b*x)/(b*c-a*d))/(b^2*(b*(c+d*x)/(b*c-a*d))^(1/6))],
[(c+d*x)^(1/6)/(a+b*x)^(5/6),x,2,6*(a+b*x)^(1/6)*(c+d*x)^(1/6)*hypergeom([-1/6,1/6],[7/6],-d*(a+b*x)/(b*c-a*d))/(b*(b*(c+d*x)/(b*c-a*d))^(1/6))],
[1/((a+b*x)^(5/6)*(c+d*x)^(5/6)),x,2,6*(a+b*x)^(1/6)*(b*(c+d*x)/(b*c-a*d))^(5/6)*hypergeom([1/6,5/6],[7/6],-d*(a+b*x)/(b*c-a*d))/(b*(c+d*x)^(5/6))],
[1/((a+b*x)^(5/6)*(c+d*x)^(11/6)),x,2,6*(a+b*x)^(1/6)*(b*(c+d*x)/(b*c-a*d))^(5/6)*hypergeom([1/6,11/6],[7/6],-d*(a+b*x)/(b*c-a*d))/((b*c-a*d)*(c+d*x)^(5/6))],
[1/((a+b*x)^(5/6)*(c+d*x)^(17/6)),x,2,6*b*(a+b*x)^(1/6)*(b*(c+d*x)/(b*c-a*d))^(5/6)*hypergeom([1/6,17/6],[7/6],-d*(a+b*x)/(b*c-a*d))/((b*c-a*d)^2*(c+d*x)^(5/6))],
[(c+d*x)^(11/6)/(a+b*x)^(5/6),x,14,11/12*(b*c-a*d)*(a+b*x)^(1/6)*(c+d*x)^(5/6)/b^2+1/2*(a+b*x)^(1/6)*(c+d*x)^(11/6)/b+55/36*(b*c-a*d)^2*arctanh(d^(1/6)*(a+b*x)^(1/6)/(b^(1/6)*(c+d*x)^(1/6)))/(b^(17/6)*d^(1/6))-55/144*(b*c-a*d)^2*log(b^(1/3)+d^(1/3)*(a+b*x)^(1/3)/(c+d*x)^(1/3)-b^(1/6)*d^(1/6)*(a+b*x)^(1/6)/(c+d*x)^(1/6))/(b^(17/6)*d^(1/6))+55/144*(b*c-a*d)^2*log(b^(1/3)+d^(1/3)*(a+b*x)^(1/3)/(c+d*x)^(1/3)+b^(1/6)*d^(1/6)*(a+b*x)^(1/6)/(c+d*x)^(1/6))/(b^(17/6)*d^(1/6))-55/24*(b*c-a*d)^2*arctan(1/sqrt(3)-2*d^(1/6)*(a+b*x)^(1/6)/(b^(1/6)*(c+d*x)^(1/6)*sqrt(3)))/(b^(17/6)*d^(1/6)*sqrt(3))+55/24*(b*c-a*d)^2*arctan(1/sqrt(3)+2*d^(1/6)*(a+b*x)^(1/6)/(b^(1/6)*(c+d*x)^(1/6)*sqrt(3)))/(b^(17/6)*d^(1/6)*sqrt(3))],
[(c+d*x)^(5/6)/(a+b*x)^(5/6),x,13,(a+b*x)^(1/6)*(c+d*x)^(5/6)/b+5/3*(b*c-a*d)*arctanh(d^(1/6)*(a+b*x)^(1/6)/(b^(1/6)*(c+d*x)^(1/6)))/(b^(11/6)*d^(1/6))-5/12*(b*c-a*d)*log(b^(1/3)+d^(1/3)*(a+b*x)^(1/3)/(c+d*x)^(1/3)-b^(1/6)*d^(1/6)*(a+b*x)^(1/6)/(c+d*x)^(1/6))/(b^(11/6)*d^(1/6))+5/12*(b*c-a*d)*log(b^(1/3)+d^(1/3)*(a+b*x)^(1/3)/(c+d*x)^(1/3)+b^(1/6)*d^(1/6)*(a+b*x)^(1/6)/(c+d*x)^(1/6))/(b^(11/6)*d^(1/6))-5/2*(b*c-a*d)*arctan(1/sqrt(3)-2*d^(1/6)*(a+b*x)^(1/6)/(b^(1/6)*(c+d*x)^(1/6)*sqrt(3)))/(b^(11/6)*d^(1/6)*sqrt(3))+5/2*(b*c-a*d)*arctan(1/sqrt(3)+2*d^(1/6)*(a+b*x)^(1/6)/(b^(1/6)*(c+d*x)^(1/6)*sqrt(3)))/(b^(11/6)*d^(1/6)*sqrt(3))],
