# Maple integration test file: "1 Algebraic functions\1.1 Binomial products\1.1.1 Linear\1.1.1.3 (a+b x)^m (c+d x)^n (e+f x)^p.txt"

lst:=[

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

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

# Integrands of the form x^m (a+b x)^n (c+d x)^p when b c+a d=0
[x^2/((-1+x)^2*(1+x)^2),x,3,1/2*x/(1-x^2)-1/2*arctanh(x)],

# Integrands of the form x^m (a+b x)^1 (c+d x)^p when b c+a d=0

# p>0
[x^2*(a+b*x)*(a*c-b*c*x)^3,x,2,1/3*a^4*c^3*x^3-1/2*a^3*b*c^3*x^4+1/3*a*b^3*c^3*x^6-1/7*b^4*c^3*x^7],
[x*(a+b*x)*(a*c-b*c*x)^3,x,2,1/2*a^4*c^3*x^2-2/3*a^3*b*c^3*x^3+2/5*a*b^3*c^3*x^5-1/6*b^4*c^3*x^6],
[(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)^3/x,x,2,-2*a^3*b*c^3*x+2/3*a*b^3*c^3*x^3-1/4*b^4*c^3*x^4+a^4*c^3*log(x)],
[(a+b*x)*(a*c-b*c*x)^3/x^2,x,2,-a^4*c^3/x+a*b^3*c^3*x^2-1/3*b^4*c^3*x^3-2*a^3*b*c^3*log(x)],
[(a+b*x)*(a*c-b*c*x)^3/x^3,x,1,-1/2*c^3*(a-b*x)^4/x^2],
[(a+b*x)*(a*c-b*c*x)^3/x^4,x,2,-1/3*a^4*c^3/x^3+a^3*b*c^3/x^2-b^4*c^3*x+2*a*b^3*c^3*log(x)],
[(a+b*x)*(a*c-b*c*x)^3/x^5,x,2,-1/4*a^4*c^3/x^4+2/3*a^3*b*c^3/x^3-2*a*b^3*c^3/x-b^4*c^3*log(x)],
[(a+b*x)*(a*c-b*c*x)^3/x^6,x,2,-1/5*a^4*c^3/x^5+1/2*a^3*b*c^3/x^4-a*b^3*c^3/x^2+b^4*c^3/x],
[(a+b*x)*(a*c-b*c*x)^3/x^7,x,2,-1/6*a^4*c^3/x^6+2/5*a^3*b*c^3/x^5-2/3*a*b^3*c^3/x^3+1/2*b^4*c^3/x^2],
[(a+b*x)*(a*c-b*c*x)^3/x^8,x,2,-1/7*a^4*c^3/x^7+1/3*a^3*b*c^3/x^6-1/2*a*b^3*c^3/x^4+1/3*b^4*c^3/x^3],
[x^4*(a+b*x)*(a*c-b*c*x)^4,x,2,1/5*a^5*c^4*x^5-1/2*a^4*b*c^4*x^6+2/7*a^3*b^2*c^4*x^7+1/4*a^2*b^3*c^4*x^8-1/3*a*b^4*c^4*x^9+1/10*b^5*c^4*x^10],
[x^3*(a+b*x)*(a*c-b*c*x)^4,x,2,1/4*a^5*c^4*x^4-3/5*a^4*b*c^4*x^5+1/3*a^3*b^2*c^4*x^6+2/7*a^2*b^3*c^4*x^7-3/8*a*b^4*c^4*x^8+1/9*b^5*c^4*x^9],
[x^2*(a+b*x)*(a*c-b*c*x)^4,x,2,-2/5*a^3*c^4*(a-b*x)^5/b^3+5/6*a^2*c^4*(a-b*x)^6/b^3-4/7*a*c^4*(a-b*x)^7/b^3+1/8*c^4*(a-b*x)^8/b^3],
[x*(a+b*x)*(a*c-b*c*x)^4,x,2,-2/5*a^2*c^4*(a-b*x)^5/b^2+1/2*a*c^4*(a-b*x)^6/b^2-1/7*c^4*(a-b*x)^7/b^2],
[(a+b*x)*(a*c-b*c*x)^4,x,2,-2/5*a*c^4*(a-b*x)^5/b+1/6*c^4*(a-b*x)^6/b],
[(a+b*x)*(a*c-b*c*x)^4/x,x,2,-3*a^4*b*c^4*x+a^3*b^2*c^4*x^2+2/3*a^2*b^3*c^4*x^3-3/4*a*b^4*c^4*x^4+1/5*b^5*c^4*x^5+a^5*c^4*log(x)],
[(a+b*x)*(a*c-b*c*x)^4/x^2,x,2,-a^5*c^4/x+2*a^3*b^2*c^4*x+a^2*b^3*c^4*x^2-a*b^4*c^4*x^3+1/4*b^5*c^4*x^4-3*a^4*b*c^4*log(x)],
[(a+b*x)*(a*c-b*c*x)^4/x^3,x,2,-1/2*a^5*c^4/x^2+3*a^4*b*c^4/x+2*a^2*b^3*c^4*x-3/2*a*b^4*c^4*x^2+1/3*b^5*c^4*x^3+2*a^3*b^2*c^4*log(x)],
[(a+b*x)*(a*c-b*c*x)^4/x^4,x,2,-1/3*a^5*c^4/x^3+3/2*a^4*b*c^4/x^2-2*a^3*b^2*c^4/x-3*a*b^4*c^4*x+1/2*b^5*c^4*x^2+2*a^2*b^3*c^4*log(x)],
[(a+b*x)*(a*c-b*c*x)^4/x^5,x,2,-1/4*a^5*c^4/x^4+a^4*b*c^4/x^3-a^3*b^2*c^4/x^2-2*a^2*b^3*c^4/x+b^5*c^4*x-3*a*b^4*c^4*log(x)],
[(a+b*x)*(a*c-b*c*x)^4/x^6,x,2,-1/5*a^5*c^4/x^5+3/4*a^4*b*c^4/x^4-2/3*a^3*b^2*c^4/x^3-a^2*b^3*c^4/x^2+3*a*b^4*c^4/x+b^5*c^4*log(x)],
[(a+b*x)*(a*c-b*c*x)^4/x^7,x,2,-1/6*c^4*(a-b*x)^5/x^6-7/30*b*c^4*(a-b*x)^5/(a*x^5)],
[(a+b*x)*(a*c-b*c*x)^4/x^8,x,2,-1/7*a^5*c^4/x^7+1/2*a^4*b*c^4/x^6-2/5*a^3*b^2*c^4/x^5-1/2*a^2*b^3*c^4/x^4+a*b^4*c^4/x^3-1/2*b^5*c^4/x^2],
[(a+b*x)*(a*c-b*c*x)^4/x^9,x,2,-1/8*a^5*c^4/x^8+3/7*a^4*b*c^4/x^7-1/3*a^3*b^2*c^4/x^6-2/5*a^2*b^3*c^4/x^5+3/4*a*b^4*c^4/x^4-1/3*b^5*c^4/x^3],
[x^4*(a+b*x)*(a*c-b*c*x)^5,x,2,1/5*a^6*c^5*x^5-2/3*a^5*b*c^5*x^6+5/7*a^4*b^2*c^5*x^7-5/9*a^2*b^4*c^5*x^9+2/5*a*b^5*c^5*x^10-1/11*b^6*c^5*x^11],
[x^3*(a+b*x)*(a*c-b*c*x)^5,x,2,1/4*a^6*c^5*x^4-4/5*a^5*b*c^5*x^5+5/6*a^4*b^2*c^5*x^6-5/8*a^2*b^4*c^5*x^8+4/9*a*b^5*c^5*x^9-1/10*b^6*c^5*x^10],
[x^2*(a+b*x)*(a*c-b*c*x)^5,x,2,-1/3*a^3*c^5*(a-b*x)^6/b^3+5/7*a^2*c^5*(a-b*x)^7/b^3-1/2*a*c^5*(a-b*x)^8/b^3+1/9*c^5*(a-b*x)^9/b^3],
[x*(a+b*x)*(a*c-b*c*x)^5,x,2,-1/3*a^2*c^5*(a-b*x)^6/b^2+3/7*a*c^5*(a-b*x)^7/b^2-1/8*c^5*(a-b*x)^8/b^2],
[(a+b*x)*(a*c-b*c*x)^5,x,2,-1/3*a*c^5*(a-b*x)^6/b+1/7*c^5*(a-b*x)^7/b],
[(a+b*x)*(a*c-b*c*x)^5/x,x,2,-4*a^5*b*c^5*x+5/2*a^4*b^2*c^5*x^2-5/4*a^2*b^4*c^5*x^4+4/5*a*b^5*c^5*x^5-1/6*b^6*c^5*x^6+a^6*c^5*log(x)],
[(a+b*x)*(a*c-b*c*x)^5/x^2,x,2,-a^6*c^5/x+5*a^4*b^2*c^5*x-5/3*a^2*b^4*c^5*x^3+a*b^5*c^5*x^4-1/5*b^6*c^5*x^5-4*a^5*b*c^5*log(x)],
[(a+b*x)*(a*c-b*c*x)^5/x^3,x,2,-1/2*a^6*c^5/x^2+4*a^5*b*c^5/x-5/2*a^2*b^4*c^5*x^2+4/3*a*b^5*c^5*x^3-1/4*b^6*c^5*x^4+5*a^4*b^2*c^5*log(x)],
[(a+b*x)*(a*c-b*c*x)^5/x^4,x,1,-1/3*c^5*(a-b*x)^6/x^3],
[(a+b*x)*(a*c-b*c*x)^5/x^5,x,2,-1/4*a^6*c^5/x^4+4/3*a^5*b*c^5/x^3-5/2*a^4*b^2*c^5/x^2+4*a*b^5*c^5*x-1/2*b^6*c^5*x^2-5*a^2*b^4*c^5*log(x)],
[(a+b*x)*(a*c-b*c*x)^5/x^6,x,2,-1/5*a^6*c^5/x^5+a^5*b*c^5/x^4-5/3*a^4*b^2*c^5/x^3+5*a^2*b^4*c^5/x-b^6*c^5*x+4*a*b^5*c^5*log(x)],
[(a+b*x)*(a*c-b*c*x)^5/x^7,x,2,-1/6*a^6*c^5/x^6+4/5*a^5*b*c^5/x^5-5/4*a^4*b^2*c^5/x^4+5/2*a^2*b^4*c^5/x^2-4*a*b^5*c^5/x-b^6*c^5*log(x)],
[(a+b*x)*(a*c-b*c*x)^5/x^8,x,2,-1/7*c^5*(a-b*x)^6/x^7-4/21*b*c^5*(a-b*x)^6/(a*x^6)],
[(a+b*x)*(a*c-b*c*x)^5/x^9,x,3,-1/8*c^5*(a-b*x)^6/x^8-5/28*b*c^5*(a-b*x)^6/(a*x^7)-5/168*b^2*c^5*(a-b*x)^6/(a^2*x^6)],
[(a+b*x)*(a*c-b*c*x)^5/x^10,x,2,-1/9*a^6*c^5/x^9+1/2*a^5*b*c^5/x^8-5/7*a^4*b^2*c^5/x^7+a^2*b^4*c^5/x^5-a*b^5*c^5/x^4+1/3*b^6*c^5/x^3],
[(a+b*x)*(a*c-b*c*x)^5/x^11,x,2,-1/10*a^6*c^5/x^10+4/9*a^5*b*c^5/x^9-5/8*a^4*b^2*c^5/x^8+5/6*a^2*b^4*c^5/x^6-4/5*a*b^5*c^5/x^5+1/4*b^6*c^5/x^4],
[(a+b*x)*(a*c-b*c*x)^5/x^12,x,2,-1/11*a^6*c^5/x^11+2/5*a^5*b*c^5/x^10-5/9*a^4*b^2*c^5/x^9+5/7*a^2*b^4*c^5/x^7-2/3*a*b^5*c^5/x^6+1/5*b^6*c^5/x^5],
[(a+b*x)*(a*c-b*c*x)^6/x^8,x,2,-1/7*a^7*c^6/x^7+5/6*a^6*b*c^6/x^6-9/5*a^5*b^2*c^6/x^5+5/4*a^4*b^3*c^6/x^4+5/3*a^3*b^4*c^6/x^3-9/2*a^2*b^5*c^6/x^2+5*a*b^6*c^6/x+b^7*c^6*log(x)],
[(a+b*x)*(a*c-b*c*x)^6/x^9,x,2,-1/8*c^6*(a-b*x)^7/x^8-9/56*b*c^6*(a-b*x)^7/(a*x^7)],
[(a+b*x)*(a*c-b*c*x)^6/x^10,x,3,-1/9*c^6*(a-b*x)^7/x^9-11/72*b*c^6*(a-b*x)^7/(a*x^8)-11/504*b^2*c^6*(a-b*x)^7/(a^2*x^7)],
[(a+b*x)*(a*c-b*c*x)^6/x^11,x,4,-1/10*c^6*(a-b*x)^7/x^10-13/90*b*c^6*(a-b*x)^7/(a*x^9)-13/360*b^2*c^6*(a-b*x)^7/(a^2*x^8)-13/2520*b^3*c^6*(a-b*x)^7/(a^3*x^7)],
[(a+b*x)*(a*c-b*c*x)^6/x^12,x,2,-1/11*a^7*c^6/x^11+1/2*a^6*b*c^6/x^10-a^5*b^2*c^6/x^9+5/8*a^4*b^3*c^6/x^8+5/7*a^3*b^4*c^6/x^7-3/2*a^2*b^5*c^6/x^6+a*b^6*c^6/x^5-1/4*b^7*c^6/x^4],
[(a+b*x)*(a*c-b*c*x)^6/x^13,x,2,-1/12*a^7*c^6/x^12+5/11*a^6*b*c^6/x^11-9/10*a^5*b^2*c^6/x^10+5/9*a^4*b^3*c^6/x^9+5/8*a^3*b^4*c^6/x^8-9/7*a^2*b^5*c^6/x^7+5/6*a*b^6*c^6/x^6-1/5*b^7*c^6/x^5],

# p<0

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

# Integrands of the form (e x)^m (a+b x)^n (c+d x)^p when b c+a d=0 and m symbolic
[(e*x)^m*(2-2*a*x)^3*(1+a*x)^4,x,2,8*(e*x)^(1+m)/(e*(1+m))+8*a*(e*x)^(2+m)/(e^2*(2+m))-24*a^2*(e*x)^(3+m)/(e^3*(3+m))-24*a^3*(e*x)^(4+m)/(e^4*(4+m))+24*a^4*(e*x)^(5+m)/(e^5*(5+m))+24*a^5*(e*x)^(6+m)/(e^6*(6+m))-8*a^6*(e*x)^(7+m)/(e^7*(7+m))-8*a^7*(e*x)^(8+m)/(e^8*(8+m))],
[(e*x)^m*(2-2*a*x)^2*(1+a*x)^3,x,2,4*(e*x)^(1+m)/(e*(1+m))+4*a*(e*x)^(2+m)/(e^2*(2+m))-8*a^2*(e*x)^(3+m)/(e^3*(3+m))-8*a^3*(e*x)^(4+m)/(e^4*(4+m))+4*a^4*(e*x)^(5+m)/(e^5*(5+m))+4*a^5*(e*x)^(6+m)/(e^6*(6+m))],
[(e*x)^m*(2-2*a*x)*(1+a*x)^2,x,2,2*(e*x)^(1+m)/(e*(1+m))+2*a*(e*x)^(2+m)/(e^2*(2+m))-2*a^2*(e*x)^(3+m)/(e^3*(3+m))-2*a^3*(e*x)^(4+m)/(e^4*(4+m))],
[(e*x)^m/((2-2*a*x)^2*(1+a*x)),x,5,1/4*(e*x)^(1+m)*hypergeom([2,1/2*(1+m)],[1/2*(3+m)],a^2*x^2)/(e*(1+m))+1/4*a*(e*x)^(2+m)*hypergeom([2,1/2*(2+m)],[1/2*(4+m)],a^2*x^2)/(e^2*(2+m))],
[(e*x)^m/((2-2*a*x)^3*(1+a*x)^2),x,5,1/8*(e*x)^(1+m)*hypergeom([3,1/2*(1+m)],[1/2*(3+m)],a^2*x^2)/(e*(1+m))+1/8*a*(e*x)^(2+m)*hypergeom([3,1/2*(2+m)],[1/2*(4+m)],a^2*x^2)/(e^2*(2+m))],
[(e*x)^m/((2-2*a*x)^4*(1+a*x)^3),x,5,1/16*(e*x)^(1+m)*hypergeom([4,1/2*(1+m)],[1/2*(3+m)],a^2*x^2)/(e*(1+m))+1/16*a*(e*x)^(2+m)*hypergeom([4,1/2*(2+m)],[1/2*(4+m)],a^2*x^2)/(e^2*(2+m))],
[(e*x)^m*(a+b*x)^4*(a*d-b*d*x)^3,x,2,a^7*d^3*(e*x)^(1+m)/(e*(1+m))+a^6*b*d^3*(e*x)^(2+m)/(e^2*(2+m))-3*a^5*b^2*d^3*(e*x)^(3+m)/(e^3*(3+m))-3*a^4*b^3*d^3*(e*x)^(4+m)/(e^4*(4+m))+3*a^3*b^4*d^3*(e*x)^(5+m)/(e^5*(5+m))+3*a^2*b^5*d^3*(e*x)^(6+m)/(e^6*(6+m))-a*b^6*d^3*(e*x)^(7+m)/(e^7*(7+m))-b^7*d^3*(e*x)^(8+m)/(e^8*(8+m))],
[(e*x)^m*(a+b*x)^3*(a*d-b*d*x)^2,x,2,a^5*d^2*(e*x)^(1+m)/(e*(1+m))+a^4*b*d^2*(e*x)^(2+m)/(e^2*(2+m))-2*a^3*b^2*d^2*(e*x)^(3+m)/(e^3*(3+m))-2*a^2*b^3*d^2*(e*x)^(4+m)/(e^4*(4+m))+a*b^4*d^2*(e*x)^(5+m)/(e^5*(5+m))+b^5*d^2*(e*x)^(6+m)/(e^6*(6+m))],
[(e*x)^m*(a+b*x)^2*(a*d-b*d*x),x,2,a^3*d*(e*x)^(1+m)/(e*(1+m))+a^2*b*d*(e*x)^(2+m)/(e^2*(2+m))-a*b^2*d*(e*x)^(3+m)/(e^3*(3+m))-b^3*d*(e*x)^(4+m)/(e^4*(4+m))],
[(e*x)^m/((a+b*x)*(a*d-b*d*x)^2),x,5,(e*x)^(1+m)*hypergeom([2,1/2*(1+m)],[1/2*(3+m)],b^2*x^2/a^2)/(a^3*d^2*e*(1+m))+b*(e*x)^(2+m)*hypergeom([2,1/2*(2+m)],[1/2*(4+m)],b^2*x^2/a^2)/(a^4*d^2*e^2*(2+m))],
[(e*x)^m/((a+b*x)^2*(a*d-b*d*x)^3),x,5,(e*x)^(1+m)*hypergeom([3,1/2*(1+m)],[1/2*(3+m)],b^2*x^2/a^2)/(a^5*d^3*e*(1+m))+b*(e*x)^(2+m)*hypergeom([3,1/2*(2+m)],[1/2*(4+m)],b^2*x^2/a^2)/(a^6*d^3*e^2*(2+m))],
[(e*x)^m/((a+b*x)^3*(a*d-b*d*x)^4),x,5,(e*x)^(1+m)*hypergeom([4,1/2*(1+m)],[1/2*(3+m)],b^2*x^2/a^2)/(a^7*d^4*e*(1+m))+b*(e*x)^(2+m)*hypergeom([4,1/2*(2+m)],[1/2*(4+m)],b^2*x^2/a^2)/(a^8*d^4*e^2*(2+m))],

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

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

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

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

# p>0
[x^4*(a+b*x)*(A+B*x),x,2,1/5*a*A*x^5+1/6*(A*b+a*B)*x^6+1/7*b*B*x^7],
[x^3*(a+b*x)*(A+B*x),x,2,1/4*a*A*x^4+1/5*(A*b+a*B)*x^5+1/6*b*B*x^6],
[x^2*(a+b*x)*(A+B*x),x,2,1/3*a*A*x^3+1/4*(A*b+a*B)*x^4+1/5*b*B*x^5],
[x*(a+b*x)*(A+B*x),x,2,1/2*a*A*x^2+1/3*(A*b+a*B)*x^3+1/4*b*B*x^4],
[(a+b*x)*(A+B*x),x,2,a*A*x+1/2*(A*b+a*B)*x^2+1/3*b*B*x^3],
[(a+b*x)*(A+B*x)/x,x,2,(A*b+a*B)*x+1/2*b*B*x^2+a*A*log(x)],
[(a+b*x)*(A+B*x)/x^2,x,2,-a*A/x+b*B*x+(A*b+a*B)*log(x)],
[(a+b*x)*(A+B*x)/x^3,x,2,-1/2*a*A/x^2+(-A*b-a*B)/x+b*B*log(x)],
[(a+b*x)*(A+B*x)/x^4,x,2,-1/3*a*A/x^3+1/2*(-A*b-a*B)/x^2-b*B/x],
[(a+b*x)*(A+B*x)/x^5,x,2,-1/4*a*A/x^4+1/3*(-A*b-a*B)/x^3-1/2*b*B/x^2],
[(a+b*x)*(A+B*x)/x^6,x,2,-1/5*a*A/x^5+1/4*(-A*b-a*B)/x^4-1/3*b*B/x^3],
[x^4*(a+b*x)^2*(A+B*x),x,2,1/5*a^2*A*x^5+1/6*a*(2*A*b+a*B)*x^6+1/7*b*(A*b+2*a*B)*x^7+1/8*b^2*B*x^8],
[x^3*(a+b*x)^2*(A+B*x),x,2,1/4*a^2*A*x^4+1/5*a*(2*A*b+a*B)*x^5+1/6*b*(A*b+2*a*B)*x^6+1/7*b^2*B*x^7],
[x^2*(a+b*x)^2*(A+B*x),x,2,1/3*a^2*A*x^3+1/4*a*(2*A*b+a*B)*x^4+1/5*b*(A*b+2*a*B)*x^5+1/6*b^2*B*x^6],
[x*(a+b*x)^2*(A+B*x),x,2,1/2*a^2*A*x^2+1/3*a*(2*A*b+a*B)*x^3+1/4*b*(A*b+2*a*B)*x^4+1/5*b^2*B*x^5],
[(a+b*x)^2*(A+B*x),x,2,1/3*(A*b-a*B)*(a+b*x)^3/b^2+1/4*B*(a+b*x)^4/b^2],
[(a+b*x)^2*(A+B*x)/x,x,3,2*a*A*b*x+1/2*A*b^2*x^2+1/3*B*(a+b*x)^3/b+a^2*A*log(x)],
[(a+b*x)^2*(A+B*x)/x^2,x,2,-a^2*A/x+b*(A*b+2*a*B)*x+1/2*b^2*B*x^2+a*(2*A*b+a*B)*log(x)],
[(a+b*x)^2*(A+B*x)/x^3,x,2,-1/2*a^2*A/x^2-a*(2*A*b+a*B)/x+b^2*B*x+b*(A*b+2*a*B)*log(x)],
[(a+b*x)^2*(A+B*x)/x^4,x,2,-1/3*a^2*A/x^3-1/2*a*(2*A*b+a*B)/x^2-b*(A*b+2*a*B)/x+b^2*B*log(x)],
[(a+b*x)^2*(A+B*x)/x^5,x,2,-1/4*A*(a+b*x)^3/(a*x^4)+1/12*(A*b-4*a*B)*(a+b*x)^3/(a^2*x^3)],
[(a+b*x)^2*(A+B*x)/x^6,x,2,-1/5*a^2*A/x^5-1/4*a*(2*A*b+a*B)/x^4-1/3*b*(A*b+2*a*B)/x^3-1/2*b^2*B/x^2],
[(a+b*x)^2*(A+B*x)/x^7,x,2,-1/6*a^2*A/x^6-1/5*a*(2*A*b+a*B)/x^5-1/4*b*(A*b+2*a*B)/x^4-1/3*b^2*B/x^3],
[(a+b*x)^2*(A+B*x)/x^8,x,2,-1/7*a^2*A/x^7-1/6*a*(2*A*b+a*B)/x^6-1/5*b*(A*b+2*a*B)/x^5-1/4*b^2*B/x^4],
[x^4*(a+b*x)^3*(A+B*x),x,2,1/5*a^3*A*x^5+1/6*a^2*(3*A*b+a*B)*x^6+3/7*a*b*(A*b+a*B)*x^7+1/8*b^2*(A*b+3*a*B)*x^8+1/9*b^3*B*x^9],
[x^3*(a+b*x)^3*(A+B*x),x,2,1/4*a^3*A*x^4+1/5*a^2*(3*A*b+a*B)*x^5+1/2*a*b*(A*b+a*B)*x^6+1/7*b^2*(A*b+3*a*B)*x^7+1/8*b^3*B*x^8],
[x^2*(a+b*x)^3*(A+B*x),x,2,1/3*a^3*A*x^3+1/4*a^2*(3*A*b+a*B)*x^4+3/5*a*b*(A*b+a*B)*x^5+1/6*b^2*(A*b+3*a*B)*x^6+1/7*b^3*B*x^7],
[x*(a+b*x)^3*(A+B*x),x,2,-1/4*a*(A*b-a*B)*(a+b*x)^4/b^3+1/5*(A*b-2*a*B)*(a+b*x)^5/b^3+1/6*B*(a+b*x)^6/b^3],
[(a+b*x)^3*(A+B*x),x,2,1/4*(A*b-a*B)*(a+b*x)^4/b^2+1/5*B*(a+b*x)^5/b^2],
[(a+b*x)^3*(A+B*x)/x,x,3,3*a^2*A*b*x+3/2*a*A*b^2*x^2+1/3*A*b^3*x^3+1/4*B*(a+b*x)^4/b+a^3*A*log(x)],
[(a+b*x)^3*(A+B*x)/x^2,x,2,-a^3*A/x+3*a*b*(A*b+a*B)*x+1/2*b^2*(A*b+3*a*B)*x^2+1/3*b^3*B*x^3+a^2*(3*A*b+a*B)*log(x)],
[(a+b*x)^3*(A+B*x)/x^3,x,2,-1/2*a^3*A/x^2-a^2*(3*A*b+a*B)/x+b^2*(A*b+3*a*B)*x+1/2*b^3*B*x^2+3*a*b*(A*b+a*B)*log(x)],
[(a+b*x)^3*(A+B*x)/x^4,x,2,-1/3*a^3*A/x^3-1/2*a^2*(3*A*b+a*B)/x^2-3*a*b*(A*b+a*B)/x+b^3*B*x+b^2*(A*b+3*a*B)*log(x)],
[(a+b*x)^3*(A+B*x)/x^5,x,3,-1/3*a^3*B/x^3-3/2*a^2*b*B/x^2-3*a*b^2*B/x-1/4*A*(a+b*x)^4/(a*x^4)+b^3*B*log(x)],
[(a+b*x)^3*(A+B*x)/x^6,x,2,-1/5*A*(a+b*x)^4/(a*x^5)+1/20*(A*b-5*a*B)*(a+b*x)^4/(a^2*x^4)],
[(a+b*x)^3*(A+B*x)/x^7,x,2,-1/6*a^3*A/x^6-1/5*a^2*(3*A*b+a*B)/x^5-3/4*a*b*(A*b+a*B)/x^4-1/3*b^2*(A*b+3*a*B)/x^3-1/2*b^3*B/x^2],
[(a+b*x)^3*(A+B*x)/x^8,x,2,-1/7*a^3*A/x^7-1/6*a^2*(3*A*b+a*B)/x^6-3/5*a*b*(A*b+a*B)/x^5-1/4*b^2*(A*b+3*a*B)/x^4-1/3*b^3*B/x^3],
[(a+b*x)^3*(A+B*x)/x^9,x,2,-1/8*a^3*A/x^8-1/7*a^2*(3*A*b+a*B)/x^7-1/2*a*b*(A*b+a*B)/x^6-1/5*b^2*(A*b+3*a*B)/x^5-1/4*b^3*B/x^4],
[(a+b*x)^3*(A+B*x)/x^10,x,2,-1/9*a^3*A/x^9-1/8*a^2*(3*A*b+a*B)/x^8-3/7*a*b*(A*b+a*B)/x^7-1/6*b^2*(A*b+3*a*B)/x^6-1/5*b^3*B/x^5],
[x^5*(a+b*x)^5*(A+B*x),x,2,1/6*a^5*A*x^6+1/7*a^4*(5*A*b+a*B)*x^7+5/8*a^3*b*(2*A*b+a*B)*x^8+10/9*a^2*b^2*(A*b+a*B)*x^9+1/2*a*b^3*(A*b+2*a*B)*x^10+1/11*b^4*(A*b+5*a*B)*x^11+1/12*b^5*B*x^12],
[x^4*(a+b*x)^5*(A+B*x),x,2,1/5*a^5*A*x^5+1/6*a^4*(5*A*b+a*B)*x^6+5/7*a^3*b*(2*A*b+a*B)*x^7+5/4*a^2*b^2*(A*b+a*B)*x^8+5/9*a*b^3*(A*b+2*a*B)*x^9+1/10*b^4*(A*b+5*a*B)*x^10+1/11*b^5*B*x^11],
[x^3*(a+b*x)^5*(A+B*x),x,2,-1/6*a^3*(A*b-a*B)*(a+b*x)^6/b^5+1/7*a^2*(3*A*b-4*a*B)*(a+b*x)^7/b^5-3/8*a*(A*b-2*a*B)*(a+b*x)^8/b^5+1/9*(A*b-4*a*B)*(a+b*x)^9/b^5+1/10*B*(a+b*x)^10/b^5],
[x^2*(a+b*x)^5*(A+B*x),x,2,1/6*a^2*(A*b-a*B)*(a+b*x)^6/b^4-1/7*a*(2*A*b-3*a*B)*(a+b*x)^7/b^4+1/8*(A*b-3*a*B)*(a+b*x)^8/b^4+1/9*B*(a+b*x)^9/b^4],
[x*(a+b*x)^5*(A+B*x),x,2,-1/6*a*(A*b-a*B)*(a+b*x)^6/b^3+1/7*(A*b-2*a*B)*(a+b*x)^7/b^3+1/8*B*(a+b*x)^8/b^3],
[(a+b*x)^5*(A+B*x),x,2,1/6*(A*b-a*B)*(a+b*x)^6/b^2+1/7*B*(a+b*x)^7/b^2],
[(a+b*x)^5*(A+B*x)/x,x,3,5*a^4*A*b*x+5*a^3*A*b^2*x^2+10/3*a^2*A*b^3*x^3+5/4*a*A*b^4*x^4+1/5*A*b^5*x^5+1/6*B*(a+b*x)^6/b+a^5*A*log(x)],
[(a+b*x)^5*(A+B*x)/x^2,x,2,-a^5*A/x+5*a^3*b*(2*A*b+a*B)*x+5*a^2*b^2*(A*b+a*B)*x^2+5/3*a*b^3*(A*b+2*a*B)*x^3+1/4*b^4*(A*b+5*a*B)*x^4+1/5*b^5*B*x^5+a^4*(5*A*b+a*B)*log(x)],
[(a+b*x)^5*(A+B*x)/x^3,x,2,-1/2*a^5*A/x^2-a^4*(5*A*b+a*B)/x+10*a^2*b^2*(A*b+a*B)*x+5/2*a*b^3*(A*b+2*a*B)*x^2+1/3*b^4*(A*b+5*a*B)*x^3+1/4*b^5*B*x^4+5*a^3*b*(2*A*b+a*B)*log(x)],
[(a+b*x)^5*(A+B*x)/x^4,x,2,-1/3*a^5*A/x^3-1/2*a^4*(5*A*b+a*B)/x^2-5*a^3*b*(2*A*b+a*B)/x+5*a*b^3*(A*b+2*a*B)*x+1/2*b^4*(A*b+5*a*B)*x^2+1/3*b^5*B*x^3+10*a^2*b^2*(A*b+a*B)*log(x)],
[(a+b*x)^5*(A+B*x)/x^5,x,2,-1/4*a^5*A/x^4-1/3*a^4*(5*A*b+a*B)/x^3-5/2*a^3*b*(2*A*b+a*B)/x^2-10*a^2*b^2*(A*b+a*B)/x+b^4*(A*b+5*a*B)*x+1/2*b^5*B*x^2+5*a*b^3*(A*b+2*a*B)*log(x)],
[(a+b*x)^5*(A+B*x)/x^6,x,2,-1/5*a^5*A/x^5-1/4*a^4*(5*A*b+a*B)/x^4-5/3*a^3*b*(2*A*b+a*B)/x^3-5*a^2*b^2*(A*b+a*B)/x^2-5*a*b^3*(A*b+2*a*B)/x+b^5*B*x+b^4*(A*b+5*a*B)*log(x)],
[(a+b*x)^5*(A+B*x)/x^7,x,3,-1/5*a^5*B/x^5-5/4*a^4*b*B/x^4-10/3*a^3*b^2*B/x^3-5*a^2*b^3*B/x^2-5*a*b^4*B/x-1/6*A*(a+b*x)^6/(a*x^6)+b^5*B*log(x)],
[(a+b*x)^5*(A+B*x)/x^8,x,2,-1/7*A*(a+b*x)^6/(a*x^7)+1/42*(A*b-7*a*B)*(a+b*x)^6/(a^2*x^6)],
[(a+b*x)^5*(A+B*x)/x^9,x,3,-1/8*A*(a+b*x)^6/(a*x^8)+1/28*(A*b-4*a*B)*(a+b*x)^6/(a^2*x^7)-1/168*b*(A*b-4*a*B)*(a+b*x)^6/(a^3*x^6)],
[(a+b*x)^5*(A+B*x)/x^10,x,2,-1/9*a^5*A/x^9-1/8*a^4*(5*A*b+a*B)/x^8-5/7*a^3*b*(2*A*b+a*B)/x^7-5/3*a^2*b^2*(A*b+a*B)/x^6-a*b^3*(A*b+2*a*B)/x^5-1/4*b^4*(A*b+5*a*B)/x^4-1/3*b^5*B/x^3],
[(a+b*x)^5*(A+B*x)/x^11,x,2,-1/10*a^5*A/x^10-1/9*a^4*(5*A*b+a*B)/x^9-5/8*a^3*b*(2*A*b+a*B)/x^8-10/7*a^2*b^2*(A*b+a*B)/x^7-5/6*a*b^3*(A*b+2*a*B)/x^6-1/5*b^4*(A*b+5*a*B)/x^5-1/4*b^5*B/x^4],
[(a+b*x)^5*(A+B*x)/x^12,x,2,-1/11*a^5*A/x^11-1/10*a^4*(5*A*b+a*B)/x^10-5/9*a^3*b*(2*A*b+a*B)/x^9-5/4*a^2*b^2*(A*b+a*B)/x^8-5/7*a*b^3*(A*b+2*a*B)/x^7-1/6*b^4*(A*b+5*a*B)/x^6-1/5*b^5*B/x^5],
[x^10*(a+b*x)^10*(A+B*x),x,2,1/11*a^10*A*x^11+1/12*a^9*(10*A*b+a*B)*x^12+5/13*a^8*b*(9*A*b+2*a*B)*x^13+15/14*a^7*b^2*(8*A*b+3*a*B)*x^14+2*a^6*b^3*(7*A*b+4*a*B)*x^15+21/8*a^5*b^4*(6*A*b+5*a*B)*x^16+42/17*a^4*b^5*(5*A*b+6*a*B)*x^17+5/3*a^3*b^6*(4*A*b+7*a*B)*x^18+15/19*a^2*b^7*(3*A*b+8*a*B)*x^19+1/4*a*b^8*(2*A*b+9*a*B)*x^20+1/21*b^9*(A*b+10*a*B)*x^21+1/22*b^10*B*x^22],
[x^9*(a+b*x)^10*(A+B*x),x,2,1/10*a^10*A*x^10+1/11*a^9*(10*A*b+a*B)*x^11+5/12*a^8*b*(9*A*b+2*a*B)*x^12+15/13*a^7*b^2*(8*A*b+3*a*B)*x^13+15/7*a^6*b^3*(7*A*b+4*a*B)*x^14+14/5*a^5*b^4*(6*A*b+5*a*B)*x^15+21/8*a^4*b^5*(5*A*b+6*a*B)*x^16+30/17*a^3*b^6*(4*A*b+7*a*B)*x^17+5/6*a^2*b^7*(3*A*b+8*a*B)*x^18+5/19*a*b^8*(2*A*b+9*a*B)*x^19+1/20*b^9*(A*b+10*a*B)*x^20+1/21*b^10*B*x^21],
[x^8*(a+b*x)^10*(A+B*x),x,2,1/11*a^8*(A*b-a*B)*(a+b*x)^11/b^10-1/12*a^7*(8*A*b-9*a*B)*(a+b*x)^12/b^10+4/13*a^6*(7*A*b-9*a*B)*(a+b*x)^13/b^10-2*a^5*(2*A*b-3*a*B)*(a+b*x)^14/b^10+14/15*a^4*(5*A*b-9*a*B)*(a+b*x)^15/b^10-7/8*a^3*(4*A*b-9*a*B)*(a+b*x)^16/b^10+28/17*a^2*(A*b-3*a*B)*(a+b*x)^17/b^10-2/9*a*(2*A*b-9*a*B)*(a+b*x)^18/b^10+1/19*(A*b-9*a*B)*(a+b*x)^19/b^10+1/20*B*(a+b*x)^20/b^10],
[x^7*(a+b*x)^10*(A+B*x),x,2,-1/11*a^7*(A*b-a*B)*(a+b*x)^11/b^9+1/12*a^6*(7*A*b-8*a*B)*(a+b*x)^12/b^9-7/13*a^5*(3*A*b-4*a*B)*(a+b*x)^13/b^9+1/2*a^4*(5*A*b-8*a*B)*(a+b*x)^14/b^9-7/3*a^3*(A*b-2*a*B)*(a+b*x)^15/b^9+7/16*a^2*(3*A*b-8*a*B)*(a+b*x)^16/b^9-7/17*a*(A*b-4*a*B)*(a+b*x)^17/b^9+1/18*(A*b-8*a*B)*(a+b*x)^18/b^9+1/19*B*(a+b*x)^19/b^9],
[x^6*(a+b*x)^10*(A+B*x),x,2,1/11*a^6*(A*b-a*B)*(a+b*x)^11/b^8-1/12*a^5*(6*A*b-7*a*B)*(a+b*x)^12/b^8+3/13*a^4*(5*A*b-7*a*B)*(a+b*x)^13/b^8-5/14*a^3*(4*A*b-7*a*B)*(a+b*x)^14/b^8+1/3*a^2*(3*A*b-7*a*B)*(a+b*x)^15/b^8-3/16*a*(2*A*b-7*a*B)*(a+b*x)^16/b^8+1/17*(A*b-7*a*B)*(a+b*x)^17/b^8+1/18*B*(a+b*x)^18/b^8],
[x^5*(a+b*x)^10*(A+B*x),x,2,-1/11*a^5*(A*b-a*B)*(a+b*x)^11/b^7+1/12*a^4*(5*A*b-6*a*B)*(a+b*x)^12/b^7-5/13*a^3*(2*A*b-3*a*B)*(a+b*x)^13/b^7+5/7*a^2*(A*b-2*a*B)*(a+b*x)^14/b^7-1/3*a*(A*b-3*a*B)*(a+b*x)^15/b^7+1/16*(A*b-6*a*B)*(a+b*x)^16/b^7+1/17*B*(a+b*x)^17/b^7],
[x^4*(a+b*x)^10*(A+B*x),x,2,1/11*a^4*(A*b-a*B)*(a+b*x)^11/b^6-1/12*a^3*(4*A*b-5*a*B)*(a+b*x)^12/b^6+2/13*a^2*(3*A*b-5*a*B)*(a+b*x)^13/b^6-1/7*a*(2*A*b-5*a*B)*(a+b*x)^14/b^6+1/15*(A*b-5*a*B)*(a+b*x)^15/b^6+1/16*B*(a+b*x)^16/b^6],
[x^3*(a+b*x)^10*(A+B*x),x,2,-1/11*a^3*(A*b-a*B)*(a+b*x)^11/b^5+1/12*a^2*(3*A*b-4*a*B)*(a+b*x)^12/b^5-3/13*a*(A*b-2*a*B)*(a+b*x)^13/b^5+1/14*(A*b-4*a*B)*(a+b*x)^14/b^5+1/15*B*(a+b*x)^15/b^5],
[x^2*(a+b*x)^10*(A+B*x),x,2,1/11*a^2*(A*b-a*B)*(a+b*x)^11/b^4-1/12*a*(2*A*b-3*a*B)*(a+b*x)^12/b^4+1/13*(A*b-3*a*B)*(a+b*x)^13/b^4+1/14*B*(a+b*x)^14/b^4],
[x*(a+b*x)^10*(A+B*x),x,2,-1/11*a*(A*b-a*B)*(a+b*x)^11/b^3+1/12*(A*b-2*a*B)*(a+b*x)^12/b^3+1/13*B*(a+b*x)^13/b^3],
[(a+b*x)^10*(A+B*x),x,2,1/11*(A*b-a*B)*(a+b*x)^11/b^2+1/12*B*(a+b*x)^12/b^2],
[(a+b*x)^10*(A+B*x)/x,x,3,10*a^9*A*b*x+45/2*a^8*A*b^2*x^2+40*a^7*A*b^3*x^3+105/2*a^6*A*b^4*x^4+252/5*a^5*A*b^5*x^5+35*a^4*A*b^6*x^6+120/7*a^3*A*b^7*x^7+45/8*a^2*A*b^8*x^8+10/9*a*A*b^9*x^9+1/10*A*b^10*x^10+1/11*B*(a+b*x)^11/b+a^10*A*log(x)],
[(a+b*x)^10*(A+B*x)/x^2,x,2,-a^10*A/x+5*a^8*b*(9*A*b+2*a*B)*x+15/2*a^7*b^2*(8*A*b+3*a*B)*x^2+10*a^6*b^3*(7*A*b+4*a*B)*x^3+21/2*a^5*b^4*(6*A*b+5*a*B)*x^4+42/5*a^4*b^5*(5*A*b+6*a*B)*x^5+5*a^3*b^6*(4*A*b+7*a*B)*x^6+15/7*a^2*b^7*(3*A*b+8*a*B)*x^7+5/8*a*b^8*(2*A*b+9*a*B)*x^8+1/9*b^9*(A*b+10*a*B)*x^9+1/10*b^10*B*x^10+a^9*(10*A*b+a*B)*log(x)],
[(a+b*x)^10*(A+B*x)/x^3,x,2,-1/2*a^10*A/x^2-a^9*(10*A*b+a*B)/x+15*a^7*b^2*(8*A*b+3*a*B)*x+15*a^6*b^3*(7*A*b+4*a*B)*x^2+14*a^5*b^4*(6*A*b+5*a*B)*x^3+21/2*a^4*b^5*(5*A*b+6*a*B)*x^4+6*a^3*b^6*(4*A*b+7*a*B)*x^5+5/2*a^2*b^7*(3*A*b+8*a*B)*x^6+5/7*a*b^8*(2*A*b+9*a*B)*x^7+1/8*b^9*(A*b+10*a*B)*x^8+1/9*b^10*B*x^9+5*a^8*b*(9*A*b+2*a*B)*log(x)],
[(a+b*x)^10*(A+B*x)/x^4,x,2,-1/3*a^10*A/x^3-1/2*a^9*(10*A*b+a*B)/x^2-5*a^8*b*(9*A*b+2*a*B)/x+30*a^6*b^3*(7*A*b+4*a*B)*x+21*a^5*b^4*(6*A*b+5*a*B)*x^2+14*a^4*b^5*(5*A*b+6*a*B)*x^3+15/2*a^3*b^6*(4*A*b+7*a*B)*x^4+3*a^2*b^7*(3*A*b+8*a*B)*x^5+5/6*a*b^8*(2*A*b+9*a*B)*x^6+1/7*b^9*(A*b+10*a*B)*x^7+1/8*b^10*B*x^8+15*a^7*b^2*(8*A*b+3*a*B)*log(x)],
[(a+b*x)^10*(A+B*x)/x^5,x,2,-1/4*a^10*A/x^4-1/3*a^9*(10*A*b+a*B)/x^3-5/2*a^8*b*(9*A*b+2*a*B)/x^2-15*a^7*b^2*(8*A*b+3*a*B)/x+42*a^5*b^4*(6*A*b+5*a*B)*x+21*a^4*b^5*(5*A*b+6*a*B)*x^2+10*a^3*b^6*(4*A*b+7*a*B)*x^3+15/4*a^2*b^7*(3*A*b+8*a*B)*x^4+a*b^8*(2*A*b+9*a*B)*x^5+1/6*b^9*(A*b+10*a*B)*x^6+1/7*b^10*B*x^7+30*a^6*b^3*(7*A*b+4*a*B)*log(x)],
[(a+b*x)^10*(A+B*x)/x^6,x,2,-1/5*a^10*A/x^5-1/4*a^9*(10*A*b+a*B)/x^4-5/3*a^8*b*(9*A*b+2*a*B)/x^3-15/2*a^7*b^2*(8*A*b+3*a*B)/x^2-30*a^6*b^3*(7*A*b+4*a*B)/x+42*a^4*b^5*(5*A*b+6*a*B)*x+15*a^3*b^6*(4*A*b+7*a*B)*x^2+5*a^2*b^7*(3*A*b+8*a*B)*x^3+5/4*a*b^8*(2*A*b+9*a*B)*x^4+1/5*b^9*(A*b+10*a*B)*x^5+1/6*b^10*B*x^6+42*a^5*b^4*(6*A*b+5*a*B)*log(x)],
[(a+b*x)^10*(A+B*x)/x^7,x,2,-1/6*a^10*A/x^6-1/5*a^9*(10*A*b+a*B)/x^5-5/4*a^8*b*(9*A*b+2*a*B)/x^4-5*a^7*b^2*(8*A*b+3*a*B)/x^3-15*a^6*b^3*(7*A*b+4*a*B)/x^2-42*a^5*b^4*(6*A*b+5*a*B)/x+30*a^3*b^6*(4*A*b+7*a*B)*x+15/2*a^2*b^7*(3*A*b+8*a*B)*x^2+5/3*a*b^8*(2*A*b+9*a*B)*x^3+1/4*b^9*(A*b+10*a*B)*x^4+1/5*b^10*B*x^5+42*a^4*b^5*(5*A*b+6*a*B)*log(x)],
[(a+b*x)^10*(A+B*x)/x^8,x,2,-1/7*a^10*A/x^7-1/6*a^9*(10*A*b+a*B)/x^6-a^8*b*(9*A*b+2*a*B)/x^5-15/4*a^7*b^2*(8*A*b+3*a*B)/x^4-10*a^6*b^3*(7*A*b+4*a*B)/x^3-21*a^5*b^4*(6*A*b+5*a*B)/x^2-42*a^4*b^5*(5*A*b+6*a*B)/x+15*a^2*b^7*(3*A*b+8*a*B)*x+5/2*a*b^8*(2*A*b+9*a*B)*x^2+1/3*b^9*(A*b+10*a*B)*x^3+1/4*b^10*B*x^4+30*a^3*b^6*(4*A*b+7*a*B)*log(x)],
[(a+b*x)^10*(A+B*x)/x^9,x,2,-1/8*a^10*A/x^8-1/7*a^9*(10*A*b+a*B)/x^7-5/6*a^8*b*(9*A*b+2*a*B)/x^6-3*a^7*b^2*(8*A*b+3*a*B)/x^5-15/2*a^6*b^3*(7*A*b+4*a*B)/x^4-14*a^5*b^4*(6*A*b+5*a*B)/x^3-21*a^4*b^5*(5*A*b+6*a*B)/x^2-30*a^3*b^6*(4*A*b+7*a*B)/x+5*a*b^8*(2*A*b+9*a*B)*x+1/2*b^9*(A*b+10*a*B)*x^2+1/3*b^10*B*x^3+15*a^2*b^7*(3*A*b+8*a*B)*log(x)],
[(a+b*x)^10*(A+B*x)/x^10,x,2,-1/9*a^10*A/x^9-1/8*a^9*(10*A*b+a*B)/x^8-5/7*a^8*b*(9*A*b+2*a*B)/x^7-5/2*a^7*b^2*(8*A*b+3*a*B)/x^6-6*a^6*b^3*(7*A*b+4*a*B)/x^5-21/2*a^5*b^4*(6*A*b+5*a*B)/x^4-14*a^4*b^5*(5*A*b+6*a*B)/x^3-15*a^3*b^6*(4*A*b+7*a*B)/x^2-15*a^2*b^7*(3*A*b+8*a*B)/x+b^9*(A*b+10*a*B)*x+1/2*b^10*B*x^2+5*a*b^8*(2*A*b+9*a*B)*log(x)],
[(a+b*x)^10*(A+B*x)/x^11,x,2,-1/10*a^10*A/x^10-1/9*a^9*(10*A*b+a*B)/x^9-5/8*a^8*b*(9*A*b+2*a*B)/x^8-15/7*a^7*b^2*(8*A*b+3*a*B)/x^7-5*a^6*b^3*(7*A*b+4*a*B)/x^6-42/5*a^5*b^4*(6*A*b+5*a*B)/x^5-21/2*a^4*b^5*(5*A*b+6*a*B)/x^4-10*a^3*b^6*(4*A*b+7*a*B)/x^3-15/2*a^2*b^7*(3*A*b+8*a*B)/x^2-5*a*b^8*(2*A*b+9*a*B)/x+b^10*B*x+b^9*(A*b+10*a*B)*log(x)],
[(a+b*x)^10*(A+B*x)/x^12,x,3,-1/10*a^10*B/x^10-10/9*a^9*b*B/x^9-45/8*a^8*b^2*B/x^8-120/7*a^7*b^3*B/x^7-35*a^6*b^4*B/x^6-252/5*a^5*b^5*B/x^5-105/2*a^4*b^6*B/x^4-40*a^3*b^7*B/x^3-45/2*a^2*b^8*B/x^2-10*a*b^9*B/x-1/11*A*(a+b*x)^11/(a*x^11)+b^10*B*log(x)],
[(a+b*x)^10*(A+B*x)/x^13,x,2,-1/12*A*(a+b*x)^11/(a*x^12)+1/132*(A*b-12*a*B)*(a+b*x)^11/(a^2*x^11)],
[(a+b*x)^10*(A+B*x)/x^14,x,3,-1/13*A*(a+b*x)^11/(a*x^13)+1/156*(2*A*b-13*a*B)*(a+b*x)^11/(a^2*x^12)-1/1716*b*(2*A*b-13*a*B)*(a+b*x)^11/(a^3*x^11)],
[(a+b*x)^10*(A+B*x)/x^15,x,4,-1/14*A*(a+b*x)^11/(a*x^14)+1/182*(3*A*b-14*a*B)*(a+b*x)^11/(a^2*x^13)-1/1092*b*(3*A*b-14*a*B)*(a+b*x)^11/(a^3*x^12)+1/12012*b^2*(3*A*b-14*a*B)*(a+b*x)^11/(a^4*x^11)],
[(a+b*x)^10*(A+B*x)/x^16,x,5,-1/15*A*(a+b*x)^11/(a*x^15)+1/210*(4*A*b-15*a*B)*(a+b*x)^11/(a^2*x^14)-1/910*b*(4*A*b-15*a*B)*(a+b*x)^11/(a^3*x^13)+1/5460*b^2*(4*A*b-15*a*B)*(a+b*x)^11/(a^4*x^12)-1/60060*b^3*(4*A*b-15*a*B)*(a+b*x)^11/(a^5*x^11)],
[(a+b*x)^10*(A+B*x)/x^17,x,6,-1/16*A*(a+b*x)^11/(a*x^16)+1/240*(5*A*b-16*a*B)*(a+b*x)^11/(a^2*x^15)-1/840*b*(5*A*b-16*a*B)*(a+b*x)^11/(a^3*x^14)+1/3640*b^2*(5*A*b-16*a*B)*(a+b*x)^11/(a^4*x^13)-1/21840*b^3*(5*A*b-16*a*B)*(a+b*x)^11/(a^5*x^12)+1/240240*b^4*(5*A*b-16*a*B)*(a+b*x)^11/(a^6*x^11)],
[(a+b*x)^10*(A+B*x)/x^18,x,7,-1/17*A*(a+b*x)^11/(a*x^17)+1/272*(6*A*b-17*a*B)*(a+b*x)^11/(a^2*x^16)-1/816*b*(6*A*b-17*a*B)*(a+b*x)^11/(a^3*x^15)+1/2856*b^2*(6*A*b-17*a*B)*(a+b*x)^11/(a^4*x^14)-1/12376*b^3*(6*A*b-17*a*B)*(a+b*x)^11/(a^5*x^13)+1/74256*b^4*(6*A*b-17*a*B)*(a+b*x)^11/(a^6*x^12)-1/816816*b^5*(6*A*b-17*a*B)*(a+b*x)^11/(a^7*x^11)],
[(a+b*x)^10*(A+B*x)/x^19,x,2,-1/18*a^10*A/x^18-1/17*a^9*(10*A*b+a*B)/x^17-5/16*a^8*b*(9*A*b+2*a*B)/x^16-a^7*b^2*(8*A*b+3*a*B)/x^15-15/7*a^6*b^3*(7*A*b+4*a*B)/x^14-42/13*a^5*b^4*(6*A*b+5*a*B)/x^13-7/2*a^4*b^5*(5*A*b+6*a*B)/x^12-30/11*a^3*b^6*(4*A*b+7*a*B)/x^11-3/2*a^2*b^7*(3*A*b+8*a*B)/x^10-5/9*a*b^8*(2*A*b+9*a*B)/x^9-1/8*b^9*(A*b+10*a*B)/x^8-1/7*b^10*B/x^7],
[(a+b*x)^10*(A+B*x)/x^20,x,2,-1/19*a^10*A/x^19-1/18*a^9*(10*A*b+a*B)/x^18-5/17*a^8*b*(9*A*b+2*a*B)/x^17-15/16*a^7*b^2*(8*A*b+3*a*B)/x^16-2*a^6*b^3*(7*A*b+4*a*B)/x^15-3*a^5*b^4*(6*A*b+5*a*B)/x^14-42/13*a^4*b^5*(5*A*b+6*a*B)/x^13-5/2*a^3*b^6*(4*A*b+7*a*B)/x^12-15/11*a^2*b^7*(3*A*b+8*a*B)/x^11-1/2*a*b^8*(2*A*b+9*a*B)/x^10-1/9*b^9*(A*b+10*a*B)/x^9-1/8*b^10*B/x^8],
[(a+b*x)^10*(A+B*x)/x^21,x,2,-1/20*a^10*A/x^20-1/19*a^9*(10*A*b+a*B)/x^19-5/18*a^8*b*(9*A*b+2*a*B)/x^18-15/17*a^7*b^2*(8*A*b+3*a*B)/x^17-15/8*a^6*b^3*(7*A*b+4*a*B)/x^16-14/5*a^5*b^4*(6*A*b+5*a*B)/x^15-3*a^4*b^5*(5*A*b+6*a*B)/x^14-30/13*a^3*b^6*(4*A*b+7*a*B)/x^13-5/4*a^2*b^7*(3*A*b+8*a*B)/x^12-5/11*a*b^8*(2*A*b+9*a*B)/x^11-1/10*b^9*(A*b+10*a*B)/x^10-1/9*b^10*B/x^9],
#  {x^14*(a + b*x)^15*(A + B*x), x, 2, (1/15)*a^15*A*x^15 + (1/16)*a^14*(15*A*b + a*B)*x^16 + (15/17)*a^13*b*(7*A*b + a*B)*x^17 + (35/18)*a^12*b^2*(13*A*b + 3*a*B)*x^18 + (455/19)*a^11*b^3*(3*A*b + a*B)*x^19 + (273/20)*a^10*b^4*(11*A*b + 5*a*B)*x^20 + (143/3)*a^9*b^5*(5*A*b + 3*a*B)*x^21 + (65/2)*a^8*b^6*(9*A*b + 7*a*B)*x^22 + (6435/23)*a^7*b^7*(A*b + a*B)*x^23 + (715/24)*a^6*b^8*(7*A*b + 9*a*B)*x^24 + (1001/25)*a^5*b^9*(3*A*b + 5*a*B)*x^25 + (21/2)*a^4*b^10*(5*A*b + 11*a*B)*x^26 + (455/27)*a^3*b^11*(A*b + 3*a*B)*x^27 + (5/4)*a^2*b^12*(3*A*b + 13*a*B)*x^28 + (15/29)*a*b^13*(A*b + 7*a*B)*x^29 + (1/30)*b^14*(A*b + 15*a*B)*x^30 + (1/31)*b^15*B*x^31}
# {x^13*(a + b*x)^15*(A + B*x), x, 2, (1/14)*a^15*A*x^14 + (1/15)*a^14*(15*A*b + a*B)*x^15 + (15/16)*a^13*b*(7*A*b + a*B)*x^16 + (35/17)*a^12*b^2*(13*A*b + 3*a*B)*x^17 + (455/18)*a^11*b^3*(3*A*b + a*B)*x^18 + (273/19)*a^10*b^4*(11*A*b + 5*a*B)*x^19 + (1001/20)*a^9*b^5*(5*A*b + 3*a*B)*x^20 + (715/21)*a^8*b^6*(9*A*b + 7*a*B)*x^21 + (585/2)*a^7*b^7*(A*b + a*B)*x^22 + (715/23)*a^6*b^8*(7*A*b + 9*a*B)*x^23 + (1001/24)*a^5*b^9*(3*A*b + 5*a*B)*x^24 + (273/25)*a^4*b^10*(5*A*b + 11*a*B)*x^25 + (35/2)*a^3*b^11*(A*b + 3*a*B)*x^26 + (35/27)*a^2*b^12*(3*A*b + 13*a*B)*x^27 + (15/28)*a*b^13*(A*b + 7*a*B)*x^28 + (1/29)*b^14*(A*b + 15*a*B)*x^29 + (1/30)*b^15*B*x^30}
# {x^12*(a + b*x)^15*(A + B*x), x, 2, (1/13)*a^15*A*x^13 + (1/14)*a^14*(15*A*b + a*B)*x^14 + a^13*b*(7*A*b + a*B)*x^15 + (35/16)*a^12*b^2*(13*A*b + 3*a*B)*x^16 + (455/17)*a^11*b^3*(3*A*b + a*B)*x^17 + (91/6)*a^10*b^4*(11*A*b + 5*a*B)*x^18 + (1001/19)*a^9*b^5*(5*A*b + 3*a*B)*x^19 + (143/4)*a^8*b^6*(9*A*b + 7*a*B)*x^20 + (2145/7)*a^7*b^7*(A*b + a*B)*x^21 + (65/2)*a^6*b^8*(7*A*b + 9*a*B)*x^22 + (1001/23)*a^5*b^9*(3*A*b + 5*a*B)*x^23 + (91/8)*a^4*b^10*(5*A*b + 11*a*B)*x^24 + (91/5)*a^3*b^11*(A*b + 3*a*B)*x^25 + (35/26)*a^2*b^12*(3*A*b + 13*a*B)*x^26 + (5/9)*a*b^13*(A*b + 7*a*B)*x^27 + (1/28)*b^14*(A*b + 15*a*B)*x^28 + (1/29)*b^15*B*x^29}
# {x^11*(a + b*x)^15*(A + B*x), x, 2, -((a^11*(A*b - a*B)*(a + b*x)^16)/(16*b^13)) + (a^10*(11*A*b - 12*a*B)*(a + b*x)^17)/(17*b^13) - (11*a^9*(5*A*b - 6*a*B)*(a + b*x)^18)/(18*b^13) + (55*a^8*(3*A*b - 4*a*B)*(a + b*x)^19)/(19*b^13) - (33*a^7*(2*A*b - 3*a*B)*(a + b*x)^20)/(4*b^13) + (22*a^6*(7*A*b - 12*a*B)*(a + b*x)^21)/(7*b^13) - (21*a^5*(A*b - 2*a*B)*(a + b*x)^22)/b^13 + (66*a^4*(5*A*b - 12*a*B)*(a + b*x)^23)/(23*b^13) - (55*a^3*(A*b - 3*a*B)*(a + b*x)^24)/(8*b^13) + (11*a^2*(A*b - 4*a*B)*(a + b*x)^25)/(5*b^13) - (11*a*(A*b - 6*a*B)*(a + b*x)^26)/(26*b^13) + ((A*b - 12*a*B)*(a + b*x)^27)/(27*b^13) + (B*(a + b*x)^28)/(28*b^13)}
# {x^10*(a + b*x)^15*(A + B*x), x, 2, (a^10*(A*b - a*B)*(a + b*x)^16)/(16*b^12) - (a^9*(10*A*b - 11*a*B)*(a + b*x)^17)/(17*b^12) + (5*a^8*(9*A*b - 11*a*B)*(a + b*x)^18)/(18*b^12) - (15*a^7*(8*A*b - 11*a*B)*(a + b*x)^19)/(19*b^12) + (3*a^6*(7*A*b - 11*a*B)*(a + b*x)^20)/(2*b^12) - (2*a^5*(6*A*b - 11*a*B)*(a + b*x)^21)/b^12 + (21*a^4*(5*A*b - 11*a*B)*(a + b*x)^22)/(11*b^12) - (30*a^3*(4*A*b - 11*a*B)*(a + b*x)^23)/(23*b^12) + (5*a^2*(3*A*b - 11*a*B)*(a + b*x)^24)/(8*b^12) - (a*(2*A*b - 11*a*B)*(a + b*x)^25)/(5*b^12) + ((A*b - 11*a*B)*(a + b*x)^26)/(26*b^12) + (B*(a + b*x)^27)/(27*b^12)}
# {x^9*(a + b*x)^15*(A + B*x), x, 2, -(a^9*(A*b - a*B)*(a + b*x)^16)/(16*b^11) + (a^8*(9*A*b - 10*a*B)*(a + b*x)^17)/(17*b^11) - (a^7*(4*A*b - 5*a*B)*(a + b*x)^18)/(2*b^11) + (12*a^6*(7*A*b - 10*a*B)*(a + b*x)^19)/(19*b^11) - (21*a^5*(3*A*b - 5*a*B)*(a + b*x)^20)/(10*b^11) + (6*a^4*(A*b - 2*a*B)*(a + b*x)^21)/b^11 - (21*a^3*(2*A*b - 5*a*B)*(a + b*x)^22)/(11*b^11) + (12*a^2*(3*A*b - 10*a*B)*(a + b*x)^23)/(23*b^11) - (3*a*(A*b - 5*a*B)*(a + b*x)^24)/(8*b^11) + ((A*b - 10*a*B)*(a + b*x)^25)/(25*b^11) + (B*(a + b*x)^26)/(26*b^11)}
# {x^8*(a + b*x)^15*(A + B*x), x, 2, (a^8*(A*b - a*B)*(a + b*x)^16)/(16*b^10) - (a^7*(8*A*b - 9*a*B)*(a + b*x)^17)/(17*b^10) + (2*a^6*(7*A*b - 9*a*B)*(a + b*x)^18)/(9*b^10) - (28*a^5*(2*A*b - 3*a*B)*(a + b*x)^19)/(19*b^10) + (7*a^4*(5*A*b - 9*a*B)*(a + b*x)^20)/(10*b^10) - (2*a^3*(4*A*b - 9*a*B)*(a + b*x)^21)/(3*b^10) + (14*a^2*(A*b - 3*a*B)*(a + b*x)^22)/(11*b^10) - (4*a*(2*A*b - 9*a*B)*(a + b*x)^23)/(23*b^10) + ((A*b - 9*a*B)*(a + b*x)^24)/(24*b^10) + (B*(a + b*x)^25)/(25*b^10)}
# {x^7*(a + b*x)^15*(A + B*x), x, 2, -(a^7*(A*b - a*B)*(a + b*x)^16)/(16*b^9) + (a^6*(7*A*b - 8*a*B)*(a + b*x)^17)/(17*b^9) - (7*a^5*(3*A*b - 4*a*B)*(a + b*x)^18)/(18*b^9) + (7*a^4*(5*A*b - 8*a*B)*(a + b*x)^19)/(19*b^9) - (7*a^3*(A*b - 2*a*B)*(a + b*x)^20)/(4*b^9) + (a^2*(3*A*b - 8*a*B)*(a + b*x)^21)/(3*b^9) - (7*a*(A*b - 4*a*B)*(a + b*x)^22)/(22*b^9) + ((A*b - 8*a*B)*(a + b*x)^23)/(23*b^9) + (B*(a + b*x)^24)/(24*b^9)}
# {x^6*(a + b*x)^15*(A + B*x), x, 2, (a^6*(A*b - a*B)*(a + b*x)^16)/(16*b^8) - (a^5*(6*A*b - 7*a*B)*(a + b*x)^17)/(17*b^8) + (a^4*(5*A*b - 7*a*B)*(a + b*x)^18)/(6*b^8) - (5*a^3*(4*A*b - 7*a*B)*(a + b*x)^19)/(19*b^8) + (a^2*(3*A*b - 7*a*B)*(a + b*x)^20)/(4*b^8) - (a*(2*A*b - 7*a*B)*(a + b*x)^21)/(7*b^8) + ((A*b - 7*a*B)*(a + b*x)^22)/(22*b^8) + (B*(a + b*x)^23)/(23*b^8)}
# {x^5*(a + b*x)^15*(A + B*x), x, 2, -(a^5*(A*b - a*B)*(a + b*x)^16)/(16*b^7) + (a^4*(5*A*b - 6*a*B)*(a + b*x)^17)/(17*b^7) - (5*a^3*(2*A*b - 3*a*B)*(a + b*x)^18)/(18*b^7) + (10*a^2*(A*b - 2*a*B)*(a + b*x)^19)/(19*b^7) - (a*(A*b - 3*a*B)*(a + b*x)^20)/(4*b^7) + ((A*b - 6*a*B)*(a + b*x)^21)/(21*b^7) + (B*(a + b*x)^22)/(22*b^7)}
# {x^4*(a + b*x)^15*(A + B*x), x, 2, (a^4*(A*b - a*B)*(a + b*x)^16)/(16*b^6) - (a^3*(4*A*b - 5*a*B)*(a + b*x)^17)/(17*b^6) + (a^2*(3*A*b - 5*a*B)*(a + b*x)^18)/(9*b^6) - (2*a*(2*A*b - 5*a*B)*(a + b*x)^19)/(19*b^6) + ((A*b - 5*a*B)*(a + b*x)^20)/(20*b^6) + (B*(a + b*x)^21)/(21*b^6)}
# {x^3*(a + b*x)^15*(A + B*x), x, 2, -(a^3*(A*b - a*B)*(a + b*x)^16)/(16*b^5) + (a^2*(3*A*b - 4*a*B)*(a + b*x)^17)/(17*b^5) - (a*(A*b - 2*a*B)*(a + b*x)^18)/(6*b^5) + ((A*b - 4*a*B)*(a + b*x)^19)/(19*b^5) + (B*(a + b*x)^20)/(20*b^5)}
# {x^2*(a + b*x)^15*(A + B*x), x, 2, (a^2*(A*b - a*B)*(a + b*x)^16)/(16*b^4) - (a*(2*A*b - 3*a*B)*(a + b*x)^17)/(17*b^4) + ((A*b - 3*a*B)*(a + b*x)^18)/(18*b^4) + (B*(a + b*x)^19)/(19*b^4)}
# {x*(a + b*x)^15*(A + B*x), x, 2, -(a*(A*b - a*B)*(a + b*x)^16)/(16*b^3) + ((A*b - 2*a*B)*(a + b*x)^17)/(17*b^3) + (B*(a + b*x)^18)/(18*b^3)}
# {(a + b*x)^15*(A + B*x), x, 2, ((A*b - a*B)*(a + b*x)^16)/(16*b^2) + (B*(a + b*x)^17)/(17*b^2)}
# {((a + b*x)^15*(A + B*x))/x, x, 3, 15*a^14*A*b*x + (105/2)*a^13*A*b^2*x^2 + (455/3)*a^12*A*b^3*x^3 + (1365/4)*a^11*A*b^4*x^4 + (3003/5)*a^10*A*b^5*x^5 + (5005/6)*a^9*A*b^6*x^6 + (6435/7)*a^8*A*b^7*x^7 + (6435/8)*a^7*A*b^8*x^8 + (5005/9)*a^6*A*b^9*x^9 + (3003/10)*a^5*A*b^10*x^10 + (1365/11)*a^4*A*b^11*x^11 + (455/12)*a^3*A*b^12*x^12 + (105/13)*a^2*A*b^13*x^13 + (15/14)*a*A*b^14*x^14 + (1/15)*A*b^15*x^15 + (B*(a + b*x)^16)/(16*b) + a^15*A*Log[x]}
# {((a + b*x)^15*(A + B*x))/x^2, x, 2, -((a^15*A)/x) + 15*a^13*b*(7*A*b + a*B)*x + (35*a^12*b^2*(13*A*b + 3*a*B)*x^2)/2 + (455*a^11*b^3*(3*A*b + a*B)*x^3)/3 + (273*a^10*b^4*(11*A*b + 5*a*B)*x^4)/4 + (1001*a^9*b^5*(5*A*b + 3*a*B)*x^5)/5 + (715*a^8*b^6*(9*A*b + 7*a*B)*x^6)/6 + (6435*a^7*b^7*(A*b + a*B)*x^7)/7 + (715*a^6*b^8*(7*A*b + 9*a*B)*x^8)/8 + (1001*a^5*b^9*(3*A*b + 5*a*B)*x^9)/9 + (273*a^4*b^10*(5*A*b + 11*a*B)*x^10)/10 + (455*a^3*b^11*(A*b + 3*a*B)*x^11)/11 + (35*a^2*b^12*(3*A*b + 13*a*B)*x^12)/12 + (15*a*b^13*(A*b + 7*a*B)*x^13)/13 + (b^14*(A*b + 15*a*B)*x^14)/14 + (b^15*B*x^15)/15 + a^14*(15*A*b + a*B)*Log[x]}
# {((a + b*x)^15*(A + B*x))/x^3, x, 2, -(a^15*A)/(2*x^2) - (a^14*(15*A*b + a*B))/x + 35*a^12*b^2*(13*A*b + 3*a*B)*x + (455*a^11*b^3*(3*A*b + a*B)*x^2)/2 + 91*a^10*b^4*(11*A*b + 5*a*B)*x^3 + (1001*a^9*b^5*(5*A*b + 3*a*B)*x^4)/4 + 143*a^8*b^6*(9*A*b + 7*a*B)*x^5 + (2145*a^7*b^7*(A*b + a*B)*x^6)/2 + (715*a^6*b^8*(7*A*b + 9*a*B)*x^7)/7 + (1001*a^5*b^9*(3*A*b + 5*a*B)*x^8)/8 + (91*a^4*b^10*(5*A*b + 11*a*B)*x^9)/3 + (91*a^3*b^11*(A*b + 3*a*B)*x^10)/2 + (35*a^2*b^12*(3*A*b + 13*a*B)*x^11)/11 + (5*a*b^13*(A*b + 7*a*B)*x^12)/4 + (b^14*(A*b + 15*a*B)*x^13)/13 + (b^15*B*x^14)/14 + 15*a^13*b*(7*A*b + a*B)*Log[x]}
# {((a + b*x)^15*(A + B*x))/x^4, x, 2, -(a^15*A)/(3*x^3) - (a^14*(15*A*b + a*B))/(2*x^2) - (15*a^13*b*(7*A*b + a*B))/x + 455*a^11*b^3*(3*A*b + a*B)*x + (273*a^10*b^4*(11*A*b + 5*a*B)*x^2)/2 + (1001*a^9*b^5*(5*A*b + 3*a*B)*x^3)/3 + (715*a^8*b^6*(9*A*b + 7*a*B)*x^4)/4 + 1287*a^7*b^7*(A*b + a*B)*x^5 + (715*a^6*b^8*(7*A*b + 9*a*B)*x^6)/6 + 143*a^5*b^9*(3*A*b + 5*a*B)*x^7 + (273*a^4*b^10*(5*A*b + 11*a*B)*x^8)/8 + (455*a^3*b^11*(A*b + 3*a*B)*x^9)/9 + (7*a^2*b^12*(3*A*b + 13*a*B)*x^10)/2 + (15*a*b^13*(A*b + 7*a*B)*x^11)/11 + (b^14*(A*b + 15*a*B)*x^12)/12 + (b^15*B*x^13)/13 + 35*a^12*b^2*(13*A*b + 3*a*B)*Log[x]}
# {((a + b*x)^15*(A + B*x))/x^5, x, 2, -(a^15*A)/(4*x^4) - (a^14*(15*A*b + a*B))/(3*x^3) - (15*a^13*b*(7*A*b + a*B))/(2*x^2) - (35*a^12*b^2*(13*A*b + 3*a*B))/x + 273*a^10*b^4*(11*A*b + 5*a*B)*x + (1001*a^9*b^5*(5*A*b + 3*a*B)*x^2)/2 + (715*a^8*b^6*(9*A*b + 7*a*B)*x^3)/3 + (6435*a^7*b^7*(A*b + a*B)*x^4)/4 + 143*a^6*b^8*(7*A*b + 9*a*B)*x^5 + (1001*a^5*b^9*(3*A*b + 5*a*B)*x^6)/6 + 39*a^4*b^10*(5*A*b + 11*a*B)*x^7 + (455*a^3*b^11*(A*b + 3*a*B)*x^8)/8 + (35*a^2*b^12*(3*A*b + 13*a*B)*x^9)/9 + (3*a*b^13*(A*b + 7*a*B)*x^10)/2 + (b^14*(A*b + 15*a*B)*x^11)/11 + (b^15*B*x^12)/12 + 455*a^11*b^3*(3*A*b + a*B)*Log[x]}
# {((a + b*x)^15*(A + B*x))/x^6, x, 2, -(a^15*A)/(5*x^5) - (a^14*(15*A*b + a*B))/(4*x^4) - (5*a^13*b*(7*A*b + a*B))/x^3 - (35*a^12*b^2*(13*A*b + 3*a*B))/(2*x^2) - (455*a^11*b^3*(3*A*b + a*B))/x + 1001*a^9*b^5*(5*A*b + 3*a*B)*x + (715*a^8*b^6*(9*A*b + 7*a*B)*x^2)/2 + 2145*a^7*b^7*(A*b + a*B)*x^3 + (715*a^6*b^8*(7*A*b + 9*a*B)*x^4)/4 + (1001*a^5*b^9*(3*A*b + 5*a*B)*x^5)/5 + (91*a^4*b^10*(5*A*b + 11*a*B)*x^6)/2 + 65*a^3*b^11*(A*b + 3*a*B)*x^7 + (35*a^2*b^12*(3*A*b + 13*a*B)*x^8)/8 + (5*a*b^13*(A*b + 7*a*B)*x^9)/3 + (b^14*(A*b + 15*a*B)*x^10)/10 + (b^15*B*x^11)/11 + 273*a^10*b^4*(11*A*b + 5*a*B)*Log[x]}
# {((a + b*x)^15*(A + B*x))/x^7, x, 2, -(a^15*A)/(6*x^6) - (a^14*(15*A*b + a*B))/(5*x^5) - (15*a^13*b*(7*A*b + a*B))/(4*x^4) - (35*a^12*b^2*(13*A*b + 3*a*B))/(3*x^3) - (455*a^11*b^3*(3*A*b + a*B))/(2*x^2) - (273*a^10*b^4*(11*A*b + 5*a*B))/x + 715*a^8*b^6*(9*A*b + 7*a*B)*x + (6435*a^7*b^7*(A*b + a*B)*x^2)/2 + (715*a^6*b^8*(7*A*b + 9*a*B)*x^3)/3 + (1001*a^5*b^9*(3*A*b + 5*a*B)*x^4)/4 + (273*a^4*b^10*(5*A*b + 11*a*B)*x^5)/5 + (455*a^3*b^11*(A*b + 3*a*B)*x^6)/6 + 5*a^2*b^12*(3*A*b + 13*a*B)*x^7 + (15*a*b^13*(A*b + 7*a*B)*x^8)/8 + (b^14*(A*b + 15*a*B)*x^9)/9 + (b^15*B*x^10)/10 + 1001*a^9*b^5*(5*A*b + 3*a*B)*Log[x]}
# {((a + b*x)^15*(A + B*x))/x^8, x, 2, -(a^15*A)/(7*x^7) - (a^14*(15*A*b + a*B))/(6*x^6) - (3*a^13*b*(7*A*b + a*B))/x^5 - (35*a^12*b^2*(13*A*b + 3*a*B))/(4*x^4) - (455*a^11*b^3*(3*A*b + a*B))/(3*x^3) - (273*a^10*b^4*(11*A*b + 5*a*B))/(2*x^2) - (1001*a^9*b^5*(5*A*b + 3*a*B))/x + 6435*a^7*b^7*(A*b + a*B)*x + (715*a^6*b^8*(7*A*b + 9*a*B)*x^2)/2 + (1001*a^5*b^9*(3*A*b + 5*a*B)*x^3)/3 + (273*a^4*b^10*(5*A*b + 11*a*B)*x^4)/4 + 91*a^3*b^11*(A*b + 3*a*B)*x^5 + (35*a^2*b^12*(3*A*b + 13*a*B)*x^6)/6 + (15*a*b^13*(A*b + 7*a*B)*x^7)/7 + (b^14*(A*b + 15*a*B)*x^8)/8 + (b^15*B*x^9)/9 + 715*a^8*b^6*(9*A*b + 7*a*B)*Log[x]}
# {((a + b*x)^15*(A + B*x))/x^9, x, 2, -(a^15*A)/(8*x^8) - (a^14*(15*A*b + a*B))/(7*x^7) - (5*a^13*b*(7*A*b + a*B))/(2*x^6) - (7*a^12*b^2*(13*A*b + 3*a*B))/x^5 - (455*a^11*b^3*(3*A*b + a*B))/(4*x^4) - (91*a^10*b^4*(11*A*b + 5*a*B))/x^3 - (1001*a^9*b^5*(5*A*b + 3*a*B))/(2*x^2) - (715*a^8*b^6*(9*A*b + 7*a*B))/x + 715*a^6*b^8*(7*A*b + 9*a*B)*x + (1001*a^5*b^9*(3*A*b + 5*a*B)*x^2)/2 + 91*a^4*b^10*(5*A*b + 11*a*B)*x^3 + (455*a^3*b^11*(A*b + 3*a*B)*x^4)/4 + 7*a^2*b^12*(3*A*b + 13*a*B)*x^5 + (5*a*b^13*(A*b + 7*a*B)*x^6)/2 + (b^14*(A*b + 15*a*B)*x^7)/7 + (b^15*B*x^8)/8 + 6435*a^7*b^7*(A*b + a*B)*Log[x]}
# {((a + b*x)^15*(A + B*x))/x^10, x, 2, -(a^15*A)/(9*x^9) - (a^14*(15*A*b + a*B))/(8*x^8) - (15*a^13*b*(7*A*b + a*B))/(7*x^7) - (35*a^12*b^2*(13*A*b + 3*a*B))/(6*x^6) - (91*a^11*b^3*(3*A*b + a*B))/x^5 - (273*a^10*b^4*(11*A*b + 5*a*B))/(4*x^4) - (1001*a^9*b^5*(5*A*b + 3*a*B))/(3*x^3) - (715*a^8*b^6*(9*A*b + 7*a*B))/(2*x^2) - (6435*a^7*b^7*(A*b + a*B))/x + 1001*a^5*b^9*(3*A*b + 5*a*B)*x + (273*a^4*b^10*(5*A*b + 11*a*B)*x^2)/2 + (455*a^3*b^11*(A*b + 3*a*B)*x^3)/3 + (35*a^2*b^12*(3*A*b + 13*a*B)*x^4)/4 + 3*a*b^13*(A*b + 7*a*B)*x^5 + (b^14*(A*b + 15*a*B)*x^6)/6 + (b^15*B*x^7)/7 + 715*a^6*b^8*(7*A*b + 9*a*B)*Log[x]}
# {((a + b*x)^15*(A + B*x))/x^11, x, 2, -(a^15*A)/(10*x^10) - (a^14*(15*A*b + a*B))/(9*x^9) - (15*a^13*b*(7*A*b + a*B))/(8*x^8) - (5*a^12*b^2*(13*A*b + 3*a*B))/x^7 - (455*a^11*b^3*(3*A*b + a*B))/(6*x^6) - (273*a^10*b^4*(11*A*b + 5*a*B))/(5*x^5) - (1001*a^9*b^5*(5*A*b + 3*a*B))/(4*x^4) - (715*a^8*b^6*(9*A*b + 7*a*B))/(3*x^3) - (6435*a^7*b^7*(A*b + a*B))/(2*x^2) - (715*a^6*b^8*(7*A*b + 9*a*B))/x + 273*a^4*b^10*(5*A*b + 11*a*B)*x + (455*a^3*b^11*(A*b + 3*a*B)*x^2)/2 + (35*a^2*b^12*(3*A*b + 13*a*B)*x^3)/3 + (15*a*b^13*(A*b + 7*a*B)*x^4)/4 + (b^14*(A*b + 15*a*B)*x^5)/5 + (b^15*B*x^6)/6 + 1001*a^5*b^9*(3*A*b + 5*a*B)*Log[x]}
# {((a + b*x)^15*(A + B*x))/x^12, x, 2, -(a^15*A)/(11*x^11) - (a^14*(15*A*b + a*B))/(10*x^10) - (5*a^13*b*(7*A*b + a*B))/(3*x^9) - (35*a^12*b^2*(13*A*b + 3*a*B))/(8*x^8) - (65*a^11*b^3*(3*A*b + a*B))/x^7 - (91*a^10*b^4*(11*A*b + 5*a*B))/(2*x^6) - (1001*a^9*b^5*(5*A*b + 3*a*B))/(5*x^5) - (715*a^8*b^6*(9*A*b + 7*a*B))/(4*x^4) - (2145*a^7*b^7*(A*b + a*B))/x^3 - (715*a^6*b^8*(7*A*b + 9*a*B))/(2*x^2) - (1001*a^5*b^9*(3*A*b + 5*a*B))/x + 455*a^3*b^11*(A*b + 3*a*B)*x + (35*a^2*b^12*(3*A*b + 13*a*B)*x^2)/2 + 5*a*b^13*(A*b + 7*a*B)*x^3 + (b^14*(A*b + 15*a*B)*x^4)/4 + (b^15*B*x^5)/5 + 273*a^4*b^10*(5*A*b + 11*a*B)*Log[x]}
# {((a + b*x)^15*(A + B*x))/x^13, x, 2, -(a^15*A)/(12*x^12) - (a^14*(15*A*b + a*B))/(11*x^11) - (3*a^13*b*(7*A*b + a*B))/(2*x^10) - (35*a^12*b^2*(13*A*b + 3*a*B))/(9*x^9) - (455*a^11*b^3*(3*A*b + a*B))/(8*x^8) - (39*a^10*b^4*(11*A*b + 5*a*B))/x^7 - (1001*a^9*b^5*(5*A*b + 3*a*B))/(6*x^6) - (143*a^8*b^6*(9*A*b + 7*a*B))/x^5 - (6435*a^7*b^7*(A*b + a*B))/(4*x^4) - (715*a^6*b^8*(7*A*b + 9*a*B))/(3*x^3) - (1001*a^5*b^9*(3*A*b + 5*a*B))/(2*x^2) - (273*a^4*b^10*(5*A*b + 11*a*B))/x + 35*a^2*b^12*(3*A*b + 13*a*B)*x + (15*a*b^13*(A*b + 7*a*B)*x^2)/2 + (b^14*(A*b + 15*a*B)*x^3)/3 + (b^15*B*x^4)/4 + 455*a^3*b^11*(A*b + 3*a*B)*Log[x]}
# {((a + b*x)^15*(A + B*x))/x^14, x, 2, -(a^15*A)/(13*x^13) - (a^14*(15*A*b + a*B))/(12*x^12) - (15*a^13*b*(7*A*b + a*B))/(11*x^11) - (7*a^12*b^2*(13*A*b + 3*a*B))/(2*x^10) - (455*a^11*b^3*(3*A*b + a*B))/(9*x^9) - (273*a^10*b^4*(11*A*b + 5*a*B))/(8*x^8) - (143*a^9*b^5*(5*A*b + 3*a*B))/x^7 - (715*a^8*b^6*(9*A*b + 7*a*B))/(6*x^6) - (1287*a^7*b^7*(A*b + a*B))/x^5 - (715*a^6*b^8*(7*A*b + 9*a*B))/(4*x^4) - (1001*a^5*b^9*(3*A*b + 5*a*B))/(3*x^3) - (273*a^4*b^10*(5*A*b + 11*a*B))/(2*x^2) - (455*a^3*b^11*(A*b + 3*a*B))/x + 15*a*b^13*(A*b + 7*a*B)*x + (b^14*(A*b + 15*a*B)*x^2)/2 + (b^15*B*x^3)/3 + 35*a^2*b^12*(3*A*b + 13*a*B)*Log[x]}
# {((a + b*x)^15*(A + B*x))/x^15, x, 2, -(a^15*A)/(14*x^14) - (a^14*(15*A*b + a*B))/(13*x^13) - (5*a^13*b*(7*A*b + a*B))/(4*x^12) - (35*a^12*b^2*(13*A*b + 3*a*B))/(11*x^11) - (91*a^11*b^3*(3*A*b + a*B))/(2*x^10) - (91*a^10*b^4*(11*A*b + 5*a*B))/(3*x^9) - (1001*a^9*b^5*(5*A*b + 3*a*B))/(8*x^8) - (715*a^8*b^6*(9*A*b + 7*a*B))/(7*x^7) - (2145*a^7*b^7*(A*b + a*B))/(2*x^6) - (143*a^6*b^8*(7*A*b + 9*a*B))/x^5 - (1001*a^5*b^9*(3*A*b + 5*a*B))/(4*x^4) - (91*a^4*b^10*(5*A*b + 11*a*B))/x^3 - (455*a^3*b^11*(A*b + 3*a*B))/(2*x^2) - (35*a^2*b^12*(3*A*b + 13*a*B))/x + b^14*(A*b + 15*a*B)*x + (b^15*B*x^2)/2 + 15*a*b^13*(A*b + 7*a*B)*Log[x]}
# {((a + b*x)^15*(A + B*x))/x^16, x, 2, -(a^15*A)/(15*x^15) - (a^14*(15*A*b + a*B))/(14*x^14) - (15*a^13*b*(7*A*b + a*B))/(13*x^13) - (35*a^12*b^2*(13*A*b + 3*a*B))/(12*x^12) - (455*a^11*b^3*(3*A*b + a*B))/(11*x^11) - (273*a^10*b^4*(11*A*b + 5*a*B))/(10*x^10) - (1001*a^9*b^5*(5*A*b + 3*a*B))/(9*x^9) - (715*a^8*b^6*(9*A*b + 7*a*B))/(8*x^8) - (6435*a^7*b^7*(A*b + a*B))/(7*x^7) - (715*a^6*b^8*(7*A*b + 9*a*B))/(6*x^6) - (1001*a^5*b^9*(3*A*b + 5*a*B))/(5*x^5) - (273*a^4*b^10*(5*A*b + 11*a*B))/(4*x^4) - (455*a^3*b^11*(A*b + 3*a*B))/(3*x^3) - (35*a^2*b^12*(3*A*b + 13*a*B))/(2*x^2) - (15*a*b^13*(A*b + 7*a*B))/x + b^15*B*x + b^14*(A*b + 15*a*B)*Log[x]}
# {((a + b*x)^15*(A + B*x))/x^17, x, 3, -(a^15*B)/(15*x^15) - (15*a^14*b*B)/(14*x^14) - (105*a^13*b^2*B)/(13*x^13) - (455*a^12*b^3*B)/(12*x^12) - (1365*a^11*b^4*B)/(11*x^11) - (3003*a^10*b^5*B)/(10*x^10) - (5005*a^9*b^6*B)/(9*x^9) - (6435*a^8*b^7*B)/(8*x^8) - (6435*a^7*b^8*B)/(7*x^7) - (5005*a^6*b^9*B)/(6*x^6) - (3003*a^5*b^10*B)/(5*x^5) - (1365*a^4*b^11*B)/(4*x^4) - (455*a^3*b^12*B)/(3*x^3) - (105*a^2*b^13*B)/(2*x^2) - (15*a*b^14*B)/x - (A*(a + b*x)^16)/(16*a*x^16) + b^15*B*Log[x]}
# {((a + b*x)^15*(A + B*x))/x^18, x, 2, -(A*(a + b*x)^16)/(17*a*x^17) + ((A*b - 17*a*B)*(a + b*x)^16)/(272*a^2*x^16)}
# {((a + b*x)^15*(A + B*x))/x^19, x, 3, -(A*(a + b*x)^16)/(18*a*x^18) + ((A*b - 9*a*B)*(a + b*x)^16)/(153*a^2*x^17) - (b*(A*b - 9*a*B)*(a + b*x)^16)/(2448*a^3*x^16)}
# {((a + b*x)^15*(A + B*x))/x^20, x, 4, -(A*(a + b*x)^16)/(19*a*x^19) + ((3*A*b - 19*a*B)*(a + b*x)^16)/(342*a^2*x^18) - (b*(3*A*b - 19*a*B)*(a + b*x)^16)/(2907*a^3*x^17) + (b^2*(3*A*b - 19*a*B)*(a + b*x)^16)/(46512*a^4*x^16)}
# {((a + b*x)^15*(A + B*x))/x^21, x, 5, -(A*(a + b*x)^16)/(20*a*x^20) + ((A*b - 5*a*B)*(a + b*x)^16)/(95*a^2*x^19) - (b*(A*b - 5*a*B)*(a + b*x)^16)/(570*a^3*x^18) + (b^2*(A*b - 5*a*B)*(a + b*x)^16)/(4845*a^4*x^17) - (b^3*(A*b - 5*a*B)*(a + b*x)^16)/(77520*a^5*x^16)}
# {((a + b*x)^15*(A + B*x))/x^22, x, 6, -(A*(a + b*x)^16)/(21*a*x^21) + ((5*A*b - 21*a*B)*(a + b*x)^16)/(420*a^2*x^20) - (b*(5*A*b - 21*a*B)*(a + b*x)^16)/(1995*a^3*x^19) + (b^2*(5*A*b - 21*a*B)*(a + b*x)^16)/(11970*a^4*x^18) - (b^3*(5*A*b - 21*a*B)*(a + b*x)^16)/(101745*a^5*x^17) + (b^4*(5*A*b - 21*a*B)*(a + b*x)^16)/(1627920*a^6*x^16)}
# {((a + b*x)^15*(A + B*x))/x^23, x, 7, -(A*(a + b*x)^16)/(22*a*x^22) + ((3*A*b - 11*a*B)*(a + b*x)^16)/(231*a^2*x^21) - (b*(3*A*b - 11*a*B)*(a + b*x)^16)/(924*a^3*x^20) + (b^2*(3*A*b - 11*a*B)*(a + b*x)^16)/(4389*a^4*x^19) - (b^3*(3*A*b - 11*a*B)*(a + b*x)^16)/(26334*a^5*x^18) + (b^4*(3*A*b - 11*a*B)*(a + b*x)^16)/(223839*a^6*x^17) - (b^5*(3*A*b - 11*a*B)*(a + b*x)^16)/(3581424*a^7*x^16)}
# {((a + b*x)^15*(A + B*x))/x^24, x, 8, -(A*(a + b*x)^16)/(23*a*x^23) + ((7*A*b - 23*a*B)*(a + b*x)^16)/(506*a^2*x^22) - (b*(7*A*b - 23*a*B)*(a + b*x)^16)/(1771*a^3*x^21) + (b^2*(7*A*b - 23*a*B)*(a + b*x)^16)/(7084*a^4*x^20) - (b^3*(7*A*b - 23*a*B)*(a + b*x)^16)/(33649*a^5*x^19) + (b^4*(7*A*b - 23*a*B)*(a + b*x)^16)/(201894*a^6*x^18) - (b^5*(7*A*b - 23*a*B)*(a + b*x)^16)/(1716099*a^7*x^17) + (b^6*(7*A*b - 23*a*B)*(a + b*x)^16)/(27457584*a^8*x^16)}
# {((a + b*x)^15*(A + B*x))/x^25, x, 9, -(A*(a + b*x)^16)/(24*a*x^24) + ((A*b - 3*a*B)*(a + b*x)^16)/(69*a^2*x^23) - (7*b*(A*b - 3*a*B)*(a + b*x)^16)/(1518*a^3*x^22) + (b^2*(A*b - 3*a*B)*(a + b*x)^16)/(759*a^4*x^21) - (b^3*(A*b - 3*a*B)*(a + b*x)^16)/(3036*a^5*x^20) + (b^4*(A*b - 3*a*B)*(a + b*x)^16)/(14421*a^6*x^19) - (b^5*(A*b - 3*a*B)*(a + b*x)^16)/(86526*a^7*x^18) + (b^6*(A*b - 3*a*B)*(a + b*x)^16)/(735471*a^8*x^17) - (b^7*(A*b - 3*a*B)*(a + b*x)^16)/(11767536*a^9*x^16)}
# {((a + b*x)^15*(A + B*x))/x^26, x, 10, -(A*(a + b*x)^16)/(25*a*x^25) + ((9*A*b - 25*a*B)*(a + b*x)^16)/(600*a^2*x^24) - (b*(9*A*b - 25*a*B)*(a + b*x)^16)/(1725*a^3*x^23) + (7*b^2*(9*A*b - 25*a*B)*(a + b*x)^16)/(37950*a^4*x^22) - (b^3*(9*A*b - 25*a*B)*(a + b*x)^16)/(18975*a^5*x^21) + (b^4*(9*A*b - 25*a*B)*(a + b*x)^16)/(75900*a^6*x^20) - (b^5*(9*A*b - 25*a*B)*(a + b*x)^16)/(360525*a^7*x^19) + (b^6*(9*A*b - 25*a*B)*(a + b*x)^16)/(2163150*a^8*x^18) - (b^7*(9*A*b - 25*a*B)*(a + b*x)^16)/(18386775*a^9*x^17) + (b^8*(9*A*b - 25*a*B)*(a + b*x)^16)/(294188400*a^10*x^16)}
# {((a + b*x)^15*(A + B*x))/x^27, x, 11, -(A*(a + b*x)^16)/(26*a*x^26) + ((5*A*b - 13*a*B)*(a + b*x)^16)/(325*a^2*x^25) - (3*b*(5*A*b - 13*a*B)*(a + b*x)^16)/(2600*a^3*x^24) + (3*b^2*(5*A*b - 13*a*B)*(a + b*x)^16)/(7475*a^4*x^23) - (21*b^3*(5*A*b - 13*a*B)*(a + b*x)^16)/(164450*a^5*x^22) + (3*b^4*(5*A*b - 13*a*B)*(a + b*x)^16)/(82225*a^6*x^21) - (3*b^5*(5*A*b - 13*a*B)*(a + b*x)^16)/(328900*a^7*x^20) + (3*b^6*(5*A*b - 13*a*B)*(a + b*x)^16)/(1562275*a^8*x^19) - (b^7*(5*A*b - 13*a*B)*(a + b*x)^16)/(3124550*a^9*x^18) + (b^8*(5*A*b - 13*a*B)*(a + b*x)^16)/(26558675*a^10*x^17) - (b^9*(5*A*b - 13*a*B)*(a + b*x)^16)/(424938800*a^11*x^16)}
# {((a + b*x)^15*(A + B*x))/x^28, x, 2, -(a^15*A)/(27*x^27) - (a^14*(15*A*b + a*B))/(26*x^26) - (3*a^13*b*(7*A*b + a*B))/(5*x^25) - (35*a^12*b^2*(13*A*b + 3*a*B))/(24*x^24) - (455*a^11*b^3*(3*A*b + a*B))/(23*x^23) - (273*a^10*b^4*(11*A*b + 5*a*B))/(22*x^22) - (143*a^9*b^5*(5*A*b + 3*a*B))/(3*x^21) - (143*a^8*b^6*(9*A*b + 7*a*B))/(4*x^20) - (6435*a^7*b^7*(A*b + a*B))/(19*x^19) - (715*a^6*b^8*(7*A*b + 9*a*B))/(18*x^18) - (1001*a^5*b^9*(3*A*b + 5*a*B))/(17*x^17) - (273*a^4*b^10*(5*A*b + 11*a*B))/(16*x^16) - (91*a^3*b^11*(A*b + 3*a*B))/(3*x^15) - (5*a^2*b^12*(3*A*b + 13*a*B))/(2*x^14) - (15*a*b^13*(A*b + 7*a*B))/(13*x^13) - (b^14*(A*b + 15*a*B))/(12*x^12) - (b^15*B)/(11*x^11)}
# {((a + b*x)^15*(A + B*x))/x^29, x, 2, -(a^15*A)/(28*x^28) - (a^14*(15*A*b + a*B))/(27*x^27) - (15*a^13*b*(7*A*b + a*B))/(26*x^26) - (7*a^12*b^2*(13*A*b + 3*a*B))/(5*x^25) - (455*a^11*b^3*(3*A*b + a*B))/(24*x^24) - (273*a^10*b^4*(11*A*b + 5*a*B))/(23*x^23) - (91*a^9*b^5*(5*A*b + 3*a*B))/(2*x^22) - (715*a^8*b^6*(9*A*b + 7*a*B))/(21*x^21) - (1287*a^7*b^7*(A*b + a*B))/(4*x^20) - (715*a^6*b^8*(7*A*b + 9*a*B))/(19*x^19) - (1001*a^5*b^9*(3*A*b + 5*a*B))/(18*x^18) - (273*a^4*b^10*(5*A*b + 11*a*B))/(17*x^17) - (455*a^3*b^11*(A*b + 3*a*B))/(16*x^16) - (7*a^2*b^12*(3*A*b + 13*a*B))/(3*x^15) - (15*a*b^13*(A*b + 7*a*B))/(14*x^14) - (b^14*(A*b + 15*a*B))/(13*x^13) - (b^15*B)/(12*x^12)}

# {((a + b*x)^15*(A + B*x))/x^30, x, 2, -(a^15*A)/(29*x^29) - (a^14*(15*A*b + a*B))/(28*x^28) - (5*a^13*b*(7*A*b + a*B))/(9*x^27) - (35*a^12*b^2*(13*A*b + 3*a*B))/(26*x^26) - (91*a^11*b^3*(3*A*b + a*B))/(5*x^25) - (91*a^10*b^4*(11*A*b + 5*a*B))/(8*x^24) - (1001*a^9*b^5*(5*A*b + 3*a*B))/(23*x^23) - (65*a^8*b^6*(9*A*b + 7*a*B))/(2*x^22) - (2145*a^7*b^7*(A*b + a*B))/(7*x^21) - (143*a^6*b^8*(7*A*b + 9*a*B))/(4*x^20) - (1001*a^5*b^9*(3*A*b + 5*a*B))/(19*x^19) - (91*a^4*b^10*(5*A*b + 11*a*B))/(6*x^18) - (455*a^3*b^11*(A*b + 3*a*B))/(17*x^17) - (35*a^2*b^12*(3*A*b + 13*a*B))/(16*x^16) - (a*b^13*(A*b + 7*a*B))/x^15 - (b^14*(A*b + 15*a*B))/(14*x^14) - (b^15*B)/(13*x^13)} 
[x^3*(a+b*x)*(c+d*x)^16,x,2,1/17*c^3*(b*c-a*d)*(c+d*x)^17/d^5-1/18*c^2*(4*b*c-3*a*d)*(c+d*x)^18/d^5+3/19*c*(2*b*c-a*d)*(c+d*x)^19/d^5-1/20*(4*b*c-a*d)*(c+d*x)^20/d^5+1/21*b*(c+d*x)^21/d^5],
[x^2*(a+b*x)*(c+d*x)^16,x,2,-1/17*c^2*(b*c-a*d)*(c+d*x)^17/d^4+1/18*c*(3*b*c-2*a*d)*(c+d*x)^18/d^4-1/19*(3*b*c-a*d)*(c+d*x)^19/d^4+1/20*b*(c+d*x)^20/d^4],
[x*(a+b*x)*(c+d*x)^16,x,2,1/17*c*(b*c-a*d)*(c+d*x)^17/d^3-1/18*(2*b*c-a*d)*(c+d*x)^18/d^3+1/19*b*(c+d*x)^19/d^3],
[(a+b*x)*(c+d*x)^16,x,2,-1/17*(b*c-a*d)*(c+d*x)^17/d^2+1/18*b*(c+d*x)^18/d^2],
[x^2*(2+x)^5*(2+3*x),x,1,1/3*x^3*(2+x)^6],

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

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

# p>0
[x^3*(a+b*x)^2*(c+d*x)^16,x,2,-1/17*c^3*(b*c-a*d)^2*(c+d*x)^17/d^6+1/18*c^2*(5*b*c-3*a*d)*(b*c-a*d)*(c+d*x)^18/d^6-1/19*c*(10*b^2*c^2-12*a*b*c*d+3*a^2*d^2)*(c+d*x)^19/d^6+1/20*(10*b^2*c^2-8*a*b*c*d+a^2*d^2)*(c+d*x)^20/d^6-1/21*b*(5*b*c-2*a*d)*(c+d*x)^21/d^6+1/22*b^2*(c+d*x)^22/d^6],
[x^2*(a+b*x)^2*(c+d*x)^16,x,2,1/17*c^2*(b*c-a*d)^2*(c+d*x)^17/d^5-1/9*c*(b*c-a*d)*(2*b*c-a*d)*(c+d*x)^18/d^5+1/19*(6*b^2*c^2-6*a*b*c*d+a^2*d^2)*(c+d*x)^19/d^5-1/10*b*(2*b*c-a*d)*(c+d*x)^20/d^5+1/21*b^2*(c+d*x)^21/d^5],
[x*(a+b*x)^2*(c+d*x)^16,x,2,-1/17*c*(b*c-a*d)^2*(c+d*x)^17/d^4+1/18*(b*c-a*d)*(3*b*c-a*d)*(c+d*x)^18/d^4-1/19*b*(3*b*c-2*a*d)*(c+d*x)^19/d^4+1/20*b^2*(c+d*x)^20/d^4],

# p<0

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

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

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

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

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

# n<0
[x^6/((a+b*x)^2*(c+d*x)^2),x,2,(3*b^2*c^2+4*a*b*c*d+3*a^2*d^2)*x/(b^4*d^4)-(b*c+a*d)*x^2/(b^3*d^3)+1/3*x^3/(b^2*d^2)-a^6/(b^5*(b*c-a*d)^2*(a+b*x))-c^6/(d^5*(b*c-a*d)^2*(c+d*x))-2*a^5*(3*b*c-2*a*d)*log(a+b*x)/(b^5*(b*c-a*d)^3)-2*c^5*(2*b*c-3*a*d)*log(c+d*x)/(d^5*(b*c-a*d)^3)],
[x^5/((a+b*x)^2*(c+d*x)^2),x,2,-2*(b*c+a*d)*x/(b^3*d^3)+1/2*x^2/(b^2*d^2)+a^5/(b^4*(b*c-a*d)^2*(a+b*x))+c^5/(d^4*(b*c-a*d)^2*(c+d*x))+a^4*(5*b*c-3*a*d)*log(a+b*x)/(b^4*(b*c-a*d)^3)+c^4*(3*b*c-5*a*d)*log(c+d*x)/(d^4*(b*c-a*d)^3)],
[x^4/((a+b*x)^2*(c+d*x)^2),x,2,x/(b^2*d^2)-a^4/(b^3*(b*c-a*d)^2*(a+b*x))-c^4/(d^3*(b*c-a*d)^2*(c+d*x))-2*a^3*(2*b*c-a*d)*log(a+b*x)/(b^3*(b*c-a*d)^3)-2*c^3*(b*c-2*a*d)*log(c+d*x)/(d^3*(b*c-a*d)^3)],
[x^3/((a+b*x)^2*(c+d*x)^2),x,2,a^3/(b^2*(b*c-a*d)^2*(a+b*x))+c^3/(d^2*(b*c-a*d)^2*(c+d*x))+a^2*(3*b*c-a*d)*log(a+b*x)/(b^2*(b*c-a*d)^3)+c^2*(b*c-3*a*d)*log(c+d*x)/(d^2*(b*c-a*d)^3)],
[x^2/((a+b*x)^2*(c+d*x)^2),x,2,-a^2/(b*(b*c-a*d)^2*(a+b*x))-c^2/(d*(b*c-a*d)^2*(c+d*x))-2*a*c*log(a+b*x)/(b*c-a*d)^3+2*a*c*log(c+d*x)/(b*c-a*d)^3],
[x/((a+b*x)^2*(c+d*x)^2),x,2,a/((b*c-a*d)^2*(a+b*x))+c/((b*c-a*d)^2*(c+d*x))+(b*c+a*d)*log(a+b*x)/(b*c-a*d)^3-(b*c+a*d)*log(c+d*x)/(b*c-a*d)^3],
[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/(x*(a+b*x)^2*(c+d*x)^2),x,2,b^2/(a*(b*c-a*d)^2*(a+b*x))+d^2/(c*(b*c-a*d)^2*(c+d*x))+log(x)/(a^2*c^2)-b^2*(b*c-3*a*d)*log(a+b*x)/(a^2*(b*c-a*d)^3)-d^2*(3*b*c-a*d)*log(c+d*x)/(c^2*(b*c-a*d)^3)],
[1/(x^2*(a+b*x)^2*(c+d*x)^2),x,2,(-1)/(a^2*c^2*x)-b^3/(a^2*(b*c-a*d)^2*(a+b*x))-d^3/(c^2*(b*c-a*d)^2*(c+d*x))-2*(b*c+a*d)*log(x)/(a^3*c^3)+2*b^3*(b*c-2*a*d)*log(a+b*x)/(a^3*(b*c-a*d)^3)+2*d^3*(2*b*c-a*d)*log(c+d*x)/(c^3*(b*c-a*d)^3)],
[1/(x^3*(a+b*x)^2*(c+d*x)^2),x,2,(-1/2)/(a^2*c^2*x^2)+2*(b*c+a*d)/(a^3*c^3*x)+b^4/(a^3*(b*c-a*d)^2*(a+b*x))+d^4/(c^3*(b*c-a*d)^2*(c+d*x))+(3*b^2*c^2+4*a*b*c*d+3*a^2*d^2)*log(x)/(a^4*c^4)-b^4*(3*b*c-5*a*d)*log(a+b*x)/(a^4*(b*c-a*d)^3)-d^4*(5*b*c-3*a*d)*log(c+d*x)/(c^4*(b*c-a*d)^3)],
[x^7/((a+b*x)^2*(c+d*x)^3),x,2,3*(2*b^2*c^2+2*a*b*c*d+a^2*d^2)*x/(b^4*d^5)-1/2*(3*b*c+2*a*d)*x^2/(b^3*d^4)+1/3*x^3/(b^2*d^3)+a^7/(b^5*(b*c-a*d)^3*(a+b*x))+1/2*c^7/(d^6*(b*c-a*d)^2*(c+d*x)^2)-c^6*(5*b*c-7*a*d)/(d^6*(b*c-a*d)^3*(c+d*x))+a^6*(7*b*c-4*a*d)*log(a+b*x)/(b^5*(b*c-a*d)^4)-c^5*(10*b^2*c^2-28*a*b*c*d+21*a^2*d^2)*log(c+d*x)/(d^6*(b*c-a*d)^4)],
[x^6/((a+b*x)^2*(c+d*x)^3),x,2,-(3*b*c+2*a*d)*x/(b^3*d^4)+1/2*x^2/(b^2*d^3)-a^6/(b^4*(b*c-a*d)^3*(a+b*x))-1/2*c^6/(d^5*(b*c-a*d)^2*(c+d*x)^2)+2*c^5*(2*b*c-3*a*d)/(d^5*(b*c-a*d)^3*(c+d*x))-3*a^5*(2*b*c-a*d)*log(a+b*x)/(b^4*(b*c-a*d)^4)+3*c^4*(2*b^2*c^2-6*a*b*c*d+5*a^2*d^2)*log(c+d*x)/(d^5*(b*c-a*d)^4)],
[x^5/((a+b*x)^2*(c+d*x)^3),x,2,x/(b^2*d^3)+a^5/(b^3*(b*c-a*d)^3*(a+b*x))+1/2*c^5/(d^4*(b*c-a*d)^2*(c+d*x)^2)-c^4*(3*b*c-5*a*d)/(d^4*(b*c-a*d)^3*(c+d*x))+a^4*(5*b*c-2*a*d)*log(a+b*x)/(b^3*(b*c-a*d)^4)-c^3*(3*b^2*c^2-10*a*b*c*d+10*a^2*d^2)*log(c+d*x)/(d^4*(b*c-a*d)^4)],
[x^4/((a+b*x)^2*(c+d*x)^3),x,2,-a^4/(b^2*(b*c-a*d)^3*(a+b*x))-1/2*c^4/(d^3*(b*c-a*d)^2*(c+d*x)^2)+2*c^3*(b*c-2*a*d)/(d^3*(b*c-a*d)^3*(c+d*x))-a^3*(4*b*c-a*d)*log(a+b*x)/(b^2*(b*c-a*d)^4)+c^2*(b^2*c^2-4*a*b*c*d+6*a^2*d^2)*log(c+d*x)/(d^3*(b*c-a*d)^4)],
[x^3/((a+b*x)^2*(c+d*x)^3),x,2,a^3/(b*(b*c-a*d)^3*(a+b*x))+1/2*c^3/(d^2*(b*c-a*d)^2*(c+d*x)^2)-c^2*(b*c-3*a*d)/(d^2*(b*c-a*d)^3*(c+d*x))+3*a^2*c*log(a+b*x)/(b*c-a*d)^4-3*a^2*c*log(c+d*x)/(b*c-a*d)^4],
[x^2/((a+b*x)^2*(c+d*x)^3),x,2,-a^2/((b*c-a*d)^3*(a+b*x))-1/2*c^2/(d*(b*c-a*d)^2*(c+d*x)^2)-2*a*c/((b*c-a*d)^3*(c+d*x))-a*(2*b*c+a*d)*log(a+b*x)/(b*c-a*d)^4+a*(2*b*c+a*d)*log(c+d*x)/(b*c-a*d)^4],
[x/((a+b*x)^2*(c+d*x)^3),x,2,a*b/((b*c-a*d)^3*(a+b*x))+1/2*c/((b*c-a*d)^2*(c+d*x)^2)+(b*c+a*d)/((b*c-a*d)^3*(c+d*x))+b*(b*c+2*a*d)*log(a+b*x)/(b*c-a*d)^4-b*(b*c+2*a*d)*log(c+d*x)/(b*c-a*d)^4],
[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/(x*(a+b*x)^2*(c+d*x)^3),x,2,b^3/(a*(b*c-a*d)^3*(a+b*x))+1/2*d^2/(c*(b*c-a*d)^2*(c+d*x)^2)+d^2*(3*b*c-a*d)/(c^2*(b*c-a*d)^3*(c+d*x))+log(x)/(a^2*c^3)-b^3*(b*c-4*a*d)*log(a+b*x)/(a^2*(b*c-a*d)^4)-d^2*(6*b^2*c^2-4*a*b*c*d+a^2*d^2)*log(c+d*x)/(c^3*(b*c-a*d)^4)],
[1/(x^2*(a+b*x)^2*(c+d*x)^3),x,2,(-1)/(a^2*c^3*x)-b^4/(a^2*(b*c-a*d)^3*(a+b*x))-1/2*d^3/(c^2*(b*c-a*d)^2*(c+d*x)^2)-2*d^3*(2*b*c-a*d)/(c^3*(b*c-a*d)^3*(c+d*x))-(2*b*c+3*a*d)*log(x)/(a^3*c^4)+b^4*(2*b*c-5*a*d)*log(a+b*x)/(a^3*(b*c-a*d)^4)+d^3*(10*b^2*c^2-10*a*b*c*d+3*a^2*d^2)*log(c+d*x)/(c^4*(b*c-a*d)^4)],
[1/(x^3*(a+b*x)^2*(c+d*x)^3),x,2,(-1/2)/(a^2*c^3*x^2)+(2*b*c+3*a*d)/(a^3*c^4*x)+b^5/(a^3*(b*c-a*d)^3*(a+b*x))+1/2*d^4/(c^3*(b*c-a*d)^2*(c+d*x)^2)+d^4*(5*b*c-3*a*d)/(c^4*(b*c-a*d)^3*(c+d*x))+3*(b^2*c^2+2*a*b*c*d+2*a^2*d^2)*log(x)/(a^4*c^5)-3*b^5*(b*c-2*a*d)*log(a+b*x)/(a^4*(b*c-a*d)^4)-3*d^4*(5*b^2*c^2-6*a*b*c*d+2*a^2*d^2)*log(c+d*x)/(c^5*(b*c-a*d)^4)],

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

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

# n<0
[x^7/((a+b*x)^3*(c+d*x)^3),x,2,-3*(b*c+a*d)*x/(b^4*d^4)+1/2*x^2/(b^3*d^3)+1/2*a^7/(b^5*(b*c-a*d)^3*(a+b*x)^2)-a^6*(7*b*c-4*a*d)/(b^5*(b*c-a*d)^4*(a+b*x))-1/2*c^7/(d^5*(b*c-a*d)^3*(c+d*x)^2)+c^6*(4*b*c-7*a*d)/(d^5*(b*c-a*d)^4*(c+d*x))-3*a^5*(7*b^2*c^2-7*a*b*c*d+2*a^2*d^2)*log(a+b*x)/(b^5*(b*c-a*d)^5)+3*c^5*(2*b^2*c^2-7*a*b*c*d+7*a^2*d^2)*log(c+d*x)/(d^5*(b*c-a*d)^5)],
[x^6/((a+b*x)^3*(c+d*x)^3),x,2,x/(b^3*d^3)-1/2*a^6/(b^4*(b*c-a*d)^3*(a+b*x)^2)+3*a^5*(2*b*c-a*d)/(b^4*(b*c-a*d)^4*(a+b*x))+1/2*c^6/(d^4*(b*c-a*d)^3*(c+d*x)^2)-3*c^5*(b*c-2*a*d)/(d^4*(b*c-a*d)^4*(c+d*x))+3*a^4*(5*b^2*c^2-4*a*b*c*d+a^2*d^2)*log(a+b*x)/(b^4*(b*c-a*d)^5)-3*c^4*(b^2*c^2-4*a*b*c*d+5*a^2*d^2)*log(c+d*x)/(d^4*(b*c-a*d)^5)],
[x^5/((a+b*x)^3*(c+d*x)^3),x,2,1/2*a^5/(b^3*(b*c-a*d)^3*(a+b*x)^2)-a^4*(5*b*c-2*a*d)/(b^3*(b*c-a*d)^4*(a+b*x))-1/2*c^5/(d^3*(b*c-a*d)^3*(c+d*x)^2)+c^4*(2*b*c-5*a*d)/(d^3*(b*c-a*d)^4*(c+d*x))-a^3*(10*b^2*c^2-5*a*b*c*d+a^2*d^2)*log(a+b*x)/(b^3*(b*c-a*d)^5)+c^3*(b^2*c^2-5*a*b*c*d+10*a^2*d^2)*log(c+d*x)/(d^3*(b*c-a*d)^5)],
[x^4/((a+b*x)^3*(c+d*x)^3),x,2,-1/2*a^4/(b^2*(b*c-a*d)^3*(a+b*x)^2)+a^3*(4*b*c-a*d)/(b^2*(b*c-a*d)^4*(a+b*x))+1/2*c^4/(d^2*(b*c-a*d)^3*(c+d*x)^2)-c^3*(b*c-4*a*d)/(d^2*(b*c-a*d)^4*(c+d*x))+6*a^2*c^2*log(a+b*x)/(b*c-a*d)^5-6*a^2*c^2*log(c+d*x)/(b*c-a*d)^5],
[x^3/((a+b*x)^3*(c+d*x)^3),x,2,1/2*a^3/(b*(b*c-a*d)^3*(a+b*x)^2)-3*a^2*c/((b*c-a*d)^4*(a+b*x))-1/2*c^3/(d*(b*c-a*d)^3*(c+d*x)^2)-3*a*c^2/((b*c-a*d)^4*(c+d*x))-3*a*c*(b*c+a*d)*log(a+b*x)/(b*c-a*d)^5+3*a*c*(b*c+a*d)*log(c+d*x)/(b*c-a*d)^5],
[x^2/((a+b*x)^3*(c+d*x)^3),x,2,-1/2*a^2/((b*c-a*d)^3*(a+b*x)^2)+a*(2*b*c+a*d)/((b*c-a*d)^4*(a+b*x))+1/2*c^2/((b*c-a*d)^3*(c+d*x)^2)+c*(b*c+2*a*d)/((b*c-a*d)^4*(c+d*x))+(b^2*c^2+4*a*b*c*d+a^2*d^2)*log(a+b*x)/(b*c-a*d)^5-(b^2*c^2+4*a*b*c*d+a^2*d^2)*log(c+d*x)/(b*c-a*d)^5],
[x/((a+b*x)^3*(c+d*x)^3),x,2,1/2*a*b/((b*c-a*d)^3*(a+b*x)^2)-b*(b*c+2*a*d)/((b*c-a*d)^4*(a+b*x))-1/2*c*d/((b*c-a*d)^3*(c+d*x)^2)-d*(2*b*c+a*d)/((b*c-a*d)^4*(c+d*x))-3*b*d*(b*c+a*d)*log(a+b*x)/(b*c-a*d)^5+3*b*d*(b*c+a*d)*log(c+d*x)/(b*c-a*d)^5],
[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],
[1/(x*(a+b*x)^3*(c+d*x)^3),x,2,1/2*b^3/(a*(b*c-a*d)^3*(a+b*x)^2)+b^3*(b*c-4*a*d)/(a^2*(b*c-a*d)^4*(a+b*x))-1/2*d^3/(c*(b*c-a*d)^3*(c+d*x)^2)-d^3*(4*b*c-a*d)/(c^2*(b*c-a*d)^4*(c+d*x))+log(x)/(a^3*c^3)-b^3*(b^2*c^2-5*a*b*c*d+10*a^2*d^2)*log(a+b*x)/(a^3*(b*c-a*d)^5)+d^3*(10*b^2*c^2-5*a*b*c*d+a^2*d^2)*log(c+d*x)/(c^3*(b*c-a*d)^5)],
[1/(x^2*(a+b*x)^3*(c+d*x)^3),x,2,(-1)/(a^3*c^3*x)-1/2*b^4/(a^2*(b*c-a*d)^3*(a+b*x)^2)-b^4*(2*b*c-5*a*d)/(a^3*(b*c-a*d)^4*(a+b*x))+1/2*d^4/(c^2*(b*c-a*d)^3*(c+d*x)^2)+d^4*(5*b*c-2*a*d)/(c^3*(b*c-a*d)^4*(c+d*x))-3*(b*c+a*d)*log(x)/(a^4*c^4)+3*b^4*(b^2*c^2-4*a*b*c*d+5*a^2*d^2)*log(a+b*x)/(a^4*(b*c-a*d)^5)-3*d^4*(5*b^2*c^2-4*a*b*c*d+a^2*d^2)*log(c+d*x)/(c^4*(b*c-a*d)^5)],

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

# p>0
[x^(7/2)*(a+b*x)*(A+B*x),x,2,2/9*a*A*x^(9/2)+2/11*(A*b+a*B)*x^(11/2)+2/13*b*B*x^(13/2)],
[x^(5/2)*(a+b*x)*(A+B*x),x,2,2/7*a*A*x^(7/2)+2/9*(A*b+a*B)*x^(9/2)+2/11*b*B*x^(11/2)],
[x^(3/2)*(a+b*x)*(A+B*x),x,2,2/5*a*A*x^(5/2)+2/7*(A*b+a*B)*x^(7/2)+2/9*b*B*x^(9/2)],
[(a+b*x)*(A+B*x)*sqrt(x),x,2,2/3*a*A*x^(3/2)+2/5*(A*b+a*B)*x^(5/2)+2/7*b*B*x^(7/2)],
[(a+b*x)*(A+B*x)/sqrt(x),x,2,2/3*(A*b+a*B)*x^(3/2)+2/5*b*B*x^(5/2)+2*a*A*sqrt(x)],
[(a+b*x)*(A+B*x)/x^(3/2),x,2,2/3*b*B*x^(3/2)-2*a*A/sqrt(x)+2*(A*b+a*B)*sqrt(x)],
[(a+b*x)*(A+B*x)/x^(5/2),x,2,-2/3*a*A/x^(3/2)-2*(A*b+a*B)/sqrt(x)+2*b*B*sqrt(x)],
[(a+b*x)*(A+B*x)/x^(7/2),x,2,-2/5*a*A/x^(5/2)-2/3*(A*b+a*B)/x^(3/2)-2*b*B/sqrt(x)],
[x^(7/2)*(a+b*x)^2*(A+B*x),x,2,2/9*a^2*A*x^(9/2)+2/11*a*(2*A*b+a*B)*x^(11/2)+2/13*b*(A*b+2*a*B)*x^(13/2)+2/15*b^2*B*x^(15/2)],
[x^(5/2)*(a+b*x)^2*(A+B*x),x,2,2/7*a^2*A*x^(7/2)+2/9*a*(2*A*b+a*B)*x^(9/2)+2/11*b*(A*b+2*a*B)*x^(11/2)+2/13*b^2*B*x^(13/2)],
[x^(3/2)*(a+b*x)^2*(A+B*x),x,2,2/5*a^2*A*x^(5/2)+2/7*a*(2*A*b+a*B)*x^(7/2)+2/9*b*(A*b+2*a*B)*x^(9/2)+2/11*b^2*B*x^(11/2)],
[(a+b*x)^2*(A+B*x)*sqrt(x),x,2,2/3*a^2*A*x^(3/2)+2/5*a*(2*A*b+a*B)*x^(5/2)+2/7*b*(A*b+2*a*B)*x^(7/2)+2/9*b^2*B*x^(9/2)],
[(a+b*x)^2*(A+B*x)/sqrt(x),x,2,2/3*a*(2*A*b+a*B)*x^(3/2)+2/5*b*(A*b+2*a*B)*x^(5/2)+2/7*b^2*B*x^(7/2)+2*a^2*A*sqrt(x)],
[(a+b*x)^2*(A+B*x)/x^(3/2),x,2,2/3*b*(A*b+2*a*B)*x^(3/2)+2/5*b^2*B*x^(5/2)-2*a^2*A/sqrt(x)+2*a*(2*A*b+a*B)*sqrt(x)],
[(a+b*x)^2*(A+B*x)/x^(5/2),x,2,-2/3*a^2*A/x^(3/2)+2/3*b^2*B*x^(3/2)-2*a*(2*A*b+a*B)/sqrt(x)+2*b*(A*b+2*a*B)*sqrt(x)],
[(a+b*x)^2*(A+B*x)/x^(7/2),x,2,-2/5*a^2*A/x^(5/2)-2/3*a*(2*A*b+a*B)/x^(3/2)-2*b*(A*b+2*a*B)/sqrt(x)+2*b^2*B*sqrt(x)],
[x^(7/2)*(a+b*x)^3*(A+B*x),x,2,2/9*a^3*A*x^(9/2)+2/11*a^2*(3*A*b+a*B)*x^(11/2)+6/13*a*b*(A*b+a*B)*x^(13/2)+2/15*b^2*(A*b+3*a*B)*x^(15/2)+2/17*b^3*B*x^(17/2)],
[x^(5/2)*(a+b*x)^3*(A+B*x),x,2,2/7*a^3*A*x^(7/2)+2/9*a^2*(3*A*b+a*B)*x^(9/2)+6/11*a*b*(A*b+a*B)*x^(11/2)+2/13*b^2*(A*b+3*a*B)*x^(13/2)+2/15*b^3*B*x^(15/2)],
[x^(3/2)*(a+b*x)^3*(A+B*x),x,2,2/5*a^3*A*x^(5/2)+2/7*a^2*(3*A*b+a*B)*x^(7/2)+2/3*a*b*(A*b+a*B)*x^(9/2)+2/11*b^2*(A*b+3*a*B)*x^(11/2)+2/13*b^3*B*x^(13/2)],
[(a+b*x)^3*(A+B*x)*sqrt(x),x,2,2/3*a^3*A*x^(3/2)+2/5*a^2*(3*A*b+a*B)*x^(5/2)+6/7*a*b*(A*b+a*B)*x^(7/2)+2/9*b^2*(A*b+3*a*B)*x^(9/2)+2/11*b^3*B*x^(11/2)],
[(a+b*x)^3*(A+B*x)/sqrt(x),x,2,2/3*a^2*(3*A*b+a*B)*x^(3/2)+6/5*a*b*(A*b+a*B)*x^(5/2)+2/7*b^2*(A*b+3*a*B)*x^(7/2)+2/9*b^3*B*x^(9/2)+2*a^3*A*sqrt(x)],
[(a+b*x)^3*(A+B*x)/x^(3/2),x,2,2*a*b*(A*b+a*B)*x^(3/2)+2/5*b^2*(A*b+3*a*B)*x^(5/2)+2/7*b^3*B*x^(7/2)-2*a^3*A/sqrt(x)+2*a^2*(3*A*b+a*B)*sqrt(x)],
[(a+b*x)^3*(A+B*x)/x^(5/2),x,2,-2/3*a^3*A/x^(3/2)+2/3*b^2*(A*b+3*a*B)*x^(3/2)+2/5*b^3*B*x^(5/2)-2*a^2*(3*A*b+a*B)/sqrt(x)+6*a*b*(A*b+a*B)*sqrt(x)],
[(a+b*x)^3*(A+B*x)/x^(7/2),x,2,-2/5*a^3*A/x^(5/2)-2/3*a^2*(3*A*b+a*B)/x^(3/2)+2/3*b^3*B*x^(3/2)-6*a*b*(A*b+a*B)/sqrt(x)+2*b^2*(A*b+3*a*B)*sqrt(x)],
[(2-3*x)^3*sqrt(x)/(1+x)^2,x,5,72*x^(3/2)-54/5*x^(5/2)+575*arctan(sqrt(x))-450*sqrt(x)-125*sqrt(x)/(1+x),575*arctan(sqrt(x))-3/5*(917-171*x)*sqrt(x)-21/5*(2-3*x)^2*sqrt(x)-(2-3*x)^3*sqrt(x)/(1+x)],

# p<0
[x^(7/2)*(A+B*x)/(a+b*x),x,7,2/3*a^2*(A*b-a*B)*x^(3/2)/b^4-2/5*a*(A*b-a*B)*x^(5/2)/b^3+2/7*(A*b-a*B)*x^(7/2)/b^2+2/9*B*x^(9/2)/b+2*a^(7/2)*(A*b-a*B)*arctan(sqrt(b)*sqrt(x)/sqrt(a))/b^(11/2)-2*a^3*(A*b-a*B)*sqrt(x)/b^5],
[x^(5/2)*(A+B*x)/(a+b*x),x,6,-2/3*a*(A*b-a*B)*x^(3/2)/b^3+2/5*(A*b-a*B)*x^(5/2)/b^2+2/7*B*x^(7/2)/b-2*a^(5/2)*(A*b-a*B)*arctan(sqrt(b)*sqrt(x)/sqrt(a))/b^(9/2)+2*a^2*(A*b-a*B)*sqrt(x)/b^4],
[x^(3/2)*(A+B*x)/(a+b*x),x,5,2/3*(A*b-a*B)*x^(3/2)/b^2+2/5*B*x^(5/2)/b+2*a^(3/2)*(A*b-a*B)*arctan(sqrt(b)*sqrt(x)/sqrt(a))/b^(7/2)-2*a*(A*b-a*B)*sqrt(x)/b^3],
[(A+B*x)*sqrt(x)/(a+b*x),x,4,2/3*B*x^(3/2)/b-2*(A*b-a*B)*arctan(sqrt(b)*sqrt(x)/sqrt(a))*sqrt(a)/b^(5/2)+2*(A*b-a*B)*sqrt(x)/b^2],
[(A+B*x)/((a+b*x)*sqrt(x)),x,3,2*(A*b-a*B)*arctan(sqrt(b)*sqrt(x)/sqrt(a))/(b^(3/2)*sqrt(a))+2*B*sqrt(x)/b],
[(A+B*x)/(x^(3/2)*(a+b*x)),x,3,-2*(A*b-a*B)*arctan(sqrt(b)*sqrt(x)/sqrt(a))/(a^(3/2)*sqrt(b))-2*A/(a*sqrt(x))],
[(A+B*x)/(x^(5/2)*(a+b*x)),x,4,-2/3*A/(a*x^(3/2))+2*(A*b-a*B)*arctan(sqrt(b)*sqrt(x)/sqrt(a))*sqrt(b)/a^(5/2)+2*(A*b-a*B)/(a^2*sqrt(x))],
[(A+B*x)/(x^(7/2)*(a+b*x)),x,5,-2/5*A/(a*x^(5/2))+2/3*(A*b-a*B)/(a^2*x^(3/2))-2*b^(3/2)*(A*b-a*B)*arctan(sqrt(b)*sqrt(x)/sqrt(a))/a^(7/2)-2*b*(A*b-a*B)/(a^3*sqrt(x))],
[(A+B*x)/(x^(9/2)*(a+b*x)),x,6,-2/7*A/(a*x^(7/2))+2/5*(A*b-a*B)/(a^2*x^(5/2))-2/3*b*(A*b-a*B)/(a^3*x^(3/2))+2*b^(5/2)*(A*b-a*B)*arctan(sqrt(b)*sqrt(x)/sqrt(a))/a^(9/2)+2*b^2*(A*b-a*B)/(a^4*sqrt(x))],
[(A+B*x)/(x^(11/2)*(a+b*x)),x,7,-2/9*A/(a*x^(9/2))+2/7*(A*b-a*B)/(a^2*x^(7/2))-2/5*b*(A*b-a*B)/(a^3*x^(5/2))+2/3*b^2*(A*b-a*B)/(a^4*x^(3/2))-2*b^(7/2)*(A*b-a*B)*arctan(sqrt(b)*sqrt(x)/sqrt(a))/a^(11/2)-2*b^3*(A*b-a*B)/(a^5*sqrt(x))],
[x^(7/2)*(A+B*x)/(a+b*x)^2,x,7,-1/3*a*(7*A*b-9*a*B)*x^(3/2)/b^4+1/5*(7*A*b-9*a*B)*x^(5/2)/b^3-1/7*(7*A*b-9*a*B)*x^(7/2)/(a*b^2)+(A*b-a*B)*x^(9/2)/(a*b*(a+b*x))-a^(5/2)*(7*A*b-9*a*B)*arctan(sqrt(b)*sqrt(x)/sqrt(a))/b^(11/2)+a^2*(7*A*b-9*a*B)*sqrt(x)/b^5],
[x^(5/2)*(A+B*x)/(a+b*x)^2,x,6,1/3*(5*A*b-7*a*B)*x^(3/2)/b^3-1/5*(5*A*b-7*a*B)*x^(5/2)/(a*b^2)+(A*b-a*B)*x^(7/2)/(a*b*(a+b*x))+a^(3/2)*(5*A*b-7*a*B)*arctan(sqrt(b)*sqrt(x)/sqrt(a))/b^(9/2)-a*(5*A*b-7*a*B)*sqrt(x)/b^4],
[x^(3/2)*(A+B*x)/(a+b*x)^2,x,5,-1/3*(3*A*b-5*a*B)*x^(3/2)/(a*b^2)+(A*b-a*B)*x^(5/2)/(a*b*(a+b*x))-(3*A*b-5*a*B)*arctan(sqrt(b)*sqrt(x)/sqrt(a))*sqrt(a)/b^(7/2)+(3*A*b-5*a*B)*sqrt(x)/b^3],
[(A+B*x)*sqrt(x)/(a+b*x)^2,x,4,(A*b-a*B)*x^(3/2)/(a*b*(a+b*x))+(A*b-3*a*B)*arctan(sqrt(b)*sqrt(x)/sqrt(a))/(b^(5/2)*sqrt(a))-(A*b-3*a*B)*sqrt(x)/(a*b^2)],
[(A+B*x)/((a+b*x)^2*sqrt(x)),x,3,(A*b+a*B)*arctan(sqrt(b)*sqrt(x)/sqrt(a))/(a^(3/2)*b^(3/2))+(A*b-a*B)*sqrt(x)/(a*b*(a+b*x))],
[(A+B*x)/(x^(3/2)*(a+b*x)^2),x,4,-(3*A*b-a*B)*arctan(sqrt(b)*sqrt(x)/sqrt(a))/(a^(5/2)*sqrt(b))+(-3*A*b+a*B)/(a^2*b*sqrt(x))+(A*b-a*B)/(a*b*(a+b*x)*sqrt(x))],
[(A+B*x)/(x^(5/2)*(a+b*x)^2),x,5,1/3*(-5*A*b+3*a*B)/(a^2*b*x^(3/2))+(A*b-a*B)/(a*b*x^(3/2)*(a+b*x))+(5*A*b-3*a*B)*arctan(sqrt(b)*sqrt(x)/sqrt(a))*sqrt(b)/a^(7/2)+(5*A*b-3*a*B)/(a^3*sqrt(x))],
[(A+B*x)/(x^(7/2)*(a+b*x)^2),x,6,1/5*(-7*A*b+5*a*B)/(a^2*b*x^(5/2))+1/3*(7*A*b-5*a*B)/(a^3*x^(3/2))+(A*b-a*B)/(a*b*x^(5/2)*(a+b*x))-b^(3/2)*(7*A*b-5*a*B)*arctan(sqrt(b)*sqrt(x)/sqrt(a))/a^(9/2)-b*(7*A*b-5*a*B)/(a^4*sqrt(x))],
[(A+B*x)/(x^(9/2)*(a+b*x)^2),x,7,1/7*(-9*A*b+7*a*B)/(a^2*b*x^(7/2))+1/5*(9*A*b-7*a*B)/(a^3*x^(5/2))-1/3*b*(9*A*b-7*a*B)/(a^4*x^(3/2))+(A*b-a*B)/(a*b*x^(7/2)*(a+b*x))+b^(5/2)*(9*A*b-7*a*B)*arctan(sqrt(b)*sqrt(x)/sqrt(a))/a^(11/2)+b^2*(9*A*b-7*a*B)/(a^5*sqrt(x))],
[x^(7/2)*(A+B*x)/(a+b*x)^3,x,7,7/12*(5*A*b-9*a*B)*x^(3/2)/b^4-7/20*(5*A*b-9*a*B)*x^(5/2)/(a*b^3)+1/2*(A*b-a*B)*x^(9/2)/(a*b*(a+b*x)^2)+1/4*(5*A*b-9*a*B)*x^(7/2)/(a*b^2*(a+b*x))+7/4*a^(3/2)*(5*A*b-9*a*B)*arctan(sqrt(b)*sqrt(x)/sqrt(a))/b^(11/2)-7/4*a*(5*A*b-9*a*B)*sqrt(x)/b^5],
[x^(5/2)*(A+B*x)/(a+b*x)^3,x,6,-5/12*(3*A*b-7*a*B)*x^(3/2)/(a*b^3)+1/2*(A*b-a*B)*x^(7/2)/(a*b*(a+b*x)^2)+1/4*(3*A*b-7*a*B)*x^(5/2)/(a*b^2*(a+b*x))-5/4*(3*A*b-7*a*B)*arctan(sqrt(b)*sqrt(x)/sqrt(a))*sqrt(a)/b^(9/2)+5/4*(3*A*b-7*a*B)*sqrt(x)/b^4],
[x^(3/2)*(A+B*x)/(a+b*x)^3,x,5,1/2*(A*b-a*B)*x^(5/2)/(a*b*(a+b*x)^2)+1/4*(A*b-5*a*B)*x^(3/2)/(a*b^2*(a+b*x))+3/4*(A*b-5*a*B)*arctan(sqrt(b)*sqrt(x)/sqrt(a))/(b^(7/2)*sqrt(a))-3/4*(A*b-5*a*B)*sqrt(x)/(a*b^3)],
[(A+B*x)*sqrt(x)/(a+b*x)^3,x,4,1/2*(A*b-a*B)*x^(3/2)/(a*b*(a+b*x)^2)+1/4*(A*b+3*a*B)*arctan(sqrt(b)*sqrt(x)/sqrt(a))/(a^(3/2)*b^(5/2))-1/4*(A*b+3*a*B)*sqrt(x)/(a*b^2*(a+b*x))],
[(A+B*x)/((a+b*x)^3*sqrt(x)),x,4,1/4*(3*A*b+a*B)*arctan(sqrt(b)*sqrt(x)/sqrt(a))/(a^(5/2)*b^(3/2))+1/2*(A*b-a*B)*sqrt(x)/(a*b*(a+b*x)^2)+1/4*(3*A*b+a*B)*sqrt(x)/(a^2*b*(a+b*x))],
[(A+B*x)/(x^(3/2)*(a+b*x)^3),x,5,-3/4*(5*A*b-a*B)*arctan(sqrt(b)*sqrt(x)/sqrt(a))/(a^(7/2)*sqrt(b))-3/4*(5*A*b-a*B)/(a^3*b*sqrt(x))+1/2*(A*b-a*B)/(a*b*(a+b*x)^2*sqrt(x))+1/4*(5*A*b-a*B)/(a^2*b*(a+b*x)*sqrt(x))],
[(A+B*x)/(x^(5/2)*(a+b*x)^3),x,6,-5/12*(7*A*b-3*a*B)/(a^3*b*x^(3/2))+1/2*(A*b-a*B)/(a*b*x^(3/2)*(a+b*x)^2)+1/4*(7*A*b-3*a*B)/(a^2*b*x^(3/2)*(a+b*x))+5/4*(7*A*b-3*a*B)*arctan(sqrt(b)*sqrt(x)/sqrt(a))*sqrt(b)/a^(9/2)+5/4*(7*A*b-3*a*B)/(a^4*sqrt(x))],
[(A+B*x)/(x^(7/2)*(a+b*x)^3),x,7,-7/20*(9*A*b-5*a*B)/(a^3*b*x^(5/2))+7/12*(9*A*b-5*a*B)/(a^4*x^(3/2))+1/2*(A*b-a*B)/(a*b*x^(5/2)*(a+b*x)^2)+1/4*(9*A*b-5*a*B)/(a^2*b*x^(5/2)*(a+b*x))-7/4*b^(3/2)*(9*A*b-5*a*B)*arctan(sqrt(b)*sqrt(x)/sqrt(a))/a^(11/2)-7/4*b*(9*A*b-5*a*B)/(a^5*sqrt(x))],

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

# p>0
[x^m*(a+b*x)^4*(A+B*x),x,2,a^4*A*x^(1+m)/(1+m)+a^3*(4*A*b+a*B)*x^(2+m)/(2+m)+2*a^2*b*(3*A*b+2*a*B)*x^(3+m)/(3+m)+2*a*b^2*(2*A*b+3*a*B)*x^(4+m)/(4+m)+b^3*(A*b+4*a*B)*x^(5+m)/(5+m)+b^4*B*x^(6+m)/(6+m)],
[x^m*(a+b*x)^3*(A+B*x),x,2,a^3*A*x^(1+m)/(1+m)+a^2*(3*A*b+a*B)*x^(2+m)/(2+m)+3*a*b*(A*b+a*B)*x^(3+m)/(3+m)+b^2*(A*b+3*a*B)*x^(4+m)/(4+m)+b^3*B*x^(5+m)/(5+m)],
[x^m*(a+b*x)^2*(A+B*x),x,2,a^2*A*x^(1+m)/(1+m)+a*(2*A*b+a*B)*x^(2+m)/(2+m)+b*(A*b+2*a*B)*x^(3+m)/(3+m)+b^2*B*x^(4+m)/(4+m)],
[x^m*(a+b*x)*(A+B*x),x,2,a*A*x^(1+m)/(1+m)+(A*b+a*B)*x^(2+m)/(2+m)+b*B*x^(3+m)/(3+m)],
[x^m*(A+B*x)/(a+b*x),x,2,B*x^(1+m)/(b*(1+m))+(A*b-a*B)*x^(1+m)*hypergeom([1,1+m],[2+m],-b*x/a)/(a*b*(1+m))],
[x^m*(A+B*x)/(a+b*x)^2,x,2,(A*b-a*B)*x^(1+m)/(a*b*(a+b*x))-(A*b*m-a*B*(1+m))*x^(1+m)*hypergeom([1,1+m],[2+m],-b*x/a)/(a^2*b*(1+m))],
[x^m*(A+B*x)/(a+b*x)^3,x,2,1/2*(A*b-a*B)*x^(1+m)/(a*b*(a+b*x)^2)+1/2*(A*b*(1-m)+a*B*(1+m))*x^(1+m)*hypergeom([2,1+m],[2+m],-b*x/a)/(a^3*b*(1+m))],
[x^m*(a+b*x)^2*(c+d*x)^5,x,2,a^2*c^5*x^(1+m)/(1+m)+a*c^4*(2*b*c+5*a*d)*x^(2+m)/(2+m)+c^3*(b^2*c^2+10*a*b*c*d+10*a^2*d^2)*x^(3+m)/(3+m)+5*c^2*d*(b^2*c^2+4*a*b*c*d+2*a^2*d^2)*x^(4+m)/(4+m)+5*c*d^2*(2*b^2*c^2+4*a*b*c*d+a^2*d^2)*x^(5+m)/(5+m)+d^3*(10*b^2*c^2+10*a*b*c*d+a^2*d^2)*x^(6+m)/(6+m)+b*d^4*(5*b*c+2*a*d)*x^(7+m)/(7+m)+b^2*d^5*x^(8+m)/(8+m)],

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

#  Following integrands are equal: 
[b^2*x^m/(b+a*x^2)^2,x,2,x^(1+m)*hypergeom([2,1/2*(1+m)],[1/2*(3+m)],-a*x^2/b)/(1+m)],
[x^m/((1-x*sqrt(a)/sqrt(-b))^2*(1+x*sqrt(a)/sqrt(-b))^2),x,2,x^(1+m)*hypergeom([2,1/2*(1+m)],[1/2*(3+m)],-a*x^2/b)/(1+m)],

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

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

# p>0
[x^4*(A+B*x)*sqrt(a+b*x),x,2,2/3*a^4*(A*b-a*B)*(a+b*x)^(3/2)/b^6-2/5*a^3*(4*A*b-5*a*B)*(a+b*x)^(5/2)/b^6+4/7*a^2*(3*A*b-5*a*B)*(a+b*x)^(7/2)/b^6-4/9*a*(2*A*b-5*a*B)*(a+b*x)^(9/2)/b^6+2/11*(A*b-5*a*B)*(a+b*x)^(11/2)/b^6+2/13*B*(a+b*x)^(13/2)/b^6],
[x^3*(A+B*x)*sqrt(a+b*x),x,2,-2/3*a^3*(A*b-a*B)*(a+b*x)^(3/2)/b^5+2/5*a^2*(3*A*b-4*a*B)*(a+b*x)^(5/2)/b^5-6/7*a*(A*b-2*a*B)*(a+b*x)^(7/2)/b^5+2/9*(A*b-4*a*B)*(a+b*x)^(9/2)/b^5+2/11*B*(a+b*x)^(11/2)/b^5],
[x^2*(A+B*x)*sqrt(a+b*x),x,2,2/3*a^2*(A*b-a*B)*(a+b*x)^(3/2)/b^4-2/5*a*(2*A*b-3*a*B)*(a+b*x)^(5/2)/b^4+2/7*(A*b-3*a*B)*(a+b*x)^(7/2)/b^4+2/9*B*(a+b*x)^(9/2)/b^4],
[x*(A+B*x)*sqrt(a+b*x),x,2,-2/3*a*(A*b-a*B)*(a+b*x)^(3/2)/b^3+2/5*(A*b-2*a*B)*(a+b*x)^(5/2)/b^3+2/7*B*(a+b*x)^(7/2)/b^3],
[(A+B*x)*sqrt(a+b*x),x,2,2/3*(A*b-a*B)*(a+b*x)^(3/2)/b^2+2/5*B*(a+b*x)^(5/2)/b^2],
[(A+B*x)*sqrt(a+b*x)/x,x,4,2/3*B*(a+b*x)^(3/2)/b-2*A*arctanh(sqrt(a+b*x)/sqrt(a))*sqrt(a)+2*A*sqrt(a+b*x)],
[(A+B*x)*sqrt(a+b*x)/x^2,x,4,-A*(a+b*x)^(3/2)/(a*x)-(A*b+2*a*B)*arctanh(sqrt(a+b*x)/sqrt(a))/sqrt(a)+(A*b+2*a*B)*sqrt(a+b*x)/a],
[(A+B*x)*sqrt(a+b*x)/x^3,x,4,-1/2*A*(a+b*x)^(3/2)/(a*x^2)+1/4*b*(A*b-4*a*B)*arctanh(sqrt(a+b*x)/sqrt(a))/a^(3/2)+1/4*(A*b-4*a*B)*sqrt(a+b*x)/(a*x)],
[(A+B*x)*sqrt(a+b*x)/x^4,x,5,-1/3*A*(a+b*x)^(3/2)/(a*x^3)-1/8*b^2*(A*b-2*a*B)*arctanh(sqrt(a+b*x)/sqrt(a))/a^(5/2)+1/4*(A*b-2*a*B)*sqrt(a+b*x)/(a*x^2)+1/8*b*(A*b-2*a*B)*sqrt(a+b*x)/(a^2*x)],
[(A+B*x)*sqrt(a+b*x)/x^5,x,6,-1/4*A*(a+b*x)^(3/2)/(a*x^4)+1/64*b^3*(5*A*b-8*a*B)*arctanh(sqrt(a+b*x)/sqrt(a))/a^(7/2)+1/24*(5*A*b-8*a*B)*sqrt(a+b*x)/(a*x^3)+1/96*b*(5*A*b-8*a*B)*sqrt(a+b*x)/(a^2*x^2)-1/64*b^2*(5*A*b-8*a*B)*sqrt(a+b*x)/(a^3*x)],
[(A+B*x)*sqrt(a+b*x)/x^6,x,7,-1/5*A*(a+b*x)^(3/2)/(a*x^5)-1/128*b^4*(7*A*b-10*a*B)*arctanh(sqrt(a+b*x)/sqrt(a))/a^(9/2)+1/40*(7*A*b-10*a*B)*sqrt(a+b*x)/(a*x^4)+1/240*b*(7*A*b-10*a*B)*sqrt(a+b*x)/(a^2*x^3)-1/192*b^2*(7*A*b-10*a*B)*sqrt(a+b*x)/(a^3*x^2)+1/128*b^3*(7*A*b-10*a*B)*sqrt(a+b*x)/(a^4*x)],
[x^4*(a+b*x)^(3/2)*(A+B*x),x,2,2/5*a^4*(A*b-a*B)*(a+b*x)^(5/2)/b^6-2/7*a^3*(4*A*b-5*a*B)*(a+b*x)^(7/2)/b^6+4/9*a^2*(3*A*b-5*a*B)*(a+b*x)^(9/2)/b^6-4/11*a*(2*A*b-5*a*B)*(a+b*x)^(11/2)/b^6+2/13*(A*b-5*a*B)*(a+b*x)^(13/2)/b^6+2/15*B*(a+b*x)^(15/2)/b^6],
[x^3*(a+b*x)^(3/2)*(A+B*x),x,2,-2/5*a^3*(A*b-a*B)*(a+b*x)^(5/2)/b^5+2/7*a^2*(3*A*b-4*a*B)*(a+b*x)^(7/2)/b^5-2/3*a*(A*b-2*a*B)*(a+b*x)^(9/2)/b^5+2/11*(A*b-4*a*B)*(a+b*x)^(11/2)/b^5+2/13*B*(a+b*x)^(13/2)/b^5],
[x^2*(a+b*x)^(3/2)*(A+B*x),x,2,2/5*a^2*(A*b-a*B)*(a+b*x)^(5/2)/b^4-2/7*a*(2*A*b-3*a*B)*(a+b*x)^(7/2)/b^4+2/9*(A*b-3*a*B)*(a+b*x)^(9/2)/b^4+2/11*B*(a+b*x)^(11/2)/b^4],
[x*(a+b*x)^(3/2)*(A+B*x),x,2,-2/5*a*(A*b-a*B)*(a+b*x)^(5/2)/b^3+2/7*(A*b-2*a*B)*(a+b*x)^(7/2)/b^3+2/9*B*(a+b*x)^(9/2)/b^3],
[(a+b*x)^(3/2)*(A+B*x),x,2,2/5*(A*b-a*B)*(a+b*x)^(5/2)/b^2+2/7*B*(a+b*x)^(7/2)/b^2],
[(a+b*x)^(3/2)*(A+B*x)/x,x,5,2/3*A*(a+b*x)^(3/2)+2/5*B*(a+b*x)^(5/2)/b-2*a^(3/2)*A*arctanh(sqrt(a+b*x)/sqrt(a))+2*a*A*sqrt(a+b*x)],
[(a+b*x)^(3/2)*(A+B*x)/x^2,x,5,1/3*(3*A*b+2*a*B)*(a+b*x)^(3/2)/a-A*(a+b*x)^(5/2)/(a*x)-(3*A*b+2*a*B)*arctanh(sqrt(a+b*x)/sqrt(a))*sqrt(a)+(3*A*b+2*a*B)*sqrt(a+b*x)],
[(a+b*x)^(3/2)*(A+B*x)/x^3,x,5,-1/4*(A*b+4*a*B)*(a+b*x)^(3/2)/(a*x)-1/2*A*(a+b*x)^(5/2)/(a*x^2)-3/4*b*(A*b+4*a*B)*arctanh(sqrt(a+b*x)/sqrt(a))/sqrt(a)+3/4*b*(A*b+4*a*B)*sqrt(a+b*x)/a],
[(a+b*x)^(3/2)*(A+B*x)/x^4,x,5,1/12*(A*b-6*a*B)*(a+b*x)^(3/2)/(a*x^2)-1/3*A*(a+b*x)^(5/2)/(a*x^3)+1/8*b^2*(A*b-6*a*B)*arctanh(sqrt(a+b*x)/sqrt(a))/a^(3/2)+1/8*b*(A*b-6*a*B)*sqrt(a+b*x)/(a*x)],
[(a+b*x)^(3/2)*(A+B*x)/x^5,x,6,1/24*(3*A*b-8*a*B)*(a+b*x)^(3/2)/(a*x^3)-1/4*A*(a+b*x)^(5/2)/(a*x^4)-1/64*b^3*(3*A*b-8*a*B)*arctanh(sqrt(a+b*x)/sqrt(a))/a^(5/2)+1/32*b*(3*A*b-8*a*B)*sqrt(a+b*x)/(a*x^2)+1/64*b^2*(3*A*b-8*a*B)*sqrt(a+b*x)/(a^2*x)],
[(a+b*x)^(3/2)*(A+B*x)/x^6,x,7,1/8*(A*b-2*a*B)*(a+b*x)^(3/2)/(a*x^4)-1/5*A*(a+b*x)^(5/2)/(a*x^5)+3/128*b^4*(A*b-2*a*B)*arctanh(sqrt(a+b*x)/sqrt(a))/a^(7/2)+1/16*b*(A*b-2*a*B)*sqrt(a+b*x)/(a*x^3)+1/64*b^2*(A*b-2*a*B)*sqrt(a+b*x)/(a^2*x^2)-3/128*b^3*(A*b-2*a*B)*sqrt(a+b*x)/(a^3*x)],
[(a+b*x)^(3/2)*(A+B*x)/x^7,x,8,1/60*(7*A*b-12*a*B)*(a+b*x)^(3/2)/(a*x^5)-1/6*A*(a+b*x)^(5/2)/(a*x^6)-1/512*b^5*(7*A*b-12*a*B)*arctanh(sqrt(a+b*x)/sqrt(a))/a^(9/2)+1/160*b*(7*A*b-12*a*B)*sqrt(a+b*x)/(a*x^4)+1/960*b^2*(7*A*b-12*a*B)*sqrt(a+b*x)/(a^2*x^3)-1/768*b^3*(7*A*b-12*a*B)*sqrt(a+b*x)/(a^3*x^2)+1/512*b^4*(7*A*b-12*a*B)*sqrt(a+b*x)/(a^4*x)],
[x^4*(a+b*x)^(5/2)*(A+B*x),x,2,2/7*a^4*(A*b-a*B)*(a+b*x)^(7/2)/b^6-2/9*a^3*(4*A*b-5*a*B)*(a+b*x)^(9/2)/b^6+4/11*a^2*(3*A*b-5*a*B)*(a+b*x)^(11/2)/b^6-4/13*a*(2*A*b-5*a*B)*(a+b*x)^(13/2)/b^6+2/15*(A*b-5*a*B)*(a+b*x)^(15/2)/b^6+2/17*B*(a+b*x)^(17/2)/b^6],
[x^3*(a+b*x)^(5/2)*(A+B*x),x,2,-2/7*a^3*(A*b-a*B)*(a+b*x)^(7/2)/b^5+2/9*a^2*(3*A*b-4*a*B)*(a+b*x)^(9/2)/b^5-6/11*a*(A*b-2*a*B)*(a+b*x)^(11/2)/b^5+2/13*(A*b-4*a*B)*(a+b*x)^(13/2)/b^5+2/15*B*(a+b*x)^(15/2)/b^5],
[x^2*(a+b*x)^(5/2)*(A+B*x),x,2,2/7*a^2*(A*b-a*B)*(a+b*x)^(7/2)/b^4-2/9*a*(2*A*b-3*a*B)*(a+b*x)^(9/2)/b^4+2/11*(A*b-3*a*B)*(a+b*x)^(11/2)/b^4+2/13*B*(a+b*x)^(13/2)/b^4],
[x*(a+b*x)^(5/2)*(A+B*x),x,2,-2/7*a*(A*b-a*B)*(a+b*x)^(7/2)/b^3+2/9*(A*b-2*a*B)*(a+b*x)^(9/2)/b^3+2/11*B*(a+b*x)^(11/2)/b^3],
[(a+b*x)^(5/2)*(A+B*x),x,2,2/7*(A*b-a*B)*(a+b*x)^(7/2)/b^2+2/9*B*(a+b*x)^(9/2)/b^2],
[(a+b*x)^(5/2)*(A+B*x)/x,x,6,2/3*a*A*(a+b*x)^(3/2)+2/5*A*(a+b*x)^(5/2)+2/7*B*(a+b*x)^(7/2)/b-2*a^(5/2)*A*arctanh(sqrt(a+b*x)/sqrt(a))+2*a^2*A*sqrt(a+b*x)],
[(a+b*x)^(5/2)*(A+B*x)/x^2,x,6,1/3*(5*A*b+2*a*B)*(a+b*x)^(3/2)+1/5*(5*A*b+2*a*B)*(a+b*x)^(5/2)/a-A*(a+b*x)^(7/2)/(a*x)-a^(3/2)*(5*A*b+2*a*B)*arctanh(sqrt(a+b*x)/sqrt(a))+a*(5*A*b+2*a*B)*sqrt(a+b*x)],
[(a+b*x)^(5/2)*(A+B*x)/x^3,x,6,5/12*b*(3*A*b+4*a*B)*(a+b*x)^(3/2)/a-1/4*(3*A*b+4*a*B)*(a+b*x)^(5/2)/(a*x)-1/2*A*(a+b*x)^(7/2)/(a*x^2)-5/4*b*(3*A*b+4*a*B)*arctanh(sqrt(a+b*x)/sqrt(a))*sqrt(a)+5/4*b*(3*A*b+4*a*B)*sqrt(a+b*x)],
[(a+b*x)^(5/2)*(A+B*x)/x^4,x,6,-5/24*b*(A*b+6*a*B)*(a+b*x)^(3/2)/(a*x)-1/12*(A*b+6*a*B)*(a+b*x)^(5/2)/(a*x^2)-1/3*A*(a+b*x)^(7/2)/(a*x^3)-5/8*b^2*(A*b+6*a*B)*arctanh(sqrt(a+b*x)/sqrt(a))/sqrt(a)+5/8*b^2*(A*b+6*a*B)*sqrt(a+b*x)/a],
[(a+b*x)^(5/2)*(A+B*x)/x^5,x,6,5/96*b*(A*b-8*a*B)*(a+b*x)^(3/2)/(a*x^2)+1/24*(A*b-8*a*B)*(a+b*x)^(5/2)/(a*x^3)-1/4*A*(a+b*x)^(7/2)/(a*x^4)+5/64*b^3*(A*b-8*a*B)*arctanh(sqrt(a+b*x)/sqrt(a))/a^(3/2)+5/64*b^2*(A*b-8*a*B)*sqrt(a+b*x)/(a*x)],
[(a+b*x)^(5/2)*(A+B*x)/x^6,x,7,1/48*b*(3*A*b-10*a*B)*(a+b*x)^(3/2)/(a*x^3)+1/40*(3*A*b-10*a*B)*(a+b*x)^(5/2)/(a*x^4)-1/5*A*(a+b*x)^(7/2)/(a*x^5)-1/128*b^4*(3*A*b-10*a*B)*arctanh(sqrt(a+b*x)/sqrt(a))/a^(5/2)+1/64*b^2*(3*A*b-10*a*B)*sqrt(a+b*x)/(a*x^2)+1/128*b^3*(3*A*b-10*a*B)*sqrt(a+b*x)/(a^2*x)],
[(a+b*x)^(5/2)*(A+B*x)/x^7,x,8,1/96*b*(5*A*b-12*a*B)*(a+b*x)^(3/2)/(a*x^4)+1/60*(5*A*b-12*a*B)*(a+b*x)^(5/2)/(a*x^5)-1/6*A*(a+b*x)^(7/2)/(a*x^6)+1/512*b^5*(5*A*b-12*a*B)*arctanh(sqrt(a+b*x)/sqrt(a))/a^(7/2)+1/192*b^2*(5*A*b-12*a*B)*sqrt(a+b*x)/(a*x^3)+1/768*b^3*(5*A*b-12*a*B)*sqrt(a+b*x)/(a^2*x^2)-1/512*b^4*(5*A*b-12*a*B)*sqrt(a+b*x)/(a^3*x)],
[(a+b*x)^(5/2)*(A+B*x)/x^8,x,9,1/24*b*(A*b-2*a*B)*(a+b*x)^(3/2)/(a*x^5)+1/12*(A*b-2*a*B)*(a+b*x)^(5/2)/(a*x^6)-1/7*A*(a+b*x)^(7/2)/(a*x^7)-5/1024*b^6*(A*b-2*a*B)*arctanh(sqrt(a+b*x)/sqrt(a))/a^(9/2)+1/64*b^2*(A*b-2*a*B)*sqrt(a+b*x)/(a*x^4)+1/384*b^3*(A*b-2*a*B)*sqrt(a+b*x)/(a^2*x^3)-5/1536*b^4*(A*b-2*a*B)*sqrt(a+b*x)/(a^3*x^2)+5/1024*b^5*(A*b-2*a*B)*sqrt(a+b*x)/(a^4*x)],

# p<0
[x^4*(A+B*x)/sqrt(a+b*x),x,2,-2/3*a^3*(4*A*b-5*a*B)*(a+b*x)^(3/2)/b^6+4/5*a^2*(3*A*b-5*a*B)*(a+b*x)^(5/2)/b^6-4/7*a*(2*A*b-5*a*B)*(a+b*x)^(7/2)/b^6+2/9*(A*b-5*a*B)*(a+b*x)^(9/2)/b^6+2/11*B*(a+b*x)^(11/2)/b^6+2*a^4*(A*b-a*B)*sqrt(a+b*x)/b^6],
[x^3*(A+B*x)/sqrt(a+b*x),x,2,2/3*a^2*(3*A*b-4*a*B)*(a+b*x)^(3/2)/b^5-6/5*a*(A*b-2*a*B)*(a+b*x)^(5/2)/b^5+2/7*(A*b-4*a*B)*(a+b*x)^(7/2)/b^5+2/9*B*(a+b*x)^(9/2)/b^5-2*a^3*(A*b-a*B)*sqrt(a+b*x)/b^5],
[x^2*(A+B*x)/sqrt(a+b*x),x,2,-2/3*a*(2*A*b-3*a*B)*(a+b*x)^(3/2)/b^4+2/5*(A*b-3*a*B)*(a+b*x)^(5/2)/b^4+2/7*B*(a+b*x)^(7/2)/b^4+2*a^2*(A*b-a*B)*sqrt(a+b*x)/b^4],
[x*(A+B*x)/sqrt(a+b*x),x,2,2/3*(A*b-2*a*B)*(a+b*x)^(3/2)/b^3+2/5*B*(a+b*x)^(5/2)/b^3-2*a*(A*b-a*B)*sqrt(a+b*x)/b^3],
[(A+B*x)/sqrt(a+b*x),x,2,2/3*B*(a+b*x)^(3/2)/b^2+2*(A*b-a*B)*sqrt(a+b*x)/b^2],
[(A+B*x)/(x*sqrt(a+b*x)),x,3,-2*A*arctanh(sqrt(a+b*x)/sqrt(a))/sqrt(a)+2*B*sqrt(a+b*x)/b],
[(A+B*x)/(x^2*sqrt(a+b*x)),x,3,(A*b-2*a*B)*arctanh(sqrt(a+b*x)/sqrt(a))/a^(3/2)-A*sqrt(a+b*x)/(a*x)],
[(A+B*x)/(x^3*sqrt(a+b*x)),x,4,-1/4*b*(3*A*b-4*a*B)*arctanh(sqrt(a+b*x)/sqrt(a))/a^(5/2)-1/2*A*sqrt(a+b*x)/(a*x^2)+1/4*(3*A*b-4*a*B)*sqrt(a+b*x)/(a^2*x)],
[(A+B*x)/(x^4*sqrt(a+b*x)),x,5,1/8*b^2*(5*A*b-6*a*B)*arctanh(sqrt(a+b*x)/sqrt(a))/a^(7/2)-1/3*A*sqrt(a+b*x)/(a*x^3)+1/12*(5*A*b-6*a*B)*sqrt(a+b*x)/(a^2*x^2)-1/8*b*(5*A*b-6*a*B)*sqrt(a+b*x)/(a^3*x)],
[(A+B*x)/(x^5*sqrt(a+b*x)),x,6,-5/64*b^3*(7*A*b-8*a*B)*arctanh(sqrt(a+b*x)/sqrt(a))/a^(9/2)-1/4*A*sqrt(a+b*x)/(a*x^4)+1/24*(7*A*b-8*a*B)*sqrt(a+b*x)/(a^2*x^3)-5/96*b*(7*A*b-8*a*B)*sqrt(a+b*x)/(a^3*x^2)+5/64*b^2*(7*A*b-8*a*B)*sqrt(a+b*x)/(a^4*x)],
[(A+B*x)/(x^6*sqrt(a+b*x)),x,7,7/128*b^4*(9*A*b-10*a*B)*arctanh(sqrt(a+b*x)/sqrt(a))/a^(11/2)-1/5*A*sqrt(a+b*x)/(a*x^5)+1/40*(9*A*b-10*a*B)*sqrt(a+b*x)/(a^2*x^4)-7/240*b*(9*A*b-10*a*B)*sqrt(a+b*x)/(a^3*x^3)+7/192*b^2*(9*A*b-10*a*B)*sqrt(a+b*x)/(a^4*x^2)-7/128*b^3*(9*A*b-10*a*B)*sqrt(a+b*x)/(a^5*x)],
[x^4*(A+B*x)/(a+b*x)^(3/2),x,2,4/3*a^2*(3*A*b-5*a*B)*(a+b*x)^(3/2)/b^6-4/5*a*(2*A*b-5*a*B)*(a+b*x)^(5/2)/b^6+2/7*(A*b-5*a*B)*(a+b*x)^(7/2)/b^6+2/9*B*(a+b*x)^(9/2)/b^6-2*a^4*(A*b-a*B)/(b^6*sqrt(a+b*x))-2*a^3*(4*A*b-5*a*B)*sqrt(a+b*x)/b^6],
[x^3*(A+B*x)/(a+b*x)^(3/2),x,2,-2*a*(A*b-2*a*B)*(a+b*x)^(3/2)/b^5+2/5*(A*b-4*a*B)*(a+b*x)^(5/2)/b^5+2/7*B*(a+b*x)^(7/2)/b^5+2*a^3*(A*b-a*B)/(b^5*sqrt(a+b*x))+2*a^2*(3*A*b-4*a*B)*sqrt(a+b*x)/b^5],
[x^2*(A+B*x)/(a+b*x)^(3/2),x,2,2/3*(A*b-3*a*B)*(a+b*x)^(3/2)/b^4+2/5*B*(a+b*x)^(5/2)/b^4-2*a^2*(A*b-a*B)/(b^4*sqrt(a+b*x))-2*a*(2*A*b-3*a*B)*sqrt(a+b*x)/b^4],
[x*(A+B*x)/(a+b*x)^(3/2),x,2,2/3*B*(a+b*x)^(3/2)/b^3+2*a*(A*b-a*B)/(b^3*sqrt(a+b*x))+2*(A*b-2*a*B)*sqrt(a+b*x)/b^3],
[(A+B*x)/(a+b*x)^(3/2),x,2,-2*(A*b-a*B)/(b^2*sqrt(a+b*x))+2*B*sqrt(a+b*x)/b^2],
[(A+B*x)/(x*(a+b*x)^(3/2)),x,3,-2*A*arctanh(sqrt(a+b*x)/sqrt(a))/a^(3/2)+2*(A*b-a*B)/(a*b*sqrt(a+b*x))],
[(A+B*x)/(x^2*(a+b*x)^(3/2)),x,4,(3*A*b-2*a*B)*arctanh(sqrt(a+b*x)/sqrt(a))/a^(5/2)+(-3*A*b+2*a*B)/(a^2*sqrt(a+b*x))-A/(a*x*sqrt(a+b*x))],
[(A+B*x)/(x^3*(a+b*x)^(3/2)),x,5,-3/4*b*(5*A*b-4*a*B)*arctanh(sqrt(a+b*x)/sqrt(a))/a^(7/2)+3/4*b*(5*A*b-4*a*B)/(a^3*sqrt(a+b*x))-1/2*A/(a*x^2*sqrt(a+b*x))+1/4*(5*A*b-4*a*B)/(a^2*x*sqrt(a+b*x))],
[(A+B*x)/(x^4*(a+b*x)^(3/2)),x,6,5/8*b^2*(7*A*b-6*a*B)*arctanh(sqrt(a+b*x)/sqrt(a))/a^(9/2)-5/8*b^2*(7*A*b-6*a*B)/(a^4*sqrt(a+b*x))-1/3*A/(a*x^3*sqrt(a+b*x))+1/12*(7*A*b-6*a*B)/(a^2*x^2*sqrt(a+b*x))-5/24*b*(7*A*b-6*a*B)/(a^3*x*sqrt(a+b*x))],
[(A+B*x)/(x^5*(a+b*x)^(3/2)),x,7,-35/64*b^3*(9*A*b-8*a*B)*arctanh(sqrt(a+b*x)/sqrt(a))/a^(11/2)+35/64*b^3*(9*A*b-8*a*B)/(a^5*sqrt(a+b*x))-1/4*A/(a*x^4*sqrt(a+b*x))+1/24*(9*A*b-8*a*B)/(a^2*x^3*sqrt(a+b*x))-7/96*b*(9*A*b-8*a*B)/(a^3*x^2*sqrt(a+b*x))+35/192*b^2*(9*A*b-8*a*B)/(a^4*x*sqrt(a+b*x))],
[x^4*(A+B*x)/(a+b*x)^(5/2),x,2,-2/3*a^4*(A*b-a*B)/(b^6*(a+b*x)^(3/2))-4/3*a*(2*A*b-5*a*B)*(a+b*x)^(3/2)/b^6+2/5*(A*b-5*a*B)*(a+b*x)^(5/2)/b^6+2/7*B*(a+b*x)^(7/2)/b^6+2*a^3*(4*A*b-5*a*B)/(b^6*sqrt(a+b*x))+4*a^2*(3*A*b-5*a*B)*sqrt(a+b*x)/b^6],
[x^3*(A+B*x)/(a+b*x)^(5/2),x,2,2/3*a^3*(A*b-a*B)/(b^5*(a+b*x)^(3/2))+2/3*(A*b-4*a*B)*(a+b*x)^(3/2)/b^5+2/5*B*(a+b*x)^(5/2)/b^5-2*a^2*(3*A*b-4*a*B)/(b^5*sqrt(a+b*x))-6*a*(A*b-2*a*B)*sqrt(a+b*x)/b^5],
[x^2*(A+B*x)/(a+b*x)^(5/2),x,2,-2/3*a^2*(A*b-a*B)/(b^4*(a+b*x)^(3/2))+2/3*B*(a+b*x)^(3/2)/b^4+2*a*(2*A*b-3*a*B)/(b^4*sqrt(a+b*x))+2*(A*b-3*a*B)*sqrt(a+b*x)/b^4],
[x*(A+B*x)/(a+b*x)^(5/2),x,2,2/3*a*(A*b-a*B)/(b^3*(a+b*x)^(3/2))-2*(A*b-2*a*B)/(b^3*sqrt(a+b*x))+2*B*sqrt(a+b*x)/b^3],
[(A+B*x)/(a+b*x)^(5/2),x,2,-2/3*(A*b-a*B)/(b^2*(a+b*x)^(3/2))-2*B/(b^2*sqrt(a+b*x))],
[(A+B*x)/(x*(a+b*x)^(5/2)),x,4,2/3*(A*b-a*B)/(a*b*(a+b*x)^(3/2))-2*A*arctanh(sqrt(a+b*x)/sqrt(a))/a^(5/2)+2*A/(a^2*sqrt(a+b*x))],
[(A+B*x)/(x^2*(a+b*x)^(5/2)),x,5,1/3*(-5*A*b+2*a*B)/(a^2*(a+b*x)^(3/2))-A/(a*x*(a+b*x)^(3/2))+(5*A*b-2*a*B)*arctanh(sqrt(a+b*x)/sqrt(a))/a^(7/2)+(-5*A*b+2*a*B)/(a^3*sqrt(a+b*x))],
[(A+B*x)/(x^3*(a+b*x)^(5/2)),x,6,5/12*b*(7*A*b-4*a*B)/(a^3*(a+b*x)^(3/2))-1/2*A/(a*x^2*(a+b*x)^(3/2))+1/4*(7*A*b-4*a*B)/(a^2*x*(a+b*x)^(3/2))-5/4*b*(7*A*b-4*a*B)*arctanh(sqrt(a+b*x)/sqrt(a))/a^(9/2)+5/4*b*(7*A*b-4*a*B)/(a^4*sqrt(a+b*x))],
[(A+B*x)/(x^4*(a+b*x)^(5/2)),x,7,-35/24*b^2*(3*A*b-2*a*B)/(a^4*(a+b*x)^(3/2))-1/3*A/(a*x^3*(a+b*x)^(3/2))+1/4*(3*A*b-2*a*B)/(a^2*x^2*(a+b*x)^(3/2))-7/8*b*(3*A*b-2*a*B)/(a^3*x*(a+b*x)^(3/2))+35/8*b^2*(3*A*b-2*a*B)*arctanh(sqrt(a+b*x)/sqrt(a))/a^(11/2)-35/8*b^2*(3*A*b-2*a*B)/(a^5*sqrt(a+b*x))],
[(A+B*x)/(x^5*(a+b*x)^(5/2)),x,8,35/64*b^3*(11*A*b-8*a*B)/(a^5*(a+b*x)^(3/2))-1/4*A/(a*x^4*(a+b*x)^(3/2))+1/24*(11*A*b-8*a*B)/(a^2*x^3*(a+b*x)^(3/2))-3/32*b*(11*A*b-8*a*B)/(a^3*x^2*(a+b*x)^(3/2))+21/64*b^2*(11*A*b-8*a*B)/(a^4*x*(a+b*x)^(3/2))-105/64*b^3*(11*A*b-8*a*B)*arctanh(sqrt(a+b*x)/sqrt(a))/a^(13/2)+105/64*b^3*(11*A*b-8*a*B)/(a^6*sqrt(a+b*x))],

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

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

# p>0
[x^3*(c+d*x)^(5/2)/(a+b*x),x,7,-2/3*a^3*(b*c-a*d)*(c+d*x)^(3/2)/b^5-2/5*a^3*(c+d*x)^(5/2)/b^4+2/7*(b^2*c^2+a*b*c*d+a^2*d^2)*(c+d*x)^(7/2)/(b^3*d^3)-2/9*(2*b*c+a*d)*(c+d*x)^(9/2)/(b^2*d^3)+2/11*(c+d*x)^(11/2)/(b*d^3)+2*a^3*(b*c-a*d)^(5/2)*arctanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/b^(13/2)-2*a^3*(b*c-a*d)^2*sqrt(c+d*x)/b^6],
[x^2*(c+d*x)^(5/2)/(a+b*x),x,7,2/3*a^2*(b*c-a*d)*(c+d*x)^(3/2)/b^4+2/5*a^2*(c+d*x)^(5/2)/b^3-2/7*(b*c+a*d)*(c+d*x)^(7/2)/(b^2*d^2)+2/9*(c+d*x)^(9/2)/(b*d^2)-2*a^2*(b*c-a*d)^(5/2)*arctanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/b^(11/2)+2*a^2*(b*c-a*d)^2*sqrt(c+d*x)/b^5],
[x*(c+d*x)^(5/2)/(a+b*x),x,6,-2/3*a*(b*c-a*d)*(c+d*x)^(3/2)/b^3-2/5*a*(c+d*x)^(5/2)/b^2+2/7*(c+d*x)^(7/2)/(b*d)+2*a*(b*c-a*d)^(5/2)*arctanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/b^(9/2)-2*a*(b*c-a*d)^2*sqrt(c+d*x)/b^4],
[(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)/(x*(a+b*x)),x,7,2/3*d*(c+d*x)^(3/2)/b-2*c^(5/2)*arctanh(sqrt(c+d*x)/sqrt(c))/a+2*(b*c-a*d)^(5/2)*arctanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/(a*b^(5/2))+2*d*(2*b*c-a*d)*sqrt(c+d*x)/b^2],
[(c+d*x)^(5/2)/(x^2*(a+b*x)),x,7,-c*(c+d*x)^(3/2)/(a*x)+c^(3/2)*(2*b*c-5*a*d)*arctanh(sqrt(c+d*x)/sqrt(c))/a^2-2*(b*c-a*d)^(5/2)*arctanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/(a^2*b^(3/2))+d*(b*c+2*a*d)*sqrt(c+d*x)/(a*b)],
[(c+d*x)^(5/2)/(x^3*(a+b*x)),x,7,-1/2*c*(c+d*x)^(3/2)/(a*x^2)+2*(b*c-a*d)^(5/2)*arctanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/(a^3*sqrt(b))-1/4*(8*b^2*c^2-20*a*b*c*d+15*a^2*d^2)*arctanh(sqrt(c+d*x)/sqrt(c))*sqrt(c)/a^3+1/4*c*(4*b*c-7*a*d)*sqrt(c+d*x)/(a^2*x)],
[(c+d*x)^(5/2)/(x^4*(a+b*x)),x,8,-1/3*c*(c+d*x)^(3/2)/(a*x^3)-2*(b*c-a*d)^(5/2)*arctanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))*sqrt(b)/a^4+1/8*(16*b^3*c^3-40*a*b^2*c^2*d+30*a^2*b*c*d^2-5*a^3*d^3)*arctanh(sqrt(c+d*x)/sqrt(c))/(a^4*sqrt(c))+1/4*c*(2*b*c-3*a*d)*sqrt(c+d*x)/(a^2*x^2)-1/8*(8*b^2*c^2-18*a*b*c*d+11*a^2*d^2)*sqrt(c+d*x)/(a^3*x)],

# p<0
[1/(x^(1/3)*(4*c+d*x)*sqrt(c+d*x)),x,2,-arctanh(c^(1/6)*(c^(1/3)-2^(1/3)*d^(1/3)*x^(1/3))/sqrt(c+d*x))/(2^(2/3)*c^(5/6)*d^(2/3))+1/3*arctanh(sqrt(c+d*x)/sqrt(c))/(2^(2/3)*c^(5/6)*d^(2/3))-arctan(c^(1/6)*(c^(1/3)+2^(1/3)*d^(1/3)*x^(1/3))*sqrt(3)/sqrt(c+d*x))/(2^(2/3)*c^(5/6)*d^(2/3)*sqrt(3))+arctan(sqrt(c+d*x)/(sqrt(3)*sqrt(c)))/(2^(2/3)*c^(5/6)*d^(2/3)*sqrt(3))],
[1/(x^(1/3)*(8*c-d*x)*sqrt(c+d*x)),x,9,1/6*arctanh(1/3*(c^(1/3)+d^(1/3)*x^(1/3))^2/(c^(1/6)*sqrt(c+d*x)))/(c^(5/6)*d^(2/3))-1/6*arctanh(1/3*sqrt(c+d*x)/sqrt(c))/(c^(5/6)*d^(2/3))-1/2*arctan(c^(1/6)*(c^(1/3)+d^(1/3)*x^(1/3))*sqrt(3)/sqrt(c+d*x))/(c^(5/6)*d^(2/3)*sqrt(3))],

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

# p>0
[(c+d*x)^(1/2)/(x^2*(a+b*x)^2),x,7,(4*b*c-a*d)*arctanh(sqrt(c+d*x)/sqrt(c))/(a^3*sqrt(c))-(4*b*c-3*a*d)*arctanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))*sqrt(b)/(a^3*sqrt(b*c-a*d))-2*b*sqrt(c+d*x)/(a^2*(a+b*x))-sqrt(c+d*x)/(a*x*(a+b*x))],
[(c+d*x)^(3/2)/(x*(a+b*x)^2),x,6,-2*c^(3/2)*arctanh(sqrt(c+d*x)/sqrt(c))/a^2+(2*b*c+a*d)*arctanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))*sqrt(b*c-a*d)/(a^2*b^(3/2))+(b*c-a*d)*sqrt(c+d*x)/(a*b*(a+b*x))],
[(c+d*x)^(3/2)/(x^2*(a+b*x)^2),x,7,(4*b*c-3*a*d)*arctanh(sqrt(c+d*x)/sqrt(c))*sqrt(c)/a^3-(4*b*c-a*d)*arctanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))*sqrt(b*c-a*d)/(a^3*sqrt(b))-(2*b*c-a*d)*sqrt(c+d*x)/(a^2*(a+b*x))-c*sqrt(c+d*x)/(a*x*(a+b*x))],
[x^3*(c+d*x)^(5/2)/(a+b*x)^2,x,7,1/3*a^2*(6*b*c-11*a*d)*(c+d*x)^(3/2)/b^5+11/9*x^2*(c+d*x)^(5/2)/b^2-x^3*(c+d*x)^(5/2)/(b*(a+b*x))-1/315*(c+d*x)^(5/2)*(20*b^2*c^2+180*a*b*c*d-693*a^2*d^2-5*b*d*(10*b*c-99*a*d)*x)/(b^4*d^2)-a^2*(6*b*c-11*a*d)*(b*c-a*d)^(3/2)*arctanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/b^(13/2)+a^2*(6*b*c-11*a*d)*(b*c-a*d)*sqrt(c+d*x)/b^6],
[x^2*(c+d*x)^(5/2)/(a+b*x)^2,x,7,-1/3*a*(4*b*c-9*a*d)*(c+d*x)^(3/2)/b^4-1/5*a*(4*b*c-9*a*d)*(c+d*x)^(5/2)/(b^3*(b*c-a*d))+2/7*(c+d*x)^(7/2)/(b^2*d)-a^2*(c+d*x)^(7/2)/(b^2*(b*c-a*d)*(a+b*x))+a*(4*b*c-9*a*d)*(b*c-a*d)^(3/2)*arctanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/b^(11/2)-a*(4*b*c-9*a*d)*(b*c-a*d)*sqrt(c+d*x)/b^5],
[x*(c+d*x)^(5/2)/(a+b*x)^2,x,6,1/3*(2*b*c-7*a*d)*(c+d*x)^(3/2)/b^3+1/5*(2*b*c-7*a*d)*(c+d*x)^(5/2)/(b^2*(b*c-a*d))+a*(c+d*x)^(7/2)/(b*(b*c-a*d)*(a+b*x))-(2*b*c-7*a*d)*(b*c-a*d)^(3/2)*arctanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/b^(9/2)+(2*b*c-7*a*d)*(b*c-a*d)*sqrt(c+d*x)/b^4],
[(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)/(x*(a+b*x)^2),x,7,(b*c-a*d)*(c+d*x)^(3/2)/(a*b*(a+b*x))-2*c^(5/2)*arctanh(sqrt(c+d*x)/sqrt(c))/a^2+(b*c-a*d)^(3/2)*(2*b*c+3*a*d)*arctanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/(a^2*b^(5/2))-d*(b*c-3*a*d)*sqrt(c+d*x)/(a*b^2)],
[(c+d*x)^(5/2)/(x^2*(a+b*x)^2),x,7,c^(3/2)*(4*b*c-5*a*d)*arctanh(sqrt(c+d*x)/sqrt(c))/a^3-(b*c-a*d)^(3/2)*(4*b*c+a*d)*arctanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/(a^3*b^(3/2))-c^2*sqrt(c+d*x)/(a^2*x)-(b*c-a*d)^2*sqrt(c+d*x)/(a^2*b*(a+b*x)),-c*(c+d*x)^(3/2)/(a*x*(a+b*x))+c^(3/2)*(4*b*c-5*a*d)*arctanh(sqrt(c+d*x)/sqrt(c))/a^3-(b*c-a*d)^(3/2)*(4*b*c+a*d)*arctanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/(a^3*b^(3/2))-(b*c-a*d)*(2*b*c-a*d)*sqrt(c+d*x)/(a^2*b*(a+b*x))],
[(c+d*x)^(5/2)/(x^3*(a+b*x)^2),x,8,-1/2*c*(c+d*x)^(3/2)/(a*x^2*(a+b*x))+(b*c-a*d)^(3/2)*(6*b*c-a*d)*arctanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/(a^4*sqrt(b))-1/4*(24*b^2*c^2-40*a*b*c*d+15*a^2*d^2)*arctanh(sqrt(c+d*x)/sqrt(c))*sqrt(c)/a^4+1/4*(12*b^2*c^2-17*a*b*c*d+4*a^2*d^2)*sqrt(c+d*x)/(a^3*(a+b*x))+1/4*c*(6*b*c-7*a*d)*sqrt(c+d*x)/(a^2*x*(a+b*x))],
[(c+d*x)^(5/2)/(x^4*(a+b*x)^2),x,9,-1/3*c*(c+d*x)^(3/2)/(a*x^3*(a+b*x))-(8*b*c-3*a*d)*(b*c-a*d)^(3/2)*arctanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))*sqrt(b)/a^5+1/8*(64*b^3*c^3-120*a*b^2*c^2*d+60*a^2*b*c*d^2-5*a^3*d^3)*arctanh(sqrt(c+d*x)/sqrt(c))/(a^5*sqrt(c))-1/8*b*(32*b^2*c^2-52*a*b*c*d+19*a^2*d^2)*sqrt(c+d*x)/(a^4*(a+b*x))+1/12*c*(8*b*c-9*a*d)*sqrt(c+d*x)/(a^2*x^2*(a+b*x))-1/24*(48*b^2*c^2-82*a*b*c*d+33*a^2*d^2)*sqrt(c+d*x)/(a^3*x*(a+b*x))],

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

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

# p>0
[x^(5/2)*(A+B*x)*sqrt(a+b*x),x,8,1/5*B*x^(7/2)*(a+b*x)^(3/2)/b-1/128*a^4*(10*A*b-7*a*B)*arctanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))/b^(9/2)-1/192*a^2*(10*A*b-7*a*B)*x^(3/2)*sqrt(a+b*x)/b^3+1/240*a*(10*A*b-7*a*B)*x^(5/2)*sqrt(a+b*x)/b^2+1/40*(10*A*b-7*a*B)*x^(7/2)*sqrt(a+b*x)/b+1/128*a^3*(10*A*b-7*a*B)*sqrt(x)*sqrt(a+b*x)/b^4],
[x^(3/2)*(A+B*x)*sqrt(a+b*x),x,7,1/4*B*x^(5/2)*(a+b*x)^(3/2)/b+1/64*a^3*(8*A*b-5*a*B)*arctanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))/b^(7/2)+1/96*a*(8*A*b-5*a*B)*x^(3/2)*sqrt(a+b*x)/b^2+1/24*(8*A*b-5*a*B)*x^(5/2)*sqrt(a+b*x)/b-1/64*a^2*(8*A*b-5*a*B)*sqrt(x)*sqrt(a+b*x)/b^3],
[(A+B*x)*sqrt(x)*sqrt(a+b*x),x,6,1/3*B*x^(3/2)*(a+b*x)^(3/2)/b-1/8*a^2*(2*A*b-a*B)*arctanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))/b^(5/2)+1/4*(2*A*b-a*B)*x^(3/2)*sqrt(a+b*x)/b+1/8*a*(2*A*b-a*B)*sqrt(x)*sqrt(a+b*x)/b^2],
[(A+B*x)*sqrt(a+b*x)/sqrt(x),x,5,1/4*a*(4*A*b-a*B)*arctanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))/b^(3/2)+1/2*B*(a+b*x)^(3/2)*sqrt(x)/b+1/4*(4*A*b-a*B)*sqrt(x)*sqrt(a+b*x)/b],
[(A+B*x)*sqrt(a+b*x)/x^(3/2),x,5,(2*A*b+a*B)*arctanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))/sqrt(b)-2*A*(a+b*x)^(3/2)/(a*sqrt(x))+(2*A*b+a*B)*sqrt(x)*sqrt(a+b*x)/a],
[(A+B*x)*sqrt(a+b*x)/x^(5/2),x,5,-2/3*A*(a+b*x)^(3/2)/(a*x^(3/2))+2*B*arctanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))*sqrt(b)-2*B*sqrt(a+b*x)/sqrt(x)],
[(A+B*x)*sqrt(a+b*x)/x^(7/2),x,2,-2/5*A*(a+b*x)^(3/2)/(a*x^(5/2))+2/15*(2*A*b-5*a*B)*(a+b*x)^(3/2)/(a^2*x^(3/2))],
[(A+B*x)*sqrt(a+b*x)/x^(9/2),x,3,-2/7*A*(a+b*x)^(3/2)/(a*x^(7/2))+2/35*(4*A*b-7*a*B)*(a+b*x)^(3/2)/(a^2*x^(5/2))-4/105*b*(4*A*b-7*a*B)*(a+b*x)^(3/2)/(a^3*x^(3/2))],
[(A+B*x)*sqrt(a+b*x)/x^(11/2),x,4,-2/9*A*(a+b*x)^(3/2)/(a*x^(9/2))+2/21*(2*A*b-3*a*B)*(a+b*x)^(3/2)/(a^2*x^(7/2))-8/105*b*(2*A*b-3*a*B)*(a+b*x)^(3/2)/(a^3*x^(5/2))+16/315*b^2*(2*A*b-3*a*B)*(a+b*x)^(3/2)/(a^4*x^(3/2))],
[(A+B*x)*sqrt(a+b*x)/x^(13/2),x,5,-2/11*A*(a+b*x)^(3/2)/(a*x^(11/2))+2/99*(8*A*b-11*a*B)*(a+b*x)^(3/2)/(a^2*x^(9/2))-4/231*b*(8*A*b-11*a*B)*(a+b*x)^(3/2)/(a^3*x^(7/2))+16/1155*b^2*(8*A*b-11*a*B)*(a+b*x)^(3/2)/(a^4*x^(5/2))-32/3465*b^3*(8*A*b-11*a*B)*(a+b*x)^(3/2)/(a^5*x^(3/2))],
[(A+B*x)*sqrt(a+b*x)/x^(15/2),x,6,-2/13*A*(a+b*x)^(3/2)/(a*x^(13/2))+2/143*(10*A*b-13*a*B)*(a+b*x)^(3/2)/(a^2*x^(11/2))-16/1287*b*(10*A*b-13*a*B)*(a+b*x)^(3/2)/(a^3*x^(9/2))+32/3003*b^2*(10*A*b-13*a*B)*(a+b*x)^(3/2)/(a^4*x^(7/2))-128/15015*b^3*(10*A*b-13*a*B)*(a+b*x)^(3/2)/(a^5*x^(5/2))+256/45045*b^4*(10*A*b-13*a*B)*(a+b*x)^(3/2)/(a^6*x^(3/2))],
[x^(5/2)*(a+b*x)^(3/2)*(A+B*x),x,9,1/60*(12*A*b-7*a*B)*x^(7/2)*(a+b*x)^(3/2)/b+1/6*B*x^(7/2)*(a+b*x)^(5/2)/b-1/512*a^5*(12*A*b-7*a*B)*arctanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))/b^(9/2)-1/768*a^3*(12*A*b-7*a*B)*x^(3/2)*sqrt(a+b*x)/b^3+1/960*a^2*(12*A*b-7*a*B)*x^(5/2)*sqrt(a+b*x)/b^2+1/160*a*(12*A*b-7*a*B)*x^(7/2)*sqrt(a+b*x)/b+1/512*a^4*(12*A*b-7*a*B)*sqrt(x)*sqrt(a+b*x)/b^4],
[x^(3/2)*(a+b*x)^(3/2)*(A+B*x),x,8,1/8*(2*A*b-a*B)*x^(5/2)*(a+b*x)^(3/2)/b+1/5*B*x^(5/2)*(a+b*x)^(5/2)/b+3/128*a^4*(2*A*b-a*B)*arctanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))/b^(7/2)+1/64*a^2*(2*A*b-a*B)*x^(3/2)*sqrt(a+b*x)/b^2+1/16*a*(2*A*b-a*B)*x^(5/2)*sqrt(a+b*x)/b-3/128*a^3*(2*A*b-a*B)*sqrt(x)*sqrt(a+b*x)/b^3],
[(a+b*x)^(3/2)*(A+B*x)*sqrt(x),x,7,1/24*(8*A*b-3*a*B)*x^(3/2)*(a+b*x)^(3/2)/b+1/4*B*x^(3/2)*(a+b*x)^(5/2)/b-1/64*a^3*(8*A*b-3*a*B)*arctanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))/b^(5/2)+1/32*a*(8*A*b-3*a*B)*x^(3/2)*sqrt(a+b*x)/b+1/64*a^2*(8*A*b-3*a*B)*sqrt(x)*sqrt(a+b*x)/b^2],
[(a+b*x)^(3/2)*(A+B*x)/sqrt(x),x,6,1/8*a^2*(6*A*b-a*B)*arctanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))/b^(3/2)+1/12*(6*A*b-a*B)*(a+b*x)^(3/2)*sqrt(x)/b+1/3*B*(a+b*x)^(5/2)*sqrt(x)/b+1/8*a*(6*A*b-a*B)*sqrt(x)*sqrt(a+b*x)/b],
[(a+b*x)^(3/2)*(A+B*x)/x^(3/2),x,6,3/4*a*(4*A*b+a*B)*arctanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))/sqrt(b)-2*A*(a+b*x)^(5/2)/(a*sqrt(x))+1/2*(4*A*b+a*B)*(a+b*x)^(3/2)*sqrt(x)/a+3/4*(4*A*b+a*B)*sqrt(x)*sqrt(a+b*x)],
[(a+b*x)^(3/2)*(A+B*x)/x^(5/2),x,6,-2/3*A*(a+b*x)^(5/2)/(a*x^(3/2))+(2*A*b+3*a*B)*arctanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))*sqrt(b)-2/3*(2*A*b+3*a*B)*(a+b*x)^(3/2)/(a*sqrt(x))+b*(2*A*b+3*a*B)*sqrt(x)*sqrt(a+b*x)/a],
[(a+b*x)^(3/2)*(A+B*x)/x^(7/2),x,6,-2/3*B*(a+b*x)^(3/2)/x^(3/2)-2/5*A*(a+b*x)^(5/2)/(a*x^(5/2))+2*b^(3/2)*B*arctanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))-2*b*B*sqrt(a+b*x)/sqrt(x)],
[(a+b*x)^(3/2)*(A+B*x)/x^(9/2),x,2,-2/7*A*(a+b*x)^(5/2)/(a*x^(7/2))+2/35*(2*A*b-7*a*B)*(a+b*x)^(5/2)/(a^2*x^(5/2))],
[(a+b*x)^(3/2)*(A+B*x)/x^(11/2),x,3,-2/9*A*(a+b*x)^(5/2)/(a*x^(9/2))+2/63*(4*A*b-9*a*B)*(a+b*x)^(5/2)/(a^2*x^(7/2))-4/315*b*(4*A*b-9*a*B)*(a+b*x)^(5/2)/(a^3*x^(5/2))],
[(a+b*x)^(3/2)*(A+B*x)/x^(13/2),x,4,-2/11*A*(a+b*x)^(5/2)/(a*x^(11/2))+2/99*(6*A*b-11*a*B)*(a+b*x)^(5/2)/(a^2*x^(9/2))-8/693*b*(6*A*b-11*a*B)*(a+b*x)^(5/2)/(a^3*x^(7/2))+16/3465*b^2*(6*A*b-11*a*B)*(a+b*x)^(5/2)/(a^4*x^(5/2))],
[(a+b*x)^(3/2)*(A+B*x)/x^(15/2),x,5,-2/13*A*(a+b*x)^(5/2)/(a*x^(13/2))+2/143*(8*A*b-13*a*B)*(a+b*x)^(5/2)/(a^2*x^(11/2))-4/429*b*(8*A*b-13*a*B)*(a+b*x)^(5/2)/(a^3*x^(9/2))+16/3003*b^2*(8*A*b-13*a*B)*(a+b*x)^(5/2)/(a^4*x^(7/2))-32/15015*b^3*(8*A*b-13*a*B)*(a+b*x)^(5/2)/(a^5*x^(5/2))],
[(a+b*x)^(3/2)*(A+B*x)/x^(17/2),x,6,-2/15*A*(a+b*x)^(5/2)/(a*x^(15/2))+2/39*(2*A*b-3*a*B)*(a+b*x)^(5/2)/(a^2*x^(13/2))-16/429*b*(2*A*b-3*a*B)*(a+b*x)^(5/2)/(a^3*x^(11/2))+32/1287*b^2*(2*A*b-3*a*B)*(a+b*x)^(5/2)/(a^4*x^(9/2))-128/9009*b^3*(2*A*b-3*a*B)*(a+b*x)^(5/2)/(a^5*x^(7/2))+256/45045*b^4*(2*A*b-3*a*B)*(a+b*x)^(5/2)/(a^6*x^(5/2))],
[x^(3/2)*(a+b*x)^(5/2)*(A+B*x),x,9,1/96*a*(12*A*b-5*a*B)*x^(5/2)*(a+b*x)^(3/2)/b+1/60*(12*A*b-5*a*B)*x^(5/2)*(a+b*x)^(5/2)/b+1/6*B*x^(5/2)*(a+b*x)^(7/2)/b+1/512*a^5*(12*A*b-5*a*B)*arctanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))/b^(7/2)+1/768*a^3*(12*A*b-5*a*B)*x^(3/2)*sqrt(a+b*x)/b^2+1/192*a^2*(12*A*b-5*a*B)*x^(5/2)*sqrt(a+b*x)/b-1/512*a^4*(12*A*b-5*a*B)*sqrt(x)*sqrt(a+b*x)/b^3],
[(a+b*x)^(5/2)*(A+B*x)*sqrt(x),x,8,1/48*a*(10*A*b-3*a*B)*x^(3/2)*(a+b*x)^(3/2)/b+1/40*(10*A*b-3*a*B)*x^(3/2)*(a+b*x)^(5/2)/b+1/5*B*x^(3/2)*(a+b*x)^(7/2)/b-1/128*a^4*(10*A*b-3*a*B)*arctanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))/b^(5/2)+1/64*a^2*(10*A*b-3*a*B)*x^(3/2)*sqrt(a+b*x)/b+1/128*a^3*(10*A*b-3*a*B)*sqrt(x)*sqrt(a+b*x)/b^2],
[(a+b*x)^(5/2)*(A+B*x)/sqrt(x),x,7,5/64*a^3*(8*A*b-a*B)*arctanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))/b^(3/2)+5/96*a*(8*A*b-a*B)*(a+b*x)^(3/2)*sqrt(x)/b+1/24*(8*A*b-a*B)*(a+b*x)^(5/2)*sqrt(x)/b+1/4*B*(a+b*x)^(7/2)*sqrt(x)/b+5/64*a^2*(8*A*b-a*B)*sqrt(x)*sqrt(a+b*x)/b],
[(a+b*x)^(5/2)*(A+B*x)/x^(3/2),x,7,5/8*a^2*(6*A*b+a*B)*arctanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))/sqrt(b)-2*A*(a+b*x)^(7/2)/(a*sqrt(x))+5/12*(6*A*b+a*B)*(a+b*x)^(3/2)*sqrt(x)+1/3*(6*A*b+a*B)*(a+b*x)^(5/2)*sqrt(x)/a+5/8*a*(6*A*b+a*B)*sqrt(x)*sqrt(a+b*x)],
[(a+b*x)^(5/2)*(A+B*x)/x^(5/2),x,7,-2/3*A*(a+b*x)^(7/2)/(a*x^(3/2))+5/4*a*(4*A*b+3*a*B)*arctanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))*sqrt(b)-2/3*(4*A*b+3*a*B)*(a+b*x)^(5/2)/(a*sqrt(x))+5/6*b*(4*A*b+3*a*B)*(a+b*x)^(3/2)*sqrt(x)/a+5/4*b*(4*A*b+3*a*B)*sqrt(x)*sqrt(a+b*x)],
[(a+b*x)^(5/2)*(A+B*x)/x^(7/2),x,7,-2/15*(2*A*b+5*a*B)*(a+b*x)^(5/2)/(a*x^(3/2))-2/5*A*(a+b*x)^(7/2)/(a*x^(5/2))+b^(3/2)*(2*A*b+5*a*B)*arctanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))-2/3*b*(2*A*b+5*a*B)*(a+b*x)^(3/2)/(a*sqrt(x))+b^2*(2*A*b+5*a*B)*sqrt(x)*sqrt(a+b*x)/a],
[(a+b*x)^(5/2)*(A+B*x)/x^(9/2),x,7,-2/3*b*B*(a+b*x)^(3/2)/x^(3/2)-2/5*B*(a+b*x)^(5/2)/x^(5/2)-2/7*A*(a+b*x)^(7/2)/(a*x^(7/2))+2*b^(5/2)*B*arctanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))-2*b^2*B*sqrt(a+b*x)/sqrt(x)],
[(a+b*x)^(5/2)*(A+B*x)/x^(11/2),x,2,-2/9*A*(a+b*x)^(7/2)/(a*x^(9/2))+2/63*(2*A*b-9*a*B)*(a+b*x)^(7/2)/(a^2*x^(7/2))],
[(a+b*x)^(5/2)*(A+B*x)/x^(13/2),x,3,-2/11*A*(a+b*x)^(7/2)/(a*x^(11/2))+2/99*(4*A*b-11*a*B)*(a+b*x)^(7/2)/(a^2*x^(9/2))-4/693*b*(4*A*b-11*a*B)*(a+b*x)^(7/2)/(a^3*x^(7/2))],
[(a+b*x)^(5/2)*(A+B*x)/x^(15/2),x,4,-2/13*A*(a+b*x)^(7/2)/(a*x^(13/2))+2/143*(6*A*b-13*a*B)*(a+b*x)^(7/2)/(a^2*x^(11/2))-8/1287*b*(6*A*b-13*a*B)*(a+b*x)^(7/2)/(a^3*x^(9/2))+16/9009*b^2*(6*A*b-13*a*B)*(a+b*x)^(7/2)/(a^4*x^(7/2))],
[(a+b*x)^(5/2)*(A+B*x)/x^(17/2),x,5,-2/15*A*(a+b*x)^(7/2)/(a*x^(15/2))+2/195*(8*A*b-15*a*B)*(a+b*x)^(7/2)/(a^2*x^(13/2))-4/715*b*(8*A*b-15*a*B)*(a+b*x)^(7/2)/(a^3*x^(11/2))+16/6435*b^2*(8*A*b-15*a*B)*(a+b*x)^(7/2)/(a^4*x^(9/2))-32/45045*b^3*(8*A*b-15*a*B)*(a+b*x)^(7/2)/(a^5*x^(7/2))],
[(a+b*x)^(5/2)*(A+B*x)/x^(19/2),x,6,-2/17*A*(a+b*x)^(7/2)/(a*x^(17/2))+2/255*(10*A*b-17*a*B)*(a+b*x)^(7/2)/(a^2*x^(15/2))-16/3315*b*(10*A*b-17*a*B)*(a+b*x)^(7/2)/(a^3*x^(13/2))+32/12155*b^2*(10*A*b-17*a*B)*(a+b*x)^(7/2)/(a^4*x^(11/2))-128/109395*b^3*(10*A*b-17*a*B)*(a+b*x)^(7/2)/(a^5*x^(9/2))+256/765765*b^4*(10*A*b-17*a*B)*(a+b*x)^(7/2)/(a^6*x^(7/2))],

# p<0
[x^(7/2)*(A+B*x)/sqrt(a+b*x),x,8,7/128*a^4*(10*A*b-9*a*B)*arctanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))/b^(11/2)+7/192*a^2*(10*A*b-9*a*B)*x^(3/2)*sqrt(a+b*x)/b^4-7/240*a*(10*A*b-9*a*B)*x^(5/2)*sqrt(a+b*x)/b^3+1/40*(10*A*b-9*a*B)*x^(7/2)*sqrt(a+b*x)/b^2+1/5*B*x^(9/2)*sqrt(a+b*x)/b-7/128*a^3*(10*A*b-9*a*B)*sqrt(x)*sqrt(a+b*x)/b^5],
[x^(5/2)*(A+B*x)/sqrt(a+b*x),x,7,-5/64*a^3*(8*A*b-7*a*B)*arctanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))/b^(9/2)-5/96*a*(8*A*b-7*a*B)*x^(3/2)*sqrt(a+b*x)/b^3+1/24*(8*A*b-7*a*B)*x^(5/2)*sqrt(a+b*x)/b^2+1/4*B*x^(7/2)*sqrt(a+b*x)/b+5/64*a^2*(8*A*b-7*a*B)*sqrt(x)*sqrt(a+b*x)/b^4],
[x^(3/2)*(A+B*x)/sqrt(a+b*x),x,6,1/8*a^2*(6*A*b-5*a*B)*arctanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))/b^(7/2)+1/12*(6*A*b-5*a*B)*x^(3/2)*sqrt(a+b*x)/b^2+1/3*B*x^(5/2)*sqrt(a+b*x)/b-1/8*a*(6*A*b-5*a*B)*sqrt(x)*sqrt(a+b*x)/b^3],
[(A+B*x)*sqrt(x)/sqrt(a+b*x),x,5,-1/4*a*(4*A*b-3*a*B)*arctanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))/b^(5/2)+1/2*B*x^(3/2)*sqrt(a+b*x)/b+1/4*(4*A*b-3*a*B)*sqrt(x)*sqrt(a+b*x)/b^2],
[(A+B*x)/(sqrt(x)*sqrt(a+b*x)),x,4,(2*A*b-a*B)*arctanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))/b^(3/2)+B*sqrt(x)*sqrt(a+b*x)/b],
[(A+B*x)/(x^(3/2)*sqrt(a+b*x)),x,4,2*B*arctanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))/sqrt(b)-2*A*sqrt(a+b*x)/(a*sqrt(x))],
[(A+B*x)/(x^(5/2)*sqrt(a+b*x)),x,2,-2/3*A*sqrt(a+b*x)/(a*x^(3/2))+2/3*(2*A*b-3*a*B)*sqrt(a+b*x)/(a^2*sqrt(x))],
[(A+B*x)/(x^(7/2)*sqrt(a+b*x)),x,3,-2/5*A*sqrt(a+b*x)/(a*x^(5/2))+2/15*(4*A*b-5*a*B)*sqrt(a+b*x)/(a^2*x^(3/2))-4/15*b*(4*A*b-5*a*B)*sqrt(a+b*x)/(a^3*sqrt(x))],
[(A+B*x)/(x^(9/2)*sqrt(a+b*x)),x,4,-2/7*A*sqrt(a+b*x)/(a*x^(7/2))+2/35*(6*A*b-7*a*B)*sqrt(a+b*x)/(a^2*x^(5/2))-8/105*b*(6*A*b-7*a*B)*sqrt(a+b*x)/(a^3*x^(3/2))+16/105*b^2*(6*A*b-7*a*B)*sqrt(a+b*x)/(a^4*sqrt(x))],
[(A+B*x)/(x^(11/2)*sqrt(a+b*x)),x,5,-2/9*A*sqrt(a+b*x)/(a*x^(9/2))+2/63*(8*A*b-9*a*B)*sqrt(a+b*x)/(a^2*x^(7/2))-4/105*b*(8*A*b-9*a*B)*sqrt(a+b*x)/(a^3*x^(5/2))+16/315*b^2*(8*A*b-9*a*B)*sqrt(a+b*x)/(a^4*x^(3/2))-32/315*b^3*(8*A*b-9*a*B)*sqrt(a+b*x)/(a^5*sqrt(x))],
[(A+B*x)/(x^(13/2)*sqrt(a+b*x)),x,6,-2/11*A*sqrt(a+b*x)/(a*x^(11/2))+2/99*(10*A*b-11*a*B)*sqrt(a+b*x)/(a^2*x^(9/2))-16/693*b*(10*A*b-11*a*B)*sqrt(a+b*x)/(a^3*x^(7/2))+32/1155*b^2*(10*A*b-11*a*B)*sqrt(a+b*x)/(a^4*x^(5/2))-128/3465*b^3*(10*A*b-11*a*B)*sqrt(a+b*x)/(a^5*x^(3/2))+256/3465*b^4*(10*A*b-11*a*B)*sqrt(a+b*x)/(a^6*sqrt(x))],
[(A+B*x)/(x^(15/2)*sqrt(a+b*x)),x,7,-2/13*A*sqrt(a+b*x)/(a*x^(13/2))+2/143*(12*A*b-13*a*B)*sqrt(a+b*x)/(a^2*x^(11/2))-20/1287*b*(12*A*b-13*a*B)*sqrt(a+b*x)/(a^3*x^(9/2))+160/9009*b^2*(12*A*b-13*a*B)*sqrt(a+b*x)/(a^4*x^(7/2))-64/3003*b^3*(12*A*b-13*a*B)*sqrt(a+b*x)/(a^5*x^(5/2))+256/9009*b^4*(12*A*b-13*a*B)*sqrt(a+b*x)/(a^6*x^(3/2))-512/9009*b^5*(12*A*b-13*a*B)*sqrt(a+b*x)/(a^7*sqrt(x))],
[x^(7/2)*(A+B*x)/(a+b*x)^(3/2),x,8,-35/64*a^3*(8*A*b-9*a*B)*arctanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))/b^(11/2)+2*(A*b-a*B)*x^(9/2)/(a*b*sqrt(a+b*x))-35/96*a*(8*A*b-9*a*B)*x^(3/2)*sqrt(a+b*x)/b^4+7/24*(8*A*b-9*a*B)*x^(5/2)*sqrt(a+b*x)/b^3-1/4*(8*A*b-9*a*B)*x^(7/2)*sqrt(a+b*x)/(a*b^2)+35/64*a^2*(8*A*b-9*a*B)*sqrt(x)*sqrt(a+b*x)/b^5],
[x^(5/2)*(A+B*x)/(a+b*x)^(3/2),x,7,5/8*a^2*(6*A*b-7*a*B)*arctanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))/b^(9/2)+2*(A*b-a*B)*x^(7/2)/(a*b*sqrt(a+b*x))+5/12*(6*A*b-7*a*B)*x^(3/2)*sqrt(a+b*x)/b^3-1/3*(6*A*b-7*a*B)*x^(5/2)*sqrt(a+b*x)/(a*b^2)-5/8*a*(6*A*b-7*a*B)*sqrt(x)*sqrt(a+b*x)/b^4],
[x^(3/2)*(A+B*x)/(a+b*x)^(3/2),x,6,-3/4*a*(4*A*b-5*a*B)*arctanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))/b^(7/2)+2*(A*b-a*B)*x^(5/2)/(a*b*sqrt(a+b*x))-1/2*(4*A*b-5*a*B)*x^(3/2)*sqrt(a+b*x)/(a*b^2)+3/4*(4*A*b-5*a*B)*sqrt(x)*sqrt(a+b*x)/b^3],
[(A+B*x)*sqrt(x)/(a+b*x)^(3/2),x,5,(2*A*b-3*a*B)*arctanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))/b^(5/2)+2*(A*b-a*B)*x^(3/2)/(a*b*sqrt(a+b*x))-(2*A*b-3*a*B)*sqrt(x)*sqrt(a+b*x)/(a*b^2)],
[(A+B*x)/((a+b*x)^(3/2)*sqrt(x)),x,4,2*B*arctanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))/b^(3/2)+2*(A*b-a*B)*sqrt(x)/(a*b*sqrt(a+b*x))],
[(A+B*x)/(x^(3/2)*(a+b*x)^(3/2)),x,2,-2*A/(a*sqrt(x)*sqrt(a+b*x))-2*(2*A*b-a*B)*sqrt(x)/(a^2*sqrt(a+b*x))],
[(A+B*x)/(x^(5/2)*(a+b*x)^(3/2)),x,3,-2/3*A/(a*x^(3/2)*sqrt(a+b*x))-2/3*(4*A*b-3*a*B)/(a^2*sqrt(x)*sqrt(a+b*x))+4/3*(4*A*b-3*a*B)*sqrt(a+b*x)/(a^3*sqrt(x))],
[(A+B*x)/(x^(7/2)*(a+b*x)^(3/2)),x,4,-2/5*A/(a*x^(5/2)*sqrt(a+b*x))-2/5*(6*A*b-5*a*B)/(a^2*x^(3/2)*sqrt(a+b*x))+8/15*(6*A*b-5*a*B)*sqrt(a+b*x)/(a^3*x^(3/2))-16/15*b*(6*A*b-5*a*B)*sqrt(a+b*x)/(a^4*sqrt(x))],
[(A+B*x)/(x^(9/2)*(a+b*x)^(3/2)),x,5,-2/7*A/(a*x^(7/2)*sqrt(a+b*x))-2/7*(8*A*b-7*a*B)/(a^2*x^(5/2)*sqrt(a+b*x))+12/35*(8*A*b-7*a*B)*sqrt(a+b*x)/(a^3*x^(5/2))-16/35*b*(8*A*b-7*a*B)*sqrt(a+b*x)/(a^4*x^(3/2))+32/35*b^2*(8*A*b-7*a*B)*sqrt(a+b*x)/(a^5*sqrt(x))],
[(A+B*x)/(x^(11/2)*(a+b*x)^(3/2)),x,6,-2/9*A/(a*x^(9/2)*sqrt(a+b*x))-2/9*(10*A*b-9*a*B)/(a^2*x^(7/2)*sqrt(a+b*x))+16/63*(10*A*b-9*a*B)*sqrt(a+b*x)/(a^3*x^(7/2))-32/105*b*(10*A*b-9*a*B)*sqrt(a+b*x)/(a^4*x^(5/2))+128/315*b^2*(10*A*b-9*a*B)*sqrt(a+b*x)/(a^5*x^(3/2))-256/315*b^3*(10*A*b-9*a*B)*sqrt(a+b*x)/(a^6*sqrt(x))],
[(A+B*x)/(x^(13/2)*(a+b*x)^(3/2)),x,7,-2/11*A/(a*x^(11/2)*sqrt(a+b*x))-2/11*(12*A*b-11*a*B)/(a^2*x^(9/2)*sqrt(a+b*x))+20/99*(12*A*b-11*a*B)*sqrt(a+b*x)/(a^3*x^(9/2))-160/693*b*(12*A*b-11*a*B)*sqrt(a+b*x)/(a^4*x^(7/2))+64/231*b^2*(12*A*b-11*a*B)*sqrt(a+b*x)/(a^5*x^(5/2))-256/693*b^3*(12*A*b-11*a*B)*sqrt(a+b*x)/(a^6*x^(3/2))+512/693*b^4*(12*A*b-11*a*B)*sqrt(a+b*x)/(a^7*sqrt(x))],
[x^(7/2)*(A+B*x)/(a+b*x)^(5/2),x,8,2/3*(A*b-a*B)*x^(9/2)/(a*b*(a+b*x)^(3/2))+35/8*a^2*(2*A*b-3*a*B)*arctanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))/b^(11/2)+2*(2*A*b-3*a*B)*x^(7/2)/(a*b^2*sqrt(a+b*x))+35/12*(2*A*b-3*a*B)*x^(3/2)*sqrt(a+b*x)/b^4-7/3*(2*A*b-3*a*B)*x^(5/2)*sqrt(a+b*x)/(a*b^3)-35/8*a*(2*A*b-3*a*B)*sqrt(x)*sqrt(a+b*x)/b^5],
[x^(5/2)*(A+B*x)/(a+b*x)^(5/2),x,7,2/3*(A*b-a*B)*x^(7/2)/(a*b*(a+b*x)^(3/2))-5/4*a*(4*A*b-7*a*B)*arctanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))/b^(9/2)+2/3*(4*A*b-7*a*B)*x^(5/2)/(a*b^2*sqrt(a+b*x))-5/6*(4*A*b-7*a*B)*x^(3/2)*sqrt(a+b*x)/(a*b^3)+5/4*(4*A*b-7*a*B)*sqrt(x)*sqrt(a+b*x)/b^4],
[x^(3/2)*(A+B*x)/(a+b*x)^(5/2),x,6,2/3*(A*b-a*B)*x^(5/2)/(a*b*(a+b*x)^(3/2))+(2*A*b-5*a*B)*arctanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))/b^(7/2)+2/3*(2*A*b-5*a*B)*x^(3/2)/(a*b^2*sqrt(a+b*x))-(2*A*b-5*a*B)*sqrt(x)*sqrt(a+b*x)/(a*b^3)],
[(A+B*x)*sqrt(x)/(a+b*x)^(5/2),x,5,2/3*(A*b-a*B)*x^(3/2)/(a*b*(a+b*x)^(3/2))+2*B*arctanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))/b^(5/2)-2*B*sqrt(x)/(b^2*sqrt(a+b*x))],
[(A+B*x)/((a+b*x)^(5/2)*sqrt(x)),x,2,2/3*(A*b-a*B)*sqrt(x)/(a*b*(a+b*x)^(3/2))+2/3*(2*A*b+a*B)*sqrt(x)/(a^2*b*sqrt(a+b*x))],
[(A+B*x)/(x^(3/2)*(a+b*x)^(5/2)),x,3,-2*A/(a*(a+b*x)^(3/2)*sqrt(x))-2/3*(4*A*b-a*B)*sqrt(x)/(a^2*(a+b*x)^(3/2))-4/3*(4*A*b-a*B)*sqrt(x)/(a^3*sqrt(a+b*x))],
[(A+B*x)/(x^(5/2)*(a+b*x)^(5/2)),x,4,-2/3*A/(a*x^(3/2)*(a+b*x)^(3/2))-2/3*(2*A*b-a*B)/(a^2*(a+b*x)^(3/2)*sqrt(x))-8/3*(2*A*b-a*B)/(a^3*sqrt(x)*sqrt(a+b*x))+16/3*(2*A*b-a*B)*sqrt(a+b*x)/(a^4*sqrt(x))],
[(A+B*x)/(x^(7/2)*(a+b*x)^(5/2)),x,5,-2/5*A/(a*x^(5/2)*(a+b*x)^(3/2))-2/15*(8*A*b-5*a*B)/(a^2*x^(3/2)*(a+b*x)^(3/2))-4/5*(8*A*b-5*a*B)/(a^3*x^(3/2)*sqrt(a+b*x))+16/15*(8*A*b-5*a*B)*sqrt(a+b*x)/(a^4*x^(3/2))-32/15*b*(8*A*b-5*a*B)*sqrt(a+b*x)/(a^5*sqrt(x))],
[(A+B*x)/(x^(9/2)*(a+b*x)^(5/2)),x,6,-2/7*A/(a*x^(7/2)*(a+b*x)^(3/2))-2/21*(10*A*b-7*a*B)/(a^2*x^(5/2)*(a+b*x)^(3/2))-16/21*(10*A*b-7*a*B)/(a^3*x^(5/2)*sqrt(a+b*x))+32/35*(10*A*b-7*a*B)*sqrt(a+b*x)/(a^4*x^(5/2))-128/105*b*(10*A*b-7*a*B)*sqrt(a+b*x)/(a^5*x^(3/2))+256/105*b^2*(10*A*b-7*a*B)*sqrt(a+b*x)/(a^6*sqrt(x))],
[(A+B*x)/(x^(11/2)*(a+b*x)^(5/2)),x,7,-2/9*A/(a*x^(9/2)*(a+b*x)^(3/2))-2/9*(4*A*b-3*a*B)/(a^2*x^(7/2)*(a+b*x)^(3/2))-20/9*(4*A*b-3*a*B)/(a^3*x^(7/2)*sqrt(a+b*x))+160/63*(4*A*b-3*a*B)*sqrt(a+b*x)/(a^4*x^(7/2))-64/21*b*(4*A*b-3*a*B)*sqrt(a+b*x)/(a^5*x^(5/2))+256/63*b^2*(4*A*b-3*a*B)*sqrt(a+b*x)/(a^6*x^(3/2))-512/63*b^3*(4*A*b-3*a*B)*sqrt(a+b*x)/(a^7*sqrt(x))],

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

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

# n>0
[x^3*sqrt(a+b*x)*sqrt(c+d*x),x,7,1/5*x^2*(a+b*x)^(3/2)*(c+d*x)^(3/2)/(b*d)+1/240*(a+b*x)^(3/2)*(c+d*x)^(3/2)*(35*b^2*c^2+38*a*b*c*d+35*a^2*d^2-42*b*d*(b*c+a*d)*x)/(b^3*d^3)+1/128*(b*c-a*d)^2*(b*c+a*d)*(7*b^2*c^2+2*a*b*c*d+7*a^2*d^2)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(9/2)*d^(9/2))-1/64*(b*c+a*d)*(7*b^2*c^2+2*a*b*c*d+7*a^2*d^2)*(a+b*x)^(3/2)*sqrt(c+d*x)/(b^4*d^3)-1/128*(7*b^4*c^4+2*a*b^3*c^3*d-2*a^3*b*c*d^3-7*a^4*d^4)*sqrt(a+b*x)*sqrt(c+d*x)/(b^4*d^4)],
[x^2*sqrt(a+b*x)*sqrt(c+d*x),x,7,-5/24*(b*c+a*d)*(a+b*x)^(3/2)*(c+d*x)^(3/2)/(b^2*d^2)+1/4*x*(a+b*x)^(3/2)*(c+d*x)^(3/2)/(b*d)+1/64*(b*c-a*d)^2*(4*a*b*c*d-5*(b*c+a*d)^2)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(7/2)*d^(7/2))-1/32*(4*a*b*c*d-5*(b*c+a*d)^2)*(a+b*x)^(3/2)*sqrt(c+d*x)/(b^3*d^2)-1/64*(b*c-a*d)*(4*a*b*c*d-5*(b*c+a*d)^2)*sqrt(a+b*x)*sqrt(c+d*x)/(b^3*d^3)],
[x*sqrt(a+b*x)*sqrt(c+d*x),x,6,1/3*(a+b*x)^(3/2)*(c+d*x)^(3/2)/(b*d)+1/8*(b*c-a*d)^2*(b*c+a*d)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(5/2)*d^(5/2))-1/4*(b*c+a*d)*(a+b*x)^(3/2)*sqrt(c+d*x)/(b^2*d)+1/8*(a^2/b^2-c^2/d^2)*sqrt(a+b*x)*sqrt(c+d*x)],
[sqrt(a+b*x)*sqrt(c+d*x),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)],
[sqrt(a+b*x)*sqrt(c+d*x)/x,x,7,-2*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))*sqrt(a)*sqrt(c)+(b*c+a*d)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(sqrt(b)*sqrt(d))+sqrt(a+b*x)*sqrt(c+d*x)],
[sqrt(a+b*x)*sqrt(c+d*x)/x^2,x,7,-(b*c+a*d)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(sqrt(a)*sqrt(c))+2*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))*sqrt(b)*sqrt(d)-sqrt(a+b*x)*sqrt(c+d*x)/x],
[sqrt(a+b*x)*sqrt(c+d*x)/x^3,x,4,1/4*(b*c-a*d)^2*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(3/2)*c^(3/2))-1/2*(c+d*x)^(3/2)*sqrt(a+b*x)/(c*x^2)-1/4*(b*c-a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(a*c*x)],
[sqrt(a+b*x)*sqrt(c+d*x)/x^4,x,5,-1/3*(a+b*x)^(3/2)*(c+d*x)^(3/2)/(a*c*x^3)-1/8*(b*c-a*d)^2*(b*c+a*d)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(5/2)*c^(5/2))+1/4*(b*c+a*d)*(c+d*x)^(3/2)*sqrt(a+b*x)/(a*c^2*x^2)+1/8*(b^2/a^2-d^2/c^2)*sqrt(a+b*x)*sqrt(c+d*x)/x],
[sqrt(a+b*x)*sqrt(c+d*x)/x^5,x,7,1/64*(b*c-a*d)^2*(5*b^2*c^2+6*a*b*c*d+5*a^2*d^2)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(7/2)*c^(7/2))-1/4*sqrt(a+b*x)*sqrt(c+d*x)/x^4-1/24*(b*c+a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(a*c*x^3)+1/96*(5*b^2*c^2-2*a*b*c*d+5*a^2*d^2)*sqrt(a+b*x)*sqrt(c+d*x)/(a^2*c^2*x^2)-1/192*(b*c+a*d)*(15*b^2*c^2-22*a*b*c*d+15*a^2*d^2)*sqrt(a+b*x)*sqrt(c+d*x)/(a^3*c^3*x)],
[sqrt(a+b*x)*sqrt(c+d*x)/x^6,x,8,-1/128*(b*c-a*d)^2*(b*c+a*d)*(7*b^2*c^2+2*a*b*c*d+7*a^2*d^2)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(9/2)*c^(9/2))-1/5*sqrt(a+b*x)*sqrt(c+d*x)/x^5-1/40*(b*c+a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(a*c*x^4)+1/240*(7*b^2*c^2-2*a*b*c*d+7*a^2*d^2)*sqrt(a+b*x)*sqrt(c+d*x)/(a^2*c^2*x^3)-1/960*(b*c+a*d)*(35*b^2*c^2-46*a*b*c*d+35*a^2*d^2)*sqrt(a+b*x)*sqrt(c+d*x)/(a^3*c^3*x^2)+1/1920*(105*b^4*c^4-40*a*b^3*c^3*d-34*a^2*b^2*c^2*d^2-40*a^3*b*c*d^3+105*a^4*d^4)*sqrt(a+b*x)*sqrt(c+d*x)/(a^4*c^4*x)],
[x^2*(c+d*x)^(3/2)*sqrt(a+b*x),x,8,1/48*(3*b^2*c^2+6*a*b*c*d+7*a^2*d^2)*(a+b*x)^(3/2)*(c+d*x)^(3/2)/(b^3*d^2)-1/40*(5*b*c+7*a*d)*(a+b*x)^(3/2)*(c+d*x)^(5/2)/(b^2*d^2)+1/5*x*(a+b*x)^(3/2)*(c+d*x)^(5/2)/(b*d)-1/128*(b*c-a*d)^3*(3*b^2*c^2+6*a*b*c*d+7*a^2*d^2)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(9/2)*d^(7/2))+1/64*(b*c-a*d)*(3*b^2*c^2+6*a*b*c*d+7*a^2*d^2)*(a+b*x)^(3/2)*sqrt(c+d*x)/(b^4*d^2)+1/128*(b*c-a*d)^2*(3*b^2*c^2+6*a*b*c*d+7*a^2*d^2)*sqrt(a+b*x)*sqrt(c+d*x)/(b^4*d^3)],
[x*(c+d*x)^(3/2)*sqrt(a+b*x),x,7,-1/24*(3*b*c+5*a*d)*(a+b*x)^(3/2)*(c+d*x)^(3/2)/(b^2*d)+1/4*(a+b*x)^(3/2)*(c+d*x)^(5/2)/(b*d)+1/64*(b*c-a*d)^3*(3*b*c+5*a*d)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(7/2)*d^(5/2))-1/32*(b*c-a*d)*(3*b*c+5*a*d)*(a+b*x)^(3/2)*sqrt(c+d*x)/(b^3*d)-1/64*(b*c-a*d)^2*(3*b*c+5*a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(b^3*d^2)],
[(c+d*x)^(3/2)*sqrt(a+b*x),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)*sqrt(a+b*x)/x,x,8,-2*c^(3/2)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))*sqrt(a)+1/4*(3*b^2*c^2+6*a*b*c*d-a^2*d^2)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(3/2)*sqrt(d))+1/2*(c+d*x)^(3/2)*sqrt(a+b*x)+1/4*(3*b*c+a*d)*sqrt(a+b*x)*sqrt(c+d*x)/b],
[(c+d*x)^(3/2)*sqrt(a+b*x)/x^2,x,8,-(b*c+3*a*d)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))*sqrt(c)/sqrt(a)+(3*b*c+a*d)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))*sqrt(d)/sqrt(b)-(c+d*x)^(3/2)*sqrt(a+b*x)/x+2*d*sqrt(a+b*x)*sqrt(c+d*x)],
[(c+d*x)^(3/2)*sqrt(a+b*x)/x^3,x,8,2*d^(3/2)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))*sqrt(b)+1/4*(b^2*c^2-6*a*b*c*d-3*a^2*d^2)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(3/2)*sqrt(c))-1/2*(c+d*x)^(3/2)*sqrt(a+b*x)/x^2-1/4*(b*c+3*a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(a*x)],
[(c+d*x)^(3/2)*sqrt(a+b*x)/x^4,x,5,-1/8*(b*c-a*d)^3*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(5/2)*c^(3/2))-1/12*(b*c-a*d)*(c+d*x)^(3/2)*sqrt(a+b*x)/(a*c*x^2)-1/3*(c+d*x)^(5/2)*sqrt(a+b*x)/(c*x^3)+1/8*(b*c-a*d)^2*sqrt(a+b*x)*sqrt(c+d*x)/(a^2*c*x)],
[(c+d*x)^(3/2)*sqrt(a+b*x)/x^5,x,6,-1/4*(a+b*x)^(3/2)*(c+d*x)^(5/2)/(a*c*x^4)+1/64*(b*c-a*d)^3*(5*b*c+3*a*d)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(7/2)*c^(5/2))+1/96*(b*c-a*d)*(5*b*c+3*a*d)*(c+d*x)^(3/2)*sqrt(a+b*x)/(a^2*c^2*x^2)+1/24*(5*b*c+3*a*d)*(c+d*x)^(5/2)*sqrt(a+b*x)/(a*c^2*x^3)-1/64*(b*c-a*d)^2*(5*b*c+3*a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(a^3*c^2*x)],
[(c+d*x)^(3/2)*sqrt(a+b*x)/x^6,x,8,-1/128*(b*c-a*d)^3*(7*b^2*c^2+6*a*b*c*d+3*a^2*d^2)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(9/2)*c^(7/2))-1/5*(c+d*x)^(3/2)*sqrt(a+b*x)/x^5-1/40*(b*c+3*a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(a*x^4)+1/240*(7*b^2*c/a-12*b*d-3*a*d^2/c)*sqrt(a+b*x)*sqrt(c+d*x)/(a*x^3)-1/960*(35*b^3*c^3-61*a*b^2*c^2*d+9*a^2*b*c*d^2-15*a^3*d^3)*sqrt(a+b*x)*sqrt(c+d*x)/(a^3*c^2*x^2)+1/1920*(105*b^4*c^4-190*a*b^3*c^3*d+36*a^2*b^2*c^2*d^2+30*a^3*b*c*d^3-45*a^4*d^4)*sqrt(a+b*x)*sqrt(c+d*x)/(a^4*c^3*x)],
[x^2*(c+d*x)^(5/2)*sqrt(a+b*x),x,9,1/192*(b*c-a*d)*(5*b^2*c^2+14*a*b*c*d+21*a^2*d^2)*(a+b*x)^(3/2)*(c+d*x)^(3/2)/(b^4*d^2)+1/160*(5*b^2*c^2+14*a*b*c*d+21*a^2*d^2)*(a+b*x)^(3/2)*(c+d*x)^(5/2)/(b^3*d^2)-1/60*(5*b*c+9*a*d)*(a+b*x)^(3/2)*(c+d*x)^(7/2)/(b^2*d^2)+1/6*x*(a+b*x)^(3/2)*(c+d*x)^(7/2)/(b*d)-1/512*(b*c-a*d)^4*(5*b^2*c^2+14*a*b*c*d+21*a^2*d^2)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(11/2)*d^(7/2))+1/256*(b*c-a*d)^2*(5*b^2*c^2+14*a*b*c*d+21*a^2*d^2)*(a+b*x)^(3/2)*sqrt(c+d*x)/(b^5*d^2)+1/512*(b*c-a*d)^3*(5*b^2*c^2+14*a*b*c*d+21*a^2*d^2)*sqrt(a+b*x)*sqrt(c+d*x)/(b^5*d^3)],
[x*(c+d*x)^(5/2)*sqrt(a+b*x),x,8,-1/48*(b*c-a*d)*(3*b*c+7*a*d)*(a+b*x)^(3/2)*(c+d*x)^(3/2)/(b^3*d)-1/40*(3*b*c+7*a*d)*(a+b*x)^(3/2)*(c+d*x)^(5/2)/(b^2*d)+1/5*(a+b*x)^(3/2)*(c+d*x)^(7/2)/(b*d)+1/128*(b*c-a*d)^4*(3*b*c+7*a*d)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(9/2)*d^(5/2))-1/64*(b*c-a*d)^2*(3*b*c+7*a*d)*(a+b*x)^(3/2)*sqrt(c+d*x)/(b^4*d)-1/128*(b*c-a*d)^3*(3*b*c+7*a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(b^4*d^2)],
[(c+d*x)^(5/2)*sqrt(a+b*x),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)*sqrt(a+b*x)/x,x,9,-2*c^(5/2)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))*sqrt(a)+1/8*(5*b^3*c^3+15*a*b^2*c^2*d-5*a^2*b*c*d^2+a^3*d^3)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(5/2)*sqrt(d))+1/12*(5*b*c+a*d)*(c+d*x)^(3/2)*sqrt(a+b*x)/b+1/3*(c+d*x)^(5/2)*sqrt(a+b*x)+1/8*(5*b*c-a*d)*(b*c+a*d)*sqrt(a+b*x)*sqrt(c+d*x)/b^2],
[(c+d*x)^(5/2)*sqrt(a+b*x)/x^2,x,9,-c^(3/2)*(b*c+5*a*d)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/sqrt(a)+1/4*(15*b^2*c^2+10*a*b*c*d-a^2*d^2)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))*sqrt(d)/b^(3/2)+3/2*d*(c+d*x)^(3/2)*sqrt(a+b*x)-(c+d*x)^(5/2)*sqrt(a+b*x)/x+1/4*d*(11*b*c+a*d)*sqrt(a+b*x)*sqrt(c+d*x)/b],
[(c+d*x)^(5/2)*sqrt(a+b*x)/x^3,x,9,d^(3/2)*(5*b*c+a*d)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/sqrt(b)+1/4*(b^2*c^2-10*a*b*c*d-15*a^2*d^2)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))*sqrt(c)/a^(3/2)-1/4*(b*c+5*a*d)*(c+d*x)^(3/2)*sqrt(a+b*x)/(a*x)-1/2*(c+d*x)^(5/2)*sqrt(a+b*x)/x^2+1/4*d*(b*c+11*a*d)*sqrt(a+b*x)*sqrt(c+d*x)/a],
[(c+d*x)^(5/2)*sqrt(a+b*x)/x^4,x,9,2*d^(5/2)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))*sqrt(b)-1/8*(b^3*c^3-5*a*b^2*c^2*d+15*a^2*b*c*d^2+5*a^3*d^3)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(5/2)*sqrt(c))-1/12*(b*c+5*a*d)*(c+d*x)^(3/2)*sqrt(a+b*x)/(a*x^2)-1/3*(c+d*x)^(5/2)*sqrt(a+b*x)/x^3+1/8*(b*c-5*a*d)*(b*c+a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(a^2*x)],
[(c+d*x)^(5/2)*sqrt(a+b*x)/x^5,x,6,5/64*(b*c-a*d)^4*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(7/2)*c^(3/2))+5/96*(b*c-a*d)^2*(c+d*x)^(3/2)*sqrt(a+b*x)/(a^2*c*x^2)-1/24*(b*c-a*d)*(c+d*x)^(5/2)*sqrt(a+b*x)/(a*c*x^3)-1/4*(c+d*x)^(7/2)*sqrt(a+b*x)/(c*x^4)-5/64*(b*c-a*d)^3*sqrt(a+b*x)*sqrt(c+d*x)/(a^3*c*x)],
[(c+d*x)^(5/2)*sqrt(a+b*x)/x^6,x,7,-1/5*(a+b*x)^(3/2)*(c+d*x)^(7/2)/(a*c*x^5)-1/128*(b*c-a*d)^4*(7*b*c+3*a*d)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(9/2)*c^(5/2))-1/192*(b*c-a*d)^2*(7*b*c+3*a*d)*(c+d*x)^(3/2)*sqrt(a+b*x)/(a^3*c^2*x^2)+1/240*(b*c-a*d)*(7*b*c+3*a*d)*(c+d*x)^(5/2)*sqrt(a+b*x)/(a^2*c^2*x^3)+1/40*(7*b*c+3*a*d)*(c+d*x)^(7/2)*sqrt(a+b*x)/(a*c^2*x^4)+1/128*(b*c-a*d)^3*(7*b*c+3*a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(a^4*c^2*x)],
[(c+d*x)^(5/2)*sqrt(a+b*x)/x^7,x,9,1/512*(b*c-a*d)^4*(21*b^2*c^2+14*a*b*c*d+5*a^2*d^2)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(11/2)*c^(7/2))-1/60*(b*c+5*a*d)*(c+d*x)^(3/2)*sqrt(a+b*x)/(a*x^5)-1/6*(c+d*x)^(5/2)*sqrt(a+b*x)/x^6+1/160*(3*b^2*c^2-6*a*b*c*d-5*a^2*d^2)*sqrt(a+b*x)*sqrt(c+d*x)/(a^2*x^4)-1/960*(21*b^3*c^3-61*a*b^2*c^2*d+51*a^2*b*c*d^2+5*a^3*d^3)*sqrt(a+b*x)*sqrt(c+d*x)/(a^3*c*x^3)+1/3840*(105*b^4*c^4-308*a*b^3*c^3*d+262*a^2*b^2*c^2*d^2-20*a^3*b*c*d^3+25*a^4*d^4)*sqrt(a+b*x)*sqrt(c+d*x)/(a^4*c^2*x^2)-1/7680*(315*b^5*c^5-945*a*b^4*c^4*d+838*a^2*b^3*c^3*d^2-90*a^3*b^2*c^2*d^3-65*a^4*b*c*d^4+75*a^5*d^5)*sqrt(a+b*x)*sqrt(c+d*x)/(a^5*c^3*x)],