[1/((a+b*x)^(5/6)*(c+d*x)^(1/6)),x,12,2*arctanh(d^(1/6)*(a+b*x)^(1/6)/(b^(1/6)*(c+d*x)^(1/6)))/(b^(5/6)*d^(1/6))-1/2*log(b^(1/3)+d^(1/3)*(a+b*x)^(1/3)/(c+d*x)^(1/3)-b^(1/6)*d^(1/6)*(a+b*x)^(1/6)/(c+d*x)^(1/6))/(b^(5/6)*d^(1/6))+1/2*log(b^(1/3)+d^(1/3)*(a+b*x)^(1/3)/(c+d*x)^(1/3)+b^(1/6)*d^(1/6)*(a+b*x)^(1/6)/(c+d*x)^(1/6))/(b^(5/6)*d^(1/6))-arctan(1/sqrt(3)-2*d^(1/6)*(a+b*x)^(1/6)/(b^(1/6)*(c+d*x)^(1/6)*sqrt(3)))*sqrt(3)/(b^(5/6)*d^(1/6))+arctan(1/sqrt(3)+2*d^(1/6)*(a+b*x)^(1/6)/(b^(1/6)*(c+d*x)^(1/6)*sqrt(3)))*sqrt(3)/(b^(5/6)*d^(1/6))],
[1/((a+b*x)^(5/6)*(c+d*x)^(7/6)),x,1,6*(a+b*x)^(1/6)/((b*c-a*d)*(c+d*x)^(1/6))],
[1/((a+b*x)^(5/6)*(c+d*x)^(13/6)),x,2,6/7*(a+b*x)^(1/6)/((b*c-a*d)*(c+d*x)^(7/6))+36/7*b*(a+b*x)^(1/6)/((b*c-a*d)^2*(c+d*x)^(1/6))],
[1/((a+b*x)^(5/6)*(c+d*x)^(19/6)),x,3,6/13*(a+b*x)^(1/6)/((b*c-a*d)*(c+d*x)^(13/6))+72/91*b*(a+b*x)^(1/6)/((b*c-a*d)^2*(c+d*x)^(7/6))+432/91*b^2*(a+b*x)^(1/6)/((b*c-a*d)^3*(c+d*x)^(1/6))],
[1/((a+b*x)^(5/6)*(c+d*x)^(25/6)),x,4,6/19*(a+b*x)^(1/6)/((b*c-a*d)*(c+d*x)^(19/6))+108/247*b*(a+b*x)^(1/6)/((b*c-a*d)^2*(c+d*x)^(13/6))+1296/1729*b^2*(a+b*x)^(1/6)/((b*c-a*d)^3*(c+d*x)^(7/6))+7776/1729*b^3*(a+b*x)^(1/6)/((b*c-a*d)^4*(c+d*x)^(1/6))],
[(c+d*x)^(13/6)/(a+b*x)^(7/6),x,15,91/12*d*(b*c-a*d)*(a+b*x)^(5/6)*(c+d*x)^(1/6)/b^3+13/2*d*(a+b*x)^(5/6)*(c+d*x)^(7/6)/b^2-6*(c+d*x)^(13/6)/(b*(a+b*x)^(1/6))+91/36*d^(1/6)*(b*c-a*d)^2*arctanh(d^(1/6)*(a+b*x)^(1/6)/(b^(1/6)*(c+d*x)^(1/6)))/b^(19/6)-91/144*d^(1/6)*(b*c-a*d)^2*log(b^(1/3)+d^(1/3)*(a+b*x)^(1/3)/(c+d*x)^(1/3)-b^(1/6)*d^(1/6)*(a+b*x)^(1/6)/(c+d*x)^(1/6))/b^(19/6)+91/144*d^