# n<0
[x^3*sqrt(a+b*x)/sqrt(c+d*x),x,6,1/64*(b*c-a*d)*(35*b^3*c^3+15*a*b^2*c^2*d+9*a^2*b*c*d^2+5*a^3*d^3)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(7/2)*d^(9/2))+1/4*x^2*(a+b*x)^(3/2)*sqrt(c+d*x)/(b*d)+1/96*(a+b*x)^(3/2)*(35*b^2*c^2+22*a*b*c*d+15*a^2*d^2-4*b*d*(7*b*c+5*a*d)*x)*sqrt(c+d*x)/(b^3*d^3)-1/64*(35*b^3*c^3+15*a*b^2*c^2*d+9*a^2*b*c*d^2+5*a^3*d^3)*sqrt(a+b*x)*sqrt(c+d*x)/(b^3*d^4)],
[x^2*sqrt(a+b*x)/sqrt(c+d*x),x,6,-1/8*(b*c-a*d)*(5*b^2*c^2+2*a*b*c*d+a^2*d^2)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(5/2)*d^(7/2))-1/12*(5*b*c+3*a*d)*(a+b*x)^(3/2)*sqrt(c+d*x)/(b^2*d^2)+1/3*x*(a+b*x)^(3/2)*sqrt(c+d*x)/(b*d)+1/8*(5*b^2*c^2+2*a*b*c*d+a^2*d^2)*sqrt(a+b*x)*sqrt(c+d*x)/(b^2*d^3)],
[x*sqrt(a+b*x)/sqrt(c+d*x),x,5,1/4*(b*c-a*d)*(3*b*c+a*d)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(3/2)*d^(5/2))+1/2*(a+b*x)^(3/2)*sqrt(c+d*x)/(b*d)-1/4*(3*b*c+a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(b*d^2)],
[sqrt(a+b*x)/sqrt(c+d*x),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],
[sqrt(a+b*x)/(x*sqrt(c+d*x)),x,7,-2*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))*sqrt(a)/sqrt(c)+2*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))*sqrt(b)/sqrt(d)],
[sqrt(a+b*x)/(x^2*sqrt(c+d*x)),x,3,-(b*c-a*d)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(c^(3/2)*sqrt(a))-sqrt(a+b*x)*sqrt(c+d*x)/(c*x)],
[sqrt(a+b*x)/(x^3*sqrt(c+d*x)),x,4,1/4*(b*c-a*d)*(b*c+3*a*d)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(3/2)*c^(5/2))-1/2*(a+b*x)^(3/2)*sqrt(c+d*x)/(a*c*x^2)+1/4*(b*c+3*a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(a*c^2*x)],
[sqrt(a+b*x)/(x^4*sqrt(c+d*x)),x,6,-1/8*(b*c-a*d)*(b^2*c^2+2*a*b*c*d+5*a^2*d^2)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(5/2)*c^(7/2))-1/3*sqrt(a+b*x)*sqrt(c+d*x)/(c*x^3)-1/12*(b*c-5*a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(a*c^2*x^2)+1/24*(3*b*c-5*a*d)*(b*c+3*a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(a^2*c^3*x)],
[sqrt(a+b*x)/(x^5*sqrt(c+d*x)),x,7,1/64*(b*c-a*d)*(5*b^3*c^3+9*a*b^2*c^2*d+15*a^2*b*c*d^2+35*a^3*d^3)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(7/2)*c^(9/2))-1/4*sqrt(a+b*x)*sqrt(c+d*x)/(c*x^4)-1/24*(b*c-7*a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(a*c^2*x^3)+1/96*(5*b^2*c^2+6*a*b*c*d-35*a^2*d^2)*sqrt(a+b*x)*sqrt(c+d*x)/(a^2*c^3*x^2)-1/192*(15*b^3*c^3+17*a*b^2*c^2*d+25*a^2*b*c*d^2-105*a^3*d^3)*sqrt(a+b*x)*sqrt(c+d*x)/(a^3*c^4*x)],
[x^2*sqrt(a+b*x)/(c+d*x)^(3/2),x,6,1/4*(15*b^2*c^2-6*a*b*c*d-a^2*d^2)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(3/2)*d^(7/2))+2*c^2*(a+b*x)^(3/2)/(d^2*(b*c-a*d)*sqrt(c+d*x))+1/2*(a+b*x)^(3/2)*sqrt(c+d*x)/(b*d^2)+1/4*(6*a*c-15*b*c^2/d+a^2*d/b)*sqrt(a+b*x)*sqrt(c+d*x)/(d^2*(b*c-a*d))],
[x*sqrt(a+b*x)/(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)))/(d^(5/2)*sqrt(b))-2*c*(a+b*x)^(3/2)/(d*(b*c-a*d)*sqrt(c+d*x))+(3*b*c-a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(d^2*(b*c-a*d))],
[sqrt(a+b*x)/(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))],
[sqrt(a+b*x)/(x*(c+d*x)^(3/2)),x,3,-2*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))*sqrt(a)/c^(3/2)+2*sqrt(a+b*x)/(c*sqrt(c+d*x))],
[sqrt(a+b*x)/(x^2*(c+d*x)^(3/2)),x,4,-(b*c-3*a*d)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(c^(5/2)*sqrt(a))-(a+b*x)^(3/2)/(a*c*x*sqrt(c+d*x))+(b*c-3*a*d)*sqrt(a+b*x)/(a*c^2*sqrt(c+d*x))],
[sqrt(a+b*x)/(x^3*(c+d*x)^(3/2)),x,6,1/4*(b^2*c^2+6*a*b*c*d-15*a^2*d^2)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(3/2)*c^(7/2))-1/4*d*(b*c-15*a*d)*sqrt(a+b*x)/(a*c^3*sqrt(c+d*x))-1/2*sqrt(a+b*x)/(c*x^2*sqrt(c+d*x))-1/4*(b*c-5*a*d)*sqrt(a+b*x)/(a*c^2*x*sqrt(c+d*x))],
[x^3*sqrt(a+b*x)/(c+d*x)^(5/2),x,6,1/4*(35*b^2*c^2-10*a*b*c*d-a^2*d^2)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(3/2)*d^(9/2))-2/3*x^3*sqrt(a+b*x)/(d*(c+d*x)^(3/2))-2/3*(7*b*c-6*a*d)*x^2*sqrt(a+b*x)/(d^2*(b*c-a*d)*sqrt(c+d*x))-1/12*(105*b^2*c^2-100*a*b*c*d+3*a^2*d^2-2*b*d*(35*b*c-31*a*d)*x)*sqrt(a+b*x)*sqrt(c+d*x)/(b*d^4*(b*c-a*d))],
[x^2*sqrt(a+b*x)/(c+d*x)^(5/2),x,6,2/3*c^2*(a+b*x)^(3/2)/(d^2*(b*c-a*d)*(c+d*x)^(3/2))-(5*b*c-a*d)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(d^(7/2)*sqrt(b))-4*c*(a+b*x)^(3/2)/(d^2*(b*c-a*d)*sqrt(c+d*x))+(5*b*c-a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(d^3*(b*c-a*d))],
[x*sqrt(a+b*x)/(c+d*x)^(5/2),x,5,-2/3*c*(a+b*x)^(3/2)/(d*(b*c-a*d)*(c+d*x)^(3/2))+2*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))*sqrt(b)/d^(5/2)-2*sqrt(a+b*x)/(d^2*sqrt(c+d*x))],
[sqrt(a+b*x)/(c+d*x)^(5/2),x,1,2/3*(a+b*x)^(3/2)/((b*c-a*d)*(c+d*x)^(3/2))],
[sqrt(a+b*x)/(x*(c+d*x)^(5/2)),x,4,-2/3*d*(a+b*x)^(3/2)/(c*(b*c-a*d)*(c+d*x)^(3/2))-2*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))*sqrt(a)/c^(5/2)+2*sqrt(a+b*x)/(c^2*sqrt(c+d*x))],
[sqrt(a+b*x)/(x^2*(c+d*x)^(5/2)),x,6,-(b*c-5*a*d)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(c^(7/2)*sqrt(a))-5/3*d*sqrt(a+b*x)/(c^2*(c+d*x)^(3/2))-sqrt(a+b*x)/(c*x*(c+d*x)^(3/2))-1/3*d*(13*b*c-15*a*d)*sqrt(a+b*x)/(c^3*(b*c-a*d)*sqrt(c+d*x))],
[sqrt(a+b*x)/(x^3*(c+d*x)^(5/2)),x,7,1/4*(b^2*c^2+10*a*b*c*d-35*a^2*d^2)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(3/2)*c^(9/2))-1/12*d*(3*b*c-35*a*d)*sqrt(a+b*x)/(a*c^3*(c+d*x)^(3/2))-1/2*sqrt(a+b*x)/(c*x^2*(c+d*x)^(3/2))-1/4*(b*c-7*a*d)*sqrt(a+b*x)/(a*c^2*x*(c+d*x)^(3/2))-1/12*d*(3*b^2*c^2-100*a*b*c*d+105*a^2*d^2)*sqrt(a+b*x)/(a*c^4*(b*c-a*d)*sqrt(c+d*x))],

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

# n>0
[x^2*(a+b*x)^(3/2)*sqrt(c+d*x),x,8,-1/40*(7*b*c+5*a*d)*(a+b*x)^(5/2)*(c+d*x)^(3/2)/(b^2*d^2)+1/5*x*(a+b*x)^(5/2)*(c+d*x)^(3/2)/(b*d)+1/128*(b*c-a*d)^3*(7*b^2*c^2+6*a*b*c*d+3*a^2*d^2)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(7/2)*d^(9/2))+1/192*(b*c-a*d)*(7*b^2*c^2+6*a*b*c*d+3*a^2*d^2)*(a+b*x)^(3/2)*sqrt(c+d*x)/(b^3*d^3)+1/48*(7*b^2*c^2+6*a*b*c*d+3*a^2*d^2)*(a+b*x)^(5/2)*sqrt(c+d*x)/(b^3*d^2)-1/128*(b*c-a*d)^2*(7*b^2*c^2+6*a*b*c*d+3*a^2*d^2)*sqrt(a+b*x)*sqrt(c+d*x)/(b^3*d^4)],
[x*(a+b*x)^(3/2)*sqrt(c+d*x),x,7,1/4*(a+b*x)^(5/2)*(c+d*x)^(3/2)/(b*d)-1/64*(b*c-a*d)^3*(5*b*c+3*a*d)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(5/2)*d^(7/2))-1/96*(b*c-a*d)*(5*b*c+3*a*d)*(a+b*x)^(3/2)*sqrt(c+d*x)/(b^2*d^2)-1/24*(5*b*c+3*a*d)*(a+b*x)^(5/2)*sqrt(c+d*x)/(b^2*d)+1/64*(b*c-a*d)^2*(5*b*c+3*a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(b^2*d^3)],
[(a+b*x)^(3/2)*sqrt(c+d*x),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)^(3/2)*sqrt(c+d*x)/x,x,8,-1/4*(b^2*c^2-6*a*b*c*d-3*a^2*d^2)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(d^(3/2)*sqrt(b))-2*a^(3/2)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))*sqrt(c)+1/2*(a+b*x)^(3/2)*sqrt(c+d*x)+1/4*(b*c+3*a*d)*sqrt(a+b*x)*sqrt(c+d*x)/d],
[(a+b*x)^(3/2)*sqrt(c+d*x)/x^2,x,8,-(3*b*c+a*d)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))*sqrt(a)/sqrt(c)+(b*c+3*a*d)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))*sqrt(b)/sqrt(d)-(a+b*x)^(3/2)*sqrt(c+d*x)/x+2*b*sqrt(a+b*x)*sqrt(c+d*x)],
[(a+b*x)^(3/2)*sqrt(c+d*x)/x^3,x,8,-1/4*(3*b^2*c^2+6*a*b*c*d-a^2*d^2)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(c^(3/2)*sqrt(a))+2*b^(3/2)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))*sqrt(d)-1/2*(a+b*x)^(3/2)*sqrt(c+d*x)/x^2-1/4*(3*b*c+a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(c*x)],
[(a+b*x)^(3/2)*sqrt(c+d*x)/x^4,x,5,-1/3*(a+b*x)^(3/2)*(c+d*x)^(3/2)/(c*x^3)+1/8*(b*c-a*d)^3*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(3/2)*c^(5/2))-1/4*(b*c-a*d)*(c+d*x)^(3/2)*sqrt(a+b*x)/(c^2*x^2)-1/8*(b*c-a*d)^2*sqrt(a+b*x)*sqrt(c+d*x)/(a*c^2*x)],
[(a+b*x)^(3/2)*sqrt(c+d*x)/x^5,x,6,1/24*(3*b*c+5*a*d)*(a+b*x)^(3/2)*(c+d*x)^(3/2)/(a*c^2*x^3)-1/4*(a+b*x)^(5/2)*(c+d*x)^(3/2)/(a*c*x^4)-1/64*(b*c-a*d)^3*(3*b*c+5*a*d)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(5/2)*c^(7/2))+1/32*(b*c-a*d)*(3*b*c+5*a*d)*(c+d*x)^(3/2)*sqrt(a+b*x)/(a*c^3*x^2)+1/64*(b*c-a*d)^2*(3*b*c+5*a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(a^2*c^3*x)],
[(a+b*x)^(3/2)*sqrt(c+d*x)/x^6,x,8,1/128*(b*c-a*d)^3*(3*b^2*c^2+6*a*b*c*d+7*a^2*d^2)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(7/2)*c^(9/2))-1/5*(a+b*x)^(3/2)*sqrt(c+d*x)/x^5-1/40*(3*b*c+a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(c*x^4)-1/240*(3*b^2*c/a+12*b*d-7*a*d^2/c)*sqrt(a+b*x)*sqrt(c+d*x)/(c*x^3)+1/960*(15*b^3*c^3-9*a*b^2*c^2*d+61*a^2*b*c*d^2-35*a^3*d^3)*sqrt(a+b*x)*sqrt(c+d*x)/(a^2*c^3*x^2)-1/1920*(45*b^4*c^4-30*a*b^3*c^3*d-36*a^2*b^2*c^2*d^2+190*a^3*b*c*d^3-105*a^4*d^4)*sqrt(a+b*x)*sqrt(c+d*x)/(a^3*c^4*x)],
[x^2*(a+b*x)^(3/2)*(c+d*x)^(3/2),x,9,-1/96*(4*a*b*c*d-7*(b*c+a*d)^2)*(a+b*x)^(5/2)*(c+d*x)^(3/2)/(b^3*d^2)-7/60*(b*c+a*d)*(a+b*x)^(5/2)*(c+d*x)^(5/2)/(b^2*d^2)+1/6*x*(a+b*x)^(5/2)*(c+d*x)^(5/2)/(b*d)-1/512*(b*c-a*d)^4*(4*a*b*c*d-7*(b*c+a*d)^2)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(9/2)*d^(9/2))-1/768*(b*c-a*d)^2*(4*a*b*c*d-7*(b*c+a*d)^2)*(a+b*x)^(3/2)*sqrt(c+d*x)/(b^4*d^3)-1/192*(b*c-a*d)*(4*a*b*c*d-7*(b*c+a*d)^2)*(a+b*x)^(5/2)*sqrt(c+d*x)/(b^4*d^2)+1/512*(b*c-a*d)^3*(4*a*b*c*d-7*(b*c+a*d)^2)*sqrt(a+b*x)*sqrt(c+d*x)/(b^4*d^4)],
[x*(a+b*x)^(3/2)*(c+d*x)^(3/2),x,8,-1/8*(b*c+a*d)*(a+b*x)^(5/2)*(c+d*x)^(3/2)/(b^2*d)+1/5*(a+b*x)^(5/2)*(c+d*x)^(5/2)/(b*d)-3/128*(b*c-a*d)^4*(b*c+a*d)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(7/2)*d^(7/2))-1/64*(b*c-a*d)^2*(b*c+a*d)*(a+b*x)^(3/2)*sqrt(c+d*x)/(b^3*d^2)-1/16*(b*c-a*d)*(b*c+a*d)*(a+b*x)^(5/2)*sqrt(c+d*x)/(b^3*d)+3/128*(b*c-a*d)^3*(b*c+a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(b^3*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)^(3/2)*(c+d*x)^(3/2)/x,x,9,1/3*(a+b*x)^(3/2)*(c+d*x)^(3/2)-2*a^(3/2)*c^(3/2)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))-1/8*(b*c+a*d)*(b^2*c^2-10*a*b*c*d+a^2*d^2)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(3/2)*d^(3/2))+1/4*(b*c+a*d)*(c+d*x)^(3/2)*sqrt(a+b*x)/d+1/8*(8*a*c-b*c^2/d+a^2*d/b)*sqrt(a+b*x)*sqrt(c+d*x)],
[(a+b*x)^(3/2)*(c+d*x)^(3/2)/x^2,x,9,-(a+b*x)^(3/2)*(c+d*x)^(3/2)/x-3*(b*c+a*d)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))*sqrt(a)*sqrt(c)+3/4*(b^2*c^2+6*a*b*c*d+a^2*d^2)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(sqrt(b)*sqrt(d))+3/2*b*(c+d*x)^(3/2)*sqrt(a+b*x)+3/4*(b*c+3*a*d)*sqrt(a+b*x)*sqrt(c+d*x)],
[(a+b*x)^(3/2)*(c+d*x)^(3/2)/x^3,x,9,-1/2*(a+b*x)^(3/2)*(c+d*x)^(3/2)/x^2-3/4*(b^2*c^2+6*a*b*c*d+a^2*d^2)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(sqrt(a)*sqrt(c))+3*(b*c+a*d)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))*sqrt(b)*sqrt(d)-3/4*(b*c+a*d)*(c+d*x)^(3/2)*sqrt(a+b*x)/(c*x)+3/4*d*(3*b*c+a*d)*sqrt(a+b*x)*sqrt(c+d*x)/c],
[(a+b*x)^(3/2)*(c+d*x)^(3/2)/x^4,x,9,-1/3*(a+b*x)^(3/2)*(c+d*x)^(3/2)/x^3+1/8*(b*c+a*d)*(b^2*c^2-10*a*b*c*d+a^2*d^2)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(3/2)*c^(3/2))+2*b^(3/2)*d^(3/2)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))-1/4*(b*c+a*d)*(c+d*x)^(3/2)*sqrt(a+b*x)/(c*x^2)-1/8*(b^2*c/a+8*b*d-a*d^2/c)*sqrt(a+b*x)*sqrt(c+d*x)/x],
[(a+b*x)^(3/2)*(c+d*x)^(3/2)/x^5,x,6,-1/4*(a+b*x)^(3/2)*(c+d*x)^(5/2)/(c*x^4)-3/64*(b*c-a*d)^4*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(5/2)*c^(5/2))-1/32*(b*c-a*d)^2*(c+d*x)^(3/2)*sqrt(a+b*x)/(a*c^2*x^2)-1/8*(b*c-a*d)*(c+d*x)^(5/2)*sqrt(a+b*x)/(c^2*x^3)+3/64*(b*c-a*d)^3*sqrt(a+b*x)*sqrt(c+d*x)/(a^2*c^2*x)],
[(a+b*x)^(3/2)*(c+d*x)^(3/2)/x^6,x,7,1/8*(b*c+a*d)*(a+b*x)^(3/2)*(c+d*x)^(5/2)/(a*c^2*x^4)-1/5*(a+b*x)^(5/2)*(c+d*x)^(5/2)/(a*c*x^5)+3/128*(b*c-a*d)^4*(b*c+a*d)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(7/2)*c^(7/2))+1/64*(b*c-a*d)^2*(b*c+a*d)*(c+d*x)^(3/2)*sqrt(a+b*x)/(a^2*c^3*x^2)+1/16*(b*c-a*d)*(b*c+a*d)*(c+d*x)^(5/2)*sqrt(a+b*x)/(a*c^3*x^3)-3/128*(b*c-a*d)^3*(b*c+a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(a^3*c^3*x)],
[x^2*(a+b*x)^(3/2)*(c+d*x)^(5/2),x,10,1/192*(b*c-a*d)*(5*b^2*c^2+10*a*b*c*d+9*a^2*d^2)*(a+b*x)^(5/2)*(c+d*x)^(3/2)/(b^4*d^2)+1/120*(5*b^2*c^2+10*a*b*c*d+9*a^2*d^2)*(a+b*x)^(5/2)*(c+d*x)^(5/2)/(b^3*d^2)-1/84*(7*b*c+9*a*d)*(a+b*x)^(5/2)*(c+d*x)^(7/2)/(b^2*d^2)+1/7*x*(a+b*x)^(5/2)*(c+d*x)^(7/2)/(b*d)+1/1024*(b*c-a*d)^5*(5*b^2*c^2+10*a*b*c*d+9*a^2*d^2)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(11/2)*d^(9/2))+1/1536*(b*c-a*d)^3*(5*b^2*c^2+10*a*b*c*d+9*a^2*d^2)*(a+b*x)^(3/2)*sqrt(c+d*x)/(b^5*d^3)+1/384*(b*c-a*d)^2*(5*b^2*c^2+10*a*b*c*d+9*a^2*d^2)*(a+b*x)^(5/2)*sqrt(c+d*x)/(b^5*d^2)-1/1024*(b*c-a*d)^4*(5*b^2*c^2+10*a*b*c*d+9*a^2*d^2)*sqrt(a+b*x)*sqrt(c+d*x)/(b^5*d^4)],
[x*(a+b*x)^(3/2)*(c+d*x)^(5/2),x,9,-1/96*(b*c-a*d)*(5*b*c+7*a*d)*(a+b*x)^(5/2)*(c+d*x)^(3/2)/(b^3*d)-1/60*(5*b*c+7*a*d)*(a+b*x)^(5/2)*(c+d*x)^(5/2)/(b^2*d)+1/6*(a+b*x)^(5/2)*(c+d*x)^(7/2)/(b*d)-1/512*(b*c-a*d)^5*(5*b*c+7*a*d)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(9/2)*d^(7/2))-1/768*(b*c-a*d)^3*(5*b*c+7*a*d)*(a+b*x)^(3/2)*sqrt(c+d*x)/(b^4*d^2)-1/192*(b*c-a*d)^2*(5*b*c+7*a*d)*(a+b*x)^(5/2)*sqrt(c+d*x)/(b^4*d)+1/512*(b*c-a*d)^4*(5*b*c+7*a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(b^4*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)^(3/2)*(c+d*x)^(5/2)/x,x,10,1/4*(a+b*x)^(3/2)*(c+d*x)^(5/2)-2*a^(3/2)*c^(5/2)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))-1/64*(5*b^4*c^4-60*a*b^3*c^3*d-90*a^2*b^2*c^2*d^2+20*a^3*b*c*d^3-3*a^4*d^4)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(5/2)*d^(3/2))+1/96*(50*a*c-5*b*c^2/d+3*a^2*d/b)*(c+d*x)^(3/2)*sqrt(a+b*x)+1/24*(5*b*c+3*a*d)*(c+d*x)^(5/2)*sqrt(a+b*x)/d-1/64*(5*b^3*c^3-55*a*b^2*c^2*d-17*a^2*b*c*d^2+3*a^3*d^3)*sqrt(a+b*x)*sqrt(c+d*x)/(b^2*d)],
[(a+b*x)^(3/2)*(c+d*x)^(5/2)/x^2,x,10,-(a+b*x)^(3/2)*(c+d*x)^(5/2)/x-c^(3/2)*(3*b*c+5*a*d)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))*sqrt(a)+1/8*(5*b^3*c^3+45*a*b^2*c^2*d+15*a^2*b*c*d^2-a^3*d^3)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(3/2)*sqrt(d))+1/12*(5*b*c+19*a*d)*(c+d*x)^(3/2)*sqrt(a+b*x)+4/3*b*(c+d*x)^(5/2)*sqrt(a+b*x)+1/8*(5*b^2*c^2+26*a*b*c*d+a^2*d^2)*sqrt(a+b*x)*sqrt(c+d*x)/b],
[(a+b*x)^(3/2)*(c+d*x)^(5/2)/x^3,x,10,-1/2*(a+b*x)^(3/2)*(c+d*x)^(5/2)/x^2-3/4*(b^2*c^2+10*a*b*c*d+5*a^2*d^2)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))*sqrt(c)/sqrt(a)+3/4*(5*b^2*c^2+10*a*b*c*d+a^2*d^2)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))*sqrt(d)/sqrt(b)+1/4*d*(7*b*c+5*a*d)*(c+d*x)^(3/2)*sqrt(a+b*x)/c-1/4*(3*b*c+5*a*d)*(c+d*x)^(5/2)*sqrt(a+b*x)/(c*x)+3*d*(b*c+a*d)*sqrt(a+b*x)*sqrt(c+d*x)],
[(a+b*x)^(3/2)*(c+d*x)^(5/2)/x^4,x,10,-1/3*(a+b*x)^(3/2)*(c+d*x)^(5/2)/x^3+d^(3/2)*(5*b*c+3*a*d)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))*sqrt(b)+1/8*(b^3*c^3-15*a*b^2*c^2*d-45*a^2*b*c*d^2-5*a^3*d^3)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(3/2)*sqrt(c))-1/24*(3*b^2*c/a+40*b*d+5*a*d^2/c)*(c+d*x)^(3/2)*sqrt(a+b*x)/x-1/12*(3*b*c+5*a*d)*(c+d*x)^(5/2)*sqrt(a+b*x)/(c*x^2)+1/8*d*(b^2*c^2+26*a*b*c*d+5*a^2*d^2)*sqrt(a+b*x)*sqrt(c+d*x)/(a*c)],
[(a+b*x)^(3/2)*(c+d*x)^(5/2)/x^5,x,10,-1/4*(a+b*x)^(3/2)*(c+d*x)^(5/2)/x^4-1/64*(3*b^4*c^4-20*a*b^3*c^3*d+90*a^2*b^2*c^2*d^2+60*a^3*b*c*d^3-5*a^4*d^4)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(5/2)*c^(3/2))+2*b^(3/2)*d^(5/2)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))-1/96*(3*b^2*c/a+50*b*d-5*a*d^2/c)*(c+d*x)^(3/2)*sqrt(a+b*x)/x^2-1/24*(3*b*c+5*a*d)*(c+d*x)^(5/2)*sqrt(a+b*x)/(c*x^3)+1/64*(3*b^3*c^3-17*a*b^2*c^2*d-55*a^2*b*c*d^2+5*a^3*d^3)*sqrt(a+b*x)*sqrt(c+d*x)/(a^2*c*x)],
[(a+b*x)^(3/2)*(c+d*x)^(5/2)/x^6,x,7,-1/5*(a+b*x)^(3/2)*(c+d*x)^(7/2)/(c*x^5)+3/128*(b*c-a*d)^5*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(7/2)*c^(5/2))+1/64*(b*c-a*d)^3*(c+d*x)^(3/2)*sqrt(a+b*x)/(a^2*c^2*x^2)-1/80*(b*c-a*d)^2*(c+d*x)^(5/2)*sqrt(a+b*x)/(a*c^2*x^3)-3/40*(b*c-a*d)*(c+d*x)^(7/2)*sqrt(a+b*x)/(c^2*x^4)-3/128*(b*c-a*d)^4*sqrt(a+b*x)*sqrt(c+d*x)/(a^3*c^2*x)],
[(a+b*x)^(3/2)*(c+d*x)^(5/2)/x^7,x,8,1/60*(7*b*c+5*a*d)*(a+b*x)^(3/2)*(c+d*x)^(7/2)/(a*c^2*x^5)-1/6*(a+b*x)^(5/2)*(c+d*x)^(7/2)/(a*c*x^6)-1/512*(b*c-a*d)^5*(7*b*c+5*a*d)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(9/2)*c^(7/2))-1/768*(b*c-a*d)^3*(7*b*c+5*a*d)*(c+d*x)^(3/2)*sqrt(a+b*x)/(a^3*c^3*x^2)+1/960*(b*c-a*d)^2*(7*b*c+5*a*d)*(c+d*x)^(5/2)*sqrt(a+b*x)/(a^2*c^3*x^3)+1/160*(b*c-a*d)*(7*b*c+5*a*d)*(c+d*x)^(7/2)*sqrt(a+b*x)/(a*c^3*x^4)+1/512*(b*c-a*d)^4*(7*b*c+5*a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(a^4*c^3*x)],

# n<0
[x^2*(a+b*x)^(3/2)/sqrt(c+d*x),x,7,1/64*(b*c-a*d)^2*(35*b^2*c^2+10*a*b*c*d+3*a^2*d^2)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(5/2)*d^(9/2))+1/96*(35*b^2*c^2+10*a*b*c*d+3*a^2*d^2)*(a+b*x)^(3/2)*sqrt(c+d*x)/(b^2*d^3)-1/24*(7*b*c+3*a*d)*(a+b*x)^(5/2)*sqrt(c+d*x)/(b^2*d^2)+1/4*x*(a+b*x)^(5/2)*sqrt(c+d*x)/(b*d)-1/64*(b*c-a*d)*(35*b^2*c^2+10*a*b*c*d+3*a^2*d^2)*sqrt(a+b*x)*sqrt(c+d*x)/(b^2*d^4)],
[x*(a+b*x)^(3/2)/sqrt(c+d*x),x,6,-1/8*(b*c-a*d)^2*(5*b*c+a*d)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(3/2)*d^(7/2))-1/12*(5*b*c+a*d)*(a+b*x)^(3/2)*sqrt(c+d*x)/(b*d^2)+1/3*(a+b*x)^(5/2)*sqrt(c+d*x)/(b*d)+1/8*(b*c-a*d)*(5*b*c+a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(b*d^3)],
[(a+b*x)^(3/2)/sqrt(c+d*x),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)^(3/2)/(x*sqrt(c+d*x)),x,7,-(b*c-3*a*d)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))*sqrt(b)/d^(3/2)-2*a^(3/2)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/sqrt(c)+b*sqrt(a+b*x)*sqrt(c+d*x)/d],
[(a+b*x)^(3/2)/(x^2*sqrt(c+d*x)),x,7,-(3*b*c-a*d)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))*sqrt(a)/c^(3/2)+2*b^(3/2)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/sqrt(d)-a*sqrt(a+b*x)*sqrt(c+d*x)/(c*x)],
[(a+b*x)^(3/2)/(x^3*sqrt(c+d*x)),x,4,-3/4*(b*c-a*d)^2*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(c^(5/2)*sqrt(a))-1/2*(a+b*x)^(3/2)*sqrt(c+d*x)/(c*x^2)-3/4*(b*c-a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(c^2*x)],
[(a+b*x)^(3/2)/(x^4*sqrt(c+d*x)),x,5,1/8*(b*c-a*d)^2*(b*c+5*a*d)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(3/2)*c^(7/2))+1/12*(b*c+5*a*d)*(a+b*x)^(3/2)*sqrt(c+d*x)/(a*c^2*x^2)-1/3*(a+b*x)^(5/2)*sqrt(c+d*x)/(a*c*x^3)+1/8*(b*c-a*d)*(b*c+5*a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(a*c^3*x)],
[(a+b*x)^(3/2)/(x^5*sqrt(c+d*x)),x,7,-1/64*(b*c-a*d)^2*(3*b^2*c^2+10*a*b*c*d+35*a^2*d^2)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(5/2)*c^(9/2))-1/4*a*sqrt(a+b*x)*sqrt(c+d*x)/(c*x^4)-1/24*(9*b*c-7*a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(c^2*x^3)-1/96*(3*b^2*c^2-46*a*b*c*d+35*a^2*d^2)*sqrt(a+b*x)*sqrt(c+d*x)/(a*c^3*x^2)+1/192*(9*b^3*c^3+15*a*b^2*c^2*d-145*a^2*b*c*d^2+105*a^3*d^3)*sqrt(a+b*x)*sqrt(c+d*x)/(a^2*c^4*x)],
[x^2*(a+b*x)^(3/2)/(c+d*x)^(3/2),x,7,-1/8*(b*c-a*d)*(35*b^2*c^2-10*a*b*c*d-a^2*d^2)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(3/2)*d^(9/2))+2*c^2*(a+b*x)^(5/2)/(d^2*(b*c-a*d)*sqrt(c+d*x))+1/12*(10*a*c-35*b*c^2/d+a^2*d/b)*(a+b*x)^(3/2)*sqrt(c+d*x)/(d^2*(b*c-a*d))+1/3*(a+b*x)^(5/2)*sqrt(c+d*x)/(b*d^2)+1/8*(35*b^2*c^2-10*a*b*c*d-a^2*d^2)*sqrt(a+b*x)*sqrt(c+d*x)/(b*d^4)],
[x*(a+b*x)^(3/2)/(c+d*x)^(3/2),x,6,3/4*(b*c-a*d)*(5*b*c-a*d)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(d^(7/2)*sqrt(b))-2*c*(a+b*x)^(5/2)/(d*(b*c-a*d)*sqrt(c+d*x))+1/2*(5*b*c-a*d)*(a+b*x)^(3/2)*sqrt(c+d*x)/(d^2*(b*c-a*d))-3/4*(5*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)^(3/2)/(x*(c+d*x)^(3/2)),x,7,-2*a^(3/2)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/c^(3/2)+2*b^(3/2)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/d^(3/2)-2*(b*c-a*d)*sqrt(a+b*x)/(c*d*sqrt(c+d*x))],
[(a+b*x)^(3/2)/(x^2*(c+d*x)^(3/2)),x,4,-3*(b*c-a*d)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))*sqrt(a)/c^(5/2)-(a+b*x)^(3/2)/(c*x*sqrt(c+d*x))+3*(b*c-a*d)*sqrt(a+b*x)/(c^2*sqrt(c+d*x))],
[(a+b*x)^(3/2)/(x^3*(c+d*x)^(3/2)),x,5,-3/4*(b*c-5*a*d)*(b*c-a*d)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(c^(7/2)*sqrt(a))-1/4*(b*c-5*a*d)*(a+b*x)^(3/2)/(a*c^2*x*sqrt(c+d*x))-1/2*(a+b*x)^(5/2)/(a*c*x^2*sqrt(c+d*x))+3/4*(b*c-5*a*d)*(b*c-a*d)*sqrt(a+b*x)/(a*c^3*sqrt(c+d*x))],
[(a+b*x)^(3/2)/(x^4*(c+d*x)^(3/2)),x,7,1/8*(b*c-a*d)*(b^2*c^2+10*a*b*c*d-35*a^2*d^2)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(3/2)*c^(9/2))-1/24*d*(3*b^2*c^2-100*a*b*c*d+105*a^2*d^2)*sqrt(a+b*x)/(a*c^4*sqrt(c+d*x))-1/3*a*sqrt(a+b*x)/(c*x^3*sqrt(c+d*x))-7/12*(b*c-a*d)*sqrt(a+b*x)/(c^2*x^2*sqrt(c+d*x))-1/24*(3*b*c-35*a*d)*(b*c-a*d)*sqrt(a+b*x)/(a*c^3*x*sqrt(c+d*x))],
[x^2*(a+b*x)^(3/2)/(c+d*x)^(5/2),x,7,2/3*c^2*(a+b*x)^(5/2)/(d^2*(b*c-a*d)*(c+d*x)^(3/2))+1/4*(35*b^2*c^2-30*a*b*c*d+3*a^2*d^2)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(d^(9/2)*sqrt(b))-4/3*c*(4*b*c-3*a*d)*(a+b*x)^(5/2)/(d^2*(b*c-a*d)^2*sqrt(c+d*x))+1/6*(35*b^2*c^2-30*a*b*c*d+3*a^2*d^2)*(a+b*x)^(3/2)*sqrt(c+d*x)/(d^3*(b*c-a*d)^2)-1/4*(35*b^2*c^2-30*a*b*c*d+3*a^2*d^2)*sqrt(a+b*x)*sqrt(c+d*x)/(d^4*(b*c-a*d))],
[x*(a+b*x)^(3/2)/(c+d*x)^(5/2),x,6,-2/3*c*(a+b*x)^(5/2)/(d*(b*c-a*d)*(c+d*x)^(3/2))-(5*b*c-3*a*d)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))*sqrt(b)/d^(7/2)-2/3*(5*b*c-3*a*d)*(a+b*x)^(3/2)/(d^2*(b*c-a*d)*sqrt(c+d*x))+b*(5*b*c-3*a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(d^3*(b*c-a*d))],
[(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)^(3/2)/(x*(c+d*x)^(5/2)),x,4,2/3*(a+b*x)^(3/2)/(c*(c+d*x)^(3/2))-2*a^(3/2)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/c^(5/2)+2*a*sqrt(a+b*x)/(c^2*sqrt(c+d*x))],
[(a+b*x)^(3/2)/(x^2*(c+d*x)^(5/2)),x,5,1/3*(3*b*c-5*a*d)*(a+b*x)^(3/2)/(a*c^2*(c+d*x)^(3/2))-(a+b*x)^(5/2)/(a*c*x*(c+d*x)^(3/2))-(3*b*c-5*a*d)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))*sqrt(a)/c^(7/2)+(3*b*c-5*a*d)*sqrt(a+b*x)/(c^3*sqrt(c+d*x))],
[(a+b*x)^(3/2)/(x^3*(c+d*x)^(5/2)),x,7,-1/4*(3*b^2*c^2-30*a*b*c*d+35*a^2*d^2)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(c^(9/2)*sqrt(a))-1/12*d*(23*b*c-35*a*d)*sqrt(a+b*x)/(c^3*(c+d*x)^(3/2))-1/2*a*sqrt(a+b*x)/(c*x^2*(c+d*x)^(3/2))-1/4*(5*b*c-7*a*d)*sqrt(a+b*x)/(c^2*x*(c+d*x)^(3/2))-5/12*d*(11*b*c-21*a*d)*sqrt(a+b*x)/(c^4*sqrt(c+d*x))],

# Integrands of the form x^m (c+d x)^(n/2) (a+b x)^(5/2)

# n>0
[x^2*(a+b*x)^(5/2)*sqrt(c+d*x),x,9,-1/60*(9*b*c+5*a*d)*(a+b*x)^(7/2)*(c+d*x)^(3/2)/(b^2*d^2)+1/6*x*(a+b*x)^(7/2)*(c+d*x)^(3/2)/(b*d)-1/512*(b*c-a*d)^4*(21*b^2*c^2+14*a*b*c*d+5*a^2*d^2)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(7/2)*d^(11/2))-1/768*(b*c-a*d)^2*(21*b^2*c^2+14*a*b*c*d+5*a^2*d^2)*(a+b*x)^(3/2)*sqrt(c+d*x)/(b^3*d^4)+1/960*(b*c-a*d)*(21*b^2*c^2+14*a*b*c*d+5*a^2*d^2)*(a+b*x)^(5/2)*sqrt(c+d*x)/(b^3*d^3)+1/160*(21*b^2*c^2+14*a*b*c*d+5*a^2*d^2)*(a+b*x)^(7/2)*sqrt(c+d*x)/(b^3*d^2)+1/512*(b*c-a*d)^3*(21*b^2*c^2+14*a*b*c*d+5*a^2*d^2)*sqrt(a+b*x)*sqrt(c+d*x)/(b^3*d^5)],
[x*(a+b*x)^(5/2)*sqrt(c+d*x),x,8,1/5*(a+b*x)^(7/2)*(c+d*x)^(3/2)/(b*d)+1/128*(b*c-a*d)^4*(7*b*c+3*a*d)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(5/2)*d^(9/2))+1/192*(b*c-a*d)^2*(7*b*c+3*a*d)*(a+b*x)^(3/2)*sqrt(c+d*x)/(b^2*d^3)-1/240*(b*c-a*d)*(7*b*c+3*a*d)*(a+b*x)^(5/2)*sqrt(c+d*x)/(b^2*d^2)-1/40*(7*b*c+3*a*d)*(a+b*x)^(7/2)*sqrt(c+d*x)/(b^2*d)-1/128*(b*c-a*d)^3*(7*b*c+3*a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(b^2*d^4)],
[(a+b*x)^(5/2)*sqrt(c+d*x),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)^(5/2)*sqrt(c+d*x)/x,x,9,1/8*(b^3*c^3-5*a*b^2*c^2*d+15*a^2*b*c*d^2+5*a^3*d^3)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(d^(5/2)*sqrt(b))-2*a^(5/2)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))*sqrt(c)+1/12*(b*c+5*a*d)*(a+b*x)^(3/2)*sqrt(c+d*x)/d+1/3*(a+b*x)^(5/2)*sqrt(c+d*x)-1/8*(b*c-5*a*d)*(b*c+a*d)*sqrt(a+b*x)*sqrt(c+d*x)/d^2],
[(a+b*x)^(5/2)*sqrt(c+d*x)/x^2,x,9,-1/4*(b^2*c^2-10*a*b*c*d-15*a^2*d^2)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))*sqrt(b)/d^(3/2)-a^(3/2)*(5*b*c+a*d)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/sqrt(c)+3/2*b*(a+b*x)^(3/2)*sqrt(c+d*x)-(a+b*x)^(5/2)*sqrt(c+d*x)/x+1/4*b*(b*c+11*a*d)*sqrt(a+b*x)*sqrt(c+d*x)/d],
[(a+b*x)^(5/2)*sqrt(c+d*x)/x^3,x,9,-1/4*(15*b^2*c^2+10*a*b*c*d-a^2*d^2)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))*sqrt(a)/c^(3/2)+b^(3/2)*(b*c+5*a*d)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/sqrt(d)-1/4*(5*b*c+a*d)*(a+b*x)^(3/2)*sqrt(c+d*x)/(c*x)-1/2*(a+b*x)^(5/2)*sqrt(c+d*x)/x^2+1/4*b*(11*b*c+a*d)*sqrt(a+b*x)*sqrt(c+d*x)/c],
[(a+b*x)^(5/2)*sqrt(c+d*x)/x^4,x,9,-1/8*(5*b^3*c^3+15*a*b^2*c^2*d-5*a^2*b*c*d^2+a^3*d^3)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(c^(5/2)*sqrt(a))+2*b^(5/2)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))*sqrt(d)-1/12*(5*b*c+a*d)*(a+b*x)^(3/2)*sqrt(c+d*x)/(c*x^2)-1/3*(a+b*x)^(5/2)*sqrt(c+d*x)/x^3-1/8*(5*b*c-a*d)*(b*c+a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(c^2*x)],
[(a+b*x)^(5/2)*sqrt(c+d*x)/x^5,x,6,-5/24*(b*c-a*d)*(a+b*x)^(3/2)*(c+d*x)^(3/2)/(c^2*x^3)-1/4*(a+b*x)^(5/2)*(c+d*x)^(3/2)/(c*x^4)+5/64*(b*c-a*d)^4*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(3/2)*c^(7/2))-5/32*(b*c-a*d)^2*(c+d*x)^(3/2)*sqrt(a+b*x)/(c^3*x^2)-5/64*(b*c-a*d)^3*sqrt(a+b*x)*sqrt(c+d*x)/(a*c^3*x)],
[(a+b*x)^(5/2)*sqrt(c+d*x)/x^6,x,7,1/48*(b*c-a*d)*(3*b*c+7*a*d)*(a+b*x)^(3/2)*(c+d*x)^(3/2)/(a*c^3*x^3)+1/40*(3*b*c+7*a*d)*(a+b*x)^(5/2)*(c+d*x)^(3/2)/(a*c^2*x^4)-1/5*(a+b*x)^(7/2)*(c+d*x)^(3/2)/(a*c*x^5)-1/128*(b*c-a*d)^4*(3*b*c+7*a*d)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(5/2)*c^(9/2))+1/64*(b*c-a*d)^2*(3*b*c+7*a*d)*(c+d*x)^(3/2)*sqrt(a+b*x)/(a*c^4*x^2)+1/128*(b*c-a*d)^3*(3*b*c+7*a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(a^2*c^4*x)],
[x^2*(a+b*x)^(5/2)*(c+d*x)^(3/2),x,10,1/120*(9*b^2*c^2+10*a*b*c*d+5*a^2*d^2)*(a+b*x)^(7/2)*(c+d*x)^(3/2)/(b^3*d^2)-1/84*(9*b*c+7*a*d)*(a+b*x)^(7/2)*(c+d*x)^(5/2)/(b^2*d^2)+1/7*x*(a+b*x)^(7/2)*(c+d*x)^(5/2)/(b*d)-1/1024*(b*c-a*d)^5*(9*b^2*c^2+10*a*b*c*d+5*a^2*d^2)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(9/2)*d^(11/2))-1/1536*(b*c-a*d)^3*(9*b^2*c^2+10*a*b*c*d+5*a^2*d^2)*(a+b*x)^(3/2)*sqrt(c+d*x)/(b^4*d^4)+1/1920*(b*c-a*d)^2*(9*b^2*c^2+10*a*b*c*d+5*a^2*d^2)*(a+b*x)^(5/2)*sqrt(c+d*x)/(b^4*d^3)+1/320*(b*c-a*d)*(9*b^2*c^2+10*a*b*c*d+5*a^2*d^2)*(a+b*x)^(7/2)*sqrt(c+d*x)/(b^4*d^2)+1/1024*(b*c-a*d)^4*(9*b^2*c^2+10*a*b*c*d+5*a^2*d^2)*sqrt(a+b*x)*sqrt(c+d*x)/(b^4*d^5)],
[x*(a+b*x)^(5/2)*(c+d*x)^(3/2),x,9,-1/60*(7*b*c+5*a*d)*(a+b*x)^(7/2)*(c+d*x)^(3/2)/(b^2*d)+1/6*(a+b*x)^(7/2)*(c+d*x)^(5/2)/(b*d)+1/512*(b*c-a*d)^5*(7*b*c+5*a*d)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(7/2)*d^(9/2))+1/768*(b*c-a*d)^3*(7*b*c+5*a*d)*(a+b*x)^(3/2)*sqrt(c+d*x)/(b^3*d^3)-1/960*(b*c-a*d)^2*(7*b*c+5*a*d)*(a+b*x)^(5/2)*sqrt(c+d*x)/(b^3*d^2)-1/160*(b*c-a*d)*(7*b*c+5*a*d)*(a+b*x)^(7/2)*sqrt(c+d*x)/(b^3*d)-1/512*(b*c-a*d)^4*(7*b*c+5*a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(b^3*d^4)],
[(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)^(5/2)*(c+d*x)^(3/2)/x,x,10,1/24*(3*b*c+5*a*d)*(a+b*x)^(3/2)*(c+d*x)^(3/2)/d+1/4*(a+b*x)^(5/2)*(c+d*x)^(3/2)-2*a^(5/2)*c^(3/2)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))+1/64*(3*b^4*c^4-20*a*b^3*c^3*d+90*a^2*b^2*c^2*d^2+60*a^3*b*c*d^3-5*a^4*d^4)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(3/2)*d^(5/2))-1/32*(b*c-5*a*d)*(3*b*c+a*d)*(c+d*x)^(3/2)*sqrt(a+b*x)/d^2+1/64*(64*a^2*b*c*d^2+(b*c-5*a*d)*(b*c-a*d)*(3*b*c+a*d))*sqrt(a+b*x)*sqrt(c+d*x)/(b*d^2)],
[(a+b*x)^(5/2)*(c+d*x)^(3/2)/x^2,x,10,4/3*b*(a+b*x)^(3/2)*(c+d*x)^(3/2)-(a+b*x)^(5/2)*(c+d*x)^(3/2)/x-1/8*(b^3*c^3-15*a*b^2*c^2*d-45*a^2*b*c*d^2-5*a^3*d^3)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(d^(3/2)*sqrt(b))-a^(3/2)*(5*b*c+3*a*d)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))*sqrt(c)+1/4*b*(b*c+7*a*d)*(c+d*x)^(3/2)*sqrt(a+b*x)/d-1/8*(b^2*c^2-14*a*b*c*d-19*a^2*d^2)*sqrt(a+b*x)*sqrt(c+d*x)/d],
[(a+b*x)^(5/2)*(c+d*x)^(3/2)/x^3,x,10,-1/4*(5*b*c+3*a*d)*(a+b*x)^(3/2)*(c+d*x)^(3/2)/(c*x)-1/2*(a+b*x)^(5/2)*(c+d*x)^(3/2)/x^2-3/4*(5*b^2*c^2+10*a*b*c*d+a^2*d^2)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))*sqrt(a)/sqrt(c)+3/4*(b^2*c^2+10*a*b*c*d+5*a^2*d^2)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))*sqrt(b)/sqrt(d)+3/4*b*(3*b*c+a*d)*(c+d*x)^(3/2)*sqrt(a+b*x)/c+3/4*(b^2*c^2+6*a*b*c*d+a^2*d^2)*sqrt(a+b*x)*sqrt(c+d*x)/c],
[(a+b*x)^(5/2)*(c+d*x)^(3/2)/x^4,x,10,-1/12*(5*b*c+3*a*d)*(a+b*x)^(3/2)*(c+d*x)^(3/2)/(c*x^2)-1/3*(a+b*x)^(5/2)*(c+d*x)^(3/2)/x^3-1/8*(5*b^3*c^3+45*a*b^2*c^2*d+15*a^2*b*c*d^2-a^3*d^3)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(c^(3/2)*sqrt(a))+b^(3/2)*(3*b*c+5*a*d)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))*sqrt(d)-1/8*(5*b^2*c^2+12*a*b*c*d-a^2*d^2)*(c+d*x)^(3/2)*sqrt(a+b*x)/(c^2*x)+1/8*d*(19*b^2*c^2+14*a*b*c*d-a^2*d^2)*sqrt(a+b*x)*sqrt(c+d*x)/c^2],
[(a+b*x)^(5/2)*(c+d*x)^(3/2)/x^5,x,10,-1/24*(5*b*c+3*a*d)*(a+b*x)^(3/2)*(c+d*x)^(3/2)/(c*x^3)-1/4*(a+b*x)^(5/2)*(c+d*x)^(3/2)/x^4+1/64*(5*b^4*c^4-60*a*b^3*c^3*d-90*a^2*b^2*c^2*d^2+20*a^3*b*c*d^3-3*a^4*d^4)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(3/2)*c^(5/2))+2*b^(5/2)*d^(3/2)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))-1/32*(5*b*c-a*d)*(b*c+3*a*d)*(c+d*x)^(3/2)*sqrt(a+b*x)/(c^2*x^2)-1/64*(5*b^3*c^3+73*a*b^2*c^2*d-17*a^2*b*c*d^2+3*a^3*d^3)*sqrt(a+b*x)*sqrt(c+d*x)/(a*c^2*x)],
[(a+b*x)^(5/2)*(c+d*x)^(3/2)/x^6,x,7,-1/8*(b*c-a*d)*(a+b*x)^(3/2)*(c+d*x)^(5/2)/(c^2*x^4)-1/5*(a+b*x)^(5/2)*(c+d*x)^(5/2)/(c*x^5)-3/128*(b*c-a*d)^5*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(5/2)*c^(7/2))-1/64*(b*c-a*d)^3*(c+d*x)^(3/2)*sqrt(a+b*x)/(a*c^3*x^2)-1/16*(b*c-a*d)^2*(c+d*x)^(5/2)*sqrt(a+b*x)/(c^3*x^3)+3/128*(b*c-a*d)^4*sqrt(a+b*x)*sqrt(c+d*x)/(a^2*c^3*x)],
[x*(a+b*x)^(5/2)*(c+d*x)^(5/2),x,10,-1/24*(b*c-a*d)*(b*c+a*d)*(a+b*x)^(7/2)*(c+d*x)^(3/2)/(b^3*d)-1/12*(b*c+a*d)*(a+b*x)^(7/2)*(c+d*x)^(5/2)/(b^2*d)+1/7*(a+b*x)^(7/2)*(c+d*x)^(7/2)/(b*d)+5/1024*(b*c-a*d)^6*(b*c+a*d)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(9/2)*d^(9/2))+5/1536*(b*c-a*d)^4*(b*c+a*d)*(a+b*x)^(3/2)*sqrt(c+d*x)/(b^4*d^3)-1/384*(b*c-a*d)^3*(b*c+a*d)*(a+b*x)^(5/2)*sqrt(c+d*x)/(b^4*d^2)-1/64*(b*c-a*d)^2*(b*c+a*d)*(a+b*x)^(7/2)*sqrt(c+d*x)/(b^4*d)-5/1024*(b*c-a*d)^5*(b*c+a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(b^4*d^4)],
[(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)^(5/2)*(c+d*x)^(5/2)/x,x,11,1/8*(b*c+a*d)*(a+b*x)^(3/2)*(c+d*x)^(5/2)/d+1/5*(a+b*x)^(5/2)*(c+d*x)^(5/2)-2*a^(5/2)*c^(5/2)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))+1/128*(b*c+a*d)*(3*b^4*c^4-28*a*b^3*c^3*d+178*a^2*b^2*c^2*d^2-28*a^3*b*c*d^3+3*a^4*d^4)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(5/2)*d^(5/2))+1/192*(3*b^3*c^3-19*a*b^2*c^2*d+109*a^2*b*c*d^2+3*a^3*d^3)*(c+d*x)^(3/2)*sqrt(a+b*x)/(b*d^2)-1/48*(3*b^2*c^2-16*a*b*c*d-3*a^2*d^2)*(c+d*x)^(5/2)*sqrt(a+b*x)/d^2+1/128*(3*b^4*c^4-22*a*b^3*c^3*d+128*a^2*b^2*c^2*d^2+22*a^3*b*c*d^3-3*a^4*d^4)*sqrt(a+b*x)*sqrt(c+d*x)/(b^2*d^2)],
[(a+b*x)^(5/2)*(c+d*x)^(5/2)/x^2,x,11,5/4*b*(a+b*x)^(3/2)*(c+d*x)^(5/2)-(a+b*x)^(5/2)*(c+d*x)^(5/2)/x-5*a^(3/2)*c^(3/2)*(b*c+a*d)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))-5/64*(b^4*c^4-20*a*b^3*c^3*d-90*a^2*b^2*c^2*d^2-20*a^3*b*c*d^3+a^4*d^4)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(3/2)*d^(3/2))-5/96*(b^2*c^2-18*a*b*c*d-31*a^2*d^2)*(c+d*x)^(3/2)*sqrt(a+b*x)/d+5/24*b*(b*c+7*a*d)*(c+d*x)^(5/2)*sqrt(a+b*x)/d-5/64*(b^3*c^3-19*a*b^2*c^2*d-45*a^2*b*c*d^2-a^3*d^3)*sqrt(a+b*x)*sqrt(c+d*x)/(b*d)],
[(a+b*x)^(5/2)*(c+d*x)^(5/2)/x^3,x,11,-5/4*(b*c+a*d)*(a+b*x)^(3/2)*(c+d*x)^(5/2)/(c*x)-1/2*(a+b*x)^(5/2)*(c+d*x)^(5/2)/x^2-5/4*(3*b*c+a*d)*(b*c+3*a*d)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))*sqrt(a)*sqrt(c)+5/8*(b*c+a*d)*(b^2*c^2+14*a*b*c*d+a^2*d^2)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(sqrt(b)*sqrt(d))+5/12*(b^2*c^2+8*a*b*c*d+3*a^2*d^2)*(c+d*x)^(3/2)*sqrt(a+b*x)/c+5/12*b*(5*b*c+3*a*d)*(c+d*x)^(5/2)*sqrt(a+b*x)/c+5/8*(b^2*c^2+10*a*b*c*d+5*a^2*d^2)*sqrt(a+b*x)*sqrt(c+d*x)],
[(a+b*x)^(5/2)*(c+d*x)^(5/2)/x^4,x,11,-5/12*(b*c+a*d)*(a+b*x)^(3/2)*(c+d*x)^(5/2)/(c*x^2)-1/3*(a+b*x)^(5/2)*(c+d*x)^(5/2)/x^3-5/8*(b*c+a*d)*(b^2*c^2+14*a*b*c*d+a^2*d^2)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(sqrt(a)*sqrt(c))+5/4*(3*b*c+a*d)*(b*c+3*a*d)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))*sqrt(b)*sqrt(d)+5/24*d*(9*b^2*c^2+14*a*b*c*d+a^2*d^2)*(c+d*x)^(3/2)*sqrt(a+b*x)/c^2-5/24*(3*b^2*c^2+12*a*b*c*d+a^2*d^2)*(c+d*x)^(5/2)*sqrt(a+b*x)/(c^2*x)+5/8*d*(5*b^2*c^2+10*a*b*c*d+a^2*d^2)*sqrt(a+b*x)*sqrt(c+d*x)/c],
[(a+b*x)^(5/2)*(c+d*x)^(5/2)/x^5,x,11,-5/24*(b*c+a*d)*(a+b*x)^(3/2)*(c+d*x)^(5/2)/(c*x^3)-1/4*(a+b*x)^(5/2)*(c+d*x)^(5/2)/x^4+5/64*(b^4*c^4-20*a*b^3*c^3*d-90*a^2*b^2*c^2*d^2-20*a^3*b*c*d^3+a^4*d^4)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(3/2)*c^(3/2))+5*b^(3/2)*d^(3/2)*(b*c+a*d)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))-5/192*(3*b*c+a*d)*(b^2*c^2+24*a*b*c*d-a^2*d^2)*(c+d*x)^(3/2)*sqrt(a+b*x)/(a*c^2*x)-5/96*(3*b^2*c^2+14*a*b*c*d-a^2*d^2)*(c+d*x)^(5/2)*sqrt(a+b*x)/(c^2*x^2)+5/64*d*(b^3*c^3+45*a*b^2*c^2*d+19*a^2*b*c*d^2-a^3*d^3)*sqrt(a+b*x)*sqrt(c+d*x)/(a*c^2)],
[(a+b*x)^(5/2)*(c+d*x)^(5/2)/x^6,x,11,-1/8*(b*c+a*d)*(a+b*x)^(3/2)*(c+d*x)^(5/2)/(c*x^4)-1/5*(a+b*x)^(5/2)*(c+d*x)^(5/2)/x^5-1/128*(b*c+a*d)*(3*b^4*c^4-28*a*b^3*c^3*d+178*a^2*b^2*c^2*d^2-28*a^3*b*c*d^3+3*a^4*d^4)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(5/2)*c^(5/2))+2*b^(5/2)*d^(5/2)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))-1/192*(3*b^3*c^3+109*a*b^2*c^2*d-19*a^2*b*c*d^2+3*a^3*d^3)*(c+d*x)^(3/2)*sqrt(a+b*x)/(a*c^2*x^2)-1/48*(3*b^2*c^2+16*a*b*c*d-3*a^2*d^2)*(c+d*x)^(5/2)*sqrt(a+b*x)/(c^2*x^3)+1/128*(3*b^4*c^4-22*a*b^3*c^3*d-128*a^2*b^2*c^2*d^2+22*a^3*b*c*d^3-3*a^4*d^4)*sqrt(a+b*x)*sqrt(c+d*x)/(a^2*c^2*x)],
[(a+b*x)^(5/2)*(c+d*x)^(5/2)/x^7,x,8,-1/12*(b*c-a*d)*(a+b*x)^(3/2)*(c+d*x)^(7/2)/(c^2*x^5)-1/6*(a+b*x)^(5/2)*(c+d*x)^(7/2)/(c*x^6)+5/512*(b*c-a*d)^6*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(7/2)*c^(7/2))+5/768*(b*c-a*d)^4*(c+d*x)^(3/2)*sqrt(a+b*x)/(a^2*c^3*x^2)-1/192*(b*c-a*d)^3*(c+d*x)^(5/2)*sqrt(a+b*x)/(a*c^3*x^3)-1/32*(b*c-a*d)^2*(c+d*x)^(7/2)*sqrt(a+b*x)/(c^3*x^4)-5/512*(b*c-a*d)^5*sqrt(a+b*x)*sqrt(c+d*x)/(a^3*c^3*x)],

# n<0
[x^2*(a+b*x)^(5/2)/sqrt(c+d*x),x,8,-1/128*(b*c-a*d)^3*(63*b^2*c^2+14*a*b*c*d+3*a^2*d^2)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(5/2)*d^(11/2))-1/192*(b*c-a*d)*(63*b^2*c^2+14*a*b*c*d+3*a^2*d^2)*(a+b*x)^(3/2)*sqrt(c+d*x)/(b^2*d^4)+1/240*(63*b^2*c^2+14*a*b*c*d+3*a^2*d^2)*(a+b*x)^(5/2)*sqrt(c+d*x)/(b^2*d^3)-3/40*(3*b*c+a*d)*(a+b*x)^(7/2)*sqrt(c+d*x)/(b^2*d^2)+1/5*x*(a+b*x)^(7/2)*sqrt(c+d*x)/(b*d)+1/128*(b*c-a*d)^2*(63*b^2*c^2+14*a*b*c*d+3*a^2*d^2)*sqrt(a+b*x)*sqrt(c+d*x)/(b^2*d^5)],
[x*(a+b*x)^(5/2)/sqrt(c+d*x),x,7,5/64*(b*c-a*d)^3*(7*b*c+a*d)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(3/2)*d^(9/2))+5/96*(b*c-a*d)*(7*b*c+a*d)*(a+b*x)^(3/2)*sqrt(c+d*x)/(b*d^3)-1/24*(7*b*c+a*d)*(a+b*x)^(5/2)*sqrt(c+d*x)/(b*d^2)+1/4*(a+b*x)^(7/2)*sqrt(c+d*x)/(b*d)-5/64*(b*c-a*d)^2*(7*b*c+a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(b*d^4)],
[(a+b*x)^(5/2)/sqrt(c+d*x),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)^(5/2)/(x*sqrt(c+d*x)),x,8,1/4*(3*b^2*c^2-10*a*b*c*d+15*a^2*d^2)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))*sqrt(b)/d^(5/2)-2*a^(5/2)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/sqrt(c)+1/2*b*(a+b*x)^(3/2)*sqrt(c+d*x)/d-1/4*b*(3*b*c-7*a*d)*sqrt(a+b*x)*sqrt(c+d*x)/d^2],
[(a+b*x)^(5/2)/(x^2*sqrt(c+d*x)),x,8,-a^(3/2)*(5*b*c-a*d)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/c^(3/2)-b^(3/2)*(b*c-5*a*d)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/d^(3/2)-a*(a+b*x)^(3/2)*sqrt(c+d*x)/(c*x)+b*(b*c+a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(c*d)],
[(a+b*x)^(5/2)/(x^3*sqrt(c+d*x)),x,8,-1/4*(15*b^2*c^2-10*a*b*c*d+3*a^2*d^2)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))*sqrt(a)/c^(5/2)+2*b^(5/2)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/sqrt(d)-1/2*a*(a+b*x)^(3/2)*sqrt(c+d*x)/(c*x^2)-1/4*a*(7*b*c-3*a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(c^2*x)],
[(a+b*x)^(5/2)/(x^4*sqrt(c+d*x)),x,5,-5/8*(b*c-a*d)^3*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(c^(7/2)*sqrt(a))-5/12*(b*c-a*d)*(a+b*x)^(3/2)*sqrt(c+d*x)/(c^2*x^2)-1/3*(a+b*x)^(5/2)*sqrt(c+d*x)/(c*x^3)-5/8*(b*c-a*d)^2*sqrt(a+b*x)*sqrt(c+d*x)/(c^3*x)],
[(a+b*x)^(5/2)/(x^5*sqrt(c+d*x)),x,6,5/64*(b*c-a*d)^3*(b*c+7*a*d)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(3/2)*c^(9/2))+5/96*(b*c-a*d)*(b*c+7*a*d)*(a+b*x)^(3/2)*sqrt(c+d*x)/(a*c^3*x^2)+1/24*(b*c+7*a*d)*(a+b*x)^(5/2)*sqrt(c+d*x)/(a*c^2*x^3)-1/4*(a+b*x)^(7/2)*sqrt(c+d*x)/(a*c*x^4)+5/64*(b*c-a*d)^2*(b*c+7*a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(a*c^4*x)],
[x^2*(a+b*x)^(5/2)/(c+d*x)^(3/2),x,8,5/64*(b*c-a*d)^2*(63*b^2*c^2-14*a*b*c*d-a^2*d^2)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(3/2)*d^(11/2))+2*c^2*(a+b*x)^(7/2)/(d^2*(b*c-a*d)*sqrt(c+d*x))+5/96*(63*b^2*c^2-14*a*b*c*d-a^2*d^2)*(a+b*x)^(3/2)*sqrt(c+d*x)/(b*d^4)+1/24*(14*a*c-63*b*c^2/d+a^2*d/b)*(a+b*x)^(5/2)*sqrt(c+d*x)/(d^2*(b*c-a*d))+1/4*(a+b*x)^(7/2)*sqrt(c+d*x)/(b*d^2)-5/64*(b*c-a*d)*(63*b^2*c^2-14*a*b*c*d-a^2*d^2)*sqrt(a+b*x)*sqrt(c+d*x)/(b*d^5)],
[x*(a+b*x)^(5/2)/(c+d*x)^(3/2),x,7,-5/8*(b*c-a*d)^2*(7*b*c-a*d)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(d^(9/2)*sqrt(b))-2*c*(a+b*x)^(7/2)/(d*(b*c-a*d)*sqrt(c+d*x))-5/12*(7*b*c-a*d)*(a+b*x)^(3/2)*sqrt(c+d*x)/d^3+1/3*(7*b*c-a*d)*(a+b*x)^(5/2)*sqrt(c+d*x)/(d^2*(b*c-a*d))+5/8*(b*c-a*d)*(7*b*c-a*d)*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)^(5/2)/(x*(c+d*x)^(3/2)),x,8,-2*a^(5/2)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/c^(3/2)-b^(3/2)*(3*b*c-5*a*d)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/d^(5/2)-2*(b*c-a*d)*(a+b*x)^(3/2)/(c*d*sqrt(c+d*x))+b*(3*b*c-2*a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(c*d^2)],
[(a+b*x)^(5/2)/(x^2*(c+d*x)^(3/2)),x,8,-a^(3/2)*(5*b*c-3*a*d)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/c^(5/2)+2*b^(5/2)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/d^(3/2)-a*(a+b*x)^(3/2)/(c*x*sqrt(c+d*x))-(2*b*c-3*a*d)*(b*c-a*d)*sqrt(a+b*x)/(c^2*d*sqrt(c+d*x))],
[(a+b*x)^(5/2)/(x^3*(c+d*x)^(3/2)),x,5,-15/4*(b*c-a*d)^2*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))*sqrt(a)/c^(7/2)-5/4*(b*c-a*d)*(a+b*x)^(3/2)/(c^2*x*sqrt(c+d*x))-1/2*(a+b*x)^(5/2)/(c*x^2*sqrt(c+d*x))+15/4*(b*c-a*d)^2*sqrt(a+b*x)/(c^3*sqrt(c+d*x))],
[(a+b*x)^(5/2)/(x^4*(c+d*x)^(3/2)),x,6,-5/8*(b*c-7*a*d)*(b*c-a*d)^2*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(c^(9/2)*sqrt(a))-5/24*(b*c-7*a*d)*(b*c-a*d)*(a+b*x)^(3/2)/(a*c^3*x*sqrt(c+d*x))-1/12*(b*c-7*a*d)*(a+b*x)^(5/2)/(a*c^2*x^2*sqrt(c+d*x))-1/3*(a+b*x)^(7/2)/(a*c*x^3*sqrt(c+d*x))+5/8*(b*c-7*a*d)*(b*c-a*d)^2*sqrt(a+b*x)/(a*c^4*sqrt(c+d*x))],
[(a+b*x)^(5/2)/(x^5*(c+d*x)^(3/2)),x,8,5/64*(b*c-a*d)^2*(b^2*c^2+14*a*b*c*d-63*a^2*d^2)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(3/2)*c^(11/2))-1/4*a*(a+b*x)^(3/2)/(c*x^4*sqrt(c+d*x))-1/192*d*(15*b^3*c^3-839*a*b^2*c^2*d+1785*a^2*b*c*d^2-945*a^3*d^3)*sqrt(a+b*x)/(a*c^5*sqrt(c+d*x))-1/24*a*(11*b*c-9*a*d)*sqrt(a+b*x)/(c^2*x^3*sqrt(c+d*x))-1/96*(59*b*c-63*a*d)*(b*c-a*d)*sqrt(a+b*x)/(c^3*x^2*sqrt(c+d*x))-1/192*(b*c-a*d)*(15*b^2*c^2-322*a*b*c*d+315*a^2*d^2)*sqrt(a+b*x)/(a*c^4*x*sqrt(c+d*x))],
[x^3*(a+b*x)^(5/2)/(c+d*x)^(5/2),x,8,-2/3*x^3*(a+b*x)^(5/2)/(d*(c+d*x)^(3/2))+5/64*(b*c-a*d)*(231*b^3*c^3-189*a*b^2*c^2*d+21*a^2*b*c*d^2+a^3*d^3)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(3/2)*d^(13/2))-2/3*(11*b*c-6*a*d)*x^2*(a+b*x)^(5/2)/(d^2*(b*c-a*d)*sqrt(c+d*x))+5/96*(231*b^3*c^3-189*a*b^2*c^2*d+21*a^2*b*c*d^2+a^3*d^3)*(a+b*x)^(3/2)*sqrt(c+d*x)/(b*d^5*(b*c-a*d))-1/24*(a+b*x)^(5/2)*(231*b^2*c^2-156*a*b*c*d+5*a^2*d^2-2*b*d*(99*b*c-59*a*d)*x)*sqrt(c+d*x)/(b*d^4*(b*c-a*d))-5/64*(231*b^3*c^3-189*a*b^2*c^2*d+21*a^2*b*c*d^2+a^3*d^3)*sqrt(a+b*x)*sqrt(c+d*x)/(b*d^6)],
[x^2*(a+b*x)^(5/2)/(c+d*x)^(5/2),x,8,2/3*c^2*(a+b*x)^(7/2)/(d^2*(b*c-a*d)*(c+d*x)^(3/2))-5/8*(b*c-a*d)*(21*b^2*c^2-14*a*b*c*d+a^2*d^2)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(d^(11/2)*sqrt(b))-4/3*c*(5*b*c-3*a*d)*(a+b*x)^(7/2)/(d^2*(b*c-a*d)^2*sqrt(c+d*x))-5/12*(21*b^2*c^2-14*a*b*c*d+a^2*d^2)*(a+b*x)^(3/2)*sqrt(c+d*x)/(d^4*(b*c-a*d))+1/3*(21*b^2*c^2-14*a*b*c*d+a^2*d^2)*(a+b*x)^(5/2)*sqrt(c+d*x)/(d^3*(b*c-a*d)^2)+5/8*(21*b^2*c^2-14*a*b*c*d+a^2*d^2)*sqrt(a+b*x)*sqrt(c+d*x)/d^5],
[x*(a+b*x)^(5/2)/(c+d*x)^(5/2),x,7,-2/3*c*(a+b*x)^(7/2)/(d*(b*c-a*d)*(c+d*x)^(3/2))+5/4*(7*b*c-3*a*d)*(b*c-a*d)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))*sqrt(b)/d^(9/2)-2/3*(7*b*c-3*a*d)*(a+b*x)^(5/2)/(d^2*(b*c-a*d)*sqrt(c+d*x))+5/6*b*(7*b*c-3*a*d)*(a+b*x)^(3/2)*sqrt(c+d*x)/(d^3*(b*c-a*d))-5/4*b*(7*b*c-3*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)^(5/2)/(x*(c+d*x)^(5/2)),x,8,-2/3*(b*c-a*d)*(a+b*x)^(3/2)/(c*d*(c+d*x)^(3/2))-2*a^(5/2)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/c^(5/2)+2*b^(5/2)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/d^(5/2)+2*(a^2/c^2-b^2/d^2)*sqrt(a+b*x)/sqrt(c+d*x)],
[(a+b*x)^(5/2)/(x^2*(c+d*x)^(5/2)),x,5,5/3*(b*c-a*d)*(a+b*x)^(3/2)/(c^2*(c+d*x)^(3/2))-(a+b*x)^(5/2)/(c*x*(c+d*x)^(3/2))-5*a^(3/2)*(b*c-a*d)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/c^(7/2)+5*a*(b*c-a*d)*sqrt(a+b*x)/(c^3*sqrt(c+d*x))],
[(a+b*x)^(5/2)/(x^3*(c+d*x)^(5/2)),x,6,5/12*(3*b*c-7*a*d)*(b*c-a*d)*(a+b*x)^(3/2)/(a*c^3*(c+d*x)^(3/2))-1/4*(3*b*c-7*a*d)*(a+b*x)^(5/2)/(a*c^2*x*(c+d*x)^(3/2))-1/2*(a+b*x)^(7/2)/(a*c*x^2*(c+d*x)^(3/2))-5/4*(3*b*c-7*a*d)*(b*c-a*d)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))*sqrt(a)/c^(9/2)+5/4*(3*b*c-7*a*d)*(b*c-a*d)*sqrt(a+b*x)/(c^4*sqrt(c+d*x))],
[(a+b*x)^(5/2)/(x^4*(c+d*x)^(5/2)),x,8,-1/3*a*(a+b*x)^(3/2)/(c*x^3*(c+d*x)^(3/2))-5/8*(b*c-a*d)*(b^2*c^2-14*a*b*c*d+21*a^2*d^2)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(c^(11/2)*sqrt(a))-7/24*d*(7*b*c-15*a*d)*(b*c-a*d)*sqrt(a+b*x)/(c^4*(c+d*x)^(3/2))-3/4*a*(b*c-a*d)*sqrt(a+b*x)/(c^2*x^2*(c+d*x)^(3/2))-1/8*(11*b*c-21*a*d)*(b*c-a*d)*sqrt(a+b*x)/(c^3*x*(c+d*x)^(3/2))-1/24*d*(113*b^2*c^2-420*a*b*c*d+315*a^2*d^2)*sqrt(a+b*x)/(c^5*sqrt(c+d*x))],
[(a+b*x)^(5/2)/(x^5*(c+d*x)^(5/2)),x,9,-1/4*a*(a+b*x)^(3/2)/(c*x^4*(c+d*x)^(3/2))+5/64*(b*c-a*d)*(b^3*c^3+21*a*b^2*c^2*d-189*a^2*b*c*d^2+231*a^3*d^3)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(3/2)*c^(13/2))-1/64*d*(b*c-a*d)*(5*b^2*c^2-238*a*b*c*d+385*a^2*d^2)*sqrt(a+b*x)/(a*c^5*(c+d*x)^(3/2))-11/24*a*(b*c-a*d)*sqrt(a+b*x)/(c^2*x^3*(c+d*x)^(3/2))-1/96*(59*b*c-99*a*d)*(b*c-a*d)*sqrt(a+b*x)/(c^3*x^2*(c+d*x)^(3/2))-1/64*(b*c-a*d)*(5*b^2*c^2-156*a*b*c*d+231*a^2*d^2)*sqrt(a+b*x)/(a*c^4*x*(c+d*x)^(3/2))-1/64*d*(5*b^3*c^3-581*a*b^2*c^2*d+1715*a^2*b*c*d^2-1155*a^3*d^3)*sqrt(a+b*x)/(a*c^6*sqrt(c+d*x))],

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

# n>0
[x^2*sqrt(c+d*x)/sqrt(a+b*x),x,6,1/8*(b*c-a*d)*(b^2*c^2+2*a*b*c*d+5*a^2*d^2)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(7/2)*d^(5/2))-1/12*(3*b*c+5*a*d)*(c+d*x)^(3/2)*sqrt(a+b*x)/(b^2*d^2)+1/3*x*(c+d*x)^(3/2)*sqrt(a+b*x)/(b*d)+1/8*(b^2*c^2+2*a*b*c*d+5*a^2*d^2)*sqrt(a+b*x)*sqrt(c+d*x)/(b^3*d^2)],
[x*sqrt(c+d*x)/sqrt(a+b*x),x,5,-1/4*(b*c-a*d)*(b*c+3*a*d)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(5/2)*d^(3/2))+1/2*(c+d*x)^(3/2)*sqrt(a+b*x)/(b*d)-1/4*(b*c+3*a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(b^2*d)],
[sqrt(c+d*x)/sqrt(a+b*x),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],
[sqrt(c+d*x)/(x*sqrt(a+b*x)),x,7,-2*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))*sqrt(c)/sqrt(a)+2*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))*sqrt(d)/sqrt(b)],
[sqrt(c+d*x)/(x^2*sqrt(a+b*x)),x,3,(b*c-a*d)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(3/2)*sqrt(c))-sqrt(a+b*x)*sqrt(c+d*x)/(a*x)],
[sqrt(c+d*x)/(x^3*sqrt(a+b*x)),x,4,-1/4*(b*c-a*d)*(3*b*c+a*d)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(5/2)*c^(3/2))-1/2*(c+d*x)^(3/2)*sqrt(a+b*x)/(a*c*x^2)+1/4*(3*b*c+a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(a^2*c*x)],
[sqrt(c+d*x)/(x^4*sqrt(a+b*x)),x,6,1/8*(b*c-a*d)*(5*b^2*c^2+2*a*b*c*d+a^2*d^2)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(7/2)*c^(5/2))-1/3*sqrt(a+b*x)*sqrt(c+d*x)/(a*x^3)+1/12*(5*b*c-a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(a^2*c*x^2)-1/24*(5*b*c-3*a*d)*(3*b*c+a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(a^3*c^2*x)],
[x^2*(c+d*x)^(3/2)/sqrt(a+b*x),x,7,1/64*(b*c-a*d)^2*(3*b^2*c^2+10*a*b*c*d+35*a^2*d^2)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(9/2)*d^(5/2))+1/96*(3*b^2*c^2+10*a*b*c*d+35*a^2*d^2)*(c+d*x)^(3/2)*sqrt(a+b*x)/(b^3*d^2)-1/24*(3*b*c+7*a*d)*(c+d*x)^(5/2)*sqrt(a+b*x)/(b^2*d^2)+1/4*x*(c+d*x)^(5/2)*sqrt(a+b*x)/(b*d)+1/64*(b*c-a*d)*(3*b^2*c^2+10*a*b*c*d+35*a^2*d^2)*sqrt(a+b*x)*sqrt(c+d*x)/(b^4*d^2)],
[x*(c+d*x)^(3/2)/sqrt(a+b*x),x,6,-1/8*(b*c-a*d)^2*(b*c+5*a*d)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(7/2)*d^(3/2))-1/12*(b*c+5*a*d)*(c+d*x)^(3/2)*sqrt(a+b*x)/(b^2*d)+1/3*(c+d*x)^(5/2)*sqrt(a+b*x)/(b*d)-1/8*(b*c-a*d)*(b*c+5*a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(b^3*d)],
[(c+d*x)^(3/2)/sqrt(a+b*x),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)/(x*sqrt(a+b*x)),x,7,-2*c^(3/2)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/sqrt(a)+(3*b*c-a*d)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))*sqrt(d)/b^(3/2)+d*sqrt(a+b*x)*sqrt(c+d*x)/b],
[(c+d*x)^(3/2)/(x^2*sqrt(a+b*x)),x,7,2*d^(3/2)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/sqrt(b)+(b*c-3*a*d)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))*sqrt(c)/a^(3/2)-c*sqrt(a+b*x)*sqrt(c+d*x)/(a*x)],
[(c+d*x)^(3/2)/(x^3*sqrt(a+b*x)),x,4,-3/4*(b*c-a*d)^2*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(5/2)*sqrt(c))-1/2*(c+d*x)^(3/2)*sqrt(a+b*x)/(a*x^2)+3/4*(b*c-a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(a^2*x)],
[(c+d*x)^(3/2)/(x^4*sqrt(a+b*x)),x,5,1/8*(b*c-a*d)^2*(5*b*c+a*d)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(7/2)*c^(3/2))+1/12*(5*b*c+a*d)*(c+d*x)^(3/2)*sqrt(a+b*x)/(a^2*c*x^2)-1/3*(c+d*x)^(5/2)*sqrt(a+b*x)/(a*c*x^3)-1/8*(b*c-a*d)*(5*b*c+a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(a^3*c*x)],
[(c+d*x)^(3/2)/(x^5*sqrt(a+b*x)),x,7,-1/64*(b*c-a*d)^2*(35*b^2*c^2+10*a*b*c*d+3*a^2*d^2)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(9/2)*c^(5/2))-1/4*c*sqrt(a+b*x)*sqrt(c+d*x)/(a*x^4)+1/24*(7*b*c-9*a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(a^2*x^3)-1/96*(35*b^2*c^2-46*a*b*c*d+3*a^2*d^2)*sqrt(a+b*x)*sqrt(c+d*x)/(a^3*c*x^2)+1/192*(105*b^3*c^3-145*a*b^2*c^2*d+15*a^2*b*c*d^2+9*a^3*d^3)*sqrt(a+b*x)*sqrt(c+d*x)/(a^4*c^2*x)],
[x^2*(c+d*x)^(5/2)/sqrt(a+b*x),x,8,1/128*(b*c-a*d)^3*(3*b^2*c^2+14*a*b*c*d+63*a^2*d^2)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(11/2)*d^(5/2))+1/192*(b*c-a*d)*(3*b^2*c^2+14*a*b*c*d+63*a^2*d^2)*(c+d*x)^(3/2)*sqrt(a+b*x)/(b^4*d^2)+1/240*(3*b^2*c^2+14*a*b*c*d+63*a^2*d^2)*(c+d*x)^(5/2)*sqrt(a+b*x)/(b^3*d^2)-3/40*(b*c+3*a*d)*(c+d*x)^(7/2)*sqrt(a+b*x)/(b^2*d^2)+1/5*x*(c+d*x)^(7/2)*sqrt(a+b*x)/(b*d)+1/128*(b*c-a*d)^2*(3*b^2*c^2+14*a*b*c*d+63*a^2*d^2)*sqrt(a+b*x)*sqrt(c+d*x)/(b^5*d^2)],
[x*(c+d*x)^(5/2)/sqrt(a+b*x),x,7,-5/64*(b*c-a*d)^3*(b*c+7*a*d)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(9/2)*d^(3/2))-5/96*(b*c-a*d)*(b*c+7*a*d)*(c+d*x)^(3/2)*sqrt(a+b*x)/(b^3*d)-1/24*(b*c+7*a*d)*(c+d*x)^(5/2)*sqrt(a+b*x)/(b^2*d)+1/4*(c+d*x)^(7/2)*sqrt(a+b*x)/(b*d)-5/64*(b*c-a*d)^2*(b*c+7*a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(b^4*d)],
[(c+d*x)^(5/2)/sqrt(a+b*x),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)/(x*sqrt(a+b*x)),x,8,-2*c^(5/2)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/sqrt(a)+1/4*(15*b^2*c^2-10*a*b*c*d+3*a^2*d^2)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))*sqrt(d)/b^(5/2)+1/2*d*(c+d*x)^(3/2)*sqrt(a+b*x)/b+1/4*d*(7*b*c-3*a*d)*sqrt(a+b*x)*sqrt(c+d*x)/b^2],
[(c+d*x)^(5/2)/(x^2*sqrt(a+b*x)),x,8,c^(3/2)*(b*c-5*a*d)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/a^(3/2)+d^(3/2)*(5*b*c-a*d)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/b^(3/2)-c*(c+d*x)^(3/2)*sqrt(a+b*x)/(a*x)+d*(b*c+a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(a*b)],
[(c+d*x)^(5/2)/(x^3*sqrt(a+b*x)),x,8,2*d^(5/2)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/sqrt(b)-1/4*(3*b^2*c^2-10*a*b*c*d+15*a^2*d^2)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))*sqrt(c)/a^(5/2)-1/2*c*(c+d*x)^(3/2)*sqrt(a+b*x)/(a*x^2)+1/4*c*(3*b*c-7*a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(a^2*x)],
[(c+d*x)^(5/2)/(x^4*sqrt(a+b*x)),x,5,5/8*(b*c-a*d)^3*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(7/2)*sqrt(c))+5/12*(b*c-a*d)*(c+d*x)^(3/2)*sqrt(a+b*x)/(a^2*x^2)-1/3*(c+d*x)^(5/2)*sqrt(a+b*x)/(a*x^3)-5/8*(b*c-a*d)^2*sqrt(a+b*x)*sqrt(c+d*x)/(a^3*x)],
[(c+d*x)^(5/2)/(x^5*sqrt(a+b*x)),x,6,-5/64*(b*c-a*d)^3*(7*b*c+a*d)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(9/2)*c^(3/2))-5/96*(b*c-a*d)*(7*b*c+a*d)*(c+d*x)^(3/2)*sqrt(a+b*x)/(a^3*c*x^2)+1/24*(7*b*c+a*d)*(c+d*x)^(5/2)*sqrt(a+b*x)/(a^2*c*x^3)-1/4*(c+d*x)^(7/2)*sqrt(a+b*x)/(a*c*x^4)+5/64*(b*c-a*d)^2*(7*b*c+a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(a^4*c*x)],
[(c+d*x)^(5/2)/(x^6*sqrt(a+b*x)),x,8,1/128*(b*c-a*d)^3*(63*b^2*c^2+14*a*b*c*d+3*a^2*d^2)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(11/2)*c^(5/2))-1/5*c*(c+d*x)^(3/2)*sqrt(a+b*x)/(a*x^5)+1/40*c*(9*b*c-13*a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(a^2*x^4)-1/240*(63*b^2*c^2-148*a*b*c*d+93*a^2*d^2)*sqrt(a+b*x)*sqrt(c+d*x)/(a^3*x^3)+1/960*(315*b^3*c^3-749*a*b^2*c^2*d+481*a^2*b*c*d^2-15*a^3*d^3)*sqrt(a+b*x)*sqrt(c+d*x)/(a^4*c*x^2)-1/1920*(945*b^4*c^4-2310*a*b^3*c^3*d+1564*a^2*b^2*c^2*d^2-90*a^3*b*c*d^3-45*a^4*d^4)*sqrt(a+b*x)*sqrt(c+d*x)/(a^5*c^2*x)],
[x^4*(1+x)^(3/2)/sqrt(1-x),x,7,11/16*arcsin(x)-11/48*(1+x)^(3/2)*sqrt(1-x)-1/15*x^2*(1+x)^(5/2)*sqrt(1-x)-1/6*x^3*(1+x)^(5/2)*sqrt(1-x)-1/120*(1+x)^(5/2)*(18+19*x)*sqrt(1-x)-11/16*sqrt(1-x)*sqrt(1+x)],
[x^3*(1+x)^(3/2)/sqrt(1-x),x,8,3/4*arcsin(x)-1/4*(1+x)^(3/2)*sqrt(1-x)-1/10*(1+x)^(5/2)*sqrt(1-x)-1/5*x^2*(1+x)^(5/2)*sqrt(1-x)-1/10*(1+x)^(7/2)*sqrt(1-x)-3/4*sqrt(1-x)*sqrt(1+x)],
[x^2*(1+x)^(3/2)/sqrt(1-x),x,6,7/8*arcsin(x)-7/24*(1+x)^(3/2)*sqrt(1-x)-1/6*(1+x)^(5/2)*sqrt(1-x)-1/4*x*(1+x)^(5/2)*sqrt(1-x)-7/8*sqrt(1-x)*sqrt(1+x)],
[x*(1+x)^(3/2)/sqrt(1-x),x,5,arcsin(x)-1/3*(1+x)^(3/2)*sqrt(1-x)-1/3*(1+x)^(5/2)*sqrt(1-x)-sqrt(1-x)*sqrt(1+x)],
[(1+x)^(3/2)/sqrt(1-x),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)/(x*sqrt(1-x)),x,6,2*arcsin(x)-arctanh(sqrt(1-x)*sqrt(1+x))-sqrt(1-x)*sqrt(1+x)],
[(1+x)^(3/2)/(x^2*sqrt(1-x)),x,6,arcsin(x)-2*arctanh(sqrt(1-x)*sqrt(1+x))-sqrt(1-x)*sqrt(1+x)/x],
[(1+x)^(3/2)/(x^3*sqrt(1-x)),x,4,-3/2*arctanh(sqrt(1-x)*sqrt(1+x))-1/2*(1+x)^(3/2)*sqrt(1-x)/x^2-3/2*sqrt(1-x)*sqrt(1+x)/x],
[(1+x)^(3/2)/(x^4*sqrt(1-x)),x,5,-arctanh(sqrt(1-x)*sqrt(1+x))-1/3*(1+x)^(3/2)*sqrt(1-x)/x^2-1/3*(1+x)^(5/2)*sqrt(1-x)/x^3-sqrt(1-x)*sqrt(1+x)/x],
[(1+x)^(3/2)/(x^5*sqrt(1-x)),x,7,-7/8*arctanh(sqrt(1-x)*sqrt(1+x))-1/4*sqrt(1-x)*sqrt(1+x)/x^4-2/3*sqrt(1-x)*sqrt(1+x)/x^3-7/8*sqrt(1-x)*sqrt(1+x)/x^2-4/3*sqrt(1-x)*sqrt(1+x)/x],

# n<0
[x^3/(sqrt(a+b*x)*sqrt(c+d*x)),x,5,-1/8*(b*c+a*d)*(5*b^2*c^2-2*a*b*c*d+5*a^2*d^2)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(7/2)*d^(7/2))+1/3*x^2*sqrt(a+b*x)*sqrt(c+d*x)/(b*d)+1/24*(15*b^2*c^2+14*a*b*c*d+15*a^2*d^2-10*b*d*(b*c+a*d)*x)*sqrt(a+b*x)*sqrt(c+d*x)/(b^3*d^3)],
[x^2/(sqrt(a+b*x)*sqrt(c+d*x)),x,5,-1/4*(4*a*b*c*d-3*(b*c+a*d)^2)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(5/2)*d^(5/2))-3/4*(b*c+a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(b^2*d^2)+1/2*x*sqrt(a+b*x)*sqrt(c+d*x)/(b*d)],
[x/(sqrt(a+b*x)*sqrt(c+d*x)),x,4,-(b*c+a*d)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(3/2)*d^(3/2))+sqrt(a+b*x)*sqrt(c+d*x)/(b*d)],
[1/(sqrt(a+b*x)*sqrt(c+d*x)),x,3,2*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(sqrt(b)*sqrt(d))],
[1/(x*sqrt(a+b*x)*sqrt(c+d*x)),x,2,-2*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(sqrt(a)*sqrt(c))],
[1/(x^2*sqrt(a+b*x)*sqrt(c+d*x)),x,3,(b*c+a*d)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(3/2)*c^(3/2))-sqrt(a+b*x)*sqrt(c+d*x)/(a*c*x)],
[1/(x^3*sqrt(a+b*x)*sqrt(c+d*x)),x,5,-1/4*(3*b^2*c^2+2*a*b*c*d+3*a^2*d^2)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(5/2)*c^(5/2))-1/2*sqrt(a+b*x)*sqrt(c+d*x)/(a*c*x^2)+3/4*(b*c+a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(a^2*c^2*x)],
[1/(x^4*sqrt(a+b*x)*sqrt(c+d*x)),x,6,1/8*(b*c+a*d)*(5*b^2*c^2-2*a*b*c*d+5*a^2*d^2)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(7/2)*c^(7/2))-1/3*sqrt(a+b*x)*sqrt(c+d*x)/(a*c*x^3)+5/12*(b*c+a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(a^2*c^2*x^2)-1/24*(15*b^2*c^2+14*a*b*c*d+15*a^2*d^2)*sqrt(a+b*x)*sqrt(c+d*x)/(a^3*c^3*x)],
[x^3/((c+d*x)^(3/2)*sqrt(a+b*x)),x,5,3/4*(5*b^2*c^2+2*a*b*c*d+a^2*d^2)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(5/2)*d^(7/2))-2*c*x^2*sqrt(a+b*x)/(d*(b*c-a*d)*sqrt(c+d*x))-1/4*((5*b*c-3*a*d)*(3*b*c+a*d)-2*b*d*(5*b*c-a*d)*x)*sqrt(a+b*x)*sqrt(c+d*x)/(b^2*d^3*(b*c-a*d))],
[x^2/((c+d*x)^(3/2)*sqrt(a+b*x)),x,5,-(3*b*c+a*d)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(3/2)*d^(5/2))+2*c^2*sqrt(a+b*x)/(d^2*(b*c-a*d)*sqrt(c+d*x))+sqrt(a+b*x)*sqrt(c+d*x)/(b*d^2)],
[x/((c+d*x)^(3/2)*sqrt(a+b*x)),x,4,2*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(d^(3/2)*sqrt(b))-2*c*sqrt(a+b*x)/(d*(b*c-a*d)*sqrt(c+d*x))],
[1/((c+d*x)^(3/2)*sqrt(a+b*x)),x,1,2*sqrt(a+b*x)/((b*c-a*d)*sqrt(c+d*x))],
[1/(x*(c+d*x)^(3/2)*sqrt(a+b*x)),x,3,-2*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(c^(3/2)*sqrt(a))-2*d*sqrt(a+b*x)/(c*(b*c-a*d)*sqrt(c+d*x))],
[1/(x^2*(c+d*x)^(3/2)*sqrt(a+b*x)),x,5,(b*c+3*a*d)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(3/2)*c^(5/2))-d*(b*c-3*a*d)*sqrt(a+b*x)/(a*c^2*(b*c-a*d)*sqrt(c+d*x))-sqrt(a+b*x)/(a*c*x*sqrt(c+d*x))],
[1/(x^3*(c+d*x)^(3/2)*sqrt(a+b*x)),x,6,-3/4*(b^2*c^2+2*a*b*c*d+5*a^2*d^2)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(5/2)*c^(7/2))+1/4*d*(3*b*c-5*a*d)*(b*c+3*a*d)*sqrt(a+b*x)/(a^2*c^3*(b*c-a*d)*sqrt(c+d*x))-1/2*sqrt(a+b*x)/(a*c*x^2*sqrt(c+d*x))+1/4*(3*b*c+5*a*d)*sqrt(a+b*x)/(a^2*c^2*x*sqrt(c+d*x))],
[x^4/((c+d*x)^(5/2)*sqrt(a+b*x)),x,6,1/4*(35*b^2*c^2+10*a*b*c*d+3*a^2*d^2)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(5/2)*d^(9/2))-2/3*c*x^3*sqrt(a+b*x)/(d*(b*c-a*d)*(c+d*x)^(3/2))-2/3*c*(7*b*c-9*a*d)*x^2*sqrt(a+b*x)/(d^2*(b*c-a*d)^2*sqrt(c+d*x))-1/12*(105*b^3*c^3-145*a*b^2*c^2*d+15*a^2*b*c*d^2+9*a^3*d^3-2*b*d*(35*b^2*c^2-46*a*b*c*d+3*a^2*d^2)*x)*sqrt(a+b*x)*sqrt(c+d*x)/(b^2*d^4*(b*c-a*d)^2)],
[x^3/((c+d*x)^(5/2)*sqrt(a+b*x)),x,5,-(5*b*c+a*d)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(3/2)*d^(7/2))-2/3*c*x^2*sqrt(a+b*x)/(d*(b*c-a*d)*(c+d*x)^(3/2))+1/3*(c*(15*b^2*c^2-22*a*b*c*d+3*a^2*d^2)+d*(5*b*c-3*a*d)*(b*c-a*d)*x)*sqrt(a+b*x)/(b*d^3*(b*c-a*d)^2*sqrt(c+d*x))],
[x^2/((c+d*x)^(5/2)*sqrt(a+b*x)),x,5,2*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(d^(5/2)*sqrt(b))+2/3*c^2*sqrt(a+b*x)/(d^2*(b*c-a*d)*(c+d*x)^(3/2))-4/3*c*(2*b*c-3*a*d)*sqrt(a+b*x)/(d^2*(b*c-a*d)^2*sqrt(c+d*x))],
[x/((c+d*x)^(5/2)*sqrt(a+b*x)),x,2,-2/3*c*sqrt(a+b*x)/(d*(b*c-a*d)*(c+d*x)^(3/2))+2/3*(b*c-3*a*d)*sqrt(a+b*x)/(d*(b*c-a*d)^2*sqrt(c+d*x))],
[1/((c+d*x)^(5/2)*sqrt(a+b*x)),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/(x*(c+d*x)^(5/2)*sqrt(a+b*x)),x,5,-2*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(c^(5/2)*sqrt(a))-2/3*d*sqrt(a+b*x)/(c*(b*c-a*d)*(c+d*x)^(3/2))-2/3*d*(5*b*c-3*a*d)*sqrt(a+b*x)/(c^2*(b*c-a*d)^2*sqrt(c+d*x))],
[1/(x^2*(c+d*x)^(5/2)*sqrt(a+b*x)),x,6,(b*c+5*a*d)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(3/2)*c^(7/2))-1/3*d*(3*b*c-5*a*d)*sqrt(a+b*x)/(a*c^2*(b*c-a*d)*(c+d*x)^(3/2))-sqrt(a+b*x)/(a*c*x*(c+d*x)^(3/2))-1/3*d*(3*b^2*c^2-22*a*b*c*d+15*a^2*d^2)*sqrt(a+b*x)/(a*c^3*(b*c-a*d)^2*sqrt(c+d*x))],
[1/(x^3*(c+d*x)^(5/2)*sqrt(a+b*x)),x,7,-1/4*(3*b^2*c^2+10*a*b*c*d+35*a^2*d^2)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(5/2)*c^(9/2))+1/12*d*(9*b^2*c^2+18*a*b*c*d-35*a^2*d^2)*sqrt(a+b*x)/(a^2*c^3*(b*c-a*d)*(c+d*x)^(3/2))-1/2*sqrt(a+b*x)/(a*c*x^2*(c+d*x)^(3/2))+1/4*(3*b*c+7*a*d)*sqrt(a+b*x)/(a^2*c^2*x*(c+d*x)^(3/2))+1/12*d*(9*b^3*c^3+15*a*b^2*c^2*d-145*a^2*b*c*d^2+105*a^3*d^3)*sqrt(a+b*x)/(a^2*c^4*(b*c-a*d)^2*sqrt(c+d*x))],
[1/(x*sqrt(c*x)*sqrt(a+b*x)),x,2,-2*sqrt(a+b*x)/(a*sqrt(c*x))],
[1/(x*sqrt(a+b*x)*sqrt(a*c-b*c*x)),x,2,-arctanh(sqrt(a+b*x)*sqrt(a*c-b*c*x)/(a*sqrt(c)))/(a*sqrt(c))],
[1/(x*sqrt(1-a-b*x)*sqrt(1+a+b*x)),x,2,-2*arctanh(sqrt(1-a)*sqrt(1+a+b*x)/(sqrt(1+a)*sqrt(1-a-b*x)))/sqrt(1-a^2)],

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

# n>0
[x^3*(c+d*x)^(3/2)/(a+b*x)^(3/2),x,7,3/64*(b*c-a*d)*(b^3*c^3+5*a*b^2*c^2*d+35*a^2*b*c*d^2-105*a^3*d^3)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(11/2)*d^(5/2))-2*x^3*(c+d*x)^(3/2)/(b*sqrt(a+b*x))+9/4*x^2*(c+d*x)^(3/2)*sqrt(a+b*x)/b^2-1/32*(c+d*x)^(3/2)*(3*b^2*c^2+14*a*b*c*d-105*a^2*d^2-4*b*d*(b*c-21*a*d)*x)*sqrt(a+b*x)/(b^4*d^2)+3/64*(b^3*c^3+5*a*b^2*c^2*d+35*a^2*b*c*d^2-105*a^3*d^3)*sqrt(a+b*x)*sqrt(c+d*x)/(b^5*d^2)],
[x^2*(c+d*x)^(3/2)/(a+b*x)^(3/2),x,7,-1/8*(b*c-a*d)*(b^2*c^2+10*a*b*c*d-35*a^2*d^2)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(9/2)*d^(3/2))-2*a^2*(c+d*x)^(5/2)/(b^2*(b*c-a*d)*sqrt(a+b*x))-1/12*(10*a*c+b*c^2/d-35*a^2*d/b)*(c+d*x)^(3/2)*sqrt(a+b*x)/(b^2*(b*c-a*d))+1/3*(c+d*x)^(5/2)*sqrt(a+b*x)/(b^2*d)-1/8*(b^2*c^2+10*a*b*c*d-35*a^2*d^2)*sqrt(a+b*x)*sqrt(c+d*x)/(b^4*d)],
[x*(c+d*x)^(3/2)/(a+b*x)^(3/2),x,6,3/4*(b*c-5*a*d)*(b*c-a*d)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(7/2)*sqrt(d))+2*a*(c+d*x)^(5/2)/(b*(b*c-a*d)*sqrt(a+b*x))+1/2*(b*c-5*a*d)*(c+d*x)^(3/2)*sqrt(a+b*x)/(b^2*(b*c-a*d))+3/4*(b*c-5*a*d)*sqrt(a+b*x)*sqrt(c+d*x)/b^3],
[(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)/(x*(a+b*x)^(3/2)),x,7,-2*c^(3/2)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/a^(3/2)+2*d^(3/2)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/b^(3/2)+2*(b*c-a*d)*sqrt(c+d*x)/(a*b*sqrt(a+b*x))],
[(c+d*x)^(3/2)/(x^2*(a+b*x)^(3/2)),x,4,3*(b*c-a*d)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))*sqrt(c)/a^(5/2)-(c+d*x)^(3/2)/(a*x*sqrt(a+b*x))-3*(b*c-a*d)*sqrt(c+d*x)/(a^2*sqrt(a+b*x))],
[(c+d*x)^(3/2)/(x^3*(a+b*x)^(3/2)),x,5,-3/4*(b*c-a*d)*(5*b*c-a*d)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(7/2)*sqrt(c))+1/4*(5*b*c-a*d)*(c+d*x)^(3/2)/(a^2*c*x*sqrt(a+b*x))-1/2*(c+d*x)^(5/2)/(a*c*x^2*sqrt(a+b*x))+3/4*(b*c-a*d)*(5*b*c-a*d)*sqrt(c+d*x)/(a^3*c*sqrt(a+b*x))],
[(c+d*x)^(3/2)/(x^4*(a+b*x)^(3/2)),x,7,1/8*(b*c-a*d)*(35*b^2*c^2-10*a*b*c*d-a^2*d^2)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(9/2)*c^(3/2))-1/24*b*(105*b^2*c^2-100*a*b*c*d+3*a^2*d^2)*sqrt(c+d*x)/(a^4*c*sqrt(a+b*x))-1/3*c*sqrt(c+d*x)/(a*x^3*sqrt(a+b*x))+7/12*(b*c-a*d)*sqrt(c+d*x)/(a^2*x^2*sqrt(a+b*x))-1/24*(35*b*c-3*a*d)*(b*c-a*d)*sqrt(c+d*x)/(a^3*c*x*sqrt(a+b*x))],
[x^3*(c+d*x)^(5/2)/(a+b*x)^(3/2),x,8,3/128*(b*c-a*d)^2*(b^3*c^3+7*a*b^2*c^2*d+63*a^2*b*c*d^2-231*a^3*d^3)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(13/2)*d^(5/2))-2*x^3*(c+d*x)^(5/2)/(b*sqrt(a+b*x))+1/64*(b^3*c^3+7*a*b^2*c^2*d+63*a^2*b*c*d^2-231*a^3*d^3)*(c+d*x)^(3/2)*sqrt(a+b*x)/(b^5*d^2)+11/5*x^2*(c+d*x)^(5/2)*sqrt(a+b*x)/b^2-1/80*(c+d*x)^(5/2)*(5*b^2*c^2+30*a*b*c*d-231*a^2*d^2-2*b*d*(5*b*c-99*a*d)*x)*sqrt(a+b*x)/(b^4*d^2)+3/128*(b*c-a*d)*(b^3*c^3+7*a*b^2*c^2*d+63*a^2*b*c*d^2-231*a^3*d^3)*sqrt(a+b*x)*sqrt(c+d*x)/(b^6*d^2)],
[x^2*(c+d*x)^(5/2)/(a+b*x)^(3/2),x,8,-5/64*(b*c-a*d)^2*(b^2*c^2+14*a*b*c*d-63*a^2*d^2)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(11/2)*d^(3/2))-2*a^2*(c+d*x)^(7/2)/(b^2*(b*c-a*d)*sqrt(a+b*x))-5/96*(b^2*c^2+14*a*b*c*d-63*a^2*d^2)*(c+d*x)^(3/2)*sqrt(a+b*x)/(b^4*d)-1/24*(14*a*c+b*c^2/d-63*a^2*d/b)*(c+d*x)^(5/2)*sqrt(a+b*x)/(b^2*(b*c-a*d))+1/4*(c+d*x)^(7/2)*sqrt(a+b*x)/(b^2*d)-5/64*(b*c-a*d)*(b^2*c^2+14*a*b*c*d-63*a^2*d^2)*sqrt(a+b*x)*sqrt(c+d*x)/(b^5*d)],
[x*(c+d*x)^(5/2)/(a+b*x)^(3/2),x,7,5/8*(b*c-7*a*d)*(b*c-a*d)^2*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(9/2)*sqrt(d))+2*a*(c+d*x)^(7/2)/(b*(b*c-a*d)*sqrt(a+b*x))+5/12*(b*c-7*a*d)*(c+d*x)^(3/2)*sqrt(a+b*x)/b^3+1/3*(b*c-7*a*d)*(c+d*x)^(5/2)*sqrt(a+b*x)/(b^2*(b*c-a*d))+5/8*(b*c-7*a*d)*(b*c-a*d)*sqrt(a+b*x)*sqrt(c+d*x)/b^4],
[(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)/(x*(a+b*x)^(3/2)),x,8,-2*c^(5/2)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/a^(3/2)+d^(3/2)*(5*b*c-3*a*d)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/b^(5/2)+2*(b*c-a*d)*(c+d*x)^(3/2)/(a*b*sqrt(a+b*x))-d*(2*b*c-3*a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(a*b^2)],
[(c+d*x)^(5/2)/(x^2*(a+b*x)^(3/2)),x,8,c^(3/2)*(3*b*c-5*a*d)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/a^(5/2)+2*d^(5/2)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/b^(3/2)-c*(c+d*x)^(3/2)/(a*x*sqrt(a+b*x))-(3*b*c-2*a*d)*(b*c-a*d)*sqrt(c+d*x)/(a^2*b*sqrt(a+b*x))],
[(c+d*x)^(5/2)/(x^3*(a+b*x)^(3/2)),x,5,-15/4*(b*c-a*d)^2*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))*sqrt(c)/a^(7/2)+5/4*(b*c-a*d)*(c+d*x)^(3/2)/(a^2*x*sqrt(a+b*x))-1/2*(c+d*x)^(5/2)/(a*x^2*sqrt(a+b*x))+15/4*(b*c-a*d)^2*sqrt(c+d*x)/(a^3*sqrt(a+b*x))],
[(c+d*x)^(5/2)/(x^4*(a+b*x)^(3/2)),x,6,5/8*(b*c-a*d)^2*(7*b*c-a*d)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(9/2)*sqrt(c))-5/24*(b*c-a*d)*(7*b*c-a*d)*(c+d*x)^(3/2)/(a^3*c*x*sqrt(a+b*x))+1/12*(7*b*c-a*d)*(c+d*x)^(5/2)/(a^2*c*x^2*sqrt(a+b*x))-1/3*(c+d*x)^(7/2)/(a*c*x^3*sqrt(a+b*x))-5/8*(b*c-a*d)^2*(7*b*c-a*d)*sqrt(c+d*x)/(a^4*c*sqrt(a+b*x))],
[(c+d*x)^(5/2)/(x^5*(a+b*x)^(3/2)),x,8,-5/64*(b*c-a*d)^2*(63*b^2*c^2-14*a*b*c*d-a^2*d^2)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(11/2)*c^(3/2))-1/4*c*(c+d*x)^(3/2)/(a*x^4*sqrt(a+b*x))+1/192*b*(945*b^3*c^3-1785*a*b^2*c^2*d+839*a^2*b*c*d^2-15*a^3*d^3)*sqrt(c+d*x)/(a^5*c*sqrt(a+b*x))+1/24*c*(9*b*c-11*a*d)*sqrt(c+d*x)/(a^2*x^3*sqrt(a+b*x))-1/96*(63*b*c-59*a*d)*(b*c-a*d)*sqrt(c+d*x)/(a^3*x^2*sqrt(a+b*x))+1/192*(b*c-a*d)*(315*b^2*c^2-322*a*b*c*d+15*a^2*d^2)*sqrt(c+d*x)/(a^4*c*x*sqrt(a+b*x))],

# n<0
[x^4/((a+b*x)^(3/2)*(c+d*x)^(3/2)),x,6,3/4*(5*b^2*c^2+6*a*b*c*d+5*a^2*d^2)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(7/2)*d^(7/2))+2*a*x^3/(b*(b*c-a*d)*sqrt(a+b*x)*sqrt(c+d*x))-2*c*(b*c+a*d)*x^2*sqrt(a+b*x)/(b*d*(b*c-a*d)^2*sqrt(c+d*x))-1/4*((b*c+a*d)*(15*b^2*c^2-22*a*b*c*d+15*a^2*d^2)-2*b*d*(5*b^2*c^2-2*a*b*c*d+5*a^2*d^2)*x)*sqrt(a+b*x)*sqrt(c+d*x)/(b^3*d^3*(b*c-a*d)^2)],
[x^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)))/(b^(5/2)*d^(5/2))+2*a*x^2/(b*(b*c-a*d)*sqrt(a+b*x)*sqrt(c+d*x))+(c*(3*b^2*c^2-2*a*b*c*d+3*a^2*d^2)+d*(b*c-3*a*d)*(b*c-a*d)*x)*sqrt(a+b*x)/(b^2*d^2*(b*c-a*d)^2*sqrt(c+d*x))],
[x^2/((a+b*x)^(3/2)*(c+d*x)^(3/2)),x,5,2*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(3/2)*d^(3/2))-2*a^2/(b^2*(b*c-a*d)*sqrt(a+b*x)*sqrt(c+d*x))-2*(b^2*c^2+a^2*d^2)*sqrt(a+b*x)/(b^2*d*(b*c-a*d)^2*sqrt(c+d*x))],
[x/((a+b*x)^(3/2)*(c+d*x)^(3/2)),x,2,-2*c/(d*(b*c-a*d)*sqrt(a+b*x)*sqrt(c+d*x))+2*(b*c+a*d)*sqrt(c+d*x)/(d*(b*c-a*d)^2*sqrt(a+b*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/(x*(a+b*x)^(3/2)*(c+d*x)^(3/2)),x,5,-2*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(3/2)*c^(3/2))+2*b/(a*(b*c-a*d)*sqrt(a+b*x)*sqrt(c+d*x))+2*d*(b*c+a*d)*sqrt(a+b*x)/(a*c*(b*c-a*d)^2*sqrt(c+d*x))],
[1/(x^2*(a+b*x)^(3/2)*(c+d*x)^(3/2)),x,6,3*(b*c+a*d)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(5/2)*c^(5/2))-b*(3*b*c-a*d)/(a^2*c*(b*c-a*d)*sqrt(a+b*x)*sqrt(c+d*x))+(-1)/(a*c*x*sqrt(a+b*x)*sqrt(c+d*x))-d*(3*b^2*c^2-2*a*b*c*d+3*a^2*d^2)*sqrt(a+b*x)/(a^2*c^2*(b*c-a*d)^2*sqrt(c+d*x))],
[1/(x^3*(a+b*x)^(3/2)*(c+d*x)^(3/2)),x,7,-3/4*(5*b^2*c^2+6*a*b*c*d+5*a^2*d^2)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(7/2)*c^(7/2))+1/4*b*(15*b^2*c^2-2*a*b*c*d-5*a^2*d^2)/(a^3*c^2*(b*c-a*d)*sqrt(a+b*x)*sqrt(c+d*x))+(-1/2)/(a*c*x^2*sqrt(a+b*x)*sqrt(c+d*x))+5/4*(b*c+a*d)/(a^2*c^2*x*sqrt(a+b*x)*sqrt(c+d*x))+1/4*d*(b*c+a*d)*(15*b^2*c^2-22*a*b*c*d+15*a^2*d^2)*sqrt(a+b*x)/(a^3*c^3*(b*c-a*d)^2*sqrt(c+d*x))],
[x^5/((a+b*x)^(3/2)*(c+d*x)^(5/2)),x,7,5/4*(7*b^2*c^2+6*a*b*c*d+3*a^2*d^2)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(7/2)*d^(9/2))+2*a*x^4/(b*(b*c-a*d)*(c+d*x)^(3/2)*sqrt(a+b*x))-2/3*c*(b*c+3*a*d)*x^3*sqrt(a+b*x)/(b*d*(b*c-a*d)^2*(c+d*x)^(3/2))-2/3*c*(7*b^2*c^2-12*a*b*c*d-3*a^2*d^2)*x^2*sqrt(a+b*x)/(b*d^2*(b*c-a*d)^3*sqrt(c+d*x))-1/12*(105*b^4*c^4-190*a*b^3*c^3*d+36*a^2*b^2*c^2*d^2+30*a^3*b*c*d^3-45*a^4*d^4-2*b*d*(35*b^3*c^3-61*a*b^2*c^2*d+9*a^2*b*c*d^2-15*a^3*d^3)*x)*sqrt(a+b*x)*sqrt(c+d*x)/(b^3*d^4*(b*c-a*d)^3)],
[x^4/((a+b*x)^(3/2)*(c+d*x)^(5/2)),x,6,-(5*b*c+3*a*d)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(5/2)*d^(7/2))+2*a*x^3/(b*(b*c-a*d)*(c+d*x)^(3/2)*sqrt(a+b*x))-2/3*c*(b*c+3*a*d)*x^2*sqrt(a+b*x)/(b*d*(b*c-a*d)^2*(c+d*x)^(3/2))+1/3*(c*(15*b^3*c^3-31*a*b^2*c^2*d+9*a^2*b*c*d^2-9*a^3*d^3)+d*(b*c-a*d)*(5*b^2*c^2-6*a*b*c*d+9*a^2*d^2)*x)*sqrt(a+b*x)/(b^2*d^3*(b*c-a*d)^3*sqrt(c+d*x))],
[x^3/((a+b*x)^(3/2)*(c+d*x)^(5/2)),x,5,2*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(3/2)*d^(5/2))+2*a*x^2/(b*(b*c-a*d)*(c+d*x)^(3/2)*sqrt(a+b*x))-2/3*c*(c*(b*c-3*a*d)*(3*b*c+a*d)+2*d*(2*b^2*c^2-3*a*b*c*d-3*a^2*d^2)*x)*sqrt(a+b*x)/(b*d^2*(b*c-a*d)^3*(c+d*x)^(3/2))],
[x^2/((a+b*x)^(3/2)*(c+d*x)^(5/2)),x,3,-2*a^2/(b^2*(b*c-a*d)*(c+d*x)^(3/2)*sqrt(a+b*x))-2/3*(b^2*c^2+3*a^2*d^2)*sqrt(a+b*x)/(b^2*d*(b*c-a*d)^2*(c+d*x)^(3/2))+2/3*(b^2*c^2-6*a*b*c*d-3*a^2*d^2)*sqrt(a+b*x)/(b*d*(b*c-a*d)^3*sqrt(c+d*x))],
[x/((a+b*x)^(3/2)*(c+d*x)^(5/2)),x,3,2*a/(b*(b*c-a*d)*(c+d*x)^(3/2)*sqrt(a+b*x))+2/3*(b*c+3*a*d)*sqrt(a+b*x)/(b*(b*c-a*d)^2*(c+d*x)^(3/2))+4/3*(b*c+3*a*d)*sqrt(a+b*x)/((b*c-a*d)^3*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/(x*(a+b*x)^(3/2)*(c+d*x)^(5/2)),x,6,-2*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(3/2)*c^(5/2))+2*b/(a*(b*c-a*d)*(c+d*x)^(3/2)*sqrt(a+b*x))+2/3*d*(3*b*c+a*d)*sqrt(a+b*x)/(a*c*(b*c-a*d)^2*(c+d*x)^(3/2))+2/3*d*(3*b*c-a*d)*(b*c+3*a*d)*sqrt(a+b*x)/(a*c^2*(b*c-a*d)^3*sqrt(c+d*x))],
[1/(x^2*(a+b*x)^(3/2)*(c+d*x)^(5/2)),x,7,(3*b*c+5*a*d)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(5/2)*c^(7/2))-b*(3*b*c-a*d)/(a^2*c*(b*c-a*d)*(c+d*x)^(3/2)*sqrt(a+b*x))+(-1)/(a*c*x*(c+d*x)^(3/2)*sqrt(a+b*x))-1/3*d*(9*b^2*c^2-6*a*b*c*d+5*a^2*d^2)*sqrt(a+b*x)/(a^2*c^2*(b*c-a*d)^2*(c+d*x)^(3/2))-1/3*d*(9*b^3*c^3-9*a*b^2*c^2*d+31*a^2*b*c*d^2-15*a^3*d^3)*sqrt(a+b*x)/(a^2*c^3*(b*c-a*d)^3*sqrt(c+d*x))],
[1/(x^3*(a+b*x)^(3/2)*(c+d*x)^(5/2)),x,8,-5/4*(3*b^2*c^2+6*a*b*c*d+7*a^2*d^2)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(7/2)*c^(9/2))+1/4*b*(15*b^2*c^2-7*a^2*d^2)/(a^3*c^2*(b*c-a*d)*(c+d*x)^(3/2)*sqrt(a+b*x))+(-1/2)/(a*c*x^2*(c+d*x)^(3/2)*sqrt(a+b*x))+1/4*(5*b*c+7*a*d)/(a^2*c^2*x*(c+d*x)^(3/2)*sqrt(a+b*x))+1/12*d*(45*b^3*c^3-15*a*b^2*c^2*d-33*a^2*b*c*d^2+35*a^3*d^3)*sqrt(a+b*x)/(a^3*c^3*(b*c-a*d)^2*(c+d*x)^(3/2))+1/12*d*(45*b^4*c^4-30*a*b^3*c^3*d-36*a^2*b^2*c^2*d^2+190*a^3*b*c*d^3-105*a^4*d^4)*sqrt(a+b*x)/(a^3*c^4*(b*c-a*d)^3*sqrt(c+d*x))],

# Integrands of the form x^m (c+d x)^(n/2) / (a+b x)^(5/2)

# n>0
[x^4*(c+d*x)^(5/2)/(a+b*x)^(5/2),x,9,-2/3*x^4*(c+d*x)^(5/2)/(b*(a+b*x)^(3/2))+1/128*(b*c-a*d)*(3*b^4*c^4+28*a*b^3*c^3*d+378*a^2*b^2*c^2*d^2-2772*a^3*b*c*d^3+3003*a^4*d^4)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(15/2)*d^(5/2))-2/3*(8*b*c-13*a*d)*x^3*(c+d*x)^(5/2)/(b^2*(b*c-a*d)*sqrt(a+b*x))+1/192*(3*b^4*c^4+28*a*b^3*c^3*d+378*a^2*b^2*c^2*d^2-2772*a^3*b*c*d^3+3003*a^4*d^4)*(c+d*x)^(3/2)*sqrt(a+b*x)/(b^6*d^2*(b*c-a*d))+1/15*(93*b*c-143*a*d)*x^2*(c+d*x)^(5/2)*sqrt(a+b*x)/(b^3*(b*c-a*d))-1/240*(c+d*x)^(5/2)*(15*b^3*c^3+125*a*b^2*c^2*d-2343*a^2*b*c*d^2+3003*a^3*d^3-2*b*d*(15*b^2*c^2-902*a*b*c*d+1287*a^2*d^2)*x)*sqrt(a+b*x)/(b^5*d^2*(b*c-a*d))+1/128*(3*b^4*c^4+28*a*b^3*c^3*d+378*a^2*b^2*c^2*d^2-2772*a^3*b*c*d^3+3003*a^4*d^4)*sqrt(a+b*x)*sqrt(c+d*x)/(b^7*d^2)],
[x^3*(c+d*x)^(5/2)/(a+b*x)^(5/2),x,8,-2/3*x^3*(c+d*x)^(5/2)/(b*(a+b*x)^(3/2))-5/64*(b*c-a*d)*(b^3*c^3+21*a*b^2*c^2*d-189*a^2*b*c*d^2+231*a^3*d^3)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(13/2)*d^(3/2))-2/3*(6*b*c-11*a*d)*x^2*(c+d*x)^(5/2)/(b^2*(b*c-a*d)*sqrt(a+b*x))-5/96*(b^3*c^3+21*a*b^2*c^2*d-189*a^2*b*c*d^2+231*a^3*d^3)*(c+d*x)^(3/2)*sqrt(a+b*x)/(b^5*d*(b*c-a*d))+1/24*(c+d*x)^(5/2)*(5*b^2*c^2-156*a*b*c*d+231*a^2*d^2+2*b*d*(59*b*c-99*a*d)*x)*sqrt(a+b*x)/(b^4*d*(b*c-a*d))-5/64*(b^3*c^3+21*a*b^2*c^2*d-189*a^2*b*c*d^2+231*a^3*d^3)*sqrt(a+b*x)*sqrt(c+d*x)/(b^6*d)],
[x^2*(c+d*x)^(5/2)/(a+b*x)^(5/2),x,8,-2/3*a^2*(c+d*x)^(7/2)/(b^2*(b*c-a*d)*(a+b*x)^(3/2))+5/8*(b*c-a*d)*(b^2*c^2-14*a*b*c*d+21*a^2*d^2)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(11/2)*sqrt(d))+4/3*a*(3*b*c-5*a*d)*(c+d*x)^(7/2)/(b^2*(b*c-a*d)^2*sqrt(a+b*x))+5/12*(b^2*c^2-14*a*b*c*d+21*a^2*d^2)*(c+d*x)^(3/2)*sqrt(a+b*x)/(b^4*(b*c-a*d))+1/3*(b^2*c^2-14*a*b*c*d+21*a^2*d^2)*(c+d*x)^(5/2)*sqrt(a+b*x)/(b^3*(b*c-a*d)^2)+5/8*(b^2*c^2-14*a*b*c*d+21*a^2*d^2)*sqrt(a+b*x)*sqrt(c+d*x)/b^5],
[x*(c+d*x)^(5/2)/(a+b*x)^(5/2),x,7,2/3*a*(c+d*x)^(7/2)/(b*(b*c-a*d)*(a+b*x)^(3/2))+5/4*(3*b*c-7*a*d)*(b*c-a*d)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))*sqrt(d)/b^(9/2)-2/3*(3*b*c-7*a*d)*(c+d*x)^(5/2)/(b^2*(b*c-a*d)*sqrt(a+b*x))+5/6*d*(3*b*c-7*a*d)*(c+d*x)^(3/2)*sqrt(a+b*x)/(b^3*(b*c-a*d))+5/4*d*(3*b*c-7*a*d)*sqrt(a+b*x)*sqrt(c+d*x)/b^4],
[(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)/(x*(a+b*x)^(5/2)),x,8,2/3*(b*c-a*d)*(c+d*x)^(3/2)/(a*b*(a+b*x)^(3/2))-2*c^(5/2)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/a^(5/2)+2*d^(5/2)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/b^(5/2)+2*(c^2/a^2-d^2/b^2)*sqrt(c+d*x)/sqrt(a+b*x)],
[(c+d*x)^(5/2)/(x^2*(a+b*x)^(5/2)),x,5,-5/3*(b*c-a*d)*(c+d*x)^(3/2)/(a^2*(a+b*x)^(3/2))-(c+d*x)^(5/2)/(a*x*(a+b*x)^(3/2))+5*c^(3/2)*(b*c-a*d)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/a^(7/2)-5*c*(b*c-a*d)*sqrt(c+d*x)/(a^3*sqrt(a+b*x))],
[(c+d*x)^(5/2)/(x^3*(a+b*x)^(5/2)),x,6,5/12*(7*b*c-3*a*d)*(b*c-a*d)*(c+d*x)^(3/2)/(a^3*c*(a+b*x)^(3/2))+1/4*(7*b*c-3*a*d)*(c+d*x)^(5/2)/(a^2*c*x*(a+b*x)^(3/2))-1/2*(c+d*x)^(7/2)/(a*c*x^2*(a+b*x)^(3/2))-5/4*(7*b*c-3*a*d)*(b*c-a*d)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))*sqrt(c)/a^(9/2)+5/4*(7*b*c-3*a*d)*(b*c-a*d)*sqrt(c+d*x)/(a^4*sqrt(a+b*x))],
[(c+d*x)^(5/2)/(x^4*(a+b*x)^(5/2)),x,8,-1/3*c*(c+d*x)^(3/2)/(a*x^3*(a+b*x)^(3/2))+5/8*(b*c-a*d)*(21*b^2*c^2-14*a*b*c*d+a^2*d^2)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(11/2)*sqrt(c))-7/24*b*(15*b*c-7*a*d)*(b*c-a*d)*sqrt(c+d*x)/(a^4*(a+b*x)^(3/2))+3/4*c*(b*c-a*d)*sqrt(c+d*x)/(a^2*x^2*(a+b*x)^(3/2))-1/8*(21*b*c-11*a*d)*(b*c-a*d)*sqrt(c+d*x)/(a^3*x*(a+b*x)^(3/2))-1/24*b*(315*b^2*c^2-420*a*b*c*d+113*a^2*d^2)*sqrt(c+d*x)/(a^5*sqrt(a+b*x))],
[(c+d*x)^(5/2)/(x^5*(a+b*x)^(5/2)),x,9,-1/4*c*(c+d*x)^(3/2)/(a*x^4*(a+b*x)^(3/2))-5/64*(b*c-a*d)*(231*b^3*c^3-189*a*b^2*c^2*d+21*a^2*b*c*d^2+a^3*d^3)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(13/2)*c^(3/2))+1/64*b*(b*c-a*d)*(385*b^2*c^2-238*a*b*c*d+5*a^2*d^2)*sqrt(c+d*x)/(a^5*c*(a+b*x)^(3/2))+11/24*c*(b*c-a*d)*sqrt(c+d*x)/(a^2*x^3*(a+b*x)^(3/2))-1/96*(99*b*c-59*a*d)*(b*c-a*d)*sqrt(c+d*x)/(a^3*x^2*(a+b*x)^(3/2))+1/64*(b*c-a*d)*(231*b^2*c^2-156*a*b*c*d+5*a^2*d^2)*sqrt(c+d*x)/(a^4*c*x*(a+b*x)^(3/2))+1/64*b*(1155*b^3*c^3-1715*a*b^2*c^2*d+581*a^2*b*c*d^2-5*a^3*d^3)*sqrt(c+d*x)/(a^6*c*sqrt(a+b*x))],

# n<0
[x^2/((a+b*x)^(5/2)*(c+d*x)^(1/2)),x,5,2*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(5/2)*sqrt(d))-2/3*a^2*sqrt(c+d*x)/(b^2*(b*c-a*d)*(a+b*x)^(3/2))+4/3*a*(3*b*c-2*a*d)*sqrt(c+d*x)/(b^2*(b*c-a*d)^2*sqrt(a+b*x))],
[x^6/((a+b*x)^(5/2)*(c+d*x)^(5/2)),x,8,2/3*a*x^5/(b*(b*c-a*d)*(a+b*x)^(3/2)*(c+d*x)^(3/2))+5/4*(7*b^2*c^2+10*a*b*c*d+7*a^2*d^2)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(9/2)*d^(9/2))+2/3*a*(13*b*c-7*a*d)*x^4/(b^2*(b*c-a*d)^2*(c+d*x)^(3/2)*sqrt(a+b*x))-2/3*c*(b^2*c^2+14*a*b*c*d-7*a^2*d^2)*x^3*sqrt(a+b*x)/(b^2*d*(b*c-a*d)^3*(c+d*x)^(3/2))-2/3*c*(b*c+a*d)*(7*b^2*c^2-22*a*b*c*d+7*a^2*d^2)*x^2*sqrt(a+b*x)/(b^2*d^2*(b*c-a*d)^4*sqrt(c+d*x))-1/12*((b*c+a*d)*(105*b^4*c^4-340*a*b^3*c^3*d+406*a^2*b^2*c^2*d^2-340*a^3*b*c*d^3+105*a^4*d^4)-2*b*d*(35*b^4*c^4-76*a*b^3*c^3*d+18*a^2*b^2*c^2*d^2-76*a^3*b*c*d^3+35*a^4*d^4)*x)*sqrt(a+b*x)*sqrt(c+d*x)/(b^4*d^4*(b*c-a*d)^4)],
[x^5/((a+b*x)^(5/2)*(c+d*x)^(5/2)),x,7,2/3*a*x^4/(b*(b*c-a*d)*(a+b*x)^(3/2)*(c+d*x)^(3/2))-5*(b*c+a*d)*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(7/2)*d^(7/2))+2/3*a*(11*b*c-5*a*d)*x^3/(b^2*(b*c-a*d)^2*(c+d*x)^(3/2)*sqrt(a+b*x))-2/3*c*(b^2*c^2+12*a*b*c*d-5*a^2*d^2)*x^2*sqrt(a+b*x)/(b^2*d*(b*c-a*d)^3*(c+d*x)^(3/2))+1/3*(c*(15*b^4*c^4-40*a*b^3*c^3*d+18*a^2*b^2*c^2*d^2-40*a^3*b*c*d^3+15*a^4*d^4)+d*(b*c-a*d)*(5*b^3*c^3-9*a*b^2*c^2*d+35*a^2*b*c*d^2-15*a^3*d^3)*x)*sqrt(a+b*x)/(b^3*d^3*(b*c-a*d)^4*sqrt(c+d*x))],
[x^4/((a+b*x)^(5/2)*(c+d*x)^(5/2)),x,6,2/3*a*x^3/(b*(b*c-a*d)*(a+b*x)^(3/2)*(c+d*x)^(3/2))+2*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(5/2)*d^(5/2))+2*a*(3*b*c-a*d)*x^2/(b^2*(b*c-a*d)^2*(c+d*x)^(3/2)*sqrt(a+b*x))-2/3*c*(c*(b*c+a*d)*(3*b^2*c^2-14*a*b*c*d+3*a^2*d^2)+2*d*(2*b^3*c^3-a*b^2*c^2*d-12*a^2*b*c*d^2+3*a^3*d^3)*x)*sqrt(a+b*x)/(b^2*d^2*(b*c-a*d)^4*(c+d*x)^(3/2))],
[x^3/((a+b*x)^(5/2)*(c+d*x)^(5/2)),x,4,-2/3*x^3/((b*c-a*d)*(a+b*x)^(3/2)*(c+d*x)^(3/2))-4*a^2*c/(b^2*(b*c-a*d)^2*(c+d*x)^(3/2)*sqrt(a+b*x))-4/3*c*(b^2*c^2+3*a^2*d^2)*sqrt(a+b*x)/(b^2*d*(b*c-a*d)^3*(c+d*x)^(3/2))+4/3*c*(b^2*c^2-6*a*b*c*d-3*a^2*d^2)*sqrt(a+b*x)/(b*d*(b*c-a*d)^4*sqrt(c+d*x))],
[x^2/((a+b*x)^(5/2)*(c+d*x)^(5/2)),x,4,-2/3*a^2/(b^2*(b*c-a*d)*(a+b*x)^(3/2)*(c+d*x)^(3/2))+4*a*c/(b*(b*c-a*d)^2*(c+d*x)^(3/2)*sqrt(a+b*x))+2/3*(b^2*c^2+6*a*b*c*d+a^2*d^2)*sqrt(a+b*x)/(b^2*(b*c-a*d)^3*(c+d*x)^(3/2))+4/3*(b^2*c^2+6*a*b*c*d+a^2*d^2)*sqrt(a+b*x)/(b*(b*c-a*d)^4*sqrt(c+d*x))],
[x/((a+b*x)^(5/2)*(c+d*x)^(5/2)),x,4,-2/3*c/(d*(b*c-a*d)*(a+b*x)^(3/2)*(c+d*x)^(3/2))+2/3*(b*c+a*d)/(d*(b*c-a*d)^2*(a+b*x)^(3/2)*sqrt(c+d*x))-8/3*(b*c+a*d)/((b*c-a*d)^3*sqrt(a+b*x)*sqrt(c+d*x))-16/3*d*(b*c+a*d)*sqrt(a+b*x)/((b*c-a*d)^4*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/(x*(a+b*x)^(5/2)*(c+d*x)^(5/2)),x,7,2/3*b/(a*(b*c-a*d)*(a+b*x)^(3/2)*(c+d*x)^(3/2))-2*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(5/2)*c^(5/2))+2*b*(b*c-3*a*d)/(a^2*(b*c-a*d)^2*(c+d*x)^(3/2)*sqrt(a+b*x))+2/3*d*(3*b^2*c^2-10*a*b*c*d-a^2*d^2)*sqrt(a+b*x)/(a^2*c*(b*c-a*d)^3*(c+d*x)^(3/2))+2/3*d*(b*c+a*d)*(3*b^2*c^2-14*a*b*c*d+3*a^2*d^2)*sqrt(a+b*x)/(a^2*c^2*(b*c-a*d)^4*sqrt(c+d*x))],
[1/(x^2*(a+b*x)^(5/2)*(c+d*x)^(5/2)),x,8,-1/3*b*(5*b*c-3*a*d)/(a^2*c*(b*c-a*d)*(a+b*x)^(3/2)*(c+d*x)^(3/2))+(-1)/(a*c*x*(a+b*x)^(3/2)*(c+d*x)^(3/2))+5*(b*c+a*d)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(7/2)*c^(7/2))-b*(5*b^2*c^2-10*a*b*c*d+a^2*d^2)/(a^3*c*(b*c-a*d)^2*(c+d*x)^(3/2)*sqrt(a+b*x))-1/3*d*(15*b^3*c^3-35*a*b^2*c^2*d+9*a^2*b*c*d^2-5*a^3*d^3)*sqrt(a+b*x)/(a^3*c^2*(b*c-a*d)^3*(c+d*x)^(3/2))-1/3*d*(15*b^4*c^4-40*a*b^3*c^3*d+18*a^2*b^2*c^2*d^2-40*a^3*b*c*d^3+15*a^4*d^4)*sqrt(a+b*x)/(a^3*c^3*(b*c-a*d)^4*sqrt(c+d*x))],
[1/(x^3*(a+b*x)^(5/2)*(c+d*x)^(5/2)),x,9,1/12*b*(35*b^2*c^2-6*a*b*c*d-21*a^2*d^2)/(a^3*c^2*(b*c-a*d)*(a+b*x)^(3/2)*(c+d*x)^(3/2))+(-1/2)/(a*c*x^2*(a+b*x)^(3/2)*(c+d*x)^(3/2))+7/4*(b*c+a*d)/(a^2*c^2*x*(a+b*x)^(3/2)*(c+d*x)^(3/2))-5/4*(7*b^2*c^2+10*a*b*c*d+7*a^2*d^2)*arctanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(9/2)*c^(9/2))+1/4*b*(35*b^3*c^3-55*a*b^2*c^2*d-3*a^2*b*c*d^2+7*a^3*d^3)/(a^4*c^2*(b*c-a*d)^2*(c+d*x)^(3/2)*sqrt(a+b*x))+1/12*d*(105*b^4*c^4-200*a*b^3*c^3*d+18*a^2*b^2*c^2*d^2+48*a^3*b*c*d^3-35*a^4*d^4)*sqrt(a+b*x)/(a^4*c^3*(b*c-a*d)^3*(c+d*x)^(3/2))+1/12*d*(b*c+a*d)*(105*b^4*c^4-340*a*b^3*c^3*d+406*a^2*b^2*c^2*d^2-340*a^3*b*c*d^3+105*a^4*d^4)*sqrt(a+b*x)/(a^4*c^4*(b*c-a*d)^4*sqrt(c+d*x))],

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

#  Note that the derivative of (a+b*x)^n/(-a-b*x)^n is zero. 
[x^2*sqrt(a+b*x)/sqrt(-a-b*x),x,2,1/3*x^3*sqrt(a+b*x)/sqrt(-a-b*x)],
[x*sqrt(a+b*x)/sqrt(-a-b*x),x,2,1/2*x^2*sqrt(a+b*x)/sqrt(-a-b*x)],
[sqrt(a+b*x)/sqrt(-a-b*x),x,2,x*sqrt(a+b*x)/sqrt(-a-b*x)],
[sqrt(a+b*x)/(x*sqrt(-a-b*x)),x,2,log(x)*sqrt(a+b*x)/sqrt(-a-b*x)],
[sqrt(a+b*x)/(x^2*sqrt(-a-b*x)),x,2,-sqrt(a+b*x)/(x*sqrt(-a-b*x))],
[sqrt(a+b*x)/(x^3*sqrt(-a-b*x)),x,2,-1/2*sqrt(a+b*x)/(x^2*sqrt(-a-b*x))],
[sqrt(a+b*x)/(x^m*sqrt(-a-b*x)),x,2,x^(1-m)*sqrt(a+b*x)/((1-m)*sqrt(-a-b*x))],
[x^2*(a+b*x)^n/(-a-b*x)^n,x,2,1/3*x^3*(a+b*x)^n/(-a-b*x)^n],
[x*(a+b*x)^n/(-a-b*x)^n,x,2,1/2*x^2*(a+b*x)^n/(-a-b*x)^n],
[(a+b*x)^n/(-a-b*x)^n,x,2,x*(a+b*x)^n/(-a-b*x)^n],
[(a+b*x)^n/(x*(-a-b*x)^n),x,2,(a+b*x)^n*log(x)/(-a-b*x)^n],
[(a+b*x)^n/(x^2*(-a-b*x)^n),x,2,-(a+b*x)^n/(x*(-a-b*x)^n)],
[(a+b*x)^n/(x^3*(-a-b*x)^n),x,2,-1/2*(a+b*x)^n/(x^2*(-a-b*x)^n)],
[(a+b*x)^n/(x^m*(-a-b*x)^n),x,2,x^(1-m)*(a+b*x)^n/((1-m)*(-a-b*x)^n)],
[x^3*sqrt(1+x)/(1-x)^(5/2),x,5,11/2*arcsin(x)+2/3*x^3*sqrt(1+x)/(1-x)^(3/2)-13/3*x^2*sqrt(1+x)/sqrt(1-x)-1/6*(52+33*x)*sqrt(1-x)*sqrt(1+x)],
[x^2*sqrt(1+x)/(1-x)^(5/2),x,6,1/3*(1+x)^(3/2)/(1-x)^(3/2)+3*arcsin(x)-4*sqrt(1+x)/sqrt(1-x)-sqrt(1-x)*sqrt(1+x),1/3*(1+x)^(3/2)/(1-x)^(3/2)+3*arcsin(x)-2*(1+x)^(3/2)/sqrt(1-x)-3*sqrt(1-x)*sqrt(1+x)],
[x*sqrt(1+x)/(1-x)^(5/2),x,4,1/3*(1+x)^(3/2)/(1-x)^(3/2)+arcsin(x)-2*sqrt(1+x)/sqrt(1-x)],
[sqrt(1+x)/(1-x)^(5/2),x,1,1/3*(1+x)^(3/2)/(1-x)^(3/2)],
[sqrt(1+x)/(-1+x)^(5/2),x,1,-1/3*(1+x)^(3/2)/(-1+x)^(3/2)],
[sqrt(1+x)/((1-x)^(5/2)*x),x,4,1/3*(1+x)^(3/2)/(1-x)^(3/2)-arctanh(sqrt(1-x)*sqrt(1+x))+2*sqrt(1+x)/sqrt(1-x)],
[sqrt(1+x)/((1-x)^(5/2)*x^2),x,6,-3*arctanh(sqrt(1-x)*sqrt(1+x))+2/3*sqrt(1+x)/((1-x)^(3/2)*x)+14/3*sqrt(1+x)/sqrt(1-x)-5/3*sqrt(1+x)/(x*sqrt(1-x))],
[sqrt(1+x)/((1-x)^(5/2)*x^3),x,7,-11/2*arctanh(sqrt(1-x)*sqrt(1+x))+2/3*sqrt(1+x)/((1-x)^(3/2)*x^2)+26/3*sqrt(1+x)/sqrt(1-x)-7/6*sqrt(1+x)/(x^2*sqrt(1-x))-19/6*sqrt(1+x)/(x*sqrt(1-x))],
[x^2/(sqrt(-1+x)*sqrt(1+x)),x,2,1/2*arccosh(x)+1/2*x*sqrt(-1+x)*sqrt(1+x)],
[x/(sqrt(-1+x)*sqrt(1+x)),x,1,sqrt(-1+x)*sqrt(1+x)],
[1/(sqrt(-1+x)*sqrt(1+x)),x,1,arccosh(x)],
[1/(x*sqrt(-1+x)*sqrt(1+x)),x,2,arctan(sqrt(-1+x)*sqrt(1+x))],
[1/(x^2*sqrt(-1+x)*sqrt(1+x)),x,1,sqrt(-1+x)*sqrt(1+x)/x],
[x^2*sqrt(-1+x)*sqrt(1+x),x,3,1/4*(-1+x)^(3/2)*x*(1+x)^(3/2)-1/8*arccosh(x)+1/8*x*sqrt(-1+x)*sqrt(1+x)],
[x*sqrt(-1+x)*sqrt(1+x),x,1,1/3*(-1+x)^(3/2)*(1+x)^(3/2)],
[sqrt(-1+x)*sqrt(1+x),x,2,-1/2*arccosh(x)+1/2*x*sqrt(-1+x)*sqrt(1+x)],
[sqrt(-1+x)*sqrt(1+x)/x,x,3,-arctan(sqrt(-1+x)*sqrt(1+x))+sqrt(-1+x)*sqrt(1+x)],
[sqrt(-1+x)*sqrt(1+x)/x^2,x,2,arccosh(x)-sqrt(-1+x)*sqrt(1+x)/x],
[1/(sqrt(1+2*x)*sqrt(3+2*x)),x,2,arcsinh(sqrt(1+2*x)/sqrt(2))],
[1/(x*sqrt(-2+3*x)*sqrt(3+5*x)),x,2,arctan(sqrt(3/2)*sqrt(-2+3*x)/sqrt(3+5*x))*sqrt(2/3)],
[1/((-1+x)^(3/2)*x*(1+x)^(3/2)),x,3,-arctan(sqrt(-1+x)*sqrt(1+x))+(-1)/(sqrt(-1+x)*sqrt(1+x))],
[x*sqrt(1-x)*sqrt(1+x),x,1,-1/3*(1-x)^(3/2)*(1+x)^(3/2)],
[x^3*(2+3*x)^(3/2)*(1+4*x)^(1/2),x,7,1/829440*(4103-7968*x)*(2+3*x)^(5/2)*(1+4*x)^(3/2)+1/72*x^2*(2+3*x)^(5/2)*(1+4*x)^(3/2)+1067875/84934656*arcsinh(sqrt(3/5)*sqrt(1+4*x))/sqrt(3)+42715/15925248*(2+3*x)^(3/2)*sqrt(1+4*x)-8543/995328*(2+3*x)^(5/2)*sqrt(1+4*x)+213575/42467328*sqrt(2+3*x)*sqrt(1+4*x)],
[1/(sqrt(-1+a+b*x)*sqrt(1+a+b*x)),x,2,2*arcsinh(sqrt(-1+a+b*x)/sqrt(2))/b],

# Integrands of the form (e x)^(m/2) (c+d x)^(n/2) (a+b x)^(p/2)
[1/(sqrt(x)*sqrt(a-b*x)*sqrt(a+b*x)),x,2,2*EllipticF(sqrt(b)*sqrt(x)/sqrt(a),I)*sqrt(a)*sqrt(1-b*x/a)*sqrt(1+b*x/a)/(sqrt(b)*sqrt(a-b*x)*sqrt(a+b*x))],
[1/(sqrt(-x)*sqrt(a-b*x)*sqrt(a+b*x)),x,2,-2*EllipticF(sqrt(b)*sqrt(-x)/sqrt(a),I)*sqrt(a)*sqrt(1-b*x/a)*sqrt(1+b*x/a)/(sqrt(b)*sqrt(a-b*x)*sqrt(a+b*x))],
[1/(sqrt(e*x)*sqrt(a-b*x)*sqrt(a+b*x)),x,2,2*EllipticF(sqrt(b)*sqrt(e*x)/(sqrt(a)*sqrt(e)),I)*sqrt(a)*sqrt(1-b*x/a)*sqrt(1+b*x/a)/(sqrt(b)*sqrt(e)*sqrt(a-b*x)*sqrt(a+b*x))],
[1/(sqrt(x)*sqrt(2-b*x)*sqrt(2+b*x)),x,1,EllipticF(sqrt(b)*sqrt(x)/sqrt(2),I)*sqrt(2)/sqrt(b)],
[1/(sqrt(-x)*sqrt(2-b*x)*sqrt(2+b*x)),x,1,-EllipticF(sqrt(b)*sqrt(-x)/sqrt(2),I)*sqrt(2)/sqrt(b)],
[1/(sqrt(e*x)*sqrt(2-b*x)*sqrt(2+b*x)),x,1,EllipticF(sqrt(b)*sqrt(e*x)/(sqrt(2)*sqrt(e)),I)*sqrt(2)/(sqrt(b)*sqrt(e))],
[1/(sqrt(2-3*x)*sqrt(x)*sqrt(2+3*x)),x,1,EllipticF(sqrt(3/2)*sqrt(x),I)*sqrt(2/3)],
[1/(sqrt(2-3*x)*sqrt(-x)*sqrt(2+3*x)),x,1,-EllipticF(sqrt(3/2)*sqrt(-x),I)*sqrt(2/3)],
[1/(sqrt(2-3*x)*sqrt(e*x)*sqrt(2+3*x)),x,1,EllipticF(sqrt(3/2)*sqrt(e*x)/sqrt(e),I)*sqrt(2/3)/sqrt(e)],
[1/(sqrt(1-x)*sqrt(x)*sqrt(1+x)),x,1,2*EllipticF(sqrt(x),I)],
[1/(sqrt(1+x)*sqrt(x-x^2)),x,2,2*EllipticF(sqrt(x),I)],
[1/(sqrt(b*x)*sqrt(1-c*x)*sqrt(1+c*x)),x,1,2*EllipticF(sqrt(c)*sqrt(b*x)/sqrt(b),I)/(sqrt(b)*sqrt(c))],
[1/(sqrt(b*x)*sqrt(1-c*x)*sqrt(1+d*x)),x,1,2*EllipticF(sqrt(c)*sqrt(b*x)/sqrt(b),sqrt(-d/c))/(sqrt(b)*sqrt(c))],
[sqrt(1+x)/(sqrt(1-x)*sqrt(x)),x,1,2*EllipticE(sqrt(x),I)],
[sqrt(1+x)/sqrt(x-x^2),x,2,2*EllipticE(sqrt(x),I)],
[sqrt(1+c*x)/(sqrt(b*x)*sqrt(1-c*x)),x,1,2*EllipticE(sqrt(c)*sqrt(b*x)/sqrt(b),I)/(sqrt(b)*sqrt(c))],
[sqrt(1+c*x)/(sqrt(b*x)*sqrt(1-d*x)),x,1,2*EllipticE(sqrt(d)*sqrt(b*x)/sqrt(b),sqrt(-c/d))/(sqrt(b)*sqrt(d))],

#  Following integrands are equal. 
[sqrt(1-x)/(sqrt(x)*sqrt(1+x)),x,2,-2*EllipticE(sqrt(-x),I)*sqrt(-x)/sqrt(x)],
[sqrt(-1+1/x)*sqrt(1/x)*sqrt(x)/sqrt(1+x),x,4,-2*EllipticE(sqrt(-x),I)*sqrt(-x)/sqrt(x),-2*EllipticE(sqrt(-x),I)*sqrt(-1+1/x)*sqrt(1/x)*sqrt(-x)*sqrt(x)/sqrt(1-x)],
[sqrt(1-c*x)/(sqrt(b*x)*sqrt(1+c*x)),x,1,-2*EllipticE(sqrt(c)*sqrt(b*x)/sqrt(-b),I)/(sqrt(-b)*sqrt(c))],
[sqrt(1-c*x)/(sqrt(b*x)*sqrt(1+d*x)),x,1,-2*EllipticE(sqrt(d)*sqrt(b*x)/sqrt(-b),sqrt(-c/d))/(sqrt(-b)*sqrt(d))],
[1/(sqrt(2-3*x)*sqrt(x)*sqrt(d+e*x)),x,2,2*EllipticF(sqrt(3/2)*sqrt(x),sqrt(-2/3*e/d))*sqrt(1+e*x/d)/(sqrt(3)*sqrt(d+e*x))],
[sqrt(d+e*x)/(sqrt(2-3*x)*sqrt(x)),x,2,2*EllipticE(sqrt(3/2)*sqrt(x),sqrt(-2/3*e/d))*sqrt(d+e*x)/(sqrt(3)*sqrt(1+e*x/d))],

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

# Integrands of the form x^m (a+b x)^(n/3) (c+d x)^(p/3)
[x^4/((1-x)^(1/3)*(2-x)^(1/3)),x,8,99/130*(1-x)^(2/3)*(2-x)^(2/3)*x^2+3/13*(1-x)^(2/3)*(2-x)^(2/3)*x^3+27/455*(1-x)^(2/3)*(2-x)^(2/3)*(89+34*x)-891/91*2^(2/3)*(2-3*x+x^2)^(1/3)*sqrt((3-2*x)^2)*sqrt((-3+2*x)^2)/((3-2*x)*(1-x)^(1/3)*(2-x)^(1/3)*(1+2^(2/3)*(2-3*x+x^2)^(1/3)+sqrt(3)))-594/91*2^(1/6)*3^(3/4)*(2-3*x+x^2)^(1/3)*(1+2^(2/3)*(2-3*x+x^2)^(1/3))*EllipticF((1+2^(2/3)*(2-3*x+x^2)^(1/3)-sqrt(3))/(1+2^(2/3)*(2-3*x+x^2)^(1/3)+sqrt(3)),sqrt(-7-4*sqrt(3)))*sqrt((-3+2*x)^2)*sqrt((1-2^(2/3)*(2-3*x+x^2)^(1/3)+2*2^(1/3)*(2-3*x+x^2)^(2/3))/(1+2^(2/3)*(2-3*x+x^2)^(1/3)+sqrt(3))^2)/((3-2*x)*(1-x)^(1/3)*(2-x)^(1/3)*sqrt((3-2*x)^2)*sqrt((1+2^(2/3)*(2-3*x+x^2)^(1/3))/(1+2^(2/3)*(2-3*x+x^2)^(1/3)+sqrt(3))^2))+891/91*3^(1/4)*(2-3*x+x^2)^(1/3)*(1+2^(2/3)*(2-3*x+x^2)^(1/3))*EllipticE((1+2^(2/3)*(2-3*x+x^2)^(1/3)-sqrt(3))/(1+2^(2/3)*(2-3*x+x^2)^(1/3)+sqrt(3)),sqrt(-7-4*sqrt(3)))*sqrt((-3+2*x)^2)*sqrt(2-sqrt(3))*sqrt((1-2^(2/3)*(2-3*x+x^2)^(1/3)+2*2^(1/3)*(2-3*x+x^2)^(2/3))/(1+2^(2/3)*(2-3*x+x^2)^(1/3)+sqrt(3))^2)/(2^(1/3)*(3-2*x)*(1-x)^(1/3)*(2-x)^(1/3)*sqrt((3-2*x)^2)*sqrt((1+2^(2/3)*(2-3*x+x^2)^(1/3))/(1+2^(2/3)*(2-3*x+x^2)^(1/3)+sqrt(3))^2))],
[x^3/((1-x)^(1/3)*(2-x)^(1/3)),x,7,3/10*(1-x)^(2/3)*(2-x)^(2/3)*x^2+9/70*(1-x)^(2/3)*(2-x)^(2/3)*(23+8*x)-81/7*(2-3*x+x^2)^(1/3)*sqrt((3-2*x)^2)*sqrt((-3+2*x)^2)/(2^(1/3)*(3-2*x)*(1-x)^(1/3)*(2-x)^(1/3)*(1+2^(2/3)*(2-3*x+x^2)^(1/3)+sqrt(3)))-27/7*2^(1/6)*3^(3/4)*(2-3*x+x^2)^(1/3)*(1+2^(2/3)*(2-3*x+x^2)^(1/3))*EllipticF((1+2^(2/3)*(2-3*x+x^2)^(1/3)-sqrt(3))/(1+2^(2/3)*(2-3*x+x^2)^(1/3)+sqrt(3)),sqrt(-7-4*sqrt(3)))*sqrt((-3+2*x)^2)*sqrt((1-2^(2/3)*(2-3*x+x^2)^(1/3)+2*2^(1/3)*(2-3*x+x^2)^(2/3))/(1+2^(2/3)*(2-3*x+x^2)^(1/3)+sqrt(3))^2)/((3-2*x)*(1-x)^(1/3)*(2-x)^(1/3)*sqrt((3-2*x)^2)*sqrt((1+2^(2/3)*(2-3*x+x^2)^(1/3))/(1+2^(2/3)*(2-3*x+x^2)^(1/3)+sqrt(3))^2))+81/14*3^(1/4)*(2-3*x+x^2)^(1/3)*(1+2^(2/3)*(2-3*x+x^2)^(1/3))*EllipticE((1+2^(2/3)*(2-3*x+x^2)^(1/3)-sqrt(3))/(1+2^(2/3)*(2-3*x+x^2)^(1/3)+sqrt(3)),sqrt(-7-4*sqrt(3)))*sqrt((-3+2*x)^2)*sqrt(2-sqrt(3))*sqrt((1-2^(2/3)*(2-3*x+x^2)^(1/3)+2*2^(1/3)*(2-3*x+x^2)^(2/3))/(1+2^(2/3)*(2-3*x+x^2)^(1/3)+sqrt(3))^2)/(2^(1/3)*(3-2*x)*(1-x)^(1/3)*(2-x)^(1/3)*sqrt((3-2*x)^2)*sqrt((1+2^(2/3)*(2-3*x+x^2)^(1/3))/(1+2^(2/3)*(2-3*x+x^2)^(1/3)+sqrt(3))^2))],
[x^2/((1-x)^(1/3)*(2-x)^(1/3)),x,7,45/28*(1-x)^(2/3)*(2-x)^(2/3)+3/7*(1-x)^(2/3)*(2-x)^(2/3)*x-99/14*(2-3*x+x^2)^(1/3)*sqrt((3-2*x)^2)*sqrt((-3+2*x)^2)/(2^(1/3)*(3-2*x)*(1-x)^(1/3)*(2-x)^(1/3)*(1+2^(2/3)*(2-3*x+x^2)^(1/3)+sqrt(3)))-33/7*3^(3/4)*(2-3*x+x^2)^(1/3)*(1+2^(2/3)*(2-3*x+x^2)^(1/3))*EllipticF((1+2^(2/3)*(2-3*x+x^2)^(1/3)-sqrt(3))/(1+2^(2/3)*(2-3*x+x^2)^(1/3)+sqrt(3)),sqrt(-7-4*sqrt(3)))*sqrt((-3+2*x)^2)*sqrt((1-2^(2/3)*(2-3*x+x^2)^(1/3)+2*2^(1/3)*(2-3*x+x^2)^(2/3))/(1+2^(2/3)*(2-3*x+x^2)^(1/3)+sqrt(3))^2)/(2^(5/6)*(3-2*x)*(1-x)^(1/3)*(2-x)^(1/3)*sqrt((3-2*x)^2)*sqrt((1+2^(2/3)*(2-3*x+x^2)^(1/3))/(1+2^(2/3)*(2-3*x+x^2)^(1/3)+sqrt(3))^2))+99/28*3^(1/4)*(2-3*x+x^2)^(1/3)*(1+2^(2/3)*(2-3*x+x^2)^(1/3))*EllipticE((1+2^(2/3)*(2-3*x+x^2)^(1/3)-sqrt(3))/(1+2^(2/3)*(2-3*x+x^2)^(1/3)+sqrt(3)),sqrt(-7-4*sqrt(3)))*sqrt((-3+2*x)^2)*sqrt(2-sqrt(3))*sqrt((1-2^(2/3)*(2-3*x+x^2)^(1/3)+2*2^(1/3)*(2-3*x+x^2)^(2/3))/(1+2^(2/3)*(2-3*x+x^2)^(1/3)+sqrt(3))^2)/(2^(1/3)*(3-2*x)*(1-x)^(1/3)*(2-x)^(1/3)*sqrt((3-2*x)^2)*sqrt((1+2^(2/3)*(2-3*x+x^2)^(1/3))/(1+2^(2/3)*(2-3*x+x^2)^(1/3)+sqrt(3))^2))],
[x/((1-x)^(1/3)*(2-x)^(1/3)),x,6,3/4*(1-x)^(2/3)*(2-x)^(2/3)-9/2*(2-3*x+x^2)^(1/3)*sqrt((3-2*x)^2)*sqrt((-3+2*x)^2)/(2^(1/3)*(3-2*x)*(1-x)^(1/3)*(2-x)^(1/3)*(1+2^(2/3)*(2-3*x+x^2)^(1/3)+sqrt(3)))-3*3^(3/4)*(2-3*x+x^2)^(1/3)*(1+2^(2/3)*(2-3*x+x^2)^(1/3))*EllipticF((1+2^(2/3)*(2-3*x+x^2)^(1/3)-sqrt(3))/(1+2^(2/3)*(2-3*x+x^2)^(1/3)+sqrt(3)),sqrt(-7-4*sqrt(3)))*sqrt((-3+2*x)^2)*sqrt((1-2^(2/3)*(2-3*x+x^2)^(1/3)+2*2^(1/3)*(2-3*x+x^2)^(2/3))/(1+2^(2/3)*(2-3*x+x^2)^(1/3)+sqrt(3))^2)/(2^(5/6)*(3-2*x)*(1-x)^(1/3)*(2-x)^(1/3)*sqrt((3-2*x)^2)*sqrt((1+2^(2/3)*(2-3*x+x^2)^(1/3))/(1+2^(2/3)*(2-3*x+x^2)^(1/3)+sqrt(3))^2))+9/4*3^(1/4)*(2-3*x+x^2)^(1/3)*(1+2^(2/3)*(2-3*x+x^2)^(1/3))*EllipticE((1+2^(2/3)*(2-3*x+x^2)^(1/3)-sqrt(3))/(1+2^(2/3)*(2-3*x+x^2)^(1/3)+sqrt(3)),sqrt(-7-4*sqrt(3)))*sqrt((-3+2*x)^2)*sqrt(2-sqrt(3))*sqrt((1-2^(2/3)*(2-3*x+x^2)^(1/3)+2*2^(1/3)*(2-3*x+x^2)^(2/3))/(1+2^(2/3)*(2-3*x+x^2)^(1/3)+sqrt(3))^2)/(2^(1/3)*(3-2*x)*(1-x)^(1/3)*(2-x)^(1/3)*sqrt((3-2*x)^2)*sqrt((1+2^(2/3)*(2-3*x+x^2)^(1/3))/(1+2^(2/3)*(2-3*x+x^2)^(1/3)+sqrt(3))^2))],
[1/((1-x)^(1/3)*(2-x)^(1/3)),x,5,-3*(2-3*x+x^2)^(1/3)*sqrt((3-2*x)^2)*sqrt((-3+2*x)^2)/(2^(1/3)*(3-2*x)*(1-x)^(1/3)*(2-x)^(1/3)*(1+2^(2/3)*(2-3*x+x^2)^(1/3)+sqrt(3)))-2^(1/6)*3^(3/4)*(2-3*x+x^2)^(1/3)*(1+2^(2/3)*(2-3*x+x^2)^(1/3))*EllipticF((1+2^(2/3)*(2-3*x+x^2)^(1/3)-sqrt(3))/(1+2^(2/3)*(2-3*x+x^2)^(1/3)+sqrt(3)),sqrt(-7-4*sqrt(3)))*sqrt((-3+2*x)^2)*sqrt((1-2^(2/3)*(2-3*x+x^2)^(1/3)+2*2^(1/3)*(2-3*x+x^2)^(2/3))/(1+2^(2/3)*(2-3*x+x^2)^(1/3)+sqrt(3))^2)/((3-2*x)*(1-x)^(1/3)*(2-x)^(1/3)*sqrt((3-2*x)^2)*sqrt((1+2^(2/3)*(2-3*x+x^2)^(1/3))/(1+2^(2/3)*(2-3*x+x^2)^(1/3)+sqrt(3))^2))+3/2*3^(1/4)*(2-3*x+x^2)^(1/3)*(1+2^(2/3)*(2-3*x+x^2)^(1/3))*EllipticE((1+2^(2/3)*(2-3*x+x^2)^(1/3)-sqrt(3))/(1+2^(2/3)*(2-3*x+x^2)^(1/3)+sqrt(3)),sqrt(-7-4*sqrt(3)))*sqrt((-3+2*x)^2)*sqrt(2-sqrt(3))*sqrt((1-2^(2/3)*(2-3*x+x^2)^(1/3)+2*2^(1/3)*(2-3*x+x^2)^(2/3))/(1+2^(2/3)*(2-3*x+x^2)^(1/3)+sqrt(3))^2)/(2^(1/3)*(3-2*x)*(1-x)^(1/3)*(2-x)^(1/3)*sqrt((3-2*x)^2)*sqrt((1+2^(2/3)*(2-3*x+x^2)^(1/3))/(1+2^(2/3)*(2-3*x+x^2)^(1/3)+sqrt(3))^2))],
[1/((1-x)^(1/3)*(2-x)^(1/3)*x),x,1,3/4*log(-(1-x)^(1/3)+(2-x)^(2/3)/2^(2/3))/2^(1/3)-1/2*log(x)/2^(1/3)-1/2*arctan(1/sqrt(3)+2^(1/3)*(2-x)^(2/3)/((1-x)^(1/3)*sqrt(3)))*sqrt(3)/2^(1/3)],
[1/((1-x)^(1/3)*(2-x)^(1/3)*x^2),x,8,-1/2*(1-x)^(2/3)*(2-x)^(2/3)/x+3/8*log(-(1-x)^(1/3)+(2-x)^(2/3)/2^(2/3))/2^(1/3)-1/4*log(x)/2^(1/3)-1/4*arctan(1/sqrt(3)+2^(1/3)*(2-x)^(2/3)/((1-x)^(1/3)*sqrt(3)))*sqrt(3)/2^(1/3)-1/2*(2-3*x+x^2)^(1/3)*sqrt((3-2*x)^2)*sqrt((-3+2*x)^2)/(2^(1/3)*(3-2*x)*(1-x)^(1/3)*(2-x)^(1/3)*(1+2^(2/3)*(2-3*x+x^2)^(1/3)+sqrt(3)))-(2-3*x+x^2)^(1/3)*(1+2^(2/3)*(2-3*x+x^2)^(1/3))*EllipticF((1+2^(2/3)*(2-3*x+x^2)^(1/3)-sqrt(3))/(1+2^(2/3)*(2-3*x+x^2)^(1/3)+sqrt(3)),sqrt(-7-4*sqrt(3)))*sqrt((-3+2*x)^2)*sqrt((1-2^(2/3)*(2-3*x+x^2)^(1/3)+2*2^(1/3)*(2-3*x+x^2)^(2/3))/(1+2^(2/3)*(2-3*x+x^2)^(1/3)+sqrt(3))^2)/(2^(5/6)*3^(1/4)*(3-2*x)*(1-x)^(1/3)*(2-x)^(1/3)*sqrt((3-2*x)^2)*sqrt((1+2^(2/3)*(2-3*x+x^2)^(1/3))/(1+2^(2/3)*(2-3*x+x^2)^(1/3)+sqrt(3))^2))+1/4*3^(1/4)*(2-3*x+x^2)^(1/3)*(1+2^(2/3)*(2-3*x+x^2)^(1/3))*EllipticE((1+2^(2/3)*(2-3*x+x^2)^(1/3)-sqrt(3))/(1+2^(2/3)*(2-3*x+x^2)^(1/3)+sqrt(3)),sqrt(-7-4*sqrt(3)))*sqrt((-3+2*x)^2)*sqrt(2-sqrt(3))*sqrt((1-2^(2/3)*(2-3*x+x^2)^(1/3)+2*2^(1/3)*(2-3*x+x^2)^(2/3))/(1+2^(2/3)*(2-3*x+x^2)^(1/3)+sqrt(3))^2)/(2^(1/3)*(3-2*x)*(1-x)^(1/3)*(2-x)^(1/3)*sqrt((3-2*x)^2)*sqrt((1+2^(2/3)*(2-3*x+x^2)^(1/3))/(1+2^(2/3)*(2-3*x+x^2)^(1/3)+sqrt(3))^2))],
[1/((1-x)^(1/3)*(2-x)^(1/3)*x^3),x,9,-1/4*(1-x)^(2/3)*(2-x)^(2/3)/x^2-1/2*(1-x)^(2/3)*(2-x)^(2/3)/x+1/4*log(-(1-x)^(1/3)+(2-x)^(2/3)/2^(2/3))/2^(1/3)-1/6*log(x)/2^(1/3)-1/2*arctan(1/sqrt(3)+2^(1/3)*(2-x)^(2/3)/((1-x)^(1/3)*sqrt(3)))/(2^(1/3)*sqrt(3))-1/2*(2-3*x+x^2)^(1/3)*sqrt((3-2*x)^2)*sqrt((-3+2*x)^2)/(2^(1/3)*(3-2*x)*(1-x)^(1/3)*(2-x)^(1/3)*(1+2^(2/3)*(2-3*x+x^2)^(1/3)+sqrt(3)))-(2-3*x+x^2)^(1/3)*(1+2^(2/3)*(2-3*x+x^2)^(1/3))*EllipticF((1+2^(2/3)*(2-3*x+x^2)^(1/3)-sqrt(3))/(1+2^(2/3)*(2-3*x+x^2)^(1/3)+sqrt(3)),sqrt(-7-4*sqrt(3)))*sqrt((-3+2*x)^2)*sqrt((1-2^(2/3)*(2-3*x+x^2)^(1/3)+2*2^(1/3)*(2-3*x+x^2)^(2/3))/(1+2^(2/3)*(2-3*x+x^2)^(1/3)+sqrt(3))^2)/(2^(5/6)*3^(1/4)*(3-2*x)*(1-x)^(1/3)*(2-x)^(1/3)*sqrt((3-2*x)^2)*sqrt((1+2^(2/3)*(2-3*x+x^2)^(1/3))/(1+2^(2/3)*(2-3*x+x^2)^(1/3)+sqrt(3))^2))+1/4*3^(1/4)*(2-3*x+x^2)^(1/3)*(1+2^(2/3)*(2-3*x+x^2)^(1/3))*EllipticE((1+2^(2/3)*(2-3*x+x^2)^(1/3)-sqrt(3))/(1+2^(2/3)*(2-3*x+x^2)^(1/3)+sqrt(3)),sqrt(-7-4*sqrt(3)))*sqrt((-3+2*x)^2)*sqrt(2-sqrt(3))*sqrt((1-2^(2/3)*(2-3*x+x^2)^(1/3)+2*2^(1/3)*(2-3*x+x^2)^(2/3))/(1+2^(2/3)*(2-3*x+x^2)^(1/3)+sqrt(3))^2)/(2^(1/3)*(3-2*x)*(1-x)^(1/3)*(2-x)^(1/3)*sqrt((3-2*x)^2)*sqrt((1+2^(2/3)*(2-3*x+x^2)^(1/3))/(1+2^(2/3)*(2-3*x+x^2)^(1/3)+sqrt(3))^2))],

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

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

# n>0
[x^3*(a+b*x)^(1/4)/(c+d*x)^(1/4),x,8,-1/512*(195*b^3*c^3+135*a*b^2*c^2*d+105*a^2*b*c*d^2+77*a^3*d^3)*(a+b*x)^(1/4)*(c+d*x)^(3/4)/(b^3*d^4)+1/4*x^2*(a+b*x)^(5/4)*(c+d*x)^(3/4)/(b*d)+1/384*(a+b*x)^(5/4)*(c+d*x)^(3/4)*(117*b^2*c^2+94*a*b*c*d+77*a^2*d^2-8*b*d*(13*b*c+11*a*d)*x)/(b^3*d^3)+1/1024*(b*c-a*d)*(195*b^3*c^3+135*a*b^2*c^2*d+105*a^2*b*c*d^2+77*a^3*d^3)*arctan(d^(1/4)*(a+b*x)^(1/4)/(b^(1/4)*(c+d*x)^(1/4)))/(b^(15/4)*d^(17/4))+1/1024*(b*c-a*d)*(195*b^3*c^3+135*a*b^2*c^2*d+105*a^2*b*c*d^2+77*a^3*d^3)*arctanh(d^(1/4)*(a+b*x)^(1/4)/(b^(1/4)*(c+d*x)^(1/4)))/(b^(15/4)*d^(17/4))],
[x^2*(a+b*x)^(1/4)/(c+d*x)^(1/4),x,8,1/32*(15*b^2*c^2+10*a*b*c*d+7*a^2*d^2)*(a+b*x)^(1/4)*(c+d*x)^(3/4)/(b^2*d^3)-1/24*(9*b*c+7*a*d)*(a+b*x)^(5/4)*(c+d*x)^(3/4)/(b^2*d^2)+1/3*x*(a+b*x)^(5/4)*(c+d*x)^(3/4)/(b*d)-1/64*(b*c-a*d)*(15*b^2*c^2+10*a*b*c*d+7*a^2*d^2)*arctan(d^(1/4)*(a+b*x)^(1/4)/(b^(1/4)*(c+d*x)^(1/4)))/(b^(11/4)*d^(13/4))-1/64*(b*c-a*d)*(15*b^2*c^2+10*a*b*c*d+7*a^2*d^2)*arctanh(d^(1/4)*(a+b*x)^(1/4)/(b^(1/4)*(c+d*x)^(1/4)))/(b^(11/4)*d^(13/4))],
[x*(a+b*x)^(1/4)/(c+d*x)^(1/4),x,7,-1/8*(5*b*c+3*a*d)*(a+b*x)^(1/4)*(c+d*x)^(3/4)/(b*d^2)+1/2*(a+b*x)^(5/4)*(c+d*x)^(3/4)/(b*d)+1/16*(b*c-a*d)*(5*b*c+3*a*d)*arctan(d^(1/4)*(a+b*x)^(1/4)/(b^(1/4)*(c+d*x)^(1/4)))/(b^(7/4)*d^(9/4))+1/16*(b*c-a*d)*(5*b*c+3*a*d)*arctanh(d^(1/4)*(a+b*x)^(1/4)/(b^(1/4)*(c+d*x)^(1/4)))/(b^(7/4)*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))],
[(a+b*x)^(1/4)/(x*(c+d*x)^(1/4)),x,11,-2*a^(1/4)*arctan(c^(1/4)*(a+b*x)^(1/4)/(a^(1/4)*(c+d*x)^(1/4)))/c^(1/4)+2*b^(1/4)*arctan(d^(1/4)*(a+b*x)^(1/4)/(b^(1/4)*(c+d*x)^(1/4)))/d^(1/4)-2*a^(1/4)*arctanh(c^(1/4)*(a+b*x)^(1/4)/(a^(1/4)*(c+d*x)^(1/4)))/c^(1/4)+2*b^(1/4)*arctanh(d^(1/4)*(a+b*x)^(1/4)/(b^(1/4)*(c+d*x)^(1/4)))/d^(1/4)],
[(a+b*x)^(1/4)/(x^2*(c+d*x)^(1/4)),x,5,-(a+b*x)^(1/4)*(c+d*x)^(3/4)/(c*x)-1/2*(b*c-a*d)*arctan(c^(1/4)*(a+b*x)^(1/4)/(a^(1/4)*(c+d*x)^(1/4)))/(a^(3/4)*c^(5/4))-1/2*(b*c-a*d)*arctanh(c^(1/4)*(a+b*x)^(1/4)/(a^(1/4)*(c+d*x)^(1/4)))/(a^(3/4)*c^(5/4))],
[(a+b*x)^(1/4)/(x^3*(c+d*x)^(1/4)),x,6,1/8*(3*b*c+5*a*d)*(a+b*x)^(1/4)*(c+d*x)^(3/4)/(a*c^2*x)-1/2*(a+b*x)^(5/4)*(c+d*x)^(3/4)/(a*c*x^2)+1/16*(b*c-a*d)*(3*b*c+5*a*d)*arctan(c^(1/4)*(a+b*x)^(1/4)/(a^(1/4)*(c+d*x)^(1/4)))/(a^(7/4)*c^(9/4))+1/16*(b*c-a*d)*(3*b*c+5*a*d)*arctanh(c^(1/4)*(a+b*x)^(1/4)/(a^(1/4)*(c+d*x)^(1/4)))/(a^(7/4)*c^(9/4))],
[(a+b*x)^(1/4)/(x^4*(c+d*x)^(1/4)),x,8,-1/3*(a+b*x)^(1/4)*(c+d*x)^(3/4)/(c*x^3)-1/24*(b*c-9*a*d)*(a+b*x)^(1/4)*(c+d*x)^(3/4)/(a*c^2*x^2)+1/96*(7*b*c-15*a*d)*(b*c+3*a*d)*(a+b*x)^(1/4)*(c+d*x)^(3/4)/(a^2*c^3*x)-1/64*(b*c-a*d)*(7*b^2*c^2+10*a*b*c*d+15*a^2*d^2)*arctan(c^(1/4)*(a+b*x)^(1/4)/(a^(1/4)*(c+d*x)^(1/4)))/(a^(11/4)*c^(13/4))-1/64*(b*c-a*d)*(7*b^2*c^2+10*a*b*c*d+15*a^2*d^2)*arctanh(c^(1/4)*(a+b*x)^(1/4)/(a^(1/4)*(c+d*x)^(1/4)))/(a^(11/4)*c^(13/4))],
[(a+b*x)^(1/4)/(x^5*(c+d*x)^(1/4)),x,9,-1/4*(a+b*x)^(1/4)*(c+d*x)^(3/4)/(c*x^4)-1/48*(b*c-13*a*d)*(a+b*x)^(1/4)*(c+d*x)^(3/4)/(a*c^2*x^3)+1/384*(11*b^2*c^2+10*a*b*c*d-117*a^2*d^2)*(a+b*x)^(1/4)*(c+d*x)^(3/4)/(a^2*c^3*x^2)-1/1536*(77*b^3*c^3+61*a*b^2*c^2*d+63*a^2*b*c*d^2-585*a^3*d^3)*(a+b*x)^(1/4)*(c+d*x)^(3/4)/(a^3*c^4*x)+1/1024*(b*c-a*d)*(77*b^3*c^3+105*a*b^2*c^2*d+135*a^2*b*c*d^2+195*a^3*d^3)*arctan(c^(1/4)*(a+b*x)^(1/4)/(a^(1/4)*(c+d*x)^(1/4)))/(a^(15/4)*c^(17/4))+1/1024*(b*c-a*d)*(77*b^3*c^3+105*a*b^2*c^2*d+135*a^2*b*c*d^2+195*a^3*d^3)*arctanh(c^(1/4)*(a+b*x)^(1/4)/(a^(1/4)*(c+d*x)^(1/4)))/(a^(15/4)*c^(17/4))],
[x^2*(1+x)^(1/4)/(1-x)^(1/4),x,14,-3/8*(1-x)^(3/4)*(1+x)^(1/4)-1/12*(1-x)^(3/4)*(1+x)^(5/4)-1/3*(1-x)^(3/4)*x*(1+x)^(5/4)+3/8*arctan(1-(1-x)^(1/4)*sqrt(2)/(1+x)^(1/4))/sqrt(2)-3/8*arctan(1+(1-x)^(1/4)*sqrt(2)/(1+x)^(1/4))/sqrt(2)-3/16*log(1-(1-x)^(1/4)*sqrt(2)/(1+x)^(1/4)+sqrt(1-x)/sqrt(1+x))/sqrt(2)+3/16*log(1+(1-x)^(1/4)*sqrt(2)/(1+x)^(1/4)+sqrt(1-x)/sqrt(1+x))/sqrt(2)],
[x*(1+x)^(1/4)/(1-x)^(1/4),x,13,-1/4*(1-x)^(3/4)*(1+x)^(1/4)-1/2*(1-x)^(3/4)*(1+x)^(5/4)+1/4*arctan(1-(1-x)^(1/4)*sqrt(2)/(1+x)^(1/4))/sqrt(2)-1/4*arctan(1+(1-x)^(1/4)*sqrt(2)/(1+x)^(1/4))/sqrt(2)-1/8*log(1-(1-x)^(1/4)*sqrt(2)/(1+x)^(1/4)+sqrt(1-x)/sqrt(1+x))/sqrt(2)+1/8*log(1+(1-x)^(1/4)*sqrt(2)/(1+x)^(1/4)+sqrt(1-x)/sqrt(1+x))/sqrt(2)],
[(1+x)^(1/4)/(1-x)^(1/4),x,12,-(1-x)^(3/4)*(1+x)^(1/4)+arctan(1-(1-x)^(1/4)*sqrt(2)/(1+x)^(1/4))/sqrt(2)-arctan(1+(1-x)^(1/4)*sqrt(2)/(1+x)^(1/4))/sqrt(2)-1/2*log(1-(1-x)^(1/4)*sqrt(2)/(1+x)^(1/4)+sqrt(1-x)/sqrt(1+x))/sqrt(2)+1/2*log(1+(1-x)^(1/4)*sqrt(2)/(1+x)^(1/4)+sqrt(1-x)/sqrt(1+x))/sqrt(2)],
[(1+x)^(1/4)/((1-x)^(1/4)*x),x,16,-2*arctan((1+x)^(1/4)/(1-x)^(1/4))-2*arctanh((1+x)^(1/4)/(1-x)^(1/4))-log(1-(1-x)^(1/4)*sqrt(2)/(1+x)^(1/4)+sqrt(1-x)/sqrt(1+x))/sqrt(2)+log(1+(1-x)^(1/4)*sqrt(2)/(1+x)^(1/4)+sqrt(1-x)/sqrt(1+x))/sqrt(2)+arctan(1-(1-x)^(1/4)*sqrt(2)/(1+x)^(1/4))*sqrt(2)-arctan(1+(1-x)^(1/4)*sqrt(2)/(1+x)^(1/4))*sqrt(2)],
[(1+x)^(1/4)/((1-x)^(1/4)*x^2),x,5,-(1-x)^(3/4)*(1+x)^(1/4)/x-arctan((1+x)^(1/4)/(1-x)^(1/4))-arctanh((1+x)^(1/4)/(1-x)^(1/4))],
[(1+x)^(1/4)/((1-x)^(1/4)*x^3),x,6,-1/4*(1-x)^(3/4)*(1+x)^(1/4)/x-1/2*(1-x)^(3/4)*(1+x)^(5/4)/x^2-1/4*arctan((1+x)^(1/4)/(1-x)^(1/4))-1/4*arctanh((1+x)^(1/4)/(1-x)^(1/4))],
[(1+x)^(1/4)/((1-x)^(1/4)*x^4),x,8,-1/3*(1-x)^(3/4)*(1+x)^(1/4)/x^3-5/12*(1-x)^(3/4)*(1+x)^(1/4)/x^2-11/24*(1-x)^(3/4)*(1+x)^(1/4)/x-3/8*arctan((1+x)^(1/4)/(1-x)^(1/4))-3/8*arctanh((1+x)^(1/4)/(1-x)^(1/4))],
[(1+x)^(1/4)/((1-x)^(1/4)*x^5),x,9,-1/4*(1-x)^(3/4)*(1+x)^(1/4)/x^4-7/24*(1-x)^(3/4)*(1+x)^(1/4)/x^3-29/96*(1-x)^(3/4)*(1+x)^(1/4)/x^2-83/192*(1-x)^(3/4)*(1+x)^(1/4)/x-11/64*arctan((1+x)^(1/4)/(1-x)^(1/4))-11/64*arctanh((1+x)^(1/4)/(1-x)^(1/4))],

# n<0
[x^3/((a+b*x)^(3/4)*(c+d*x)^(1/4)),x,7,1/3*x^2*(a+b*x)^(1/4)*(c+d*x)^(3/4)/(b*d)+1/96*(a+b*x)^(1/4)*(c+d*x)^(3/4)*(45*b^2*c^2+54*a*b*c*d+77*a^2*d^2-4*b*d*(9*b*c+11*a*d)*x)/(b^3*d^3)-1/64*(15*b^3*c^3+15*a*b^2*c^2*d+21*a^2*b*c*d^2+77*a^3*d^3)*arctan(d^(1/4)*(a+b*x)^(1/4)/(b^(1/4)*(c+d*x)^(1/4)))/(b^(15/4)*d^(13/4))-1/64*(15*b^3*c^3+15*a*b^2*c^2*d+21*a^2*b*c*d^2+77*a^3*d^3)*arctanh(d^(1/4)*(a+b*x)^(1/4)/(b^(1/4)*(c+d*x)^(1/4)))/(b^(15/4)*d^(13/4))],
[x^2/((a+b*x)^(3/4)*(c+d*x)^(1/4)),x,7,-1/8*(5*b*c+7*a*d)*(a+b*x)^(1/4)*(c+d*x)^(3/4)/(b^2*d^2)+1/2*x*(a+b*x)^(1/4)*(c+d*x)^(3/4)/(b*d)+1/16*(5*b^2*c^2+6*a*b*c*d+21*a^2*d^2)*arctan(d^(1/4)*(a+b*x)^(1/4)/(b^(1/4)*(c+d*x)^(1/4)))/(b^(11/4)*d^(9/4))+1/16*(5*b^2*c^2+6*a*b*c*d+21*a^2*d^2)*arctanh(d^(1/4)*(a+b*x)^(1/4)/(b^(1/4)*(c+d*x)^(1/4)))/(b^(11/4)*d^(9/4))],
[x/((a+b*x)^(3/4)*(c+d*x)^(1/4)),x,6,(a+b*x)^(1/4)*(c+d*x)^(3/4)/(b*d)-1/2*(b*c+3*a*d)*arctan(d^(1/4)*(a+b*x)^(1/4)/(b^(1/4)*(c+d*x)^(1/4)))/(b^(7/4)*d^(5/4))-1/2*(b*c+3*a*d)*arctanh(d^(1/4)*(a+b*x)^(1/4)/(b^(1/4)*(c+d*x)^(1/4)))/(b^(7/4)*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/(x*(a+b*x)^(3/4)*(c+d*x)^(1/4)),x,4,-2*arctan(c^(1/4)*(a+b*x)^(1/4)/(a^(1/4)*(c+d*x)^(1/4)))/(a^(3/4)*c^(1/4))-2*arctanh(c^(1/4)*(a+b*x)^(1/4)/(a^(1/4)*(c+d*x)^(1/4)))/(a^(3/4)*c^(1/4))],
[1/(x^2*(a+b*x)^(3/4)*(c+d*x)^(1/4)),x,5,-(a+b*x)^(1/4)*(c+d*x)^(3/4)/(a*c*x)+1/2*(3*b*c+a*d)*arctan(c^(1/4)*(a+b*x)^(1/4)/(a^(1/4)*(c+d*x)^(1/4)))/(a^(7/4)*c^(5/4))+1/2*(3*b*c+a*d)*arctanh(c^(1/4)*(a+b*x)^(1/4)/(a^(1/4)*(c+d*x)^(1/4)))/(a^(7/4)*c^(5/4))],
[1/(x^3*(a+b*x)^(3/4)*(c+d*x)^(1/4)),x,7,-1/2*(a+b*x)^(1/4)*(c+d*x)^(3/4)/(a*c*x^2)+1/8*(7*b*c+5*a*d)*(a+b*x)^(1/4)*(c+d*x)^(3/4)/(a^2*c^2*x)-1/16*(21*b^2*c^2+6*a*b*c*d+5*a^2*d^2)*arctan(c^(1/4)*(a+b*x)^(1/4)/(a^(1/4)*(c+d*x)^(1/4)))/(a^(11/4)*c^(9/4))-1/16*(21*b^2*c^2+6*a*b*c*d+5*a^2*d^2)*arctanh(c^(1/4)*(a+b*x)^(1/4)/(a^(1/4)*(c+d*x)^(1/4)))/(a^(11/4)*c^(9/4))],
[1/(x^4*(a+b*x)^(3/4)*(c+d*x)^(1/4)),x,8,-1/3*(a+b*x)^(1/4)*(c+d*x)^(3/4)/(a*c*x^3)+1/24*(11*b*c+9*a*d)*(a+b*x)^(1/4)*(c+d*x)^(3/4)/(a^2*c^2*x^2)-1/96*(77*b^2*c^2+54*a*b*c*d+45*a^2*d^2)*(a+b*x)^(1/4)*(c+d*x)^(3/4)/(a^3*c^3*x)+1/64*(77*b^3*c^3+21*a*b^2*c^2*d+15*a^2*b*c*d^2+15*a^3*d^3)*arctan(c^(1/4)*(a+b*x)^(1/4)/(a^(1/4)*(c+d*x)^(1/4)))/(a^(15/4)*c^(13/4))+1/64*(77*b^3*c^3+21*a*b^2*c^2*d+15*a^2*b*c*d^2+15*a^3*d^3)*arctanh(c^(1/4)*(a+b*x)^(1/4)/(a^(1/4)*(c+d*x)^(1/4)))/(a^(15/4)*c^(13/4))],

# Integrands of the form (e x)^(m/2) (a+b x)^(n/4) (c+d x)^(p/4)
[(e*x)^(3/2)/((1-x)^(1/4)*(1+x)^(1/4)),x,13,-1/4*e^(3/2)*arctan(1-sqrt(2)*sqrt(e*x)/((1-x^2)^(1/4)*sqrt(e)))/sqrt(2)+1/4*e^(3/2)*arctan(1+sqrt(2)*sqrt(e*x)/((1-x^2)^(1/4)*sqrt(e)))/sqrt(2)-1/8*e^(3/2)*log(sqrt(e)-sqrt(2)*sqrt(e*x)/(1-x^2)^(1/4)+x*sqrt(e)/sqrt(1-x^2))/sqrt(2)+1/8*e^(3/2)*log(sqrt(e)+sqrt(2)*sqrt(e*x)/(1-x^2)^(1/4)+x*sqrt(e)/sqrt(1-x^2))/sqrt(2)-1/2*e*(1-x^2)^(3/4)*sqrt(e*x)],
[1/((1-x)^(1/4)*(e*x)^(1/2)*(1+x)^(1/4)),x,12,-arctan(1-sqrt(2)*sqrt(e*x)/((1-x^2)^(1/4)*sqrt(e)))/(sqrt(2)*sqrt(e))+arctan(1+sqrt(2)*sqrt(e*x)/((1-x^2)^(1/4)*sqrt(e)))/(sqrt(2)*sqrt(e))-1/2*log(sqrt(e)-sqrt(2)*sqrt(e*x)/(1-x^2)^(1/4)+x*sqrt(e)/sqrt(1-x^2))/(sqrt(2)*sqrt(e))+1/2*log(sqrt(e)+sqrt(2)*sqrt(e*x)/(1-x^2)^(1/4)+x*sqrt(e)/sqrt(1-x^2))/(sqrt(2)*sqrt(e))],
[1/((1-x)^(1/4)*(e*x)^(5/2)*(1+x)^(1/4)),x,1,-2/3*(1-x)^(3/4)*(1+x)^(3/4)/(e*(e*x)^(3/2))],
[1/((1-x)^(1/4)*(e*x)^(9/2)*(1+x)^(1/4)),x,3,-2/3*(1-x^2)^(3/4)/(e*(e*x)^(7/2))+8/21*(1-x^2)^(7/4)/(e*(e*x)^(7/2))],
[1/((1-x)^(1/4)*(e*x)^(13/2)*(1+x)^(1/4)),x,4,-2/3*(1-x^2)^(3/4)/(e*(e*x)^(11/2))+16/21*(1-x^2)^(7/4)/(e*(e*x)^(11/2))-64/231*(1-x^2)^(11/4)/(e*(e*x)^(11/2))],
[(e*x)^(5/2)/((1-x)^(1/4)*(1+x)^(1/4)),x,6,-1/3*e*(e*x)^(3/2)*(1-x^2)^(3/4)-1/2*e^3*(1-x^2)^(3/4)/sqrt(e*x)+1/2*e^2*(1+(-1)/x^2)^(1/4)*sqrt(cos(1/2*arccsc(x))^2)/cos(1/2*arccsc(x))*EllipticE(sin(1/2*arccsc(x)),sqrt(2))*sqrt(e*x)/(1-x^2)^(1/4)],
[(e*x)^(1/2)/((1-x)^(1/4)*(1+x)^(1/4)),x,5,-e*(1-x^2)^(3/4)/sqrt(e*x)+(1+(-1)/x^2)^(1/4)*sqrt(cos(1/2*arccsc(x))^2)/cos(1/2*arccsc(x))*EllipticE(sin(1/2*arccsc(x)),sqrt(2))*sqrt(e*x)/(1-x^2)^(1/4)],
[1/((1-x)^(1/4)*(e*x)^(3/2)*(1+x)^(1/4)),x,4,-2*(1+(-1)/x^2)^(1/4)*sqrt(cos(1/2*arccsc(x))^2)/cos(1/2*arccsc(x))*EllipticE(sin(1/2*arccsc(x)),sqrt(2))*sqrt(e*x)/(e^2*(1-x^2)^(1/4))],
[1/((1-x)^(1/4)*(e*x)^(7/2)*(1+x)^(1/4)),x,5,-2/5*(1-x^2)^(3/4)/(e*(e*x)^(5/2))-4/5*(1+(-1)/x^2)^(1/4)*sqrt(cos(1/2*arccsc(x))^2)/cos(1/2*arccsc(x))*EllipticE(sin(1/2*arccsc(x)),sqrt(2))*sqrt(e*x)/(e^4*(1-x^2)^(1/4))],
[1/((1-x)^(1/4)*(e*x)^(11/2)*(1+x)^(1/4)),x,6,-2/9*(1-x^2)^(3/4)/(e*(e*x)^(9/2))-4/15*(1-x^2)^(3/4)/(e^3*(e*x)^(5/2))-8/15*(1+(-1)/x^2)^(1/4)*sqrt(cos(1/2*arccsc(x))^2)/cos(1/2*arccsc(x))*EllipticE(sin(1/2*arccsc(x)),sqrt(2))*sqrt(e*x)/(e^6*(1-x^2)^(1/4))],

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

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

# p>0
[x^2*(a+b*x)^n*(c+d*x),x,2,a^2*(b*c-a*d)*(a+b*x)^(1+n)/(b^4*(1+n))-a*(2*b*c-3*a*d)*(a+b*x)^(2+n)/(b^4*(2+n))+(b*c-3*a*d)*(a+b*x)^(3+n)/(b^4*(3+n))+d*(a+b*x)^(4+n)/(b^4*(4+n))],
[x*(a+b*x)^n*(c+d*x),x,2,-a*(b*c-a*d)*(a+b*x)^(1+n)/(b^3*(1+n))+(b*c-2*a*d)*(a+b*x)^(2+n)/(b^3*(2+n))+d*(a+b*x)^(3+n)/(b^3*(3+n))],
[(a+b*x)^n*(c+d*x),x,2,(b*c-a*d)*(a+b*x)^(1+n)/(b^2*(1+n))+d*(a+b*x)^(2+n)/(b^2*(2+n))],
[(a+b*x)^n*(c+d*x)/x,x,2,d*(a+b*x)^(1+n)/(b*(1+n))-c*(a+b*x)^(1+n)*hypergeom([1,1+n],[2+n],1+b*x/a)/(a*(1+n))],
[(a+b*x)^n*(c+d*x)/x^2,x,2,-c*(a+b*x)^(1+n)/(a*x)-(a*d+b*c*n)*(a+b*x)^(1+n)*hypergeom([1,1+n],[2+n],1+b*x/a)/(a^2*(1+n))],
[x^2*(a+b*x)^n*(c+d*x)^2,x,2,a^2*(b*c-a*d)^2*(a+b*x)^(1+n)/(b^5*(1+n))-2*a*(b*c-2*a*d)*(b*c-a*d)*(a+b*x)^(2+n)/(b^5*(2+n))+(b^2*c^2-6*a*b*c*d+6*a^2*d^2)*(a+b*x)^(3+n)/(b^5*(3+n))+2*d*(b*c-2*a*d)*(a+b*x)^(4+n)/(b^5*(4+n))+d^2*(a+b*x)^(5+n)/(b^5*(5+n))],
[x*(a+b*x)^n*(c+d*x)^2,x,2,-a*(b*c-a*d)^2*(a+b*x)^(1+n)/(b^4*(1+n))+(b*c-3*a*d)*(b*c-a*d)*(a+b*x)^(2+n)/(b^4*(2+n))+d*(2*b*c-3*a*d)*(a+b*x)^(3+n)/(b^4*(3+n))+d^2*(a+b*x)^(4+n)/(b^4*(4+n))],
[(a+b*x)^n*(c+d*x)^2,x,2,(b*c-a*d)^2*(a+b*x)^(1+n)/(b^3*(1+n))+2*d*(b*c-a*d)*(a+b*x)^(2+n)/(b^3*(2+n))+d^2*(a+b*x)^(3+n)/(b^3*(3+n))],
[(a+b*x)^n*(c+d*x)^2/x,x,3,d*(2*b*c-a*d)*(a+b*x)^(1+n)/(b^2*(1+n))+d^2*(a+b*x)^(2+n)/(b^2*(2+n))-c^2*(a+b*x)^(1+n)*hypergeom([1,1+n],[2+n],1+b*x/a)/(a*(1+n))],
[(a+b*x)^n*(c+d*x)^2/x^2,x,3,d^2*(a+b*x)^(1+n)/(b*(1+n))-c^2*(a+b*x)^(1+n)/(a*x)-c*(2*a*d+b*c*n)*(a+b*x)^(1+n)*hypergeom([1,1+n],[2+n],1+b*x/a)/(a^2*(1+n))],
[(a+b*x)^n*(c+d*x)^2/x^3,x,3,-1/2*c^2*(a+b*x)^(1+n)/(a*x^2)-1/2*c*(4*a*d-b*c*(1-n))*(a+b*x)^(1+n)/(a^2*x)-1/2*(2*a^2*d^2+4*a*b*c*d*n-b^2*c^2*(1-n)*n)*(a+b*x)^(1+n)*hypergeom([1,1+n],[2+n],1+b*x/a)/(a^3*(1+n))],
[(a+b*x)^n*(c+d*x)^2/x^4,x,3,-1/3*c^2*(a+b*x)^(1+n)/(a*x^3)-1/6*c*(6*a*d-b*c*(2-n))*(a+b*x)^(1+n)/(a^2*x^2)+1/6*b*(6*a^2*d^2-6*a*b*c*d*(1-n)+b^2*c^2*(2-3*n+n^2))*(a+b*x)^(1+n)*hypergeom([2,1+n],[2+n],1+b*x/a)/(a^4*(1+n))],
[x^2*(a+b*x)^n*(c+d*x)^3,x,2,a^2*(b*c-a*d)^3*(a+b*x)^(1+n)/(b^6*(1+n))-a*(2*b*c-5*a*d)*(b*c-a*d)^2*(a+b*x)^(2+n)/(b^6*(2+n))+(b*c-a*d)*(b^2*c^2-8*a*b*c*d+10*a^2*d^2)*(a+b*x)^(3+n)/(b^6*(3+n))+d*(3*b^2*c^2-12*a*b*c*d+10*a^2*d^2)*(a+b*x)^(4+n)/(b^6*(4+n))+d^2*(3*b*c-5*a*d)*(a+b*x)^(5+n)/(b^6*(5+n))+d^3*(a+b*x)^(6+n)/(b^6*(6+n))],
[x*(a+b*x)^n*(c+d*x)^3,x,2,-a*(b*c-a*d)^3*(a+b*x)^(1+n)/(b^5*(1+n))+(b*c-4*a*d)*(b*c-a*d)^2*(a+b*x)^(2+n)/(b^5*(2+n))+3*d*(b*c-2*a*d)*(b*c-a*d)*(a+b*x)^(3+n)/(b^5*(3+n))+d^2*(3*b*c-4*a*d)*(a+b*x)^(4+n)/(b^5*(4+n))+d^3*(a+b*x)^(5+n)/(b^5*(5+n))],
[(a+b*x)^n*(c+d*x)^3,x,2,(b*c-a*d)^3*(a+b*x)^(1+n)/(b^4*(1+n))+3*d*(b*c-a*d)^2*(a+b*x)^(2+n)/(b^4*(2+n))+3*d^2*(b*c-a*d)*(a+b*x)^(3+n)/(b^4*(3+n))+d^3*(a+b*x)^(4+n)/(b^4*(4+n))],
[(a+b*x)^n*(c+d*x)^3/x,x,3,d*(3*b^2*c^2-3*a*b*c*d+a^2*d^2)*(a+b*x)^(1+n)/(b^3*(1+n))+d^2*(3*b*c-2*a*d)*(a+b*x)^(2+n)/(b^3*(2+n))+d^3*(a+b*x)^(3+n)/(b^3*(3+n))-c^3*(a+b*x)^(1+n)*hypergeom([1,1+n],[2+n],1+b*x/a)/(a*(1+n))],
[(a+b*x)^n*(c+d*x)^3/x^2,x,3,d*(a+b*x)^(1+n)*(c+d*x)^2/(b*(2+n)*x)-(a+b*x)^(1+n)*(b*c^2*(1+n)*(a*d+b*c*(2+n))+a*d^2*(a*d-b*c*(4+n))*x)/(a*b^2*(1+n)*(2+n)*x)-c^2*(3*a*d+b*c*n)*(a+b*x)^(1+n)*hypergeom([1,1+n],[2+n],1+b*x/a)/(a^2*(1+n))],
[(a+b*x)^n*(c+d*x)^3/x^3,x,3,d*(a+b*x)^(1+n)*(c+d*x)^2/(b*(1+n)*x^2)-1/2*c*(a+b*x)^(1+n)*(a*c*(2*a*d+b*c*(1+n))+(4*a^2*d^2+6*a*b*c*d*(1+n)-b^2*c^2*(1-n^2))*x)/(a^2*b*(1+n)*x^2)-1/2*c*(6*a^2*d^2+6*a*b*c*d*n-b^2*c^2*(1-n)*n)*(a+b*x)^(1+n)*hypergeom([1,1+n],[2+n],1+b*x/a)/(a^3*(1+n))],
[x^(1+2*n)*(a+b*x)^n*(2*a+3*b*x),x,1,x^(2*(1+n))*(a+b*x)^(1+n)/(1+n)],

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

# Integrands of the form (e x)^(m/2) (a+b x)^n (c+d x)^p with n symbolic
[(b*x)^(5/2)*(c+d*x)^n*(e+f*x)^2,x,4,-2*f*(9*c*f-d*e*(13+2*n))*(b*x)^(7/2)*(c+d*x)^(1+n)/(b*d^2*(9+2*n)*(11+2*n))+2*f*(b*x)^(7/2)*(c+d*x)^(1+n)*(e+f*x)/(b*d*(11+2*n))+2/7*(63*c^2*f^2-14*c*d*e*f*(11+2*n)+d^2*e^2*(99+40*n+4*n^2))*(b*x)^(7/2)*(c+d*x)^n*hypergeom([7/2,-n],[9/2],-d*x/c)/(b*d^2*(9+2*n)*(11+2*n)*(1+d*x/c)^n)],
[(b*x)^(5/2)*(c+d*x)^n*(e+f*x),x,3,2*f*(b*x)^(7/2)*(c+d*x)^(1+n)/(b*d*(9+2*n))-2/7*(7*c*f-d*e*(9+2*n))*(b*x)^(7/2)*(c+d*x)^n*hypergeom([7/2,-n],[9/2],-d*x/c)/(b*d*(9+2*n)*(1+d*x/c)^n)],
[(b*x)^(5/2)*(c+d*x)^n/(e+f*x),x,3,2/7*(b*x)^(7/2)*(c+d*x)^n*AppellF1(7/2,-n,1,9/2,-d*x/c,-f*x/e)/(b*e*(1+d*x/c)^n)],
[(b*x)^(5/2)*(c+d*x)^n/(e+f*x)^2,x,3,2/7*(b*x)^(7/2)*(c+d*x)^n*AppellF1(7/2,-n,2,9/2,-d*x/c,-f*x/e)/(b*e^2*(1+d*x/c)^n)],

# Integrands of the form (e x)^m (a+b x)^n (c+d x)^p with m and n symbolic
[(b*x)^m*(c+d*x)^n*(e+f*x)^2,x,4,-f*(c*f*(2+m)-d*e*(4+m+n))*(b*x)^(1+m)*(c+d*x)^(1+n)/(b*d^2*(2+m+n)*(3+m+n))+f*(b*x)^(1+m)*(c+d*x)^(1+n)*(e+f*x)/(b*d*(3+m+n))+(c^2*f^2*(2+3*m+m^2)-2*c*d*e*f*(1+m)*(3+m+n)+d^2*e^2*(6+m^2+5*n+n^2+m*(5+2*n)))*(b*x)^(1+m)*(c+d*x)^n*hypergeom([1+m,-n],[2+m],-d*x/c)/(b*d^2*(1+m)*(2+m+n)*(3+m+n)*(1+d*x/c)^n)],
[(b*x)^m*(c+d*x)^n*(e+f*x),x,3,f*(b*x)^(1+m)*(c+d*x)^(1+n)/(b*d*(2+m+n))-(c*f*(1+m)-d*e*(2+m+n))*(b*x)^(1+m)*(c+d*x)^n*hypergeom([1+m,-n],[2+m],-d*x/c)/(b*d*(1+m)*(2+m+n)*(1+d*x/c)^n)],
[(b*x)^m*(c+d*x)^n/(e+f*x),x,2,(b*x)^(1+m)*(c+d*x)^n*AppellF1(1+m,-n,1,2+m,-d*x/c,-f*x/e)/(b*e*(1+m)*(1+d*x/c)^n)],
[(b*x)^m*(c+d*x)^n/(e+f*x)^2,x,2,(b*x)^(1+m)*(c+d*x)^n*AppellF1(1+m,-n,2,2+m,-d*x/c,-f*x/e)/(b*e^2*(1+m)*(1+d*x/c)^n)],

# Integrands of the form (e x)^m (a+b x)^n (c+d x)^p with n and p symbolic
[(b*x)^m*(c+d*x)^n*(e+f*x)^p,x,3,(b*x)^(1+m)*(c+d*x)^n*(e+f*x)^p*AppellF1(1+m,-n,-p,2+m,-d*x/c,-f*x/e)/(b*(1+m)*(1+d*x/c)^n*(1+f*x/e)^p)],
[(e*x)^m*(a-b*x)^(2+n)*(a+b*x)^n,x,-11,-(e*x)^(1+m)*(a-b*x)^(1+n)*(a+b*x)^(1+n)/(e*(3+m+2*n))+2*a^2*(2+m+n)*(e*x)^(1+m)*(a-b*x)^n*(a+b*x)^n*hypergeom([1/2*(1+m),-n],[1/2*(3+m)],b^2*x^2/a^2)/(e*(1+m)*(3+m+2*n)*(1-b^2*x^2/a^2)^n)-2*a*b*(e*x)^(2+m)*(a-b*x)^n*(a+b*x)^n*hypergeom([1/2*(2+m),-n],[1/2*(4+m)],b^2*x^2/a^2)/(e^2*(2+m)*(1-b^2*x^2/a^2)^n)],
[x^2*(a+b*x)^n*(c+d*x)^p,x,4,-(b*c*(2+n)+a*d*(2+p))*(a+b*x)^(1+n)*(c+d*x)^(1+p)/(b^2*d^2*(2+n+p)*(3+n+p))+x*(a+b*x)^(1+n)*(c+d*x)^(1+p)/(b*d*(3+n+p))-(b^2*c^2*(2+3*n+n^2)+2*a*b*c*d*(1+n)*(1+p)+a^2*d^2*(2+3*p+p^2))*(a+b*x)^(1+n)*(c+d*x)^(1+p)*hypergeom([1,2+n+p],[2+p],b*(c+d*x)/(b*c-a*d))/(b^2*d^2*(b*c-a*d)*(1+p)*(2+n+p)*(3+n+p)),-(b*c*(2+n)+a*d*(2+p))*(a+b*x)^(1+n)*(c+d*x)^(1+p)/(b^2*d^2*(2+n+p)*(3+n+p))+x*(a+b*x)^(1+n)*(c+d*x)^(1+p)/(b*d*(3+n+p))+(b^2*c^2*(2+3*n+n^2)+2*a*b*c*d*(1+n)*(1+p)+a^2*d^2*(2+3*p+p^2))*(a+b*x)^(1+n)*(c+d*x)^p*hypergeom([1+n,-p],[2+n],-d*(a+b*x)/(b*c-a*d))/(b^3*d^2*(1+n)*(2+n+p)*(3+n+p)*(b*(c+d*x)/(b*c-a*d))^p)],
[x*(a+b*x)^n*(c+d*x)^p,x,3,(a+b*x)^(1+n)*(c+d*x)^(1+p)/(b*d*(2+n+p))+(b*c*(1+n)+a*d*(1+p))*(a+b*x)^(1+n)*(c+d*x)^(1+p)*hypergeom([1,2+n+p],[2+p],b*(c+d*x)/(b*c-a*d))/(b*d*(b*c-a*d)*(1+p)*(2+n+p)),(a+b*x)^(1+n)*(c+d*x)^(1+p)/(b*d*(2+n+p))-(b*c*(1+n)+a*d*(1+p))*(a+b*x)^(1+n)*(c+d*x)^p*hypergeom([1+n,-p],[2+n],-d*(a+b*x)/(b*c-a*d))/(b^2*d*(1+n)*(2+n+p)*(b*(c+d*x)/(b*c-a*d))^p)],
[(a+b*x)^n*(c+d*x)^p,x,2,-(a+b*x)^(1+n)*(c+d*x)^(1+p)*hypergeom([1,2+n+p],[2+p],b*(c+d*x)/(b*c-a*d))/((b*c-a*d)*(1+p)),(a+b*x)^(1+n)*(c+d*x)^p*hypergeom([1+n,-p],[2+n],-d*(a+b*x)/(b*c-a*d))/(b*(1+n)*(b*(c+d*x)/(b*c-a*d))^p)],
[(a+b*x)^n*(c+d*x)^p/x,x,2,-(a+b*x)^(1+n)*(c+d*x)^p*AppellF1(1+n,-p,1,2+n,-d*(a+b*x)/(b*c-a*d),(a+b*x)/a)/(a*(1+n)*(b*(c+d*x)/(b*c-a*d))^p)],
[(a+b*x)^n*(c+d*x)^p/x^2,x,2,b*(a+b*x)^(1+n)*(c+d*x)^p*AppellF1(1+n,-p,2,2+n,-d*(a+b*x)/(b*c-a*d),(a+b*x)/a)/(a^2*(1+n)*(b*(c+d*x)/(b*c-a*d))^p)],
[(b*x)^(3/2)*(c+d*x)^n*(e+f*x)^p,x,3,2/5*(b*x)^(5/2)*(c+d*x)^n*(e+f*x)^p*AppellF1(5/2,-n,-p,7/2,-d*x/c,-f*x/e)/(b*(1+d*x/c)^n*(1+f*x/e)^p)],
[(b*x)^(1/2)*(c+d*x)^n*(e+f*x)^p,x,3,2/3*(b*x)^(3/2)*(c+d*x)^n*(e+f*x)^p*AppellF1(3/2,-n,-p,5/2,-d*x/c,-f*x/e)/(b*(1+d*x/c)^n*(1+f*x/e)^p)],
[(c+d*x)^n*(e+f*x)^p/(b*x)^(1/2),x,3,2*(c+d*x)^n*(e+f*x)^p*AppellF1(1/2,-n,-p,3/2,-d*x/c,-f*x/e)*sqrt(b*x)/(b*(1+d*x/c)^n*(1+f*x/e)^p)],
[(b*x)^m*(Pi+d*x)^n*(E+f*x)^p,x,1,exp(p)*Pi^n*(b*x)^(1+m)*AppellF1(1+m,-n,-p,2+m,-d*x/Pi,-f*x/E)/(b*(1+m))],
[(b*x)^m*(Pi+d*x)^n*(e+f*x)^p,x,2,Pi^n*(b*x)^(1+m)*(e+f*x)^p*AppellF1(1+m,-n,-p,2+m,-d*x/Pi,-f*x/e)/(b*(1+m)*(1+f*x/e)^p)],
[(b*x)^(5/2)*(Pi+d*x)^n*(E+f*x)^p,x,1,2/7*exp(p)*Pi^n*(b*x)^(7/2)*AppellF1(7/2,-n,-p,9/2,-d*x/Pi,-f*x/E)/b],
[(b*x)^(5/2)*(Pi+d*x)^n*(e+f*x)^p,x,2,2/7*Pi^n*(b*x)^(7/2)*(e+f*x)^p*AppellF1(7/2,-n,-p,9/2,-d*x/Pi,-f*x/e)/(b*(1+f*x/e)^p)],
[x^3*(a+b*x)^n/(c+d*x)^n,x,4,1/4*x^2*(a+b*x)^(1+n)*(c+d*x)^(1-n)/(b*d)+1/24*(a+b*x)^(1+n)*(c+d*x)^(1-n)*(2*a*b*c*d*(3-n^2)+a^2*d^2*(6-5*n+n^2)+b^2*c^2*(6+5*n+n^2)-2*b*d*(a*d*(3-n)+b*c*(3+n))*x)/(b^3*d^3)-1/24*(3*a*b^2*c^2*d*(2+n-2*n^2-n^3)+a^3*d^3*(6-11*n+6*n^2-n^3)+3*a^2*b*c*d^2*(2-n-2*n^2+n^3)+b^3*c^3*(6+11*n+6*n^2+n^3))*(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^4*d^3*(1+n)*(c+d*x)^n)],
[x^2*(a+b*x)^n/(c+d*x)^n,x,4,-1/6*(a*d*(2-n)+b*c*(2+n))*(a+b*x)^(1+n)*(c+d*x)^(1-n)/(b^2*d^2)+1/3*x*(a+b*x)^(1+n)*(c+d*x)^(1-n)/(b*d)+1/6*(2*a*b*c*d*(1-n^2)+a^2*d^2*(2-3*n+n^2)+b^2*c^2*(2+3*n+n^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^3*d^2*(1+n)*(c+d*x)^n)],
[x*(a+b*x)^n/(c+d*x)^n,x,3,1/2*(a+b*x)^(1+n)*(c+d*x)^(1-n)/(b*d)-1/2*(a*d*(1-n)+b*c*(1+n))*(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^2*d*(1+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)^n/(x*(c+d*x)^n),x,5,-(a+b*x)^n*hypergeom([1,n],[1+n],c*(a+b*x)/(a*(c+d*x)))/(n*(c+d*x)^n)+(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))/(n*(c+d*x)^n)],
[(a+b*x)^n/(x^2*(c+d*x)^n),x,1,(b*c-a*d)*(a+b*x)^(1+n)*(c+d*x)^(-1-n)*hypergeom([2,1+n],[2+n],c*(a+b*x)/(a*(c+d*x)))/(a^2*(1+n))],
[(a+b*x)^n/(x^3*(c+d*x)^n),x,2,-1/2*(a+b*x)^(1+n)*(c+d*x)^(1-n)/(a*c*x^2)-1/2*(b*c-a*d)*(a*d*(1+n)+b*(c-c*n))*(a+b*x)^(1+n)*(c+d*x)^(-1-n)*hypergeom([2,1+n],[2+n],c*(a+b*x)/(a*(c+d*x)))/(a^3*c*(1+n))],
[(a+b*x)^n/(x^4*(c+d*x)^n),x,4,-1/3*(a+b*x)^(1+n)*(c+d*x)^(1-n)/(a*c*x^3)+1/6*(b*c*(2-n)+a*d*(2+n))*(a+b*x)^(1+n)*(c+d*x)^(1-n)/(a^2*c^2*x^2)+1/6*(b*c-a*d)*(2*a*b*c*d*(1-n^2)+b^2*c^2*(2-3*n+n^2)+a^2*d^2*(2+3*n+n^2))*(a+b*x)^(1+n)*(c+d*x)^(-1-n)*hypergeom([2,1+n],[2+n],c*(a+b*x)/(a*(c+d*x)))/(a^4*c^2*(1+n))],
[(1-x)^n*x^3/(1+x)^n,x,3,-1/4*(1-x)^(1+n)*x^2*(1+x)^(1-n)-1/12*(1-x)^(1+n)*(1+x)^(1-n)*(3+2*n^2-2*n*x)+1/3*n*(2+n^2)*(1-x)^(1+n)*hypergeom([n,1+n],[2+n],1/2*(1-x))/(2^n*(1+n))],
[(1-x)^n*x^2/(1+x)^n,x,3,1/3*n*(1-x)^(1+n)*(1+x)^(1-n)-1/3*(1-x)^(1+n)*x*(1+x)^(1-n)-1/3*(1+2*n^2)*(1-x)^(1+n)*hypergeom([n,1+n],[2+n],1/2*(1-x))/(2^n*(1+n))],
[(1-x)^n*x/(1+x)^n,x,2,-1/2*(1-x)^(1+n)*(1+x)^(1-n)+n*(1-x)^(1+n)*hypergeom([n,1+n],[2+n],1/2*(1-x))/(2^n*(1+n))],
[(1-x)^n/(1+x)^n,x,1,-(1-x)^(1+n)*hypergeom([n,1+n],[2+n],1/2*(1-x))/(2^n*(1+n))],
[(1-x)^n/(x*(1+x)^n),x,3,-(1-x)^n*hypergeom([1,n],[1+n],(1-x)/(1+x))/(n*(1+x)^n)+(1-x)^n*hypergeom([n,n],[1+n],1/2*(1-x))/(2^n*n)],
[(1-x)^n/(x^2*(1+x)^n),x,1,-2*(1-x)^(1+n)*(1+x)^(-1-n)*hypergeom([2,1+n],[2+n],(1-x)/(1+x))/(1+n)],
[(1-x)^n/(x^3*(1+x)^n),x,2,-1/2*(1-x)^(1+n)*(1+x)^(1-n)/x^2+2*n*(1-x)^(1+n)*(1+x)^(-1-n)*hypergeom([2,1+n],[2+n],(1-x)/(1+x))/(1+n)],
[(1-x)^n/(x^4*(1+x)^n),x,4,-1/3*(1-x)^(1+n)*(1+x)^(1-n)/x^3+1/3*n*(1-x)^(1+n)*(1+x)^(1-n)/x^2-2/3*(1+2*n^2)*(1-x)^(1+n)*(1+x)^(-1-n)*hypergeom([2,1+n],[2+n],(1-x)/(1+x))/(1+n)],

#  Mathematica 8 cannot verify the second antiderivatives of the following pairs correct, although they are. 
[x^m*(1-a*x)^n*(1+a*x)^n,x,2,x^(1+m)*hypergeom([1/2*(1+m),-n],[1/2*(3+m)],a^2*x^2)/(1+m)],
[x^m*(1-a*x)^n*(2+2*a*x)^n,x,2,2^n*x^(1+m)*hypergeom([1/2*(1+m),-n],[1/2*(3+m)],a^2*x^2)/(1+m)],
[x^m*(2-a*x)^n*(2+a*x)^n,x,2,4^n*x^(1+m)*hypergeom([1/2*(1+m),-n],[1/2*(3+m)],1/4*a^2*x^2)/(1+m)],
[x^m*(1-1/2*a*x)^n*(2+a*x)^n,x,2,2^n*x^(1+m)*hypergeom([1/2*(1+m),-n],[1/2*(3+m)],1/4*a^2*x^2)/(1+m)],

#  Mathematica 8 cannot verify the following antiderivatives correct, although they are. 
[x^m*(3-2*a*x)^(2+n)*(6+4*a*x)^n,x,8,2^n*9^(1+n)*x^(1+m)*hypergeom([1/2*(1+m),-n],[1/2*(3+m)],4/9*a^2*x^2)/(1+m)-2^(2+n)*3^(1+2*n)*a*x^(2+m)*hypergeom([1/2*(2+m),-n],[1/2*(4+m)],4/9*a^2*x^2)/(2+m)+2^(2+n)*9^n*a^2*x^(3+m)*hypergeom([1/2*(3+m),-n],[1/2*(5+m)],4/9*a^2*x^2)/(3+m)],
[x^m*(3-2*a*x)^(1+n)*(6+4*a*x)^n,x,5,2^n*3^(1+2*n)*x^(1+m)*hypergeom([1/2*(1+m),-n],[1/2*(3+m)],4/9*a^2*x^2)/(1+m)-2^(1+n)*9^n*a*x^(2+m)*hypergeom([1/2*(2+m),-n],[1/2*(4+m)],4/9*a^2*x^2)/(2+m)],
[x^m*(3-2*a*x)^n*(6+4*a*x)^n,x,2,18^n*x^(1+m)*hypergeom([1/2*(1+m),-n],[1/2*(3+m)],4/9*a^2*x^2)/(1+m)],
[x^m*(3-2*a*x)^(-1+n)*(6+4*a*x)^n,x,5,2^n*3^(-1+2*n)*x^(1+m)*hypergeom([1/2*(1+m),1-n],[1/2*(3+m)],4/9*a^2*x^2)/(1+m)+2^(1+n)*9^(-1+n)*a*x^(2+m)*hypergeom([1/2*(2+m),1-n],[1/2*(4+m)],4/9*a^2*x^2)/(2+m)],
[x^m*(3-2*a*x)^(-2+n)*(6+4*a*x)^n,x,8,2^n*9^(-1+n)*x^(1+m)*hypergeom([1/2*(1+m),2-n],[1/2*(3+m)],4/9*a^2*x^2)/(1+m)+2^(2+n)*3^(-3+2*n)*a*x^(2+m)*hypergeom([1/2*(2+m),2-n],[1/2*(4+m)],4/9*a^2*x^2)/(2+m)+2^(2+n)*9^(-2+n)*a^2*x^(3+m)*hypergeom([1/2*(3+m),2-n],[1/2*(5+m)],4/9*a^2*x^2)/(3+m)],
[x^m*(a+b*x)^(1+n)*(c+d*x)^n,x,3,a*x^(1+m)*(a+b*x)^n*(c+d*x)^n*AppellF1(1+m,-1-n,-n,2+m,-b*x/a,-d*x/c)/((1+m)*(1+b*x/a)^n*(1+d*x/c)^n)],
[(a-x)^m*(f*x)^p*(c+d*x)^n,x,3,(a-x)^m*(f*x)^(1+p)*(c+d*x)^n*AppellF1(1+p,-m,-n,2+p,x/a,-d*x/c)/(f*(1+p)*(1-x/a)^m*(1+d*x/c)^n)],
[(1-x)^(-1/2+p)*(1+x)^(1/2+p)/(c*x)^(2*(1+p)),x,1,-4^(1+p)*(1-x)^(1/2+p)*(x/(1+x))^(2*(1+p))*(1+x)^(3/2+p)*hypergeom([1/2+p,2*(1+p)],[3/2+p],(1-x)/(1+x))/((1+2*p)*(c*x)^(2*(1+p)))],
[(1+x/a)^(1/2*n)/(x^2*(1-x/a)^(1/2*n)),x,1,-4*(1-x/a)^(1-1/2*n)*(1+x/a)^(1/2*(-2+n))*hypergeom([2,1-1/2*n],[2-1/2*n],(a-x)/(a+x))/(a*(2-n))],
[(b*x)^(-2-2*m)*(1-a*x)^m*(1+a*x)^m,x,2,-(b*x)^(-1-2*m)*hypergeom([1/2*(-1-2*m),-m],[1/2*(1-2*m)],a^2*x^2)/(b*(1+2*m))],
[(1+a*x)^n/(x*(1-a*x)^n),x,3,(1+a*x)^n*hypergeom([1,-n],[1-n],(1-a*x)/(1+a*x))/(n*(1-a*x)^n)-2^n*hypergeom([-n,-n],[1-n],1/2*(1-a*x))/(n*(1-a*x)^n)],
[(1-a*x)^(1-n)*(1+a*x)^(1+n)/x^2,x,3,-2*a*(1-a*x)^(1-n)*(1+a*x)^(-1+n)*hypergeom([2,1-n],[2-n],(1-a*x)/(1+a*x))/(1-n)+2^n*a*(1-a*x)^(1-n)*hypergeom([1-n,-n],[2-n],1/2*(1-a*x))/(1-n)],
[x^2/((1-a*x)^7*(1+a*x)^4),x,1,1/24*(-1+3*a*x)/(a^3*(1-a*x)^6*(1+a*x)^3)],
[x^2/((1-a*x)^11*(1+a*x)^7),x,1,1/60*(-1+4*a*x)/(a^3*(1-a*x)^10*(1+a*x)^6)],
[x^2/((1-a*x)^16*(1+a*x)^11),x,1,1/120*(-1+5*a*x)/(a^3*(1-a*x)^15*(1+a*x)^10)],
[x^2*(1-a*x)^(-1-1/2*n*(1+n))*(1+a*x)^(-1-1/2*(-1+n)*n),x,1,(1+a*x)^(1/2*(1-n)*n)*(1-a*n*x)/(a^3*n*(1-n^2)*(1-a*x)^(1/2*n*(1+n)))],
[(a+b*x)^(1+n)/(x*(a-b*x)^n),x,6,1/2*(a-b*x)^(1-n)*(a+b*x)^n/n-a*(a+b*x)^n*hypergeom([1,n],[1+n],(a+b*x)/(a-b*x))/(n*(a-b*x)^n)+2^(-1-n)*(1+2*n)*((a-b*x)/a)^n*(a+b*x)^(1+n)*hypergeom([n,1+n],[2+n],1/2*(a+b*x)/a)/(n*(1+n)*(a-b*x)^n)],
[(a+b*x)^(1+n)/(x^2*(a-b*x)^n),x,5,-(a+b*x)^(1+n)/(x*(a-b*x)^n)+b*(1+2*n)*(a+b*x)^n*hypergeom([1,-n],[1-n],(a-b*x)/(a+b*x))/(n*(a-b*x)^n)-2^n*b*(a+b*x)^n*hypergeom([-n,-n],[1-n],1/2*(a-b*x)/a)/(n*(a-b*x)^n*((a+b*x)/a)^n)],
[(a+b*x)^(1+n)/(x^3*(a-b*x)^n),x,1,-4*b^2*(a-b*x)^(1-n)*(a+b*x)^(-1+n)*hypergeom([3,1-n],[2-n],(a-b*x)/(a+b*x))/(a*(1-n))],
[(a+b*x)^(1+n)/(x^4*(a-b*x)^n),x,2,-1/3*(a-b*x)^(1-n)*(a+b*x)^(2+n)/(a^2*x^3)-4/3*b^3*(1+2*n)*(a-b*x)^(1-n)*(a+b*x)^(-1+n)*hypergeom([3,1-n],[2-n],(a-b*x)/(a+b*x))/(a^2*(1-n))],
[(a+b*x)^(1+n)/(x^5*(a-b*x)^n),x,4,-1/4*(a-b*x)^(1-n)*(a+b*x)^(2+n)/(a^2*x^4)-1/12*b*(1+2*n)*(a-b*x)^(1-n)*(a+b*x)^(2+n)/(a^3*x^3)-4/3*b^4*(1+n+n^2)*(a-b*x)^(1-n)*(a+b*x)^(-1+n)*hypergeom([3,1-n],[2-n],(a-b*x)/(a+b*x))/(a^3*(1-n))],