(1/6)*(b*c-a*d)^2*log(b^(1/3)+d^(1/3)*(a+b*x)^(1/3)/(c+d*x)^(1/3)+b^(1/6)*d^(1/6)*(a+b*x)^(1/6)/(c+d*x)^(1/6))/b^(19/6)+91/24*d^(1/6)*(b*c-a*d)^2*arctan(1/sqrt(3)-2*d^(1/6)*(a+b*x)^(1/6)/(b^(1/6)*(c+d*x)^(1/6)*sqrt(3)))/(b^(19/6)*sqrt(3))-91/24*d^(1/6)*(b*c-a*d)^2*arctan(1/sqrt(3)+2*d^(1/6)*(a+b*x)^(1/6)/(b^(1/6)*(c+d*x)^(1/6)*sqrt(3)))/(b^(19/6)*sqrt(3))],
[(c+d*x)^(7/6)/(a+b*x)^(7/6),x,14,7*d*(a+b*x)^(5/6)*(c+d*x)^(1/6)/b^2-6*(c+d*x)^(7/6)/(b*(a+b*x)^(1/6))+7/3*d^(1/6)*(b*c-a*d)*arctanh(d^(1/6)*(a+b*x)^(1/6)/(b^(1/6)*(c+d*x)^(1/6)))/b^(13/6)-7/12*d^(1/6)*(b*c-a*d)*log(b^(1/3)+d^(1/3)*(a+b*x)^(1/3)/(c+d*x)^(1/3)-b^(1/6)*d^(1/6)*(a+b*x)^(1/6)/(c+d*x)^(1/6))/b^(13/6)+7/12*d^(1/6)*(b*c-a*d)*log(b^(1/3)+d^(1/3)*(a+b*x)^(1/3)/(c+d*x)^(1/3)+b^(1/6)*d^(1/6)*(a+b*x)^(1/6)/(c+d*x)^(1/6))/b^(13/6)+7/2*d^(1/6)*(b*c-a*d)*arctan(1/sqrt(3)-2*d^(1/6)*(a+b*x)^(1/6)/(b^(1/6)*(c+d*x)^(1/6)*sqrt(3)))/(b^(13/6)*sqrt(3))-7/2*d^(1/6)*(b*c-a*d)*arctan(1/sqrt(3)+2*d^(1/6)*(a+b*x)^(1/6)/(b^(1/6)*(c+d*x)^(1/6)*sqrt(3)))/(b^(13/6)*sqrt(3))],
[(c+d*x)^(1/6)/(a+b*x)^(7/6),x,13,-6*(c+d*x)^(1/6)/(b*(a+b*x)^(1/6))+2*d^(1/6)*arctanh(d^(1/6)*(a+b*x)^(1/6)/(b^(1/6)*(c+d*x)^(1/6)))/b^(7/6)-1/2*d^(1/6)*log(b^(1/3)+d^(1/3)*(a+b*x)^(1/3)/(c+d*x)^(1/3)-b^(1/6)*d^(1/6)*(a+b*x)^(1/6)/(c+d*x)^(1/6))/b^(7/6)+1/2*d^(1/6)*log(b^(1/3)+d^(1/3)*(a+b*x)^(1/3)/(c+d*x)^(1/3)+b^(1/6)*d^(1/6)*(a+b*x)^(1/6)/(c+d*x)^(1/6))/b^(7/6)+d^(1/6)*arctan(1/sqrt(3)-2*d^(1/6)*(a+b*x)^(1/6)/(b^(1/6)*(c+d*x)^(1/6)*sqrt(3)))*sqrt(3)/b^(7/6)-d^(1/6)*arctan(1/sqrt(3)+2*d^(1/6)*(a+b*x)^(1/6)/(b^(1/6)*(c+d*x)^(1/6)*sqrt(3)))*sqrt(3)/b^(7/6)],
[1/((a+b*x)^(7/6)*(c+d*x)^(5/6)),x,1,-6*(c+d*x)^(1/6)/((b*c-a*d)*(a+b*x)^(1/6))],
[1/((a+b*x)^(7/6)*(c+d*x)^(11/6)),x,2,(-6)/((b*c-a*d)*(a+b*x)^(1/6)*(c+d*x)^(5/6))-36/5*d*(a+b*x)^(5/6)/((b*c-a*d)^2*(c+d*x)^(5/6))],
[1/((a+b*x)^(7/6)*(c+d*x)^(17/6)),x,3,(-6)/((b*c-a*d)*(a+b*x)^(1/6)*(c+d*x)^(11/6))-72/11*d*(a+b*x)^(5/6)/((b*c-a*d)^2*(c+d*x)^(11/6))-432/55*b*d*(a+b*x)^(5/6)/((b*c-a*d)^3*(c+d*x)^(5/6))],
[1/((a+b*x)^(7/6)*(c+d*x)^(23/6)),x,4,(-6)/((b*c-a*d)*(a+b*x)^(1/6)*(c+d*x)^(17/6))-108/17*d*(a+b*x)^(5/6)/((b*c-a*d)^2*(c+d*x)^(17/6))-1296/187*b*d*(a+b*x)^(5/6)/((b*c-a*d)^3*(c+d*x)^(11/6))-7776/935*b^2*d*(a+b*x)^(5/6)/((b*c-a*d)^4*(c+d*x)^(5/6))],
[(c+d*x)^(11/6)/(a+b*x)^(7/6),x,2,-6*(b*c-a*d)*(c+d*x)^(5/6)*hypergeom([-11/6,-1/6],[5/6],-d*(a+b*x)/(b*c-a*d))/(b^2*(a+b*x)^(1/6)*(b*(c+d*x)/(b*c-a*d))^(5/6))],
[(c+d*x)^(5/6)/(a+b*x)^(7/6),x,2,-6*(c+d*x)^(5/6)*hypergeom([-5/6,-1/6],[5/6],-d*(a+b*x)/(b*c-a*d))/(b*(a+b*x)^(1/6)*(b*(c+d*x)/(b*c-a*d))^(5/6))],
[1/((a+b*x)^(7/6)*(c+d*x)^(1/6)),x,2,-6*(b*(c+d*x)/(b*c-a*d))^(1/6)*hypergeom([-1/6,1/6],[5/6],-d*(a+b*x)/(b*c-a*d))/(b*(a+b*x)^(1/6)*(c+d*x)^(1/6))],
[1/((a+b*x)^(7/6)*(c+d*x)^(7/6)),x,2,-6*(b*(c+d*x)/(b*c-a*d))^(1/6)*hypergeom([-1/6,7/6],[5/6],-d*(a+b*x)/(b*c-a*d))/((b*c-a*d)*(a+b*x)^(1/6)*(c+d*x)^(1/6))],
[1/((a+b*x)^(7/6)*(c+d*x)^(13/6)),x,2,-6*b*(b*(c+d*x)/(b*c-a*d))^(1/6)*hypergeom([-1/6,13/6],[5/6],-d*(a+b*x)/(b*c-a*d))/((b*c-a*d)^2*(a+b*x)^(1/6)*(c+d*x)^(1/6))],
[1/((a+b*x)^(7/6)*(c+d*x)^(19/6)),x,2,-6*b^2*(b*(c+d*x)/(b*c-a*d))^(1/6)*hypergeom([-1/6,19/6],[5/6],-d*(a+b*x)/(b*c-a*d))/((b*c-a*d)^3*(a+b*x)^(1/6)*(c+d*x)^(1/6))],

# Integrands of the form (a+b x)^m (c+d x)^n where m and/or symbolic
[(a+b*x)^m*(a+b*(2+m)*x),x,1,x*(a+b*x)^(1+m)],
[(a+b*x)^m*(c+d*x)^n,x,2,-(a+b*x)^(1+m)*(c+d*x)^(1+n)*hypergeom([1,2+m+n],[2+n],b*(c+d*x)/(b*c-a*d))/((b*c-a*d)*(1+n)),(a+b*x)^(1+m)*(c+d*x)^n*hypergeom([1+m,-n],[2+m],-d*(a+b*x)/(b*c-a*d))/(b*(1+m)*(b*(c+d*x)/(b*c-a*d))^n)],