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

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

# Integrands of the form (a+b x)^m (A+B x) (d+e x)^p

# m>0
[(a+b*x)*(A+B*x)*(d+e*x)^4,x,2,1/5*(b*d-a*e)*(B*d-A*e)*(d+e*x)^5/e^3-1/6*(2*b*B*d-A*b*e-a*B*e)*(d+e*x)^6/e^3+1/7*b*B*(d+e*x)^7/e^3],
[(a+b*x)*(A+B*x)*(d+e*x)^3,x,2,1/4*(b*d-a*e)*(B*d-A*e)*(d+e*x)^4/e^3-1/5*(2*b*B*d-A*b*e-a*B*e)*(d+e*x)^5/e^3+1/6*b*B*(d+e*x)^6/e^3],
[(a+b*x)*(A+B*x)*(d+e*x)^2,x,2,1/3*(b*d-a*e)*(B*d-A*e)*(d+e*x)^3/e^3-1/4*(2*b*B*d-A*b*e-a*B*e)*(d+e*x)^4/e^3+1/5*b*B*(d+e*x)^5/e^3],
[(a+b*x)*(A+B*x)*(d+e*x),x,2,a*A*d*x+1/2*(A*b*d+a*B*d+a*A*e)*x^2+1/3*(b*B*d+A*b*e+a*B*e)*x^3+1/4*b*B*e*x^4],
[(a+b*x)*(A+B*x),x,2,a*A*x+1/2*(A*b+a*B)*x^2+1/3*b*B*x^3],
[(a+b*x)*(A+B*x)/(d+e*x),x,2,-b*(B*d-A*e)*x/e^2+1/2*B*(a+b*x)^2/(b*e)+(b*d-a*e)*(B*d-A*e)*log(d+e*x)/e^3],
[(a+b*x)*(A+B*x)/(d+e*x)^2,x,2,b*B*x/e^2-(b*d-a*e)*(B*d-A*e)/(e^3*(d+e*x))-(2*b*B*d-A*b*e-a*B*e)*log(d+e*x)/e^3],
[(a+b*x)*(A+B*x)/(d+e*x)^3,x,2,-1/2*(b*d-a*e)*(B*d-A*e)/(e^3*(d+e*x)^2)+(2*b*B*d-A*b*e-a*B*e)/(e^3*(d+e*x))+b*B*log(d+e*x)/e^3],
[(a+b*x)*(A+B*x)/(d+e*x)^4,x,2,-1/3*(b*d-a*e)*(B*d-A*e)/(e^3*(d+e*x)^3)+1/2*(2*b*B*d-A*b*e-a*B*e)/(e^3*(d+e*x)^2)-b*B/(e^3*(d+e*x))],
[(a+b*x)*(A+B*x)/(d+e*x)^5,x,2,-1/4*(b*d-a*e)*(B*d-A*e)/(e^3*(d+e*x)^4)+1/3*(2*b*B*d-A*b*e-a*B*e)/(e^3*(d+e*x)^3)-1/2*b*B/(e^3*(d+e*x)^2)],
[(a+b*x)*(A+B*x)/(d+e*x)^6,x,2,-1/5*(b*d-a*e)*(B*d-A*e)/(e^3*(d+e*x)^5)+1/4*(2*b*B*d-A*b*e-a*B*e)/(e^3*(d+e*x)^4)-1/3*b*B/(e^3*(d+e*x)^3)],
[(a+b*x)^2*(A+B*x)*(d+e*x)^4,x,2,-1/5*(b*d-a*e)^2*(B*d-A*e)*(d+e*x)^5/e^4+1/6*(b*d-a*e)*(3*b*B*d-2*A*b*e-a*B*e)*(d+e*x)^6/e^4-1/7*b*(3*b*B*d-A*b*e-2*a*B*e)*(d+e*x)^7/e^4+1/8*b^2*B*(d+e*x)^8/e^4],
[(a+b*x)^2*(A+B*x)*(d+e*x)^3,x,2,-1/4*(b*d-a*e)^2*(B*d-A*e)*(d+e*x)^4/e^4+1/5*(b*d-a*e)*(3*b*B*d-2*A*b*e-a*B*e)*(d+e*x)^5/e^4-1/6*b*(3*b*B*d-A*b*e-2*a*B*e)*(d+e*x)^6/e^4+1/7*b^2*B*(d+e*x)^7/e^4],
[(a+b*x)^2*(A+B*x)*(d+e*x)^2,x,2,1/3*(A*b-a*B)*(b*d-a*e)^2*(a+b*x)^3/b^4+1/4*(b*d-a*e)*(b*B*d+2*A*b*e-3*a*B*e)*(a+b*x)^4/b^4+1/5*e*(2*b*B*d+A*b*e-3*a*B*e)*(a+b*x)^5/b^4+1/6*B*e^2*(a+b*x)^6/b^4],
[(a+b*x)^2*(A+B*x)*(d+e*x),x,2,1/3*(A*b-a*B)*(b*d-a*e)*(a+b*x)^3/b^3+1/4*(b*B*d+A*b*e-2*a*B*e)*(a+b*x)^4/b^3+1/5*B*e*(a+b*x)^5/b^3],
[(a+b*x)^2*(A+B*x),x,2,1/3*(A*b-a*B)*(a+b*x)^3/b^2+1/4*B*(a+b*x)^4/b^2],
[(a+b*x)^2*(A+B*x)/(d+e*x),x,2,b*(b*d-a*e)*(B*d-A*e)*x/e^3-1/2*(B*d-A*e)*(a+b*x)^2/e^2+1/3*B*(a+b*x)^3/(b*e)-(b*d-a*e)^2*(B*d-A*e)*log(d+e*x)/e^4],
[(a+b*x)^2*(A+B*x)/(d+e*x)^2,x,2,-b*(2*b*B*d-A*b*e-2*a*B*e)*x/e^3+1/2*b^2*B*x^2/e^2+(b*d-a*e)^2*(B*d-A*e)/(e^4*(d+e*x))+(b*d-a*e)*(3*b*B*d-2*A*b*e-a*B*e)*log(d+e*x)/e^4],
[(a+b*x)^2*(A+B*x)/(d+e*x)^3,x,2,b^2*B*x/e^3+1/2*(b*d-a*e)^2*(B*d-A*e)/(e^4*(d+e*x)^2)-(b*d-a*e)*(3*b*B*d-2*A*b*e-a*B*e)/(e^4*(d+e*x))-b*(3*b*B*d-A*b*e-2*a*B*e)*log(d+e*x)/e^4],
[(a+b*x)^2*(A+B*x)/(d+e*x)^4,x,3,-1/3*(B*d-A*e)*(a+b*x)^3/(e*(b*d-a*e)*(d+e*x)^3)-1/2*B*(b*d-a*e)^2/(e^4*(d+e*x)^2)+2*b*B*(b*d-a*e)/(e^4*(d+e*x))+b^2*B*log(d+e*x)/e^4],
[(a+b*x)^2*(A+B*x)/(d+e*x)^5,x,2,-1/4*(B*d-A*e)*(a+b*x)^3/(e*(b*d-a*e)*(d+e*x)^4)+1/12*(3*b*B*d+A*b*e-4*a*B*e)*(a+b*x)^3/(e*(b*d-a*e)^2*(d+e*x)^3)],
[(a+b*x)^2*(A+B*x)/(d+e*x)^6,x,2,1/5*(b*d-a*e)^2*(B*d-A*e)/(e^4*(d+e*x)^5)-1/4*(b*d-a*e)*(3*b*B*d-2*A*b*e-a*B*e)/(e^4*(d+e*x)^4)+1/3*b*(3*b*B*d-A*b*e-2*a*B*e)/(e^4*(d+e*x)^3)-1/2*b^2*B/(e^4*(d+e*x)^2)],
[(a+b*x)^2*(A+B*x)/(d+e*x)^7,x,2,1/6*(b*d-a*e)^2*(B*d-A*e)/(e^4*(d+e*x)^6)-1/5*(b*d-a*e)*(3*b*B*d-2*A*b*e-a*B*e)/(e^4*(d+e*x)^5)+1/4*b*(3*b*B*d-A*b*e-2*a*B*e)/(e^4*(d+e*x)^4)-1/3*b^2*B/(e^4*(d+e*x)^3)],
[(a+b*x)^2*(A+B*x)/(d+e*x)^8,x,2,1/7*(b*d-a*e)^2*(B*d-A*e)/(e^4*(d+e*x)^7)-1/6*(b*d-a*e)*(3*b*B*d-2*A*b*e-a*B*e)/(e^4*(d+e*x)^6)+1/5*b*(3*b*B*d-A*b*e-2*a*B*e)/(e^4*(d+e*x)^5)-1/4*b^2*B/(e^4*(d+e*x)^4)],
[(a+b*x)^3*(A+B*x)*(d+e*x)^5,x,2,1/6*(b*d-a*e)^3*(B*d-A*e)*(d+e*x)^6/e^5-1/7*(b*d-a*e)^2*(4*b*B*d-3*A*b*e-a*B*e)*(d+e*x)^7/e^5+3/8*b*(b*d-a*e)*(2*b*B*d-A*b*e-a*B*e)*(d+e*x)^8/e^5-1/9*b^2*(4*b*B*d-A*b*e-3*a*B*e)*(d+e*x)^9/e^5+1/10*b^3*B*(d+e*x)^10/e^5],
[(a+b*x)^3*(A+B*x)*(d+e*x)^4,x,2,1/5*(b*d-a*e)^3*(B*d-A*e)*(d+e*x)^5/e^5-1/6*(b*d-a*e)^2*(4*b*B*d-3*A*b*e-a*B*e)*(d+e*x)^6/e^5+3/7*b*(b*d-a*e)*(2*b*B*d-A*b*e-a*B*e)*(d+e*x)^7/e^5-1/8*b^2*(4*b*B*d-A*b*e-3*a*B*e)*(d+e*x)^8/e^5+1/9*b^3*B*(d+e*x)^9/e^5],
[(a+b*x)^3*(A+B*x)*(d+e*x)^3,x,2,1/4*(A*b-a*B)*(b*d-a*e)^3*(a+b*x)^4/b^5+1/5*(b*d-a*e)^2*(b*B*d+3*A*b*e-4*a*B*e)*(a+b*x)^5/b^5+1/2*e*(b*d-a*e)*(b*B*d+A*b*e-2*a*B*e)*(a+b*x)^6/b^5+1/7*e^2*(3*b*B*d+A*b*e-4*a*B*e)*(a+b*x)^7/b^5+1/8*B*e^3*(a+b*x)^8/b^5],
[(a+b*x)^3*(A+B*x)*(d+e*x)^2,x,2,1/4*(A*b-a*B)*(b*d-a*e)^2*(a+b*x)^4/b^4+1/5*(b*d-a*e)*(b*B*d+2*A*b*e-3*a*B*e)*(a+b*x)^5/b^4+1/6*e*(2*b*B*d+A*b*e-3*a*B*e)*(a+b*x)^6/b^4+1/7*B*e^2*(a+b*x)^7/b^4],
[(a+b*x)^3*(A+B*x)*(d+e*x),x,2,1/4*(A*b-a*B)*(b*d-a*e)*(a+b*x)^4/b^3+1/5*(b*B*d+A*b*e-2*a*B*e)*(a+b*x)^5/b^3+1/6*B*e*(a+b*x)^6/b^3],
[(a+b*x)^3*(A+B*x),x,2,1/4*(A*b-a*B)*(a+b*x)^4/b^2+1/5*B*(a+b*x)^5/b^2],
[(a+b*x)^3*(A+B*x)/(d+e*x),x,2,-b*(b*d-a*e)^2*(B*d-A*e)*x/e^4+1/2*(b*d-a*e)*(B*d-A*e)*(a+b*x)^2/e^3-1/3*(B*d-A*e)*(a+b*x)^3/e^2+1/4*B*(a+b*x)^4/(b*e)+(b*d-a*e)^3*(B*d-A*e)*log(d+e*x)/e^5],
[(a+b*x)^3*(A+B*x)/(d+e*x)^2,x,2,3*b*(b*d-a*e)*(2*b*B*d-A*b*e-a*B*e)*x/e^4-(b*d-a*e)^3*(B*d-A*e)/(e^5*(d+e*x))-1/2*b^2*(4*b*B*d-A*b*e-3*a*B*e)*(d+e*x)^2/e^5+1/3*b^3*B*(d+e*x)^3/e^5-(b*d-a*e)^2*(4*b*B*d-3*A*b*e-a*B*e)*log(d+e*x)/e^5],
[(a+b*x)^3*(A+B*x)/(d+e*x)^3,x,2,-b^2*(3*b*B*d-A*b*e-3*a*B*e)*x/e^4+1/2*b^3*B*x^2/e^3-1/2*(b*d-a*e)^3*(B*d-A*e)/(e^5*(d+e*x)^2)+(b*d-a*e)^2*(4*b*B*d-3*A*b*e-a*B*e)/(e^5*(d+e*x))+3*b*(b*d-a*e)*(2*b*B*d-A*b*e-a*B*e)*log(d+e*x)/e^5],
[(a+b*x)^3*(A+B*x)/(d+e*x)^4,x,2,b^3*B*x/e^4-1/3*(b*d-a*e)^3*(B*d-A*e)/(e^5*(d+e*x)^3)+1/2*(b*d-a*e)^2*(4*b*B*d-3*A*b*e-a*B*e)/(e^5*(d+e*x)^2)-3*b*(b*d-a*e)*(2*b*B*d-A*b*e-a*B*e)/(e^5*(d+e*x))-b^2*(4*b*B*d-A*b*e-3*a*B*e)*log(d+e*x)/e^5],
[(a+b*x)^3*(A+B*x)/(d+e*x)^5,x,3,-1/4*(B*d-A*e)*(a+b*x)^4/(e*(b*d-a*e)*(d+e*x)^4)+1/3*B*(b*d-a*e)^3/(e^5*(d+e*x)^3)-3/2*b*B*(b*d-a*e)^2/(e^5*(d+e*x)^2)+3*b^2*B*(b*d-a*e)/(e^5*(d+e*x))+b^3*B*log(d+e*x)/e^5],
[(a+b*x)^3*(A+B*x)/(d+e*x)^6,x,2,-1/5*(B*d-A*e)*(a+b*x)^4/(e*(b*d-a*e)*(d+e*x)^5)+1/20*(4*b*B*d+A*b*e-5*a*B*e)*(a+b*x)^4/(e*(b*d-a*e)^2*(d+e*x)^4)],
[(a+b*x)^3*(A+B*x)/(d+e*x)^7,x,3,-1/6*(B*d-A*e)*(a+b*x)^4/(e*(b*d-a*e)*(d+e*x)^6)+1/15*(2*b*B*d+A*b*e-3*a*B*e)*(a+b*x)^4/(e*(b*d-a*e)^2*(d+e*x)^5)+1/60*b*(2*b*B*d+A*b*e-3*a*B*e)*(a+b*x)^4/(e*(b*d-a*e)^3*(d+e*x)^4)],
[(a+b*x)^3*(A+B*x)/(d+e*x)^8,x,2,-1/7*(b*d-a*e)^3*(B*d-A*e)/(e^5*(d+e*x)^7)+1/6*(b*d-a*e)^2*(4*b*B*d-3*A*b*e-a*B*e)/(e^5*(d+e*x)^6)-3/5*b*(b*d-a*e)*(2*b*B*d-A*b*e-a*B*e)/(e^5*(d+e*x)^5)+1/4*b^2*(4*b*B*d-A*b*e-3*a*B*e)/(e^5*(d+e*x)^4)-1/3*b^3*B/(e^5*(d+e*x)^3)],
[(a+b*x)^3*(A+B*x)/(d+e*x)^9,x,2,-1/8*(b*d-a*e)^3*(B*d-A*e)/(e^5*(d+e*x)^8)+1/7*(b*d-a*e)^2*(4*b*B*d-3*A*b*e-a*B*e)/(e^5*(d+e*x)^7)-1/2*b*(b*d-a*e)*(2*b*B*d-A*b*e-a*B*e)/(e^5*(d+e*x)^6)+1/5*b^2*(4*b*B*d-A*b*e-3*a*B*e)/(e^5*(d+e*x)^5)-1/4*b^3*B/(e^5*(d+e*x)^4)],
[(a+b*x)^3*(A+B*x)/(d+e*x)^10,x,2,-1/9*(b*d-a*e)^3*(B*d-A*e)/(e^5*(d+e*x)^9)+1/8*(b*d-a*e)^2*(4*b*B*d-3*A*b*e-a*B*e)/(e^5*(d+e*x)^8)-3/7*b*(b*d-a*e)*(2*b*B*d-A*b*e-a*B*e)/(e^5*(d+e*x)^7)+1/6*b^2*(4*b*B*d-A*b*e-3*a*B*e)/(e^5*(d+e*x)^6)-1/5*b^3*B/(e^5*(d+e*x)^5)],
[(a+b*x)^6*(A+B*x)*(d+e*x)^8,x,2,-1/9*(b*d-a*e)^6*(B*d-A*e)*(d+e*x)^9/e^8+1/10*(b*d-a*e)^5*(7*b*B*d-6*A*b*e-a*B*e)*(d+e*x)^10/e^8-3/11*b*(b*d-a*e)^4*(7*b*B*d-5*A*b*e-2*a*B*e)*(d+e*x)^11/e^8+5/12*b^2*(b*d-a*e)^3*(7*b*B*d-4*A*b*e-3*a*B*e)*(d+e*x)^12/e^8-5/13*b^3*(b*d-a*e)^2*(7*b*B*d-3*A*b*e-4*a*B*e)*(d+e*x)^13/e^8+3/14*b^4*(b*d-a*e)*(7*b*B*d-2*A*b*e-5*a*B*e)*(d+e*x)^14/e^8-1/15*b^5*(7*b*B*d-A*b*e-6*a*B*e)*(d+e*x)^15/e^8+1/16*b^6*B*(d+e*x)^16/e^8],
[(a+b*x)^6*(A+B*x)*(d+e*x)^7,x,2,-1/8*(b*d-a*e)^6*(B*d-A*e)*(d+e*x)^8/e^8+1/9*(b*d-a*e)^5*(7*b*B*d-6*A*b*e-a*B*e)*(d+e*x)^9/e^8-3/10*b*(b*d-a*e)^4*(7*b*B*d-5*A*b*e-2*a*B*e)*(d+e*x)^10/e^8+5/11*b^2*(b*d-a*e)^3*(7*b*B*d-4*A*b*e-3*a*B*e)*(d+e*x)^11/e^8-5/12*b^3*(b*d-a*e)^2*(7*b*B*d-3*A*b*e-4*a*B*e)*(d+e*x)^12/e^8+3/13*b^4*(b*d-a*e)*(7*b*B*d-2*A*b*e-5*a*B*e)*(d+e*x)^13/e^8-1/14*b^5*(7*b*B*d-A*b*e-6*a*B*e)*(d+e*x)^14/e^8+1/15*b^6*B*(d+e*x)^15/e^8],
[(a+b*x)^6*(A+B*x)*(d+e*x)^6,x,2,1/7*(A*b-a*B)*(b*d-a*e)^6*(a+b*x)^7/b^8+1/8*(b*d-a*e)^5*(b*B*d+6*A*b*e-7*a*B*e)*(a+b*x)^8/b^8+1/3*e*(b*d-a*e)^4*(2*b*B*d+5*A*b*e-7*a*B*e)*(a+b*x)^9/b^8+1/2*e^2*(b*d-a*e)^3*(3*b*B*d+4*A*b*e-7*a*B*e)*(a+b*x)^10/b^8+5/11*e^3*(b*d-a*e)^2*(4*b*B*d+3*A*b*e-7*a*B*e)*(a+b*x)^11/b^8+1/4*e^4*(b*d-a*e)*(5*b*B*d+2*A*b*e-7*a*B*e)*(a+b*x)^12/b^8+1/13*e^5*(6*b*B*d+A*b*e-7*a*B*e)*(a+b*x)^13/b^8+1/14*B*e^6*(a+b*x)^14/b^8],
[(a+b*x)^6*(A+B*x)*(d+e*x)^5,x,2,1/7*(A*b-a*B)*(b*d-a*e)^5*(a+b*x)^7/b^7+1/8*(b*d-a*e)^4*(b*B*d+5*A*b*e-6*a*B*e)*(a+b*x)^8/b^7+5/9*e*(b*d-a*e)^3*(b*B*d+2*A*b*e-3*a*B*e)*(a+b*x)^9/b^7+e^2*(b*d-a*e)^2*(b*B*d+A*b*e-2*a*B*e)*(a+b*x)^10/b^7+5/11*e^3*(b*d-a*e)*(2*b*B*d+A*b*e-3*a*B*e)*(a+b*x)^11/b^7+1/12*e^4*(5*b*B*d+A*b*e-6*a*B*e)*(a+b*x)^12/b^7+1/13*B*e^5*(a+b*x)^13/b^7],
[(a+b*x)^6*(A+B*x)*(d+e*x)^4,x,2,1/7*(A*b-a*B)*(b*d-a*e)^4*(a+b*x)^7/b^6+1/8*(b*d-a*e)^3*(b*B*d+4*A*b*e-5*a*B*e)*(a+b*x)^8/b^6+2/9*e*(b*d-a*e)^2*(2*b*B*d+3*A*b*e-5*a*B*e)*(a+b*x)^9/b^6+1/5*e^2*(b*d-a*e)*(3*b*B*d+2*A*b*e-5*a*B*e)*(a+b*x)^10/b^6+1/11*e^3*(4*b*B*d+A*b*e-5*a*B*e)*(a+b*x)^11/b^6+1/12*B*e^4*(a+b*x)^12/b^6],
[(a+b*x)^6*(A+B*x)*(d+e*x)^3,x,2,1/7*(A*b-a*B)*(b*d-a*e)^3*(a+b*x)^7/b^5+1/8*(b*d-a*e)^2*(b*B*d+3*A*b*e-4*a*B*e)*(a+b*x)^8/b^5+1/3*e*(b*d-a*e)*(b*B*d+A*b*e-2*a*B*e)*(a+b*x)^9/b^5+1/10*e^2*(3*b*B*d+A*b*e-4*a*B*e)*(a+b*x)^10/b^5+1/11*B*e^3*(a+b*x)^11/b^5],
[(a+b*x)^6*(A+B*x)*(d+e*x)^2,x,2,1/7*(A*b-a*B)*(b*d-a*e)^2*(a+b*x)^7/b^4+1/8*(b*d-a*e)*(b*B*d+2*A*b*e-3*a*B*e)*(a+b*x)^8/b^4+1/9*e*(2*b*B*d+A*b*e-3*a*B*e)*(a+b*x)^9/b^4+1/10*B*e^2*(a+b*x)^10/b^4],
[(a+b*x)^6*(A+B*x)*(d+e*x),x,2,1/7*(A*b-a*B)*(b*d-a*e)*(a+b*x)^7/b^3+1/8*(b*B*d+A*b*e-2*a*B*e)*(a+b*x)^8/b^3+1/9*B*e*(a+b*x)^9/b^3],
[(a+b*x)^6*(A+B*x),x,2,1/7*(A*b-a*B)*(a+b*x)^7/b^2+1/8*B*(a+b*x)^8/b^2],
[(a+b*x)^6*(A+B*x)/(d+e*x),x,2,b*(b*d-a*e)^5*(B*d-A*e)*x/e^7-1/2*(b*d-a*e)^4*(B*d-A*e)*(a+b*x)^2/e^6+1/3*(b*d-a*e)^3*(B*d-A*e)*(a+b*x)^3/e^5-1/4*(b*d-a*e)^2*(B*d-A*e)*(a+b*x)^4/e^4+1/5*(b*d-a*e)*(B*d-A*e)*(a+b*x)^5/e^3-1/6*(B*d-A*e)*(a+b*x)^6/e^2+1/7*B*(a+b*x)^7/(b*e)-(b*d-a*e)^6*(B*d-A*e)*log(d+e*x)/e^8],
[(a+b*x)^6*(A+B*x)/(d+e*x)^2,x,2,-3*b*(b*d-a*e)^4*(7*b*B*d-5*A*b*e-2*a*B*e)*x/e^7+(b*d-a*e)^6*(B*d-A*e)/(e^8*(d+e*x))+5/2*b^2*(b*d-a*e)^3*(7*b*B*d-4*A*b*e-3*a*B*e)*(d+e*x)^2/e^8-5/3*b^3*(b*d-a*e)^2*(7*b*B*d-3*A*b*e-4*a*B*e)*(d+e*x)^3/e^8+3/4*b^4*(b*d-a*e)*(7*b*B*d-2*A*b*e-5*a*B*e)*(d+e*x)^4/e^8-1/5*b^5*(7*b*B*d-A*b*e-6*a*B*e)*(d+e*x)^5/e^8+1/6*b^6*B*(d+e*x)^6/e^8+(b*d-a*e)^5*(7*b*B*d-6*A*b*e-a*B*e)*log(d+e*x)/e^8],
[(a+b*x)^6*(A+B*x)/(d+e*x)^3,x,2,5*b^2*(b*d-a*e)^3*(7*b*B*d-4*A*b*e-3*a*B*e)*x/e^7+1/2*(b*d-a*e)^6*(B*d-A*e)/(e^8*(d+e*x)^2)-(b*d-a*e)^5*(7*b*B*d-6*A*b*e-a*B*e)/(e^8*(d+e*x))-5/2*b^3*(b*d-a*e)^2*(7*b*B*d-3*A*b*e-4*a*B*e)*(d+e*x)^2/e^8+b^4*(b*d-a*e)*(7*b*B*d-2*A*b*e-5*a*B*e)*(d+e*x)^3/e^8-1/4*b^5*(7*b*B*d-A*b*e-6*a*B*e)*(d+e*x)^4/e^8+1/5*b^6*B*(d+e*x)^5/e^8-3*b*(b*d-a*e)^4*(7*b*B*d-5*A*b*e-2*a*B*e)*log(d+e*x)/e^8],
[(a+b*x)^6*(A+B*x)/(d+e*x)^4,x,2,-5*b^3*(b*d-a*e)^2*(7*b*B*d-3*A*b*e-4*a*B*e)*x/e^7+1/3*(b*d-a*e)^6*(B*d-A*e)/(e^8*(d+e*x)^3)-1/2*(b*d-a*e)^5*(7*b*B*d-6*A*b*e-a*B*e)/(e^8*(d+e*x)^2)+3*b*(b*d-a*e)^4*(7*b*B*d-5*A*b*e-2*a*B*e)/(e^8*(d+e*x))+3/2*b^4*(b*d-a*e)*(7*b*B*d-2*A*b*e-5*a*B*e)*(d+e*x)^2/e^8-1/3*b^5*(7*b*B*d-A*b*e-6*a*B*e)*(d+e*x)^3/e^8+1/4*b^6*B*(d+e*x)^4/e^8+5*b^2*(b*d-a*e)^3*(7*b*B*d-4*A*b*e-3*a*B*e)*log(d+e*x)/e^8],
[(a+b*x)^6*(A+B*x)/(d+e*x)^5,x,2,3*b^4*(b*d-a*e)*(7*b*B*d-2*A*b*e-5*a*B*e)*x/e^7+1/4*(b*d-a*e)^6*(B*d-A*e)/(e^8*(d+e*x)^4)-1/3*(b*d-a*e)^5*(7*b*B*d-6*A*b*e-a*B*e)/(e^8*(d+e*x)^3)+3/2*b*(b*d-a*e)^4*(7*b*B*d-5*A*b*e-2*a*B*e)/(e^8*(d+e*x)^2)-5*b^2*(b*d-a*e)^3*(7*b*B*d-4*A*b*e-3*a*B*e)/(e^8*(d+e*x))-1/2*b^5*(7*b*B*d-A*b*e-6*a*B*e)*(d+e*x)^2/e^8+1/3*b^6*B*(d+e*x)^3/e^8-5*b^3*(b*d-a*e)^2*(7*b*B*d-3*A*b*e-4*a*B*e)*log(d+e*x)/e^8],
[(a+b*x)^6*(A+B*x)/(d+e*x)^6,x,2,-b^5*(6*b*B*d-A*b*e-6*a*B*e)*x/e^7+1/2*b^6*B*x^2/e^6+1/5*(b*d-a*e)^6*(B*d-A*e)/(e^8*(d+e*x)^5)-1/4*(b*d-a*e)^5*(7*b*B*d-6*A*b*e-a*B*e)/(e^8*(d+e*x)^4)+b*(b*d-a*e)^4*(7*b*B*d-5*A*b*e-2*a*B*e)/(e^8*(d+e*x)^3)-5/2*b^2*(b*d-a*e)^3*(7*b*B*d-4*A*b*e-3*a*B*e)/(e^8*(d+e*x)^2)+5*b^3*(b*d-a*e)^2*(7*b*B*d-3*A*b*e-4*a*B*e)/(e^8*(d+e*x))+3*b^4*(b*d-a*e)*(7*b*B*d-2*A*b*e-5*a*B*e)*log(d+e*x)/e^8],
[(a+b*x)^6*(A+B*x)/(d+e*x)^7,x,2,b^6*B*x/e^7+1/6*(b*d-a*e)^6*(B*d-A*e)/(e^8*(d+e*x)^6)-1/5*(b*d-a*e)^5*(7*b*B*d-6*A*b*e-a*B*e)/(e^8*(d+e*x)^5)+3/4*b*(b*d-a*e)^4*(7*b*B*d-5*A*b*e-2*a*B*e)/(e^8*(d+e*x)^4)-5/3*b^2*(b*d-a*e)^3*(7*b*B*d-4*A*b*e-3*a*B*e)/(e^8*(d+e*x)^3)+5/2*b^3*(b*d-a*e)^2*(7*b*B*d-3*A*b*e-4*a*B*e)/(e^8*(d+e*x)^2)-3*b^4*(b*d-a*e)*(7*b*B*d-2*A*b*e-5*a*B*e)/(e^8*(d+e*x))-b^5*(7*b*B*d-A*b*e-6*a*B*e)*log(d+e*x)/e^8],
[(a+b*x)^6*(A+B*x)/(d+e*x)^8,x,3,-1/7*(B*d-A*e)*(a+b*x)^7/(e*(b*d-a*e)*(d+e*x)^7)-1/6*B*(b*d-a*e)^6/(e^8*(d+e*x)^6)+6/5*b*B*(b*d-a*e)^5/(e^8*(d+e*x)^5)-15/4*b^2*B*(b*d-a*e)^4/(e^8*(d+e*x)^4)+20/3*b^3*B*(b*d-a*e)^3/(e^8*(d+e*x)^3)-15/2*b^4*B*(b*d-a*e)^2/(e^8*(d+e*x)^2)+6*b^5*B*(b*d-a*e)/(e^8*(d+e*x))+b^6*B*log(d+e*x)/e^8],
[(a+b*x)^6*(A+B*x)/(d+e*x)^9,x,2,-1/8*(B*d-A*e)*(a+b*x)^7/(e*(b*d-a*e)*(d+e*x)^8)+1/56*(7*b*B*d+A*b*e-8*a*B*e)*(a+b*x)^7/(e*(b*d-a*e)^2*(d+e*x)^7)],
[(a+b*x)^6*(A+B*x)/(d+e*x)^10,x,3,-1/9*(B*d-A*e)*(a+b*x)^7/(e*(b*d-a*e)*(d+e*x)^9)+1/72*(7*b*B*d+2*A*b*e-9*a*B*e)*(a+b*x)^7/(e*(b*d-a*e)^2*(d+e*x)^8)+1/504*b*(7*b*B*d+2*A*b*e-9*a*B*e)*(a+b*x)^7/(e*(b*d-a*e)^3*(d+e*x)^7)],
[(a+b*x)^6*(A+B*x)/(d+e*x)^11,x,4,-1/10*(B*d-A*e)*(a+b*x)^7/(e*(b*d-a*e)*(d+e*x)^10)+1/90*(7*b*B*d+3*A*b*e-10*a*B*e)*(a+b*x)^7/(e*(b*d-a*e)^2*(d+e*x)^9)+1/360*b*(7*b*B*d+3*A*b*e-10*a*B*e)*(a+b*x)^7/(e*(b*d-a*e)^3*(d+e*x)^8)+1/2520*b^2*(7*b*B*d+3*A*b*e-10*a*B*e)*(a+b*x)^7/(e*(b*d-a*e)^4*(d+e*x)^7)],
[(a+b*x)^6*(A+B*x)/(d+e*x)^12,x,5,-1/11*(B*d-A*e)*(a+b*x)^7/(e*(b*d-a*e)*(d+e*x)^11)+1/110*(7*b*B*d+4*A*b*e-11*a*B*e)*(a+b*x)^7/(e*(b*d-a*e)^2*(d+e*x)^10)+1/330*b*(7*b*B*d+4*A*b*e-11*a*B*e)*(a+b*x)^7/(e*(b*d-a*e)^3*(d+e*x)^9)+1/1320*b^2*(7*b*B*d+4*A*b*e-11*a*B*e)*(a+b*x)^7/(e*(b*d-a*e)^4*(d+e*x)^8)+1/9240*b^3*(7*b*B*d+4*A*b*e-11*a*B*e)*(a+b*x)^7/(e*(b*d-a*e)^5*(d+e*x)^7)],
[(a+b*x)^6*(A+B*x)/(d+e*x)^13,x,2,1/12*(b*d-a*e)^6*(B*d-A*e)/(e^8*(d+e*x)^12)-1/11*(b*d-a*e)^5*(7*b*B*d-6*A*b*e-a*B*e)/(e^8*(d+e*x)^11)+3/10*b*(b*d-a*e)^4*(7*b*B*d-5*A*b*e-2*a*B*e)/(e^8*(d+e*x)^10)-5/9*b^2*(b*d-a*e)^3*(7*b*B*d-4*A*b*e-3*a*B*e)/(e^8*(d+e*x)^9)+5/8*b^3*(b*d-a*e)^2*(7*b*B*d-3*A*b*e-4*a*B*e)/(e^8*(d+e*x)^8)-3/7*b^4*(b*d-a*e)*(7*b*B*d-2*A*b*e-5*a*B*e)/(e^8*(d+e*x)^7)+1/6*b^5*(7*b*B*d-A*b*e-6*a*B*e)/(e^8*(d+e*x)^6)-1/5*b^6*B/(e^8*(d+e*x)^5)],
[(a+b*x)^6*(A+B*x)/(d+e*x)^14,x,2,1/13*(b*d-a*e)^6*(B*d-A*e)/(e^8*(d+e*x)^13)-1/12*(b*d-a*e)^5*(7*b*B*d-6*A*b*e-a*B*e)/(e^8*(d+e*x)^12)+3/11*b*(b*d-a*e)^4*(7*b*B*d-5*A*b*e-2*a*B*e)/(e^8*(d+e*x)^11)-1/2*b^2*(b*d-a*e)^3*(7*b*B*d-4*A*b*e-3*a*B*e)/(e^8*(d+e*x)^10)+5/9*b^3*(b*d-a*e)^2*(7*b*B*d-3*A*b*e-4*a*B*e)/(e^8*(d+e*x)^9)-3/8*b^4*(b*d-a*e)*(7*b*B*d-2*A*b*e-5*a*B*e)/(e^8*(d+e*x)^8)+1/7*b^5*(7*b*B*d-A*b*e-6*a*B*e)/(e^8*(d+e*x)^7)-1/6*b^6*B/(e^8*(d+e*x)^6)],
[(a+b*x)^6*(A+B*x)/(d+e*x)^15,x,2,1/14*(b*d-a*e)^6*(B*d-A*e)/(e^8*(d+e*x)^14)-1/13*(b*d-a*e)^5*(7*b*B*d-6*A*b*e-a*B*e)/(e^8*(d+e*x)^13)+1/4*b*(b*d-a*e)^4*(7*b*B*d-5*A*b*e-2*a*B*e)/(e^8*(d+e*x)^12)-5/11*b^2*(b*d-a*e)^3*(7*b*B*d-4*A*b*e-3*a*B*e)/(e^8*(d+e*x)^11)+1/2*b^3*(b*d-a*e)^2*(7*b*B*d-3*A*b*e-4*a*B*e)/(e^8*(d+e*x)^10)-1/3*b^4*(b*d-a*e)*(7*b*B*d-2*A*b*e-5*a*B*e)/(e^8*(d+e*x)^9)+1/8*b^5*(7*b*B*d-A*b*e-6*a*B*e)/(e^8*(d+e*x)^8)-1/7*b^6*B/(e^8*(d+e*x)^7)],
[(a+b*x)^10*(A+B*x)*(d+e*x)^13,x,2,-1/14*(b*d-a*e)^10*(B*d-A*e)*(d+e*x)^14/e^12+1/15*(b*d-a*e)^9*(11*b*B*d-10*A*b*e-a*B*e)*(d+e*x)^15/e^12-5/16*b*(b*d-a*e)^8*(11*b*B*d-9*A*b*e-2*a*B*e)*(d+e*x)^16/e^12+15/17*b^2*(b*d-a*e)^7*(11*b*B*d-8*A*b*e-3*a*B*e)*(d+e*x)^17/e^12-5/3*b^3*(b*d-a*e)^6*(11*b*B*d-7*A*b*e-4*a*B*e)*(d+e*x)^18/e^12+42/19*b^4*(b*d-a*e)^5*(11*b*B*d-6*A*b*e-5*a*B*e)*(d+e*x)^19/e^12-21/10*b^5*(b*d-a*e)^4*(11*b*B*d-5*A*b*e-6*a*B*e)*(d+e*x)^20/e^12+10/7*b^6*(b*d-a*e)^3*(11*b*B*d-4*A*b*e-7*a*B*e)*(d+e*x)^21/e^12-15/22*b^7*(b*d-a*e)^2*(11*b*B*d-3*A*b*e-8*a*B*e)*(d+e*x)^22/e^12+5/23*b^8*(b*d-a*e)*(11*b*B*d-2*A*b*e-9*a*B*e)*(d+e*x)^23/e^12-1/24*b^9*(11*b*B*d-A*b*e-10*a*B*e)*(d+e*x)^24/e^12+1/25*b^10*B*(d+e*x)^25/e^12],
[(a+b*x)^10*(A+B*x)*(d+e*x)^12,x,2,-1/13*(b*d-a*e)^10*(B*d-A*e)*(d+e*x)^13/e^12+1/14*(b*d-a*e)^9*(11*b*B*d-10*A*b*e-a*B*e)*(d+e*x)^14/e^12-1/3*b*(b*d-a*e)^8*(11*b*B*d-9*A*b*e-2*a*B*e)*(d+e*x)^15/e^12+15/16*b^2*(b*d-a*e)^7*(11*b*B*d-8*A*b*e-3*a*B*e)*(d+e*x)^16/e^12-30/17*b^3*(b*d-a*e)^6*(11*b*B*d-7*A*b*e-4*a*B*e)*(d+e*x)^17/e^12+7/3*b^4*(b*d-a*e)^5*(11*b*B*d-6*A*b*e-5*a*B*e)*(d+e*x)^18/e^12-42/19*b^5*(b*d-a*e)^4*(11*b*B*d-5*A*b*e-6*a*B*e)*(d+e*x)^19/e^12+3/2*b^6*(b*d-a*e)^3*(11*b*B*d-4*A*b*e-7*a*B*e)*(d+e*x)^20/e^12-5/7*b^7*(b*d-a*e)^2*(11*b*B*d-3*A*b*e-8*a*B*e)*(d+e*x)^21/e^12+5/22*b^8*(b*d-a*e)*(11*b*B*d-2*A*b*e-9*a*B*e)*(d+e*x)^22/e^12-1/23*b^9*(11*b*B*d-A*b*e-10*a*B*e)*(d+e*x)^23/e^12+1/24*b^10*B*(d+e*x)^24/e^12],
[(a+b*x)^10*(A+B*x)*(d+e*x)^11,x,2,-1/12*(b*d-a*e)^10*(B*d-A*e)*(d+e*x)^12/e^12+1/13*(b*d-a*e)^9*(11*b*B*d-10*A*b*e-a*B*e)*(d+e*x)^13/e^12-5/14*b*(b*d-a*e)^8*(11*b*B*d-9*A*b*e-2*a*B*e)*(d+e*x)^14/e^12+b^2*(b*d-a*e)^7*(11*b*B*d-8*A*b*e-3*a*B*e)*(d+e*x)^15/e^12-15/8*b^3*(b*d-a*e)^6*(11*b*B*d-7*A*b*e-4*a*B*e)*(d+e*x)^16/e^12+42/17*b^4*(b*d-a*e)^5*(11*b*B*d-6*A*b*e-5*a*B*e)*(d+e*x)^17/e^12-7/3*b^5*(b*d-a*e)^4*(11*b*B*d-5*A*b*e-6*a*B*e)*(d+e*x)^18/e^12+30/19*b^6*(b*d-a*e)^3*(11*b*B*d-4*A*b*e-7*a*B*e)*(d+e*x)^19/e^12-3/4*b^7*(b*d-a*e)^2*(11*b*B*d-3*A*b*e-8*a*B*e)*(d+e*x)^20/e^12+5/21*b^8*(b*d-a*e)*(11*b*B*d-2*A*b*e-9*a*B*e)*(d+e*x)^21/e^12-1/22*b^9*(11*b*B*d-A*b*e-10*a*B*e)*(d+e*x)^22/e^12+1/23*b^10*B*(d+e*x)^23/e^12],
[(a+b*x)^10*(A+B*x)*(d+e*x)^10,x,2,1/11*(A*b-a*B)*(b*d-a*e)^10*(a+b*x)^11/b^12+1/12*(b*d-a*e)^9*(b*B*d+10*A*b*e-11*a*B*e)*(a+b*x)^12/b^12+5/13*e*(b*d-a*e)^8*(2*b*B*d+9*A*b*e-11*a*B*e)*(a+b*x)^13/b^12+15/14*e^2*(b*d-a*e)^7*(3*b*B*d+8*A*b*e-11*a*B*e)*(a+b*x)^14/b^12+2*e^3*(b*d-a*e)^6*(4*b*B*d+7*A*b*e-11*a*B*e)*(a+b*x)^15/b^12+21/8*e^4*(b*d-a*e)^5*(5*b*B*d+6*A*b*e-11*a*B*e)*(a+b*x)^16/b^12+42/17*e^5*(b*d-a*e)^4*(6*b*B*d+5*A*b*e-11*a*B*e)*(a+b*x)^17/b^12+5/3*e^6*(b*d-a*e)^3*(7*b*B*d+4*A*b*e-11*a*B*e)*(a+b*x)^18/b^12+15/19*e^7*(b*d-a*e)^2*(8*b*B*d+3*A*b*e-11*a*B*e)*(a+b*x)^19/b^12+1/4*e^8*(b*d-a*e)*(9*b*B*d+2*A*b*e-11*a*B*e)*(a+b*x)^20/b^12+1/21*e^9*(10*b*B*d+A*b*e-11*a*B*e)*(a+b*x)^21/b^12+1/22*B*e^10*(a+b*x)^22/b^12],
[(a+b*x)^10*(A+B*x)*(d+e*x)^9,x,2,1/11*(A*b-a*B)*(b*d-a*e)^9*(a+b*x)^11/b^11+1/12*(b*d-a*e)^8*(b*B*d+9*A*b*e-10*a*B*e)*(a+b*x)^12/b^11+9/13*e*(b*d-a*e)^7*(b*B*d+4*A*b*e-5*a*B*e)*(a+b*x)^13/b^11+6/7*e^2*(b*d-a*e)^6*(3*b*B*d+7*A*b*e-10*a*B*e)*(a+b*x)^14/b^11+14/5*e^3*(b*d-a*e)^5*(2*b*B*d+3*A*b*e-5*a*B*e)*(a+b*x)^15/b^11+63/8*e^4*(b*d-a*e)^4*(b*B*d+A*b*e-2*a*B*e)*(a+b*x)^16/b^11+42/17*e^5*(b*d-a*e)^3*(3*b*B*d+2*A*b*e-5*a*B*e)*(a+b*x)^17/b^11+2/3*e^6*(b*d-a*e)^2*(7*b*B*d+3*A*b*e-10*a*B*e)*(a+b*x)^18/b^11+9/19*e^7*(b*d-a*e)*(4*b*B*d+A*b*e-5*a*B*e)*(a+b*x)^19/b^11+1/20*e^8*(9*b*B*d+A*b*e-10*a*B*e)*(a+b*x)^20/b^11+1/21*B*e^9*(a+b*x)^21/b^11],
[(a+b*x)^10*(A+B*x)*(d+e*x)^8,x,2,1/11*(A*b-a*B)*(b*d-a*e)^8*(a+b*x)^11/b^10+1/12*(b*d-a*e)^7*(b*B*d+8*A*b*e-9*a*B*e)*(a+b*x)^12/b^10+4/13*e*(b*d-a*e)^6*(2*b*B*d+7*A*b*e-9*a*B*e)*(a+b*x)^13/b^10+2*e^2*(b*d-a*e)^5*(b*B*d+2*A*b*e-3*a*B*e)*(a+b*x)^14/b^10+14/15*e^3*(b*d-a*e)^4*(4*b*B*d+5*A*b*e-9*a*B*e)*(a+b*x)^15/b^10+7/8*e^4*(b*d-a*e)^3*(5*b*B*d+4*A*b*e-9*a*B*e)*(a+b*x)^16/b^10+28/17*e^5*(b*d-a*e)^2*(2*b*B*d+A*b*e-3*a*B*e)*(a+b*x)^17/b^10+2/9*e^6*(b*d-a*e)*(7*b*B*d+2*A*b*e-9*a*B*e)*(a+b*x)^18/b^10+1/19*e^7*(8*b*B*d+A*b*e-9*a*B*e)*(a+b*x)^19/b^10+1/20*B*e^8*(a+b*x)^20/b^10],
[(a+b*x)^10*(A+B*x)*(d+e*x)^7,x,2,1/11*(A*b-a*B)*(b*d-a*e)^7*(a+b*x)^11/b^9+1/12*(b*d-a*e)^6*(b*B*d+7*A*b*e-8*a*B*e)*(a+b*x)^12/b^9+7/13*e*(b*d-a*e)^5*(b*B*d+3*A*b*e-4*a*B*e)*(a+b*x)^13/b^9+1/2*e^2*(b*d-a*e)^4*(3*b*B*d+5*A*b*e-8*a*B*e)*(a+b*x)^14/b^9+7/3*e^3*(b*d-a*e)^3*(b*B*d+A*b*e-2*a*B*e)*(a+b*x)^15/b^9+7/16*e^4*(b*d-a*e)^2*(5*b*B*d+3*A*b*e-8*a*B*e)*(a+b*x)^16/b^9+7/17*e^5*(b*d-a*e)*(3*b*B*d+A*b*e-4*a*B*e)*(a+b*x)^17/b^9+1/18*e^6*(7*b*B*d+A*b*e-8*a*B*e)*(a+b*x)^18/b^9+1/19*B*e^7*(a+b*x)^19/b^9],
[(a+b*x)^10*(A+B*x)*(d+e*x)^6,x,2,1/11*(A*b-a*B)*(b*d-a*e)^6*(a+b*x)^11/b^8+1/12*(b*d-a*e)^5*(b*B*d+6*A*b*e-7*a*B*e)*(a+b*x)^12/b^8+3/13*e*(b*d-a*e)^4*(2*b*B*d+5*A*b*e-7*a*B*e)*(a+b*x)^13/b^8+5/14*e^2*(b*d-a*e)^3*(3*b*B*d+4*A*b*e-7*a*B*e)*(a+b*x)^14/b^8+1/3*e^3*(b*d-a*e)^2*(4*b*B*d+3*A*b*e-7*a*B*e)*(a+b*x)^15/b^8+3/16*e^4*(b*d-a*e)*(5*b*B*d+2*A*b*e-7*a*B*e)*(a+b*x)^16/b^8+1/17*e^5*(6*b*B*d+A*b*e-7*a*B*e)*(a+b*x)^17/b^8+1/18*B*e^6*(a+b*x)^18/b^8],
[(a+b*x)^10*(A+B*x)*(d+e*x)^5,x,2,1/11*(A*b-a*B)*(b*d-a*e)^5*(a+b*x)^11/b^7+1/12*(b*d-a*e)^4*(b*B*d+5*A*b*e-6*a*B*e)*(a+b*x)^12/b^7+5/13*e*(b*d-a*e)^3*(b*B*d+2*A*b*e-3*a*B*e)*(a+b*x)^13/b^7+5/7*e^2*(b*d-a*e)^2*(b*B*d+A*b*e-2*a*B*e)*(a+b*x)^14/b^7+1/3*e^3*(b*d-a*e)*(2*b*B*d+A*b*e-3*a*B*e)*(a+b*x)^15/b^7+1/16*e^4*(5*b*B*d+A*b*e-6*a*B*e)*(a+b*x)^16/b^7+1/17*B*e^5*(a+b*x)^17/b^7],
[(a+b*x)^10*(A+B*x)*(d+e*x)^4,x,2,1/11*(A*b-a*B)*(b*d-a*e)^4*(a+b*x)^11/b^6+1/12*(b*d-a*e)^3*(b*B*d+4*A*b*e-5*a*B*e)*(a+b*x)^12/b^6+2/13*e*(b*d-a*e)^2*(2*b*B*d+3*A*b*e-5*a*B*e)*(a+b*x)^13/b^6+1/7*e^2*(b*d-a*e)*(3*b*B*d+2*A*b*e-5*a*B*e)*(a+b*x)^14/b^6+1/15*e^3*(4*b*B*d+A*b*e-5*a*B*e)*(a+b*x)^15/b^6+1/16*B*e^4*(a+b*x)^16/b^6],
[(a+b*x)^10*(A+B*x)*(d+e*x)^3,x,2,1/11*(A*b-a*B)*(b*d-a*e)^3*(a+b*x)^11/b^5+1/12*(b*d-a*e)^2*(b*B*d+3*A*b*e-4*a*B*e)*(a+b*x)^12/b^5+3/13*e*(b*d-a*e)*(b*B*d+A*b*e-2*a*B*e)*(a+b*x)^13/b^5+1/14*e^2*(3*b*B*d+A*b*e-4*a*B*e)*(a+b*x)^14/b^5+1/15*B*e^3*(a+b*x)^15/b^5],
[(a+b*x)^10*(A+B*x)*(d+e*x)^2,x,2,1/11*(A*b-a*B)*(b*d-a*e)^2*(a+b*x)^11/b^4+1/12*(b*d-a*e)*(b*B*d+2*A*b*e-3*a*B*e)*(a+b*x)^12/b^4+1/13*e*(2*b*B*d+A*b*e-3*a*B*e)*(a+b*x)^13/b^4+1/14*B*e^2*(a+b*x)^14/b^4],
[(a+b*x)^10*(A+B*x)*(d+e*x),x,2,1/11*(A*b-a*B)*(b*d-a*e)*(a+b*x)^11/b^3+1/12*(b*B*d+A*b*e-2*a*B*e)*(a+b*x)^12/b^3+1/13*B*e*(a+b*x)^13/b^3],
[(a+b*x)^10*(A+B*x),x,2,1/11*(A*b-a*B)*(a+b*x)^11/b^2+1/12*B*(a+b*x)^12/b^2],
[(a+b*x)^10*(A+B*x)/(d+e*x),x,2,b*(b*d-a*e)^9*(B*d-A*e)*x/e^11-1/2*(b*d-a*e)^8*(B*d-A*e)*(a+b*x)^2/e^10+1/3*(b*d-a*e)^7*(B*d-A*e)*(a+b*x)^3/e^9-1/4*(b*d-a*e)^6*(B*d-A*e)*(a+b*x)^4/e^8+1/5*(b*d-a*e)^5*(B*d-A*e)*(a+b*x)^5/e^7-1/6*(b*d-a*e)^4*(B*d-A*e)*(a+b*x)^6/e^6+1/7*(b*d-a*e)^3*(B*d-A*e)*(a+b*x)^7/e^5-1/8*(b*d-a*e)^2*(B*d-A*e)*(a+b*x)^8/e^4+1/9*(b*d-a*e)*(B*d-A*e)*(a+b*x)^9/e^3-1/10*(B*d-A*e)*(a+b*x)^10/e^2+1/11*B*(a+b*x)^11/(b*e)-(b*d-a*e)^10*(B*d-A*e)*log(d+e*x)/e^12],
[(a+b*x)^10*(A+B*x)/(d+e*x)^2,x,2,-5*b*(b*d-a*e)^8*(11*b*B*d-9*A*b*e-2*a*B*e)*x/e^11+(b*d-a*e)^10*(B*d-A*e)/(e^12*(d+e*x))+15/2*b^2*(b*d-a*e)^7*(11*b*B*d-8*A*b*e-3*a*B*e)*(d+e*x)^2/e^12-10*b^3*(b*d-a*e)^6*(11*b*B*d-7*A*b*e-4*a*B*e)*(d+e*x)^3/e^12+21/2*b^4*(b*d-a*e)^5*(11*b*B*d-6*A*b*e-5*a*B*e)*(d+e*x)^4/e^12-42/5*b^5*(b*d-a*e)^4*(11*b*B*d-5*A*b*e-6*a*B*e)*(d+e*x)^5/e^12+5*b^6*(b*d-a*e)^3*(11*b*B*d-4*A*b*e-7*a*B*e)*(d+e*x)^6/e^12-15/7*b^7*(b*d-a*e)^2*(11*b*B*d-3*A*b*e-8*a*B*e)*(d+e*x)^7/e^12+5/8*b^8*(b*d-a*e)*(11*b*B*d-2*A*b*e-9*a*B*e)*(d+e*x)^8/e^12-1/9*b^9*(11*b*B*d-A*b*e-10*a*B*e)*(d+e*x)^9/e^12+1/10*b^10*B*(d+e*x)^10/e^12+(b*d-a*e)^9*(11*b*B*d-10*A*b*e-a*B*e)*log(d+e*x)/e^12],
[(a+b*x)^10*(A+B*x)/(d+e*x)^3,x,2,15*b^2*(b*d-a*e)^7*(11*b*B*d-8*A*b*e-3*a*B*e)*x/e^11+1/2*(b*d-a*e)^10*(B*d-A*e)/(e^12*(d+e*x)^2)-(b*d-a*e)^9*(11*b*B*d-10*A*b*e-a*B*e)/(e^12*(d+e*x))-15*b^3*(b*d-a*e)^6*(11*b*B*d-7*A*b*e-4*a*B*e)*(d+e*x)^2/e^12+14*b^4*(b*d-a*e)^5*(11*b*B*d-6*A*b*e-5*a*B*e)*(d+e*x)^3/e^12-21/2*b^5*(b*d-a*e)^4*(11*b*B*d-5*A*b*e-6*a*B*e)*(d+e*x)^4/e^12+6*b^6*(b*d-a*e)^3*(11*b*B*d-4*A*b*e-7*a*B*e)*(d+e*x)^5/e^12-5/2*b^7*(b*d-a*e)^2*(11*b*B*d-3*A*b*e-8*a*B*e)*(d+e*x)^6/e^12+5/7*b^8*(b*d-a*e)*(11*b*B*d-2*A*b*e-9*a*B*e)*(d+e*x)^7/e^12-1/8*b^9*(11*b*B*d-A*b*e-10*a*B*e)*(d+e*x)^8/e^12+1/9*b^10*B*(d+e*x)^9/e^12-5*b*(b*d-a*e)^8*(11*b*B*d-9*A*b*e-2*a*B*e)*log(d+e*x)/e^12],
[(a+b*x)^10*(A+B*x)/(d+e*x)^4,x,2,-30*b^3*(b*d-a*e)^6*(11*b*B*d-7*A*b*e-4*a*B*e)*x/e^11+1/3*(b*d-a*e)^10*(B*d-A*e)/(e^12*(d+e*x)^3)-1/2*(b*d-a*e)^9*(11*b*B*d-10*A*b*e-a*B*e)/(e^12*(d+e*x)^2)+5*b*(b*d-a*e)^8*(11*b*B*d-9*A*b*e-2*a*B*e)/(e^12*(d+e*x))+21*b^4*(b*d-a*e)^5*(11*b*B*d-6*A*b*e-5*a*B*e)*(d+e*x)^2/e^12-14*b^5*(b*d-a*e)^4*(11*b*B*d-5*A*b*e-6*a*B*e)*(d+e*x)^3/e^12+15/2*b^6*(b*d-a*e)^3*(11*b*B*d-4*A*b*e-7*a*B*e)*(d+e*x)^4/e^12-3*b^7*(b*d-a*e)^2*(11*b*B*d-3*A*b*e-8*a*B*e)*(d+e*x)^5/e^12+5/6*b^8*(b*d-a*e)*(11*b*B*d-2*A*b*e-9*a*B*e)*(d+e*x)^6/e^12-1/7*b^9*(11*b*B*d-A*b*e-10*a*B*e)*(d+e*x)^7/e^12+1/8*b^10*B*(d+e*x)^8/e^12+15*b^2*(b*d-a*e)^7*(11*b*B*d-8*A*b*e-3*a*B*e)*log(d+e*x)/e^12],
[(a+b*x)^10*(A+B*x)/(d+e*x)^5,x,2,42*b^4*(b*d-a*e)^5*(11*b*B*d-6*A*b*e-5*a*B*e)*x/e^11+1/4*(b*d-a*e)^10*(B*d-A*e)/(e^12*(d+e*x)^4)-1/3*(b*d-a*e)^9*(11*b*B*d-10*A*b*e-a*B*e)/(e^12*(d+e*x)^3)+5/2*b*(b*d-a*e)^8*(11*b*B*d-9*A*b*e-2*a*B*e)/(e^12*(d+e*x)^2)-15*b^2*(b*d-a*e)^7*(11*b*B*d-8*A*b*e-3*a*B*e)/(e^12*(d+e*x))-21*b^5*(b*d-a*e)^4*(11*b*B*d-5*A*b*e-6*a*B*e)*(d+e*x)^2/e^12+10*b^6*(b*d-a*e)^3*(11*b*B*d-4*A*b*e-7*a*B*e)*(d+e*x)^3/e^12-15/4*b^7*(b*d-a*e)^2*(11*b*B*d-3*A*b*e-8*a*B*e)*(d+e*x)^4/e^12+b^8*(b*d-a*e)*(11*b*B*d-2*A*b*e-9*a*B*e)*(d+e*x)^5/e^12-1/6*b^9*(11*b*B*d-A*b*e-10*a*B*e)*(d+e*x)^6/e^12+1/7*b^10*B*(d+e*x)^7/e^12-30*b^3*(b*d-a*e)^6*(11*b*B*d-7*A*b*e-4*a*B*e)*log(d+e*x)/e^12],
[(a+b*x)^10*(A+B*x)/(d+e*x)^6,x,2,-42*b^5*(b*d-a*e)^4*(11*b*B*d-5*A*b*e-6*a*B*e)*x/e^11+1/5*(b*d-a*e)^10*(B*d-A*e)/(e^12*(d+e*x)^5)-1/4*(b*d-a*e)^9*(11*b*B*d-10*A*b*e-a*B*e)/(e^12*(d+e*x)^4)+5/3*b*(b*d-a*e)^8*(11*b*B*d-9*A*b*e-2*a*B*e)/(e^12*(d+e*x)^3)-15/2*b^2*(b*d-a*e)^7*(11*b*B*d-8*A*b*e-3*a*B*e)/(e^12*(d+e*x)^2)+30*b^3*(b*d-a*e)^6*(11*b*B*d-7*A*b*e-4*a*B*e)/(e^12*(d+e*x))+15*b^6*(b*d-a*e)^3*(11*b*B*d-4*A*b*e-7*a*B*e)*(d+e*x)^2/e^12-5*b^7*(b*d-a*e)^2*(11*b*B*d-3*A*b*e-8*a*B*e)*(d+e*x)^3/e^12+5/4*b^8*(b*d-a*e)*(11*b*B*d-2*A*b*e-9*a*B*e)*(d+e*x)^4/e^12-1/5*b^9*(11*b*B*d-A*b*e-10*a*B*e)*(d+e*x)^5/e^12+1/6*b^10*B*(d+e*x)^6/e^12+42*b^4*(b*d-a*e)^5*(11*b*B*d-6*A*b*e-5*a*B*e)*log(d+e*x)/e^12],
[(a+b*x)^10*(A+B*x)/(d+e*x)^7,x,2,30*b^6*(b*d-a*e)^3*(11*b*B*d-4*A*b*e-7*a*B*e)*x/e^11+1/6*(b*d-a*e)^10*(B*d-A*e)/(e^12*(d+e*x)^6)-1/5*(b*d-a*e)^9*(11*b*B*d-10*A*b*e-a*B*e)/(e^12*(d+e*x)^5)+5/4*b*(b*d-a*e)^8*(11*b*B*d-9*A*b*e-2*a*B*e)/(e^12*(d+e*x)^4)-5*b^2*(b*d-a*e)^7*(11*b*B*d-8*A*b*e-3*a*B*e)/(e^12*(d+e*x)^3)+15*b^3*(b*d-a*e)^6*(11*b*B*d-7*A*b*e-4*a*B*e)/(e^12*(d+e*x)^2)-42*b^4*(b*d-a*e)^5*(11*b*B*d-6*A*b*e-5*a*B*e)/(e^12*(d+e*x))-15/2*b^7*(b*d-a*e)^2*(11*b*B*d-3*A*b*e-8*a*B*e)*(d+e*x)^2/e^12+5/3*b^8*(b*d-a*e)*(11*b*B*d-2*A*b*e-9*a*B*e)*(d+e*x)^3/e^12-1/4*b^9*(11*b*B*d-A*b*e-10*a*B*e)*(d+e*x)^4/e^12+1/5*b^10*B*(d+e*x)^5/e^12-42*b^5*(b*d-a*e)^4*(11*b*B*d-5*A*b*e-6*a*B*e)*log(d+e*x)/e^12],
[(a+b*x)^10*(A+B*x)/(d+e*x)^8,x,2,-15*b^7*(b*d-a*e)^2*(11*b*B*d-3*A*b*e-8*a*B*e)*x/e^11+1/7*(b*d-a*e)^10*(B*d-A*e)/(e^12*(d+e*x)^7)-1/6*(b*d-a*e)^9*(11*b*B*d-10*A*b*e-a*B*e)/(e^12*(d+e*x)^6)+b*(b*d-a*e)^8*(11*b*B*d-9*A*b*e-2*a*B*e)/(e^12*(d+e*x)^5)-15/4*b^2*(b*d-a*e)^7*(11*b*B*d-8*A*b*e-3*a*B*e)/(e^12*(d+e*x)^4)+10*b^3*(b*d-a*e)^6*(11*b*B*d-7*A*b*e-4*a*B*e)/(e^12*(d+e*x)^3)-21*b^4*(b*d-a*e)^5*(11*b*B*d-6*A*b*e-5*a*B*e)/(e^12*(d+e*x)^2)+42*b^5*(b*d-a*e)^4*(11*b*B*d-5*A*b*e-6*a*B*e)/(e^12*(d+e*x))+5/2*b^8*(b*d-a*e)*(11*b*B*d-2*A*b*e-9*a*B*e)*(d+e*x)^2/e^12-1/3*b^9*(11*b*B*d-A*b*e-10*a*B*e)*(d+e*x)^3/e^12+1/4*b^10*B*(d+e*x)^4/e^12+30*b^6*(b*d-a*e)^3*(11*b*B*d-4*A*b*e-7*a*B*e)*log(d+e*x)/e^12],
[(a+b*x)^10*(A+B*x)/(d+e*x)^9,x,2,5*b^8*(b*d-a*e)*(11*b*B*d-2*A*b*e-9*a*B*e)*x/e^11+1/8*(b*d-a*e)^10*(B*d-A*e)/(e^12*(d+e*x)^8)-1/7*(b*d-a*e)^9*(11*b*B*d-10*A*b*e-a*B*e)/(e^12*(d+e*x)^7)+5/6*b*(b*d-a*e)^8*(11*b*B*d-9*A*b*e-2*a*B*e)/(e^12*(d+e*x)^6)-3*b^2*(b*d-a*e)^7*(11*b*B*d-8*A*b*e-3*a*B*e)/(e^12*(d+e*x)^5)+15/2*b^3*(b*d-a*e)^6*(11*b*B*d-7*A*b*e-4*a*B*e)/(e^12*(d+e*x)^4)-14*b^4*(b*d-a*e)^5*(11*b*B*d-6*A*b*e-5*a*B*e)/(e^12*(d+e*x)^3)+21*b^5*(b*d-a*e)^4*(11*b*B*d-5*A*b*e-6*a*B*e)/(e^12*(d+e*x)^2)-30*b^6*(b*d-a*e)^3*(11*b*B*d-4*A*b*e-7*a*B*e)/(e^12*(d+e*x))-1/2*b^9*(11*b*B*d-A*b*e-10*a*B*e)*(d+e*x)^2/e^12+1/3*b^10*B*(d+e*x)^3/e^12-15*b^7*(b*d-a*e)^2*(11*b*B*d-3*A*b*e-8*a*B*e)*log(d+e*x)/e^12],
[(a+b*x)^10*(A+B*x)/(d+e*x)^10,x,2,-b^9*(10*b*B*d-A*b*e-10*a*B*e)*x/e^11+1/2*b^10*B*x^2/e^10+1/9*(b*d-a*e)^10*(B*d-A*e)/(e^12*(d+e*x)^9)-1/8*(b*d-a*e)^9*(11*b*B*d-10*A*b*e-a*B*e)/(e^12*(d+e*x)^8)+5/7*b*(b*d-a*e)^8*(11*b*B*d-9*A*b*e-2*a*B*e)/(e^12*(d+e*x)^7)-5/2*b^2*(b*d-a*e)^7*(11*b*B*d-8*A*b*e-3*a*B*e)/(e^12*(d+e*x)^6)+6*b^3*(b*d-a*e)^6*(11*b*B*d-7*A*b*e-4*a*B*e)/(e^12*(d+e*x)^5)-21/2*b^4*(b*d-a*e)^5*(11*b*B*d-6*A*b*e-5*a*B*e)/(e^12*(d+e*x)^4)+14*b^5*(b*d-a*e)^4*(11*b*B*d-5*A*b*e-6*a*B*e)/(e^12*(d+e*x)^3)-15*b^6*(b*d-a*e)^3*(11*b*B*d-4*A*b*e-7*a*B*e)/(e^12*(d+e*x)^2)+15*b^7*(b*d-a*e)^2*(11*b*B*d-3*A*b*e-8*a*B*e)/(e^12*(d+e*x))+5*b^8*(b*d-a*e)*(11*b*B*d-2*A*b*e-9*a*B*e)*log(d+e*x)/e^12],
[(a+b*x)^10*(A+B*x)/(d+e*x)^11,x,2,b^10*B*x/e^11+1/10*(b*d-a*e)^10*(B*d-A*e)/(e^12*(d+e*x)^10)-1/9*(b*d-a*e)^9*(11*b*B*d-10*A*b*e-a*B*e)/(e^12*(d+e*x)^9)+5/8*b*(b*d-a*e)^8*(11*b*B*d-9*A*b*e-2*a*B*e)/(e^12*(d+e*x)^8)-15/7*b^2*(b*d-a*e)^7*(11*b*B*d-8*A*b*e-3*a*B*e)/(e^12*(d+e*x)^7)+5*b^3*(b*d-a*e)^6*(11*b*B*d-7*A*b*e-4*a*B*e)/(e^12*(d+e*x)^6)-42/5*b^4*(b*d-a*e)^5*(11*b*B*d-6*A*b*e-5*a*B*e)/(e^12*(d+e*x)^5)+21/2*b^5*(b*d-a*e)^4*(11*b*B*d-5*A*b*e-6*a*B*e)/(e^12*(d+e*x)^4)-10*b^6*(b*d-a*e)^3*(11*b*B*d-4*A*b*e-7*a*B*e)/(e^12*(d+e*x)^3)+15/2*b^7*(b*d-a*e)^2*(11*b*B*d-3*A*b*e-8*a*B*e)/(e^12*(d+e*x)^2)-5*b^8*(b*d-a*e)*(11*b*B*d-2*A*b*e-9*a*B*e)/(e^12*(d+e*x))-b^9*(11*b*B*d-A*b*e-10*a*B*e)*log(d+e*x)/e^12],
[(a+b*x)^10*(A+B*x)/(d+e*x)^12,x,3,-1/11*(B*d-A*e)*(a+b*x)^11/(e*(b*d-a*e)*(d+e*x)^11)-1/10*B*(b*d-a*e)^10/(e^12*(d+e*x)^10)+10/9*b*B*(b*d-a*e)^9/(e^12*(d+e*x)^9)-45/8*b^2*B*(b*d-a*e)^8/(e^12*(d+e*x)^8)+120/7*b^3*B*(b*d-a*e)^7/(e^12*(d+e*x)^7)-35*b^4*B*(b*d-a*e)^6/(e^12*(d+e*x)^6)+252/5*b^5*B*(b*d-a*e)^5/(e^12*(d+e*x)^5)-105/2*b^6*B*(b*d-a*e)^4/(e^12*(d+e*x)^4)+40*b^7*B*(b*d-a*e)^3/(e^12*(d+e*x)^3)-45/2*b^8*B*(b*d-a*e)^2/(e^12*(d+e*x)^2)+10*b^9*B*(b*d-a*e)/(e^12*(d+e*x))+b^10*B*log(d+e*x)/e^12],
[(a+b*x)^10*(A+B*x)/(d+e*x)^13,x,2,-1/12*(B*d-A*e)*(a+b*x)^11/(e*(b*d-a*e)*(d+e*x)^12)+1/132*(11*b*B*d+A*b*e-12*a*B*e)*(a+b*x)^11/(e*(b*d-a*e)^2*(d+e*x)^11)],
[(a+b*x)^10*(A+B*x)/(d+e*x)^14,x,3,-1/13*(B*d-A*e)*(a+b*x)^11/(e*(b*d-a*e)*(d+e*x)^13)+1/156*(11*b*B*d+2*A*b*e-13*a*B*e)*(a+b*x)^11/(e*(b*d-a*e)^2*(d+e*x)^12)+1/1716*b*(11*b*B*d+2*A*b*e-13*a*B*e)*(a+b*x)^11/(e*(b*d-a*e)^3*(d+e*x)^11)],
[(a+b*x)^10*(A+B*x)/(d+e*x)^15,x,4,-1/14*(B*d-A*e)*(a+b*x)^11/(e*(b*d-a*e)*(d+e*x)^14)+1/182*(11*b*B*d+3*A*b*e-14*a*B*e)*(a+b*x)^11/(e*(b*d-a*e)^2*(d+e*x)^13)+1/1092*b*(11*b*B*d+3*A*b*e-14*a*B*e)*(a+b*x)^11/(e*(b*d-a*e)^3*(d+e*x)^12)+1/12012*b^2*(11*b*B*d+3*A*b*e-14*a*B*e)*(a+b*x)^11/(e*(b*d-a*e)^4*(d+e*x)^11)],
[(a+b*x)^10*(A+B*x)/(d+e*x)^16,x,5,-1/15*(B*d-A*e)*(a+b*x)^11/(e*(b*d-a*e)*(d+e*x)^15)+1/210*(11*b*B*d+4*A*b*e-15*a*B*e)*(a+b*x)^11/(e*(b*d-a*e)^2*(d+e*x)^14)+1/910*b*(11*b*B*d+4*A*b*e-15*a*B*e)*(a+b*x)^11/(e*(b*d-a*e)^3*(d+e*x)^13)+1/5460*b^2*(11*b*B*d+4*A*b*e-15*a*B*e)*(a+b*x)^11/(e*(b*d-a*e)^4*(d+e*x)^12)+1/60060*b^3*(11*b*B*d+4*A*b*e-15*a*B*e)*(a+b*x)^11/(e*(b*d-a*e)^5*(d+e*x)^11)],
[(a+b*x)^10*(A+B*x)/(d+e*x)^17,x,6,-1/16*(B*d-A*e)*(a+b*x)^11/(e*(b*d-a*e)*(d+e*x)^16)+1/240*(11*b*B*d+5*A*b*e-16*a*B*e)*(a+b*x)^11/(e*(b*d-a*e)^2*(d+e*x)^15)+1/840*b*(11*b*B*d+5*A*b*e-16*a*B*e)*(a+b*x)^11/(e*(b*d-a*e)^3*(d+e*x)^14)+1/3640*b^2*(11*b*B*d+5*A*b*e-16*a*B*e)*(a+b*x)^11/(e*(b*d-a*e)^4*(d+e*x)^13)+1/21840*b^3*(11*b*B*d+5*A*b*e-16*a*B*e)*(a+b*x)^11/(e*(b*d-a*e)^5*(d+e*x)^12)+1/240240*b^4*(11*b*B*d+5*A*b*e-16*a*B*e)*(a+b*x)^11/(e*(b*d-a*e)^6*(d+e*x)^11)],
[(a+b*x)^10*(A+B*x)/(d+e*x)^18,x,7,-1/17*(B*d-A*e)*(a+b*x)^11/(e*(b*d-a*e)*(d+e*x)^17)+1/272*(11*b*B*d+6*A*b*e-17*a*B*e)*(a+b*x)^11/(e*(b*d-a*e)^2*(d+e*x)^16)+1/816*b*(11*b*B*d+6*A*b*e-17*a*B*e)*(a+b*x)^11/(e*(b*d-a*e)^3*(d+e*x)^15)+1/2856*b^2*(11*b*B*d+6*A*b*e-17*a*B*e)*(a+b*x)^11/(e*(b*d-a*e)^4*(d+e*x)^14)+1/12376*b^3*(11*b*B*d+6*A*b*e-17*a*B*e)*(a+b*x)^11/(e*(b*d-a*e)^5*(d+e*x)^13)+1/74256*b^4*(11*b*B*d+6*A*b*e-17*a*B*e)*(a+b*x)^11/(e*(b*d-a*e)^6*(d+e*x)^12)+1/816816*b^5*(11*b*B*d+6*A*b*e-17*a*B*e)*(a+b*x)^11/(e*(b*d-a*e)^7*(d+e*x)^11)],
[(a+b*x)^10*(A+B*x)/(d+e*x)^19,x,8,-1/18*(B*d-A*e)*(a+b*x)^11/(e*(b*d-a*e)*(d+e*x)^18)+1/306*(11*b*B*d+7*A*b*e-18*a*B*e)*(a+b*x)^11/(e*(b*d-a*e)^2*(d+e*x)^17)+1/816*b*(11*b*B*d+7*A*b*e-18*a*B*e)*(a+b*x)^11/(e*(b*d-a*e)^3*(d+e*x)^16)+1/2448*b^2*(11*b*B*d+7*A*b*e-18*a*B*e)*(a+b*x)^11/(e*(b*d-a*e)^4*(d+e*x)^15)+1/8568*b^3*(11*b*B*d+7*A*b*e-18*a*B*e)*(a+b*x)^11/(e*(b*d-a*e)^5*(d+e*x)^14)+1/37128*b^4*(11*b*B*d+7*A*b*e-18*a*B*e)*(a+b*x)^11/(e*(b*d-a*e)^6*(d+e*x)^13)+1/222768*b^5*(11*b*B*d+7*A*b*e-18*a*B*e)*(a+b*x)^11/(e*(b*d-a*e)^7*(d+e*x)^12)+1/2450448*b^6*(11*b*B*d+7*A*b*e-18*a*B*e)*(a+b*x)^11/(e*(b*d-a*e)^8*(d+e*x)^11)],
[(a+b*x)^10*(A+B*x)/(d+e*x)^20,x,2,1/19*(b*d-a*e)^10*(B*d-A*e)/(e^12*(d+e*x)^19)-1/18*(b*d-a*e)^9*(11*b*B*d-10*A*b*e-a*B*e)/(e^12*(d+e*x)^18)+5/17*b*(b*d-a*e)^8*(11*b*B*d-9*A*b*e-2*a*B*e)/(e^12*(d+e*x)^17)-15/16*b^2*(b*d-a*e)^7*(11*b*B*d-8*A*b*e-3*a*B*e)/(e^12*(d+e*x)^16)+2*b^3*(b*d-a*e)^6*(11*b*B*d-7*A*b*e-4*a*B*e)/(e^12*(d+e*x)^15)-3*b^4*(b*d-a*e)^5*(11*b*B*d-6*A*b*e-5*a*B*e)/(e^12*(d+e*x)^14)+42/13*b^5*(b*d-a*e)^4*(11*b*B*d-5*A*b*e-6*a*B*e)/(e^12*(d+e*x)^13)-5/2*b^6*(b*d-a*e)^3*(11*b*B*d-4*A*b*e-7*a*B*e)/(e^12*(d+e*x)^12)+15/11*b^7*(b*d-a*e)^2*(11*b*B*d-3*A*b*e-8*a*B*e)/(e^12*(d+e*x)^11)-1/2*b^8*(b*d-a*e)*(11*b*B*d-2*A*b*e-9*a*B*e)/(e^12*(d+e*x)^10)+1/9*b^9*(11*b*B*d-A*b*e-10*a*B*e)/(e^12*(d+e*x)^9)-1/8*b^10*B/(e^12*(d+e*x)^8)],
[(a+b*x)^10*(A+B*x)/(d+e*x)^21,x,2,1/20*(b*d-a*e)^10*(B*d-A*e)/(e^12*(d+e*x)^20)-1/19*(b*d-a*e)^9*(11*b*B*d-10*A*b*e-a*B*e)/(e^12*(d+e*x)^19)+5/18*b*(b*d-a*e)^8*(11*b*B*d-9*A*b*e-2*a*B*e)/(e^12*(d+e*x)^18)-15/17*b^2*(b*d-a*e)^7*(11*b*B*d-8*A*b*e-3*a*B*e)/(e^12*(d+e*x)^17)+15/8*b^3*(b*d-a*e)^6*(11*b*B*d-7*A*b*e-4*a*B*e)/(e^12*(d+e*x)^16)-14/5*b^4*(b*d-a*e)^5*(11*b*B*d-6*A*b*e-5*a*B*e)/(e^12*(d+e*x)^15)+3*b^5*(b*d-a*e)^4*(11*b*B*d-5*A*b*e-6*a*B*e)/(e^12*(d+e*x)^14)-30/13*b^6*(b*d-a*e)^3*(11*b*B*d-4*A*b*e-7*a*B*e)/(e^12*(d+e*x)^13)+5/4*b^7*(b*d-a*e)^2*(11*b*B*d-3*A*b*e-8*a*B*e)/(e^12*(d+e*x)^12)-5/11*b^8*(b*d-a*e)*(11*b*B*d-2*A*b*e-9*a*B*e)/(e^12*(d+e*x)^11)+1/10*b^9*(11*b*B*d-A*b*e-10*a*B*e)/(e^12*(d+e*x)^10)-1/9*b^10*B/(e^12*(d+e*x)^9)],
[(a+b*x)^10*(A+B*x)/(d+e*x)^22,x,2,1/21*(b*d-a*e)^10*(B*d-A*e)/(e^12*(d+e*x)^21)-1/20*(b*d-a*e)^9*(11*b*B*d-10*A*b*e-a*B*e)/(e^12*(d+e*x)^20)+5/19*b*(b*d-a*e)^8*(11*b*B*d-9*A*b*e-2*a*B*e)/(e^12*(d+e*x)^19)-5/6*b^2*(b*d-a*e)^7*(11*b*B*d-8*A*b*e-3*a*B*e)/(e^12*(d+e*x)^18)+30/17*b^3*(b*d-a*e)^6*(11*b*B*d-7*A*b*e-4*a*B*e)/(e^12*(d+e*x)^17)-21/8*b^4*(b*d-a*e)^5*(11*b*B*d-6*A*b*e-5*a*B*e)/(e^12*(d+e*x)^16)+14/5*b^5*(b*d-a*e)^4*(11*b*B*d-5*A*b*e-6*a*B*e)/(e^12*(d+e*x)^15)-15/7*b^6*(b*d-a*e)^3*(11*b*B*d-4*A*b*e-7*a*B*e)/(e^12*(d+e*x)^14)+15/13*b^7*(b*d-a*e)^2*(11*b*B*d-3*A*b*e-8*a*B*e)/(e^12*(d+e*x)^13)-5/12*b^8*(b*d-a*e)*(11*b*B*d-2*A*b*e-9*a*B*e)/(e^12*(d+e*x)^12)+1/11*b^9*(11*b*B*d-A*b*e-10*a*B*e)/(e^12*(d+e*x)^11)-1/10*b^10*B/(e^12*(d+e*x)^10)],

# m<0
[(A+B*x)*(d+e*x)^5/(a+b*x),x,2,(A*b-a*B)*e*(b*d-a*e)^4*x/b^6+1/2*(A*b-a*B)*(b*d-a*e)^3*(d+e*x)^2/b^5+1/3*(A*b-a*B)*(b*d-a*e)^2*(d+e*x)^3/b^4+1/4*(A*b-a*B)*(b*d-a*e)*(d+e*x)^4/b^3+1/5*(A*b-a*B)*(d+e*x)^5/b^2+1/6*B*(d+e*x)^6/(b*e)+(A*b-a*B)*(b*d-a*e)^5*log(a+b*x)/b^7],
[(A+B*x)*(d+e*x)^4/(a+b*x),x,2,(A*b-a*B)*e*(b*d-a*e)^3*x/b^5+1/2*(A*b-a*B)*(b*d-a*e)^2*(d+e*x)^2/b^4+1/3*(A*b-a*B)*(b*d-a*e)*(d+e*x)^3/b^3+1/4*(A*b-a*B)*(d+e*x)^4/b^2+1/5*B*(d+e*x)^5/(b*e)+(A*b-a*B)*(b*d-a*e)^4*log(a+b*x)/b^6],
[(A+B*x)*(d+e*x)^3/(a+b*x),x,2,(A*b-a*B)*e*(b*d-a*e)^2*x/b^4+1/2*(A*b-a*B)*(b*d-a*e)*(d+e*x)^2/b^3+1/3*(A*b-a*B)*(d+e*x)^3/b^2+1/4*B*(d+e*x)^4/(b*e)+(A*b-a*B)*(b*d-a*e)^3*log(a+b*x)/b^5],
[(A+B*x)*(d+e*x)^2/(a+b*x),x,2,(A*b-a*B)*e*(b*d-a*e)*x/b^3+1/2*(A*b-a*B)*(d+e*x)^2/b^2+1/3*B*(d+e*x)^3/(b*e)+(A*b-a*B)*(b*d-a*e)^2*log(a+b*x)/b^4],
[(A+B*x)*(d+e*x)/(a+b*x),x,2,B*(b*d-a*e)*x/b^2+1/2*e*(A+B*x)^2/(b*B)+(A*b-a*B)*(b*d-a*e)*log(a+b*x)/b^3],
[(A+B*x)/(a+b*x),x,2,B*x/b+(A*b-a*B)*log(a+b*x)/b^2],
[(A+B*x)/((a+b*x)*(d+e*x)),x,2,(A*b-a*B)*log(a+b*x)/(b*(b*d-a*e))+(B*d-A*e)*log(d+e*x)/(e*(b*d-a*e))],
[(A+B*x)/((a+b*x)*(d+e*x)^2),x,2,(-B*d+A*e)/(e*(b*d-a*e)*(d+e*x))+(A*b-a*B)*log(a+b*x)/(b*d-a*e)^2-(A*b-a*B)*log(d+e*x)/(b*d-a*e)^2],
[(A+B*x)/((a+b*x)*(d+e*x)^3),x,2,1/2*(-B*d+A*e)/(e*(b*d-a*e)*(d+e*x)^2)+(A*b-a*B)/((b*d-a*e)^2*(d+e*x))+b*(A*b-a*B)*log(a+b*x)/(b*d-a*e)^3-b*(A*b-a*B)*log(d+e*x)/(b*d-a*e)^3],
[(A+B*x)/((a+b*x)*(d+e*x)^4),x,2,1/3*(-B*d+A*e)/(e*(b*d-a*e)*(d+e*x)^3)+1/2*(A*b-a*B)/((b*d-a*e)^2*(d+e*x)^2)+b*(A*b-a*B)/((b*d-a*e)^3*(d+e*x))+b^2*(A*b-a*B)*log(a+b*x)/(b*d-a*e)^4-b^2*(A*b-a*B)*log(d+e*x)/(b*d-a*e)^4],
[(A+B*x)/((a+b*x)*(d+e*x)^5),x,2,1/4*(-B*d+A*e)/(e*(b*d-a*e)*(d+e*x)^4)+1/3*(A*b-a*B)/((b*d-a*e)^2*(d+e*x)^3)+1/2*b*(A*b-a*B)/((b*d-a*e)^3*(d+e*x)^2)+b^2*(A*b-a*B)/((b*d-a*e)^4*(d+e*x))+b^3*(A*b-a*B)*log(a+b*x)/(b*d-a*e)^5-b^3*(A*b-a*B)*log(d+e*x)/(b*d-a*e)^5],
[(A+B*x)*(d+e*x)^5/(a+b*x)^2,x,2,5*e*(b*d-a*e)^3*(b*B*d+2*A*b*e-3*a*B*e)*x/b^6-(A*b-a*B)*(b*d-a*e)^5/(b^7*(a+b*x))+5*e^2*(b*d-a*e)^2*(b*B*d+A*b*e-2*a*B*e)*(a+b*x)^2/b^7+5/3*e^3*(b*d-a*e)*(2*b*B*d+A*b*e-3*a*B*e)*(a+b*x)^3/b^7+1/4*e^4*(5*b*B*d+A*b*e-6*a*B*e)*(a+b*x)^4/b^7+1/5*B*e^5*(a+b*x)^5/b^7+(b*d-a*e)^4*(b*B*d+5*A*b*e-6*a*B*e)*log(a+b*x)/b^7],
[(A+B*x)*(d+e*x)^4/(a+b*x)^2,x,2,2*e*(b*d-a*e)^2*(2*b*B*d+3*A*b*e-5*a*B*e)*x/b^5-(A*b-a*B)*(b*d-a*e)^4/(b^6*(a+b*x))+e^2*(b*d-a*e)*(3*b*B*d+2*A*b*e-5*a*B*e)*(a+b*x)^2/b^6+1/3*e^3*(4*b*B*d+A*b*e-5*a*B*e)*(a+b*x)^3/b^6+1/4*B*e^4*(a+b*x)^4/b^6+(b*d-a*e)^3*(b*B*d+4*A*b*e-5*a*B*e)*log(a+b*x)/b^6],
[(A+B*x)*(d+e*x)^3/(a+b*x)^2,x,2,3*e*(b*d-a*e)*(b*B*d+A*b*e-2*a*B*e)*x/b^4-(A*b-a*B)*(b*d-a*e)^3/(b^5*(a+b*x))+1/2*e^2*(3*b*B*d+A*b*e-4*a*B*e)*(a+b*x)^2/b^5+1/3*B*e^3*(a+b*x)^3/b^5+(b*d-a*e)^2*(b*B*d+3*A*b*e-4*a*B*e)*log(a+b*x)/b^5],
[(A+B*x)*(d+e*x)^2/(a+b*x)^2,x,2,e*(2*b*B*d+A*b*e-2*a*B*e)*x/b^3+1/2*B*e^2*x^2/b^2-(A*b-a*B)*(b*d-a*e)^2/(b^4*(a+b*x))+(b*d-a*e)*(b*B*d+2*A*b*e-3*a*B*e)*log(a+b*x)/b^4],
[(A+B*x)*(d+e*x)/(a+b*x)^2,x,2,B*e*x/b^2-(A*b-a*B)*(b*d-a*e)/(b^3*(a+b*x))+(b*B*d+A*b*e-2*a*B*e)*log(a+b*x)/b^3],
[(A+B*x)/(a+b*x)^2,x,2,(-A*b+a*B)/(b^2*(a+b*x))+B*log(a+b*x)/b^2],
[(A+B*x)/((a+b*x)^2*(d+e*x)),x,2,(-A*b+a*B)/(b*(b*d-a*e)*(a+b*x))+(B*d-A*e)*log(a+b*x)/(b*d-a*e)^2-(B*d-A*e)*log(d+e*x)/(b*d-a*e)^2],
[(A+B*x)/((a+b*x)^2*(d+e*x)^2),x,2,(-A*b+a*B)/((b*d-a*e)^2*(a+b*x))+(B*d-A*e)/((b*d-a*e)^2*(d+e*x))+(b*B*d-2*A*b*e+a*B*e)*log(a+b*x)/(b*d-a*e)^3-(b*B*d-2*A*b*e+a*B*e)*log(d+e*x)/(b*d-a*e)^3],
[(A+B*x)/((a+b*x)^2*(d+e*x)^3),x,2,-b*(A*b-a*B)/((b*d-a*e)^3*(a+b*x))+1/2*(B*d-A*e)/((b*d-a*e)^2*(d+e*x)^2)+(b*B*d-2*A*b*e+a*B*e)/((b*d-a*e)^3*(d+e*x))+b*(b*B*d-3*A*b*e+2*a*B*e)*log(a+b*x)/(b*d-a*e)^4-b*(b*B*d-3*A*b*e+2*a*B*e)*log(d+e*x)/(b*d-a*e)^4],
[(A+B*x)/((a+b*x)^2*(d+e*x)^4),x,2,-b^2*(A*b-a*B)/((b*d-a*e)^4*(a+b*x))+1/3*(B*d-A*e)/((b*d-a*e)^2*(d+e*x)^3)+1/2*(b*B*d-2*A*b*e+a*B*e)/((b*d-a*e)^3*(d+e*x)^2)+b*(b*B*d-3*A*b*e+2*a*B*e)/((b*d-a*e)^4*(d+e*x))+b^2*(b*B*d-4*A*b*e+3*a*B*e)*log(a+b*x)/(b*d-a*e)^5-b^2*(b*B*d-4*A*b*e+3*a*B*e)*log(d+e*x)/(b*d-a*e)^5],
[(A+B*x)/((a+b*x)^2*(d+e*x)^5),x,2,-b^3*(A*b-a*B)/((b*d-a*e)^5*(a+b*x))+1/4*(B*d-A*e)/((b*d-a*e)^2*(d+e*x)^4)+1/3*(b*B*d-2*A*b*e+a*B*e)/((b*d-a*e)^3*(d+e*x)^3)+1/2*b*(b*B*d-3*A*b*e+2*a*B*e)/((b*d-a*e)^4*(d+e*x)^2)+b^2*(b*B*d-4*A*b*e+3*a*B*e)/((b*d-a*e)^5*(d+e*x))+b^3*(b*B*d-5*A*b*e+4*a*B*e)*log(a+b*x)/(b*d-a*e)^6-b^3*(b*B*d-5*A*b*e+4*a*B*e)*log(d+e*x)/(b*d-a*e)^6],
[(A+B*x)*(d+e*x)^5/(a+b*x)^3,x,2,10*e^2*(b*d-a*e)^2*(b*B*d+A*b*e-2*a*B*e)*x/b^6-1/2*(A*b-a*B)*(b*d-a*e)^5/(b^7*(a+b*x)^2)-(b*d-a*e)^4*(b*B*d+5*A*b*e-6*a*B*e)/(b^7*(a+b*x))+5/2*e^3*(b*d-a*e)*(2*b*B*d+A*b*e-3*a*B*e)*(a+b*x)^2/b^7+1/3*e^4*(5*b*B*d+A*b*e-6*a*B*e)*(a+b*x)^3/b^7+1/4*B*e^5*(a+b*x)^4/b^7+5*e*(b*d-a*e)^3*(b*B*d+2*A*b*e-3*a*B*e)*log(a+b*x)/b^7],
[(A+B*x)*(d+e*x)^4/(a+b*x)^3,x,2,2*e^2*(b*d-a*e)*(3*b*B*d+2*A*b*e-5*a*B*e)*x/b^5-1/2*(A*b-a*B)*(b*d-a*e)^4/(b^6*(a+b*x)^2)-(b*d-a*e)^3*(b*B*d+4*A*b*e-5*a*B*e)/(b^6*(a+b*x))+1/2*e^3*(4*b*B*d+A*b*e-5*a*B*e)*(a+b*x)^2/b^6+1/3*B*e^4*(a+b*x)^3/b^6+2*e*(b*d-a*e)^2*(2*b*B*d+3*A*b*e-5*a*B*e)*log(a+b*x)/b^6],
[(A+B*x)*(d+e*x)^3/(a+b*x)^3,x,2,e^2*(3*b*B*d+A*b*e-3*a*B*e)*x/b^4+1/2*B*e^3*x^2/b^3-1/2*(A*b-a*B)*(b*d-a*e)^3/(b^5*(a+b*x)^2)-(b*d-a*e)^2*(b*B*d+3*A*b*e-4*a*B*e)/(b^5*(a+b*x))+3*e*(b*d-a*e)*(b*B*d+A*b*e-2*a*B*e)*log(a+b*x)/b^5],
[(A+B*x)*(d+e*x)^2/(a+b*x)^3,x,2,B*e^2*x/b^3-1/2*(A*b-a*B)*(b*d-a*e)^2/(b^4*(a+b*x)^2)-(b*d-a*e)*(b*B*d+2*A*b*e-3*a*B*e)/(b^4*(a+b*x))+e*(2*b*B*d+A*b*e-3*a*B*e)*log(a+b*x)/b^4],
[(A+B*x)*(d+e*x)/(a+b*x)^3,x,2,-1/2*(A*b-a*B)*(b*d-a*e)/(b^3*(a+b*x)^2)+(-b*B*d-A*b*e+2*a*B*e)/(b^3*(a+b*x))+B*e*log(a+b*x)/b^3],
[(A+B*x)/(a+b*x)^3,x,1,-1/2*(A+B*x)^2/((A*b-a*B)*(a+b*x)^2)],
[(A+B*x)/((a+b*x)^3*(d+e*x)),x,2,1/2*(-A*b+a*B)/(b*(b*d-a*e)*(a+b*x)^2)+(-B*d+A*e)/((b*d-a*e)^2*(a+b*x))-e*(B*d-A*e)*log(a+b*x)/(b*d-a*e)^3+e*(B*d-A*e)*log(d+e*x)/(b*d-a*e)^3],
[(A+B*x)/((a+b*x)^3*(d+e*x)^2),x,2,1/2*(-A*b+a*B)/((b*d-a*e)^2*(a+b*x)^2)+(-b*B*d+2*A*b*e-a*B*e)/((b*d-a*e)^3*(a+b*x))-e*(B*d-A*e)/((b*d-a*e)^3*(d+e*x))-e*(2*b*B*d-3*A*b*e+a*B*e)*log(a+b*x)/(b*d-a*e)^4+e*(2*b*B*d-3*A*b*e+a*B*e)*log(d+e*x)/(b*d-a*e)^4],
[(A+B*x)/((a+b*x)^3*(d+e*x)^3),x,2,-1/2*b*(A*b-a*B)/((b*d-a*e)^3*(a+b*x)^2)-b*(b*B*d-3*A*b*e+2*a*B*e)/((b*d-a*e)^4*(a+b*x))-1/2*e*(B*d-A*e)/((b*d-a*e)^3*(d+e*x)^2)-e*(2*b*B*d-3*A*b*e+a*B*e)/((b*d-a*e)^4*(d+e*x))-3*b*e*(b*B*d-2*A*b*e+a*B*e)*log(a+b*x)/(b*d-a*e)^5+3*b*e*(b*B*d-2*A*b*e+a*B*e)*log(d+e*x)/(b*d-a*e)^5],
[(A+B*x)/((a+b*x)^3*(d+e*x)^4),x,2,-1/2*b^2*(A*b-a*B)/((b*d-a*e)^4*(a+b*x)^2)-b^2*(b*B*d-4*A*b*e+3*a*B*e)/((b*d-a*e)^5*(a+b*x))-1/3*e*(B*d-A*e)/((b*d-a*e)^3*(d+e*x)^3)-1/2*e*(2*b*B*d-3*A*b*e+a*B*e)/((b*d-a*e)^4*(d+e*x)^2)-3*b*e*(b*B*d-2*A*b*e+a*B*e)/((b*d-a*e)^5*(d+e*x))-2*b^2*e*(2*b*B*d-5*A*b*e+3*a*B*e)*log(a+b*x)/(b*d-a*e)^6+2*b^2*e*(2*b*B*d-5*A*b*e+3*a*B*e)*log(d+e*x)/(b*d-a*e)^6],

# Integrands of the form (a+b x)^m (c+d x)^n (e+f x)^1

# n>0
[(1-2*x)*(2+3*x)^8*(3+5*x),x,2,-7/243*(2+3*x)^9+37/270*(2+3*x)^10-10/297*(2+3*x)^11],
[(1-2*x)*(2+3*x)^7*(3+5*x),x,2,-7/216*(2+3*x)^8+37/243*(2+3*x)^9-1/27*(2+3*x)^10],
[(1-2*x)*(2+3*x)^6*(3+5*x),x,2,-1/27*(2+3*x)^7+37/216*(2+3*x)^8-10/243*(2+3*x)^9],
[(1-2*x)*(2+3*x)^5*(3+5*x),x,2,-7/162*(2+3*x)^6+37/189*(2+3*x)^7-5/108*(2+3*x)^8],
[(1-2*x)*(2+3*x)^4*(3+5*x),x,2,-7/135*(2+3*x)^5+37/162*(2+3*x)^6-10/189*(2+3*x)^7],
[(1-2*x)*(2+3*x)^3*(3+5*x),x,2,-7/108*(2+3*x)^4+37/135*(2+3*x)^5-5/81*(2+3*x)^6],
[(1-2*x)*(2+3*x)^2*(3+5*x),x,2,12*x+16*x^2-25/3*x^3-129/4*x^4-18*x^5],
[(1-2*x)*(2+3*x)*(3+5*x),x,2,6*x+7/2*x^2-23/3*x^3-15/2*x^4],
[(1-2*x)*(3+5*x),x,2,3*x-1/2*x^2-10/3*x^3],
[(1-2*x)*(3+5*x)/(2+3*x),x,2,17/9*x-5/3*x^2-7/27*log(2+3*x)],
[(1-2*x)*(3+5*x)/(2+3*x)^2,x,2,-10/9*x+7/27/(2+3*x)+37/27*log(2+3*x)],
[(1-2*x)*(3+5*x)/(2+3*x)^3,x,2,7/54/(2+3*x)^2+(-37/27)/(2+3*x)-10/27*log(2+3*x)],
[(1-2*x)*(3+5*x)/(2+3*x)^4,x,2,7/81/(2+3*x)^3+(-37/54)/(2+3*x)^2+10/27/(2+3*x)],
[(1-2*x)*(3+5*x)/(2+3*x)^5,x,2,7/108/(2+3*x)^4+(-37/81)/(2+3*x)^3+5/27/(2+3*x)^2],
[(1-2*x)*(3+5*x)/(2+3*x)^6,x,2,7/135/(2+3*x)^5+(-37/108)/(2+3*x)^4+10/81/(2+3*x)^3],
[(1-2*x)*(2+3*x)^8*(3+5*x)^2,x,2,7/729*(2+3*x)^9-4/45*(2+3*x)^10+65/297*(2+3*x)^11-25/486*(2+3*x)^12],
[(1-2*x)*(2+3*x)^7*(3+5*x)^2,x,2,7/648*(2+3*x)^8-8/81*(2+3*x)^9+13/54*(2+3*x)^10-50/891*(2+3*x)^11],
[(1-2*x)*(2+3*x)^6*(3+5*x)^2,x,2,1/81*(2+3*x)^7-1/9*(2+3*x)^8+65/243*(2+3*x)^9-5/81*(2+3*x)^10],
[(1-2*x)*(2+3*x)^5*(3+5*x)^2,x,2,7/486*(2+3*x)^6-8/63*(2+3*x)^7+65/216*(2+3*x)^8-50/729*(2+3*x)^9],
[(1-2*x)*(2+3*x)^4*(3+5*x)^2,x,2,7/405*(2+3*x)^5-4/27*(2+3*x)^6+65/189*(2+3*x)^7-25/324*(2+3*x)^8],
[(1-2*x)*(2+3*x)^3*(3+5*x)^2,x,2,72*x+210*x^2+638/3*x^3-769/4*x^4-3366/5*x^5-1215/2*x^6-1350/7*x^7],
[(1-2*x)*(2+3*x)^2*(3+5*x)^2,x,2,36*x+78*x^2+85/3*x^3-128*x^4-183*x^5-75*x^6],
[(1-2*x)*(2+3*x)*(3+5*x)^2,x,2,18*x+51/2*x^2-34/3*x^3-205/4*x^4-30*x^5],
[(1-2*x)*(3+5*x)^2,x,2,9*x+6*x^2-35/3*x^3-25/2*x^4],
[(1-2*x)*(3+5*x)^2/(2+3*x),x,2,118/27*x-5/18*x^2-50/9*x^3+7/81*log(2+3*x)],
[(1-2*x)*(3+5*x)^2/(2+3*x)^2,x,2,95/27*x-25/9*x^2+(-7/81)/(2+3*x)-8/9*log(2+3*x)],
[(1-2*x)*(3+5*x)^2/(2+3*x)^3,x,2,-50/27*x+(-7/162)/(2+3*x)^2+8/9/(2+3*x)+65/27*log(2+3*x)],
[(1-2*x)*(3+5*x)^2/(2+3*x)^4,x,2,(-7/243)/(2+3*x)^3+4/9/(2+3*x)^2+(-65/27)/(2+3*x)-50/81*log(2+3*x)],
[(1-2*x)*(3+5*x)^2/(2+3*x)^5,x,2,7/12*(3+5*x)^3/(2+3*x)^4+3/4*(3+5*x)^3/(2+3*x)^3],
[(1-2*x)*(3+5*x)^2/(2+3*x)^6,x,2,(-7/405)/(2+3*x)^5+2/9/(2+3*x)^4+(-65/81)/(2+3*x)^3+25/81/(2+3*x)^2],
[(1-2*x)*(3+5*x)^2/(2+3*x)^7,x,2,(-7/486)/(2+3*x)^6+8/45/(2+3*x)^5+(-65/108)/(2+3*x)^4+50/243/(2+3*x)^3],
[(1-2*x)*(3+5*x)^2/(2+3*x)^8,x,2,(-1/81)/(2+3*x)^7+4/27/(2+3*x)^6+(-13/27)/(2+3*x)^5+25/162/(2+3*x)^4],
[(1-2*x)*(2+3*x)^8*(3+5*x)^3,x,2,-7/2187*(2+3*x)^9+107/2430*(2+3*x)^10-185/891*(2+3*x)^11+1025/2916*(2+3*x)^12-250/3159*(2+3*x)^13],
[(1-2*x)*(2+3*x)^7*(3+5*x)^3,x,2,-7/1944*(2+3*x)^8+107/2187*(2+3*x)^9-37/162*(2+3*x)^10+1025/2673*(2+3*x)^11-125/1458*(2+3*x)^12],
[(1-2*x)*(2+3*x)^6*(3+5*x)^3,x,2,-1/243*(2+3*x)^7+107/1944*(2+3*x)^8-185/729*(2+3*x)^9+205/486*(2+3*x)^10-250/2673*(2+3*x)^11],
[(1-2*x)*(2+3*x)^5*(3+5*x)^3,x,2,-7/1458*(2+3*x)^6+107/1701*(2+3*x)^7-185/648*(2+3*x)^8+1025/2187*(2+3*x)^9-25/243*(2+3*x)^10],
[(1-2*x)*(2+3*x)^4*(3+5*x)^3,x,2,-7/1215*(2+3*x)^5+107/1458*(2+3*x)^6-185/567*(2+3*x)^7+1025/1944*(2+3*x)^8-250/2187*(2+3*x)^9],
[(1-2*x)*(2+3*x)^3*(3+5*x)^3,x,2,216*x+810*x^2+1338*x^3+883/4*x^4-13943/5*x^5-9255/2*x^6-22275/7*x^7-3375/4*x^8],
[(1-2*x)*(2+3*x)^2*(3+5*x)^3,x,2,108*x+324*x^2+345*x^3-1111/4*x^4-1061*x^5-1975/2*x^6-2250/7*x^7],
[(1-2*x)*(2+3*x)*(3+5*x)^3,x,2,11/500*(3+5*x)^4+31/625*(3+5*x)^5-1/125*(3+5*x)^6],
[(1-2*x)*(3+5*x)^3,x,2,11/100*(3+5*x)^4-2/125*(3+5*x)^5],
[(1-2*x)*(3+5*x)^3/(2+3*x),x,2,1097/81*x+545/54*x^2-475/27*x^3-125/6*x^4-7/243*log(2+3*x)],
[(1-2*x)*(3+5*x)^3/(2+3*x)^2,x,2,55/9*x+25/54*x^2-250/27*x^3+7/243/(2+3*x)+107/243*log(2+3*x)],
[(1-2*x)*(3+5*x)^3/(2+3*x)^3,x,2,175/27*x-125/27*x^2+7/486/(2+3*x)^2+(-107/243)/(2+3*x)-185/81*log(2+3*x)],
[(1-2*x)*(3+5*x)^3/(2+3*x)^4,x,2,-250/81*x+7/729/(2+3*x)^3+(-107/486)/(2+3*x)^2+185/81/(2+3*x)+1025/243*log(2+3*x)],
[(1-2*x)*(3+5*x)^3/(2+3*x)^5,x,2,7/972/(2+3*x)^4+(-107/729)/(2+3*x)^3+185/162/(2+3*x)^2+(-1025/243)/(2+3*x)-250/243*log(2+3*x)],
[(1-2*x)*(3+5*x)^3/(2+3*x)^6,x,2,7/15*(3+5*x)^4/(2+3*x)^5+5/12*(3+5*x)^4/(2+3*x)^4],
[(1-2*x)*(3+5*x)^3/(2+3*x)^7,x,3,7/18*(3+5*x)^4/(2+3*x)^6+29/45*(3+5*x)^4/(2+3*x)^5+29/36*(3+5*x)^4/(2+3*x)^4],
[(1-2*x)*(3+5*x)^3/(2+3*x)^8,x,2,1/243/(2+3*x)^7+(-107/1458)/(2+3*x)^6+37/81/(2+3*x)^5+(-1025/972)/(2+3*x)^4+250/729/(2+3*x)^3],
[(5-2*x)^6*(2+3*x)^3*(-16+33*x),x,1,-1/2*(5-2*x)^7*(2+3*x)^4],

# n<0
[(1-2*x)*(2+3*x)^6/(3+5*x),x,2,1666663/78125*x+1777779/31250*x^2+152469/3125*x^3-152469/2500*x^4-106677/625*x^5-7047/50*x^6-1458/35*x^7+11/390625*log(3+5*x)],
[(1-2*x)*(2+3*x)^5/(3+5*x),x,2,166663/15625*x+127779/6250*x^2+2469/625*x^3-17469/500*x^4-5427/125*x^5-81/5*x^6+11/78125*log(3+5*x)],
[(1-2*x)*(2+3*x)^4/(3+5*x),x,2,16663/3125*x+7779/1250*x^2-531/125*x^3-1269/100*x^4-162/25*x^5+11/15625*log(3+5*x)],
[(1-2*x)*(2+3*x)^3/(3+5*x),x,2,1663/625*x+279/250*x^2-81/25*x^3-27/10*x^4+11/3125*log(3+5*x)],
[(1-2*x)*(2+3*x)^2/(3+5*x),x,2,163/125*x-21/50*x^2-6/5*x^3+11/625*log(3+5*x)],
[(1-2*x)*(2+3*x)/(3+5*x),x,2,13/25*x-3/5*x^2+11/125*log(3+5*x)],
[(1-2*x)/(3+5*x),x,2,-2/5*x+11/25*log(3+5*x)],
[(1-2*x)/((2+3*x)*(3+5*x)),x,2,-7/3*log(2+3*x)+11/5*log(3+5*x)],
[(1-2*x)/((2+3*x)^2*(3+5*x)),x,2,7/3/(2+3*x)-11*log(2+3*x)+11*log(3+5*x)],
[(1-2*x)/((2+3*x)^3*(3+5*x)),x,2,7/6/(2+3*x)^2+11/(2+3*x)-55*log(2+3*x)+55*log(3+5*x)],
[(1-2*x)/((2+3*x)^4*(3+5*x)),x,2,7/9/(2+3*x)^3+11/2/(2+3*x)^2+55/(2+3*x)-275*log(2+3*x)+275*log(3+5*x)],
[(1-2*x)/((2+3*x)^5*(3+5*x)),x,2,7/12/(2+3*x)^4+11/3/(2+3*x)^3+55/2/(2+3*x)^2+275/(2+3*x)-1375*log(2+3*x)+1375*log(3+5*x)],
[(1-2*x)/((2+3*x)^6*(3+5*x)),x,2,7/15/(2+3*x)^5+11/4/(2+3*x)^4+55/3/(2+3*x)^3+275/2/(2+3*x)^2+1375/(2+3*x)-6875*log(2+3*x)+6875*log(3+5*x)],
[(1-2*x)/((2+3*x)^7*(3+5*x)),x,2,7/18/(2+3*x)^6+11/5/(2+3*x)^5+55/4/(2+3*x)^4+275/3/(2+3*x)^3+1375/2/(2+3*x)^2+6875/(2+3*x)-34375*log(2+3*x)+34375*log(3+5*x)],
[(1-2*x)*(2+3*x)^7/(3+5*x)^2,x,2,5555478/390625*x+5740767/156250*x^2+92592/3125*x^3-513783/12500*x^4-336798/3125*x^5-21627/250*x^6-4374/175*x^7+(-11/1953125)/(3+5*x)+229/1953125*log(3+5*x)],
[(1-2*x)*(2+3*x)^6/(3+5*x)^2,x,2,555489/78125*x+40743/3125*x^2+5553/3125*x^3-14094/625*x^4-16767/625*x^5-243/25*x^6+(-11/390625)/(3+5*x)+196/390625*log(3+5*x)],
[(1-2*x)*(2+3*x)^5/(3+5*x)^2,x,2,444/125*x+24093/6250*x^2-1854/625*x^3-3969/500*x^4-486/125*x^5+(-11/78125)/(3+5*x)+163/78125*log(3+5*x)],
[(1-2*x)*(2+3*x)^4/(3+5*x)^2,x,2,5511/3125*x+378/625*x^2-261/125*x^3-81/50*x^4+(-11/15625)/(3+5*x)+26/3125*log(3+5*x)],
[(1-2*x)*(2+3*x)^3/(3+5*x)^2,x,2,522/625*x-81/250*x^2-18/25*x^3+(-11/3125)/(3+5*x)+97/3125*log(3+5*x)],
[(1-2*x)*(2+3*x)^2/(3+5*x)^2,x,2,33/125*x-9/25*x^2+(-11/625)/(3+5*x)+64/625*log(3+5*x)],
[(1-2*x)*(2+3*x)/(3+5*x)^2,x,2,-6/25*x+(-11/125)/(3+5*x)+31/125*log(3+5*x)],
[(1-2*x)/(3+5*x)^2,x,2,(-11/25)/(3+5*x)-2/25*log(3+5*x)],
[(1-2*x)/((2+3*x)*(3+5*x)^2),x,2,(-11/5)/(3+5*x)+7*log(2+3*x)-7*log(3+5*x)],
[(1-2*x)/((2+3*x)^2*(3+5*x)^2),x,2,(-7)/(2+3*x)+(-11)/(3+5*x)+68*log(2+3*x)-68*log(3+5*x)],
[(1-2*x)/((2+3*x)^3*(3+5*x)^2),x,2,(-7/2)/(2+3*x)^2+(-68)/(2+3*x)+(-55)/(3+5*x)+505*log(2+3*x)-505*log(3+5*x)],
[(1-2*x)/((2+3*x)^4*(3+5*x)^2),x,2,(-7/3)/(2+3*x)^3+(-34)/(2+3*x)^2+(-505)/(2+3*x)+(-275)/(3+5*x)+3350*log(2+3*x)-3350*log(3+5*x)],
[(1-2*x)/((2+3*x)^5*(3+5*x)^2),x,2,(-7/4)/(2+3*x)^4+(-68/3)/(2+3*x)^3+(-505/2)/(2+3*x)^2+(-3350)/(2+3*x)+(-1375)/(3+5*x)+20875*log(2+3*x)-20875*log(3+5*x)],
[(1-2*x)/((2+3*x)^6*(3+5*x)^2),x,2,(-7/5)/(2+3*x)^5+(-17)/(2+3*x)^4+(-505/3)/(2+3*x)^3+(-1675)/(2+3*x)^2+(-20875)/(2+3*x)+(-6875)/(3+5*x)+125000*log(2+3*x)-125000*log(3+5*x)],
[(1-2*x)/((2+3*x)^7*(3+5*x)^2),x,2,(-7/6)/(2+3*x)^6+(-68/5)/(2+3*x)^5+(-505/4)/(2+3*x)^4+(-3350/3)/(2+3*x)^3+(-20875/2)/(2+3*x)^2+(-125000)/(2+3*x)+(-34375)/(3+5*x)+728125*log(2+3*x)-728125*log(3+5*x)],
[(1-2*x)*(2+3*x)^7/(3+5*x)^3,x,2,1851147/390625*x+129654/15625*x^2+2052/3125*x^3-181521/12500*x^4-51759/3125*x^5-729/125*x^6+(-11/3906250)/(3+5*x)^2+(-229/1953125)/(3+5*x)+2037/1953125*log(3+5*x)],
[(1-2*x)*(2+3*x)^6/(3+5*x)^3,x,2,36936/15625*x+297/125*x^2-6399/3125*x^3-12393/2500*x^4-1458/625*x^5+(-11/781250)/(3+5*x)^2+(-196/390625)/(3+5*x)+1449/390625*log(3+5*x)],
[(1-2*x)*(2+3*x)^5/(3+5*x)^3,x,2,3636/3125*x+1971/6250*x^2-837/625*x^3-243/250*x^4+(-11/156250)/(3+5*x)^2+(-163/78125)/(3+5*x)+192/15625*log(3+5*x)],
[(1-2*x)*(2+3*x)^4/(3+5*x)^3,x,2,1647/3125*x-297/1250*x^2-54/125*x^3+(-11/31250)/(3+5*x)^2+(-26/3125)/(3+5*x)+114/3125*log(3+5*x)],
[(1-2*x)*(2+3*x)^3/(3+5*x)^3,x,2,81/625*x-27/125*x^2+(-11/6250)/(3+5*x)^2+(-97/3125)/(3+5*x)+279/3125*log(3+5*x)],
[(1-2*x)*(2+3*x)^2/(3+5*x)^3,x,2,-18/125*x+(-11/1250)/(3+5*x)^2+(-64/625)/(3+5*x)+87/625*log(3+5*x)],
[(1-2*x)*(2+3*x)/(3+5*x)^3,x,2,(-11/250)/(3+5*x)^2+(-31/125)/(3+5*x)-6/125*log(3+5*x)],
[(1-2*x)/(3+5*x)^3,x,1,-1/22*(1-2*x)^2/(3+5*x)^2],
[(1-2*x)/((2+3*x)*(3+5*x)^3),x,2,(-11/10)/(3+5*x)^2+7/(3+5*x)-21*log(2+3*x)+21*log(3+5*x)],
[(1-2*x)/((2+3*x)^2*(3+5*x)^3),x,2,21/(2+3*x)+(-11/2)/(3+5*x)^2+68/(3+5*x)-309*log(2+3*x)+309*log(3+5*x)],
[(1-2*x)/((2+3*x)^3*(3+5*x)^3),x,2,21/2/(2+3*x)^2+309/(2+3*x)+(-55/2)/(3+5*x)^2+505/(3+5*x)-3060*log(2+3*x)+3060*log(3+5*x)],
[(1-2*x)/((2+3*x)^4*(3+5*x)^3),x,2,7/(2+3*x)^3+309/2/(2+3*x)^2+3060/(2+3*x)+(-275/2)/(3+5*x)^2+3350/(3+5*x)-25350*log(2+3*x)+25350*log(3+5*x)],
[(1-2*x)/((2+3*x)^5*(3+5*x)^3),x,2,21/4/(2+3*x)^4+103/(2+3*x)^3+1530/(2+3*x)^2+25350/(2+3*x)+(-1375/2)/(3+5*x)^2+20875/(3+5*x)-189375*log(2+3*x)+189375*log(3+5*x)],
[(1-2*x)/((2+3*x)^6*(3+5*x)^3),x,2,21/5/(2+3*x)^5+309/4/(2+3*x)^4+1020/(2+3*x)^3+12675/(2+3*x)^2+189375/(2+3*x)+(-6875/2)/(3+5*x)^2+125000/(3+5*x)-1321875*log(2+3*x)+1321875*log(3+5*x)],