[(a+b*x)^m*(c+d*x)^3,x,2,(b*c-a*d)^3*(a+b*x)^(1+m)/(b^4*(1+m))+3*d*(b*c-a*d)^2*(a+b*x)^(2+m)/(b^4*(2+m))+3*d^2*(b*c-a*d)*(a+b*x)^(3+m)/(b^4*(3+m))+d^3*(a+b*x)^(4+m)/(b^4*(4+m))],
[(a+b*x)^m*(c+d*x)^2,x,2,(b*c-a*d)^2*(a+b*x)^(1+m)/(b^3*(1+m))+2*d*(b*c-a*d)*(a+b*x)^(2+m)/(b^3*(2+m))+d^2*(a+b*x)^(3+m)/(b^3*(3+m))],
[(a+b*x)^m*(c+d*x),x,2,(b*c-a*d)*(a+b*x)^(1+m)/(b^2*(1+m))+d*(a+b*x)^(2+m)/(b^2*(2+m))],
[(a+b*x)^m/(c+d*x),x,1,(a+b*x)^(1+m)*hypergeom([1,1+m],[2+m],-d*(a+b*x)/(b*c-a*d))/((b*c-a*d)*(1+m))],
[(a+b*x)^m/(c+d*x)^2,x,1,b*(a+b*x)^(1+m)*hypergeom([2,1+m],[2+m],-d*(a+b*x)/(b*c-a*d))/((b*c-a*d)^2*(1+m))],
[(a+b*x)^m/(c+d*x)^3,x,1,b^2*(a+b*x)^(1+m)*hypergeom([3,1+m],[2+m],-d*(a+b*x)/(b*c-a*d))/((b*c-a*d)^3*(1+m))],
[(a+b*x)^3*(c+d*x)^n,x,2,-(b*c-a*d)^3*(c+d*x)^(1+n)/(d^4*(1+n))+3*b*(b*c-a*d)^2*(c+d*x)^(2+n)/(d^4*(2+n))-3*b^2*(b*c-a*d)*(c+d*x)^(3+n)/(d^4*(3+n))+b^3*(c+d*x)^(4+n)/(d^4*(4+n))],
[(a+b*x)^2*(c+d*x)^n,x,2,(b*c-a*d)^2*(c+d*x)^(1+n)/(d^3*(1+n))-2*b*(b*c-a*d)*(c+d*x)^(2+n)/(d^3*(2+n))+b^2*(c+d*x)^(3+n)/(d^3*(3+n))],
[(a+b*x)*(c+d*x)^n,x,2,-(b*c-a*d)*(c+d*x)^(1+n)/(d^2*(1+n))+b*(c+d*x)^(2+n)/(d^2*(2+n))],
[(c+d*x)^n,x,1,(c+d*x)^(1+n)/(d*(1+n))],
[(c+d*x)^n/(a+b*x),x,1,-(c+d*x)^(1+n)*hypergeom([1,1+n],[2+n],b*(c+d*x)/(b*c-a*d))/((b*c-a*d)*(1+n))],
[(c+d*x)^n/(a+b*x)^2,x,1,d*(c+d*x)^(1+n)*hypergeom([2,1+n],[2+n],b*(c+d*x)/(b*c-a*d))/((b*c-a*d)^2*(1+n))],
[(c+d*x)^n/(a+b*x)^3,x,1,-d^2*(c+d*x)^(1+n)*hypergeom([3,1+n],[2+n],b*(c+d*x)/(b*c-a*d))/((b*c-a*d)^3*(1+n))],
[(a+b*x)^(-4+n)/(c+d*x)^n,x,3,-(a+b*x)^(-3+n)*(c+d*x)^(1-n)/((b*c-a*d)*(3-n))+2*d*(a+b*x)^(-2+n)*(c+d*x)^(1-n)/((b*c-a*d)^2*(2-n)*(3-n))-2*d^2*(a+b*x)^(-1+n)*(c+d*x)^(1-n)/((b*c-a*d)^3*(1-n)*(2-n)*(3-n))],
[(a+b*x)^(-3+n)/(c+d*x)^n,x,2,-(a+b*x)^(-2+n)*(c+d*x)^(1-n)/((b*c-a*d)*(2-n))+d*(a+b*x)^(-1+n)*(c+d*x)^(1-n)/((b*c-a*d)^2*(1-n)*(2-n))],