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

# n>0
[(1-2*x)^2*(2+3*x)^8*(3+5*x),x,2,-49/729*(2+3*x)^9+91/270*(2+3*x)^10-16/99*(2+3*x)^11+5/243*(2+3*x)^12],
[(1-2*x)^2*(2+3*x)^7*(3+5*x),x,2,-49/648*(2+3*x)^8+91/243*(2+3*x)^9-8/45*(2+3*x)^10+20/891*(2+3*x)^11],
[(1-2*x)^2*(2+3*x)^6*(3+5*x),x,2,-7/81*(2+3*x)^7+91/216*(2+3*x)^8-16/81*(2+3*x)^9+2/81*(2+3*x)^10],
[(1-2*x)^2*(2+3*x)^5*(3+5*x),x,2,-49/486*(2+3*x)^6+13/27*(2+3*x)^7-2/9*(2+3*x)^8+20/729*(2+3*x)^9],
[(1-2*x)^2*(2+3*x)^4*(3+5*x),x,2,-49/405*(2+3*x)^5+91/162*(2+3*x)^6-16/63*(2+3*x)^7+5/162*(2+3*x)^8],
[(1-2*x)^2*(2+3*x)^3*(3+5*x),x,2,24*x+26*x^2-154/3*x^3-425/4*x^4+99/5*x^5+144*x^6+540/7*x^7],
[(1-2*x)^2*(2+3*x)^2*(3+5*x),x,2,12*x+4*x^2-89/3*x^3-79/4*x^4+168/5*x^5+30*x^6],
[(1-2*x)^2*(2+3*x)*(3+5*x),x,2,6*x-5/2*x^2-37/3*x^3+4*x^4+12*x^5],
[(1-2*x)^2*(3+5*x),x,2,3*x-7/2*x^2-8/3*x^3+5*x^4],
[(1-2*x)^2*(3+5*x)/(2+3*x),x,2,65/27*x-32/9*x^2+20/9*x^3-49/81*log(2+3*x)],
[(1-2*x)^2*(3+5*x)/(2+3*x)^2,x,2,-104/27*x+10/9*x^2+49/81/(2+3*x)+91/27*log(2+3*x)],
[(1-2*x)^2*(3+5*x)/(2+3*x)^3,x,2,20/27*x+49/162/(2+3*x)^2+(-91/27)/(2+3*x)-16/9*log(2+3*x)],
[(1-2*x)^2*(3+5*x)/(2+3*x)^4,x,2,49/243/(2+3*x)^3+(-91/54)/(2+3*x)^2+16/9/(2+3*x)+20/81*log(2+3*x)],
[(1-2*x)^2*(3+5*x)/(2+3*x)^5,x,2,1/84*(1-2*x)^3/(2+3*x)^4-23/294*(1-2*x)^3/(2+3*x)^3],
[(1-2*x)^2*(3+5*x)/(2+3*x)^6,x,2,49/405/(2+3*x)^5+(-91/108)/(2+3*x)^4+16/27/(2+3*x)^3+(-10/81)/(2+3*x)^2],
[(1-2*x)^2*(3+5*x)/(2+3*x)^7,x,2,49/486/(2+3*x)^6+(-91/135)/(2+3*x)^5+4/9/(2+3*x)^4+(-20/243)/(2+3*x)^3],
[(1-2*x)^2*(3+5*x)/(2+3*x)^8,x,2,7/81/(2+3*x)^7+(-91/162)/(2+3*x)^6+16/45/(2+3*x)^5+(-5/81)/(2+3*x)^4],
[(1-2*x)^2*(2+3*x)^8*(3+5*x)^2,x,2,49/2187*(2+3*x)^9-259/1215*(2+3*x)^10+503/891*(2+3*x)^11-185/729*(2+3*x)^12+100/3159*(2+3*x)^13],
[(1-2*x)^2*(2+3*x)^7*(3+5*x)^2,x,2,49/1944*(2+3*x)^8-518/2187*(2+3*x)^9+503/810*(2+3*x)^10-740/2673*(2+3*x)^11+25/729*(2+3*x)^12],
[(1-2*x)^2*(2+3*x)^6*(3+5*x)^2,x,2,7/243*(2+3*x)^7-259/972*(2+3*x)^8+503/729*(2+3*x)^9-74/243*(2+3*x)^10+100/2673*(2+3*x)^11],
[(1-2*x)^2*(2+3*x)^5*(3+5*x)^2,x,2,49/1458*(2+3*x)^6-74/243*(2+3*x)^7+503/648*(2+3*x)^8-740/2187*(2+3*x)^9+10/243*(2+3*x)^10],
[(1-2*x)^2*(2+3*x)^4*(3+5*x)^2,x,2,49/1215*(2+3*x)^5-259/729*(2+3*x)^6+503/567*(2+3*x)^7-185/486*(2+3*x)^8+100/2187*(2+3*x)^9],
[(1-2*x)^2*(2+3*x)^3*(3+5*x)^2,x,2,72*x+138*x^2-202/3*x^3-2045/4*x^4-1828/5*x^5+1029/2*x^6+5940/7*x^7+675/2*x^8],
[(1-2*x)^2*(2+3*x)^2*(3+5*x)^2,x,2,36*x+42*x^2-227/3*x^3-341/2*x^4+109/5*x^5+230*x^6+900/7*x^7],
[(1-2*x)^2*(2+3*x)*(3+5*x)^2,x,2,18*x+15/2*x^2-136/3*x^3-137/4*x^4+52*x^5+50*x^6],
[(1-2*x)^2*(3+5*x)^2,x,2,9*x-3*x^2-59/3*x^3+5*x^4+20*x^5],
[(1-2*x)^2*(3+5*x)^2/(2+3*x),x,2,340/81*x-251/54*x^2-140/27*x^3+25/3*x^4+49/243*log(2+3*x)],
[(1-2*x)^2*(3+5*x)^2/(2+3*x)^2,x,2,143/27*x-170/27*x^2+100/27*x^3+(-49/243)/(2+3*x)-518/243*log(2+3*x)],
[(1-2*x)^2*(3+5*x)^2/(2+3*x)^3,x,2,-20/3*x+50/27*x^2+(-49/486)/(2+3*x)^2+518/243/(2+3*x)+503/81*log(2+3*x)],
[(1-2*x)^2*(3+5*x)^2/(2+3*x)^4,x,2,100/81*x+(-49/729)/(2+3*x)^3+259/243/(2+3*x)^2+(-503/81)/(2+3*x)-740/243*log(2+3*x)],
[(1-2*x)^2*(3+5*x)^2/(2+3*x)^5,x,2,(-49/972)/(2+3*x)^4+518/729/(2+3*x)^3+(-503/162)/(2+3*x)^2+740/243/(2+3*x)+100/243*log(2+3*x)],
[(1-2*x)^2*(3+5*x)^2/(2+3*x)^6,x,2,(-49/1215)/(2+3*x)^5+259/486/(2+3*x)^4+(-503/243)/(2+3*x)^3+370/243/(2+3*x)^2+(-100/243)/(2+3*x)],
[(1-2*x)^2*(3+5*x)^2/(2+3*x)^7,x,2,(-49/1458)/(2+3*x)^6+518/1215/(2+3*x)^5+(-503/324)/(2+3*x)^4+740/729/(2+3*x)^3+(-50/243)/(2+3*x)^2],
[(1-2*x)^2*(3+5*x)^2/(2+3*x)^8,x,2,(-7/243)/(2+3*x)^7+259/729/(2+3*x)^6+(-503/405)/(2+3*x)^5+185/243/(2+3*x)^4+(-100/729)/(2+3*x)^3],
[(1-2*x)^2*(2+3*x)^10*(3+5*x)^3,x,2,-49/8019*(2+3*x)^11+763/8748*(2+3*x)^12-4099/9477*(2+3*x)^13+8285/10206*(2+3*x)^14-760/2187*(2+3*x)^15+125/2916*(2+3*x)^16],
[(1-2*x)^2*(2+3*x)^9*(3+5*x)^3,x,2,-49/7290*(2+3*x)^10+763/8019*(2+3*x)^11-4099/8748*(2+3*x)^12+8285/9477*(2+3*x)^13-1900/5103*(2+3*x)^14+100/2187*(2+3*x)^15],
[(1-2*x)^2*(2+3*x)^8*(3+5*x)^3,x,2,-49/6561*(2+3*x)^9+763/7290*(2+3*x)^10-4099/8019*(2+3*x)^11+8285/8748*(2+3*x)^12-3800/9477*(2+3*x)^13+250/5103*(2+3*x)^14],
[(1-2*x)^2*(2+3*x)^7*(3+5*x)^3,x,2,-49/5832*(2+3*x)^8+763/6561*(2+3*x)^9-4099/7290*(2+3*x)^10+8285/8019*(2+3*x)^11-950/2187*(2+3*x)^12+500/9477*(2+3*x)^13],
[(1-2*x)^2*(2+3*x)^6*(3+5*x)^3,x,2,-7/729*(2+3*x)^7+763/5832*(2+3*x)^8-4099/6561*(2+3*x)^9+1657/1458*(2+3*x)^10-3800/8019*(2+3*x)^11+125/2187*(2+3*x)^12],
[(1-2*x)^2*(2+3*x)^5*(3+5*x)^3,x,2,-49/4374*(2+3*x)^6+109/729*(2+3*x)^7-4099/5832*(2+3*x)^8+8285/6561*(2+3*x)^9-380/729*(2+3*x)^10+500/8019*(2+3*x)^11],
[(1-2*x)^2*(2+3*x)^4*(3+5*x)^3,x,2,-49/3645*(2+3*x)^5+763/4374*(2+3*x)^6-4099/5103*(2+3*x)^7+8285/5832*(2+3*x)^8-3800/6561*(2+3*x)^9+50/729*(2+3*x)^10],
[(1-2*x)^2*(2+3*x)^3*(3+5*x)^3,x,2,216*x+594*x^2+258*x^3-7145/4*x^4-15709/5*x^5+121/6*x^6+33255/7*x^7+4725*x^8+1500*x^9],
[(1-2*x)^2*(2+3*x)^2*(3+5*x)^3,x,2,108*x+216*x^2-87*x^3-3181/4*x^4-3083/5*x^5+4685/6*x^6+9600/7*x^7+1125/2*x^8],
[(1-2*x)^2*(2+3*x)*(3+5*x)^3,x,2,54*x+135/2*x^2-111*x^3-1091/4*x^4+19*x^5+1100/3*x^6+1500/7*x^7],
[(1-2*x)^2*(3+5*x)^3,x,2,121/500*(3+5*x)^4-44/625*(3+5*x)^5+2/375*(3+5*x)^6],
[(1-2*x)^2*(3+5*x)^3/(2+3*x),x,2,3305/243*x-559/162*x^2-2515/81*x^3+50/9*x^4+100/3*x^5-49/729*log(2+3*x)],
[(1-2*x)^2*(3+5*x)^3/(2+3*x)^2,x,2,1271/243*x-305/54*x^2-800/81*x^3+125/9*x^4+49/729/(2+3*x)+763/729*log(2+3*x)],
[(1-2*x)^2*(3+5*x)^3/(2+3*x)^3,x,2,895/81*x-100/9*x^2+500/81*x^3+49/1458/(2+3*x)^2+(-763/729)/(2+3*x)-4099/729*log(2+3*x)],
[(1-2*x)^2*(3+5*x)^3/(2+3*x)^4,x,2,-2800/243*x+250/81*x^2+49/2187/(2+3*x)^3+(-763/1458)/(2+3*x)^2+4099/729/(2+3*x)+8285/729*log(2+3*x)],
[(1-2*x)^2*(3+5*x)^3/(2+3*x)^5,x,2,500/243*x+49/2916/(2+3*x)^4+(-763/2187)/(2+3*x)^3+4099/1458/(2+3*x)^2+(-8285/729)/(2+3*x)-3800/729*log(2+3*x)],
[(1-2*x)^2*(3+5*x)^3/(2+3*x)^6,x,2,49/3645/(2+3*x)^5+(-763/2916)/(2+3*x)^4+4099/2187/(2+3*x)^3+(-8285/1458)/(2+3*x)^2+3800/729/(2+3*x)+500/729*log(2+3*x)],
[(1-2*x)^2*(3+5*x)^3/(2+3*x)^7,x,2,49/4374/(2+3*x)^6+(-763/3645)/(2+3*x)^5+4099/2916/(2+3*x)^4+(-8285/2187)/(2+3*x)^3+1900/729/(2+3*x)^2+(-500/729)/(2+3*x)],
[(1-2*x)^2*(3+5*x)^3/(2+3*x)^8,x,2,7/729/(2+3*x)^7+(-763/4374)/(2+3*x)^6+4099/3645/(2+3*x)^5+(-8285/2916)/(2+3*x)^4+3800/2187/(2+3*x)^3+(-250/729)/(2+3*x)^2],

# n<0
[(1-2*x)^2*(2+3*x)^7/(3+5*x),x,2,83333293/1953125*x+80555569/781250*x^2+1327159/78125*x^3-20577159/62500*x^4-7315947/15625*x^5+130383/1250*x^6+672867/875*x^7+16767/25*x^8+972/5*x^9+121/9765625*log(3+5*x)],
[(1-2*x)^2*(2+3*x)^6/(3+5*x),x,2,8333293/390625*x+5555569/156250*x^2-422841/15625*x^3-1677159/12500*x^4-228447/3125*x^5+35883/250*x^6+34992/175*x^7+729/10*x^8+121/1953125*log(3+5*x)],
[(1-2*x)^2*(2+3*x)^5/(3+5*x),x,2,833293/78125*x+305569/31250*x^2-72841/3125*x^3-102159/2500*x^4+7803/625*x^5+1404/25*x^6+972/35*x^7+121/390625*log(3+5*x)],
[(1-2*x)^2*(2+3*x)^4/(3+5*x),x,2,83293/15625*x+5569/6250*x^2-7841/625*x^3-3159/500*x^4+1728/125*x^5+54/5*x^6+121/78125*log(3+5*x)],
[(1-2*x)^2*(2+3*x)^3/(3+5*x),x,2,8293/3125*x-1931/1250*x^2-591/125*x^3+54/25*x^4+108/25*x^5+121/15625*log(3+5*x)],
[(1-2*x)^2*(2+3*x)^2/(3+5*x),x,2,793/625*x-431/250*x^2-16/25*x^3+9/5*x^4+121/3125*log(3+5*x)],
[(1-2*x)^2*(2+3*x)/(3+5*x),x,2,43/125*x-28/25*x^2+4/5*x^3+121/625*log(3+5*x)],
[(1-2*x)^2/(3+5*x),x,2,-32/25*x+2/5*x^2+121/125*log(3+5*x)],
[(1-2*x)^2/((2+3*x)*(3+5*x)),x,2,4/15*x-49/9*log(2+3*x)+121/25*log(3+5*x)],
[(1-2*x)^2/((2+3*x)^2*(3+5*x)),x,2,49/9/(2+3*x)-217/9*log(2+3*x)+121/5*log(3+5*x)],
[(1-2*x)^2/((2+3*x)^3*(3+5*x)),x,2,49/18/(2+3*x)^2+217/9/(2+3*x)-121*log(2+3*x)+121*log(3+5*x)],
[(1-2*x)^2/((2+3*x)^4*(3+5*x)),x,2,49/27/(2+3*x)^3+217/18/(2+3*x)^2+121/(2+3*x)-605*log(2+3*x)+605*log(3+5*x)],
[(1-2*x)^2/((2+3*x)^5*(3+5*x)),x,2,49/36/(2+3*x)^4+217/27/(2+3*x)^3+121/2/(2+3*x)^2+605/(2+3*x)-3025*log(2+3*x)+3025*log(3+5*x)],
[(1-2*x)^2/((2+3*x)^6*(3+5*x)),x,2,49/45/(2+3*x)^5+217/36/(2+3*x)^4+121/3/(2+3*x)^3+605/2/(2+3*x)^2+3025/(2+3*x)-15125*log(2+3*x)+15125*log(3+5*x)],
[(1-2*x)^2/((2+3*x)^7*(3+5*x)),x,2,49/54/(2+3*x)^6+217/45/(2+3*x)^5+121/4/(2+3*x)^4+605/3/(2+3*x)^3+3025/2/(2+3*x)^2+15125/(2+3*x)-75625*log(2+3*x)+75625*log(3+5*x)],
[(1-2*x)^2/((2+3*x)^8*(3+5*x)),x,2,7/9/(2+3*x)^7+217/54/(2+3*x)^6+121/5/(2+3*x)^5+605/4/(2+3*x)^4+3025/3/(2+3*x)^3+15125/2/(2+3*x)^2+75625/(2+3*x)-378125*log(2+3*x)+378125*log(3+5*x)],
[(1-2*x)^2*(2+3*x)^7/(3+5*x)^2,x,2,27776932/1953125*x+17592879/781250*x^2-1512378/78125*x^3-213867/2500*x^4-656424/15625*x^5+116397/1250*x^6+107892/875*x^7+2187/50*x^8+(-121/9765625)/(3+5*x)+2497/9765625*log(3+5*x)],
[(1-2*x)^2*(2+3*x)^6/(3+5*x)^2,x,2,2777053/390625*x+463086/78125*x^2-48771/3125*x^3-157599/6250*x^4+28917/3125*x^5+4374/125*x^6+2916/175*x^7+(-121/1953125)/(3+5*x)+2134/1953125*log(3+5*x)],
[(1-2*x)^2*(2+3*x)^5/(3+5*x)^2,x,2,277174/78125*x+1893/6250*x^2-25332/3125*x^3-8721/2500*x^4+5508/625*x^5+162/25*x^6+(-121/390625)/(3+5*x)+1771/390625*log(3+5*x)],
[(1-2*x)^2*(2+3*x)^4/(3+5*x)^2,x,2,5459/3125*x-3621/3125*x^2-1809/625*x^3+189/125*x^4+324/125*x^5+(-121/78125)/(3+5*x)+1408/78125*log(3+5*x)],
[(1-2*x)^2*(2+3*x)^3/(3+5*x)^2,x,2,2416/3125*x-1449/1250*x^2-36/125*x^3+27/25*x^4+(-121/15625)/(3+5*x)+209/3125*log(3+5*x)],
[(1-2*x)^2*(2+3*x)^2/(3+5*x)^2,x,2,37/625*x-78/125*x^2+12/25*x^3+(-121/3125)/(3+5*x)+682/3125*log(3+5*x)],
[(1-2*x)^2*(2+3*x)/(3+5*x)^2,x,2,-92/125*x+6/25*x^2+(-121/625)/(3+5*x)+319/625*log(3+5*x)],
[(1-2*x)^2/(3+5*x)^2,x,2,4/25*x+(-121/125)/(3+5*x)-44/125*log(3+5*x)],
[(1-2*x)^2/((2+3*x)*(3+5*x)^2),x,2,(-121/25)/(3+5*x)+49/3*log(2+3*x)-407/25*log(3+5*x)],
[(1-2*x)^2/((2+3*x)^2*(3+5*x)^2),x,2,(-49/3)/(2+3*x)+(-121/5)/(3+5*x)+154*log(2+3*x)-154*log(3+5*x)],
[(1-2*x)^2/((2+3*x)^3*(3+5*x)^2),x,2,(-49/6)/(2+3*x)^2+(-154)/(2+3*x)+(-121)/(3+5*x)+1133*log(2+3*x)-1133*log(3+5*x)],
[(1-2*x)^2/((2+3*x)^4*(3+5*x)^2),x,2,(-49/9)/(2+3*x)^3+(-77)/(2+3*x)^2+(-1133)/(2+3*x)+(-605)/(3+5*x)+7480*log(2+3*x)-7480*log(3+5*x)],
[(1-2*x)^2/((2+3*x)^5*(3+5*x)^2),x,2,(-49/12)/(2+3*x)^4+(-154/3)/(2+3*x)^3+(-1133/2)/(2+3*x)^2+(-7480)/(2+3*x)+(-3025)/(3+5*x)+46475*log(2+3*x)-46475*log(3+5*x)],
[(1-2*x)^2/((2+3*x)^6*(3+5*x)^2),x,2,(-49/15)/(2+3*x)^5+(-77/2)/(2+3*x)^4+(-1133/3)/(2+3*x)^3+(-3740)/(2+3*x)^2+(-46475)/(2+3*x)+(-15125)/(3+5*x)+277750*log(2+3*x)-277750*log(3+5*x)],
[(1-2*x)^2/((2+3*x)^7*(3+5*x)^2),x,2,(-49/18)/(2+3*x)^6+(-154/5)/(2+3*x)^5+(-1133/4)/(2+3*x)^4+(-7480/3)/(2+3*x)^3+(-46475/2)/(2+3*x)^2+(-277750)/(2+3*x)+(-75625)/(3+5*x)+1615625*log(2+3*x)-1615625*log(3+5*x)],
[(1-2*x)^2/((2+3*x)^8*(3+5*x)^2),x,2,(-7/3)/(2+3*x)^7+(-77/3)/(2+3*x)^6+(-1133/5)/(2+3*x)^5+(-1870)/(2+3*x)^4+(-46475/3)/(2+3*x)^3+(-138875)/(2+3*x)^2+(-1615625)/(2+3*x)+(-378125)/(3+5*x)+9212500*log(2+3*x)-9212500*log(3+5*x)],
[(1-2*x)^2*(2+3*x)^8/(3+5*x)^3,x,2,92582457/9765625*x+55559043/3906250*x^2-5350194/390625*x^3-1700919/31250*x^4-74601/3125*x^5+376407/6250*x^6+332424/4375*x^7+6561/250*x^8+(-121/97656250)/(3+5*x)^2+(-572/9765625)/(3+5*x)+5888/9765625*log(3+5*x)],
[(1-2*x)^2*(2+3*x)^7/(3+5*x)^3,x,2,9251661/1953125*x+1390203/390625*x^2-162612/15625*x^3-193833/12500*x^4+104247/15625*x^5+13608/625*x^6+8748/875*x^7+(-121/19531250)/(3+5*x)^2+(-2497/9765625)/(3+5*x)+21949/9765625*log(3+5*x)],
[(1-2*x)^2*(2+3*x)^6/(3+5*x)^3,x,2,920502/390625*x+189/15625*x^2-16299/3125*x^3-23571/12500*x^4+17496/3125*x^5+486/125*x^6+(-121/3906250)/(3+5*x)^2+(-2134/1953125)/(3+5*x)+15547/1953125*log(3+5*x)],
[(1-2*x)^2*(2+3*x)^5/(3+5*x)^3,x,2,17796/15625*x-5301/6250*x^2-5499/3125*x^3+648/625*x^4+972/625*x^5+(-121/781250)/(3+5*x)^2+(-1771/390625)/(3+5*x)+10234/390625*log(3+5*x)],
[(1-2*x)^2*(2+3*x)^4/(3+5*x)^3,x,2,1419/3125*x-4779/6250*x^2-72/625*x^3+81/125*x^4+(-121/156250)/(3+5*x)^2+(-1408/78125)/(3+5*x)+1202/15625*log(3+5*x)],
[(1-2*x)^2*(2+3*x)^3/(3+5*x)^3,x,2,-153/3125*x-216/625*x^2+36/125*x^3+(-121/31250)/(3+5*x)^2+(-209/3125)/(3+5*x)+23/125*log(3+5*x)],
[(1-2*x)^2*(2+3*x)^2/(3+5*x)^3,x,2,-264/625*x+18/125*x^2+(-121/6250)/(3+5*x)^2+(-682/3125)/(3+5*x)+829/3125*log(3+5*x)],
[(1-2*x)^2*(2+3*x)/(3+5*x)^3,x,2,12/125*x+(-121/1250)/(3+5*x)^2+(-319/625)/(3+5*x)-128/625*log(3+5*x)],
[(1-2*x)^2/(3+5*x)^3,x,2,(-121/250)/(3+5*x)^2+44/125/(3+5*x)+4/125*log(3+5*x)],
[(1-2*x)^2/((2+3*x)*(3+5*x)^3),x,2,(-121/50)/(3+5*x)^2+407/25/(3+5*x)-49*log(2+3*x)+49*log(3+5*x)],
[(1-2*x)^2/((2+3*x)^2*(3+5*x)^3),x,2,49/(2+3*x)+(-121/10)/(3+5*x)^2+154/(3+5*x)-707*log(2+3*x)+707*log(3+5*x)],
[(1-2*x)^2/((2+3*x)^3*(3+5*x)^3),x,2,49/2/(2+3*x)^2+707/(2+3*x)+(-121/2)/(3+5*x)^2+1133/(3+5*x)-6934*log(2+3*x)+6934*log(3+5*x)],
[(1-2*x)^2/((2+3*x)^4*(3+5*x)^3),x,2,49/3/(2+3*x)^3+707/2/(2+3*x)^2+6934/(2+3*x)+(-605/2)/(3+5*x)^2+7480/(3+5*x)-57110*log(2+3*x)+57110*log(3+5*x)],
[(1-2*x)^2/((2+3*x)^5*(3+5*x)^3),x,2,49/4/(2+3*x)^4+707/3/(2+3*x)^3+3467/(2+3*x)^2+57110/(2+3*x)+(-3025/2)/(3+5*x)^2+46475/(3+5*x)-424975*log(2+3*x)+424975*log(3+5*x)],
[(1-2*x)^2/((2+3*x)^6*(3+5*x)^3),x,2,49/5/(2+3*x)^5+707/4/(2+3*x)^4+6934/3/(2+3*x)^3+28555/(2+3*x)^2+424975/(2+3*x)+(-15125/2)/(3+5*x)^2+277750/(3+5*x)-2958125*log(2+3*x)+2958125*log(3+5*x)],
[(1-2*x)^2/((2+3*x)^7*(3+5*x)^3),x,2,49/6/(2+3*x)^6+707/5/(2+3*x)^5+3467/2/(2+3*x)^4+57110/3/(2+3*x)^3+424975/2/(2+3*x)^2+2958125/(2+3*x)+(-75625/2)/(3+5*x)^2+1615625/(3+5*x)-19637500*log(2+3*x)+19637500*log(3+5*x)],
[(1-2*x)^2/((2+3*x)^8*(3+5*x)^3),x,2,7/(2+3*x)^7+707/6/(2+3*x)^6+6934/5/(2+3*x)^5+28555/2/(2+3*x)^4+424975/3/(2+3*x)^3+2958125/2/(2+3*x)^2+19637500/(2+3*x)+(-378125/2)/(3+5*x)^2+9212500/(3+5*x)-125825000*log(2+3*x)+125825000*log(3+5*x)],

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

# n>0
[(1-2*x)^3*(2+3*x)^8*(3+5*x),x,2,-343/2187*(2+3*x)^9+2009/2430*(2+3*x)^10-518/891*(2+3*x)^11+107/729*(2+3*x)^12-40/3159*(2+3*x)^13],
[(1-2*x)^3*(2+3*x)^7*(3+5*x),x,2,-343/1944*(2+3*x)^8+2009/2187*(2+3*x)^9-259/405*(2+3*x)^10+428/2673*(2+3*x)^11-10/729*(2+3*x)^12],
[(1-2*x)^3*(2+3*x)^6*(3+5*x),x,2,-49/243*(2+3*x)^7+2009/1944*(2+3*x)^8-518/729*(2+3*x)^9+214/1215*(2+3*x)^10-40/2673*(2+3*x)^11],
[(1-2*x)^3*(2+3*x)^5*(3+5*x),x,2,-343/1458*(2+3*x)^6+287/243*(2+3*x)^7-259/324*(2+3*x)^8+428/2187*(2+3*x)^9-4/243*(2+3*x)^10],
[(1-2*x)^3*(2+3*x)^4*(3+5*x),x,2,-343/1215*(2+3*x)^5+2009/1458*(2+3*x)^6-74/81*(2+3*x)^7+107/486*(2+3*x)^8-40/2187*(2+3*x)^9],
[(1-2*x)^3*(2+3*x)^3*(3+5*x),x,2,24*x+2*x^2-86*x^3-117/4*x^4+949/5*x^5+111*x^6-1188/7*x^7-135*x^8],
[(1-2*x)^3*(2+3*x)^2*(3+5*x),x,2,12*x-8*x^2-35*x^3+99/4*x^4+326/5*x^5-26*x^6-360/7*x^7],
[(1-2*x)^3*(2+3*x)*(3+5*x),x,2,-77/32*(1-2*x)^4+17/10*(1-2*x)^5-5/16*(1-2*x)^6],
[(1-2*x)^3*(3+5*x),x,2,-11/16*(1-2*x)^4+1/4*(1-2*x)^5],
[(1-2*x)^3*(3+5*x)/(2+3*x),x,2,293/81*x-161/27*x^2+188/27*x^3-10/3*x^4-343/243*log(2+3*x)],
[(1-2*x)^3*(3+5*x)/(2+3*x)^2,x,2,-286/27*x+134/27*x^2-40/27*x^3+343/243/(2+3*x)+2009/243*log(2+3*x)],
[(1-2*x)^3*(3+5*x)/(2+3*x)^3,x,2,116/27*x-20/27*x^2+343/486/(2+3*x)^2+(-2009/243)/(2+3*x)-518/81*log(2+3*x)],
[(1-2*x)^3*(3+5*x)/(2+3*x)^4,x,2,-40/81*x+343/729/(2+3*x)^3+(-2009/486)/(2+3*x)^2+518/81/(2+3*x)+428/243*log(2+3*x)],
[(1-2*x)^3*(3+5*x)/(2+3*x)^5,x,2,343/972/(2+3*x)^4+(-2009/729)/(2+3*x)^3+259/81/(2+3*x)^2+(-428/243)/(2+3*x)-40/243*log(2+3*x)],
[(1-2*x)^3*(3+5*x)/(2+3*x)^6,x,2,1/105*(1-2*x)^4/(2+3*x)^5-173/2940*(1-2*x)^4/(2+3*x)^4],
[(1-2*x)^3*(3+5*x)/(2+3*x)^7,x,3,1/126*(1-2*x)^4/(2+3*x)^6-103/2205*(1-2*x)^4/(2+3*x)^5-103/30870*(1-2*x)^4/(2+3*x)^4],
[(1-2*x)^3*(3+5*x)/(2+3*x)^8,x,2,49/243/(2+3*x)^7+(-2009/1458)/(2+3*x)^6+518/405/(2+3*x)^5+(-107/243)/(2+3*x)^4+40/729/(2+3*x)^3],
[(1-2*x)^3*(2+3*x)^8*(3+5*x)^2,x,2,343/6561*(2+3*x)^9-1862/3645*(2+3*x)^10+11599/8019*(2+3*x)^11-4099/4374*(2+3*x)^12+2180/9477*(2+3*x)^13-100/5103*(2+3*x)^14],
[(1-2*x)^3*(2+3*x)^7*(3+5*x)^2,x,2,343/5832*(2+3*x)^8-3724/6561*(2+3*x)^9+11599/7290*(2+3*x)^10-8198/8019*(2+3*x)^11+545/2187*(2+3*x)^12-200/9477*(2+3*x)^13],
[(1-2*x)^3*(2+3*x)^6*(3+5*x)^2,x,2,49/729*(2+3*x)^7-931/1458*(2+3*x)^8+11599/6561*(2+3*x)^9-4099/3645*(2+3*x)^10+2180/8019*(2+3*x)^11-50/2187*(2+3*x)^12],
[(1-2*x)^3*(2+3*x)^5*(3+5*x)^2,x,2,343/4374*(2+3*x)^6-532/729*(2+3*x)^7+11599/5832*(2+3*x)^8-8198/6561*(2+3*x)^9+218/729*(2+3*x)^10-200/8019*(2+3*x)^11],
[(1-2*x)^3*(2+3*x)^4*(3+5*x)^2,x,2,343/3645*(2+3*x)^5-1862/2187*(2+3*x)^6+1657/729*(2+3*x)^7-4099/2916*(2+3*x)^8+2180/6561*(2+3*x)^9-20/729*(2+3*x)^10],
[(1-2*x)^3*(2+3*x)^3*(3+5*x)^2,x,2,72*x+66*x^2-754/3*x^3-1641/4*x^4+2262/5*x^5+6743/6*x^6-234/7*x^7-2295/2*x^8-600*x^9],
[(1-2*x)^3*(2+3*x)^2*(3+5*x)^2,x,2,36*x+6*x^2-395/3*x^3-57*x^4+1473/5*x^5+581/3*x^6-1860/7*x^7-225*x^8],
[(1-2*x)^3*(2+3*x)*(3+5*x)^2,x,2,18*x-21/2*x^2-166/3*x^3+135/4*x^4+534/5*x^5-110/3*x^6-600/7*x^7],
[(1-2*x)^3*(3+5*x)^2,x,2,-121/32*(1-2*x)^4+11/4*(1-2*x)^5-25/48*(1-2*x)^6],
[(1-2*x)^3*(3+5*x)^2/(2+3*x),x,2,922/243*x-1433/162*x^2+82/81*x^3+145/9*x^4-40/3*x^5+343/729*log(2+3*x)],
[(1-2*x)^3*(3+5*x)^2/(2+3*x)^2,x,2,2323/243*x-313/27*x^2+980/81*x^3-50/9*x^4+(-343/729)/(2+3*x)-3724/729*log(2+3*x)],
[(1-2*x)^3*(3+5*x)^2/(2+3*x)^3,x,2,-1546/81*x+230/27*x^2-200/81*x^3+(-343/1458)/(2+3*x)^2+3724/729/(2+3*x)+11599/729*log(2+3*x)],
[(1-2*x)^3*(3+5*x)^2/(2+3*x)^4,x,2,1780/243*x-100/81*x^2+(-343/2187)/(2+3*x)^3+1862/729/(2+3*x)^2+(-11599/729)/(2+3*x)-8198/729*log(2+3*x)],
[(1-2*x)^3*(3+5*x)^2/(2+3*x)^5,x,2,-200/243*x+(-343/2916)/(2+3*x)^4+3724/2187/(2+3*x)^3+(-11599/1458)/(2+3*x)^2+8198/729/(2+3*x)+2180/729*log(2+3*x)],
[(1-2*x)^3*(3+5*x)^2/(2+3*x)^6,x,2,(-343/3645)/(2+3*x)^5+931/729/(2+3*x)^4+(-11599/2187)/(2+3*x)^3+4099/729/(2+3*x)^2+(-2180/729)/(2+3*x)-200/729*log(2+3*x)],
[(1-2*x)^3*(3+5*x)^2/(2+3*x)^7,x,2,(-343/4374)/(2+3*x)^6+3724/3645/(2+3*x)^5+(-11599/2916)/(2+3*x)^4+8198/2187/(2+3*x)^3+(-1090/729)/(2+3*x)^2+200/729/(2+3*x)],
[(1-2*x)^3*(3+5*x)^2/(2+3*x)^8,x,2,(-49/729)/(2+3*x)^7+1862/2187/(2+3*x)^6+(-11599/3645)/(2+3*x)^5+4099/1458/(2+3*x)^4+(-2180/2187)/(2+3*x)^3+100/729/(2+3*x)^2],
[(1-2*x)^3*(2+3*x)^7*(3+5*x)^3,x,2,-343/17496*(2+3*x)^8+1813/6561*(2+3*x)^9-10073/7290*(2+3*x)^10+66193/24057*(2+3*x)^11-7195/4374*(2+3*x)^12+3700/9477*(2+3*x)^13-500/15309*(2+3*x)^14],
[(1-2*x)^3*(2+3*x)^6*(3+5*x)^3,x,2,-49/2187*(2+3*x)^7+1813/5832*(2+3*x)^8-10073/6561*(2+3*x)^9+66193/21870*(2+3*x)^10-14390/8019*(2+3*x)^11+925/2187*(2+3*x)^12-1000/28431*(2+3*x)^13],
[(1-2*x)^3*(2+3*x)^5*(3+5*x)^3,x,2,-343/13122*(2+3*x)^6+259/729*(2+3*x)^7-10073/5832*(2+3*x)^8+66193/19683*(2+3*x)^9-1439/729*(2+3*x)^10+3700/8019*(2+3*x)^11-250/6561*(2+3*x)^12],
[(1-2*x)^3*(2+3*x)^4*(3+5*x)^3,x,2,432*x+1080*x^2-312*x^3-5548*x^4-28917/5*x^5+19607/2*x^6+22949*x^7+41619/8*x^8-23370*x^9-24030*x^10-81000/11*x^11],
[(1-2*x)^3*(2+3*x)^3*(3+5*x)^3,x,2,216*x+378*x^2-534*x^3-8693/4*x^4-1419/5*x^5+10513/2*x^6+33013/7*x^7-14355/4*x^8-6900*x^9-2700*x^10],
[(1-2*x)^3*(2+3*x)^2*(3+5*x)^3,x,2,108*x+108*x^2-375*x^3-2659/4*x^4+3279/5*x^5+3617/2*x^6+230/7*x^7-3675/2*x^8-1000*x^9],
[(1-2*x)^3*(2+3*x)*(3+5*x)^3,x,2,54*x+27/2*x^2-201*x^3-425/4*x^4+2277/5*x^5+335*x^6-2900/7*x^7-375*x^8],
[(1-2*x)^3*(3+5*x)^3,x,2,27*x-27/2*x^2-87*x^3+179/4*x^4+174*x^5-50*x^6-1000/7*x^7],
[(1-2*x)^3*(3+5*x)^3/(2+3*x),x,2,10013/729*x-8287/486*x^2-6427/243*x^3+2815/54*x^4+220/9*x^5-500/9*x^6-343/2187*log(2+3*x)],
[(1-2*x)^3*(3+5*x)^3/(2+3*x)^2,x,2,2287/729*x-5287/486*x^2-190/81*x^3+775/27*x^4-200/9*x^5+343/2187/(2+3*x)+1813/729*log(2+3*x)],
[(1-2*x)^3*(3+5*x)^3/(2+3*x)^3,x,2,16253/729*x-1795/81*x^2+1700/81*x^3-250/27*x^4+343/4374/(2+3*x)^2+(-1813/729)/(2+3*x)-10073/729*log(2+3*x)],
[(1-2*x)^3*(3+5*x)^3/(2+3*x)^4,x,2,-24970/729*x+3550/243*x^2-1000/243*x^3+343/6561/(2+3*x)^3+(-1813/1458)/(2+3*x)^2+10073/729/(2+3*x)+66193/2187*log(2+3*x)],
[(1-2*x)^3*(3+5*x)^3/(2+3*x)^5,x,2,9100/729*x-500/243*x^2+343/8748/(2+3*x)^4+(-1813/2187)/(2+3*x)^3+10073/1458/(2+3*x)^2+(-66193/2187)/(2+3*x)-14390/729*log(2+3*x)],
[(1-2*x)^3*(3+5*x)^3/(2+3*x)^6,x,2,-1000/729*x+343/10935/(2+3*x)^5+(-1813/2916)/(2+3*x)^4+10073/2187/(2+3*x)^3+(-66193/4374)/(2+3*x)^2+14390/729/(2+3*x)+3700/729*log(2+3*x)],
[(1-2*x)^3*(3+5*x)^3/(2+3*x)^7,x,2,343/13122/(2+3*x)^6+(-1813/3645)/(2+3*x)^5+10073/2916/(2+3*x)^4+(-66193/6561)/(2+3*x)^3+7195/729/(2+3*x)^2+(-3700/729)/(2+3*x)-1000/2187*log(2+3*x)],
[(1-2*x)^3*(3+5*x)^3/(2+3*x)^8,x,2,49/2187/(2+3*x)^7+(-1813/4374)/(2+3*x)^6+10073/3645/(2+3*x)^5+(-66193/8748)/(2+3*x)^4+14390/2187/(2+3*x)^3+(-1850/729)/(2+3*x)^2+1000/2187/(2+3*x)],

# n<0
[(1-2*x)^3*(2+3*x)^6/(3+5*x),x,2,41666223/1953125*x+11111259/781250*x^2-17453753/234375*x^3-5848749/62500*x^4+2212083/15625*x^5+331713/1250*x^6-40338/875*x^7-13851/50*x^8-648/5*x^9+1331/9765625*log(3+5*x)],
[(1-2*x)^3*(2+3*x)^5/(3+5*x),x,2,4166223/390625*x-138741/156250*x^2-1703753/46875*x^3-73749/12500*x^4+243333/3125*x^5+4419/125*x^6-11988/175*x^7-243/5*x^8+1331/1953125*log(3+5*x)],
[(1-2*x)^3*(2+3*x)^4/(3+5*x),x,2,416223/78125*x-138741/31250*x^2-128753/9375*x^3+31251/2500*x^4+14958/625*x^5-306/25*x^6-648/35*x^7+1331/390625*log(3+5*x)],
[(1-2*x)^3*(2+3*x)^3/(3+5*x),x,2,41223/15625*x-26241/6250*x^2-5003/1875*x^3+2313/250*x^4+108/125*x^5-36/5*x^6+1331/78125*log(3+5*x)],
[(1-2*x)^3*(2+3*x)^2/(3+5*x),x,2,3723/3125*x-3741/1250*x^2+622/375*x^3+69/25*x^4-72/25*x^5+1331/15625*log(3+5*x)],
[(1-2*x)^3*(2+3*x)/(3+5*x),x,2,-27/625*x-183/125*x^2+172/75*x^3-6/5*x^4+1331/3125*log(3+5*x)],
[(1-2*x)^3/(3+5*x),x,2,-402/125*x+42/25*x^2-8/15*x^3+1331/625*log(3+5*x)],
[(1-2*x)^3/((2+3*x)*(3+5*x)),x,2,332/225*x-4/15*x^2-343/27*log(2+3*x)+1331/125*log(3+5*x)],
[(1-2*x)^3/((2+3*x)^2*(3+5*x)),x,2,-8/45*x+343/27/(2+3*x)-1421/27*log(2+3*x)+1331/25*log(3+5*x)],
[(1-2*x)^3/((2+3*x)^3*(3+5*x)),x,2,343/54/(2+3*x)^2+1421/27/(2+3*x)-7189/27*log(2+3*x)+1331/5*log(3+5*x)],
[(1-2*x)^3/((2+3*x)^4*(3+5*x)),x,2,343/81/(2+3*x)^3+1421/54/(2+3*x)^2+7189/27/(2+3*x)-1331*log(2+3*x)+1331*log(3+5*x)],
[(1-2*x)^3/((2+3*x)^5*(3+5*x)),x,2,343/108/(2+3*x)^4+1421/81/(2+3*x)^3+7189/54/(2+3*x)^2+1331/(2+3*x)-6655*log(2+3*x)+6655*log(3+5*x)],
[(1-2*x)^3/((2+3*x)^6*(3+5*x)),x,2,343/135/(2+3*x)^5+1421/108/(2+3*x)^4+7189/81/(2+3*x)^3+1331/2/(2+3*x)^2+6655/(2+3*x)-33275*log(2+3*x)+33275*log(3+5*x)],
[(1-2*x)^3/((2+3*x)^7*(3+5*x)),x,2,343/162/(2+3*x)^6+1421/135/(2+3*x)^5+7189/108/(2+3*x)^4+1331/3/(2+3*x)^3+6655/2/(2+3*x)^2+33275/(2+3*x)-166375*log(2+3*x)+166375*log(3+5*x)],
[(1-2*x)^3/((2+3*x)^8*(3+5*x)),x,2,49/27/(2+3*x)^7+1421/162/(2+3*x)^6+7189/135/(2+3*x)^5+1331/4/(2+3*x)^4+6655/3/(2+3*x)^3+33275/2/(2+3*x)^2+166375/(2+3*x)-831875*log(2+3*x)+831875*log(3+5*x)],
[(1-2*x)^3*(2+3*x)^6/(3+5*x)^2,x,2,13880997/1953125*x-461623/390625*x^2-1836723/78125*x^3-5643/3125*x^4+774981/15625*x^5+12231/625*x^6-37908/875*x^7-729/25*x^8+(-1331/9765625)/(3+5*x)+23232/9765625*log(3+5*x)],
[(1-2*x)^3*(2+3*x)^5/(3+5*x)^2,x,2,1382328/390625*x-507023/156250*x^2-26594/3125*x^3+108387/12500*x^4+44982/3125*x^5-1026/125*x^6-1944/175*x^7+(-1331/1953125)/(3+5*x)+19239/1953125*log(3+5*x)],
[(1-2*x)^3*(2+3*x)^4/(3+5*x)^2,x,2,133659/78125*x-1816/625*x^2-4217/3125*x^3+7317/1250*x^4+108/625*x^5-108/25*x^6+(-1331/390625)/(3+5*x)+15246/390625*log(3+5*x)],
[(1-2*x)^3*(2+3*x)^3/(3+5*x)^2,x,2,1998/3125*x-12077/6250*x^2+786/625*x^3+189/125*x^4-216/125*x^5+(-1331/78125)/(3+5*x)+11253/78125*log(3+5*x)],
[(1-2*x)^3*(2+3*x)^2/(3+5*x)^2,x,2,-1179/3125*x-427/625*x^2+164/125*x^3-18/25*x^4+(-1331/15625)/(3+5*x)+1452/3125*log(3+5*x)],
[(1-2*x)^3*(2+3*x)/(3+5*x)^2,x,2,-1098/625*x+122/125*x^2-8/25*x^3+(-1331/3125)/(3+5*x)+3267/3125*log(3+5*x)],
[(1-2*x)^3/(3+5*x)^2,x,2,108/125*x-4/25*x^2+(-1331/625)/(3+5*x)-726/625*log(3+5*x)],
[(1-2*x)^3/((2+3*x)*(3+5*x)^2),x,2,-8/75*x+(-1331/125)/(3+5*x)+343/9*log(2+3*x)-4719/125*log(3+5*x)],
[(1-2*x)^3/((2+3*x)^2*(3+5*x)^2),x,2,(-343/9)/(2+3*x)+(-1331/25)/(3+5*x)+3136/9*log(2+3*x)-8712/25*log(3+5*x)],
[(1-2*x)^3/((2+3*x)^3*(3+5*x)^2),x,2,(-343/18)/(2+3*x)^2+(-3136/9)/(2+3*x)+(-1331/5)/(3+5*x)+2541*log(2+3*x)-2541*log(3+5*x)],
[(1-2*x)^3/((2+3*x)^4*(3+5*x)^2),x,2,(-343/27)/(2+3*x)^3+(-1568/9)/(2+3*x)^2+(-2541)/(2+3*x)+(-1331)/(3+5*x)+16698*log(2+3*x)-16698*log(3+5*x)],
[(1-2*x)^3/((2+3*x)^5*(3+5*x)^2),x,2,(-343/36)/(2+3*x)^4+(-3136/27)/(2+3*x)^3+(-2541/2)/(2+3*x)^2+(-16698)/(2+3*x)+(-6655)/(3+5*x)+103455*log(2+3*x)-103455*log(3+5*x)],
[(1-2*x)^3/((2+3*x)^6*(3+5*x)^2),x,2,(-343/45)/(2+3*x)^5+(-784/9)/(2+3*x)^4+(-847)/(2+3*x)^3+(-8349)/(2+3*x)^2+(-103455)/(2+3*x)+(-33275)/(3+5*x)+617100*log(2+3*x)-617100*log(3+5*x)],
[(1-2*x)^3/((2+3*x)^7*(3+5*x)^2),x,2,(-343/54)/(2+3*x)^6+(-3136/45)/(2+3*x)^5+(-2541/4)/(2+3*x)^4+(-5566)/(2+3*x)^3+(-103455/2)/(2+3*x)^2+(-617100)/(2+3*x)+(-166375)/(3+5*x)+3584625*log(2+3*x)-3584625*log(3+5*x)],
[(1-2*x)^3/((2+3*x)^8*(3+5*x)^2),x,2,(-49/9)/(2+3*x)^7+(-1568/27)/(2+3*x)^6+(-2541/5)/(2+3*x)^5+(-8349/2)/(2+3*x)^4+(-34485)/(2+3*x)^3+(-308550)/(2+3*x)^2+(-3584625)/(2+3*x)+(-831875)/(3+5*x)+20418750*log(2+3*x)-20418750*log(3+5*x)],
[(1-2*x)^3*(2+3*x)^7/(3+5*x)^3,x,2,46214407/9765625*x-2300646/1953125*x^2-5918904/390625*x^3+6507/62500*x^4+491913/15625*x^5+33291/3125*x^6-119556/4375*x^7-2187/125*x^8+(-1331/97656250)/(3+5*x)^2+(-1089/1953125)/(3+5*x)+47289/9765625*log(3+5*x)],
[(1-2*x)^3*(2+3*x)^6/(3+5*x)^3,x,2,4571416/1953125*x-915777/390625*x^2-81747/15625*x^3+74223/12500*x^4+134622/15625*x^5-3402/625*x^6-5832/875*x^7+(-1331/19531250)/(3+5*x)^2+(-23232/9765625)/(3+5*x)+166749/9765625*log(3+5*x)],
[(1-2*x)^3*(2+3*x)^5/(3+5*x)^3,x,2,424432/390625*x-62097/31250*x^2-393/625*x^3+22977/6250*x^4-324/3125*x^5-324/125*x^6+(-1331/3906250)/(3+5*x)^2+(-19239/1953125)/(3+5*x)+109032/1953125*log(3+5*x)],
[(1-2*x)^3*(2+3*x)^4/(3+5*x)^3,x,2,4691/15625*x-7617/6250*x^2+2826/3125*x^3+513/625*x^4-648/625*x^5+(-1331/781250)/(3+5*x)^2+(-15246/390625)/(3+5*x)+63294/390625*log(3+5*x)],
[(1-2*x)^3*(2+3*x)^3/(3+5*x)^3,x,2,-1303/3125*x-927/3125*x^2+468/625*x^3-54/125*x^4+(-1331/156250)/(3+5*x)^2+(-11253/78125)/(3+5*x)+5907/15625*log(3+5*x)],
[(1-2*x)^3*(2+3*x)^2/(3+5*x)^3,x,2,-2978/3125*x+354/625*x^2-24/125*x^3+(-1331/31250)/(3+5*x)^2+(-1452/3125)/(3+5*x)+1551/3125*log(3+5*x)],
[(1-2*x)^3*(2+3*x)/(3+5*x)^3,x,2,316/625*x-12/125*x^2+(-1331/6250)/(3+5*x)^2+(-3267/3125)/(3+5*x)-2046/3125*log(3+5*x)],
[(1-2*x)^3/(3+5*x)^3,x,2,-8/125*x+(-1331/1250)/(3+5*x)^2+726/625/(3+5*x)+132/625*log(3+5*x)],
[(1-2*x)^3/((2+3*x)*(3+5*x)^3),x,2,(-1331/250)/(3+5*x)^2+4719/125/(3+5*x)-343/3*log(2+3*x)+14289/125*log(3+5*x)],
[(1-2*x)^3/((2+3*x)^2*(3+5*x)^3),x,2,343/3/(2+3*x)+(-1331/50)/(3+5*x)^2+8712/25/(3+5*x)-1617*log(2+3*x)+1617*log(3+5*x)],
[(1-2*x)^3/((2+3*x)^3*(3+5*x)^3),x,2,343/6/(2+3*x)^2+1617/(2+3*x)+(-1331/10)/(3+5*x)^2+2541/(3+5*x)-15708*log(2+3*x)+15708*log(3+5*x)],
[(1-2*x)^3/((2+3*x)^4*(3+5*x)^3),x,2,343/9/(2+3*x)^3+1617/2/(2+3*x)^2+15708/(2+3*x)+(-1331/2)/(3+5*x)^2+16698/(3+5*x)-128634*log(2+3*x)+128634*log(3+5*x)],
[(1-2*x)^3/((2+3*x)^5*(3+5*x)^3),x,2,343/12/(2+3*x)^4+539/(2+3*x)^3+7854/(2+3*x)^2+128634/(2+3*x)+(-6655/2)/(3+5*x)^2+103455/(3+5*x)-953535*log(2+3*x)+953535*log(3+5*x)],
[(1-2*x)^3/((2+3*x)^6*(3+5*x)^3),x,2,343/15/(2+3*x)^5+1617/4/(2+3*x)^4+5236/(2+3*x)^3+64317/(2+3*x)^2+953535/(2+3*x)+(-33275/2)/(3+5*x)^2+617100/(3+5*x)-6618975*log(2+3*x)+6618975*log(3+5*x)],
[(1-2*x)^3/((2+3*x)^7*(3+5*x)^3),x,2,343/18/(2+3*x)^6+1617/5/(2+3*x)^5+3927/(2+3*x)^4+42878/(2+3*x)^3+953535/2/(2+3*x)^2+6618975/(2+3*x)+(-166375/2)/(3+5*x)^2+3584625/(3+5*x)-43848750*log(2+3*x)+43848750*log(3+5*x)],
[(1-2*x)^3/((2+3*x)^8*(3+5*x)^3),x,2,49/3/(2+3*x)^7+539/2/(2+3*x)^6+15708/5/(2+3*x)^5+64317/2/(2+3*x)^4+317845/(2+3*x)^3+6618975/2/(2+3*x)^2+43848750/(2+3*x)+(-831875/2)/(3+5*x)^2+20418750/(3+5*x)-280500000*log(2+3*x)+280500000*log(3+5*x)],

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

# n>0
[(2+3*x)^8*(3+5*x)/(1-2*x),x,2,-63019595/512*x-60332619/512*x^2-17391129/128*x^3-37722699/256*x^4-21272139/160*x^5-2929689/32*x^6-353565/8*x^7-422091/32*x^8-3645/2*x^9-63412811/1024*log(1-2*x)],
[(2+3*x)^7*(3+5*x)/(1-2*x),x,2,-8960669/256*x-8362653/256*x^2-2257119/64*x^3-4352157/128*x^4-2053917/80*x^5-218943/16*x^6-126117/28*x^7-10935/16*x^8-9058973/512*log(1-2*x)],
[(2+3*x)^6*(3+5*x)/(1-2*x),x,2,-1269563/128*x-1138491/128*x^2-279657/32*x^3-458811/64*x^4-169371/40*x^5-12393/8*x^6-3645/14*x^7-1294139/256*log(1-2*x)],
[(2+3*x)^5*(3+5*x)/(1-2*x),x,2,-178733/64*x-150573/64*x^2-32271/16*x^3-42093/32*x^4-10773/20*x^5-405/4*x^6-184877/128*log(1-2*x)],
[(2+3*x)^4*(3+5*x)/(1-2*x),x,2,-24875/32*x-18987/32*x^2-3321/8*x^3-3051/16*x^4-81/2*x^5-26411/64*log(1-2*x)],
[(2+3*x)^3*(3+5*x)/(1-2*x),x,2,-3389/16*x-2205/16*x^2-279/4*x^3-135/8*x^4-3773/32*log(1-2*x)],
[(2+3*x)^2*(3+5*x)/(1-2*x),x,2,-443/8*x-219/8*x^2-15/2*x^3-539/16*log(1-2*x)],
[(2+3*x)*(3+5*x)/(1-2*x),x,2,-53/4*x-15/4*x^2-77/8*log(1-2*x)],
[(3+5*x)/(1-2*x),x,2,-5/2*x-11/4*log(1-2*x)],
[(3+5*x)/((1-2*x)*(2+3*x)),x,2,-11/14*log(1-2*x)-1/21*log(2+3*x)],
[(3+5*x)/((1-2*x)*(2+3*x)^2),x,2,1/21/(2+3*x)-11/49*log(1-2*x)+11/49*log(2+3*x)],
[(3+5*x)/((1-2*x)*(2+3*x)^3),x,2,1/42/(2+3*x)^2+(-11/49)/(2+3*x)-22/343*log(1-2*x)+22/343*log(2+3*x)],
[(3+5*x)/((1-2*x)*(2+3*x)^4),x,2,1/63/(2+3*x)^3+(-11/98)/(2+3*x)^2+(-22/343)/(2+3*x)-44/2401*log(1-2*x)+44/2401*log(2+3*x)],
[(3+5*x)/((1-2*x)*(2+3*x)^5),x,2,1/84/(2+3*x)^4+(-11/147)/(2+3*x)^3+(-11/343)/(2+3*x)^2+(-44/2401)/(2+3*x)-88/16807*log(1-2*x)+88/16807*log(2+3*x)],
[(3+5*x)/((1-2*x)*(2+3*x)^6),x,2,1/105/(2+3*x)^5+(-11/196)/(2+3*x)^4+(-22/1029)/(2+3*x)^3+(-22/2401)/(2+3*x)^2+(-88/16807)/(2+3*x)-176/117649*log(1-2*x)+176/117649*log(2+3*x)],
[(3+5*x)/((1-2*x)*(2+3*x)^7),x,2,1/126/(2+3*x)^6+(-11/245)/(2+3*x)^5+(-11/686)/(2+3*x)^4+(-44/7203)/(2+3*x)^3+(-44/16807)/(2+3*x)^2+(-176/117649)/(2+3*x)-352/823543*log(1-2*x)+352/823543*log(2+3*x)],
[(3+5*x)/((1-2*x)*(2+3*x)^8),x,2,1/147/(2+3*x)^7+(-11/294)/(2+3*x)^6+(-22/1715)/(2+3*x)^5+(-11/2401)/(2+3*x)^4+(-88/50421)/(2+3*x)^3+(-88/117649)/(2+3*x)^2+(-352/823543)/(2+3*x)-704/5764801*log(1-2*x)+704/5764801*log(2+3*x)],
[(2+3*x)^8*(3+5*x)^2/(1-2*x),x,2,-695181625/1024*x-677093689/1024*x^2-204901139/256*x^3-487203129/512*x^4-316246329/320*x^5-53031699/64*x^6-8399295/16*x^7-14907321/64*x^8-256365/4*x^9-32805/4*x^10-697540921/2048*log(1-2*x)],
[(2+3*x)^7*(3+5*x)^2/(1-2*x),x,2,-99058879/512*x-94979263/512*x^2-27480469/128*x^3-59969727/256*x^4-34084287/160*x^5-4736853/32*x^6-4040847/56*x^7-696195/32*x^8-6075/2*x^9-99648703/1024*log(1-2*x)],
[(2+3*x)^6*(3+5*x)^2/(1-2*x),x,2,-14088073/256*x-13178761/256*x^2-3575427/64*x^3-6947721/128*x^4-3310281/80*x^5-356643/16*x^6-207765/28*x^7-18225/16*x^8-14235529/512*log(1-2*x)],
[(2+3*x)^5*(3+5*x)^2/(1-2*x),x,2,-1996783/128*x-1797103/128*x^2-444581/32*x^3-736623/64*x^4-275103/40*x^5-20385/8*x^6-6075/14*x^7-2033647/256*log(1-2*x)],
[(2+3*x)^4*(3+5*x)^2/(1-2*x),x,2,-281305/64*x-238297/64*x^2-51571/16*x^3-68121/32*x^4-3537/4*x^5-675/4*x^6-290521/128*log(1-2*x)],
[(2+3*x)^3*(3+5*x)^2/(1-2*x),x,2,-39199/32*x-30175/32*x^2-5349/8*x^3-4995/16*x^4-135/2*x^5-41503/64*log(1-2*x)],
[(2+3*x)^2*(3+5*x)^2/(1-2*x),x,2,-5353/16*x-3529/16*x^2-455/4*x^3-225/8*x^4-5929/32*log(1-2*x)],
[(2+3*x)*(3+5*x)^2/(1-2*x),x,2,-703/8*x-355/8*x^2-25/2*x^3-847/16*log(1-2*x)],
[(3+5*x)^2/(1-2*x),x,2,-85/4*x-25/4*x^2-121/8*log(1-2*x)],
[(3+5*x)^2/((1-2*x)*(2+3*x)),x,2,-25/6*x-121/28*log(1-2*x)+1/63*log(2+3*x)],
[(3+5*x)^2/((1-2*x)*(2+3*x)^2),x,2,(-1/63)/(2+3*x)-121/98*log(1-2*x)-68/441*log(2+3*x)],
[(3+5*x)^2/((1-2*x)*(2+3*x)^3),x,2,(-1/126)/(2+3*x)^2+68/441/(2+3*x)-121/343*log(1-2*x)+121/343*log(2+3*x)],
[(3+5*x)^2/((1-2*x)*(2+3*x)^4),x,2,(-1/189)/(2+3*x)^3+34/441/(2+3*x)^2+(-121/343)/(2+3*x)-242/2401*log(1-2*x)+242/2401*log(2+3*x)],
[(3+5*x)^2/((1-2*x)*(2+3*x)^5),x,2,(-1/252)/(2+3*x)^4+68/1323/(2+3*x)^3+(-121/686)/(2+3*x)^2+(-242/2401)/(2+3*x)-484/16807*log(1-2*x)+484/16807*log(2+3*x)],
[(3+5*x)^2/((1-2*x)*(2+3*x)^6),x,2,(-1/315)/(2+3*x)^5+17/441/(2+3*x)^4+(-121/1029)/(2+3*x)^3+(-121/2401)/(2+3*x)^2+(-484/16807)/(2+3*x)-968/117649*log(1-2*x)+968/117649*log(2+3*x)],
[(3+5*x)^2/((1-2*x)*(2+3*x)^7),x,2,(-1/378)/(2+3*x)^6+68/2205/(2+3*x)^5+(-121/1372)/(2+3*x)^4+(-242/7203)/(2+3*x)^3+(-242/16807)/(2+3*x)^2+(-968/117649)/(2+3*x)-1936/823543*log(1-2*x)+1936/823543*log(2+3*x)],
[(3+5*x)^2/((1-2*x)*(2+3*x)^8),x,2,(-1/441)/(2+3*x)^7+34/1323/(2+3*x)^6+(-121/1715)/(2+3*x)^5+(-121/4802)/(2+3*x)^4+(-484/50421)/(2+3*x)^3+(-484/117649)/(2+3*x)^2+(-1936/823543)/(2+3*x)-3872/5764801*log(1-2*x)+3872/5764801*log(2+3*x)],
[(2+3*x)^7*(3+5*x)^3/(1-2*x),x,2,-1092596789/1024*x-1065169973/1024*x^2-969544757/768*x^3-772025397/512*x^4-504354357/320*x^5-85228263/64*x^6-95297877/112*x^7-24381405/64*x^8-423225/4*x^9-54675/4*x^10-1096135733/2048*log(1-2*x)],
[(2+3*x)^6*(3+5*x)^3/(1-2*x),x,2,-155706083/512*x-149512931/512*x^2-130251491/384*x^3-95317731/256*x^4-54600291/160*x^5-7656993/32*x^6-6596235/56*x^7-1148175/32*x^8-10125/2*x^9-156590819/1024*log(1-2*x)],
[(2+3*x)^5*(3+5*x)^3/(1-2*x),x,2,-22148933/256*x-20766533/256*x^2-16987973/192*x^3-11088453/128*x^4-5333733/80*x^5-580815/16*x^6-342225/28*x^7-30375/16*x^8-22370117/512*log(1-2*x)],
[(2+3*x)^4*(3+5*x)^3/(1-2*x),x,2,-3140435/128*x-2836307/128*x^2-2119763/96*x^3-1182291/64*x^4-89343/8*x^5-33525/8*x^6-10125/14*x^7-3195731/256*log(1-2*x)],
[(2+3*x)^3*(3+5*x)^3/(1-2*x),x,2,-442709/64*x-377045/64*x^2-247157/48*x^3-110205/32*x^4-5805/4*x^5-1125/4*x^6-456533/128*log(1-2*x)],
[(2+3*x)^2*(3+5*x)^3/(1-2*x),x,2,-61763/32*x-47939/32*x^2-25835/24*x^3-8175/16*x^4-225/2*x^5-65219/64*log(1-2*x)],
[(2+3*x)*(3+5*x)^3/(1-2*x),x,2,-8453/16*x-5645/16*x^2-2225/12*x^3-375/8*x^4-9317/32*log(1-2*x)],
[(3+5*x)^3/(1-2*x),x,2,-1115/8*x-575/8*x^2-125/6*x^3-1331/16*log(1-2*x)],
[(3+5*x)^3/((1-2*x)*(2+3*x)),x,2,-1225/36*x-125/12*x^2-1331/56*log(1-2*x)-1/189*log(2+3*x)],
[(3+5*x)^3/((1-2*x)*(2+3*x)^2),x,2,-125/18*x+1/189/(2+3*x)-1331/196*log(1-2*x)+103/1323*log(2+3*x)],
[(3+5*x)^3/((1-2*x)*(2+3*x)^3),x,2,1/378/(2+3*x)^2+(-103/1323)/(2+3*x)-1331/686*log(1-2*x)-3469/9261*log(2+3*x)],
[(3+5*x)^3/((1-2*x)*(2+3*x)^4),x,2,1/567/(2+3*x)^3+(-103/2646)/(2+3*x)^2+3469/9261/(2+3*x)-1331/2401*log(1-2*x)+1331/2401*log(2+3*x)],
[(3+5*x)^3/((1-2*x)*(2+3*x)^5),x,2,1/756/(2+3*x)^4+(-103/3969)/(2+3*x)^3+3469/18522/(2+3*x)^2+(-1331/2401)/(2+3*x)-2662/16807*log(1-2*x)+2662/16807*log(2+3*x)],
[(3+5*x)^3/((1-2*x)*(2+3*x)^6),x,2,1/945/(2+3*x)^5+(-103/5292)/(2+3*x)^4+3469/27783/(2+3*x)^3+(-1331/4802)/(2+3*x)^2+(-2662/16807)/(2+3*x)-5324/117649*log(1-2*x)+5324/117649*log(2+3*x)],
[(3+5*x)^3/((1-2*x)*(2+3*x)^7),x,2,1/1134/(2+3*x)^6+(-103/6615)/(2+3*x)^5+3469/37044/(2+3*x)^4+(-1331/7203)/(2+3*x)^3+(-1331/16807)/(2+3*x)^2+(-5324/117649)/(2+3*x)-10648/823543*log(1-2*x)+10648/823543*log(2+3*x)],
[(3+5*x)^3/((1-2*x)*(2+3*x)^8),x,2,1/1323/(2+3*x)^7+(-103/7938)/(2+3*x)^6+3469/46305/(2+3*x)^5+(-1331/9604)/(2+3*x)^4+(-2662/50421)/(2+3*x)^3+(-2662/117649)/(2+3*x)^2+(-10648/823543)/(2+3*x)-21296/5764801*log(1-2*x)+21296/5764801*log(2+3*x)],

# n<0
[(a+b*x)^3/((c+d*x)*(e+f*x)),x,2,-b^2*(b*d*e+b*c*f-3*a*d*f)*x/(d^2*f^2)+1/2*b^3*x^2/(d*f)-(b*c-a*d)^3*log(c+d*x)/(d^3*(d*e-c*f))+(b*e-a*f)^3*log(e+f*x)/(f^3*(d*e-c*f))],
[(2+3*x)^8/((1-2*x)*(3+5*x)),x,2,-40089855591/10000000*x-7136193339/2000000*x^2-345533877/100000*x^3-111146499/40000*x^4-8018271/5000*x^5-114453/200*x^6-6561/70*x^7-5764801/2816*log(1-2*x)+1/4296875*log(3+5*x)],
[(2+3*x)^7/((1-2*x)*(3+5*x)),x,2,-1127138733/1000000*x-187738857/200000*x^2-7889751/10000*x^3-2006937/4000*x^4-99873/500*x^5-729/20*x^6-823543/1408*log(1-2*x)+1/859375*log(3+5*x)],
[(2+3*x)^6/((1-2*x)*(3+5*x)),x,2,-31289679/100000*x-4693491/20000*x^2-159813/1000*x^3-28431/400*x^4-729/50*x^5-117649/704*log(1-2*x)+1/171875*log(3+5*x)],
[(2+3*x)^5/((1-2*x)*(3+5*x)),x,2,-848277/10000*x-107433/2000*x^2-2619/100*x^3-243/40*x^4-16807/352*log(1-2*x)+1/34375*log(3+5*x)],
[(2+3*x)^4/((1-2*x)*(3+5*x)),x,2,-21951/1000*x-2079/200*x^2-27/10*x^3-2401/176*log(1-2*x)+1/6875*log(3+5*x)],
[(2+3*x)^3/((1-2*x)*(3+5*x)),x,2,-513/100*x-27/20*x^2-343/88*log(1-2*x)+1/1375*log(3+5*x)],
[(2+3*x)^2/((1-2*x)*(3+5*x)),x,2,-9/10*x-49/44*log(1-2*x)+1/275*log(3+5*x)],
[(2+3*x)/((1-2*x)*(3+5*x)),x,2,-7/22*log(1-2*x)+1/55*log(3+5*x)],
[1/((1-2*x)*(3+5*x)),x,3,-1/11*log(1-2*x)+1/11*log(3+5*x)],
[1/((1-2*x)*(2+3*x)*(3+5*x)),x,2,-2/77*log(1-2*x)-3/7*log(2+3*x)+5/11*log(3+5*x)],
[1/((1-2*x)*(2+3*x)^2*(3+5*x)),x,2,3/7/(2+3*x)-4/539*log(1-2*x)-111/49*log(2+3*x)+25/11*log(3+5*x)],
[1/((1-2*x)*(2+3*x)^3*(3+5*x)),x,2,3/14/(2+3*x)^2+111/49/(2+3*x)-8/3773*log(1-2*x)-3897/343*log(2+3*x)+125/11*log(3+5*x)],
[1/((1-2*x)*(2+3*x)^4*(3+5*x)),x,2,1/7/(2+3*x)^3+111/98/(2+3*x)^2+3897/343/(2+3*x)-16/26411*log(1-2*x)-136419/2401*log(2+3*x)+625/11*log(3+5*x)],
[1/((1-2*x)*(2+3*x)^5*(3+5*x)),x,2,3/28/(2+3*x)^4+37/49/(2+3*x)^3+3897/686/(2+3*x)^2+136419/2401/(2+3*x)-32/184877*log(1-2*x)-4774713/16807*log(2+3*x)+3125/11*log(3+5*x)],
[1/((1-2*x)*(2+3*x)^6*(3+5*x)),x,2,3/35/(2+3*x)^5+111/196/(2+3*x)^4+1299/343/(2+3*x)^3+136419/4802/(2+3*x)^2+4774713/16807/(2+3*x)-64/1294139*log(1-2*x)-167115051/117649*log(2+3*x)+15625/11*log(3+5*x)],
[1/((1-2*x)*(2+3*x)^7*(3+5*x)),x,2,1/14/(2+3*x)^6+111/245/(2+3*x)^5+3897/1372/(2+3*x)^4+45473/2401/(2+3*x)^3+4774713/33614/(2+3*x)^2+167115051/117649/(2+3*x)-128/9058973*log(1-2*x)-5849026977/823543*log(2+3*x)+78125/11*log(3+5*x)],
[(2+3*x)^8/((1-2*x)*(3+5*x)^2),x,2,-3579885909/5000000*x-118543581/200000*x^2-24660207/50000*x^3-6194313/20000*x^4-303993/2500*x^5-2187/100*x^6+(-1/4296875)/(3+5*x)-5764801/15488*log(1-2*x)+266/47265625*log(3+5*x)],
[(2+3*x)^7/((1-2*x)*(3+5*x)^2),x,2,-19846971/100000*x-14750667/100000*x^2-495477/5000*x^3-86751/2000*x^4-2187/250*x^5+(-1/859375)/(3+5*x)-823543/7744*log(1-2*x)+233/9453125*log(3+5*x)],
[(2+3*x)^6/((1-2*x)*(3+5*x)^2),x,2,-2682909/50000*x-335097/10000*x^2-8019/500*x^3-729/200*x^4+(-1/171875)/(3+5*x)-117649/3872*log(1-2*x)+8/75625*log(3+5*x)],
[(2+3*x)^5/((1-2*x)*(3+5*x)^2),x,2,-69039/5000*x-6399/1000*x^2-81/50*x^3+(-1/34375)/(3+5*x)-16807/1936*log(1-2*x)+167/378125*log(3+5*x)],
[(2+3*x)^4/((1-2*x)*(3+5*x)^2),x,2,-1593/500*x-81/100*x^2+(-1/6875)/(3+5*x)-2401/968*log(1-2*x)+134/75625*log(3+5*x)],
[(2+3*x)^3/((1-2*x)*(3+5*x)^2),x,2,-27/50*x+(-1/1375)/(3+5*x)-343/484*log(1-2*x)+101/15125*log(3+5*x)],
[(2+3*x)^2/((1-2*x)*(3+5*x)^2),x,2,(-1/275)/(3+5*x)-49/242*log(1-2*x)+68/3025*log(3+5*x)],
[(2+3*x)/((1-2*x)*(3+5*x)^2),x,2,(-1/55)/(3+5*x)-7/121*log(1-2*x)+7/121*log(3+5*x)],
[1/((1-2*x)*(3+5*x)^2),x,2,(-1/11)/(3+5*x)-2/121*log(1-2*x)+2/121*log(3+5*x)],
[1/((1-2*x)*(2+3*x)*(3+5*x)^2),x,2,(-5/11)/(3+5*x)-4/847*log(1-2*x)+9/7*log(2+3*x)-155/121*log(3+5*x)],
[1/((1-2*x)*(2+3*x)^2*(3+5*x)^2),x,2,(-9/7)/(2+3*x)+(-25/11)/(3+5*x)-8/5929*log(1-2*x)+648/49*log(2+3*x)-1600/121*log(3+5*x)],
[1/((1-2*x)*(2+3*x)^3*(3+5*x)^2),x,2,(-9/14)/(2+3*x)^2+(-648/49)/(2+3*x)+(-125/11)/(3+5*x)-16/41503*log(1-2*x)+34371/343*log(2+3*x)-12125/121*log(3+5*x)],
[1/((1-2*x)*(2+3*x)^4*(3+5*x)^2),x,2,(-3/7)/(2+3*x)^3+(-324/49)/(2+3*x)^2+(-34371/343)/(2+3*x)+(-625/11)/(3+5*x)-32/290521*log(1-2*x)+1612242/2401*log(2+3*x)-81250/121*log(3+5*x)],
[1/((1-2*x)*(2+3*x)^5*(3+5*x)^2),x,2,(-9/28)/(2+3*x)^4+(-216/49)/(2+3*x)^3+(-34371/686)/(2+3*x)^2+(-1612242/2401)/(2+3*x)+(-3125/11)/(3+5*x)-64/2033647*log(1-2*x)+70752609/16807*log(2+3*x)-509375/121*log(3+5*x)],
[1/((1-2*x)*(2+3*x)^6*(3+5*x)^2),x,2,(-9/35)/(2+3*x)^5+(-162/49)/(2+3*x)^4+(-11457/343)/(2+3*x)^3+(-806121/2401)/(2+3*x)^2+(-70752609/16807)/(2+3*x)+(-15625/11)/(3+5*x)-128/14235529*log(1-2*x)+2977686468/117649*log(2+3*x)-3062500/121*log(3+5*x)],
[(2+3*x)^8/((1-2*x)*(3+5*x)^3),x,2,-62934003/500000*x-9268263/100000*x^2-1535517/25000*x^3-264627/10000*x^4-6561/1250*x^5+(-1/8593750)/(3+5*x)^2+(-266/47265625)/(3+5*x)-5764801/85184*log(1-2*x)+31024/519921875*log(3+5*x)],
[(2+3*x)^7/((1-2*x)*(3+5*x)^3),x,2,-339309/10000*x-1044657/50000*x^2-24543/2500*x^3-2187/1000*x^4+(-1/1718750)/(3+5*x)^2+(-233/9453125)/(3+5*x)-823543/42592*log(1-2*x)+4667/20796875*log(3+5*x)],
[(2+3*x)^6/((1-2*x)*(3+5*x)^3),x,2,-216999/25000*x-19683/5000*x^2-243/250*x^3+(-1/343750)/(3+5*x)^2+(-8/75625)/(3+5*x)-117649/21296*log(1-2*x)+3347/4159375*log(3+5*x)],
[(2+3*x)^5/((1-2*x)*(3+5*x)^3),x,2,-4941/2500*x-243/500*x^2+(-1/68750)/(3+5*x)^2+(-167/378125)/(3+5*x)-16807/10648*log(1-2*x)+11224/4159375*log(3+5*x)],
[(2+3*x)^4/((1-2*x)*(3+5*x)^3),x,2,-81/250*x+(-1/13750)/(3+5*x)^2+(-134/75625)/(3+5*x)-2401/5324*log(1-2*x)+6802/831875*log(3+5*x)],
[(2+3*x)^3/((1-2*x)*(3+5*x)^3),x,2,(-1/2750)/(3+5*x)^2+(-101/15125)/(3+5*x)-343/2662*log(1-2*x)+3469/166375*log(3+5*x)],
[(2+3*x)^2/((1-2*x)*(3+5*x)^3),x,2,(-1/550)/(3+5*x)^2+(-68/3025)/(3+5*x)-49/1331*log(1-2*x)+49/1331*log(3+5*x)],
[(2+3*x)/((1-2*x)*(3+5*x)^3),x,2,(-1/110)/(3+5*x)^2+(-7/121)/(3+5*x)-14/1331*log(1-2*x)+14/1331*log(3+5*x)],
[1/((1-2*x)*(3+5*x)^3),x,2,(-1/22)/(3+5*x)^2+(-2/121)/(3+5*x)-4/1331*log(1-2*x)+4/1331*log(3+5*x)],
[1/((1-2*x)*(2+3*x)*(3+5*x)^3),x,2,(-5/22)/(3+5*x)^2+155/121/(3+5*x)-8/9317*log(1-2*x)-27/7*log(2+3*x)+5135/1331*log(3+5*x)],
[1/((1-2*x)*(2+3*x)^2*(3+5*x)^3),x,2,27/7/(2+3*x)+(-25/22)/(3+5*x)^2+1600/121/(3+5*x)-16/65219*log(1-2*x)-2889/49*log(2+3*x)+78475/1331*log(3+5*x)],
[1/((1-2*x)*(2+3*x)^3*(3+5*x)^3),x,2,27/14/(2+3*x)^2+2889/49/(2+3*x)+(-125/22)/(3+5*x)^2+12125/121/(3+5*x)-32/456533*log(1-2*x)-204228/343*log(2+3*x)+792500/1331*log(3+5*x)],
[1/((1-2*x)*(2+3*x)^4*(3+5*x)^3),x,2,9/7/(2+3*x)^3+2889/98/(2+3*x)^2+204228/343/(2+3*x)+(-625/22)/(3+5*x)^2+81250/121/(3+5*x)-64/3195731*log(1-2*x)-11984706/2401*log(2+3*x)+6643750/1331*log(3+5*x)],
[1/((1-2*x)*(2+3*x)^5*(3+5*x)^3),x,2,27/28/(2+3*x)^4+963/49/(2+3*x)^3+102114/343/(2+3*x)^2+11984706/2401/(2+3*x)+(-3125/22)/(3+5*x)^2+509375/121/(3+5*x)-128/22370117*log(1-2*x)-631722537/16807*log(2+3*x)+50028125/1331*log(3+5*x)],
[(c+d*x)^4/((a-b*x)*(a+b*x)),x,2,-d^2*(6*b^2*c^2+a^2*d^2)*x/b^4-2*c*d^3*x^2/b^2-1/3*d^4*x^3/b^2-1/2*(b*c+a*d)^4*log(a-b*x)/(a*b^5)+1/2*(b*c-a*d)^4*log(a+b*x)/(a*b^5)],
[(c+d*x)^3/((a-b*x)*(a+b*x)),x,2,-3*c*d^2*x/b^2-1/2*d^3*x^2/b^2-1/2*(b*c+a*d)^3*log(a-b*x)/(a*b^4)+1/2*(b*c-a*d)^3*log(a+b*x)/(a*b^4)],
[(c+d*x)^2/((a-b*x)*(a+b*x)),x,2,-d^2*x/b^2-1/2*(b*c+a*d)^2*log(a-b*x)/(a*b^3)+1/2*(b*c-a*d)^2*log(a+b*x)/(a*b^3)],
[(c+d*x)/((a-b*x)*(a+b*x)),x,2,-1/2*(b*c+a*d)*log(a-b*x)/(a*b^2)+1/2*(b*c-a*d)*log(a+b*x)/(a*b^2)],
[1/((a-b*x)*(a+b*x)),x,2,arctanh(b*x/a)/(a*b)],
[1/((a-b*x)*(a+b*x)*(c+d*x)),x,2,-1/2*log(a-b*x)/(a*(b*c+a*d))+1/2*log(a+b*x)/(a*(b*c-a*d))-d*log(c+d*x)/(b^2*c^2-a^2*d^2)],
[1/((a-b*x)*(a+b*x)*(c+d*x)^2),x,2,d/((b^2*c^2-a^2*d^2)*(c+d*x))-1/2*b*log(a-b*x)/(a*(b*c+a*d)^2)+1/2*b*log(a+b*x)/(a*(b*c-a*d)^2)-2*b^2*c*d*log(c+d*x)/(b^2*c^2-a^2*d^2)^2],
[1/((a-b*x)*(a+b*x)*(c+d*x)^3),x,2,1/2*d/((b^2*c^2-a^2*d^2)*(c+d*x)^2)+2*b^2*c*d/((b^2*c^2-a^2*d^2)^2*(c+d*x))-1/2*b^2*log(a-b*x)/(a*(b*c+a*d)^3)+1/2*b^2*log(a+b*x)/(a*(b*c-a*d)^3)-b^2*d*(3*b^2*c^2+a^2*d^2)*log(c+d*x)/(b^2*c^2-a^2*d^2)^3],

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

# n>0
[(2+3*x)^8*(3+5*x)/(1-2*x)^2,x,2,63412811/1024/(1-2*x)+91609881/256*x+122887143/512*x^2+5892813/32*x^3+32991057/256*x^4+5859459/80*x^5+976617/32*x^6+56862/7*x^7+32805/32*x^8+246239357/1024*log(1-2*x)],
[(2+3*x)^7*(3+5*x)/(1-2*x)^2,x,2,9058973/512/(1-2*x)+22333965/256*x+873207/16*x^2+2399985/64*x^3+1423899/64*x^4+793881/80*x^5+11421/4*x^6+10935/28*x^7+15647317/256*log(1-2*x)],
[(2+3*x)^6*(3+5*x)/(1-2*x)^2,x,2,1294139/256/(1-2*x)+661617/32*x+1507977/128*x^2+111501/16*x^3+210195/64*x^4+5103/5*x^5+1215/8*x^6+3916031/256*log(1-2*x)],
[(2+3*x)^5*(3+5*x)/(1-2*x)^2,x,2,184877/128/(1-2*x)+301467/64*x+75447/32*x^2+18027/16*x^3+2997/8*x^4+243/4*x^5+60025/16*log(1-2*x)],
[(2+3*x)^4*(3+5*x)/(1-2*x)^2,x,2,26411/64/(1-2*x)+16203/16*x+13419/32*x^2+144*x^3+405/16*x^4+57281/64*log(1-2*x)],
[(2+3*x)^3*(3+5*x)/(1-2*x)^2,x,2,3773/32/(1-2*x)+3177/16*x+243/4*x^2+45/4*x^3+3283/16*log(1-2*x)],
[(2+3*x)^2*(3+5*x)/(1-2*x)^2,x,2,539/16/(1-2*x)+33*x+45/8*x^2+707/16*log(1-2*x)],
[(2+3*x)*(3+5*x)/(1-2*x)^2,x,2,77/8/(1-2*x)+15/4*x+17/2*log(1-2*x)],
[(3+5*x)/(1-2*x)^2,x,2,11/4/(1-2*x)+5/4*log(1-2*x)],
[(3+5*x)/((1-2*x)^2*(2+3*x)),x,2,11/14/(1-2*x)+1/49*log(1-2*x)-1/49*log(2+3*x)],
[(3+5*x)/((1-2*x)^2*(2+3*x)^2),x,2,11/49/(1-2*x)+1/49/(2+3*x)-31/343*log(1-2*x)+31/343*log(2+3*x)],
[(3+5*x)/((1-2*x)^2*(2+3*x)^3),x,2,22/343/(1-2*x)+1/98/(2+3*x)^2+(-31/343)/(2+3*x)-128/2401*log(1-2*x)+128/2401*log(2+3*x)],
[(3+5*x)/((1-2*x)^2*(2+3*x)^4),x,2,44/2401/(1-2*x)+1/147/(2+3*x)^3+(-31/686)/(2+3*x)^2+(-128/2401)/(2+3*x)-388/16807*log(1-2*x)+388/16807*log(2+3*x)],
[(3+5*x)/((1-2*x)^2*(2+3*x)^5),x,2,88/16807/(1-2*x)+1/196/(2+3*x)^4+(-31/1029)/(2+3*x)^3+(-64/2401)/(2+3*x)^2+(-388/16807)/(2+3*x)-1040/117649*log(1-2*x)+1040/117649*log(2+3*x)],
[(3+5*x)/((1-2*x)^2*(2+3*x)^6),x,2,176/117649/(1-2*x)+1/245/(2+3*x)^5+(-31/1372)/(2+3*x)^4+(-128/7203)/(2+3*x)^3+(-194/16807)/(2+3*x)^2+(-1040/117649)/(2+3*x)-2608/823543*log(1-2*x)+2608/823543*log(2+3*x)],
[(3+5*x)/((1-2*x)^2*(2+3*x)^7),x,2,352/823543/(1-2*x)+1/294/(2+3*x)^6+(-31/1715)/(2+3*x)^5+(-32/2401)/(2+3*x)^4+(-388/50421)/(2+3*x)^3+(-520/117649)/(2+3*x)^2+(-2608/823543)/(2+3*x)-128/117649*log(1-2*x)+128/117649*log(2+3*x)],
[(2+3*x)^8*(3+5*x)^2/(1-2*x)^2,x,2,697540921/2048/(1-2*x)+2330515357/1024*x+413355417/256*x^2+346239417/256*x^3+275757561/256*x^4+235268793/320*x^5+396738*x^6+17378631/112*x^7+1235655/32*x^8+18225/4*x^9+1512848491/1024*log(1-2*x)],
[(2+3*x)^7*(3+5*x)^2/(1-2*x)^2,x,2,99648703/1024/(1-2*x)+9077405/16*x+195497697/512*x^2+18842715/64*x^3+53086563/256*x^4+4750569/40*x^5+1597239/32*x^6+375435/28*x^7+54675/32*x^8+389535839/1024*log(1-2*x)],
[(2+3*x)^6*(3+5*x)^2/(1-2*x)^2,x,2,14235529/512/(1-2*x)+35458963/256*x+11140101/128*x^2+3851307/64*x^3+575775/16*x^4+1295919/80*x^5+37665/8*x^6+18225/28*x^7+12386759/128*log(1-2*x)],
[(2+3*x)^5*(3+5*x)^2/(1-2*x)^2,x,2,2033647/256/(1-2*x)+2104901/64*x+2412699/128*x^2+89913/8*x^3+342333/64*x^4+6723/4*x^5+2025/8*x^6+6206585/256*log(1-2*x)],
[(2+3*x)^4*(3+5*x)^2/(1-2*x)^2,x,2,290521/128/(1-2*x)+480841/64*x+15159/4*x^2+29277/16*x^3+9855/16*x^4+405/4*x^5+381073/64*log(1-2*x)],
[(2+3*x)^3*(3+5*x)^2/(1-2*x)^2,x,2,41503/64/(1-2*x)+12973/8*x+21717/32*x^2+945/4*x^3+675/16*x^4+91091/64*log(1-2*x)],
[(2+3*x)^2*(3+5*x)^2/(1-2*x)^2,x,2,5929/32/(1-2*x)+5119/16*x+795/8*x^2+75/4*x^3+1309/4*log(1-2*x)],
[(2+3*x)*(3+5*x)^2/(1-2*x)^2,x,2,847/16/(1-2*x)+215/4*x+75/8*x^2+1133/16*log(1-2*x)],
[(3+5*x)^2/(1-2*x)^2,x,2,121/8/(1-2*x)+25/4*x+55/4*log(1-2*x)],
[(3+5*x)^2/((1-2*x)^2*(2+3*x)),x,2,121/28/(1-2*x)+407/196*log(1-2*x)+1/147*log(2+3*x)],
[(3+5*x)^2/((1-2*x)^2*(2+3*x)^2),x,2,121/98/(1-2*x)+(-1/147)/(2+3*x)+22/343*log(1-2*x)-22/343*log(2+3*x)],
[(3+5*x)^2/((1-2*x)^2*(2+3*x)^3),x,2,121/343/(1-2*x)+(-1/294)/(2+3*x)^2+22/343/(2+3*x)-319/2401*log(1-2*x)+319/2401*log(2+3*x)],
[(3+5*x)^2/((1-2*x)^2*(2+3*x)^4),x,2,242/2401/(1-2*x)+(-1/441)/(2+3*x)^3+11/343/(2+3*x)^2+(-319/2401)/(2+3*x)-1364/16807*log(1-2*x)+1364/16807*log(2+3*x)],
[(3+5*x)^2/((1-2*x)^2*(2+3*x)^5),x,2,484/16807/(1-2*x)+(-1/588)/(2+3*x)^4+22/1029/(2+3*x)^3+(-319/4802)/(2+3*x)^2+(-1364/16807)/(2+3*x)-4180/117649*log(1-2*x)+4180/117649*log(2+3*x)],
[(3+5*x)^2/((1-2*x)^2*(2+3*x)^6),x,2,968/117649/(1-2*x)+(-1/735)/(2+3*x)^5+11/686/(2+3*x)^4+(-319/7203)/(2+3*x)^3+(-682/16807)/(2+3*x)^2+(-4180/117649)/(2+3*x)-11264/823543*log(1-2*x)+11264/823543*log(2+3*x)],
[(3+5*x)^2/((1-2*x)^2*(2+3*x)^7),x,2,1936/823543/(1-2*x)+(-1/882)/(2+3*x)^6+22/1715/(2+3*x)^5+(-319/9604)/(2+3*x)^4+(-1364/50421)/(2+3*x)^3+(-2090/117649)/(2+3*x)^2+(-11264/823543)/(2+3*x)-4048/823543*log(1-2*x)+4048/823543*log(2+3*x)],
[(3+5*x)^2/((1-2*x)^2*(2+3*x)^8),x,2,3872/5764801/(1-2*x)+(-1/1029)/(2+3*x)^7+11/1029/(2+3*x)^6+(-319/12005)/(2+3*x)^5+(-341/16807)/(2+3*x)^4+(-4180/352947)/(2+3*x)^3+(-5632/823543)/(2+3*x)^2+(-4048/823543)/(2+3*x)-68288/40353607*log(1-2*x)+68288/40353607*log(2+3*x)],
[(2+3*x)^8*(3+5*x)^3/(1-2*x)^2,x,2,7672950131/4096/(1-2*x)+7277894263/512*x+21573106793/2048*x^2+2416569641/256*x^3+8502681987/1024*x^4+260574273/40*x^5+544462047/128*x^6+242570133/112*x^7+101721015/128*x^8+370575/2*x^9+164025/8*x^10+36770371407/4096*log(1-2*x)],
[(2+3*x)^7*(3+5*x)^3/(1-2*x)^2,x,2,1096135733/2048/(1-2*x)+3690540955/1024*x+1312685491/512*x^2+551942075/256*x^3+220950207/128*x^4+379446471/320*x^5+20626947/32*x^6+28463805/112*x^7+127575/2*x^8+30375/4*x^9+298946109/128*log(1-2*x)],
[(2+3*x)^6*(3+5*x)^3/(1-2*x)^2,x,2,156590819/1024/(1-2*x)+230244479/256*x+310976027/512*x^2+7530189/16*x^3+85406805/256*x^4+15403257/80*x^5+2611845/32*x^6+309825/14*x^7+91125/32*x^8+616195041/1024*log(1-2*x)],
[(2+3*x)^5*(3+5*x)^3/(1-2*x)^2,x,2,22370117/512/(1-2*x)+56291737/256*x+8881301/64*x^2+6179077/64*x^3+3724389/64*x^4+423009/16*x^5+15525/2*x^6+30375/28*x^7+39220335/256*log(1-2*x)],
[(2+3*x)^4*(3+5*x)^3/(1-2*x)^2,x,2,3195731/256/(1-2*x)+209243/4*x+3859469/128*x^2+289951/16*x^3+557415/64*x^4+5535/2*x^5+3375/8*x^6+9836211/256*log(1-2*x)],
[(2+3*x)^3*(3+5*x)^3/(1-2*x)^2,x,2,456533/128/(1-2*x)+766807/64*x+194881/32*x^2+47535/16*x^3+2025/2*x^4+675/4*x^5+302379/32*log(1-2*x)],
[(2+3*x)^2*(3+5*x)^3/(1-2*x)^2,x,2,65219/64/(1-2*x)+41537/16*x+35135/32*x^2+775/2*x^3+1125/16*x^4+144837/64*log(1-2*x)],
[(2+3*x)*(3+5*x)^3/(1-2*x)^2,x,2,9317/32/(1-2*x)+8245/16*x+325/2*x^2+125/4*x^3+8349/16*log(1-2*x)],
[(3+5*x)^3/(1-2*x)^2,x,2,1331/16/(1-2*x)+175/2*x+125/8*x^2+1815/16*log(1-2*x)],
[(3+5*x)^3/((1-2*x)^2*(2+3*x)),x,2,1331/56/(1-2*x)+125/12*x+1089/49*log(1-2*x)-1/441*log(2+3*x)],
[(3+5*x)^3/((1-2*x)^2*(2+3*x)^2),x,2,1331/196/(1-2*x)+1/441/(2+3*x)+4719/1372*log(1-2*x)+101/3087*log(2+3*x)],
[(3+5*x)^3/((1-2*x)^2*(2+3*x)^3),x,2,1331/686/(1-2*x)+1/882/(2+3*x)^2+(-101/3087)/(2+3*x)+363/2401*log(1-2*x)-363/2401*log(2+3*x)],
[(3+5*x)^3/((1-2*x)^2*(2+3*x)^4),x,2,1331/2401/(1-2*x)+1/1323/(2+3*x)^3+(-101/6174)/(2+3*x)^2+363/2401/(2+3*x)-3267/16807*log(1-2*x)+3267/16807*log(2+3*x)],
[(3+5*x)^3/((1-2*x)^2*(2+3*x)^5),x,2,2662/16807/(1-2*x)+1/1764/(2+3*x)^4+(-101/9261)/(2+3*x)^3+363/4802/(2+3*x)^2+(-3267/16807)/(2+3*x)-14520/117649*log(1-2*x)+14520/117649*log(2+3*x)],
[(3+5*x)^3/((1-2*x)^2*(2+3*x)^6),x,2,5324/117649/(1-2*x)+1/2205/(2+3*x)^5+(-101/12348)/(2+3*x)^4+121/2401/(2+3*x)^3+(-3267/33614)/(2+3*x)^2+(-14520/117649)/(2+3*x)-45012/823543*log(1-2*x)+45012/823543*log(2+3*x)],
[(3+5*x)^3/((1-2*x)^2*(2+3*x)^7),x,2,10648/823543/(1-2*x)+1/2646/(2+3*x)^6+(-101/15435)/(2+3*x)^5+363/9604/(2+3*x)^4+(-1089/16807)/(2+3*x)^3+(-7260/117649)/(2+3*x)^2+(-45012/823543)/(2+3*x)-17424/823543*log(1-2*x)+17424/823543*log(2+3*x)],
[(3+5*x)^3/((1-2*x)^2*(2+3*x)^8),x,2,21296/5764801/(1-2*x)+1/3087/(2+3*x)^7+(-101/18522)/(2+3*x)^6+363/12005/(2+3*x)^5+(-3267/67228)/(2+3*x)^4+(-4840/117649)/(2+3*x)^3+(-22506/823543)/(2+3*x)^2+(-17424/823543)/(2+3*x)-307824/40353607*log(1-2*x)+307824/40353607*log(2+3*x)],

# n<0
[(2+3*x)^8/((1-2*x)^2*(3+5*x)),x,2,5764801/2816/(1-2*x)+2041906293/250000*x+1839811401/400000*x^2+26773659/10000*x^3+9899091/8000*x^4+94041/250*x^5+2187/40*x^6+188591347/30976*log(1-2*x)+1/9453125*log(3+5*x)],
[(2+3*x)^7/((1-2*x)^2*(3+5*x)),x,2,823543/1408/(1-2*x)+370109547/200000*x+18237069/20000*x^2+853659/2000*x^3+13851/100*x^4+2187/100*x^5+5764801/3872*log(1-2*x)+1/1890625*log(3+5*x)],
[(2+3*x)^6/((1-2*x)^2*(3+5*x)),x,2,117649/704/(1-2*x)+3946293/10000*x+639819/4000*x^2+2673/50*x^3+729/80*x^4+2739541/7744*log(1-2*x)+1/378125*log(3+5*x)],
[(2+3*x)^5/((1-2*x)^2*(3+5*x)),x,2,16807/352/(1-2*x)+152793/2000*x+567/25*x^2+81/20*x^3+156065/1936*log(1-2*x)+1/75625*log(3+5*x)],
[(2+3*x)^4/((1-2*x)^2*(3+5*x)),x,2,2401/176/(1-2*x)+621/50*x+81/40*x^2+33271/1936*log(1-2*x)+1/15125*log(3+5*x)],
[(2+3*x)^3/((1-2*x)^2*(3+5*x)),x,2,343/88/(1-2*x)+27/20*x+392/121*log(1-2*x)+1/3025*log(3+5*x)],
[(2+3*x)^2/((1-2*x)^2*(3+5*x)),x,2,49/44/(1-2*x)+217/484*log(1-2*x)+1/605*log(3+5*x)],
[(2+3*x)/((1-2*x)^2*(3+5*x)),x,2,7/22/(1-2*x)-1/121*log(1-2*x)+1/121*log(3+5*x)],
[1/((1-2*x)^2*(3+5*x)),x,2,1/11/(1-2*x)-5/121*log(1-2*x)+5/121*log(3+5*x)],
[1/((1-2*x)^2*(2+3*x)*(3+5*x)),x,2,2/77/(1-2*x)-136/5929*log(1-2*x)-9/49*log(2+3*x)+25/121*log(3+5*x)],
[1/((1-2*x)^2*(2+3*x)^2*(3+5*x)),x,2,4/539/(1-2*x)+9/49/(2+3*x)-404/41503*log(1-2*x)-351/343*log(2+3*x)+125/121*log(3+5*x)],
[1/((1-2*x)^2*(2+3*x)^3*(3+5*x)),x,2,8/3773/(1-2*x)+9/98/(2+3*x)^2+351/343/(2+3*x)-1072/290521*log(1-2*x)-12393/2401*log(2+3*x)+625/121*log(3+5*x)],
[1/((1-2*x)^2*(2+3*x)^4*(3+5*x)),x,2,16/26411/(1-2*x)+3/49/(2+3*x)^3+351/686/(2+3*x)^2+12393/2401/(2+3*x)-2672/2033647*log(1-2*x)-434043/16807*log(2+3*x)+3125/121*log(3+5*x)],
[1/((1-2*x)^2*(2+3*x)^5*(3+5*x)),x,2,32/184877/(1-2*x)+9/196/(2+3*x)^4+117/343/(2+3*x)^3+12393/4802/(2+3*x)^2+434043/16807/(2+3*x)-6400/14235529*log(1-2*x)-15192225/117649*log(2+3*x)+15625/121*log(3+5*x)],
[1/((1-2*x)^2*(2+3*x)^6*(3+5*x)),x,2,64/1294139/(1-2*x)+9/245/(2+3*x)^5+351/1372/(2+3*x)^4+4131/2401/(2+3*x)^3+434043/33614/(2+3*x)^2+15192225/117649/(2+3*x)-14912/99648703*log(1-2*x)-531729603/823543*log(2+3*x)+78125/121*log(3+5*x)],
[(2+3*x)^8/((1-2*x)^2*(3+5*x)^2),x,2,5764801/15488/(1-2*x)+231915717/200000*x+14171517/25000*x^2+2626101/10000*x^3+168399/2000*x^4+6561/500*x^5+(-1/9453125)/(3+5*x)+79883671/85184*log(1-2*x)+268/103984375*log(3+5*x)],
[(2+3*x)^7/((1-2*x)^2*(3+5*x)^2),x,2,823543/7744/(1-2*x)+6156243/25000*x+1974861/20000*x^2+16281/500*x^3+2187/400*x^4+(-1/1890625)/(3+5*x)+18941489/85184*log(1-2*x)+47/4159375*log(3+5*x)],
[(2+3*x)^6/((1-2*x)^2*(3+5*x)^2),x,2,117649/3872/(1-2*x)+473607/10000*x+13851/1000*x^2+243/100*x^3+(-1/378125)/(3+5*x)+67228/1331*log(1-2*x)+202/4159375*log(3+5*x)],
[(2+3*x)^5/((1-2*x)^2*(3+5*x)^2),x,2,16807/1936/(1-2*x)+3807/500*x+243/200*x^2+(-1/75625)/(3+5*x)+228095/21296*log(1-2*x)+169/831875*log(3+5*x)],
[(2+3*x)^4/((1-2*x)^2*(3+5*x)^2),x,2,2401/968/(1-2*x)+81/100*x+(-1/15125)/(3+5*x)+10633/5324*log(1-2*x)+136/166375*log(3+5*x)],
[(2+3*x)^3/((1-2*x)^2*(3+5*x)^2),x,2,343/484/(1-2*x)+(-1/3025)/(3+5*x)+1421/5324*log(1-2*x)+103/33275*log(3+5*x)],
[(2+3*x)^2/((1-2*x)^2*(3+5*x)^2),x,2,49/242/(1-2*x)+(-1/605)/(3+5*x)-14/1331*log(1-2*x)+14/1331*log(3+5*x)],
[(2+3*x)/((1-2*x)^2*(3+5*x)^2),x,2,7/121/(1-2*x)+(-1/121)/(3+5*x)-37/1331*log(1-2*x)+37/1331*log(3+5*x)],
[1/((1-2*x)^2*(3+5*x)^2),x,2,2/121/(1-2*x)+(-5/121)/(3+5*x)-20/1331*log(1-2*x)+20/1331*log(3+5*x)],
[1/((1-2*x)^2*(2+3*x)*(3+5*x)^2),x,2,4/847/(1-2*x)+(-25/121)/(3+5*x)-412/65219*log(1-2*x)+27/49*log(2+3*x)-725/1331*log(3+5*x)],
[1/((1-2*x)^2*(2+3*x)^2*(3+5*x)^2),x,2,8/5929/(1-2*x)+(-27/49)/(2+3*x)+(-125/121)/(3+5*x)-1088/456533*log(1-2*x)+1998/343*log(2+3*x)-7750/1331*log(3+5*x)],
[1/((1-2*x)^2*(2+3*x)^3*(3+5*x)^2),x,2,16/41503/(1-2*x)+(-27/98)/(2+3*x)^2+(-1998/343)/(2+3*x)+(-625/121)/(3+5*x)-2704/3195731*log(1-2*x)+107109/2401*log(2+3*x)-59375/1331*log(3+5*x)],
[1/((1-2*x)^2*(2+3*x)^4*(3+5*x)^2),x,2,32/290521/(1-2*x)+(-9/49)/(2+3*x)^3+(-999/343)/(2+3*x)^2+(-107109/2401)/(2+3*x)+(-3125/121)/(3+5*x)-6464/22370117*log(1-2*x)+5050944/16807*log(2+3*x)-400000/1331*log(3+5*x)],
[1/((1-2*x)^2*(2+3*x)^5*(3+5*x)^2),x,2,64/2033647/(1-2*x)+(-27/196)/(2+3*x)^4+(-666/343)/(2+3*x)^3+(-107109/4802)/(2+3*x)^2+(-5050944/16807)/(2+3*x)+(-15625/121)/(3+5*x)-15040/156590819*log(1-2*x)+222359715/117649*log(2+3*x)-2515625/1331*log(3+5*x)],
[(2+3*x)^8/((1-2*x)^2*(3+5*x)^3),x,2,5764801/85184/(1-2*x)+7680987/50000*x+6093711/100000*x^2+12393/625*x^3+6561/2000*x^4+(-1/18906250)/(3+5*x)^2+(-268/103984375)/(3+5*x)+130943337/937024*log(1-2*x)+6312/228765625*log(3+5*x)],
[(2+3*x)^7/((1-2*x)^2*(3+5*x)^3),x,2,823543/42592/(1-2*x)+1467477/50000*x+21141/2500*x^2+729/500*x^3+(-1/3781250)/(3+5*x)^2+(-47/4159375)/(3+5*x)+7411887/234256*log(1-2*x)+4761/45753125*log(3+5*x)],
[(2+3*x)^6/((1-2*x)^2*(3+5*x)^3),x,2,117649/21296/(1-2*x)+2916/625*x+729/1000*x^2+(-1/756250)/(3+5*x)^2+(-202/4159375)/(3+5*x)+1563051/234256*log(1-2*x)+17139/45753125*log(3+5*x)],
[(2+3*x)^5/((1-2*x)^2*(3+5*x)^3),x,2,16807/10648/(1-2*x)+243/500*x+(-1/151250)/(3+5*x)^2+(-169/831875)/(3+5*x)+36015/29282*log(1-2*x)+11562/9150625*log(3+5*x)],
[(2+3*x)^4/((1-2*x)^2*(3+5*x)^3),x,2,2401/5324/(1-2*x)+(-1/30250)/(3+5*x)^2+(-136/166375)/(3+5*x)+9261/58564*log(1-2*x)+7074/1830125*log(3+5*x)],
[(2+3*x)^3/((1-2*x)^2*(3+5*x)^3),x,2,343/2662/(1-2*x)+(-1/6050)/(3+5*x)^2+(-103/33275)/(3+5*x)-147/14641*log(1-2*x)+147/14641*log(3+5*x)],
[(2+3*x)^2/((1-2*x)^2*(3+5*x)^3),x,2,49/1331/(1-2*x)+(-1/1210)/(3+5*x)^2+(-14/1331)/(3+5*x)-273/14641*log(1-2*x)+273/14641*log(3+5*x)],
[(2+3*x)/((1-2*x)^2*(3+5*x)^3),x,2,14/1331/(1-2*x)+(-1/242)/(3+5*x)^2+(-37/1331)/(3+5*x)-144/14641*log(1-2*x)+144/14641*log(3+5*x)],
[1/((1-2*x)^2*(3+5*x)^3),x,2,4/1331/(1-2*x)+(-5/242)/(3+5*x)^2+(-20/1331)/(3+5*x)-60/14641*log(1-2*x)+60/14641*log(3+5*x)],
[1/((1-2*x)^2*(2+3*x)*(3+5*x)^3),x,2,8/9317/(1-2*x)+(-25/242)/(3+5*x)^2+725/1331/(3+5*x)-1104/717409*log(1-2*x)-81/49*log(2+3*x)+24225/14641*log(3+5*x)],
[1/((1-2*x)^2*(2+3*x)^2*(3+5*x)^3),x,2,16/65219/(1-2*x)+81/49/(2+3*x)+(-125/242)/(3+5*x)^2+7750/1331/(3+5*x)-2736/5021863*log(1-2*x)-8829/343*log(2+3*x)+376875/14641*log(3+5*x)],
[1/((1-2*x)^2*(2+3*x)^3*(3+5*x)^3),x,2,32/456533/(1-2*x)+81/98/(2+3*x)^2+8829/343/(2+3*x)+(-625/242)/(3+5*x)^2+59375/1331/(3+5*x)-6528/35153041*log(1-2*x)-630342/2401*log(2+3*x)+3843750/14641*log(3+5*x)],
[1/((1-2*x)^2*(2+3*x)^4*(3+5*x)^3),x,2,64/3195731/(1-2*x)+27/49/(2+3*x)^3+8829/686/(2+3*x)^2+630342/2401/(2+3*x)+(-3125/242)/(3+5*x)^2+400000/1331/(3+5*x)-15168/246071287*log(1-2*x)-37214802/16807*log(2+3*x)+32418750/14641*log(3+5*x)],

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

# n>0
[(2+3*x)^8*(3+5*x)/(1-2*x)^3,x,2,63412811/2048/(1-2*x)^2+(-246239357/1024)/(1-2*x)-120864213/256*x-118841283/512*x^2-16042509/128*x^3-7568235/128*x^4-213597/10*x^5-162567/32*x^6-32805/56*x^7-106237047/256*log(1-2*x)],
[(2+3*x)^7*(3+5*x)/(1-2*x)^3,x,2,9058973/1024/(1-2*x)^2+(-15647317/256)/(1-2*x)-24960933/256*x-10989621/256*x^2-631611/32*x^3-235467/32*x^4-147987/80*x^5-3645/16*x^6-23647449/256*log(1-2*x)],
[(2+3*x)^6*(3+5*x)/(1-2*x)^3,x,2,1294139/512/(1-2*x)^2+(-3916031/256)/(1-2*x)-2431647/128*x-461835/64*x^2-10611/4*x^3-44469/64*x^4-729/8*x^5-5078115/256*log(1-2*x)],
[(2+3*x)^5*(3+5*x)/(1-2*x)^3,x,2,184877/256/(1-2*x)^2+(-60025/16)/(1-2*x)-109089/32*x-16821/16*x^2-4401/16*x^3-1215/32*x^4-519645/128*log(1-2*x)],
[(2+3*x)^4*(3+5*x)/(1-2*x)^3,x,2,26411/128/(1-2*x)^2+(-57281/64)/(1-2*x)-540*x-3861/32*x^2-135/8*x^3-24843/32*log(1-2*x)],
[(2+3*x)^3*(3+5*x)/(1-2*x)^3,x,2,3773/64/(1-2*x)^2+(-3283/16)/(1-2*x)-1107/16*x-135/16*x^2-1071/8*log(1-2*x)],
[(2+3*x)^2*(3+5*x)/(1-2*x)^3,x,2,539/32/(1-2*x)^2+(-707/16)/(1-2*x)-45/8*x-309/16*log(1-2*x)],
[(2+3*x)*(3+5*x)/(1-2*x)^3,x,2,77/16/(1-2*x)^2+(-17/2)/(1-2*x)-15/8*log(1-2*x)],
[(3+5*x)/(1-2*x)^3,x,1,1/22*(3+5*x)^2/(1-2*x)^2],
[(3+5*x)/((1-2*x)^3*(2+3*x)),x,2,11/28/(1-2*x)^2+(-1/49)/(1-2*x)+3/343*log(1-2*x)-3/343*log(2+3*x)],
[(3+5*x)/((1-2*x)^3*(2+3*x)^2),x,2,11/98/(1-2*x)^2+31/343/(1-2*x)+3/343/(2+3*x)-87/2401*log(1-2*x)+87/2401*log(2+3*x)],
[(3+5*x)/((1-2*x)^3*(2+3*x)^3),x,2,11/343/(1-2*x)^2+128/2401/(1-2*x)+3/686/(2+3*x)^2+(-87/2401)/(2+3*x)-558/16807*log(1-2*x)+558/16807*log(2+3*x)],
[(3+5*x)/((1-2*x)^3*(2+3*x)^4),x,2,22/2401/(1-2*x)^2+388/16807/(1-2*x)+1/343/(2+3*x)^3+(-87/4802)/(2+3*x)^2+(-558/16807)/(2+3*x)-2280/117649*log(1-2*x)+2280/117649*log(2+3*x)],
[(3+5*x)/((1-2*x)^3*(2+3*x)^5),x,2,44/16807/(1-2*x)^2+1040/117649/(1-2*x)+3/1372/(2+3*x)^4+(-29/2401)/(2+3*x)^3+(-279/16807)/(2+3*x)^2+(-2280/117649)/(2+3*x)-7680/823543*log(1-2*x)+7680/823543*log(2+3*x)],
[(3+5*x)/((1-2*x)^3*(2+3*x)^6),x,2,88/117649/(1-2*x)^2+2608/823543/(1-2*x)+3/1715/(2+3*x)^5+(-87/9604)/(2+3*x)^4+(-186/16807)/(2+3*x)^3+(-1140/117649)/(2+3*x)^2+(-7680/823543)/(2+3*x)-3312/823543*log(1-2*x)+3312/823543*log(2+3*x)],
[(2+3*x)^7*(3+5*x)^2/(1-2*x)^3,x,2,99648703/2048/(1-2*x)^2+(-389535839/1024)/(1-2*x)-48280011/64*x-190742391/512*x^2-25895367/128*x^3-12299769/128*x^4-2798631/80*x^5-268515/32*x^6-54675/56*x^7-84589631/128*log(1-2*x)],
[(2+3*x)^6*(3+5*x)^2/(1-2*x)^3,x,2,14235529/1024/(1-2*x)^2+(-12386759/128)/(1-2*x)-39980457/256*x-17700255/256*x^2-1024389/32*x^3-770067/64*x^4-48843/16*x^5-6075/16*x^6-18859855/128*log(1-2*x)],
[(2+3*x)^5*(3+5*x)^2/(1-2*x)^3,x,2,2033647/512/(1-2*x)^2+(-6206585/256)/(1-2*x)-3907293/128*x-747297/64*x^2-69273/16*x^3-73305/64*x^4-1215/8*x^5-8117095/256*log(1-2*x)],
[(2+3*x)^4*(3+5*x)^2/(1-2*x)^3,x,2,290521/256/(1-2*x)^2+(-381073/64)/(1-2*x)-176055/32*x-54783/32*x^2-7245/16*x^3-2025/32*x^4-832951/128*log(1-2*x)],
[(2+3*x)^3*(3+5*x)^2/(1-2*x)^3,x,2,41503/128/(1-2*x)^2+(-91091/64)/(1-2*x)-14031/16*x-6345/32*x^2-225/8*x^3-39977/32*log(1-2*x)],
[(2+3*x)^2*(3+5*x)^2/(1-2*x)^3,x,2,5929/64/(1-2*x)^2+(-1309/4)/(1-2*x)-1815/16*x-225/16*x^2-3467/16*log(1-2*x)],
[(2+3*x)*(3+5*x)^2/(1-2*x)^3,x,2,847/32/(1-2*x)^2+(-1133/16)/(1-2*x)-75/8*x-505/16*log(1-2*x)],
[(3+5*x)^2/(1-2*x)^3,x,2,121/16/(1-2*x)^2+(-55/4)/(1-2*x)-25/8*log(1-2*x)],
[(3+5*x)^2/((1-2*x)^3*(2+3*x)),x,2,121/56/(1-2*x)^2+(-407/196)/(1-2*x)-1/343*log(1-2*x)+1/343*log(2+3*x)],
[(3+5*x)^2/((1-2*x)^3*(2+3*x)^2),x,2,121/196/(1-2*x)^2+(-22/343)/(1-2*x)+(-1/343)/(2+3*x)+64/2401*log(1-2*x)-64/2401*log(2+3*x)],
[(3+5*x)^2/((1-2*x)^3*(2+3*x)^3),x,2,121/686/(1-2*x)^2+319/2401/(1-2*x)+(-1/686)/(2+3*x)^2+64/2401/(2+3*x)-829/16807*log(1-2*x)+829/16807*log(2+3*x)],
[(3+5*x)^2/((1-2*x)^3*(2+3*x)^4),x,2,121/2401/(1-2*x)^2+1364/16807/(1-2*x)+(-1/1029)/(2+3*x)^3+32/2401/(2+3*x)^2+(-829/16807)/(2+3*x)-5750/117649*log(1-2*x)+5750/117649*log(2+3*x)],
[(3+5*x)^2/((1-2*x)^3*(2+3*x)^5),x,2,242/16807/(1-2*x)^2+4180/117649/(1-2*x)+(-1/1372)/(2+3*x)^4+64/7203/(2+3*x)^3+(-829/33614)/(2+3*x)^2+(-5750/117649)/(2+3*x)-24040/823543*log(1-2*x)+24040/823543*log(2+3*x)],
[(3+5*x)^2/((1-2*x)^3*(2+3*x)^6),x,2,484/117649/(1-2*x)^2+11264/823543/(1-2*x)+(-1/1715)/(2+3*x)^5+16/2401/(2+3*x)^4+(-829/50421)/(2+3*x)^3+(-2875/117649)/(2+3*x)^2+(-24040/823543)/(2+3*x)-11696/823543*log(1-2*x)+11696/823543*log(2+3*x)],
[(2+3*x)^6*(3+5*x)^3/(1-2*x)^3,x,2,156590819/2048/(1-2*x)^2+(-616195041/1024)/(1-2*x)-308539921/256*x-306103815/512*x^2-41793093/128*x^3-19986237/128*x^4-229149/4*x^5-443475/32*x^6-91125/56*x^7-33674025/32*log(1-2*x)],
[(2+3*x)^5*(3+5*x)^3/(1-2*x)^3,x,2,22370117/1024/(1-2*x)^2+(-39220335/256)/(1-2*x)-64029233/256*x-28504029/256*x^2-1661133/32*x^3-629505/32*x^4-80595/16*x^5-10125/16*x^6-60160485/256*log(1-2*x)],
[(2+3*x)^4*(3+5*x)^3/(1-2*x)^3,x,2,3195731/512/(1-2*x)^2+(-9836211/256)/(1-2*x)-6277415/128*x-1208973/64*x^2-7065*x^3-120825/64*x^4-2025/8*x^5-12973191/256*log(1-2*x)],
[(2+3*x)^3*(3+5*x)^3/(1-2*x)^3,x,2,456533/256/(1-2*x)^2+(-302379/32)/(1-2*x)-284071/32*x-44595/16*x^2-11925/16*x^3-3375/32*x^4-1334949/128*log(1-2*x)],
[(2+3*x)^2*(3+5*x)^3/(1-2*x)^3,x,2,65219/128/(1-2*x)^2+(-144837/64)/(1-2*x)-5695/4*x-10425/32*x^2-375/8*x^3-64317/32*log(1-2*x)],
[(2+3*x)*(3+5*x)^3/(1-2*x)^3,x,2,9317/64/(1-2*x)^2+(-8349/16)/(1-2*x)-2975/16*x-375/16*x^2-2805/8*log(1-2*x)],
[(3+5*x)^3/(1-2*x)^3,x,2,1331/32/(1-2*x)^2+(-1815/16)/(1-2*x)-125/8*x-825/16*log(1-2*x)],
[(3+5*x)^3/((1-2*x)^3*(2+3*x)),x,2,1331/112/(1-2*x)^2+(-1089/49)/(1-2*x)-14289/2744*log(1-2*x)-1/1029*log(2+3*x)],
[(3+5*x)^3/((1-2*x)^3*(2+3*x)^2),x,2,1331/392/(1-2*x)^2+(-4719/1372)/(1-2*x)+1/1029/(2+3*x)-33/2401*log(1-2*x)+33/2401*log(2+3*x)],
[(3+5*x)^3/((1-2*x)^3*(2+3*x)^3),x,2,1331/1372/(1-2*x)^2+(-363/2401)/(1-2*x)+1/2058/(2+3*x)^2+(-33/2401)/(2+3*x)+1023/16807*log(1-2*x)-1023/16807*log(2+3*x)],
[(3+5*x)^3/((1-2*x)^3*(2+3*x)^4),x,2,1331/4802/(1-2*x)^2+3267/16807/(1-2*x)+1/3087/(2+3*x)^3+(-33/4802)/(2+3*x)^2+1023/16807/(2+3*x)-7755/117649*log(1-2*x)+7755/117649*log(2+3*x)],
[(3+5*x)^3/((1-2*x)^3*(2+3*x)^5),x,2,1331/16807/(1-2*x)^2+14520/117649/(1-2*x)+1/4116/(2+3*x)^4+(-11/2401)/(2+3*x)^3+1023/33614/(2+3*x)^2+(-7755/117649)/(2+3*x)-59070/823543*log(1-2*x)+59070/823543*log(2+3*x)],

# n<0
[(2+3*x)^8/((1-2*x)^3*(3+5*x)),x,2,5764801/5632/(1-2*x)^2+(-188591347/30976)/(1-2*x)-2941619571/400000*x-110180817/40000*x^2-124416/125*x^3-408969/1600*x^4-6561/200*x^5-2644396573/340736*log(1-2*x)+1/20796875*log(3+5*x)],
[(2+3*x)^7/((1-2*x)^3*(3+5*x)),x,2,823543/2816/(1-2*x)^2+(-5764801/3872)/(1-2*x)-26161299/20000*x-792423/2000*x^2-40581/400*x^3-2187/160*x^4-269063263/170368*log(1-2*x)+1/4159375*log(3+5*x)],
[(2+3*x)^6/((1-2*x)^3*(3+5*x)),x,2,117649/1408/(1-2*x)^2+(-2739541/7744)/(1-2*x)-102303/500*x-35721/800*x^2-243/40*x^3-12761315/42592*log(1-2*x)+1/831875*log(3+5*x)],
[(2+3*x)^5/((1-2*x)^3*(3+5*x)),x,2,16807/704/(1-2*x)^2+(-156065/1936)/(1-2*x)-10287/400*x-243/80*x^2-543655/10648*log(1-2*x)+1/166375*log(3+5*x)],
[(2+3*x)^4/((1-2*x)^3*(3+5*x)),x,2,2401/352/(1-2*x)^2+(-33271/1936)/(1-2*x)-81/40*x-153811/21296*log(1-2*x)+1/33275*log(3+5*x)],
[(2+3*x)^3/((1-2*x)^3*(3+5*x)),x,2,343/176/(1-2*x)^2+(-392/121)/(1-2*x)-7189/10648*log(1-2*x)+1/6655*log(3+5*x)],
[(2+3*x)^2/((1-2*x)^3*(3+5*x)),x,2,49/88/(1-2*x)^2+(-217/484)/(1-2*x)-1/1331*log(1-2*x)+1/1331*log(3+5*x)],
[(2+3*x)/((1-2*x)^3*(3+5*x)),x,2,7/44/(1-2*x)^2+1/121/(1-2*x)-5/1331*log(1-2*x)+5/1331*log(3+5*x)],
[1/((1-2*x)^3*(3+5*x)),x,2,1/22/(1-2*x)^2+5/121/(1-2*x)-25/1331*log(1-2*x)+25/1331*log(3+5*x)],
[1/((1-2*x)^3*(2+3*x)*(3+5*x)),x,2,1/77/(1-2*x)^2+136/5929/(1-2*x)-6938/456533*log(1-2*x)-27/343*log(2+3*x)+125/1331*log(3+5*x)],
[1/((1-2*x)^3*(2+3*x)^2*(3+5*x)),x,2,2/539/(1-2*x)^2+404/41503/(1-2*x)+27/343/(2+3*x)-27208/3195731*log(1-2*x)-1107/2401*log(2+3*x)+625/1331*log(3+5*x)],
[1/((1-2*x)^3*(2+3*x)^3*(3+5*x)),x,2,4/3773/(1-2*x)^2+1072/290521/(1-2*x)+27/686/(2+3*x)^2+1107/2401/(2+3*x)-89792/22370117*log(1-2*x)-39393/16807*log(2+3*x)+3125/1331*log(3+5*x)],
[1/((1-2*x)^3*(2+3*x)^4*(3+5*x)),x,2,8/26411/(1-2*x)^2+2672/2033647/(1-2*x)+9/343/(2+3*x)^3+1107/4802/(2+3*x)^2+39393/16807/(2+3*x)-267760/156590819*log(1-2*x)-1380915/117649*log(2+3*x)+15625/1331*log(3+5*x)],
[(2+3*x)^8/((1-2*x)^3*(3+5*x)^2),x,2,5764801/30976/(1-2*x)^2+(-79883671/85184)/(1-2*x)-81001863/100000*x-4863159/20000*x^2-123201/2000*x^3-6561/800*x^4+(-1/20796875)/(3+5*x)-1845559863/1874048*log(1-2*x)+54/45753125*log(3+5*x)],
[(2+3*x)^7/((1-2*x)^3*(3+5*x)^2),x,2,823543/15488/(1-2*x)^2+(-18941489/85184)/(1-2*x)-1258983/10000*x-108621/4000*x^2-729/200*x^3+(-1/4159375)/(3+5*x)-87177909/468512*log(1-2*x)+237/45753125*log(3+5*x)],
[(2+3*x)^6/((1-2*x)^3*(3+5*x)^2),x,2,117649/7744/(1-2*x)^2+(-67228/1331)/(1-2*x)-31347/2000*x-729/400*x^2+(-1/831875)/(3+5*x)-7383075/234256*log(1-2*x)+204/9150625*log(3+5*x)],
[(2+3*x)^5/((1-2*x)^3*(3+5*x)^2),x,2,16807/3872/(1-2*x)^2+(-228095/21296)/(1-2*x)-243/200*x+(-1/166375)/(3+5*x)-1034145/234256*log(1-2*x)+171/1830125*log(3+5*x)],
[(2+3*x)^4/((1-2*x)^3*(3+5*x)^2),x,2,2401/1936/(1-2*x)^2+(-10633/5324)/(1-2*x)+(-1/33275)/(3+5*x)-47481/117128*log(1-2*x)+138/366025*log(3+5*x)],
[(2+3*x)^3/((1-2*x)^3*(3+5*x)^2),x,2,343/968/(1-2*x)^2+(-1421/5324)/(1-2*x)+(-1/6655)/(3+5*x)-21/14641*log(1-2*x)+21/14641*log(3+5*x)],
[(2+3*x)^2/((1-2*x)^3*(3+5*x)^2),x,2,49/484/(1-2*x)^2+14/1331/(1-2*x)+(-1/1331)/(3+5*x)-72/14641*log(1-2*x)+72/14641*log(3+5*x)],
[(2+3*x)/((1-2*x)^3*(3+5*x)^2),x,2,7/242/(1-2*x)^2+37/1331/(1-2*x)+(-5/1331)/(3+5*x)-195/14641*log(1-2*x)+195/14641*log(3+5*x)],
[1/((1-2*x)^3*(3+5*x)^2),x,2,1/121/(1-2*x)^2+20/1331/(1-2*x)+(-25/1331)/(3+5*x)-150/14641*log(1-2*x)+150/14641*log(3+5*x)],
[1/((1-2*x)^3*(2+3*x)*(3+5*x)^2),x,2,2/847/(1-2*x)^2+412/65219/(1-2*x)+(-125/1331)/(3+5*x)-28296/5021863*log(1-2*x)+81/343*log(2+3*x)-3375/14641*log(3+5*x)],
[1/((1-2*x)^3*(2+3*x)^2*(3+5*x)^2),x,2,4/5929/(1-2*x)^2+1088/456533/(1-2*x)+(-81/343)/(2+3*x)+(-625/1331)/(3+5*x)-92496/35153041*log(1-2*x)+6156/2401*log(2+3*x)-37500/14641*log(3+5*x)],
[1/((1-2*x)^3*(2+3*x)^3*(3+5*x)^2),x,2,8/41503/(1-2*x)^2+2704/3195731/(1-2*x)+(-81/686)/(2+3*x)^2+(-6156/2401)/(2+3*x)+(-3125/1331)/(3+5*x)-274224/246071287*log(1-2*x)+333639/16807*log(2+3*x)-290625/14641*log(3+5*x)],
[1/((1-2*x)^3*(2+3*x)^4*(3+5*x)^2),x,2,16/290521/(1-2*x)^2+6464/22370117/(1-2*x)+(-27/343)/(2+3*x)^3+(-3078/2401)/(2+3*x)^2+(-333639/16807)/(2+3*x)+(-15625/1331)/(3+5*x)-761760/1722499009*log(1-2*x)+15820110/117649*log(2+3*x)-1968750/14641*log(3+5*x)],
[(2+3*x)^9/((1-2*x)^3*(3+5*x)^3),x,2,40353607/340736/(1-2*x)^2+(-17294403/29282)/(1-2*x)-50150097/100000*x-7459857/50000*x^2-373977/10000*x^3-19683/4000*x^4+(-1/207968750)/(3+5*x)^2+(-303/1143828125)/(3+5*x)-12657032367/20614528*log(1-2*x)+8202/2516421875*log(3+5*x)],
[(2+3*x)^8/((1-2*x)^3*(3+5*x)^3),x,2,5764801/170368/(1-2*x)^2+(-130943337/937024)/(1-2*x)-242028/3125*x-330237/20000*x^2-2187/1000*x^3+(-1/41593750)/(3+5*x)^2+(-54/45753125)/(3+5*x)-595421589/5153632*log(1-2*x)+1284/100656875*log(3+5*x)],
[(2+3*x)^7/((1-2*x)^3*(3+5*x)^3),x,2,823543/85184/(1-2*x)^2+(-7411887/234256)/(1-2*x)-95499/10000*x-2187/2000*x^2+(-1/8318750)/(3+5*x)^2+(-237/45753125)/(3+5*x)-25059237/1288408*log(1-2*x)+24279/503284375*log(3+5*x)],
[(2+3*x)^6/((1-2*x)^3*(3+5*x)^3),x,2,117649/42592/(1-2*x)^2+(-1563051/234256)/(1-2*x)-729/1000*x+(-1/1663750)/(3+5*x)^2+(-204/9150625)/(3+5*x)-6950895/2576816*log(1-2*x)+17547/100656875*log(3+5*x)],
[(2+3*x)^5/((1-2*x)^3*(3+5*x)^3),x,2,16807/21296/(1-2*x)^2+(-36015/29282)/(1-2*x)+(-1/332750)/(3+5*x)^2+(-171/1830125)/(3+5*x)-313845/1288408*log(1-2*x)+11904/20131375*log(3+5*x)],
[(2+3*x)^4/((1-2*x)^3*(3+5*x)^3),x,2,2401/10648/(1-2*x)^2+(-9261/58564)/(1-2*x)+(-1/66550)/(3+5*x)^2+(-138/366025)/(3+5*x)-294/161051*log(1-2*x)+294/161051*log(3+5*x)],
[(2+3*x)^3/((1-2*x)^3*(3+5*x)^3),x,2,343/5324/(1-2*x)^2+147/14641/(1-2*x)+(-1/13310)/(3+5*x)^2+(-21/14641)/(3+5*x)-777/161051*log(1-2*x)+777/161051*log(3+5*x)],
[(2+3*x)^2/((1-2*x)^3*(3+5*x)^3),x,2,49/2662/(1-2*x)^2+273/14641/(1-2*x)+(-1/2662)/(3+5*x)^2+(-72/14641)/(3+5*x)-1509/161051*log(1-2*x)+1509/161051*log(3+5*x)],
[(2+3*x)/((1-2*x)^3*(3+5*x)^3),x,2,7/1331/(1-2*x)^2+144/14641/(1-2*x)+(-5/2662)/(3+5*x)^2+(-195/14641)/(3+5*x)-1110/161051*log(1-2*x)+1110/161051*log(3+5*x)],
[1/((1-2*x)^3*(3+5*x)^3),x,2,2/1331/(1-2*x)^2+60/14641/(1-2*x)+(-25/2662)/(3+5*x)^2+(-150/14641)/(3+5*x)-600/161051*log(1-2*x)+600/161051*log(3+5*x)],
[1/((1-2*x)^3*(2+3*x)*(3+5*x)^3),x,2,4/9317/(1-2*x)^2+1104/717409/(1-2*x)+(-125/2662)/(3+5*x)^2+3375/14641/(3+5*x)-95232/55240493*log(1-2*x)-243/343*log(2+3*x)+114375/161051*log(3+5*x)],
[1/((1-2*x)^3*(2+3*x)^2*(3+5*x)^3),x,2,8/65219/(1-2*x)^2+2736/5021863/(1-2*x)+243/343/(2+3*x)+(-625/2662)/(3+5*x)^2+37500/14641/(3+5*x)-280752/386683451*log(1-2*x)-26973/2401*log(2+3*x)+1809375/161051*log(3+5*x)],
[1/((1-2*x)^3*(2+3*x)^3*(3+5*x)^3),x,2,16/456533/(1-2*x)^2+6528/35153041/(1-2*x)+243/686/(2+3*x)^2+26973/2401/(2+3*x)+(-3125/2662)/(3+5*x)^2+290625/14641/(3+5*x)-776928/2706784157*log(1-2*x)-1944972/16807*log(2+3*x)+18637500/161051*log(3+5*x)],
[1/((1-2*x)^3*(2+3*x)^4*(3+5*x)^3),x,2,32/3195731/(1-2*x)^2+15168/246071287/(1-2*x)+81/343/(2+3*x)^3+26973/4802/(2+3*x)^2+1944972/16807/(2+3*x)+(-15625/2662)/(3+5*x)^2+1968750/14641/(3+5*x)-2054400/18947489099*log(1-2*x)-115534350/117649*log(2+3*x)+158156250/161051*log(3+5*x)],

# Integrands of the form (a+b x)^m (c+d x)^n (e+f x)^p
[(a+b*x)^3*(c+d*x)^3*(e+f*x)^3,x,2,1/4*(b*c-a*d)^3*(b*e-a*f)^3*(a+b*x)^4/b^7+3/5*(b*c-a*d)^2*(b*e-a*f)^2*(b*d*e+b*c*f-2*a*d*f)*(a+b*x)^5/b^7+1/2*(b*c-a*d)*(b*e-a*f)*(5*a^2*d^2*f^2-5*a*b*d*f*(d*e+c*f)+b^2*(d^2*e^2+3*c*d*e*f+c^2*f^2))*(a+b*x)^6/b^7+1/7*(b*d*e+b*c*f-2*a*d*f)*(10*a^2*d^2*f^2-10*a*b*d*f*(d*e+c*f)+b^2*(d^2*e^2+8*c*d*e*f+c^2*f^2))*(a+b*x)^7/b^7+3/8*d*f*(5*a^2*d^2*f^2-5*a*b*d*f*(d*e+c*f)+b^2*(d^2*e^2+3*c*d*e*f+c^2*f^2))*(a+b*x)^8/b^7+1/3*d^2*f^2*(b*d*e+b*c*f-2*a*d*f)*(a+b*x)^9/b^7+1/10*d^3*f^3*(a+b*x)^10/b^7],
[(a+b*x)^2*(c+d*x)^2*(e+f*x)^2,x,2,1/3*(b*c-a*d)^2*(b*e-a*f)^2*(a+b*x)^3/b^5+1/2*(b*c-a*d)*(b*e-a*f)*(b*d*e+b*c*f-2*a*d*f)*(a+b*x)^4/b^5+1/5*(6*a^2*d^2*f^2-6*a*b*d*f*(d*e+c*f)+b^2*(d^2*e^2+4*c*d*e*f+c^2*f^2))*(a+b*x)^5/b^5+1/3*d*f*(b*d*e+b*c*f-2*a*d*f)*(a+b*x)^6/b^5+1/7*d^2*f^2*(a+b*x)^7/b^5],
[(a+b*x)*(c+d*x)*(e+f*x),x,2,a*c*e*x+1/2*(b*c*e+a*d*e+a*c*f)*x^2+1/3*(b*d*e+b*c*f+a*d*f)*x^3+1/4*b*d*f*x^4],
[1/((a+b*x)*(c+d*x)*(e+f*x)),x,2,b*log(a+b*x)/((b*c-a*d)*(b*e-a*f))-d*log(c+d*x)/((b*c-a*d)*(d*e-c*f))+f*log(e+f*x)/((b*e-a*f)*(d*e-c*f))],
[1/((a+b*x)^2*(c+d*x)^2*(e+f*x)^2),x,2,-b^3/((b*c-a*d)^2*(b*e-a*f)^2*(a+b*x))-d^3/((b*c-a*d)^2*(d*e-c*f)^2*(c+d*x))-f^3/((b*e-a*f)^2*(d*e-c*f)^2*(e+f*x))-2*b^3*(b*d*e+b*c*f-2*a*d*f)*log(a+b*x)/((b*c-a*d)^3*(b*e-a*f)^3)+2*d^3*(b*d*e-2*b*c*f+a*d*f)*log(c+d*x)/((b*c-a*d)^3*(d*e-c*f)^3)+2*f^3*(2*b*d*e-b*c*f-a*d*f)*log(e+f*x)/((b*e-a*f)^3*(d*e-c*f)^3)],
[1/((a+b*x)^3*(c+d*x)^3*(e+f*x)^3),x,2,-1/2*b^5/((b*c-a*d)^3*(b*e-a*f)^3*(a+b*x)^2)+3*b^5*(b*d*e+b*c*f-2*a*d*f)/((b*c-a*d)^4*(b*e-a*f)^4*(a+b*x))+1/2*d^5/((b*c-a*d)^3*(d*e-c*f)^3*(c+d*x)^2)+3*d^5*(b*d*e-2*b*c*f+a*d*f)/((b*c-a*d)^4*(d*e-c*f)^4*(c+d*x))-1/2*f^5/((b*e-a*f)^3*(d*e-c*f)^3*(e+f*x)^2)-3*f^5*(2*b*d*e-b*c*f-a*d*f)/((b*e-a*f)^4*(d*e-c*f)^4*(e+f*x))+3*b^5*(7*a^2*d^2*f^2-7*a*b*d*f*(d*e+c*f)+b^2*(2*d^2*e^2+3*c*d*e*f+2*c^2*f^2))*log(a+b*x)/((b*c-a*d)^5*(b*e-a*f)^5)-3*d^5*(2*a^2*d^2*f^2+a*b*d*f*(3*d*e-7*c*f)+b^2*(2*d^2*e^2-7*c*d*e*f+7*c^2*f^2))*log(c+d*x)/((b*c-a*d)^5*(d*e-c*f)^5)+3*f^5*(2*a^2*d^2*f^2-a*b*d*f*(7*d*e-3*c*f)+b^2*(7*d^2*e^2-7*c*d*e*f+2*c^2*f^2))*log(e+f*x)/((b*e-a*f)^5*(d*e-c*f)^5)],

# Integrands of the form (a+b x)^m (c+d x)^n (e+f x)^(p/2)
[(c+d*x)^(3/2)/((a+b*x)^2*(e+f*x)),x,6,-(3*b*d*e-2*b*c*f-a*d*f)*arctanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))*sqrt(b*c-a*d)/(b^(3/2)*(b*e-a*f)^2)+2*(d*e-c*f)^(3/2)*arctan(sqrt(f)*sqrt(c+d*x)/sqrt(d*e-c*f))/((b*e-a*f)^2*sqrt(f))-(b*c-a*d)*sqrt(c+d*x)/(b*(b*e-a*f)*(a+b*x))],

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

# m>0
[(a+b*x)*(A+B*x)*(d+e*x)^(7/2),x,2,2/9*(b*d-a*e)*(B*d-A*e)*(d+e*x)^(9/2)/e^3-2/11*(2*b*B*d-A*b*e-a*B*e)*(d+e*x)^(11/2)/e^3+2/13*b*B*(d+e*x)^(13/2)/e^3],
[(a+b*x)*(A+B*x)*(d+e*x)^(5/2),x,2,2/7*(b*d-a*e)*(B*d-A*e)*(d+e*x)^(7/2)/e^3-2/9*(2*b*B*d-A*b*e-a*B*e)*(d+e*x)^(9/2)/e^3+2/11*b*B*(d+e*x)^(11/2)/e^3],
[(a+b*x)*(A+B*x)*(d+e*x)^(3/2),x,2,2/5*(b*d-a*e)*(B*d-A*e)*(d+e*x)^(5/2)/e^3-2/7*(2*b*B*d-A*b*e-a*B*e)*(d+e*x)^(7/2)/e^3+2/9*b*B*(d+e*x)^(9/2)/e^3],
[(a+b*x)*(A+B*x)*sqrt(d+e*x),x,2,2/3*(b*d-a*e)*(B*d-A*e)*(d+e*x)^(3/2)/e^3-2/5*(2*b*B*d-A*b*e-a*B*e)*(d+e*x)^(5/2)/e^3+2/7*b*B*(d+e*x)^(7/2)/e^3],
[(a+b*x)*(A+B*x)/sqrt(d+e*x),x,2,-2/3*(2*b*B*d-A*b*e-a*B*e)*(d+e*x)^(3/2)/e^3+2/5*b*B*(d+e*x)^(5/2)/e^3+2*(b*d-a*e)*(B*d-A*e)*sqrt(d+e*x)/e^3],
[(a+b*x)*(A+B*x)/(d+e*x)^(3/2),x,2,2/3*b*B*(d+e*x)^(3/2)/e^3-2*(b*d-a*e)*(B*d-A*e)/(e^3*sqrt(d+e*x))-2*(2*b*B*d-A*b*e-a*B*e)*sqrt(d+e*x)/e^3],
[(a+b*x)*(A+B*x)/(d+e*x)^(5/2),x,2,-2/3*(b*d-a*e)*(B*d-A*e)/(e^3*(d+e*x)^(3/2))+2*(2*b*B*d-A*b*e-a*B*e)/(e^3*sqrt(d+e*x))+2*b*B*sqrt(d+e*x)/e^3],
[(a+b*x)*(A+B*x)/(d+e*x)^(7/2),x,2,-2/5*(b*d-a*e)*(B*d-A*e)/(e^3*(d+e*x)^(5/2))+2/3*(2*b*B*d-A*b*e-a*B*e)/(e^3*(d+e*x)^(3/2))-2*b*B/(e^3*sqrt(d+e*x))],
[(a+b*x)^2*(A+B*x)*(d+e*x)^(7/2),x,2,-2/9*(b*d-a*e)^2*(B*d-A*e)*(d+e*x)^(9/2)/e^4+2/11*(b*d-a*e)*(3*b*B*d-2*A*b*e-a*B*e)*(d+e*x)^(11/2)/e^4-2/13*b*(3*b*B*d-A*b*e-2*a*B*e)*(d+e*x)^(13/2)/e^4+2/15*b^2*B*(d+e*x)^(15/2)/e^4],
[(a+b*x)^2*(A+B*x)*(d+e*x)^(5/2),x,2,-2/7*(b*d-a*e)^2*(B*d-A*e)*(d+e*x)^(7/2)/e^4+2/9*(b*d-a*e)*(3*b*B*d-2*A*b*e-a*B*e)*(d+e*x)^(9/2)/e^4-2/11*b*(3*b*B*d-A*b*e-2*a*B*e)*(d+e*x)^(11/2)/e^4+2/13*b^2*B*(d+e*x)^(13/2)/e^4],
[(a+b*x)^2*(A+B*x)*(d+e*x)^(3/2),x,2,-2/5*(b*d-a*e)^2*(B*d-A*e)*(d+e*x)^(5/2)/e^4+2/7*(b*d-a*e)*(3*b*B*d-2*A*b*e-a*B*e)*(d+e*x)^(7/2)/e^4-2/9*b*(3*b*B*d-A*b*e-2*a*B*e)*(d+e*x)^(9/2)/e^4+2/11*b^2*B*(d+e*x)^(11/2)/e^4],
[(a+b*x)^2*(A+B*x)*sqrt(d+e*x),x,2,-2/3*(b*d-a*e)^2*(B*d-A*e)*(d+e*x)^(3/2)/e^4+2/5*(b*d-a*e)*(3*b*B*d-2*A*b*e-a*B*e)*(d+e*x)^(5/2)/e^4-2/7*b*(3*b*B*d-A*b*e-2*a*B*e)*(d+e*x)^(7/2)/e^4+2/9*b^2*B*(d+e*x)^(9/2)/e^4],
[(a+b*x)^2*(A+B*x)/sqrt(d+e*x),x,2,2/3*(b*d-a*e)*(3*b*B*d-2*A*b*e-a*B*e)*(d+e*x)^(3/2)/e^4-2/5*b*(3*b*B*d-A*b*e-2*a*B*e)*(d+e*x)^(5/2)/e^4+2/7*b^2*B*(d+e*x)^(7/2)/e^4-2*(b*d-a*e)^2*(B*d-A*e)*sqrt(d+e*x)/e^4],
[(a+b*x)^2*(A+B*x)/(d+e*x)^(3/2),x,2,-2/3*b*(3*b*B*d-A*b*e-2*a*B*e)*(d+e*x)^(3/2)/e^4+2/5*b^2*B*(d+e*x)^(5/2)/e^4+2*(b*d-a*e)^2*(B*d-A*e)/(e^4*sqrt(d+e*x))+2*(b*d-a*e)*(3*b*B*d-2*A*b*e-a*B*e)*sqrt(d+e*x)/e^4],
[(a+b*x)^2*(A+B*x)/(d+e*x)^(5/2),x,2,2/3*(b*d-a*e)^2*(B*d-A*e)/(e^4*(d+e*x)^(3/2))+2/3*b^2*B*(d+e*x)^(3/2)/e^4-2*(b*d-a*e)*(3*b*B*d-2*A*b*e-a*B*e)/(e^4*sqrt(d+e*x))-2*b*(3*b*B*d-A*b*e-2*a*B*e)*sqrt(d+e*x)/e^4],
[(a+b*x)^2*(A+B*x)/(d+e*x)^(7/2),x,2,2/5*(b*d-a*e)^2*(B*d-A*e)/(e^4*(d+e*x)^(5/2))-2/3*(b*d-a*e)*(3*b*B*d-2*A*b*e-a*B*e)/(e^4*(d+e*x)^(3/2))+2*b*(3*b*B*d-A*b*e-2*a*B*e)/(e^4*sqrt(d+e*x))+2*b^2*B*sqrt(d+e*x)/e^4],
[(a+b*x)^3*(A+B*x)*(d+e*x)^(7/2),x,2,2/9*(b*d-a*e)^3*(B*d-A*e)*(d+e*x)^(9/2)/e^5-2/11*(b*d-a*e)^2*(4*b*B*d-3*A*b*e-a*B*e)*(d+e*x)^(11/2)/e^5+6/13*b*(b*d-a*e)*(2*b*B*d-A*b*e-a*B*e)*(d+e*x)^(13/2)/e^5-2/15*b^2*(4*b*B*d-A*b*e-3*a*B*e)*(d+e*x)^(15/2)/e^5+2/17*b^3*B*(d+e*x)^(17/2)/e^5],
[(a+b*x)^3*(A+B*x)*(d+e*x)^(5/2),x,2,2/7*(b*d-a*e)^3*(B*d-A*e)*(d+e*x)^(7/2)/e^5-2/9*(b*d-a*e)^2*(4*b*B*d-3*A*b*e-a*B*e)*(d+e*x)^(9/2)/e^5+6/11*b*(b*d-a*e)*(2*b*B*d-A*b*e-a*B*e)*(d+e*x)^(11/2)/e^5-2/13*b^2*(4*b*B*d-A*b*e-3*a*B*e)*(d+e*x)^(13/2)/e^5+2/15*b^3*B*(d+e*x)^(15/2)/e^5],
[(a+b*x)^3*(A+B*x)*(d+e*x)^(3/2),x,2,2/5*(b*d-a*e)^3*(B*d-A*e)*(d+e*x)^(5/2)/e^5-2/7*(b*d-a*e)^2*(4*b*B*d-3*A*b*e-a*B*e)*(d+e*x)^(7/2)/e^5+2/3*b*(b*d-a*e)*(2*b*B*d-A*b*e-a*B*e)*(d+e*x)^(9/2)/e^5-2/11*b^2*(4*b*B*d-A*b*e-3*a*B*e)*(d+e*x)^(11/2)/e^5+2/13*b^3*B*(d+e*x)^(13/2)/e^5],
[(a+b*x)^3*(A+B*x)*sqrt(d+e*x),x,2,2/3*(b*d-a*e)^3*(B*d-A*e)*(d+e*x)^(3/2)/e^5-2/5*(b*d-a*e)^2*(4*b*B*d-3*A*b*e-a*B*e)*(d+e*x)^(5/2)/e^5+6/7*b*(b*d-a*e)*(2*b*B*d-A*b*e-a*B*e)*(d+e*x)^(7/2)/e^5-2/9*b^2*(4*b*B*d-A*b*e-3*a*B*e)*(d+e*x)^(9/2)/e^5+2/11*b^3*B*(d+e*x)^(11/2)/e^5],
[(a+b*x)^3*(A+B*x)/sqrt(d+e*x),x,2,-2/3*(b*d-a*e)^2*(4*b*B*d-3*A*b*e-a*B*e)*(d+e*x)^(3/2)/e^5+6/5*b*(b*d-a*e)*(2*b*B*d-A*b*e-a*B*e)*(d+e*x)^(5/2)/e^5-2/7*b^2*(4*b*B*d-A*b*e-3*a*B*e)*(d+e*x)^(7/2)/e^5+2/9*b^3*B*(d+e*x)^(9/2)/e^5+2*(b*d-a*e)^3*(B*d-A*e)*sqrt(d+e*x)/e^5],
[(a+b*x)^3*(A+B*x)/(d+e*x)^(3/2),x,2,2*b*(b*d-a*e)*(2*b*B*d-A*b*e-a*B*e)*(d+e*x)^(3/2)/e^5-2/5*b^2*(4*b*B*d-A*b*e-3*a*B*e)*(d+e*x)^(5/2)/e^5+2/7*b^3*B*(d+e*x)^(7/2)/e^5-2*(b*d-a*e)^3*(B*d-A*e)/(e^5*sqrt(d+e*x))-2*(b*d-a*e)^2*(4*b*B*d-3*A*b*e-a*B*e)*sqrt(d+e*x)/e^5],
[(a+b*x)^3*(A+B*x)/(d+e*x)^(5/2),x,2,-2/3*(b*d-a*e)^3*(B*d-A*e)/(e^5*(d+e*x)^(3/2))-2/3*b^2*(4*b*B*d-A*b*e-3*a*B*e)*(d+e*x)^(3/2)/e^5+2/5*b^3*B*(d+e*x)^(5/2)/e^5+2*(b*d-a*e)^2*(4*b*B*d-3*A*b*e-a*B*e)/(e^5*sqrt(d+e*x))+6*b*(b*d-a*e)*(2*b*B*d-A*b*e-a*B*e)*sqrt(d+e*x)/e^5],
[(a+b*x)^3*(A+B*x)/(d+e*x)^(7/2),x,2,-2/5*(b*d-a*e)^3*(B*d-A*e)/(e^5*(d+e*x)^(5/2))+2/3*(b*d-a*e)^2*(4*b*B*d-3*A*b*e-a*B*e)/(e^5*(d+e*x)^(3/2))+2/3*b^3*B*(d+e*x)^(3/2)/e^5-6*b*(b*d-a*e)*(2*b*B*d-A*b*e-a*B*e)/(e^5*sqrt(d+e*x))-2*b^2*(4*b*B*d-A*b*e-3*a*B*e)*sqrt(d+e*x)/e^5],

# m<0
[(A+B*x)*(d+e*x)^(7/2)/(a+b*x),x,7,2/3*(A*b-a*B)*(b*d-a*e)^2*(d+e*x)^(3/2)/b^4+2/5*(A*b-a*B)*(b*d-a*e)*(d+e*x)^(5/2)/b^3+2/7*(A*b-a*B)*(d+e*x)^(7/2)/b^2+2/9*B*(d+e*x)^(9/2)/(b*e)-2*(A*b-a*B)*(b*d-a*e)^(7/2)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/b^(11/2)+2*(A*b-a*B)*(b*d-a*e)^3*sqrt(d+e*x)/b^5],
[(A+B*x)*(d+e*x)^(5/2)/(a+b*x),x,6,2/3*(A*b-a*B)*(b*d-a*e)*(d+e*x)^(3/2)/b^3+2/5*(A*b-a*B)*(d+e*x)^(5/2)/b^2+2/7*B*(d+e*x)^(7/2)/(b*e)-2*(A*b-a*B)*(b*d-a*e)^(5/2)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/b^(9/2)+2*(A*b-a*B)*(b*d-a*e)^2*sqrt(d+e*x)/b^4],
[(A+B*x)*(d+e*x)^(3/2)/(a+b*x),x,5,2/3*(A*b-a*B)*(d+e*x)^(3/2)/b^2+2/5*B*(d+e*x)^(5/2)/(b*e)-2*(A*b-a*B)*(b*d-a*e)^(3/2)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/b^(7/2)+2*(A*b-a*B)*(b*d-a*e)*sqrt(d+e*x)/b^3],
[(A+B*x)*sqrt(d+e*x)/(a+b*x),x,4,2/3*B*(d+e*x)^(3/2)/(b*e)-2*(A*b-a*B)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b*d-a*e)/b^(5/2)+2*(A*b-a*B)*sqrt(d+e*x)/b^2],
[(A+B*x)/((a+b*x)*sqrt(d+e*x)),x,3,-2*(A*b-a*B)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(3/2)*sqrt(b*d-a*e))+2*B*sqrt(d+e*x)/(b*e)],
[(A+B*x)/((a+b*x)*(d+e*x)^(3/2)),x,3,-2*(A*b-a*B)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/((b*d-a*e)^(3/2)*sqrt(b))-2*(B*d-A*e)/(e*(b*d-a*e)*sqrt(d+e*x))],
[(A+B*x)/((a+b*x)*(d+e*x)^(5/2)),x,4,-2/3*(B*d-A*e)/(e*(b*d-a*e)*(d+e*x)^(3/2))-2*(A*b-a*B)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b)/(b*d-a*e)^(5/2)+2*(A*b-a*B)/((b*d-a*e)^2*sqrt(d+e*x))],
[(A+B*x)/((a+b*x)*(d+e*x)^(7/2)),x,5,-2/5*(B*d-A*e)/(e*(b*d-a*e)*(d+e*x)^(5/2))+2/3*(A*b-a*B)/((b*d-a*e)^2*(d+e*x)^(3/2))-2*b^(3/2)*(A*b-a*B)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b*d-a*e)^(7/2)+2*b*(A*b-a*B)/((b*d-a*e)^3*sqrt(d+e*x))],
[(A+B*x)*(d+e*x)^(7/2)/(a+b*x)^2,x,7,1/3*(b*d-a*e)*(2*b*B*d+7*A*b*e-9*a*B*e)*(d+e*x)^(3/2)/b^4+1/5*(2*b*B*d+7*A*b*e-9*a*B*e)*(d+e*x)^(5/2)/b^3+1/7*(2*b*B*d+7*A*b*e-9*a*B*e)*(d+e*x)^(7/2)/(b^2*(b*d-a*e))-(A*b-a*B)*(d+e*x)^(9/2)/(b*(b*d-a*e)*(a+b*x))-(b*d-a*e)^(5/2)*(2*b*B*d+7*A*b*e-9*a*B*e)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/b^(11/2)+(b*d-a*e)^2*(2*b*B*d+7*A*b*e-9*a*B*e)*sqrt(d+e*x)/b^5],
[(A+B*x)*(d+e*x)^(5/2)/(a+b*x)^2,x,6,1/3*(2*b*B*d+5*A*b*e-7*a*B*e)*(d+e*x)^(3/2)/b^3+1/5*(2*b*B*d+5*A*b*e-7*a*B*e)*(d+e*x)^(5/2)/(b^2*(b*d-a*e))-(A*b-a*B)*(d+e*x)^(7/2)/(b*(b*d-a*e)*(a+b*x))-(b*d-a*e)^(3/2)*(2*b*B*d+5*A*b*e-7*a*B*e)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/b^(9/2)+(b*d-a*e)*(2*b*B*d+5*A*b*e-7*a*B*e)*sqrt(d+e*x)/b^4],
[(A+B*x)*(d+e*x)^(3/2)/(a+b*x)^2,x,5,1/3*(2*b*B*d+3*A*b*e-5*a*B*e)*(d+e*x)^(3/2)/(b^2*(b*d-a*e))-(A*b-a*B)*(d+e*x)^(5/2)/(b*(b*d-a*e)*(a+b*x))-(2*b*B*d+3*A*b*e-5*a*B*e)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b*d-a*e)/b^(7/2)+(2*b*B*d+3*A*b*e-5*a*B*e)*sqrt(d+e*x)/b^3],
[(A+B*x)*sqrt(d+e*x)/(a+b*x)^2,x,4,-(A*b-a*B)*(d+e*x)^(3/2)/(b*(b*d-a*e)*(a+b*x))-(2*b*B*d+A*b*e-3*a*B*e)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(5/2)*sqrt(b*d-a*e))+(2*b*B*d+A*b*e-3*a*B*e)*sqrt(d+e*x)/(b^2*(b*d-a*e))],
[(A+B*x)/((a+b*x)^2*sqrt(d+e*x)),x,3,-(2*b*B*d-A*b*e-a*B*e)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(3/2)*(b*d-a*e)^(3/2))-(A*b-a*B)*sqrt(d+e*x)/(b*(b*d-a*e)*(a+b*x))],
[(A+B*x)/((a+b*x)^2*(d+e*x)^(3/2)),x,4,-(2*b*B*d-3*A*b*e+a*B*e)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/((b*d-a*e)^(5/2)*sqrt(b))+(2*b*B*d-3*A*b*e+a*B*e)/(b*(b*d-a*e)^2*sqrt(d+e*x))+(-A*b+a*B)/(b*(b*d-a*e)*(a+b*x)*sqrt(d+e*x))],
[(A+B*x)/((a+b*x)^2*(d+e*x)^(5/2)),x,5,1/3*(2*b*B*d-5*A*b*e+3*a*B*e)/(b*(b*d-a*e)^2*(d+e*x)^(3/2))+(-A*b+a*B)/(b*(b*d-a*e)*(a+b*x)*(d+e*x)^(3/2))-(2*b*B*d-5*A*b*e+3*a*B*e)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b)/(b*d-a*e)^(7/2)+(2*b*B*d-5*A*b*e+3*a*B*e)/((b*d-a*e)^3*sqrt(d+e*x))],
[(A+B*x)/((a+b*x)^2*(d+e*x)^(7/2)),x,6,1/5*(2*b*B*d-7*A*b*e+5*a*B*e)/(b*(b*d-a*e)^2*(d+e*x)^(5/2))+(-A*b+a*B)/(b*(b*d-a*e)*(a+b*x)*(d+e*x)^(5/2))+1/3*(2*b*B*d-7*A*b*e+5*a*B*e)/((b*d-a*e)^3*(d+e*x)^(3/2))-b^(3/2)*(2*b*B*d-7*A*b*e+5*a*B*e)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b*d-a*e)^(9/2)+b*(2*b*B*d-7*A*b*e+5*a*B*e)/((b*d-a*e)^4*sqrt(d+e*x))],
[(A+B*x)*(d+e*x)^(7/2)/(a+b*x)^3,x,7,7/12*e*(4*b*B*d+5*A*b*e-9*a*B*e)*(d+e*x)^(3/2)/b^4+7/20*e*(4*b*B*d+5*A*b*e-9*a*B*e)*(d+e*x)^(5/2)/(b^3*(b*d-a*e))-1/4*(4*b*B*d+5*A*b*e-9*a*B*e)*(d+e*x)^(7/2)/(b^2*(b*d-a*e)*(a+b*x))-1/2*(A*b-a*B)*(d+e*x)^(9/2)/(b*(b*d-a*e)*(a+b*x)^2)-7/4*e*(b*d-a*e)^(3/2)*(4*b*B*d+5*A*b*e-9*a*B*e)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/b^(11/2)+7/4*e*(b*d-a*e)*(4*b*B*d+5*A*b*e-9*a*B*e)*sqrt(d+e*x)/b^5],
[(A+B*x)*(d+e*x)^(5/2)/(a+b*x)^3,x,6,5/12*e*(4*b*B*d+3*A*b*e-7*a*B*e)*(d+e*x)^(3/2)/(b^3*(b*d-a*e))-1/4*(4*b*B*d+3*A*b*e-7*a*B*e)*(d+e*x)^(5/2)/(b^2*(b*d-a*e)*(a+b*x))-1/2*(A*b-a*B)*(d+e*x)^(7/2)/(b*(b*d-a*e)*(a+b*x)^2)-5/4*e*(4*b*B*d+3*A*b*e-7*a*B*e)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b*d-a*e)/b^(9/2)+5/4*e*(4*b*B*d+3*A*b*e-7*a*B*e)*sqrt(d+e*x)/b^4],
[(A+B*x)*(d+e*x)^(3/2)/(a+b*x)^3,x,5,-1/4*(4*b*B*d+A*b*e-5*a*B*e)*(d+e*x)^(3/2)/(b^2*(b*d-a*e)*(a+b*x))-1/2*(A*b-a*B)*(d+e*x)^(5/2)/(b*(b*d-a*e)*(a+b*x)^2)-3/4*e*(4*b*B*d+A*b*e-5*a*B*e)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(7/2)*sqrt(b*d-a*e))+3/4*e*(4*b*B*d+A*b*e-5*a*B*e)*sqrt(d+e*x)/(b^3*(b*d-a*e))],
[(A+B*x)*sqrt(d+e*x)/(a+b*x)^3,x,4,-1/2*(A*b-a*B)*(d+e*x)^(3/2)/(b*(b*d-a*e)*(a+b*x)^2)-1/4*e*(4*b*B*d-A*b*e-3*a*B*e)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(5/2)*(b*d-a*e)^(3/2))-1/4*(4*b*B*d-A*b*e-3*a*B*e)*sqrt(d+e*x)/(b^2*(b*d-a*e)*(a+b*x))],
[(A+B*x)/((a+b*x)^3*sqrt(d+e*x)),x,4,1/4*e*(4*b*B*d-3*A*b*e-a*B*e)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(3/2)*(b*d-a*e)^(5/2))-1/2*(A*b-a*B)*sqrt(d+e*x)/(b*(b*d-a*e)*(a+b*x)^2)-1/4*(4*b*B*d-3*A*b*e-a*B*e)*sqrt(d+e*x)/(b*(b*d-a*e)^2*(a+b*x))],
[(A+B*x)/((a+b*x)^3*(d+e*x)^(3/2)),x,5,3/4*e*(4*b*B*d-5*A*b*e+a*B*e)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/((b*d-a*e)^(7/2)*sqrt(b))-3/4*e*(4*b*B*d-5*A*b*e+a*B*e)/(b*(b*d-a*e)^3*sqrt(d+e*x))+1/2*(-A*b+a*B)/(b*(b*d-a*e)*(a+b*x)^2*sqrt(d+e*x))+1/4*(-4*b*B*d+5*A*b*e-a*B*e)/(b*(b*d-a*e)^2*(a+b*x)*sqrt(d+e*x))],
[(A+B*x)/((a+b*x)^3*(d+e*x)^(5/2)),x,6,-5/12*e*(4*b*B*d-7*A*b*e+3*a*B*e)/(b*(b*d-a*e)^3*(d+e*x)^(3/2))+1/2*(-A*b+a*B)/(b*(b*d-a*e)*(a+b*x)^2*(d+e*x)^(3/2))+1/4*(-4*b*B*d+7*A*b*e-3*a*B*e)/(b*(b*d-a*e)^2*(a+b*x)*(d+e*x)^(3/2))+5/4*e*(4*b*B*d-7*A*b*e+3*a*B*e)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b)/(b*d-a*e)^(9/2)-5/4*e*(4*b*B*d-7*A*b*e+3*a*B*e)/((b*d-a*e)^4*sqrt(d+e*x))],
[(A+B*x)/((a+b*x)^3*(d+e*x)^(7/2)),x,7,-7/20*e*(4*b*B*d-9*A*b*e+5*a*B*e)/(b*(b*d-a*e)^3*(d+e*x)^(5/2))+1/2*(-A*b+a*B)/(b*(b*d-a*e)*(a+b*x)^2*(d+e*x)^(5/2))+1/4*(-4*b*B*d+9*A*b*e-5*a*B*e)/(b*(b*d-a*e)^2*(a+b*x)*(d+e*x)^(5/2))-7/12*e*(4*b*B*d-9*A*b*e+5*a*B*e)/((b*d-a*e)^4*(d+e*x)^(3/2))+7/4*b^(3/2)*e*(4*b*B*d-9*A*b*e+5*a*B*e)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b*d-a*e)^(11/2)-7/4*b*e*(4*b*B*d-9*A*b*e+5*a*B*e)/((b*d-a*e)^5*sqrt(d+e*x))],

# Integrands of the form (a+b x)^m / (c+d x) (e+f x)^(p/2)
[(a+b*x)*(e+f*x)^(5/2)/(c+d*x),x,6,-2/3*(b*c-a*d)*(d*e-c*f)*(e+f*x)^(3/2)/d^3-2/5*(b*c-a*d)*(e+f*x)^(5/2)/d^2+2/7*b*(e+f*x)^(7/2)/(d*f)+2*(b*c-a*d)*(d*e-c*f)^(5/2)*arctanh(sqrt(d)*sqrt(e+f*x)/sqrt(d*e-c*f))/d^(9/2)-2*(b*c-a*d)*(d*e-c*f)^2*sqrt(e+f*x)/d^4],
[(a+b*x)*(e+f*x)^(3/2)/(c+d*x),x,5,-2/3*(b*c-a*d)*(e+f*x)^(3/2)/d^2+2/5*b*(e+f*x)^(5/2)/(d*f)+2*(b*c-a*d)*(d*e-c*f)^(3/2)*arctanh(sqrt(d)*sqrt(e+f*x)/sqrt(d*e-c*f))/d^(7/2)-2*(b*c-a*d)*(d*e-c*f)*sqrt(e+f*x)/d^3],
[(a+b*x)*(e+f*x)^(1/2)/(c+d*x),x,4,2/3*b*(e+f*x)^(3/2)/(d*f)+2*(b*c-a*d)*arctanh(sqrt(d)*sqrt(e+f*x)/sqrt(d*e-c*f))*sqrt(d*e-c*f)/d^(5/2)-2*(b*c-a*d)*sqrt(e+f*x)/d^2],
[(a+b*x)/((c+d*x)*(e+f*x)^(1/2)),x,3,2*(b*c-a*d)*arctanh(sqrt(d)*sqrt(e+f*x)/sqrt(d*e-c*f))/(d^(3/2)*sqrt(d*e-c*f))+2*b*sqrt(e+f*x)/(d*f)],
[(a+b*x)/((c+d*x)*(e+f*x)^(3/2)),x,3,2*(b*c-a*d)*arctanh(sqrt(d)*sqrt(e+f*x)/sqrt(d*e-c*f))/((d*e-c*f)^(3/2)*sqrt(d))-2*(b*e-a*f)/(f*(d*e-c*f)*sqrt(e+f*x))],
[(a+b*x)/((c+d*x)*(e+f*x)^(5/2)),x,4,-2/3*(b*e-a*f)/(f*(d*e-c*f)*(e+f*x)^(3/2))+2*(b*c-a*d)*arctanh(sqrt(d)*sqrt(e+f*x)/sqrt(d*e-c*f))*sqrt(d)/(d*e-c*f)^(5/2)-2*(b*c-a*d)/((d*e-c*f)^2*sqrt(e+f*x))],
[(a+b*x)/((c+d*x)*(e+f*x)^(7/2)),x,5,-2/5*(b*e-a*f)/(f*(d*e-c*f)*(e+f*x)^(5/2))-2/3*(b*c-a*d)/((d*e-c*f)^2*(e+f*x)^(3/2))+2*d^(3/2)*(b*c-a*d)*arctanh(sqrt(d)*sqrt(e+f*x)/sqrt(d*e-c*f))/(d*e-c*f)^(7/2)-2*d*(b*c-a*d)/((d*e-c*f)^3*sqrt(e+f*x))],
[(a+b*x)/((c+d*x)*(e+f*x)^(9/2)),x,6,-2/7*(b*e-a*f)/(f*(d*e-c*f)*(e+f*x)^(7/2))-2/5*(b*c-a*d)/((d*e-c*f)^2*(e+f*x)^(5/2))-2/3*d*(b*c-a*d)/((d*e-c*f)^3*(e+f*x)^(3/2))+2*d^(5/2)*(b*c-a*d)*arctanh(sqrt(d)*sqrt(e+f*x)/sqrt(d*e-c*f))/(d*e-c*f)^(9/2)-2*d^2*(b*c-a*d)/((d*e-c*f)^4*sqrt(e+f*x))],
[(a+b*x)^2*(e+f*x)^(5/2)/(c+d*x),x,7,2/3*(b*c-a*d)^2*(d*e-c*f)*(e+f*x)^(3/2)/d^4+2/5*(b*c-a*d)^2*(e+f*x)^(5/2)/d^3-2/7*b*(b*d*e+b*c*f-2*a*d*f)*(e+f*x)^(7/2)/(d^2*f^2)+2/9*b^2*(e+f*x)^(9/2)/(d*f^2)-2*(b*c-a*d)^2*(d*e-c*f)^(5/2)*arctanh(sqrt(d)*sqrt(e+f*x)/sqrt(d*e-c*f))/d^(11/2)+2*(b*c-a*d)^2*(d*e-c*f)^2*sqrt(e+f*x)/d^5],
[(a+b*x)^2*(e+f*x)^(3/2)/(c+d*x),x,6,2/3*(b*c-a*d)^2*(e+f*x)^(3/2)/d^3-2/5*b*(b*d*e+b*c*f-2*a*d*f)*(e+f*x)^(5/2)/(d^2*f^2)+2/7*b^2*(e+f*x)^(7/2)/(d*f^2)-2*(b*c-a*d)^2*(d*e-c*f)^(3/2)*arctanh(sqrt(d)*sqrt(e+f*x)/sqrt(d*e-c*f))/d^(9/2)+2*(b*c-a*d)^2*(d*e-c*f)*sqrt(e+f*x)/d^4],
[(a+b*x)^2*(e+f*x)^(1/2)/(c+d*x),x,5,-2/3*b*(b*d*e+b*c*f-2*a*d*f)*(e+f*x)^(3/2)/(d^2*f^2)+2/5*b^2*(e+f*x)^(5/2)/(d*f^2)-2*(b*c-a*d)^2*arctanh(sqrt(d)*sqrt(e+f*x)/sqrt(d*e-c*f))*sqrt(d*e-c*f)/d^(7/2)+2*(b*c-a*d)^2*sqrt(e+f*x)/d^3],
[(a+b*x)^2/((c+d*x)*(e+f*x)^(1/2)),x,4,2/3*b^2*(e+f*x)^(3/2)/(d*f^2)-2*(b*c-a*d)^2*arctanh(sqrt(d)*sqrt(e+f*x)/sqrt(d*e-c*f))/(d^(5/2)*sqrt(d*e-c*f))-2*b*(b*d*e+b*c*f-2*a*d*f)*sqrt(e+f*x)/(d^2*f^2)],
[(a+b*x)^2/((c+d*x)*(e+f*x)^(3/2)),x,4,-2*(b*c-a*d)^2*arctanh(sqrt(d)*sqrt(e+f*x)/sqrt(d*e-c*f))/(d^(3/2)*(d*e-c*f)^(3/2))+2*(b*e-a*f)^2/(f^2*(d*e-c*f)*sqrt(e+f*x))+2*b^2*sqrt(e+f*x)/(d*f^2)],
[(a+b*x)^2/((c+d*x)*(e+f*x)^(5/2)),x,4,2/3*(b*e-a*f)^2/(f^2*(d*e-c*f)*(e+f*x)^(3/2))-2*(b*c-a*d)^2*arctanh(sqrt(d)*sqrt(e+f*x)/sqrt(d*e-c*f))/((d*e-c*f)^(5/2)*sqrt(d))-2*(b*e-a*f)*(b*d*e-2*b*c*f+a*d*f)/(f^2*(d*e-c*f)^2*sqrt(e+f*x))],
[(a+b*x)^2/((c+d*x)*(e+f*x)^(7/2)),x,4,2/5*(b*e-a*f)^2/(f^2*(d*e-c*f)*(e+f*x)^(5/2))-2/3*(b*e-a*f)*(b*d*e-2*b*c*f+a*d*f)/(f^2*(d*e-c*f)^2*(e+f*x)^(3/2))-2*(b*c-a*d)^2*arctanh(sqrt(d)*sqrt(e+f*x)/sqrt(d*e-c*f))*sqrt(d)/(d*e-c*f)^(7/2)+2*(b*c-a*d)^2/((d*e-c*f)^3*sqrt(e+f*x))],
[(a+b*x)^2/((c+d*x)*(e+f*x)^(9/2)),x,4,2/7*(b*e-a*f)^2/(f^2*(d*e-c*f)*(e+f*x)^(7/2))-2/5*(b*e-a*f)*(b*d*e-2*b*c*f+a*d*f)/(f^2*(d*e-c*f)^2*(e+f*x)^(5/2))+2/3*(b*c-a*d)^2/((d*e-c*f)^3*(e+f*x)^(3/2))-2*d^(3/2)*(b*c-a*d)^2*arctanh(sqrt(d)*sqrt(e+f*x)/sqrt(d*e-c*f))/(d*e-c*f)^(9/2)+2*d*(b*c-a*d)^2/((d*e-c*f)^4*sqrt(e+f*x))],
[(a+b*x)^3*(e+f*x)^(5/2)/(c+d*x),x,7,-2/3*(b*c-a*d)^3*(d*e-c*f)*(e+f*x)^(3/2)/d^5-2/5*(b*c-a*d)^3*(e+f*x)^(5/2)/d^4+2/7*b*(3*a^2*d^2*f^2-3*a*b*d*f*(d*e+c*f)+b^2*(d^2*e^2+c*d*e*f+c^2*f^2))*(e+f*x)^(7/2)/(d^3*f^3)-2/9*b^2*(2*b*d*e+b*c*f-3*a*d*f)*(e+f*x)^(9/2)/(d^2*f^3)+2/11*b^3*(e+f*x)^(11/2)/(d*f^3)+2*(b*c-a*d)^3*(d*e-c*f)^(5/2)*arctanh(sqrt(d)*sqrt(e+f*x)/sqrt(d*e-c*f))/d^(13/2)-2*(b*c-a*d)^3*(d*e-c*f)^2*sqrt(e+f*x)/d^6],
[(a+b*x)^3*(e+f*x)^(3/2)/(c+d*x),x,6,-2/3*(b*c-a*d)^3*(e+f*x)^(3/2)/d^4+2/5*b*(3*a^2*d^2*f^2-3*a*b*d*f*(d*e+c*f)+b^2*(d^2*e^2+c*d*e*f+c^2*f^2))*(e+f*x)^(5/2)/(d^3*f^3)-2/7*b^2*(2*b*d*e+b*c*f-3*a*d*f)*(e+f*x)^(7/2)/(d^2*f^3)+2/9*b^3*(e+f*x)^(9/2)/(d*f^3)+2*(b*c-a*d)^3*(d*e-c*f)^(3/2)*arctanh(sqrt(d)*sqrt(e+f*x)/sqrt(d*e-c*f))/d^(11/2)-2*(b*c-a*d)^3*(d*e-c*f)*sqrt(e+f*x)/d^5],
[(a+b*x)^3*(e+f*x)^(1/2)/(c+d*x),x,5,2/3*b*(3*a^2*d^2*f^2-3*a*b*d*f*(d*e+c*f)+b^2*(d^2*e^2+c*d*e*f+c^2*f^2))*(e+f*x)^(3/2)/(d^3*f^3)-2/5*b^2*(2*b*d*e+b*c*f-3*a*d*f)*(e+f*x)^(5/2)/(d^2*f^3)+2/7*b^3*(e+f*x)^(7/2)/(d*f^3)+2*(b*c-a*d)^3*arctanh(sqrt(d)*sqrt(e+f*x)/sqrt(d*e-c*f))*sqrt(d*e-c*f)/d^(9/2)-2*(b*c-a*d)^3*sqrt(e+f*x)/d^4],
[(a+b*x)^3/((c+d*x)*(e+f*x)^(1/2)),x,4,-2/3*b^2*(2*b*d*e+b*c*f-3*a*d*f)*(e+f*x)^(3/2)/(d^2*f^3)+2/5*b^3*(e+f*x)^(5/2)/(d*f^3)+2*(b*c-a*d)^3*arctanh(sqrt(d)*sqrt(e+f*x)/sqrt(d*e-c*f))/(d^(7/2)*sqrt(d*e-c*f))+2*b*(3*a^2*d^2*f^2-3*a*b*d*f*(d*e+c*f)+b^2*(d^2*e^2+c*d*e*f+c^2*f^2))*sqrt(e+f*x)/(d^3*f^3)],
[(a+b*x)^3/((c+d*x)*(e+f*x)^(3/2)),x,6,2/3*b^3*(e+f*x)^(3/2)/(d*f^3)+2*(b*c-a*d)^3*arctanh(sqrt(d)*sqrt(e+f*x)/sqrt(d*e-c*f))/(d^(5/2)*(d*e-c*f)^(3/2))-2*(b*e-a*f)^3/(f^3*(d*e-c*f)*sqrt(e+f*x))-2*b^2*(2*b*d*e+b*c*f-3*a*d*f)*sqrt(e+f*x)/(d^2*f^3),2/3*b^3*(e+f*x)^(3/2)/(d*f^3)+2*(b*c-a*d)^3*arctanh(sqrt(d)*sqrt(e+f*x)/sqrt(d*e-c*f))/(d^(5/2)*(d*e-c*f)^(3/2))-2*(b*e-a*f)^3/(f^3*(d*e-c*f)*sqrt(e+f*x))-2*b^3*e*sqrt(e+f*x)/(d*f^3)-2*b^2*(b*d*e+b*c*f-3*a*d*f)*sqrt(e+f*x)/(d^2*f^3)],
[(a+b*x)^3/((c+d*x)*(e+f*x)^(5/2)),x,4,-2/3*(b*e-a*f)^3/(f^3*(d*e-c*f)*(e+f*x)^(3/2))+2*(b*c-a*d)^3*arctanh(sqrt(d)*sqrt(e+f*x)/sqrt(d*e-c*f))/(d^(3/2)*(d*e-c*f)^(5/2))+2*(b*e-a*f)^2*(2*b*d*e-3*b*c*f+a*d*f)/(f^3*(d*e-c*f)^2*sqrt(e+f*x))+2*b^3*sqrt(e+f*x)/(d*f^3)],
[(a+b*x)^3/((c+d*x)*(e+f*x)^(7/2)),x,4,-2/5*(b*e-a*f)^3/(f^3*(d*e-c*f)*(e+f*x)^(5/2))+2/3*(b*e-a*f)^2*(2*b*d*e-3*b*c*f+a*d*f)/(f^3*(d*e-c*f)^2*(e+f*x)^(3/2))+2*(b*c-a*d)^3*arctanh(sqrt(d)*sqrt(e+f*x)/sqrt(d*e-c*f))/((d*e-c*f)^(7/2)*sqrt(d))-2*(b*e-a*f)*(a^2*d^2*f^2+a*b*d*f*(d*e-3*c*f)+b^2*(d^2*e^2-3*c*d*e*f+3*c^2*f^2))/(f^3*(d*e-c*f)^3*sqrt(e+f*x))],
[(a+b*x)^3/((c+d*x)*(e+f*x)^(9/2)),x,4,-2/7*(b*e-a*f)^3/(f^3*(d*e-c*f)*(e+f*x)^(7/2))+2/5*(b*e-a*f)^2*(2*b*d*e-3*b*c*f+a*d*f)/(f^3*(d*e-c*f)^2*(e+f*x)^(5/2))-2/3*(b*e-a*f)*(a^2*d^2*f^2+a*b*d*f*(d*e-3*c*f)+b^2*(d^2*e^2-3*c*d*e*f+3*c^2*f^2))/(f^3*(d*e-c*f)^3*(e+f*x)^(3/2))+2*(b*c-a*d)^3*arctanh(sqrt(d)*sqrt(e+f*x)/sqrt(d*e-c*f))*sqrt(d)/(d*e-c*f)^(9/2)-2*(b*c-a*d)^3/((d*e-c*f)^4*sqrt(e+f*x))],

# Integrands of the form (2+3 x)^m (3+5 x)^n (1-2 x)^(1/2)

# n>0
[(2+3*x)^6*(3+5*x)*sqrt(1-2*x),x,2,-1294139/384*(1-2*x)^(3/2)+3916031/640*(1-2*x)^(5/2)-725445/128*(1-2*x)^(7/2)+406455/128*(1-2*x)^(9/2)-1580985/1408*(1-2*x)^(11/2)+409941/1664*(1-2*x)^(13/2)-19683/640*(1-2*x)^(15/2)+3645/2176*(1-2*x)^(17/2)],
[(2+3*x)^5*(3+5*x)*sqrt(1-2*x),x,2,-184877/192*(1-2*x)^(3/2)+12005/8*(1-2*x)^(5/2)-74235/64*(1-2*x)^(7/2)+4165/8*(1-2*x)^(9/2)-97335/704*(1-2*x)^(11/2)+81/4*(1-2*x)^(13/2)-81/64*(1-2*x)^(15/2)],
[(2+3*x)^4*(3+5*x)*sqrt(1-2*x),x,2,-26411/96*(1-2*x)^(3/2)+57281/160*(1-2*x)^(5/2)-3549/16*(1-2*x)^(7/2)+1197/16*(1-2*x)^(9/2)-4671/352*(1-2*x)^(11/2)+405/416*(1-2*x)^(13/2)],
[(2+3*x)^3*(3+5*x)*sqrt(1-2*x),x,2,-3773/48*(1-2*x)^(3/2)+3283/40*(1-2*x)^(5/2)-153/4*(1-2*x)^(7/2)+69/8*(1-2*x)^(9/2)-135/176*(1-2*x)^(11/2)],
[(2+3*x)^2*(3+5*x)*sqrt(1-2*x),x,2,-539/24*(1-2*x)^(3/2)+707/40*(1-2*x)^(5/2)-309/56*(1-2*x)^(7/2)+5/8*(1-2*x)^(9/2)],
[(2+3*x)*(3+5*x)*sqrt(1-2*x),x,2,-77/12*(1-2*x)^(3/2)+17/5*(1-2*x)^(5/2)-15/28*(1-2*x)^(7/2)],
[(3+5*x)*sqrt(1-2*x),x,2,-11/6*(1-2*x)^(3/2)+1/2*(1-2*x)^(5/2)],
[(3+5*x)*sqrt(1-2*x)/(2+3*x),x,4,-5/9*(1-2*x)^(3/2)+2/9*arctanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(7/3)-2/9*sqrt(1-2*x)],
[(3+5*x)*sqrt(1-2*x)/(2+3*x)^2,x,4,1/21*(1-2*x)^(3/2)/(2+3*x)-8*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+8/7*sqrt(1-2*x)],
[(3+5*x)*sqrt(1-2*x)/(2+3*x)^3,x,4,1/42*(1-2*x)^(3/2)/(2+3*x)^2+23/21*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-23/42*sqrt(1-2*x)/(2+3*x)],
[(3+5*x)*sqrt(1-2*x)/(2+3*x)^4,x,5,1/63*(1-2*x)^(3/2)/(2+3*x)^3+34/441*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-17/63*sqrt(1-2*x)/(2+3*x)^2+17/441*sqrt(1-2*x)/(2+3*x)],
[(3+5*x)*sqrt(1-2*x)/(2+3*x)^5,x,6,1/84*(1-2*x)^(3/2)/(2+3*x)^4+5/1372*arctanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-5/28*sqrt(1-2*x)/(2+3*x)^3+5/392*sqrt(1-2*x)/(2+3*x)^2+15/2744*sqrt(1-2*x)/(2+3*x)],
[(3+5*x)*sqrt(1-2*x)/(2+3*x)^6,x,7,1/105*(1-2*x)^(3/2)/(2+3*x)^5+2/1029*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-2/15*sqrt(1-2*x)/(2+3*x)^4+2/315*sqrt(1-2*x)/(2+3*x)^3+1/441*sqrt(1-2*x)/(2+3*x)^2+1/1029*sqrt(1-2*x)/(2+3*x)],
[(2+3*x)^4*(3+5*x)^2*sqrt(1-2*x),x,2,-290521/192*(1-2*x)^(3/2)+381073/160*(1-2*x)^(5/2)-118993/64*(1-2*x)^(7/2)+40453/48*(1-2*x)^(9/2)-159111/704*(1-2*x)^(11/2)+13905/416*(1-2*x)^(13/2)-135/64*(1-2*x)^(15/2)],
[(2+3*x)^3*(3+5*x)^2*sqrt(1-2*x),x,2,-41503/96*(1-2*x)^(3/2)+91091/160*(1-2*x)^(5/2)-5711/16*(1-2*x)^(7/2)+1949/16*(1-2*x)^(9/2)-7695/352*(1-2*x)^(11/2)+675/416*(1-2*x)^(13/2)],
[(2+3*x)^2*(3+5*x)^2*sqrt(1-2*x),x,2,-5929/48*(1-2*x)^(3/2)+1309/10*(1-2*x)^(5/2)-3467/56*(1-2*x)^(7/2)+85/6*(1-2*x)^(9/2)-225/176*(1-2*x)^(11/2)],
[(2+3*x)*(3+5*x)^2*sqrt(1-2*x),x,2,-847/24*(1-2*x)^(3/2)+1133/40*(1-2*x)^(5/2)-505/56*(1-2*x)^(7/2)+25/24*(1-2*x)^(9/2)],
[(3+5*x)^2*sqrt(1-2*x),x,2,-121/12*(1-2*x)^(3/2)+11/2*(1-2*x)^(5/2)-25/28*(1-2*x)^(7/2)],
[(3+5*x)^2*sqrt(1-2*x)/(2+3*x),x,5,-155/54*(1-2*x)^(3/2)+5/6*(1-2*x)^(5/2)-2/27*arctanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(7/3)+2/27*sqrt(1-2*x)],
[(3+5*x)^2*sqrt(1-2*x)/(2+3*x)^2,x,5,-25/27*(1-2*x)^(3/2)-1/63*(1-2*x)^(3/2)/(2+3*x)+142/27*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-142/189*sqrt(1-2*x)],
[(3+5*x)^2*sqrt(1-2*x)/(2+3*x)^3,x,5,-1/126*(1-2*x)^(3/2)/(2+3*x)^2+139/882*(1-2*x)^(3/2)/(2+3*x)-863/63*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+863/441*sqrt(1-2*x)],
[(3+5*x)^2*sqrt(1-2*x)/(2+3*x)^4,x,5,-1/189*(1-2*x)^(3/2)/(2+3*x)^3+23/294*(1-2*x)^(3/2)/(2+3*x)^2+2381/1323*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-2381/2646*sqrt(1-2*x)/(2+3*x)],
[(3+5*x)^2*sqrt(1-2*x)/(2+3*x)^5,x,6,-1/252*(1-2*x)^(3/2)/(2+3*x)^4+275/5292*(1-2*x)^(3/2)/(2+3*x)^3+4625/37044*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-4625/10584*sqrt(1-2*x)/(2+3*x)^2+4625/74088*sqrt(1-2*x)/(2+3*x)],
[(3+5*x)^2*sqrt(1-2*x)/(2+3*x)^6,x,7,-1/315*(1-2*x)^(3/2)/(2+3*x)^5+7/180*(1-2*x)^(3/2)/(2+3*x)^4+31/1764*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-31/108*sqrt(1-2*x)/(2+3*x)^3+31/1512*sqrt(1-2*x)/(2+3*x)^2+31/3528*sqrt(1-2*x)/(2+3*x)],
[(3+5*x)^2*sqrt(1-2*x)/(2+3*x)^7,x,8,-1/378*(1-2*x)^(3/2)/(2+3*x)^6+137/4410*(1-2*x)^(3/2)/(2+3*x)^5+1613/518616*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-1613/7560*sqrt(1-2*x)/(2+3*x)^4+1613/158760*sqrt(1-2*x)/(2+3*x)^3+1613/444528*sqrt(1-2*x)/(2+3*x)^2+1613/1037232*sqrt(1-2*x)/(2+3*x)],
[(2+3*x)^4*(3+5*x)^3*sqrt(1-2*x),x,2,-3195731/384*(1-2*x)^(3/2)+9836211/640*(1-2*x)^(5/2)-1853313/128*(1-2*x)^(7/2)+9504551/1152*(1-2*x)^(9/2)-4177401/1408*(1-2*x)^(11/2)+1101465/1664*(1-2*x)^(13/2)-10755/128*(1-2*x)^(15/2)+10125/2176*(1-2*x)^(17/2)],
[(2+3*x)^3*(3+5*x)^3*sqrt(1-2*x),x,2,-456533/192*(1-2*x)^(3/2)+302379/80*(1-2*x)^(5/2)-190707/64*(1-2*x)^(7/2)+98209/72*(1-2*x)^(9/2)-260055/704*(1-2*x)^(11/2)+11475/208*(1-2*x)^(13/2)-225/64*(1-2*x)^(15/2)],
[(2+3*x)^2*(3+5*x)^3*sqrt(1-2*x),x,2,-65219/96*(1-2*x)^(3/2)+144837/160*(1-2*x)^(5/2)-64317/112*(1-2*x)^(7/2)+28555/144*(1-2*x)^(9/2)-12675/352*(1-2*x)^(11/2)+1125/416*(1-2*x)^(13/2)],
[(2+3*x)*(3+5*x)^3*sqrt(1-2*x),x,2,-9317/48*(1-2*x)^(3/2)+8349/40*(1-2*x)^(5/2)-2805/28*(1-2*x)^(7/2)+1675/72*(1-2*x)^(9/2)-375/176*(1-2*x)^(11/2)],
[(3+5*x)^3*sqrt(1-2*x),x,2,-1331/24*(1-2*x)^(3/2)+363/8*(1-2*x)^(5/2)-825/56*(1-2*x)^(7/2)+125/72*(1-2*x)^(9/2)],
[(3+5*x)^3*sqrt(1-2*x)/(2+3*x),x,5,-5135/324*(1-2*x)^(3/2)+80/9*(1-2*x)^(5/2)-125/84*(1-2*x)^(7/2)+2/81*arctanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(7/3)-2/81*sqrt(1-2*x)],
[(3+5*x)^3*sqrt(1-2*x)/(2+3*x)^2,x,5,-212/81*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+7/9*(3+5*x)^2*sqrt(1-2*x)-1/3*(3+5*x)^3*sqrt(1-2*x)/(2+3*x)-2/81*(211+170*x)*sqrt(1-2*x)],
[(3+5*x)^3*sqrt(1-2*x)/(2+3*x)^3,x,5,7559/567*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-53/63*(3+5*x)^2*sqrt(1-2*x)/(2+3*x)-1/6*(3+5*x)^3*sqrt(1-2*x)/(2+3*x)^2+5/1134*(323+2815*x)*sqrt(1-2*x)],
[(3+5*x)^3*sqrt(1-2*x)/(2+3*x)^4,x,5,-92996/3969*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-53/189*(3+5*x)^2*sqrt(1-2*x)/(2+3*x)^2-1/9*(3+5*x)^3*sqrt(1-2*x)/(2+3*x)^3+2/3969*(18016+26075*x)*sqrt(1-2*x)/(2+3*x)],
[(3+5*x)^3*sqrt(1-2*x)/(2+3*x)^5,x,5,328715/111132*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-53/378*(3+5*x)^2*sqrt(1-2*x)/(2+3*x)^3-1/12*(3+5*x)^3*sqrt(1-2*x)/(2+3*x)^4-5/222264*(70429+110981*x)*sqrt(1-2*x)/(2+3*x)^2],
[(3+5*x)^3*sqrt(1-2*x)/(2+3*x)^6,x,6,11237/55566*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+11237/111132*sqrt(1-2*x)/(2+3*x)-53/630*(3+5*x)^2*sqrt(1-2*x)/(2+3*x)^4-1/15*(3+5*x)^3*sqrt(1-2*x)/(2+3*x)^5-1/79380*(37224+59665*x)*sqrt(1-2*x)/(2+3*x)^3],
[(3+5*x)^3*sqrt(1-2*x)/(2+3*x)^7,x,7,43957/1555848*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+43957/1333584*sqrt(1-2*x)/(2+3*x)^2+43957/3111696*sqrt(1-2*x)/(2+3*x)-53/945*(3+5*x)^2*sqrt(1-2*x)/(2+3*x)^5-1/18*(3+5*x)^3*sqrt(1-2*x)/(2+3*x)^6-1/476280*(98995+160029*x)*sqrt(1-2*x)/(2+3*x)^4],
[(3+5*x)^3*sqrt(1-2*x)/(2+3*x)^8,x,8,47434/9529569*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+47434/2917215*sqrt(1-2*x)/(2+3*x)^3+23717/4084101*sqrt(1-2*x)/(2+3*x)^2+23717/9529569*sqrt(1-2*x)/(2+3*x)-53/1323*(3+5*x)^2*sqrt(1-2*x)/(2+3*x)^6-1/21*(3+5*x)^3*sqrt(1-2*x)/(2+3*x)^7-2/972405*(54227+88099*x)*sqrt(1-2*x)/(2+3*x)^5],

# n<0
[(2+3*x)^4*sqrt(1-2*x)/(3+5*x),x,5,-45473/5000*(1-2*x)^(3/2)+34371/5000*(1-2*x)^(5/2)-2889/1400*(1-2*x)^(7/2)+9/40*(1-2*x)^(9/2)-2/3125*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+2/3125*sqrt(1-2*x)],
[(2+3*x)^3*sqrt(1-2*x)/(3+5*x),x,5,-1299/500*(1-2*x)^(3/2)+162/125*(1-2*x)^(5/2)-27/140*(1-2*x)^(7/2)-2/625*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+2/625*sqrt(1-2*x)],
[(2+3*x)^2*sqrt(1-2*x)/(3+5*x),x,5,-37/50*(1-2*x)^(3/2)+9/50*(1-2*x)^(5/2)-2/125*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+2/125*sqrt(1-2*x)],
[(2+3*x)*sqrt(1-2*x)/(3+5*x),x,4,-1/5*(1-2*x)^(3/2)-2/25*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+2/25*sqrt(1-2*x)],
[sqrt(1-2*x)/(3+5*x),x,3,-2/5*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+2/5*sqrt(1-2*x)],
[sqrt(1-2*x)/((2+3*x)*(3+5*x)),x,5,-2*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+2*arctanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(7/3)],
[sqrt(1-2*x)/((2+3*x)^2*(3+5*x)),x,6,68*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-2*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(55)+sqrt(1-2*x)/(2+3*x)],
[sqrt(1-2*x)/((2+3*x)^3*(3+5*x)),x,7,793/7*arctanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-10*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(55)+1/2*sqrt(1-2*x)/(2+3*x)^2+69/14*sqrt(1-2*x)/(2+3*x)],
[sqrt(1-2*x)/((2+3*x)^4*(3+5*x)),x,8,83264/49*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-50*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(55)+1/3*sqrt(1-2*x)/(2+3*x)^3+52/21*sqrt(1-2*x)/(2+3*x)^2+1207/49*sqrt(1-2*x)/(2+3*x)],
[sqrt(1-2*x)/((2+3*x)^5*(3+5*x)),x,9,11656955/1372*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-250*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(55)+1/4*sqrt(1-2*x)/(2+3*x)^4+139/84*sqrt(1-2*x)/(2+3*x)^3+14555/1176*sqrt(1-2*x)/(2+3*x)^2+337955/2744*sqrt(1-2*x)/(2+3*x)],
[(2+3*x)^5*sqrt(1-2*x)/(3+5*x)^2,x,7,-328/15625*arctanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-172/3125*(2+3*x)^2*sqrt(1-2*x)+64/2625*(2+3*x)^3*sqrt(1-2*x)+11/75*(2+3*x)^4*sqrt(1-2*x)-1/5*(2+3*x)^5*sqrt(1-2*x)/(3+5*x)-4/15625*(10998+3625*x)*sqrt(1-2*x)],
[(2+3*x)^4*sqrt(1-2*x)/(3+5*x)^2,x,6,-262/3125*arctanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+12/625*(2+3*x)^2*sqrt(1-2*x)+27/175*(2+3*x)^3*sqrt(1-2*x)-1/5*(2+3*x)^4*sqrt(1-2*x)/(3+5*x)-3/3125*(1256+375*x)*sqrt(1-2*x)],
[(2+3*x)^3*sqrt(1-2*x)/(3+5*x)^2,x,6,-196/625*arctanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-294/625*sqrt(1-2*x)+21/125*(2+3*x)^2*sqrt(1-2*x)-1/5*(2+3*x)^3*sqrt(1-2*x)/(3+5*x)],
[(2+3*x)^2*sqrt(1-2*x)/(3+5*x)^2,x,5,-3/25*(1-2*x)^(3/2)-1/275*(1-2*x)^(3/2)/(3+5*x)-26/25*arctanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+26/275*sqrt(1-2*x)],
[(2+3*x)*sqrt(1-2*x)/(3+5*x)^2,x,4,-1/55*(1-2*x)^(3/2)/(3+5*x)-64/25*arctanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+64/275*sqrt(1-2*x)],
[sqrt(1-2*x)/(3+5*x)^2,x,3,2/5*arctanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-1/5*sqrt(1-2*x)/(3+5*x)],
[sqrt(1-2*x)/((2+3*x)*(3+5*x)^2),x,6,-2*arctanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(21)+68*arctanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-sqrt(1-2*x)/(3+5*x)],
[sqrt(1-2*x)/((2+3*x)^2*(3+5*x)^2),x,7,-138*arctanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)+134*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)-10*sqrt(1-2*x)/(3+5*x)+sqrt(1-2*x)/((2+3*x)*(3+5*x))],
[sqrt(1-2*x)/((2+3*x)^3*(3+5*x)^2),x,8,-7209/7*arctanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)+1000*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)-1045/14*sqrt(1-2*x)/(3+5*x)+1/2*sqrt(1-2*x)/((2+3*x)^2*(3+5*x))+52/7*sqrt(1-2*x)/((2+3*x)*(3+5*x))],
[sqrt(1-2*x)/((2+3*x)^4*(3+5*x)^2),x,9,-335579/49*arctanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)+6650*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)-48645/98*sqrt(1-2*x)/(3+5*x)+1/3*sqrt(1-2*x)/((2+3*x)^3*(3+5*x))+139/42*sqrt(1-2*x)/((2+3*x)^2*(3+5*x))+7261/147*sqrt(1-2*x)/((2+3*x)*(3+5*x))],
[(2+3*x)^4*sqrt(1-2*x)/(3+5*x)^3,x,6,-12803/34375*arctanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-21/68750*(704-375*x)*sqrt(1-2*x)+1428/6875*(2+3*x)^2*sqrt(1-2*x)-1/10*(2+3*x)^4*sqrt(1-2*x)/(3+5*x)^2-131/550*(2+3*x)^3*sqrt(1-2*x)/(3+5*x)],
[(2+3*x)^3*sqrt(1-2*x)/(3+5*x)^3,x,5,-1267/1375*arctanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-1/10*(2+3*x)^3*sqrt(1-2*x)/(3+5*x)^2-49/275*(2+3*x)^2*sqrt(1-2*x)/(3+5*x)+21/2750*(44+75*x)*sqrt(1-2*x)],
[(2+3*x)^2*sqrt(1-2*x)/(3+5*x)^3,x,5,-1/550*(1-2*x)^(3/2)/(3+5*x)^2-133/6050*(1-2*x)^(3/2)/(3+5*x)-409/275*arctanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+409/3025*sqrt(1-2*x)],
[(2+3*x)*sqrt(1-2*x)/(3+5*x)^3,x,4,-1/110*(1-2*x)^(3/2)/(3+5*x)^2+67/275*arctanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-67/550*sqrt(1-2*x)/(3+5*x)],
[sqrt(1-2*x)/(3+5*x)^3,x,4,1/55*arctanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-1/10*sqrt(1-2*x)/(3+5*x)^2+1/110*sqrt(1-2*x)/(3+5*x)],
[sqrt(1-2*x)/((2+3*x)*(3+5*x)^3),x,7,6*arctanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(21)-2243/11*arctanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-1/2*sqrt(1-2*x)/(3+5*x)^2+67/22*sqrt(1-2*x)/(3+5*x)],
[sqrt(1-2*x)/((2+3*x)^2*(3+5*x)^3),x,8,624*arctanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-6665/11*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)-15/2*sqrt(1-2*x)/(3+5*x)^2+sqrt(1-2*x)/((2+3*x)*(3+5*x)^2)+995/22*sqrt(1-2*x)/(3+5*x)],
[sqrt(1-2*x)/((2+3*x)^3*(3+5*x)^3),x,9,43467/7*arctanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-66325/11*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)-1045/14*sqrt(1-2*x)/(3+5*x)^2+1/2*sqrt(1-2*x)/((2+3*x)^2*(3+5*x)^2)+139/14*sqrt(1-2*x)/((2+3*x)*(3+5*x)^2)+34655/77*sqrt(1-2*x)/(3+5*x)],
[sqrt(1-2*x)/((2+3*x)^4*(3+5*x)^3),x,10,2528082/49*arctanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-551075/11*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)-182335/294*sqrt(1-2*x)/(3+5*x)^2+1/3*sqrt(1-2*x)/((2+3*x)^3*(3+5*x)^2)+29/7*sqrt(1-2*x)/((2+3*x)^2*(3+5*x)^2)+4042/49*sqrt(1-2*x)/((2+3*x)*(3+5*x)^2)+4031135/1078*sqrt(1-2*x)/(3+5*x)],

# Integrands of the form (2+3 x)^m (3+5 x)^n (1-2 x)^(3/2)

# n>0
[(1-2*x)^(3/2)*(2+3*x)^6*(3+5*x),x,2,-1294139/640*(1-2*x)^(5/2)+559433/128*(1-2*x)^(7/2)-564235/128*(1-2*x)^(9/2)+3658095/1408*(1-2*x)^(11/2)-1580985/1664*(1-2*x)^(13/2)+136647/640*(1-2*x)^(15/2)-59049/2176*(1-2*x)^(17/2)+3645/2432*(1-2*x)^(19/2)],
[(1-2*x)^(3/2)*(2+3*x)^5*(3+5*x),x,2,-184877/320*(1-2*x)^(5/2)+8575/8*(1-2*x)^(7/2)-173215/192*(1-2*x)^(9/2)+37485/88*(1-2*x)^(11/2)-97335/832*(1-2*x)^(13/2)+351/20*(1-2*x)^(15/2)-1215/1088*(1-2*x)^(17/2)],
[(1-2*x)^(3/2)*(2+3*x)^4*(3+5*x),x,2,-26411/160*(1-2*x)^(5/2)+8183/32*(1-2*x)^(7/2)-8281/48*(1-2*x)^(9/2)+10773/176*(1-2*x)^(11/2)-4671/416*(1-2*x)^(13/2)+27/32*(1-2*x)^(15/2)],
[(1-2*x)^(3/2)*(2+3*x)^3*(3+5*x),x,2,-3773/80*(1-2*x)^(5/2)+469/8*(1-2*x)^(7/2)-119/4*(1-2*x)^(9/2)+621/88*(1-2*x)^(11/2)-135/208*(1-2*x)^(13/2)],
[(1-2*x)^(3/2)*(2+3*x)^2*(3+5*x),x,2,-539/40*(1-2*x)^(5/2)+101/8*(1-2*x)^(7/2)-103/24*(1-2*x)^(9/2)+45/88*(1-2*x)^(11/2)],
[(1-2*x)^(3/2)*(2+3*x)*(3+5*x),x,2,-77/20*(1-2*x)^(5/2)+17/7*(1-2*x)^(7/2)-5/12*(1-2*x)^(9/2)],
[(1-2*x)^(3/2)*(3+5*x),x,2,-11/10*(1-2*x)^(5/2)+5/14*(1-2*x)^(7/2)],
[(1-2*x)^(3/2)*(3+5*x)/(2+3*x),x,5,-2/27*(1-2*x)^(3/2)-1/3*(1-2*x)^(5/2)+14/27*arctanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(7/3)-14/27*sqrt(1-2*x)],
[(1-2*x)^(3/2)*(3+5*x)/(2+3*x)^2,x,5,76/189*(1-2*x)^(3/2)+1/21*(1-2*x)^(5/2)/(2+3*x)-76/27*arctanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(7/3)+76/27*sqrt(1-2*x)],
[(1-2*x)^(3/2)*(3+5*x)/(2+3*x)^3,x,5,1/42*(1-2*x)^(5/2)/(2+3*x)^2-71/126*(1-2*x)^(3/2)/(2+3*x)+71/9*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-71/63*sqrt(1-2*x)],
[(1-2*x)^(3/2)*(3+5*x)/(2+3*x)^4,x,5,1/63*(1-2*x)^(5/2)/(2+3*x)^3-52/189*(1-2*x)^(3/2)/(2+3*x)^2-104/189*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+52/189*sqrt(1-2*x)/(2+3*x)],
[(1-2*x)^(3/2)*(3+5*x)/(2+3*x)^5,x,6,1/84*(1-2*x)^(5/2)/(2+3*x)^4-137/756*(1-2*x)^(3/2)/(2+3*x)^3-137/5292*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+137/1512*sqrt(1-2*x)/(2+3*x)^2-137/10584*sqrt(1-2*x)/(2+3*x)],
[(1-2*x)^(3/2)*(3+5*x)/(2+3*x)^6,x,7,1/105*(1-2*x)^(5/2)/(2+3*x)^5-17/126*(1-2*x)^(3/2)/(2+3*x)^4-17/6174*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+17/378*sqrt(1-2*x)/(2+3*x)^3-17/5292*sqrt(1-2*x)/(2+3*x)^2-17/12348*sqrt(1-2*x)/(2+3*x)],
[(1-2*x)^(3/2)*(2+3*x)^4*(3+5*x)^2,x,2,-290521/320*(1-2*x)^(5/2)+54439/32*(1-2*x)^(7/2)-832951/576*(1-2*x)^(9/2)+121359/176*(1-2*x)^(11/2)-159111/832*(1-2*x)^(13/2)+927/32*(1-2*x)^(15/2)-2025/1088*(1-2*x)^(17/2)],
[(1-2*x)^(3/2)*(2+3*x)^3*(3+5*x)^2,x,2,-41503/160*(1-2*x)^(5/2)+13013/32*(1-2*x)^(7/2)-39977/144*(1-2*x)^(9/2)+17541/176*(1-2*x)^(11/2)-7695/416*(1-2*x)^(13/2)+45/32*(1-2*x)^(15/2)],
[(1-2*x)^(3/2)*(2+3*x)^2*(3+5*x)^2,x,2,-5929/80*(1-2*x)^(5/2)+187/2*(1-2*x)^(7/2)-3467/72*(1-2*x)^(9/2)+255/22*(1-2*x)^(11/2)-225/208*(1-2*x)^(13/2)],
[(1-2*x)^(3/2)*(2+3*x)*(3+5*x)^2,x,2,-847/40*(1-2*x)^(5/2)+1133/56*(1-2*x)^(7/2)-505/72*(1-2*x)^(9/2)+75/88*(1-2*x)^(11/2)],
[(1-2*x)^(3/2)*(3+5*x)^2,x,2,-121/20*(1-2*x)^(5/2)+55/14*(1-2*x)^(7/2)-25/36*(1-2*x)^(9/2)],
[(1-2*x)^(3/2)*(3+5*x)^2/(2+3*x),x,6,2/81*(1-2*x)^(3/2)-31/18*(1-2*x)^(5/2)+25/42*(1-2*x)^(7/2)-14/81*arctanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(7/3)+14/81*sqrt(1-2*x)],
[(1-2*x)^(3/2)*(3+5*x)^2/(2+3*x)^2,x,6,-146/567*(1-2*x)^(3/2)-5/9*(1-2*x)^(5/2)-1/63*(1-2*x)^(5/2)/(2+3*x)+146/81*arctanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(7/3)-146/81*sqrt(1-2*x)],
[(1-2*x)^(3/2)*(3+5*x)^2/(2+3*x)^3,x,6,2873/3969*(1-2*x)^(3/2)-1/126*(1-2*x)^(5/2)/(2+3*x)^2+47/294*(1-2*x)^(5/2)/(2+3*x)-2873/81*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+2873/567*sqrt(1-2*x)],
[(1-2*x)^(3/2)*(3+5*x)^2/(2+3*x)^4,x,6,-1/189*(1-2*x)^(5/2)/(2+3*x)^3+209/2646*(1-2*x)^(5/2)/(2+3*x)^2-7559/7938*(1-2*x)^(3/2)/(2+3*x)+7559/567*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-7559/3969*sqrt(1-2*x)],
[(1-2*x)^(3/2)*(3+5*x)^2/(2+3*x)^5,x,6,-1/252*(1-2*x)^(5/2)/(2+3*x)^4+277/5292*(1-2*x)^(5/2)/(2+3*x)^3-14423/31752*(1-2*x)^(3/2)/(2+3*x)^2-14423/15876*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+14423/31752*sqrt(1-2*x)/(2+3*x)],
[(1-2*x)^(3/2)*(3+5*x)^2/(2+3*x)^6,x,7,-1/315*(1-2*x)^(5/2)/(2+3*x)^5+23/588*(1-2*x)^(5/2)/(2+3*x)^4-4693/15876*(1-2*x)^(3/2)/(2+3*x)^3-4693/111132*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+4693/31752*sqrt(1-2*x)/(2+3*x)^2-4693/222264*sqrt(1-2*x)/(2+3*x)],
[(1-2*x)^(3/2)*(3+5*x)^2/(2+3*x)^7,x,8,-1/378*(1-2*x)^(5/2)/(2+3*x)^6+59/1890*(1-2*x)^(5/2)/(2+3*x)^5-991/4536*(1-2*x)^(3/2)/(2+3*x)^4-991/222264*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+991/13608*sqrt(1-2*x)/(2+3*x)^3-991/190512*sqrt(1-2*x)/(2+3*x)^2-991/444528*sqrt(1-2*x)/(2+3*x)],
[(1-2*x)^(3/2)*(2+3*x)^4*(3+5*x)^3,x,2,-3195731/640*(1-2*x)^(5/2)+1405173/128*(1-2*x)^(7/2)-4324397/384*(1-2*x)^(9/2)+9504551/1408*(1-2*x)^(11/2)-4177401/1664*(1-2*x)^(13/2)+73431/128*(1-2*x)^(15/2)-161325/2176*(1-2*x)^(17/2)+10125/2432*(1-2*x)^(19/2)],
[(1-2*x)^(3/2)*(2+3*x)^3*(3+5*x)^3,x,2,-456533/320*(1-2*x)^(5/2)+43197/16*(1-2*x)^(7/2)-444983/192*(1-2*x)^(9/2)+98209/88*(1-2*x)^(11/2)-260055/832*(1-2*x)^(13/2)+765/16*(1-2*x)^(15/2)-3375/1088*(1-2*x)^(17/2)],
[(1-2*x)^(3/2)*(2+3*x)^2*(3+5*x)^3,x,2,-65219/160*(1-2*x)^(5/2)+20691/32*(1-2*x)^(7/2)-21439/48*(1-2*x)^(9/2)+28555/176*(1-2*x)^(11/2)-975/32*(1-2*x)^(13/2)+75/32*(1-2*x)^(15/2)],
[(1-2*x)^(3/2)*(2+3*x)*(3+5*x)^3,x,2,-9317/80*(1-2*x)^(5/2)+8349/56*(1-2*x)^(7/2)-935/12*(1-2*x)^(9/2)+1675/88*(1-2*x)^(11/2)-375/208*(1-2*x)^(13/2)],
[(1-2*x)^(3/2)*(3+5*x)^3,x,2,-1331/40*(1-2*x)^(5/2)+1815/56*(1-2*x)^(7/2)-275/24*(1-2*x)^(9/2)+125/88*(1-2*x)^(11/2)],
[(1-2*x)^(3/2)*(3+5*x)^3/(2+3*x),x,6,-2/243*(1-2*x)^(3/2)-1027/108*(1-2*x)^(5/2)+400/63*(1-2*x)^(7/2)-125/108*(1-2*x)^(9/2)+14/243*arctanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(7/3)-14/243*sqrt(1-2*x)],
[(1-2*x)^(3/2)*(3+5*x)^3/(2+3*x)^2,x,6,5/7*(1-2*x)^(3/2)*(3+5*x)^2-1/3*(1-2*x)^(3/2)*(3+5*x)^3/(2+3*x)-10/63*(1-2*x)^(3/2)*(22+27*x)-8/9*arctanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(7/3)+8/9*sqrt(1-2*x)],
[(1-2*x)^(3/2)*(3+5*x)^3/(2+3*x)^3,x,6,-1/6*(1-2*x)^(3/2)*(3+5*x)^3/(2+3*x)^2+887/27*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-31/3*(3+5*x)^2*sqrt(1-2*x)+6*(3+5*x)^3*sqrt(1-2*x)/(2+3*x)+1/54*(367+1715*x)*sqrt(1-2*x)],
[(1-2*x)^(3/2)*(3+5*x)^3/(2+3*x)^4,x,6,-1/9*(1-2*x)^(3/2)*(3+5*x)^3/(2+3*x)^3-36038/567*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+251/63*(3+5*x)^2*sqrt(1-2*x)/(2+3*x)+2*(3+5*x)^3*sqrt(1-2*x)/(2+3*x)^2-5/567*(2323+7265*x)*sqrt(1-2*x)],
[(1-2*x)^(3/2)*(3+5*x)^3/(2+3*x)^5,x,6,-1/12*(1-2*x)^(3/2)*(3+5*x)^3/(2+3*x)^4+13243/588*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+13/56*(3+5*x)^2*sqrt(1-2*x)/(2+3*x)^2+(3+5*x)^3*sqrt(1-2*x)/(2+3*x)^3-1/1176*(18187+26775*x)*sqrt(1-2*x)/(2+3*x)],
[(1-2*x)^(3/2)*(3+5*x)^3/(2+3*x)^6,x,6,-1/15*(1-2*x)^(3/2)*(3+5*x)^3/(2+3*x)^5-13892/9261*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-67/315*(3+5*x)^2*sqrt(1-2*x)/(2+3*x)^3+3/5*(3+5*x)^3*sqrt(1-2*x)/(2+3*x)^4-2/9261*(9529+15074*x)*sqrt(1-2*x)/(2+3*x)^2],
[(1-2*x)^(3/2)*(3+5*x)^3/(2+3*x)^7,x,7,-1/18*(1-2*x)^(3/2)*(3+5*x)^3/(2+3*x)^6-15313/222264*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-15313/444528*sqrt(1-2*x)/(2+3*x)-653/2520*(3+5*x)^2*sqrt(1-2*x)/(2+3*x)^4+2/5*(3+5*x)^3*sqrt(1-2*x)/(2+3*x)^5-1/317520*(413424+664915*x)*sqrt(1-2*x)/(2+3*x)^3],
[(1-2*x)^(3/2)*(3+5*x)^3/(2+3*x)^8,x,8,-1/21*(1-2*x)^(3/2)*(3+5*x)^3/(2+3*x)^7-4369/605052*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-4369/518616*sqrt(1-2*x)/(2+3*x)^2-4369/1210104*sqrt(1-2*x)/(2+3*x)-173/735*(3+5*x)^2*sqrt(1-2*x)/(2+3*x)^5+2/7*(3+5*x)^3*sqrt(1-2*x)/(2+3*x)^6-1/185220*(146585+237807*x)*sqrt(1-2*x)/(2+3*x)^4],

# n<0
[(1-2*x)^(3/2)*(2+3*x)^6/(3+5*x),x,6,2/234375*(1-2*x)^(3/2)-167115051/2500000*(1-2*x)^(5/2)+70752609/700000*(1-2*x)^(7/2)-665817/10000*(1-2*x)^(9/2)+507627/22000*(1-2*x)^(11/2)-43011/10400*(1-2*x)^(13/2)+243/800*(1-2*x)^(15/2)-22/390625*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+22/390625*sqrt(1-2*x)],
[(1-2*x)^(3/2)*(2+3*x)^5/(3+5*x),x,6,2/46875*(1-2*x)^(3/2)-4774713/250000*(1-2*x)^(5/2)+806121/35000*(1-2*x)^(7/2)-5673/500*(1-2*x)^(9/2)+5751/2200*(1-2*x)^(11/2)-243/1040*(1-2*x)^(13/2)-22/78125*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+22/78125*sqrt(1-2*x)],
[(1-2*x)^(3/2)*(2+3*x)^4/(3+5*x),x,6,2/9375*(1-2*x)^(3/2)-136419/25000*(1-2*x)^(5/2)+34371/7000*(1-2*x)^(7/2)-321/200*(1-2*x)^(9/2)+81/440*(1-2*x)^(11/2)-22/15625*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+22/15625*sqrt(1-2*x)],
[(1-2*x)^(3/2)*(2+3*x)^3/(3+5*x),x,6,2/1875*(1-2*x)^(3/2)-3897/2500*(1-2*x)^(5/2)+162/175*(1-2*x)^(7/2)-3/20*(1-2*x)^(9/2)-22/3125*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+22/3125*sqrt(1-2*x)],
[(1-2*x)^(3/2)*(2+3*x)^2/(3+5*x),x,6,2/375*(1-2*x)^(3/2)-111/250*(1-2*x)^(5/2)+9/70*(1-2*x)^(7/2)-22/625*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+22/625*sqrt(1-2*x)],
[(1-2*x)^(3/2)*(2+3*x)/(3+5*x),x,5,2/75*(1-2*x)^(3/2)-3/25*(1-2*x)^(5/2)-22/125*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+22/125*sqrt(1-2*x)],
[(1-2*x)^(3/2)/(3+5*x),x,4,2/15*(1-2*x)^(3/2)-22/25*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+22/25*sqrt(1-2*x)],
[(1-2*x)^(3/2)/((2+3*x)*(3+5*x)),x,6,-22/5*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+14/3*arctanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(7/3)-4/15*sqrt(1-2*x)],
[(1-2*x)^(3/2)/((2+3*x)^2*(3+5*x)),x,6,-22*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+64/3*arctanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(7/3)+7/3*sqrt(1-2*x)/(2+3*x)],
[(1-2*x)^(3/2)/((2+3*x)^3*(3+5*x)),x,7,2243/3*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-22*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(55)+7/6*sqrt(1-2*x)/(2+3*x)^2+65/6*sqrt(1-2*x)/(2+3*x)],
[(1-2*x)^(3/2)/((2+3*x)^4*(3+5*x)),x,8,78506/21*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-110*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(55)+7/9*sqrt(1-2*x)/(2+3*x)^3+49/9*sqrt(1-2*x)/(2+3*x)^2+1138/21*sqrt(1-2*x)/(2+3*x)],
[(1-2*x)^(3/2)/((2+3*x)^5*(3+5*x)),x,9,10990843/588*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-550*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(55)+7/12*sqrt(1-2*x)/(2+3*x)^4+131/36*sqrt(1-2*x)/(2+3*x)^3+13723/504*sqrt(1-2*x)/(2+3*x)^2+318643/1176*sqrt(1-2*x)/(2+3*x)],
[(1-2*x)^(3/2)/((2+3*x)^6*(3+5*x)),x,10,96169877/1029*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-2750*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(55)+7/15*sqrt(1-2*x)/(2+3*x)^5+41/15*sqrt(1-2*x)/(2+3*x)^4+5732/315*sqrt(1-2*x)/(2+3*x)^3+120077/882*sqrt(1-2*x)/(2+3*x)^2+2788127/2058*sqrt(1-2*x)/(2+3*x)],
[(1-2*x)^(3/2)*(2+3*x)^5/(3+5*x)^2,x,8,-4016/48125*(1-2*x)^(3/2)*(2+3*x)^2+38/4125*(1-2*x)^(3/2)*(2+3*x)^3+39/275*(1-2*x)^(3/2)*(2+3*x)^4-1/5*(1-2*x)^(3/2)*(2+3*x)^5/(3+5*x)-2/515625*(1-2*x)^(3/2)*(298462+204777*x)-324/78125*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+324/78125*sqrt(1-2*x)],
[(1-2*x)^(3/2)*(2+3*x)^4/(3+5*x)^2,x,7,-2/875*(1-2*x)^(3/2)*(2+3*x)^2+11/75*(1-2*x)^(3/2)*(2+3*x)^3-1/5*(1-2*x)^(3/2)*(2+3*x)^4/(3+5*x)-1/9375*(1-2*x)^(3/2)*(5678+3663*x)-258/15625*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+258/15625*sqrt(1-2*x)],
[(1-2*x)^(3/2)*(2+3*x)^3/(3+5*x)^2,x,6,27/175*(1-2*x)^(3/2)*(2+3*x)^2-1/5*(1-2*x)^(3/2)*(2+3*x)^3/(3+5*x)-6/625*(1-2*x)^(3/2)*(29+9*x)-192/3125*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+192/3125*sqrt(1-2*x)],
[(1-2*x)^(3/2)*(2+3*x)^2/(3+5*x)^2,x,6,42/1375*(1-2*x)^(3/2)-9/125*(1-2*x)^(5/2)-1/275*(1-2*x)^(5/2)/(3+5*x)-126/625*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+126/625*sqrt(1-2*x)],
[(1-2*x)^(3/2)*(2+3*x)/(3+5*x)^2,x,5,4/55*(1-2*x)^(3/2)-1/55*(1-2*x)^(5/2)/(3+5*x)-12/25*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+12/25*sqrt(1-2*x)],
[(1-2*x)^(3/2)/(3+5*x)^2,x,4,-1/5*(1-2*x)^(3/2)/(3+5*x)+6/25*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)-6/25*sqrt(1-2*x)],
[(1-2*x)^(3/2)/((2+3*x)*(3+5*x)^2),x,6,72/5*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)-14*arctanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(7/3)-11/5*sqrt(1-2*x)/(3+5*x)],
[(1-2*x)^(3/2)/((2+3*x)^2*(3+5*x)^2),x,7,138*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)-134*arctanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(7/3)-68/3*sqrt(1-2*x)/(3+5*x)+7/3*sqrt(1-2*x)/((2+3*x)*(3+5*x))],
[(1-2*x)^(3/2)/((2+3*x)^3*(3+5*x)^2),x,8,-2311*arctanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)+204*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(55)-335/2*sqrt(1-2*x)/(3+5*x)+7/6*sqrt(1-2*x)/((2+3*x)^2*(3+5*x))+50/3*sqrt(1-2*x)/((2+3*x)*(3+5*x))],
[(1-2*x)^(3/2)/((2+3*x)^4*(3+5*x)^2),x,9,-321161/7*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+1350*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(55)-46555/42*sqrt(1-2*x)/(3+5*x)+7/9*sqrt(1-2*x)/((2+3*x)^3*(3+5*x))+133/18*sqrt(1-2*x)/((2+3*x)^2*(3+5*x))+6949/63*sqrt(1-2*x)/((2+3*x)*(3+5*x))],
[(1-2*x)^(3/2)/((2+3*x)^5*(3+5*x)^2),x,10,-55953383/196*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+8400*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(55)-8110915/1176*sqrt(1-2*x)/(3+5*x)+7/12*sqrt(1-2*x)/((2+3*x)^4*(3+5*x))+83/18*sqrt(1-2*x)/((2+3*x)^3*(3+5*x))+23173/504*sqrt(1-2*x)/((2+3*x)^2*(3+5*x))+302668/441*sqrt(1-2*x)/((2+3*x)*(3+5*x))],
[(1-2*x)^(3/2)*(2+3*x)^4/(3+5*x)^3,x,7,-1/10*(1-2*x)^(3/2)*(2+3*x)^4/(3+5*x)^2-12279/15625*arctanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+1404/3125*(2+3*x)^2*sqrt(1-2*x)+2643/1750*(2+3*x)^3*sqrt(1-2*x)-129/50*(2+3*x)^4*sqrt(1-2*x)/(3+5*x)+9/31250*(32+1375*x)*sqrt(1-2*x)],
[(1-2*x)^(3/2)*(2+3*x)^3/(3+5*x)^3,x,6,-1/10*(1-2*x)^(3/2)*(2+3*x)^3/(3+5*x)^2-5943/3125*arctanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+693/625*(2+3*x)^2*sqrt(1-2*x)-48/25*(2+3*x)^3*sqrt(1-2*x)/(3+5*x)+63/6250*(92+125*x)*sqrt(1-2*x)],
[(1-2*x)^(3/2)*(2+3*x)^2/(3+5*x)^3,x,6,119/3025*(1-2*x)^(3/2)-1/550*(1-2*x)^(5/2)/(3+5*x)^2-131/6050*(1-2*x)^(5/2)/(3+5*x)-357/125*arctanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+357/1375*sqrt(1-2*x)],
[(1-2*x)^(3/2)*(2+3*x)/(3+5*x)^3,x,5,-1/110*(1-2*x)^(5/2)/(3+5*x)^2-13/110*(1-2*x)^(3/2)/(3+5*x)+39/25*arctanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-39/275*sqrt(1-2*x)],
[(1-2*x)^(3/2)/(3+5*x)^3,x,4,-1/10*(1-2*x)^(3/2)/(3+5*x)^2-3/25*arctanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+3/50*sqrt(1-2*x)/(3+5*x)],
[(1-2*x)^(3/2)/((2+3*x)*(3+5*x)^3),x,7,14*arctanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(21)-2379/5*arctanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-11/10*sqrt(1-2*x)/(3+5*x)^2+71/10*sqrt(1-2*x)/(3+5*x)],
[(1-2*x)^(3/2)/((2+3*x)^2*(3+5*x)^3),x,8,204*arctanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(21)-6933*arctanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-103/6*sqrt(1-2*x)/(3+5*x)^2+7/3*sqrt(1-2*x)/((2+3*x)*(3+5*x)^2)+207/2*sqrt(1-2*x)/(3+5*x)],
[(1-2*x)^(3/2)/((2+3*x)^3*(3+5*x)^3),x,9,14073*arctanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-13665*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)-1015/6*sqrt(1-2*x)/(3+5*x)^2+7/6*sqrt(1-2*x)/((2+3*x)^2*(3+5*x)^2)+45/2*sqrt(1-2*x)/((2+3*x)*(3+5*x)^2)+1020*sqrt(1-2*x)/(3+5*x)],
[(1-2*x)^(3/2)/((2+3*x)^4*(3+5*x)^3),x,10,813716/7*arctanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-112875*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)-176065/126*sqrt(1-2*x)/(3+5*x)^2+7/9*sqrt(1-2*x)/((2+3*x)^3*(3+5*x)^2)+28/3*sqrt(1-2*x)/((2+3*x)^2*(3+5*x)^2)+1301/7*sqrt(1-2*x)/((2+3*x)*(3+5*x)^2)+117955/14*sqrt(1-2*x)/(3+5*x)],