[(a+b*x)^(-2+n)/(c+d*x)^n,x,1,-(a+b*x)^(-1+n)*(c+d*x)^(1-n)/((b*c-a*d)*(1-n))],
[(a+b*x)^(-1+n)/(c+d*x)^n,x,2,(a+b*x)^n*(b*(c+d*x)/(b*c-a*d))^n*hypergeom([n,n],[1+n],-d*(a+b*x)/(b*c-a*d))/(b*n*(c+d*x)^n)],
[(a+b*x)^n/(c+d*x)^n,x,2,(a+b*x)^(1+n)*(b*(c+d*x)/(b*c-a*d))^n*hypergeom([n,1+n],[2+n],-d*(a+b*x)/(b*c-a*d))/(b*(1+n)*(c+d*x)^n)],
[(a+b*x)^(1+n)/(c+d*x)^n,x,2,(a+b*x)^(2+n)*(b*(c+d*x)/(b*c-a*d))^n*hypergeom([n,2+n],[3+n],-d*(a+b*x)/(b*c-a*d))/(b*(2+n)*(c+d*x)^n)],
[(a+b*x)^(2+n)/(c+d*x)^n,x,2,(a+b*x)^(3+n)*(b*(c+d*x)/(b*c-a*d))^n*hypergeom([n,3+n],[4+n],-d*(a+b*x)/(b*c-a*d))/(b*(3+n)*(c+d*x)^n)],
[(c+d*x)^n/(a+b*x)^n,x,2,(-d*(a+b*x)/(b*c-a*d))^n*(c+d*x)^(1+n)*hypergeom([n,1+n],[2+n],b*(c+d*x)/(b*c-a*d))/(d*(1+n)*(a+b*x)^n)],
[(a+b*x)^(-1-n)*(c+d*x)^n,x,2,-(c+d*x)^n*hypergeom([-n,-n],[1-n],-d*(a+b*x)/(b*c-a*d))/(b*n*(a+b*x)^n*(b*(c+d*x)/(b*c-a*d))^n)],
[(a+b*x)^(-2-n)*(c+d*x)^n,x,1,-(a+b*x)^(-1-n)*(c+d*x)^(1+n)/((b*c-a*d)*(1+n))],
[(a+b*x)^(-3-n)*(c+d*x)^n,x,2,-(a+b*x)^(-2-n)*(c+d*x)^(1+n)/((b*c-a*d)*(2+n))+d*(a+b*x)^(-1-n)*(c+d*x)^(1+n)/((b*c-a*d)^2*(1+n)*(2+n))],
[(a+b*x)^(-4-n)*(c+d*x)^n,x,3,-(a+b*x)^(-3-n)*(c+d*x)^(1+n)/((b*c-a*d)*(3+n))+2*d*(a+b*x)^(-2-n)*(c+d*x)^(1+n)/((b*c-a*d)^2*(2+n)*(3+n))-2*d^2*(a+b*x)^(-1-n)*(c+d*x)^(1+n)/((b*c-a*d)^3*(1+n)*(2+n)*(3+n))],
[(a+b*x)^(-5-n)*(c+d*x)^n,x,4,-(a+b*x)^(-4-n)*(c+d*x)^(1+n)/((b*c-a*d)*(4+n))+3*d*(a+b*x)^(-3-n)*(c+d*x)^(1+n)/((b*c-a*d)^2*(3+n)*(4+n))-6*d^2*(a+b*x)^(-2-n)*(c+d*x)^(1+n)/((b*c-a*d)^3*(2+n)*(3+n)*(4+n))+6*d^3*(a+b*x)^(-1-n)*(c+d*x)^(1+n)/((b*c-a*d)^4*(1+n)*(2+n)*(3+n)*(4+n))],
[(a+b*x)^n/(c+d*x)^n,x,2,(a+b*x)^(1+n)*(b*(c+d*x)/(b*c-a*d))^n*hypergeom([n,1+n],[2+n],-d*(a+b*x)/(b*c-a*d))/(b*(1+n)*(c+d*x)^n)],
[(a+b*x)^n*(c+d*x)^(-1-n),x,2,-(a+b*x)^n*hypergeom([-n,-n],[1-n],b*(c+d*x)/(b*c-a*d))/(d*n*(-d*(a+b*x)/(b*c-a*d))^n*(c+d*x)^n)],
[(a+b*x)^n*(c+d*x)^(-2-n),x,1,(a+b*x)^(1+n)*(c+d*x)^(-1-n)/((b*c-a*d)*(1+n))],
[(a+b*x)^n*(c+d*x)^(-3-n),x,2,(a+b*x)^(1+n)*(c+d*x)^(-2-n)/((b*c-a*d)*(2+n))+b*(a+b*x)^(1+n)*(c+d*x)^(-1-n)/((b*c-a*d)^2*(1+n)*(2+n))],
[(a+b*x)^n*(c+d*x)^(-4-n),x,3,(a+b*x)^(1+n)*(c+d*x)^(-3-n)/((b*c-a*d)*(3+n))+2*b*(a+b*x)^(1+n)*(c+d*x)^(-2-n)/((b*c-a*d)^2*(2+n)*(3+n))+2*b^2*(a+b*x)^(1+n)*(c+d*x)^(-1-n)/((b*c-a*d)^3*(1+n)*(2+n)*(3+n))],
[(a+b*x)^n*(c+d*x)^(-5-n),x,4,(a+b*x)^(1+n)*(c+d*x)^(-4-n)/((b*c-a*d)*(4+n))+3*b*(a+b*x)^(1+n)*(c+d*x)^(-3-n)/((b*c-a*d)^2*(3+n)*(4+n))+6*b^2*(a+b*x)^(1+n)*(c+d*x)^(-2-n)/((b*c-a*d)^3*(2+n)*(3+n)*(4+n))+6*b^3*(a+b*x)^(1+n)*(c+d*x)^(-1-n)/((b*c-a*d)^4*(1+n)*(2+n)*(3+n)*(4+n))],
[(a+b*x)^(-2+n)*(c+d*x)^(1-n),x,2,-(b*c-a*d)*(a+b*x)^(-1+n)*(b*(c+d*x)/(b*c-a*d))^n*hypergeom([-1+n,-1+n],[n],-d*(a+b*x)/(b*c-a*d))/(b^2*(1-n)*(c+d*x)^n)],
[(a+b*x)^(1+n)*(c+d*x)^(-1-n),x,2,(b*c-a*d)*(a+b*x)^n*hypergeom([-1-n,-n],[1-n],b*(c+d*x)/(b*c-a*d))/(d^2*n*(-d*(a+b*x)/(b*c-a*d))^n*(c+d*x)^n)],

#  Pseudo-symbolic exponent must be recognized as equal to -1. 
[(a+b*x)^m*(c+d*x)^(1+2*n-2*(1+n)),x,2,(a+b*x)^(1+m)*hypergeom([1,1+m],[2+m],-d*(a+b*x)/(b*c-a*d))/((b*c-a*d)*(1+m))],
[(c+d*x)^(1+2*n-2*(1+n))/(a+b*x)^2,x,3,(-1)/((b*c-a*d)*(a+b*x))-d*log(a+b*x)/(b*c-a*d)^2+d*log(c+d*x)/(b*c-a*d)^2],
[(a+b*x)^m*(a*c*(1+m)+b*c*(2+m)*x)^(-3-m),x,2,-(a+b*x)^(1+m)*(a*c*(1+m)+b*c*(2+m)*x)^(-2-m)/(a*b*c*(2+m))+(a+b*x)^(1+m)*(a*c*(1+m)+b*c*(2+m)*x)^(-1-m)/(a^2*b*c^2*(2+3*m+m^2))],
[(a+b*x)^(-1-b*c/(b*c-a*d))*(c+d*x)^(-1+a*d/(b*c-a*d)),x,2,-(c+d*x)^(a*d/(b*c-a*d))/(b*c*(a+b*x)^(b*c/(b*c-a*d)))+(c+d*x)^(a*d/(b*c-a*d))/(a*b*c*(a+b*x)^(a*d/(b*c-a*d)))],
[(a+b*x)^((-2*b*c+a*d)/(b*c-a*d))*(c+d*x)^((b*c-2*a*d)/(-b*c+a*d)),x,2,-(c+d*x)^(a*d/(b*c-a*d))/(b*c*(a+b*x)^(b*c/(b*c-a*d)))+(c+d*x)^(a*d/(b*c-a*d))/(a*b*c*(a+b*x)^(a*d/(b*c-a*d)))],