# Integrands of the form (2+3 x)^m (3+5 x)^n (1-2 x)^(5/2)

# n>0
[(1-2*x)^(5/2)*(2+3*x)^6*(3+5*x),x,2,-184877/128*(1-2*x)^(7/2)+3916031/1152*(1-2*x)^(9/2)-5078115/1408*(1-2*x)^(11/2)+3658095/1664*(1-2*x)^(13/2)-105399/128*(1-2*x)^(15/2)+409941/2176*(1-2*x)^(17/2)-59049/2432*(1-2*x)^(19/2)+1215/896*(1-2*x)^(21/2)],
[(1-2*x)^(5/2)*(2+3*x)^5*(3+5*x),x,2,-26411/64*(1-2*x)^(7/2)+60025/72*(1-2*x)^(9/2)-519645/704*(1-2*x)^(11/2)+37485/104*(1-2*x)^(13/2)-6489/64*(1-2*x)^(15/2)+1053/68*(1-2*x)^(17/2)-1215/1216*(1-2*x)^(19/2)],
[(1-2*x)^(5/2)*(2+3*x)^4*(3+5*x),x,2,-3773/32*(1-2*x)^(7/2)+57281/288*(1-2*x)^(9/2)-24843/176*(1-2*x)^(11/2)+10773/208*(1-2*x)^(13/2)-1557/160*(1-2*x)^(15/2)+405/544*(1-2*x)^(17/2)],
[(1-2*x)^(5/2)*(2+3*x)^3*(3+5*x),x,2,-539/16*(1-2*x)^(7/2)+3283/72*(1-2*x)^(9/2)-1071/44*(1-2*x)^(11/2)+621/104*(1-2*x)^(13/2)-9/16*(1-2*x)^(15/2)],
[(1-2*x)^(5/2)*(2+3*x)^2*(3+5*x),x,2,-77/8*(1-2*x)^(7/2)+707/72*(1-2*x)^(9/2)-309/88*(1-2*x)^(11/2)+45/104*(1-2*x)^(13/2)],
[(1-2*x)^(5/2)*(2+3*x)*(3+5*x),x,2,-11/4*(1-2*x)^(7/2)+17/9*(1-2*x)^(9/2)-15/44*(1-2*x)^(11/2)],
[(1-2*x)^(5/2)*(3+5*x),x,2,-11/14*(1-2*x)^(7/2)+5/18*(1-2*x)^(9/2)],
[(1-2*x)^(5/2)*(3+5*x)/(2+3*x),x,6,-14/81*(1-2*x)^(3/2)-2/45*(1-2*x)^(5/2)-5/21*(1-2*x)^(7/2)+98/81*arctanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(7/3)-98/81*sqrt(1-2*x)],
[(1-2*x)^(5/2)*(3+5*x)/(2+3*x)^2,x,6,80/81*(1-2*x)^(3/2)+16/63*(1-2*x)^(5/2)+1/21*(1-2*x)^(7/2)/(2+3*x)-560/81*arctanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(7/3)+560/81*sqrt(1-2*x)],
[(1-2*x)^(5/2)*(3+5*x)/(2+3*x)^3,x,6,-365/567*(1-2*x)^(3/2)+1/42*(1-2*x)^(7/2)/(2+3*x)^2-73/126*(1-2*x)^(5/2)/(2+3*x)+365/81*arctanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(7/3)-365/81*sqrt(1-2*x)],
[(1-2*x)^(5/2)*(3+5*x)/(2+3*x)^4,x,6,1/63*(1-2*x)^(7/2)/(2+3*x)^3-53/189*(1-2*x)^(5/2)/(2+3*x)^2+265/567*(1-2*x)^(3/2)/(2+3*x)-530/81*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+530/567*sqrt(1-2*x)],
[(1-2*x)^(5/2)*(3+5*x)/(2+3*x)^5,x,6,1/84*(1-2*x)^(7/2)/(2+3*x)^4-139/756*(1-2*x)^(5/2)/(2+3*x)^3+695/4536*(1-2*x)^(3/2)/(2+3*x)^2+695/2268*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-695/4536*sqrt(1-2*x)/(2+3*x)],
[(1-2*x)^(5/2)*(3+5*x)/(2+3*x)^6,x,7,1/105*(1-2*x)^(7/2)/(2+3*x)^5-43/315*(1-2*x)^(5/2)/(2+3*x)^4+43/567*(1-2*x)^(3/2)/(2+3*x)^3+43/3969*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-43/1134*sqrt(1-2*x)/(2+3*x)^2+43/7938*sqrt(1-2*x)/(2+3*x)],
[(1-2*x)^(5/2)*(3+5*x)/(2+3*x)^7,x,8,1/126*(1-2*x)^(7/2)/(2+3*x)^6-41/378*(1-2*x)^(5/2)/(2+3*x)^5+205/4536*(1-2*x)^(3/2)/(2+3*x)^4+205/222264*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-205/13608*sqrt(1-2*x)/(2+3*x)^3+205/190512*sqrt(1-2*x)/(2+3*x)^2+205/444528*sqrt(1-2*x)/(2+3*x)],
[(1-2*x)^(5/2)*(2+3*x)^4*(3+5*x)^2,x,2,-41503/64*(1-2*x)^(7/2)+381073/288*(1-2*x)^(9/2)-832951/704*(1-2*x)^(11/2)+121359/208*(1-2*x)^(13/2)-53037/320*(1-2*x)^(15/2)+13905/544*(1-2*x)^(17/2)-2025/1216*(1-2*x)^(19/2)],
[(1-2*x)^(5/2)*(2+3*x)^3*(3+5*x)^2,x,2,-5929/32*(1-2*x)^(7/2)+91091/288*(1-2*x)^(9/2)-39977/176*(1-2*x)^(11/2)+17541/208*(1-2*x)^(13/2)-513/32*(1-2*x)^(15/2)+675/544*(1-2*x)^(17/2)],
[(1-2*x)^(5/2)*(2+3*x)^2*(3+5*x)^2,x,2,-847/16*(1-2*x)^(7/2)+1309/18*(1-2*x)^(9/2)-3467/88*(1-2*x)^(11/2)+255/26*(1-2*x)^(13/2)-15/16*(1-2*x)^(15/2)],
[(1-2*x)^(5/2)*(2+3*x)*(3+5*x)^2,x,2,-121/8*(1-2*x)^(7/2)+1133/72*(1-2*x)^(9/2)-505/88*(1-2*x)^(11/2)+75/104*(1-2*x)^(13/2)],
[(1-2*x)^(5/2)*(3+5*x)^2,x,2,-121/28*(1-2*x)^(7/2)+55/18*(1-2*x)^(9/2)-25/44*(1-2*x)^(11/2)],
[(1-2*x)^(5/2)*(3+5*x)^2/(2+3*x),x,7,14/243*(1-2*x)^(3/2)+2/135*(1-2*x)^(5/2)-155/126*(1-2*x)^(7/2)+25/54*(1-2*x)^(9/2)-98/243*arctanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(7/3)+98/243*sqrt(1-2*x)],
[(1-2*x)^(5/2)*(3+5*x)^2/(2+3*x)^2,x,7,-50/81*(1-2*x)^(3/2)-10/63*(1-2*x)^(5/2)-25/63*(1-2*x)^(7/2)-1/63*(1-2*x)^(7/2)/(2+3*x)+350/81*arctanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(7/3)-350/81*sqrt(1-2*x)],
[(1-2*x)^(5/2)*(3+5*x)^2/(2+3*x)^3,x,7,1055/567*(1-2*x)^(3/2)+211/441*(1-2*x)^(5/2)-1/126*(1-2*x)^(7/2)/(2+3*x)^2+143/882*(1-2*x)^(7/2)/(2+3*x)-1055/81*arctanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(7/3)+1055/81*sqrt(1-2*x)],
[(1-2*x)^(5/2)*(3+5*x)^2/(2+3*x)^4,x,7,-4435/3969*(1-2*x)^(3/2)-1/189*(1-2*x)^(7/2)/(2+3*x)^3+211/2646*(1-2*x)^(7/2)/(2+3*x)^2-887/882*(1-2*x)^(5/2)/(2+3*x)+4435/81*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-4435/567*sqrt(1-2*x)],
[(1-2*x)^(5/2)*(3+5*x)^2/(2+3*x)^5,x,7,-1/252*(1-2*x)^(7/2)/(2+3*x)^4+31/588*(1-2*x)^(7/2)/(2+3*x)^3-4993/10584*(1-2*x)^(5/2)/(2+3*x)^2+24965/31752*(1-2*x)^(3/2)/(2+3*x)-24965/2268*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+24965/15876*sqrt(1-2*x)],
[(1-2*x)^(5/2)*(3+5*x)^2/(2+3*x)^6,x,7,-1/315*(1-2*x)^(7/2)/(2+3*x)^5+347/8820*(1-2*x)^(7/2)/(2+3*x)^4-8051/26460*(1-2*x)^(5/2)/(2+3*x)^3+8051/31752*(1-2*x)^(3/2)/(2+3*x)^2+8051/15876*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-8051/31752*sqrt(1-2*x)/(2+3*x)],
[(1-2*x)^(5/2)*(3+5*x)^2/(2+3*x)^7,x,8,-1/378*(1-2*x)^(7/2)/(2+3*x)^6+83/2646*(1-2*x)^(7/2)/(2+3*x)^5-263/1176*(1-2*x)^(5/2)/(2+3*x)^4+1315/10584*(1-2*x)^(3/2)/(2+3*x)^3+1315/74088*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-1315/21168*sqrt(1-2*x)/(2+3*x)^2+1315/148176*sqrt(1-2*x)/(2+3*x)],
[(1-2*x)^(5/2)*(3+5*x)^2/(2+3*x)^8,x,9,-1/441*(1-2*x)^(7/2)/(2+3*x)^7+23/882*(1-2*x)^(7/2)/(2+3*x)^6-467/2646*(1-2*x)^(5/2)/(2+3*x)^5+2335/31752*(1-2*x)^(3/2)/(2+3*x)^4+2335/1555848*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-2335/95256*sqrt(1-2*x)/(2+3*x)^3+2335/1333584*sqrt(1-2*x)/(2+3*x)^2+2335/3111696*sqrt(1-2*x)/(2+3*x)],
[(1-2*x)^(5/2)*(2+3*x)^4*(3+5*x)^3,x,2,-456533/128*(1-2*x)^(7/2)+3278737/384*(1-2*x)^(9/2)-1179381/128*(1-2*x)^(11/2)+9504551/1664*(1-2*x)^(13/2)-1392467/640*(1-2*x)^(15/2)+1101465/2176*(1-2*x)^(17/2)-161325/2432*(1-2*x)^(19/2)+3375/896*(1-2*x)^(21/2)],
[(1-2*x)^(5/2)*(2+3*x)^3*(3+5*x)^3,x,2,-65219/64*(1-2*x)^(7/2)+100793/48*(1-2*x)^(9/2)-121359/64*(1-2*x)^(11/2)+98209/104*(1-2*x)^(13/2)-17337/64*(1-2*x)^(15/2)+675/16*(1-2*x)^(17/2)-3375/1216*(1-2*x)^(19/2)],
[(1-2*x)^(5/2)*(2+3*x)^2*(3+5*x)^3,x,2,-9317/32*(1-2*x)^(7/2)+16093/32*(1-2*x)^(9/2)-5847/16*(1-2*x)^(11/2)+28555/208*(1-2*x)^(13/2)-845/32*(1-2*x)^(15/2)+1125/544*(1-2*x)^(17/2)],
[(1-2*x)^(5/2)*(2+3*x)*(3+5*x)^3,x,2,-1331/16*(1-2*x)^(7/2)+2783/24*(1-2*x)^(9/2)-255/4*(1-2*x)^(11/2)+1675/104*(1-2*x)^(13/2)-25/16*(1-2*x)^(15/2)],
[(1-2*x)^(5/2)*(3+5*x)^3,x,2,-1331/56*(1-2*x)^(7/2)+605/24*(1-2*x)^(9/2)-75/8*(1-2*x)^(11/2)+125/104*(1-2*x)^(13/2)],
[(1-2*x)^(5/2)*(3+5*x)^3/(2+3*x),x,7,-14/729*(1-2*x)^(3/2)-2/405*(1-2*x)^(5/2)-5135/756*(1-2*x)^(7/2)+400/81*(1-2*x)^(9/2)-125/132*(1-2*x)^(11/2)+98/729*arctanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(7/3)-98/729*sqrt(1-2*x)],
[(1-2*x)^(5/2)*(3+5*x)^3/(2+3*x)^2,x,8,220/729*(1-2*x)^(3/2)+55/81*(1-2*x)^(5/2)*(3+5*x)^2-1/3*(1-2*x)^(5/2)*(3+5*x)^3/(2+3*x)-22/567*(1-2*x)^(5/2)*(69+100*x)-1540/729*arctanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(7/3)+1540/729*sqrt(1-2*x)],
[(1-2*x)^(5/2)*(3+5*x)^3/(2+3*x)^3,x,8,-220/21*(1-2*x)^(3/2)*(3+5*x)^2-1/6*(1-2*x)^(5/2)*(3+5*x)^3/(2+3*x)^2+55/9*(1-2*x)^(3/2)*(3+5*x)^3/(2+3*x)+55/1134*(1-2*x)^(3/2)*(209+603*x)+935/81*arctanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(7/3)-935/81*sqrt(1-2*x)],
[(1-2*x)^(5/2)*(3+5*x)^3/(2+3*x)^4,x,8,-1/9*(1-2*x)^(5/2)*(3+5*x)^3/(2+3*x)^3+55/27*(1-2*x)^(3/2)*(3+5*x)^3/(2+3*x)^2-41360/243*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+1441/27*(3+5*x)^2*sqrt(1-2*x)-275/9*(3+5*x)^3*sqrt(1-2*x)/(2+3*x)-22/243*(578+1885*x)*sqrt(1-2*x)],
[(1-2*x)^(5/2)*(3+5*x)^3/(2+3*x)^5,x,8,-1/12*(1-2*x)^(5/2)*(3+5*x)^3/(2+3*x)^4+55/54*(1-2*x)^(3/2)*(3+5*x)^3/(2+3*x)^3+645865/6804*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-2255/378*(3+5*x)^2*sqrt(1-2*x)/(2+3*x)-55/24*(3+5*x)^3*sqrt(1-2*x)/(2+3*x)^2+275/13608*(1123+4595*x)*sqrt(1-2*x)],
[(1-2*x)^(5/2)*(3+5*x)^3/(2+3*x)^6,x,8,-1/15*(1-2*x)^(5/2)*(3+5*x)^3/(2+3*x)^5+11/18*(1-2*x)^(3/2)*(3+5*x)^3/(2+3*x)^4-146971/7938*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-209/756*(3+5*x)^2*sqrt(1-2*x)/(2+3*x)^2+11/9*(3+5*x)^3*sqrt(1-2*x)/(2+3*x)^3-11/15876*(3911+6475*x)*sqrt(1-2*x)/(2+3*x)],
[(1-2*x)^(5/2)*(3+5*x)^3/(2+3*x)^7,x,10,-121/4536*(1-2*x)^(3/2)/(2+3*x)^4+33275/95256*(1-2*x)^(3/2)/(2+3*x)^3-1/18*(1-2*x)^(5/2)*(3+5*x)^3/(2+3*x)^6+11/27*(1-2*x)^(3/2)*(3+5*x)^3/(2+3*x)^5+559625/666792*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-559625/190512*sqrt(1-2*x)/(2+3*x)^2+559625/1333584*sqrt(1-2*x)/(2+3*x)],
[(1-2*x)^(5/2)*(3+5*x)^3/(2+3*x)^8,x,9,-1/21*(1-2*x)^(5/2)*(3+5*x)^3/(2+3*x)^7+55/189*(1-2*x)^(3/2)*(3+5*x)^3/(2+3*x)^6+33935/1166886*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+33935/2333772*sqrt(1-2*x)/(2+3*x)-3223/2646*(3+5*x)^2*sqrt(1-2*x)/(2+3*x)^4+11/7*(3+5*x)^3*sqrt(1-2*x)/(2+3*x)^5-11/333396*(187704+301765*x)*sqrt(1-2*x)/(2+3*x)^3],

# n<0
[(1-2*x)^(5/2)*(2+3*x)^4/(3+5*x),x,7,22/46875*(1-2*x)^(3/2)+2/15625*(1-2*x)^(5/2)-136419/35000*(1-2*x)^(7/2)+3819/1000*(1-2*x)^(9/2)-2889/2200*(1-2*x)^(11/2)+81/520*(1-2*x)^(13/2)-242/78125*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+242/78125*sqrt(1-2*x)],
[(1-2*x)^(5/2)*(2+3*x)^3/(3+5*x),x,7,22/9375*(1-2*x)^(3/2)+2/3125*(1-2*x)^(5/2)-3897/3500*(1-2*x)^(7/2)+18/25*(1-2*x)^(9/2)-27/220*(1-2*x)^(11/2)-242/15625*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+242/15625*sqrt(1-2*x)],
[(1-2*x)^(5/2)*(2+3*x)^2/(3+5*x),x,7,22/1875*(1-2*x)^(3/2)+2/625*(1-2*x)^(5/2)-111/350*(1-2*x)^(7/2)+1/10*(1-2*x)^(9/2)-242/3125*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+242/3125*sqrt(1-2*x)],
[(1-2*x)^(5/2)*(2+3*x)/(3+5*x),x,6,22/375*(1-2*x)^(3/2)+2/125*(1-2*x)^(5/2)-3/35*(1-2*x)^(7/2)-242/625*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+242/625*sqrt(1-2*x)],
[(1-2*x)^(5/2)/(3+5*x),x,5,22/75*(1-2*x)^(3/2)+2/25*(1-2*x)^(5/2)-242/125*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+242/125*sqrt(1-2*x)],
[(1-2*x)^(5/2)/((2+3*x)*(3+5*x)),x,7,-4/45*(1-2*x)^(3/2)-242/25*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+98/9*arctanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(7/3)-272/225*sqrt(1-2*x)],
[(1-2*x)^(5/2)/((2+3*x)^2*(3+5*x)),x,7,7/3*(1-2*x)^(3/2)/(2+3*x)-242/5*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+140/3*arctanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(7/3)+26/15*sqrt(1-2*x)],
[(1-2*x)^(5/2)/((2+3*x)^3*(3+5*x)),x,7,7/6*(1-2*x)^(3/2)/(2+3*x)^2-242*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+235*arctanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(7/3)+49/2*sqrt(1-2*x)/(2+3*x)],
[(1-2*x)^(5/2)/((2+3*x)^4*(3+5*x)),x,8,7/9*(1-2*x)^(3/2)/(2+3*x)^3+74020/9*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-242*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(55)+112/9*sqrt(1-2*x)/(2+3*x)^2+1073/9*sqrt(1-2*x)/(2+3*x)],
[(1-2*x)^(5/2)/((2+3*x)^5*(3+5*x)),x,9,7/12*(1-2*x)^(3/2)/(2+3*x)^4+3454265/84*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-1210*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(55)+301/36*sqrt(1-2*x)/(2+3*x)^3+4313/72*sqrt(1-2*x)/(2+3*x)^2+100145/168*sqrt(1-2*x)/(2+3*x)],
[(1-2*x)^(5/2)/((2+3*x)^6*(3+5*x)),x,10,7/15*(1-2*x)^(3/2)/(2+3*x)^5+20149879/98*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-6050*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(55)+63/10*sqrt(1-2*x)/(2+3*x)^4+1201/30*sqrt(1-2*x)/(2+3*x)^3+25159/84*sqrt(1-2*x)/(2+3*x)^2+584179/196*sqrt(1-2*x)/(2+3*x)],
[(1-2*x)^(5/2)/((2+3*x)^7*(3+5*x)),x,11,7/18*(1-2*x)^(3/2)/(2+3*x)^6+25388847535/24696*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-30250*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(55)+91/18*sqrt(1-2*x)/(2+3*x)^5+2165/72*sqrt(1-2*x)/(2+3*x)^4+302651/1512*sqrt(1-2*x)/(2+3*x)^3+31700335/21168*sqrt(1-2*x)/(2+3*x)^2+736065535/49392*sqrt(1-2*x)/(2+3*x)],
[(1-2*x)^(5/2)*(2+3*x)^4/(3+5*x)^2,x,8,254/46875*(1-2*x)^(3/2)-32/4125*(1-2*x)^(5/2)*(2+3*x)^2+39/275*(1-2*x)^(5/2)*(2+3*x)^3-1/5*(1-2*x)^(5/2)*(2+3*x)^4/(3+5*x)-1/3609375*(1-2*x)^(5/2)*(1347116+1110975*x)-2794/78125*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+2794/78125*sqrt(1-2*x)],
[(1-2*x)^(5/2)*(2+3*x)^3/(3+5*x)^2,x,7,188/9375*(1-2*x)^(3/2)+11/75*(1-2*x)^(5/2)*(2+3*x)^2-1/5*(1-2*x)^(5/2)*(2+3*x)^3/(3+5*x)-2/65625*(1-2*x)^(5/2)*(6191+2850*x)-2068/15625*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+2068/15625*sqrt(1-2*x)],
[(1-2*x)^(5/2)*(2+3*x)^2/(3+5*x)^2,x,7,122/1875*(1-2*x)^(3/2)+122/6875*(1-2*x)^(5/2)-9/175*(1-2*x)^(7/2)-1/275*(1-2*x)^(7/2)/(3+5*x)-1342/3125*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+1342/3125*sqrt(1-2*x)],
[(1-2*x)^(5/2)*(2+3*x)/(3+5*x)^2,x,6,56/375*(1-2*x)^(3/2)+56/1375*(1-2*x)^(5/2)-1/55*(1-2*x)^(7/2)/(3+5*x)-616/625*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+616/625*sqrt(1-2*x)],
[(1-2*x)^(5/2)/(3+5*x)^2,x,5,-2/15*(1-2*x)^(3/2)-1/5*(1-2*x)^(5/2)/(3+5*x)+22/25*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)-22/25*sqrt(1-2*x)],
[(1-2*x)^(5/2)/((2+3*x)*(3+5*x)^2),x,7,-11/5*(1-2*x)^(3/2)/(3+5*x)+836/25*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)-98/3*arctanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(7/3)-58/75*sqrt(1-2*x)],
[(1-2*x)^(5/2)/((2+3*x)^2*(3+5*x)^2),x,7,7/3*(1-2*x)^(3/2)/((2+3*x)*(3+5*x))+1562/5*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)-910/3*arctanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(7/3)-748/15*sqrt(1-2*x)/(3+5*x)],
[(1-2*x)^(5/2)/((2+3*x)^3*(3+5*x)^2),x,8,7/6*(1-2*x)^(3/2)/((2+3*x)^2*(3+5*x))+2288*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)-6665/3*arctanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(7/3)-6763/18*sqrt(1-2*x)/(3+5*x)+343/9*sqrt(1-2*x)/((2+3*x)*(3+5*x))],
[(1-2*x)^(5/2)/((2+3*x)^4*(3+5*x)^2),x,9,7/9*(1-2*x)^(3/2)/((2+3*x)^3*(3+5*x))-307295/3*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+3014*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(55)-44545/18*sqrt(1-2*x)/(3+5*x)+917/54*sqrt(1-2*x)/((2+3*x)^2*(3+5*x))+6649/27*sqrt(1-2*x)/((2+3*x)*(3+5*x))],
[(1-2*x)^(5/2)/((2+3*x)^5*(3+5*x)^2),x,10,7/12*(1-2*x)^(3/2)/((2+3*x)^4*(3+5*x))-53384095/84*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+18700*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(55)-7738475/504*sqrt(1-2*x)/(3+5*x)+287/27*sqrt(1-2*x)/((2+3*x)^3*(3+5*x))+22109/216*sqrt(1-2*x)/((2+3*x)^2*(3+5*x))+288770/189*sqrt(1-2*x)/((2+3*x)*(3+5*x))],
[(1-2*x)^(5/2)/((2+3*x)^6*(3+5*x)^2),x,11,7/15*(1-2*x)^(3/2)/((2+3*x)^5*(3+5*x))-2231141147/588*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+111650*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(55)-323422735/3528*sqrt(1-2*x)/(3+5*x)+1379/180*sqrt(1-2*x)/((2+3*x)^4*(3+5*x))+16549/270*sqrt(1-2*x)/((2+3*x)^3*(3+5*x))+924025/1512*sqrt(1-2*x)/((2+3*x)^2*(3+5*x))+12068887/1323*sqrt(1-2*x)/((2+3*x)*(3+5*x))],
[(1-2*x)^(5/2)*(2+3*x)^4/(3+5*x)^3,x,8,1903/4375*(1-2*x)^(3/2)*(2+3*x)^2+1117/750*(1-2*x)^(3/2)*(2+3*x)^3-1/10*(1-2*x)^(5/2)*(2+3*x)^4/(3+5*x)^2-127/50*(1-2*x)^(3/2)*(2+3*x)^4/(3+5*x)+1/93750*(1-2*x)^(3/2)*(734+24939*x)-11763/78125*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+11763/78125*sqrt(1-2*x)],
[(1-2*x)^(5/2)*(2+3*x)^3/(3+5*x)^3,x,7,954/875*(1-2*x)^(3/2)*(2+3*x)^2-1/10*(1-2*x)^(5/2)*(2+3*x)^3/(3+5*x)^2-47/25*(1-2*x)^(3/2)*(2+3*x)^3/(3+5*x)+3/6250*(1-2*x)^(3/2)*(1618+2403*x)-5559/15625*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+5559/15625*sqrt(1-2*x)],
[(1-2*x)^(5/2)*(2+3*x)^2/(3+5*x)^3,x,7,511/6875*(1-2*x)^(3/2)+1533/75625*(1-2*x)^(5/2)-1/550*(1-2*x)^(7/2)/(3+5*x)^2-129/6050*(1-2*x)^(7/2)/(3+5*x)-1533/3125*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+1533/3125*sqrt(1-2*x)],
[(1-2*x)^(5/2)*(2+3*x)/(3+5*x)^3,x,6,-21/275*(1-2*x)^(3/2)-1/110*(1-2*x)^(7/2)/(3+5*x)^2-63/550*(1-2*x)^(5/2)/(3+5*x)+63/125*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)-63/125*sqrt(1-2*x)],
[(1-2*x)^(5/2)/(3+5*x)^3,x,5,-1/10*(1-2*x)^(5/2)/(3+5*x)^2+1/10*(1-2*x)^(3/2)/(3+5*x)-3/25*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+3/25*sqrt(1-2*x)],
[(1-2*x)^(5/2)/((2+3*x)*(3+5*x)^3),x,7,-11/10*(1-2*x)^(3/2)/(3+5*x)^2-2523/25*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+98*arctanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(7/3)+803/50*sqrt(1-2*x)/(3+5*x)],
[(1-2*x)^(5/2)/((2+3*x)^2*(3+5*x)^3),x,8,7/3*(1-2*x)^(3/2)/((2+3*x)*(3+5*x)^2)-7209/5*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+1400*arctanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(7/3)-1133/30*sqrt(1-2*x)/(3+5*x)^2+7103/30*sqrt(1-2*x)/(3+5*x)],
[(1-2*x)^(5/2)/((2+3*x)^3*(3+5*x)^3),x,9,7/6*(1-2*x)^(3/2)/((2+3*x)^2*(3+5*x)^2)-14073*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+4555*arctanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(21)-6899/18*sqrt(1-2*x)/(3+5*x)^2+931/18*sqrt(1-2*x)/((2+3*x)*(3+5*x)^2)+2311*sqrt(1-2*x)/(3+5*x)],
[(1-2*x)^(5/2)/((2+3*x)^4*(3+5*x)^3),x,10,7/9*(1-2*x)^(3/2)/((2+3*x)^3*(3+5*x)^2)+785570*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-23115*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(55)-169975/54*sqrt(1-2*x)/(3+5*x)^2+581/27*sqrt(1-2*x)/((2+3*x)^2*(3+5*x)^2)+1256/3*sqrt(1-2*x)/((2+3*x)*(3+5*x)^2)+113875/6*sqrt(1-2*x)/(3+5*x)],
[(1-2*x)^(5/2)/((2+3*x)^5*(3+5*x)^3),x,11,7/12*(1-2*x)^(3/2)/((2+3*x)^4*(3+5*x)^2)+163363895/28*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-171675*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(55)-8836825/378*sqrt(1-2*x)/(3+5*x)^2+1393/108*sqrt(1-2*x)/((2+3*x)^3*(3+5*x)^2)+11243/72*sqrt(1-2*x)/((2+3*x)^2*(3+5*x)^2)+522385/168*sqrt(1-2*x)/((2+3*x)*(3+5*x)^2)+23680975/168*sqrt(1-2*x)/(3+5*x)],

# Integrands of the form (2+3 x)^m (3+5 x)^n / (1-2 x)^(1/2)

# n>0
[(2+3*x)^5*(3+5*x)/sqrt(1-2*x),x,2,60025/24*(1-2*x)^(3/2)-103929/64*(1-2*x)^(5/2)+5355/8*(1-2*x)^(7/2)-10815/64*(1-2*x)^(9/2)+1053/44*(1-2*x)^(11/2)-1215/832*(1-2*x)^(13/2)-184877/64*sqrt(1-2*x)],
[(2+3*x)^4*(3+5*x)/sqrt(1-2*x),x,2,57281/96*(1-2*x)^(3/2)-24843/80*(1-2*x)^(5/2)+1539/16*(1-2*x)^(7/2)-519/32*(1-2*x)^(9/2)+405/352*(1-2*x)^(11/2)-26411/32*sqrt(1-2*x)],
[(2+3*x)^3*(3+5*x)/sqrt(1-2*x),x,2,3283/24*(1-2*x)^(3/2)-1071/20*(1-2*x)^(5/2)+621/56*(1-2*x)^(7/2)-15/16*(1-2*x)^(9/2)-3773/16*sqrt(1-2*x)],
[(2+3*x)^2*(3+5*x)/sqrt(1-2*x),x,2,707/24*(1-2*x)^(3/2)-309/40*(1-2*x)^(5/2)+45/56*(1-2*x)^(7/2)-539/8*sqrt(1-2*x)],
[(2+3*x)*(3+5*x)/sqrt(1-2*x),x,2,17/3*(1-2*x)^(3/2)-3/4*(1-2*x)^(5/2)-77/4*sqrt(1-2*x)],
[(3+5*x)/sqrt(1-2*x),x,2,5/6*(1-2*x)^(3/2)-11/2*sqrt(1-2*x)],
[(3+5*x)/((2+3*x)*sqrt(1-2*x)),x,3,2/3*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-5/3*sqrt(1-2*x)],
[(3+5*x)/((2+3*x)^2*sqrt(1-2*x)),x,3,-68/21*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+1/21*sqrt(1-2*x)/(2+3*x)],
[(3+5*x)/((2+3*x)^3*sqrt(1-2*x)),x,4,-67/147*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+1/42*sqrt(1-2*x)/(2+3*x)^2-67/294*sqrt(1-2*x)/(2+3*x)],
[(3+5*x)/((2+3*x)^4*sqrt(1-2*x)),x,5,-100/1029*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+1/63*sqrt(1-2*x)/(2+3*x)^3-50/441*sqrt(1-2*x)/(2+3*x)^2-50/1029*sqrt(1-2*x)/(2+3*x)],
[(3+5*x)/((2+3*x)^5*sqrt(1-2*x)),x,6,-95/4116*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+1/84*sqrt(1-2*x)/(2+3*x)^4-19/252*sqrt(1-2*x)/(2+3*x)^3-95/3528*sqrt(1-2*x)/(2+3*x)^2-95/8232*sqrt(1-2*x)/(2+3*x)],
[(2+3*x)^5*(3+5*x)^2/sqrt(1-2*x),x,2,6206585/384*(1-2*x)^(3/2)-1623419/128*(1-2*x)^(5/2)+842415/128*(1-2*x)^(7/2)-285565/128*(1-2*x)^(9/2)+672003/1408*(1-2*x)^(11/2)-97605/1664*(1-2*x)^(13/2)+405/128*(1-2*x)^(15/2)-2033647/128*sqrt(1-2*x)],
[(2+3*x)^4*(3+5*x)^2/sqrt(1-2*x),x,2,381073/96*(1-2*x)^(3/2)-832951/320*(1-2*x)^(5/2)+17337/16*(1-2*x)^(7/2)-17679/64*(1-2*x)^(9/2)+13905/352*(1-2*x)^(11/2)-2025/832*(1-2*x)^(13/2)-290521/64*sqrt(1-2*x)],
[(2+3*x)^3*(3+5*x)^2/sqrt(1-2*x),x,2,91091/96*(1-2*x)^(3/2)-39977/80*(1-2*x)^(5/2)+17541/112*(1-2*x)^(7/2)-855/32*(1-2*x)^(9/2)+675/352*(1-2*x)^(11/2)-41503/32*sqrt(1-2*x)],
[(2+3*x)^2*(3+5*x)^2/sqrt(1-2*x),x,2,1309/6*(1-2*x)^(3/2)-3467/40*(1-2*x)^(5/2)+255/14*(1-2*x)^(7/2)-25/16*(1-2*x)^(9/2)-5929/16*sqrt(1-2*x)],
[(2+3*x)*(3+5*x)^2/sqrt(1-2*x),x,2,1133/24*(1-2*x)^(3/2)-101/8*(1-2*x)^(5/2)+75/56*(1-2*x)^(7/2)-847/8*sqrt(1-2*x)],
[(3+5*x)^2/sqrt(1-2*x),x,2,55/6*(1-2*x)^(3/2)-5/4*(1-2*x)^(5/2)-121/4*sqrt(1-2*x)],
[(3+5*x)^2/((2+3*x)*sqrt(1-2*x)),x,4,25/18*(1-2*x)^(3/2)-2/9*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-155/18*sqrt(1-2*x)],
[(3+5*x)^2/((2+3*x)^2*sqrt(1-2*x)),x,4,46/21*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-25/9*sqrt(1-2*x)-1/63*sqrt(1-2*x)/(2+3*x)],
[(3+5*x)^2/((2+3*x)^3*sqrt(1-2*x)),x,4,-257/49*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-1/126*sqrt(1-2*x)/(2+3*x)^2+137/882*sqrt(1-2*x)/(2+3*x)],
[(3+5*x)^2/((2+3*x)^4*sqrt(1-2*x)),x,5,-2245/3087*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-1/189*sqrt(1-2*x)/(2+3*x)^3+205/2646*sqrt(1-2*x)/(2+3*x)^2-2245/6174*sqrt(1-2*x)/(2+3*x)],
[(3+5*x)^2/((2+3*x)^5*sqrt(1-2*x)),x,6,-635/4116*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-1/252*sqrt(1-2*x)/(2+3*x)^4+13/252*sqrt(1-2*x)/(2+3*x)^3-635/3528*sqrt(1-2*x)/(2+3*x)^2-635/8232*sqrt(1-2*x)/(2+3*x)],
[(3+5*x)^2/((2+3*x)^6*sqrt(1-2*x)),x,7,-117/9604*arctanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-1/315*sqrt(1-2*x)/(2+3*x)^5+341/8820*sqrt(1-2*x)/(2+3*x)^4-117/980*sqrt(1-2*x)/(2+3*x)^3-117/2744*sqrt(1-2*x)/(2+3*x)^2-351/19208*sqrt(1-2*x)/(2+3*x)],
[(2+3*x)^4*(3+5*x)^3/sqrt(1-2*x),x,2,3278737/128*(1-2*x)^(3/2)-12973191/640*(1-2*x)^(5/2)+1357793/128*(1-2*x)^(7/2)-1392467/384*(1-2*x)^(9/2)+1101465/1408*(1-2*x)^(11/2)-161325/1664*(1-2*x)^(13/2)+675/128*(1-2*x)^(15/2)-3195731/128*sqrt(1-2*x)],
[(2+3*x)^3*(3+5*x)^3/sqrt(1-2*x),x,2,100793/16*(1-2*x)^(3/2)-1334949/320*(1-2*x)^(5/2)+98209/56*(1-2*x)^(7/2)-28895/64*(1-2*x)^(9/2)+11475/176*(1-2*x)^(11/2)-3375/832*(1-2*x)^(13/2)-456533/64*sqrt(1-2*x)],
[(2+3*x)^2*(3+5*x)^3/sqrt(1-2*x),x,2,48279/32*(1-2*x)^(3/2)-64317/80*(1-2*x)^(5/2)+28555/112*(1-2*x)^(7/2)-4225/96*(1-2*x)^(9/2)+1125/352*(1-2*x)^(11/2)-65219/32*sqrt(1-2*x)],
[(2+3*x)*(3+5*x)^3/sqrt(1-2*x),x,2,2783/8*(1-2*x)^(3/2)-561/4*(1-2*x)^(5/2)+1675/56*(1-2*x)^(7/2)-125/48*(1-2*x)^(9/2)-9317/16*sqrt(1-2*x)],
[(3+5*x)^3/sqrt(1-2*x),x,2,605/8*(1-2*x)^(3/2)-165/8*(1-2*x)^(5/2)+125/56*(1-2*x)^(7/2)-1331/8*sqrt(1-2*x)],
[(3+5*x)^3/((2+3*x)*sqrt(1-2*x)),x,4,400/27*(1-2*x)^(3/2)-25/12*(1-2*x)^(5/2)+2/27*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-5135/108*sqrt(1-2*x)],
[(3+5*x)^3/((2+3*x)^2*sqrt(1-2*x)),x,4,-208/189*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+1/21*(3+5*x)^2*sqrt(1-2*x)/(2+3*x)-10/189*(214+95*x)*sqrt(1-2*x)],
[(3+5*x)^3/((2+3*x)^3*sqrt(1-2*x)),x,4,2381/441*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+1/42*(3+5*x)^2*sqrt(1-2*x)/(2+3*x)^2-1/882*(8329+12425*x)*sqrt(1-2*x)/(2+3*x)],
[(3+5*x)^3/((2+3*x)^4*sqrt(1-2*x)),x,4,-78710/9261*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+1/63*(3+5*x)^2*sqrt(1-2*x)/(2+3*x)^3+5/9261*(1205+1867*x)*sqrt(1-2*x)/(2+3*x)^2],
[(3+5*x)^3/((2+3*x)^5*sqrt(1-2*x)),x,5,-42995/37044*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-42995/74088*sqrt(1-2*x)/(2+3*x)+1/84*(3+5*x)^2*sqrt(1-2*x)/(2+3*x)^4+1/10584*(3168+4955*x)*sqrt(1-2*x)/(2+3*x)^3],
[(3+5*x)^3/((2+3*x)^6*sqrt(1-2*x)),x,6,-5293/21609*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-5293/18522*sqrt(1-2*x)/(2+3*x)^2-5293/43218*sqrt(1-2*x)/(2+3*x)+1/105*(3+5*x)^2*sqrt(1-2*x)/(2+3*x)^5+1/6615*(1255+1971*x)*sqrt(1-2*x)/(2+3*x)^4],

# n<0
[(a+b*x)^2/((c+d*x)^2*sqrt(e+f*x)),x,4,(b*c-a*d)*(4*b*d*e-3*b*c*f-a*d*f)*arctanh(sqrt(d)*sqrt(e+f*x)/sqrt(d*e-c*f))/(d^(5/2)*(d*e-c*f)^(3/2))+2*b^2*sqrt(e+f*x)/(d^2*f)-(b*c-a*d)^2*sqrt(e+f*x)/(d^2*(d*e-c*f)*(c+d*x))],
[(2+3*x)^5/((3+5*x)*sqrt(1-2*x)),x,4,268707/5000*(1-2*x)^(3/2)-51057/2500*(1-2*x)^(5/2)+5751/1400*(1-2*x)^(7/2)-27/80*(1-2*x)^(9/2)-2/3125*arctanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-4774713/50000*sqrt(1-2*x)],
[(2+3*x)^4/((3+5*x)*sqrt(1-2*x)),x,4,11457/1000*(1-2*x)^(3/2)-2889/1000*(1-2*x)^(5/2)+81/280*(1-2*x)^(7/2)-2/625*arctanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-136419/5000*sqrt(1-2*x)],
[(2+3*x)^3/((3+5*x)*sqrt(1-2*x)),x,4,54/25*(1-2*x)^(3/2)-27/100*(1-2*x)^(5/2)-2/125*arctanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-3897/500*sqrt(1-2*x)],
[(2+3*x)^2/((3+5*x)*sqrt(1-2*x)),x,4,3/10*(1-2*x)^(3/2)-2/25*arctanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-111/50*sqrt(1-2*x)],
[(2+3*x)/((3+5*x)*sqrt(1-2*x)),x,3,-2/5*arctanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-3/5*sqrt(1-2*x)],
[1/((3+5*x)*sqrt(1-2*x)),x,2,-2*arctanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)],
[1/((2+3*x)*(3+5*x)*sqrt(1-2*x)),x,5,2*arctanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-2*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)],
[1/((2+3*x)^2*(3+5*x)*sqrt(1-2*x)),x,6,72/7*arctanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-10*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+3/7*sqrt(1-2*x)/(2+3*x)],
[1/((2+3*x)^3*(3+5*x)*sqrt(1-2*x)),x,7,2523/49*arctanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-50*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+3/14*sqrt(1-2*x)/(2+3*x)^2+219/98*sqrt(1-2*x)/(2+3*x)],
[1/((2+3*x)^4*(3+5*x)*sqrt(1-2*x)),x,8,88310/343*arctanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-250*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+1/7*sqrt(1-2*x)/(2+3*x)^3+55/49*sqrt(1-2*x)/(2+3*x)^2+3840/343*sqrt(1-2*x)/(2+3*x)],
[1/((2+3*x)^5*(3+5*x)*sqrt(1-2*x)),x,9,36045/28*arctanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-1250*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+3/28*sqrt(1-2*x)/(2+3*x)^4+3/4*sqrt(1-2*x)/(2+3*x)^3+45/8*sqrt(1-2*x)/(2+3*x)^2+3135/56*sqrt(1-2*x)/(2+3*x)],
[(2+3*x)^6/((3+5*x)^2*sqrt(1-2*x)),x,7,-398/171875*arctanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-26352/34375*(2+3*x)^2*sqrt(1-2*x)-1717/9625*(2+3*x)^3*sqrt(1-2*x)-8/275*(2+3*x)^4*sqrt(1-2*x)-1/55*(2+3*x)^5*sqrt(1-2*x)/(3+5*x)-3/171875*(1847824+615875*x)*sqrt(1-2*x)],
[(2+3*x)^5/((3+5*x)^2*sqrt(1-2*x)),x,6,-332/34375*arctanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-1668/6875*(2+3*x)^2*sqrt(1-2*x)-78/1925*(2+3*x)^3*sqrt(1-2*x)-1/55*(2+3*x)^4*sqrt(1-2*x)/(3+5*x)-6/34375*(59708+19875*x)*sqrt(1-2*x)],
[(2+3*x)^4/((3+5*x)^2*sqrt(1-2*x)),x,5,-266/6875*arctanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-84/1375*(2+3*x)^2*sqrt(1-2*x)-1/55*(2+3*x)^3*sqrt(1-2*x)/(3+5*x)-21/6875*(1144+375*x)*sqrt(1-2*x)],
[(2+3*x)^3/((3+5*x)^2*sqrt(1-2*x)),x,4,-8/55*arctanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-6/55*(11+3*x)*sqrt(1-2*x)-1/55*(2+3*x)^2*sqrt(1-2*x)/(3+5*x)],
[(2+3*x)^2/((3+5*x)^2*sqrt(1-2*x)),x,4,-134/275*arctanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-9/25*sqrt(1-2*x)-1/275*sqrt(1-2*x)/(3+5*x)],
[(2+3*x)/((3+5*x)^2*sqrt(1-2*x)),x,3,-68/55*arctanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-1/55*sqrt(1-2*x)/(3+5*x)],
[1/((3+5*x)^2*sqrt(1-2*x)),x,3,-2/11*arctanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-1/11*sqrt(1-2*x)/(3+5*x)],
[1/((2+3*x)*(3+5*x)^2*sqrt(1-2*x)),x,6,-6*arctanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)+64/11*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)-5/11*sqrt(1-2*x)/(3+5*x)],
[1/((2+3*x)^2*(3+5*x)^2*sqrt(1-2*x)),x,7,-426/7*arctanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)+650/11*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)-340/77*sqrt(1-2*x)/(3+5*x)+3/7*sqrt(1-2*x)/((2+3*x)*(3+5*x))],
[1/((2+3*x)^3*(3+5*x)^2*sqrt(1-2*x)),x,8,-22479/49*arctanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)+4900/11*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)-35845/1078*sqrt(1-2*x)/(3+5*x)+3/14*sqrt(1-2*x)/((2+3*x)^2*(3+5*x))+162/49*sqrt(1-2*x)/((2+3*x)*(3+5*x))],
[1/((2+3*x)^4*(3+5*x)^2*sqrt(1-2*x)),x,9,-1051695/343*arctanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)+32750/11*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)-1676975/7546*sqrt(1-2*x)/(3+5*x)+1/7*sqrt(1-2*x)/((2+3*x)^3*(3+5*x))+145/98*sqrt(1-2*x)/((2+3*x)^2*(3+5*x))+7585/343*sqrt(1-2*x)/((2+3*x)*(3+5*x))],
[(2+3*x)^6/((3+5*x)^3*sqrt(1-2*x)),x,7,-33069/1890625*arctanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-56556/378125*(2+3*x)^2*sqrt(1-2*x)-927/211750*(2+3*x)^3*sqrt(1-2*x)-1/110*(2+3*x)^5*sqrt(1-2*x)/(3+5*x)^2-117/3025*(2+3*x)^4*sqrt(1-2*x)/(3+5*x)-9/3781250*(2815648+934875*x)*sqrt(1-2*x)],
[(2+3*x)^5/((3+5*x)^3*sqrt(1-2*x)),x,6,-22113/378125*arctanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-1512/75625*(2+3*x)^2*sqrt(1-2*x)-1/110*(2+3*x)^4*sqrt(1-2*x)/(3+5*x)^2-201/6050*(2+3*x)^3*sqrt(1-2*x)/(3+5*x)-189/756250*(8976+2875*x)*sqrt(1-2*x)],
[(2+3*x)^4/((3+5*x)^3*sqrt(1-2*x)),x,5,-2667/15125*arctanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-1/110*(2+3*x)^3*sqrt(1-2*x)/(3+5*x)^2-84/3025*(2+3*x)^2*sqrt(1-2*x)/(3+5*x)-63/30250*(352+75*x)*sqrt(1-2*x)],
[(2+3*x)^3/((3+5*x)^3*sqrt(1-2*x)),x,4,-1347/3025*arctanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-1/110*(2+3*x)^2*sqrt(1-2*x)/(3+5*x)^2-9/6050*(432+715*x)*sqrt(1-2*x)/(3+5*x)],
[(2+3*x)^2/((3+5*x)^3*sqrt(1-2*x)),x,4,-2313/3025*arctanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-1/550*sqrt(1-2*x)/(3+5*x)^2-27/1210*sqrt(1-2*x)/(3+5*x)],
[(2+3*x)/((3+5*x)^3*sqrt(1-2*x)),x,4,-69/605*arctanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-1/110*sqrt(1-2*x)/(3+5*x)^2-69/1210*sqrt(1-2*x)/(3+5*x)],
[1/((3+5*x)^3*sqrt(1-2*x)),x,4,-3/121*arctanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-1/22*sqrt(1-2*x)/(3+5*x)^2-3/242*sqrt(1-2*x)/(3+5*x)],
[1/((2+3*x)*(3+5*x)^3*sqrt(1-2*x)),x,7,18*arctanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-2115/121*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)-5/22*sqrt(1-2*x)/(3+5*x)^2+315/242*sqrt(1-2*x)/(3+5*x)],
[1/((2+3*x)^2*(3+5*x)^3*sqrt(1-2*x)),x,8,1908/7*arctanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-32025/121*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)-505/154*sqrt(1-2*x)/(3+5*x)^2+3/7*sqrt(1-2*x)/((2+3*x)*(3+5*x)^2)+33465/1694*sqrt(1-2*x)/(3+5*x)],
[1/((2+3*x)^3*(3+5*x)^3*sqrt(1-2*x)),x,9,134217/49*arctanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-321825/121*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)-35495/1078*sqrt(1-2*x)/(3+5*x)^2+3/14*sqrt(1-2*x)/((2+3*x)^2*(3+5*x)^2)+429/98*sqrt(1-2*x)/((2+3*x)*(3+5*x)^2)+1177080/5929*sqrt(1-2*x)/(3+5*x)],
[1/((2+3*x)^4*(3+5*x)^3*sqrt(1-2*x)),x,10,7852680/343*arctanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-2689875/121*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)-2076675/7546*sqrt(1-2*x)/(3+5*x)^2+1/7*sqrt(1-2*x)/((2+3*x)^3*(3+5*x)^2)+90/49*sqrt(1-2*x)/((2+3*x)^2*(3+5*x)^2)+12555/343*sqrt(1-2*x)/((2+3*x)*(3+5*x)^2)+137735775/83006*sqrt(1-2*x)/(3+5*x)],

# Integrands of the form (2+3 x)^m (3+5 x)^n / (1-2 x)^(3/2)

# n>0
[(2+3*x)^7*(3+5*x)/(1-2*x)^(3/2),x,2,-7882483/128*(1-2*x)^(3/2)+4084101/128*(1-2*x)^(5/2)-787185/64*(1-2*x)^(7/2)+422919/128*(1-2*x)^(9/2)-821583/1408*(1-2*x)^(11/2)+101331/1664*(1-2*x)^(13/2)-729/256*(1-2*x)^(15/2)+9058973/256/sqrt(1-2*x)+15647317/128*sqrt(1-2*x)],
[(2+3*x)^6*(3+5*x)/(1-2*x)^(3/2),x,2,-1692705/128*(1-2*x)^(3/2)+731619/128*(1-2*x)^(5/2)-225855/128*(1-2*x)^(7/2)+45549/128*(1-2*x)^(9/2)-59049/1408*(1-2*x)^(11/2)+3645/1664*(1-2*x)^(13/2)+1294139/128/sqrt(1-2*x)+3916031/128*sqrt(1-2*x)],
[(2+3*x)^5*(3+5*x)/(1-2*x)^(3/2),x,2,-173215/64*(1-2*x)^(3/2)+7497/8*(1-2*x)^(5/2)-13905/64*(1-2*x)^(7/2)+117/4*(1-2*x)^(9/2)-1215/704*(1-2*x)^(11/2)+184877/64/sqrt(1-2*x)+60025/8*sqrt(1-2*x)],
[(2+3*x)^4*(3+5*x)/(1-2*x)^(3/2),x,2,-8281/16*(1-2*x)^(3/2)+10773/80*(1-2*x)^(5/2)-4671/224*(1-2*x)^(7/2)+45/32*(1-2*x)^(9/2)+26411/32/sqrt(1-2*x)+57281/32*sqrt(1-2*x)],
[(2+3*x)^3*(3+5*x)/(1-2*x)^(3/2),x,2,-357/4*(1-2*x)^(3/2)+621/40*(1-2*x)^(5/2)-135/112*(1-2*x)^(7/2)+3773/16/sqrt(1-2*x)+3283/8*sqrt(1-2*x)],
[(2+3*x)^2*(3+5*x)/(1-2*x)^(3/2),x,2,-103/8*(1-2*x)^(3/2)+9/8*(1-2*x)^(5/2)+539/8/sqrt(1-2*x)+707/8*sqrt(1-2*x)],
[(2+3*x)*(3+5*x)/(1-2*x)^(3/2),x,2,-5/4*(1-2*x)^(3/2)+77/4/sqrt(1-2*x)+17*sqrt(1-2*x)],
[(3+5*x)/(1-2*x)^(3/2),x,2,11/2/sqrt(1-2*x)+5/2*sqrt(1-2*x)],
[(3+5*x)/((1-2*x)^(3/2)*(2+3*x)),x,3,2/7*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+11/7/sqrt(1-2*x)],
[(3+5*x)/((1-2*x)^(3/2)*(2+3*x)^2),x,4,-64/49*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+64/147/sqrt(1-2*x)+1/21/((2+3*x)*sqrt(1-2*x))],
[(3+5*x)/((1-2*x)^(3/2)*(2+3*x)^3),x,5,-65/343*arctanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)+65/343/sqrt(1-2*x)+1/42/((2+3*x)^2*sqrt(1-2*x))+(-65/294)/((2+3*x)*sqrt(1-2*x))],
[(3+5*x)/((1-2*x)^(3/2)*(2+3*x)^4),x,6,-10/49*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+10/147/sqrt(1-2*x)+1/63/((2+3*x)^3*sqrt(1-2*x))+(-1/9)/((2+3*x)^2*sqrt(1-2*x))+(-5/63)/((2+3*x)*sqrt(1-2*x))],
[(3+5*x)/((1-2*x)^(3/2)*(2+3*x)^5),x,7,-655/9604*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+655/28812/sqrt(1-2*x)+1/84/((2+3*x)^4*sqrt(1-2*x))+(-131/1764)/((2+3*x)^3*sqrt(1-2*x))+(-131/3528)/((2+3*x)^2*sqrt(1-2*x))+(-655/24696)/((2+3*x)*sqrt(1-2*x))],
[(3+5*x)/((1-2*x)^(3/2)*(2+3*x)^6),x,8,-123/16807*arctanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)+123/16807/sqrt(1-2*x)+1/105/((2+3*x)^5*sqrt(1-2*x))+(-41/735)/((2+3*x)^4*sqrt(1-2*x))+(-41/1715)/((2+3*x)^3*sqrt(1-2*x))+(-41/3430)/((2+3*x)^2*sqrt(1-2*x))+(-41/4802)/((2+3*x)*sqrt(1-2*x))],
[(2+3*x)^5*(3+5*x)^2/(1-2*x)^(3/2),x,2,-8117095/384*(1-2*x)^(3/2)+1179381/128*(1-2*x)^(5/2)-367155/128*(1-2*x)^(7/2)+74667/128*(1-2*x)^(9/2)-97605/1408*(1-2*x)^(11/2)+6075/1664*(1-2*x)^(13/2)+2033647/128/sqrt(1-2*x)+6206585/128*sqrt(1-2*x)],
[(2+3*x)^4*(3+5*x)^2/(1-2*x)^(3/2),x,2,-832951/192*(1-2*x)^(3/2)+121359/80*(1-2*x)^(5/2)-159111/448*(1-2*x)^(7/2)+1545/32*(1-2*x)^(9/2)-2025/704*(1-2*x)^(11/2)+290521/64/sqrt(1-2*x)+381073/32*sqrt(1-2*x)],
[(2+3*x)^3*(3+5*x)^2/(1-2*x)^(3/2),x,2,-39977/48*(1-2*x)^(3/2)+17541/80*(1-2*x)^(5/2)-7695/224*(1-2*x)^(7/2)+75/32*(1-2*x)^(9/2)+41503/32/sqrt(1-2*x)+91091/32*sqrt(1-2*x)],
[(2+3*x)^2*(3+5*x)^2/(1-2*x)^(3/2),x,2,-3467/24*(1-2*x)^(3/2)+51/2*(1-2*x)^(5/2)-225/112*(1-2*x)^(7/2)+5929/16/sqrt(1-2*x)+1309/2*sqrt(1-2*x)],
[(2+3*x)*(3+5*x)^2/(1-2*x)^(3/2),x,2,-505/24*(1-2*x)^(3/2)+15/8*(1-2*x)^(5/2)+847/8/sqrt(1-2*x)+1133/8*sqrt(1-2*x)],
[(3+5*x)^2/(1-2*x)^(3/2),x,2,-25/12*(1-2*x)^(3/2)+121/4/sqrt(1-2*x)+55/2*sqrt(1-2*x)],
[(3+5*x)^2/((1-2*x)^(3/2)*(2+3*x)),x,4,-2/21*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+121/14/sqrt(1-2*x)+25/6*sqrt(1-2*x)],
[(3+5*x)^2/((1-2*x)^(3/2)*(2+3*x)^2),x,4,134/147*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+121/14/((2+3*x)*sqrt(1-2*x))-1091/294*sqrt(1-2*x)/(2+3*x)],
[(3+5*x)^2/((1-2*x)^(3/2)*(2+3*x)^3),x,5,-2045/1029*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+121/14/((2+3*x)^2*sqrt(1-2*x))-545/147*sqrt(1-2*x)/(2+3*x)^2-2045/2058*sqrt(1-2*x)/(2+3*x)],
[(3+5*x)^2/((1-2*x)^(3/2)*(2+3*x)^4),x,6,-905/1029*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+121/14/((2+3*x)^3*sqrt(1-2*x))-467/126*sqrt(1-2*x)/(2+3*x)^3-905/882*sqrt(1-2*x)/(2+3*x)^2-905/2058*sqrt(1-2*x)/(2+3*x)],
[(3+5*x)^2/((1-2*x)^(3/2)*(2+3*x)^5),x,7,-9145/28812*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+121/14/((2+3*x)^4*sqrt(1-2*x))-2179/588*sqrt(1-2*x)/(2+3*x)^4-1829/1764*sqrt(1-2*x)/(2+3*x)^3-9145/24696*sqrt(1-2*x)/(2+3*x)^2-9145/57624*sqrt(1-2*x)/(2+3*x)],
[(2+3*x)^4*(3+5*x)^3/(1-2*x)^(3/2),x,2,-4324397/128*(1-2*x)^(3/2)+9504551/640*(1-2*x)^(5/2)-4177401/896*(1-2*x)^(7/2)+122385/128*(1-2*x)^(9/2)-161325/1408*(1-2*x)^(11/2)+10125/1664*(1-2*x)^(13/2)+3195731/128/sqrt(1-2*x)+9836211/128*sqrt(1-2*x)],
[(2+3*x)^3*(3+5*x)^3/(1-2*x)^(3/2),x,2,-444983/64*(1-2*x)^(3/2)+98209/40*(1-2*x)^(5/2)-260055/448*(1-2*x)^(7/2)+1275/16*(1-2*x)^(9/2)-3375/704*(1-2*x)^(11/2)+456533/64/sqrt(1-2*x)+302379/16*sqrt(1-2*x)],
[(2+3*x)^2*(3+5*x)^3/(1-2*x)^(3/2),x,2,-21439/16*(1-2*x)^(3/2)+5711/16*(1-2*x)^(5/2)-12675/224*(1-2*x)^(7/2)+125/32*(1-2*x)^(9/2)+65219/32/sqrt(1-2*x)+144837/32*sqrt(1-2*x)],
[(2+3*x)*(3+5*x)^3/(1-2*x)^(3/2),x,2,-935/4*(1-2*x)^(3/2)+335/8*(1-2*x)^(5/2)-375/112*(1-2*x)^(7/2)+9317/16/sqrt(1-2*x)+8349/8*sqrt(1-2*x)],
[(3+5*x)^3/(1-2*x)^(3/2),x,2,-275/8*(1-2*x)^(3/2)+25/8*(1-2*x)^(5/2)+1331/8/sqrt(1-2*x)+1815/8*sqrt(1-2*x)],
[(3+5*x)^3/((1-2*x)^(3/2)*(2+3*x)),x,6,-125/36*(1-2*x)^(3/2)+2/63*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+1331/28/sqrt(1-2*x)+400/9*sqrt(1-2*x)],
[(3+5*x)^3/((1-2*x)^(3/2)*(2+3*x)^2),x,4,-68/147*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+11/7*(3+5*x)^2/((2+3*x)*sqrt(1-2*x))+2/147*(1978+2975*x)*sqrt(1-2*x)/(2+3*x)],
[(3+5*x)^3/((1-2*x)^(3/2)*(2+3*x)^3),x,4,2245/1029*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+11/7*(3+5*x)^2/((2+3*x)^2*sqrt(1-2*x))+5/2058*(541+857*x)*sqrt(1-2*x)/(2+3*x)^2],
[(3+5*x)^3/((1-2*x)^(3/2)*(2+3*x)^4),x,5,-9320/3087*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+11/7*(3+5*x)^2/((2+3*x)^3*sqrt(1-2*x))-4660/3087*sqrt(1-2*x)/(2+3*x)+2/441*(297+470*x)*sqrt(1-2*x)/(2+3*x)^3],
[(3+5*x)^3/((1-2*x)^(3/2)*(2+3*x)^5),x,6,-39185/28812*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+11/7*(3+5*x)^2/((2+3*x)^4*sqrt(1-2*x))-39185/24696*sqrt(1-2*x)/(2+3*x)^2-39185/57624*sqrt(1-2*x)/(2+3*x)+1/1764*(2395+3789*x)*sqrt(1-2*x)/(2+3*x)^4],

# n<0
[(2+3*x)^6/((1-2*x)^(3/2)*(3+5*x)),x,12,-1997451/10000*(1-2*x)^(3/2)+507627/10000*(1-2*x)^(5/2)-43011/5600*(1-2*x)^(7/2)+81/160*(1-2*x)^(9/2)-2/34375*arctanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+117649/352/sqrt(1-2*x)+70752609/100000*sqrt(1-2*x)],
[(2+3*x)^5/((1-2*x)^(3/2)*(3+5*x)),x,10,-17019/500*(1-2*x)^(3/2)+5751/1000*(1-2*x)^(5/2)-243/560*(1-2*x)^(7/2)-2/6875*arctanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+16807/176/sqrt(1-2*x)+806121/5000*sqrt(1-2*x)],
[(2+3*x)^4/((1-2*x)^(3/2)*(3+5*x)),x,8,-963/200*(1-2*x)^(3/2)+81/200*(1-2*x)^(5/2)-2/1375*arctanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+2401/88/sqrt(1-2*x)+34371/1000*sqrt(1-2*x)],
[(2+3*x)^3/((1-2*x)^(3/2)*(3+5*x)),x,6,-9/20*(1-2*x)^(3/2)-2/275*arctanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+343/44/sqrt(1-2*x)+162/25*sqrt(1-2*x)],
[(2+3*x)^2/((1-2*x)^(3/2)*(3+5*x)),x,4,-2/55*arctanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+49/22/sqrt(1-2*x)+9/10*sqrt(1-2*x)],
[(2+3*x)/((1-2*x)^(3/2)*(3+5*x)),x,3,-2/11*arctanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+7/11/sqrt(1-2*x)],
[1/((1-2*x)^(3/2)*(3+5*x)),x,3,-2/11*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+2/11/sqrt(1-2*x)],
[1/((1-2*x)^(3/2)*(2+3*x)*(3+5*x)),x,6,6/7*arctanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-10/11*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+4/77/sqrt(1-2*x)],
[1/((1-2*x)^(3/2)*(2+3*x)^2*(3+5*x)),x,7,228/49*arctanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-50/11*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+(-58/539)/sqrt(1-2*x)+3/7/((2+3*x)*sqrt(1-2*x))],
[1/((1-2*x)^(3/2)*(2+3*x)^3*(3+5*x)),x,8,8025/343*arctanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-250/11*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+(-2525/3773)/sqrt(1-2*x)+3/14/((2+3*x)^2*sqrt(1-2*x))+225/98/((2+3*x)*sqrt(1-2*x))],
[1/((1-2*x)^(3/2)*(2+3*x)^4*(3+5*x)),x,9,40140/343*arctanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-1250/11*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+(-12790/3773)/sqrt(1-2*x)+1/7/((2+3*x)^3*sqrt(1-2*x))+8/7/((2+3*x)^2*sqrt(1-2*x))+565/49/((2+3*x)*sqrt(1-2*x))],
[(2+3*x)^6/((1-2*x)^(3/2)*(3+5*x)^2),x,7,-402/378125*arctanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+7/11*(2+3*x)^5/((3+5*x)*sqrt(1-2*x))+217152/75625*(2+3*x)^2*sqrt(1-2*x)+14517/21175*(2+3*x)^3*sqrt(1-2*x)-36/605*(2+3*x)^4*sqrt(1-2*x)/(3+5*x)+9/378125*(5065808+1688625*x)*sqrt(1-2*x)],
[(2+3*x)^5/((1-2*x)^(3/2)*(3+5*x)^2),x,6,-336/75625*arctanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+7/11*(2+3*x)^4/((3+5*x)*sqrt(1-2*x))+10836/15125*(2+3*x)^2*sqrt(1-2*x)-36/605*(2+3*x)^3*sqrt(1-2*x)/(3+5*x)+504/75625*(4499+1500*x)*sqrt(1-2*x)],
[(2+3*x)^4/((1-2*x)^(3/2)*(3+5*x)^2),x,5,-54/3025*arctanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+7/11*(2+3*x)^3/((3+5*x)*sqrt(1-2*x))-36/605*(2+3*x)^2*sqrt(1-2*x)/(3+5*x)+27/3025*(792+265*x)*sqrt(1-2*x)],
[(2+3*x)^3/((1-2*x)^(3/2)*(3+5*x)^2),x,4,-204/3025*arctanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+7/11*(2+3*x)^2/((3+5*x)*sqrt(1-2*x))+18/3025*(559+935*x)*sqrt(1-2*x)/(3+5*x)],
[(2+3*x)^2/((1-2*x)^(3/2)*(3+5*x)^2),x,4,-138/605*arctanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+49/22/((3+5*x)*sqrt(1-2*x))-1227/1210*sqrt(1-2*x)/(3+5*x)],
[(2+3*x)/((1-2*x)^(3/2)*(3+5*x)^2),x,4,-72/121*arctanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+72/605/sqrt(1-2*x)+(-1/55)/((3+5*x)*sqrt(1-2*x))],
[1/((1-2*x)^(3/2)*(3+5*x)^2),x,4,-6/121*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+6/121/sqrt(1-2*x)+(-1/11)/((3+5*x)*sqrt(1-2*x))],
[1/((1-2*x)^(3/2)*(2+3*x)*(3+5*x)^2),x,7,-18/7*arctanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)+300/121*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+78/847/sqrt(1-2*x)+(-5/11)/((3+5*x)*sqrt(1-2*x))],
[1/((1-2*x)^(3/2)*(2+3*x)^2*(3+5*x)^2),x,8,-1314/49*arctanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)+3150/121*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+4644/5929/sqrt(1-2*x)+(-340/77)/((3+5*x)*sqrt(1-2*x))+3/7/((2+3*x)*(3+5*x)*sqrt(1-2*x))],
[1/((1-2*x)^(3/2)*(2+3*x)^3*(3+5*x)^2),x,9,-70065/343*arctanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)+24000/121*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+245865/41503/sqrt(1-2*x)+(-36175/1078)/((3+5*x)*sqrt(1-2*x))+3/14/((2+3*x)^2*(3+5*x)*sqrt(1-2*x))+165/49/((2+3*x)*(3+5*x)*sqrt(1-2*x))],
[(2+3*x)^6/((1-2*x)^(3/2)*(3+5*x)^3),x,7,-33873/4159375*arctanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+7/11*(2+3*x)^5/((3+5*x)^2*sqrt(1-2*x))+377748/831875*(2+3*x)^2*sqrt(1-2*x)-71/1210*(2+3*x)^4*sqrt(1-2*x)/(3+5*x)^2-2721/66550*(2+3*x)^3*sqrt(1-2*x)/(3+5*x)+63/8318750*(2492512+831375*x)*sqrt(1-2*x)],
[(2+3*x)^5/((1-2*x)^(3/2)*(3+5*x)^3),x,6,-4557/166375*arctanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+7/11*(2+3*x)^4/((3+5*x)^2*sqrt(1-2*x))-71/1210*(2+3*x)^3*sqrt(1-2*x)/(3+5*x)^2-1344/33275*(2+3*x)^2*sqrt(1-2*x)/(3+5*x)+441/332750*(3344+1125*x)*sqrt(1-2*x)],
[(2+3*x)^4/((1-2*x)^(3/2)*(3+5*x)^3),x,5,-111/1331*arctanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+7/11*(2+3*x)^3/((3+5*x)^2*sqrt(1-2*x))-71/1210*(2+3*x)^2*sqrt(1-2*x)/(3+5*x)^2+9/13310*(3044+5093*x)*sqrt(1-2*x)/(3+5*x)],
[(2+3*x)^3/((1-2*x)^(3/2)*(3+5*x)^3),x,4,-7143/33275*arctanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+7/11*(2+3*x)^2/((3+5*x)^2*sqrt(1-2*x))-1/66550*(15676+24825*x)*sqrt(1-2*x)/(3+5*x)^2],
[(2+3*x)^2/((1-2*x)^(3/2)*(3+5*x)^3),x,5,-2589/6655*arctanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+49/22/((3+5*x)^2*sqrt(1-2*x))-613/605*sqrt(1-2*x)/(3+5*x)^2-2589/13310*sqrt(1-2*x)/(3+5*x)],
[(2+3*x)/((1-2*x)^(3/2)*(3+5*x)^3),x,5,-213/1331*arctanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+213/6655/sqrt(1-2*x)+(-1/110)/((3+5*x)^2*sqrt(1-2*x))+(-71/1210)/((3+5*x)*sqrt(1-2*x))],
[1/((1-2*x)^(3/2)*(3+5*x)^3),x,5,-15/1331*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+15/1331/sqrt(1-2*x)+(-1/22)/((3+5*x)^2*sqrt(1-2*x))+(-5/242)/((3+5*x)*sqrt(1-2*x))],
[1/((1-2*x)^(3/2)*(2+3*x)*(3+5*x)^3),x,8,54/7*arctanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-9975/1331*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+(-2049/9317)/sqrt(1-2*x)+(-5/22)/((3+5*x)^2*sqrt(1-2*x))+305/242/((3+5*x)*sqrt(1-2*x))],
[1/((1-2*x)^(3/2)*(2+3*x)^2*(3+5*x)^3),x,9,5832/49*arctanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-153825/1331*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+(-224967/65219)/sqrt(1-2*x)+(-505/154)/((3+5*x)^2*sqrt(1-2*x))+3/7/((2+3*x)*(3+5*x)^2*sqrt(1-2*x))+33115/1694/((3+5*x)*sqrt(1-2*x))],
[1/((1-2*x)^(3/2)*(2+3*x)^3*(3+5*x)^3),x,10,414315/343*arctanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-1561125/1331*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+(-15987390/456533)/sqrt(1-2*x)+(-35825/1078)/((3+5*x)^2*sqrt(1-2*x))+3/14/((2+3*x)^2*(3+5*x)^2*sqrt(1-2*x))+435/98/((2+3*x)*(3+5*x)^2*sqrt(1-2*x))+1176400/5929/((3+5*x)*sqrt(1-2*x))],

# Integrands of the form (2+3 x)^m (3+5 x)^n / (1-2 x)^(5/2)

# n>0
[(2+3*x)^5*(3+5*x)/(1-2*x)^(5/2),x,2,184877/192/(1-2*x)^(3/2)+12495/8*(1-2*x)^(3/2)-19467/64*(1-2*x)^(5/2)+1053/28*(1-2*x)^(7/2)-135/64*(1-2*x)^(9/2)+(-60025/8)/sqrt(1-2*x)-519645/64*sqrt(1-2*x)],
[(2+3*x)^4*(3+5*x)/(1-2*x)^(5/2),x,2,26411/96/(1-2*x)^(3/2)+3591/16*(1-2*x)^(3/2)-4671/160*(1-2*x)^(5/2)+405/224*(1-2*x)^(7/2)+(-57281/32)/sqrt(1-2*x)-24843/16*sqrt(1-2*x)],
[(2+3*x)^3*(3+5*x)/(1-2*x)^(5/2),x,2,3773/48/(1-2*x)^(3/2)+207/8*(1-2*x)^(3/2)-27/16*(1-2*x)^(5/2)+(-3283/8)/sqrt(1-2*x)-1071/4*sqrt(1-2*x)],
[(2+3*x)^2*(3+5*x)/(1-2*x)^(5/2),x,2,539/24/(1-2*x)^(3/2)+15/8*(1-2*x)^(3/2)+(-707/8)/sqrt(1-2*x)-309/8*sqrt(1-2*x)],
[(2+3*x)*(3+5*x)/(1-2*x)^(5/2),x,2,77/12/(1-2*x)^(3/2)+(-17)/sqrt(1-2*x)-15/4*sqrt(1-2*x)],
[(3+5*x)/(1-2*x)^(5/2),x,2,11/6/(1-2*x)^(3/2)+(-5/2)/sqrt(1-2*x)],
[(3+5*x)/((1-2*x)^(5/2)*(2+3*x)),x,4,11/21/(1-2*x)^(3/2)+2/49*arctanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)+(-2/49)/sqrt(1-2*x)],
[(3+5*x)/((1-2*x)^(5/2)*(2+3*x)^2),x,5,20/147/(1-2*x)^(3/2)+1/21/((1-2*x)^(3/2)*(2+3*x))-60/343*arctanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)+60/343/sqrt(1-2*x)],
[(3+5*x)/((1-2*x)^(5/2)*(2+3*x)^3),x,6,5/49/(1-2*x)^(3/2)+1/42/((1-2*x)^(3/2)*(2+3*x)^2)+(-3/14)/((1-2*x)^(3/2)*(2+3*x))-45/343*arctanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)+45/343/sqrt(1-2*x)],
[(3+5*x)/((1-2*x)^(5/2)*(2+3*x)^4),x,7,160/3087/(1-2*x)^(3/2)+1/63/((1-2*x)^(3/2)*(2+3*x)^3)+(-16/147)/((1-2*x)^(3/2)*(2+3*x)^2)+(-16/147)/((1-2*x)^(3/2)*(2+3*x))-160/2401*arctanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)+160/2401/sqrt(1-2*x)],
[(3+5*x)/((1-2*x)^(5/2)*(2+3*x)^5),x,8,215/9604/(1-2*x)^(3/2)+1/84/((1-2*x)^(3/2)*(2+3*x)^4)+(-43/588)/((1-2*x)^(3/2)*(2+3*x)^3)+(-129/2744)/((1-2*x)^(3/2)*(2+3*x)^2)+(-129/2744)/((1-2*x)^(3/2)*(2+3*x))-1935/67228*arctanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)+1935/67228/sqrt(1-2*x)],
[(2+3*x)^5*(3+5*x)^2/(1-2*x)^(5/2),x,2,2033647/384/(1-2*x)^(3/2)+1965635/128*(1-2*x)^(3/2)-514017/128*(1-2*x)^(5/2)+672003/896*(1-2*x)^(7/2)-10845/128*(1-2*x)^(9/2)+6075/1408*(1-2*x)^(11/2)+(-6206585/128)/sqrt(1-2*x)-8117095/128*sqrt(1-2*x)],
[(2+3*x)^4*(3+5*x)^2/(1-2*x)^(5/2),x,2,290521/192/(1-2*x)^(3/2)+40453/16*(1-2*x)^(3/2)-159111/320*(1-2*x)^(5/2)+13905/224*(1-2*x)^(7/2)-225/64*(1-2*x)^(9/2)+(-381073/32)/sqrt(1-2*x)-832951/64*sqrt(1-2*x)],
[(2+3*x)^3*(3+5*x)^2/(1-2*x)^(5/2),x,2,41503/96/(1-2*x)^(3/2)+5847/16*(1-2*x)^(3/2)-1539/32*(1-2*x)^(5/2)+675/224*(1-2*x)^(7/2)+(-91091/32)/sqrt(1-2*x)-39977/16*sqrt(1-2*x)],
[(2+3*x)^2*(3+5*x)^2/(1-2*x)^(5/2),x,2,5929/48/(1-2*x)^(3/2)+85/2*(1-2*x)^(3/2)-45/16*(1-2*x)^(5/2)+(-1309/2)/sqrt(1-2*x)-3467/8*sqrt(1-2*x)],
[(2+3*x)*(3+5*x)^2/(1-2*x)^(5/2),x,2,847/24/(1-2*x)^(3/2)+25/8*(1-2*x)^(3/2)+(-1133/8)/sqrt(1-2*x)-505/8*sqrt(1-2*x)],
[(3+5*x)^2/(1-2*x)^(5/2),x,2,121/12/(1-2*x)^(3/2)+(-55/2)/sqrt(1-2*x)-25/4*sqrt(1-2*x)],
[(3+5*x)^2/((1-2*x)^(5/2)*(2+3*x)),x,4,121/42/(1-2*x)^(3/2)-2/49*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+(-407/98)/sqrt(1-2*x)],
[(3+5*x)^2/((1-2*x)^(5/2)*(2+3*x)^2),x,5,121/42/((1-2*x)^(3/2)*(2+3*x))+130/343*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+(-130/1029)/sqrt(1-2*x)+(-365/294)/((2+3*x)*sqrt(1-2*x))],
[(3+5*x)^2/((1-2*x)^(5/2)*(2+3*x)^3),x,6,121/42/((1-2*x)^(3/2)*(2+3*x)^2)-85/343*arctanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)+85/343/sqrt(1-2*x)+(-26/21)/((2+3*x)^2*sqrt(1-2*x))+(-85/294)/((2+3*x)*sqrt(1-2*x))],
[(3+5*x)^2/((1-2*x)^(5/2)*(2+3*x)^4),x,7,121/42/((1-2*x)^(3/2)*(2+3*x)^3)-1415/2401*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+1415/7203/sqrt(1-2*x)+(-1091/882)/((2+3*x)^3*sqrt(1-2*x))+(-283/882)/((2+3*x)^2*sqrt(1-2*x))+(-1415/6174)/((2+3*x)*sqrt(1-2*x))],
[(3+5*x)^2/((1-2*x)^(5/2)*(2+3*x)^5),x,8,121/42/((1-2*x)^(3/2)*(2+3*x)^4)-20465/67228*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+20465/201684/sqrt(1-2*x)+(-727/588)/((2+3*x)^4*sqrt(1-2*x))+(-4093/12348)/((2+3*x)^3*sqrt(1-2*x))+(-4093/24696)/((2+3*x)^2*sqrt(1-2*x))+(-20465/172872)/((2+3*x)*sqrt(1-2*x))],
[(2+3*x)^5*(3+5*x)^3/(1-2*x)^(5/2),x,2,22370117/768/(1-2*x)^(3/2)+52725715/384*(1-2*x)^(3/2)-2887773/64*(1-2*x)^(5/2)+10121229/896*(1-2*x)^(7/2)-246315/128*(1-2*x)^(9/2)+277425/1408*(1-2*x)^(11/2)-30375/3328*(1-2*x)^(13/2)+(-39220335/128)/sqrt(1-2*x)-60160485/128*sqrt(1-2*x)],
[(2+3*x)^4*(3+5*x)^3/(1-2*x)^(5/2),x,2,3195731/384/(1-2*x)^(3/2)+9504551/384*(1-2*x)^(3/2)-4177401/640*(1-2*x)^(5/2)+1101465/896*(1-2*x)^(7/2)-17925/128*(1-2*x)^(9/2)+10125/1408*(1-2*x)^(11/2)+(-9836211/128)/sqrt(1-2*x)-12973191/128*sqrt(1-2*x)],
[(2+3*x)^3*(3+5*x)^3/(1-2*x)^(5/2),x,2,456533/192/(1-2*x)^(3/2)+98209/24*(1-2*x)^(3/2)-52011/64*(1-2*x)^(5/2)+11475/112*(1-2*x)^(7/2)-375/64*(1-2*x)^(9/2)+(-302379/16)/sqrt(1-2*x)-1334949/64*sqrt(1-2*x)],
[(2+3*x)^2*(3+5*x)^3/(1-2*x)^(5/2),x,2,65219/96/(1-2*x)^(3/2)+28555/48*(1-2*x)^(3/2)-2535/32*(1-2*x)^(5/2)+1125/224*(1-2*x)^(7/2)+(-144837/32)/sqrt(1-2*x)-64317/16*sqrt(1-2*x)],
[(2+3*x)*(3+5*x)^3/(1-2*x)^(5/2),x,2,9317/48/(1-2*x)^(3/2)+1675/24*(1-2*x)^(3/2)-75/16*(1-2*x)^(5/2)+(-8349/8)/sqrt(1-2*x)-2805/4*sqrt(1-2*x)],
[(3+5*x)^3/(1-2*x)^(5/2),x,2,1331/24/(1-2*x)^(3/2)+125/24*(1-2*x)^(3/2)+(-1815/8)/sqrt(1-2*x)-825/8*sqrt(1-2*x)],
[(3+5*x)^3/((1-2*x)^(5/2)*(2+3*x)),x,4,1331/84/(1-2*x)^(3/2)+2/147*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+(-2178/49)/sqrt(1-2*x)-125/12*sqrt(1-2*x)],
[(3+5*x)^3/((1-2*x)^(5/2)*(2+3*x)^2),x,4,11/21*(3+5*x)^2/((1-2*x)^(3/2)*(2+3*x))-200/1029*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-10/1029*(969+1450*x)/((2+3*x)*sqrt(1-2*x))],
[(3+5*x)^3/((1-2*x)^(5/2)*(2+3*x)^3),x,5,11/21*(3+5*x)^2/((1-2*x)^(3/2)*(2+3*x)^2)+905/1029*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+1/294*(-487-720*x)/((2+3*x)^2*sqrt(1-2*x))+905/2058*sqrt(1-2*x)/(2+3*x)],
[(3+5*x)^3/((1-2*x)^(5/2)*(2+3*x)^4),x,6,11/21*(3+5*x)^2/((1-2*x)^(3/2)*(2+3*x)^3)-7510/7203*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+2/441*(1346+2027*x)/((2+3*x)^3*sqrt(1-2*x))-3755/3087*sqrt(1-2*x)/(2+3*x)^2-3755/7203*sqrt(1-2*x)/(2+3*x)],
[(3+5*x)^3/((1-2*x)^(5/2)*(2+3*x)^5),x,7,11/21*(3+5*x)^2/((1-2*x)^(3/2)*(2+3*x)^4)-177635/201684*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+1/4116*(57069+85754*x)/((2+3*x)^4*sqrt(1-2*x))-35527/12348*sqrt(1-2*x)/(2+3*x)^3-177635/172872*sqrt(1-2*x)/(2+3*x)^2-177635/403368*sqrt(1-2*x)/(2+3*x)],
[(3+5*x)^3/((1-2*x)^(5/2)*(2+3*x)^6),x,8,11/21*(3+5*x)^2/((1-2*x)^(3/2)*(2+3*x)^5)-163474/352947*arctanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+2/5145*(55633+83544*x)/((2+3*x)^5*sqrt(1-2*x))-163474/36015*sqrt(1-2*x)/(2+3*x)^4-163474/108045*sqrt(1-2*x)/(2+3*x)^3-81737/151263*sqrt(1-2*x)/(2+3*x)^2-81737/352947*sqrt(1-2*x)/(2+3*x)],

# n<0
[(2+3*x)^6/((1-2*x)^(5/2)*(3+5*x)),x,10,117649/1056/(1-2*x)^(3/2)+169209/2000*(1-2*x)^(3/2)-43011/4000*(1-2*x)^(5/2)+729/1120*(1-2*x)^(7/2)-2/75625*arctanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+(-2739541/3872)/sqrt(1-2*x)-5992353/10000*sqrt(1-2*x)],
[(2+3*x)^5/((1-2*x)^(5/2)*(3+5*x)),x,8,16807/528/(1-2*x)^(3/2)+1917/200*(1-2*x)^(3/2)-243/400*(1-2*x)^(5/2)-2/15125*arctanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+(-156065/968)/sqrt(1-2*x)-51057/500*sqrt(1-2*x)],
[(2+3*x)^4/((1-2*x)^(5/2)*(3+5*x)),x,6,2401/264/(1-2*x)^(3/2)+27/40*(1-2*x)^(3/2)-2/3025*arctanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+(-33271/968)/sqrt(1-2*x)-2889/200*sqrt(1-2*x)],
[(2+3*x)^3/((1-2*x)^(5/2)*(3+5*x)),x,4,343/132/(1-2*x)^(3/2)-2/605*arctanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+(-784/121)/sqrt(1-2*x)-27/20*sqrt(1-2*x)],
[(2+3*x)^2/((1-2*x)^(5/2)*(3+5*x)),x,4,49/66/(1-2*x)^(3/2)-2/121*arctanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+(-217/242)/sqrt(1-2*x)],
[(2+3*x)/((1-2*x)^(5/2)*(3+5*x)),x,4,7/33/(1-2*x)^(3/2)-2/121*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+2/121/sqrt(1-2*x)],
[1/((1-2*x)^(5/2)*(3+5*x)),x,4,2/33/(1-2*x)^(3/2)-10/121*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+10/121/sqrt(1-2*x)],
[1/((1-2*x)^(5/2)*(2+3*x)*(3+5*x)),x,7,4/231/(1-2*x)^(3/2)+18/49*arctanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-50/121*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+272/5929/sqrt(1-2*x)],
[1/((1-2*x)^(5/2)*(2+3*x)^2*(3+5*x)),x,8,(-190/1617)/(1-2*x)^(3/2)+3/7/((1-2*x)^(3/2)*(2+3*x))+720/343*arctanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-250/121*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+(-1370/41503)/sqrt(1-2*x)],
[1/((1-2*x)^(5/2)*(2+3*x)^3*(3+5*x)),x,9,(-1115/1617)/(1-2*x)^(3/2)+3/14/((1-2*x)^(3/2)*(2+3*x)^2)+33/14/((1-2*x)^(3/2)*(2+3*x))+3645/343*arctanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-1250/121*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+(-12295/41503)/sqrt(1-2*x)],
[1/((1-2*x)^(5/2)*(2+3*x)^4*(3+5*x)),x,10,(-39520/11319)/(1-2*x)^(3/2)+1/7/((1-2*x)^(3/2)*(2+3*x)^3)+57/49/((1-2*x)^(3/2)*(2+3*x)^2)+582/49/((1-2*x)^(3/2)*(2+3*x))+127710/2401*arctanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-6250/121*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+(-446660/290521)/sqrt(1-2*x)],
[(2+3*x)^6/((1-2*x)^(5/2)*(3+5*x)^2),x,7,7/33*(2+3*x)^5/((1-2*x)^(3/2)*(3+5*x))-406/831875*arctanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-10283/6655*(2+3*x)^3/sqrt(1-2*x)-38/1815*(2+3*x)^4/((3+5*x)*sqrt(1-2*x))-463344/166375*(2+3*x)^2*sqrt(1-2*x)-21/831875*(4633904+1544625*x)*sqrt(1-2*x)],
[(2+3*x)^5/((1-2*x)^(5/2)*(3+5*x)^2),x,6,7/33*(2+3*x)^4/((1-2*x)^(3/2)*(3+5*x))-68/33275*arctanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-7588/6655*(2+3*x)^2/sqrt(1-2*x)-38/1815*(2+3*x)^3/((3+5*x)*sqrt(1-2*x))-6/33275*(114092+38025*x)*sqrt(1-2*x)],
[(2+3*x)^4/((1-2*x)^(5/2)*(3+5*x)^2),x,5,7/33*(2+3*x)^3/((1-2*x)^(3/2)*(3+5*x))-274/33275*arctanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-3/33275*(40912-24739*x)/sqrt(1-2*x)-38/1815*(2+3*x)^2/((3+5*x)*sqrt(1-2*x))],
[(2+3*x)^3/((1-2*x)^(5/2)*(3+5*x)^2),x,4,7/33*(2+3*x)^2/((1-2*x)^(3/2)*(3+5*x))-208/6655*arctanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-2/19965*(10309+17112*x)/((3+5*x)*sqrt(1-2*x))],
[(2+3*x)^2/((1-2*x)^(5/2)*(3+5*x)^2),x,5,49/66/((1-2*x)^(3/2)*(3+5*x))-142/1331*arctanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+142/6655/sqrt(1-2*x)+(-1231/3630)/((3+5*x)*sqrt(1-2*x))],
[(2+3*x)/((1-2*x)^(5/2)*(3+5*x)^2),x,5,76/1815/(1-2*x)^(3/2)+(-1/55)/((1-2*x)^(3/2)*(3+5*x))-76/1331*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+76/1331/sqrt(1-2*x)],
[1/((1-2*x)^(5/2)*(3+5*x)^2),x,5,10/363/(1-2*x)^(3/2)+(-1/11)/((1-2*x)^(3/2)*(3+5*x))-50/1331*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+50/1331/sqrt(1-2*x)],
[1/((1-2*x)^(5/2)*(2+3*x)*(3+5*x)^2),x,8,218/2541/(1-2*x)^(3/2)+(-5/11)/((1-2*x)^(3/2)*(3+5*x))-54/49*arctanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)+1400/1331*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+3274/65219/sqrt(1-2*x)],
[1/((1-2*x)^(5/2)*(2+3*x)^2*(3+5*x)^2),x,9,13900/17787/(1-2*x)^(3/2)+(-340/77)/((1-2*x)^(3/2)*(3+5*x))+3/7/((1-2*x)^(3/2)*(2+3*x)*(3+5*x))-4050/343*arctanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)+15250/1331*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+159800/456533/sqrt(1-2*x)],
[1/((1-2*x)^(5/2)*(2+3*x)^3*(3+5*x)^2),x,10,15185/2541/(1-2*x)^(3/2)+(-745/22)/((1-2*x)^(3/2)*(3+5*x))+3/14/((1-2*x)^(3/2)*(2+3*x)^2*(3+5*x))+24/7/((1-2*x)^(3/2)*(2+3*x)*(3+5*x))-4455/49*arctanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)+117500/1331*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+172105/65219/sqrt(1-2*x)],
[(2+3*x)^6/((1-2*x)^(5/2)*(3+5*x)^3),x,7,7/33*(2+3*x)^5/((1-2*x)^(3/2)*(3+5*x)^2)-6937/1830125*arctanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-256172/366025*(2+3*x)^2/sqrt(1-2*x)-73/3630*(2+3*x)^4/((3+5*x)^2*sqrt(1-2*x))-3269/199650*(2+3*x)^3/((3+5*x)*sqrt(1-2*x))-21/3660250*(2211616+736875*x)*sqrt(1-2*x)],
[(2+3*x)^5/((1-2*x)^(5/2)*(3+5*x)^3),x,6,7/33*(2+3*x)^4/((1-2*x)^(3/2)*(3+5*x)^2)-4693/366025*arctanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-3/732050*(544568-333311*x)/sqrt(1-2*x)-73/3630*(2+3*x)^3/((3+5*x)^2*sqrt(1-2*x))-317/19965*(2+3*x)^2/((3+5*x)*sqrt(1-2*x))],
[(2+3*x)^4/((1-2*x)^(5/2)*(3+5*x)^3),x,5,7/33*(2+3*x)^3/((1-2*x)^(3/2)*(3+5*x)^2)-14423/366025*arctanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-73/3630*(2+3*x)^2/((3+5*x)^2*sqrt(1-2*x))+1/2196150*(-1287116-2133933*x)/((3+5*x)*sqrt(1-2*x))],
[(2+3*x)^3/((1-2*x)^(5/2)*(3+5*x)^3),x,5,7/33*(2+3*x)^2/((1-2*x)^(3/2)*(3+5*x)^2)-7559/73205*arctanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+1/39930*(10217+17296*x)/((3+5*x)^2*sqrt(1-2*x))-7559/146410*sqrt(1-2*x)/(3+5*x)],
[(2+3*x)^2/((1-2*x)^(5/2)*(3+5*x)^3),x,6,49/66/((1-2*x)^(3/2)*(3+5*x)^2)-2873/14641*arctanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+2873/73205/sqrt(1-2*x)+(-614/1815)/((3+5*x)^2*sqrt(1-2*x))+(-2873/39930)/((3+5*x)*sqrt(1-2*x))],
[(2+3*x)/((1-2*x)^(5/2)*(3+5*x)^3),x,6,73/3993/(1-2*x)^(3/2)+(-1/110)/((1-2*x)^(3/2)*(3+5*x)^2)+(-73/1210)/((1-2*x)^(3/2)*(3+5*x))-365/14641*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+365/14641/sqrt(1-2*x)],
[1/((1-2*x)^(5/2)*(3+5*x)^3),x,6,35/3993/(1-2*x)^(3/2)+(-1/22)/((1-2*x)^(3/2)*(3+5*x)^2)+(-7/242)/((1-2*x)^(3/2)*(3+5*x))-175/14641*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+175/14641/sqrt(1-2*x)],
[1/((1-2*x)^(5/2)*(2+3*x)*(3+5*x)^3),x,9,(-5969/27951)/(1-2*x)^(3/2)+(-5/22)/((1-2*x)^(3/2)*(3+5*x)^2)+295/242/((1-2*x)^(3/2)*(3+5*x))+162/49*arctanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-47075/14641*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+(-65167/717409)/sqrt(1-2*x)],
[1/((1-2*x)^(5/2)*(2+3*x)^2*(3+5*x)^3),x,10,(-667615/195657)/(1-2*x)^(3/2)+(-505/154)/((1-2*x)^(3/2)*(3+5*x)^2)+3/7/((1-2*x)^(3/2)*(2+3*x)*(3+5*x)^2)+32765/1694/((1-2*x)^(3/2)*(3+5*x))+17820/343*arctanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-738625/14641*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+(-7554245/5021863)/sqrt(1-2*x)],
[1/((1-2*x)^(5/2)*(2+3*x)^3*(3+5*x)^3),x,11,(-6845810/195657)/(1-2*x)^(3/2)+(-5165/154)/((1-2*x)^(3/2)*(3+5*x)^2)+3/14/((1-2*x)^(3/2)*(2+3*x)^2*(3+5*x)^2)+9/2/((1-2*x)^(3/2)*(2+3*x)*(3+5*x)^2)+167960/847/((1-2*x)^(3/2)*(3+5*x))+182655/343*arctanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-7570625/14641*arctanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+(-77527480/5021863)/sqrt(1-2*x)],

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

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

# m>0
[(A+B*x)*(d+e*x)^(5/2)*sqrt(a+b*x),x,8,-1/48*(b*d-a*e)*(3*b*B*d-10*A*b*e+7*a*B*e)*(a+b*x)^(3/2)*(d+e*x)^(3/2)/(b^3*e)-1/40*(3*b*B*d-10*A*b*e+7*a*B*e)*(a+b*x)^(3/2)*(d+e*x)^(5/2)/(b^2*e)+1/5*B*(a+b*x)^(3/2)*(d+e*x)^(7/2)/(b*e)+1/128*(b*d-a*e)^4*(3*b*B*d-10*A*b*e+7*a*B*e)*arctanh(sqrt(e)*sqrt(a+b*x)/(sqrt(b)*sqrt(d+e*x)))/(b^(9/2)*e^(5/2))-1/64*(b*d-a*e)^2*(3*b*B*d-10*A*b*e+7*a*B*e)*(a+b*x)^(3/2)*sqrt(d+e*x)/(b^4*e)-1/128*(b*d-a*e)^3*(3*b*B*d-10*A*b*e+7*a*B*e)*sqrt(a+b*x)*sqrt(d+e*x)/(b^4*e^2)],
[(A+B*x)*(d+e*x)^(3/2)*sqrt(a+b*x),x,7,-1/24*(3*b*B*d-8*A*b*e+5*a*B*e)*(a+b*x)^(3/2)*(d+e*x)^(3/2)/(b^2*e)+1/4*B*(a+b*x)^(3/2)*(d+e*x)^(5/2)/(b*e)+1/64*(b*d-a*e)^3*(3*b*B*d-8*A*b*e+5*a*B*e)*arctanh(sqrt(e)*sqrt(a+b*x)/(sqrt(b)*sqrt(d+e*x)))/(b^(7/2)*e^(5/2))-1/32*(b*d-a*e)*(3*b*B*d-8*A*b*e+5*a*B*e)*(a+b*x)^(3/2)*sqrt(d+e*x)/(b^3*e)-1/64*(b*d-a*e)^2*(3*b*B*d-8*A*b*e+5*a*B*e)*sqrt(a+b*x)*sqrt(d+e*x)/(b^3*e^2)],
[(A+B*x)*sqrt(a+b*x)*sqrt(d+e*x),x,6,1/3*B*(a+b*x)^(3/2)*(d+e*x)^(3/2)/(b*e)-1/8*(b*d-a*e)^2*(2*A*b*e-B*(b*d+a*e))*arctanh(sqrt(e)*sqrt(a+b*x)/(sqrt(b)*sqrt(d+e*x)))/(b^(5/2)*e^(5/2))+1/4*(2*A*b*e-B*(b*d+a*e))*(a+b*x)^(3/2)*sqrt(d+e*x)/(b^2*e)+1/8*(b*d-a*e)*(2*A*b*e-B*(b*d+a*e))*sqrt(a+b*x)*sqrt(d+e*x)/(b^2*e^2)],
[(A+B*x)*sqrt(a+b*x)/sqrt(d+e*x),x,5,1/4*(b*d-a*e)*(3*b*B*d-4*A*b*e+a*B*e)*arctanh(sqrt(e)*sqrt(a+b*x)/(sqrt(b)*sqrt(d+e*x)))/(b^(3/2)*e^(5/2))+1/2*B*(a+b*x)^(3/2)*sqrt(d+e*x)/(b*e)-1/4*(3*b*B*d-4*A*b*e+a*B*e)*sqrt(a+b*x)*sqrt(d+e*x)/(b*e^2)],
[(A+B*x)*sqrt(a+b*x)/(d+e*x)^(3/2),x,5,-(3*b*B*d-2*A*b*e-a*B*e)*arctanh(sqrt(e)*sqrt(a+b*x)/(sqrt(b)*sqrt(d+e*x)))/(e^(5/2)*sqrt(b))-2*(B*d-A*e)*(a+b*x)^(3/2)/(e*(b*d-a*e)*sqrt(d+e*x))+(3*b*B*d-2*A*b*e-a*B*e)*sqrt(a+b*x)*sqrt(d+e*x)/(e^2*(b*d-a*e))],
[(A+B*x)*sqrt(a+b*x)/(d+e*x)^(5/2),x,5,-2/3*(B*d-A*e)*(a+b*x)^(3/2)/(e*(b*d-a*e)*(d+e*x)^(3/2))+2*B*arctanh(sqrt(e)*sqrt(a+b*x)/(sqrt(b)*sqrt(d+e*x)))*sqrt(b)/e^(5/2)-2*B*sqrt(a+b*x)/(e^2*sqrt(d+e*x))],
[(A+B*x)*sqrt(a+b*x)/(d+e*x)^(7/2),x,2,-2/5*(B*d-A*e)*(a+b*x)^(3/2)/(e*(b*d-a*e)*(d+e*x)^(5/2))+2/15*(3*b*B*d+2*A*b*e-5*a*B*e)*(a+b*x)^(3/2)/(e*(b*d-a*e)^2*(d+e*x)^(3/2))],
[(A+B*x)*sqrt(a+b*x)/(d+e*x)^(9/2),x,3,-2/7*(B*d-A*e)*(a+b*x)^(3/2)/(e*(b*d-a*e)*(d+e*x)^(7/2))+2/35*(3*b*B*d+4*A*b*e-7*a*B*e)*(a+b*x)^(3/2)/(e*(b*d-a*e)^2*(d+e*x)^(5/2))+4/105*b*(3*b*B*d+4*A*b*e-7*a*B*e)*(a+b*x)^(3/2)/(e*(b*d-a*e)^3*(d+e*x)^(3/2))],
[(A+B*x)*sqrt(a+b*x)/(d+e*x)^(11/2),x,4,-2/9*(B*d-A*e)*(a+b*x)^(3/2)/(e*(b*d-a*e)*(d+e*x)^(9/2))+2/21*(b*B*d+2*A*b*e-3*a*B*e)*(a+b*x)^(3/2)/(e*(b*d-a*e)^2*(d+e*x)^(7/2))+8/105*b*(b*B*d+2*A*b*e-3*a*B*e)*(a+b*x)^(3/2)/(e*(b*d-a*e)^3*(d+e*x)^(5/2))+16/315*b^2*(b*B*d+2*A*b*e-3*a*B*e)*(a+b*x)^(3/2)/(e*(b*d-a*e)^4*(d+e*x)^(3/2))],
[(A+B*x)*sqrt(a+b*x)/(d+e*x)^(13/2),x,5,-2/11*(B*d-A*e)*(a+b*x)^(3/2)/(e*(b*d-a*e)*(d+e*x)^(11/2))+2/99*(3*b*B*d+8*A*b*e-11*a*B*e)*(a+b*x)^(3/2)/(e*(b*d-a*e)^2*(d+e*x)^(9/2))+4/231*b*(3*b*B*d+8*A*b*e-11*a*B*e)*(a+b*x)^(3/2)/(e*(b*d-a*e)^3*(d+e*x)^(7/2))+16/1155*b^2*(3*b*B*d+8*A*b*e-11*a*B*e)*(a+b*x)^(3/2)/(e*(b*d-a*e)^4*(d+e*x)^(5/2))+32/3465*b^3*(3*b*B*d+8*A*b*e-11*a*B*e)*(a+b*x)^(3/2)/(e*(b*d-a*e)^5*(d+e*x)^(3/2))],
[(A+B*x)*sqrt(a+b*x)/(d+e*x)^(15/2),x,6,-2/13*(B*d-A*e)*(a+b*x)^(3/2)/(e*(b*d-a*e)*(d+e*x)^(13/2))+2/143*(3*b*B*d+10*A*b*e-13*a*B*e)*(a+b*x)^(3/2)/(e*(b*d-a*e)^2*(d+e*x)^(11/2))+16/1287*b*(3*b*B*d+10*A*b*e-13*a*B*e)*(a+b*x)^(3/2)/(e*(b*d-a*e)^3*(d+e*x)^(9/2))+32/3003*b^2*(3*b*B*d+10*A*b*e-13*a*B*e)*(a+b*x)^(3/2)/(e*(b*d-a*e)^4*(d+e*x)^(7/2))+128/15015*b^3*(3*b*B*d+10*A*b*e-13*a*B*e)*(a+b*x)^(3/2)/(e*(b*d-a*e)^5*(d+e*x)^(5/2))+256/45045*b^4*(3*b*B*d+10*A*b*e-13*a*B*e)*(a+b*x)^(3/2)/(e*(b*d-a*e)^6*(d+e*x)^(3/2))],
[(a+b*x)^(3/2)*(A+B*x)*(d+e*x)^(5/2),x,9,-1/96*(b*d-a*e)*(5*b*B*d-12*A*b*e+7*a*B*e)*(a+b*x)^(5/2)*(d+e*x)^(3/2)/(b^3*e)-1/60*(5*b*B*d-12*A*b*e+7*a*B*e)*(a+b*x)^(5/2)*(d+e*x)^(5/2)/(b^2*e)+1/6*B*(a+b*x)^(5/2)*(d+e*x)^(7/2)/(b*e)-1/512*(b*d-a*e)^5*(5*b*B*d-12*A*b*e+7*a*B*e)*arctanh(sqrt(e)*sqrt(a+b*x)/(sqrt(b)*sqrt(d+e*x)))/(b^(9/2)*e^(7/2))-1/768*(b*d-a*e)^3*(5*b*B*d-12*A*b*e+7*a*B*e)*(a+b*x)^(3/2)*sqrt(d+e*x)/(b^4*e^2)-1/192*(b*d-a*e)^2*(5*b*B*d-12*A*b*e+7*a*B*e)*(a+b*x)^(5/2)*sqrt(d+e*x)/(b^4*e)+1/512*(b*d-a*e)^4*(5*b*B*d-12*A*b*e+7*a*B*e)*sqrt(a+b*x)*sqrt(d+e*x)/(b^4*e^3)],
[(a+b*x)^(3/2)*(A+B*x)*(d+e*x)^(3/2),x,8,1/8*(2*A*b*e-B*(b*d+a*e))*(a+b*x)^(5/2)*(d+e*x)^(3/2)/(b^2*e)+1/5*B*(a+b*x)^(5/2)*(d+e*x)^(5/2)/(b*e)+3/128*(b*d-a*e)^4*(2*A*b*e-B*(b*d+a*e))*arctanh(sqrt(e)*sqrt(a+b*x)/(sqrt(b)*sqrt(d+e*x)))/(b^(7/2)*e^(7/2))+1/64*(b*d-a*e)^2*(2*A*b*e-B*(b*d+a*e))*(a+b*x)^(3/2)*sqrt(d+e*x)/(b^3*e^2)+1/16*(b*d-a*e)*(2*A*b*e-B*(b*d+a*e))*(a+b*x)^(5/2)*sqrt(d+e*x)/(b^3*e)-3/128*(b*d-a*e)^3*(2*A*b*e-B*(b*d+a*e))*sqrt(a+b*x)*sqrt(d+e*x)/(b^3*e^3)],
[(a+b*x)^(3/2)*(A+B*x)*sqrt(d+e*x),x,7,1/4*B*(a+b*x)^(5/2)*(d+e*x)^(3/2)/(b*e)-1/64*(b*d-a*e)^3*(5*b*B*d-8*A*b*e+3*a*B*e)*arctanh(sqrt(e)*sqrt(a+b*x)/(sqrt(b)*sqrt(d+e*x)))/(b^(5/2)*e^(7/2))-1/96*(b*d-a*e)*(5*b*B*d-8*A*b*e+3*a*B*e)*(a+b*x)^(3/2)*sqrt(d+e*x)/(b^2*e^2)-1/24*(5*b*B*d-8*A*b*e+3*a*B*e)*(a+b*x)^(5/2)*sqrt(d+e*x)/(b^2*e)+1/64*(b*d-a*e)^2*(5*b*B*d-8*A*b*e+3*a*B*e)*sqrt(a+b*x)*sqrt(d+e*x)/(b^2*e^3)],
[(a+b*x)^(3/2)*(A+B*x)/sqrt(d+e*x),x,6,-1/8*(b*d-a*e)^2*(5*b*B*d-6*A*b*e+a*B*e)*arctanh(sqrt(e)*sqrt(a+b*x)/(sqrt(b)*sqrt(d+e*x)))/(b^(3/2)*e^(7/2))-1/12*(5*b*B*d-6*A*b*e+a*B*e)*(a+b*x)^(3/2)*sqrt(d+e*x)/(b*e^2)+1/3*B*(a+b*x)^(5/2)*sqrt(d+e*x)/(b*e)+1/8*(b*d-a*e)*(5*b*B*d-6*A*b*e+a*B*e)*sqrt(a+b*x)*sqrt(d+e*x)/(b*e^3)],
[(a+b*x)^(3/2)*(A+B*x)/(d+e*x)^(3/2),x,6,3/4*(b*d-a*e)*(5*b*B*d-4*A*b*e-a*B*e)*arctanh(sqrt(e)*sqrt(a+b*x)/(sqrt(b)*sqrt(d+e*x)))/(e^(7/2)*sqrt(b))-2*(B*d-A*e)*(a+b*x)^(5/2)/(e*(b*d-a*e)*sqrt(d+e*x))+1/2*(5*b*B*d-4*A*b*e-a*B*e)*(a+b*x)^(3/2)*sqrt(d+e*x)/(e^2*(b*d-a*e))-3/4*(5*b*B*d-4*A*b*e-a*B*e)*sqrt(a+b*x)*sqrt(d+e*x)/e^3],
[(a+b*x)^(3/2)*(A+B*x)/(d+e*x)^(5/2),x,6,-2/3*(B*d-A*e)*(a+b*x)^(5/2)/(e*(b*d-a*e)*(d+e*x)^(3/2))-(5*b*B*d-2*A*b*e-3*a*B*e)*arctanh(sqrt(e)*sqrt(a+b*x)/(sqrt(b)*sqrt(d+e*x)))*sqrt(b)/e^(7/2)-2/3*(5*b*B*d-2*A*b*e-3*a*B*e)*(a+b*x)^(3/2)/(e^2*(b*d-a*e)*sqrt(d+e*x))+b*(5*b*B*d-2*A*b*e-3*a*B*e)*sqrt(a+b*x)*sqrt(d+e*x)/(e^3*(b*d-a*e))],
[(a+b*x)^(3/2)*(A+B*x)/(d+e*x)^(7/2),x,6,-2/5*(B*d-A*e)*(a+b*x)^(5/2)/(e*(b*d-a*e)*(d+e*x)^(5/2))-2/3*B*(a+b*x)^(3/2)/(e^2*(d+e*x)^(3/2))+2*b^(3/2)*B*arctanh(sqrt(e)*sqrt(a+b*x)/(sqrt(b)*sqrt(d+e*x)))/e^(7/2)-2*b*B*sqrt(a+b*x)/(e^3*sqrt(d+e*x))],
[(a+b*x)^(3/2)*(A+B*x)/(d+e*x)^(9/2),x,2,-2/7*(B*d-A*e)*(a+b*x)^(5/2)/(e*(b*d-a*e)*(d+e*x)^(7/2))+2/35*(5*b*B*d+2*A*b*e-7*a*B*e)*(a+b*x)^(5/2)/(e*(b*d-a*e)^2*(d+e*x)^(5/2))],
[(a+b*x)^(3/2)*(A+B*x)/(d+e*x)^(11/2),x,3,-2/9*(B*d-A*e)*(a+b*x)^(5/2)/(e*(b*d-a*e)*(d+e*x)^(9/2))+2/63*(5*b*B*d+4*A*b*e-9*a*B*e)*(a+b*x)^(5/2)/(e*(b*d-a*e)^2*(d+e*x)^(7/2))+4/315*b*(5*b*B*d+4*A*b*e-9*a*B*e)*(a+b*x)^(5/2)/(e*(b*d-a*e)^3*(d+e*x)^(5/2))],
[(a+b*x)^(3/2)*(A+B*x)/(d+e*x)^(13/2),x,4,-2/11*(B*d-A*e)*(a+b*x)^(5/2)/(e*(b*d-a*e)*(d+e*x)^(11/2))+2/99*(5*b*B*d+6*A*b*e-11*a*B*e)*(a+b*x)^(5/2)/(e*(b*d-a*e)^2*(d+e*x)^(9/2))+8/693*b*(5*b*B*d+6*A*b*e-11*a*B*e)*(a+b*x)^(5/2)/(e*(b*d-a*e)^3*(d+e*x)^(7/2))+16/3465*b^2*(5*b*B*d+6*A*b*e-11*a*B*e)*(a+b*x)^(5/2)/(e*(b*d-a*e)^4*(d+e*x)^(5/2))],
[(a+b*x)^(3/2)*(A+B*x)/(d+e*x)^(15/2),x,5,-2/13*(B*d-A*e)*(a+b*x)^(5/2)/(e*(b*d-a*e)*(d+e*x)^(13/2))+2/143*(5*b*B*d+8*A*b*e-13*a*B*e)*(a+b*x)^(5/2)/(e*(b*d-a*e)^2*(d+e*x)^(11/2))+4/429*b*(5*b*B*d+8*A*b*e-13*a*B*e)*(a+b*x)^(5/2)/(e*(b*d-a*e)^3*(d+e*x)^(9/2))+16/3003*b^2*(5*b*B*d+8*A*b*e-13*a*B*e)*(a+b*x)^(5/2)/(e*(b*d-a*e)^4*(d+e*x)^(7/2))+32/15015*b^3*(5*b*B*d+8*A*b*e-13*a*B*e)*(a+b*x)^(5/2)/(e*(b*d-a*e)^5*(d+e*x)^(5/2))],
[(a+b*x)^(3/2)*(A+B*x)/(d+e*x)^(17/2),x,6,-2/15*(B*d-A*e)*(a+b*x)^(5/2)/(e*(b*d-a*e)*(d+e*x)^(15/2))+2/39*(b*B*d+2*A*b*e-3*a*B*e)*(a+b*x)^(5/2)/(e*(b*d-a*e)^2*(d+e*x)^(13/2))+16/429*b*(b*B*d+2*A*b*e-3*a*B*e)*(a+b*x)^(5/2)/(e*(b*d-a*e)^3*(d+e*x)^(11/2))+32/1287*b^2*(b*B*d+2*A*b*e-3*a*B*e)*(a+b*x)^(5/2)/(e*(b*d-a*e)^4*(d+e*x)^(9/2))+128/9009*b^3*(b*B*d+2*A*b*e-3*a*B*e)*(a+b*x)^(5/2)/(e*(b*d-a*e)^5*(d+e*x)^(7/2))+256/45045*b^4*(b*B*d+2*A*b*e-3*a*B*e)*(a+b*x)^(5/2)/(e*(b*d-a*e)^6*(d+e*x)^(5/2))],
[(a+b*x)^(5/2)*(A+B*x)*(d+e*x)^(5/2),x,10,1/24*(b*d-a*e)*(2*A*b*e-B*(b*d+a*e))*(a+b*x)^(7/2)*(d+e*x)^(3/2)/(b^3*e)+1/12*(2*A*b*e-B*(b*d+a*e))*(a+b*x)^(7/2)*(d+e*x)^(5/2)/(b^2*e)+1/7*B*(a+b*x)^(7/2)*(d+e*x)^(7/2)/(b*e)-5/1024*(b*d-a*e)^6*(2*A*b*e-B*(b*d+a*e))*arctanh(sqrt(e)*sqrt(a+b*x)/(sqrt(b)*sqrt(d+e*x)))/(b^(9/2)*e^(9/2))-5/1536*(b*d-a*e)^4*(2*A*b*e-B*(b*d+a*e))*(a+b*x)^(3/2)*sqrt(d+e*x)/(b^4*e^3)+1/384*(b*d-a*e)^3*(2*A*b*e-B*(b*d+a*e))*(a+b*x)^(5/2)*sqrt(d+e*x)/(b^4*e^2)+1/64*(b*d-a*e)^2*(2*A*b*e-B*(b*d+a*e))*(a+b*x)^(7/2)*sqrt(d+e*x)/(b^4*e)+5/1024*(b*d-a*e)^5*(2*A*b*e-B*(b*d+a*e))*sqrt(a+b*x)*sqrt(d+e*x)/(b^4*e^4)],
[(a+b*x)^(5/2)*(A+B*x)*(d+e*x)^(3/2),x,9,-1/60*(7*b*B*d-12*A*b*e+5*a*B*e)*(a+b*x)^(7/2)*(d+e*x)^(3/2)/(b^2*e)+1/6*B*(a+b*x)^(7/2)*(d+e*x)^(5/2)/(b*e)+1/512*(b*d-a*e)^5*(7*b*B*d-12*A*b*e+5*a*B*e)*arctanh(sqrt(e)*sqrt(a+b*x)/(sqrt(b)*sqrt(d+e*x)))/(b^(7/2)*e^(9/2))+1/768*(b*d-a*e)^3*(7*b*B*d-12*A*b*e+5*a*B*e)*(a+b*x)^(3/2)*sqrt(d+e*x)/(b^3*e^3)-1/960*(b*d-a*e)^2*(7*b*B*d-12*A*b*e+5*a*B*e)*(a+b*x)^(5/2)*sqrt(d+e*x)/(b^3*e^2)-1/160*(b*d-a*e)*(7*b*B*d-12*A*b*e+5*a*B*e)*(a+b*x)^(7/2)*sqrt(d+e*x)/(b^3*e)-1/512*(b*d-a*e)^4*(7*b*B*d-12*A*b*e+5*a*B*e)*sqrt(a+b*x)*sqrt(d+e*x)/(b^3*e^4)],
[(a+b*x)^(5/2)*(A+B*x)*sqrt(d+e*x),x,8,1/5*B*(a+b*x)^(7/2)*(d+e*x)^(3/2)/(b*e)+1/128*(b*d-a*e)^4*(7*b*B*d-10*A*b*e+3*a*B*e)*arctanh(sqrt(e)*sqrt(a+b*x)/(sqrt(b)*sqrt(d+e*x)))/(b^(5/2)*e^(9/2))+1/192*(b*d-a*e)^2*(7*b*B*d-10*A*b*e+3*a*B*e)*(a+b*x)^(3/2)*sqrt(d+e*x)/(b^2*e^3)-1/240*(b*d-a*e)*(7*b*B*d-10*A*b*e+3*a*B*e)*(a+b*x)^(5/2)*sqrt(d+e*x)/(b^2*e^2)-1/40*(7*b*B*d-10*A*b*e+3*a*B*e)*(a+b*x)^(7/2)*sqrt(d+e*x)/(b^2*e)-1/128*(b*d-a*e)^3*(7*b*B*d-10*A*b*e+3*a*B*e)*sqrt(a+b*x)*sqrt(d+e*x)/(b^2*e^4)],
[(a+b*x)^(5/2)*(A+B*x)/sqrt(d+e*x),x,7,5/64*(b*d-a*e)^3*(7*b*B*d-8*A*b*e+a*B*e)*arctanh(sqrt(e)*sqrt(a+b*x)/(sqrt(b)*sqrt(d+e*x)))/(b^(3/2)*e^(9/2))+5/96*(b*d-a*e)*(7*b*B*d-8*A*b*e+a*B*e)*(a+b*x)^(3/2)*sqrt(d+e*x)/(b*e^3)-1/24*(7*b*B*d-8*A*b*e+a*B*e)*(a+b*x)^(5/2)*sqrt(d+e*x)/(b*e^2)+1/4*B*(a+b*x)^(7/2)*sqrt(d+e*x)/(b*e)-5/64*(b*d-a*e)^2*(7*b*B*d-8*A*b*e+a*B*e)*sqrt(a+b*x)*sqrt(d+e*x)/(b*e^4)],
[(a+b*x)^(5/2)*(A+B*x)/(d+e*x)^(3/2),x,7,-5/8*(b*d-a*e)^2*(7*b*B*d-6*A*b*e-a*B*e)*arctanh(sqrt(e)*sqrt(a+b*x)/(sqrt(b)*sqrt(d+e*x)))/(e^(9/2)*sqrt(b))-2*(B*d-A*e)*(a+b*x)^(7/2)/(e*(b*d-a*e)*sqrt(d+e*x))-5/12*(7*b*B*d-6*A*b*e-a*B*e)*(a+b*x)^(3/2)*sqrt(d+e*x)/e^3+1/