[(1-x)^n/sqrt(1+x),x,1,2^(1+n)*hypergeom([1/2,-n],[3/2],1/2*(1+x))*sqrt(1+x)],
[(1+x)^n/sqrt(1-x),x,1,-2^(1+n)*hypergeom([1/2,-n],[3/2],1/2*(1-x))*sqrt(1-x)],
[(1-x)^n*(1+x)^(7/3),x,1,3/5*2^(-1+n)*(1+x)^(10/3)*hypergeom([10/3,-n],[13/3],1/2*(1+x))],
[(1-x)^(7/3)*(1+x)^n,x,1,-3/5*2^(-1+n)*(1-x)^(10/3)*hypergeom([10/3,-n],[13/3],1/2*(1-x))],
[(2+3*x)^m/(1+2*x)^m,x,1,2^(-1-m)*(1+2*x)^(1-m)*hypergeom([1-m,-m],[2-m],-3*(1+2*x))/(1-m)],
[(d*(a+b*x)/(-b*c+a*d))^m*(c+d*x)^n,x,2,(c+d*x)^(1+n)*hypergeom([-m,1+n],[2+n],b*(c+d*x)/(b*c-a*d))/(d*(1+n))],

# Multinomial integrands

# Polynomial integrands
[a+b*x+c*x^2+d*x^3,x,1,a*x+1/2*b*x^2+1/3*c*x^3+1/4*d*x^4],
[-x^3+x^4,x,1,-1/4*x^4+1/5*x^5],
[-1+x^5,x,1,-x+1/6*x^6],
[7+4*x,x,1,7*x+2*x^2],
[4*x+Pi*x^3,x,1,2*x^2+1/4*Pi*x^4],
[2*x+5*x^2,x,1,x^2+5/3*x^3],
[1/2*x^2+1/3*x^3,x,1,1/6*x^3+1/12*x^4],
[3-5*x+2*x^2,x,1,3*x-5/2*x^2+2/3*x^3],
[-2*x+x^2+x^3,x,1,-x^2+1/3*x^3+1/4*x^4],
[1-x^2-3*x^5,x,1,x-1/3*x^3-1/2*x^6],
[5+2*x+3*x^2+4*x^3,x,1,5*x+x^2+x^3+x^4],

# Multinomial integrands
[a+d/x^3+c/x^2+b/x,x,1,-1/2*d/x^2-c/x+a*x+b*log(x)],
[1/x^5+x+x^5,x,1,(-1/4)/x^4+1/2*x^2+1/6*x^6],
[1/x^3+1/x^2+1/x,x,1,(-1/2)/x^2+(-1)/x+log(x)],
[(-2)/x^2+3/x,x,1,2/x+3*log(x)],
[(-1/7)/x^6+x^6,x,1,1/35/x^5+1/7*x^7],
[1+1/x+x,x,1,x+1/2*x^2+log(x)],
[(-3)/x^3+4/x^2,x,1,3/2/x^2+(-4)/x],
[1/x+2*x+x^2,x,1,x^2+1/3*x^3+log(x)],
[x^(5/6)-x^3,x,1,6/11*x^(11/6)-1/4*x^4],
[33+x^(1/33),x,1,33*x+33/34*x^(34/33)],
[1/2/sqrt(x)+2*sqrt(x),x,1,4/3*x^(3/2)+sqrt(x)],
[(-1)/x^2+10/x+6*sqrt(x),x,1,1/x+4*x^(3/2)+10*log(x)],
[1/x^(3/2)+x^(3/2),x,1,2/5*x^(5/2)+(-2)/sqrt(x)],
[-5*x^(3/2)+7*x^(5/2),x,1,-2*x^(5/2)+2*x^(7/2)],
[-1/2*x+2/sqrt(x)+sqrt(x),x,1,2/3*x^(3/2)-1/4*x^2+4*sqrt(x)],
[(-2)/x+x^(3/2)+1/5*sqrt(x),x,1,2/15*x^(3/2)+2/5*x^(5/2)-2*log(x)]]:
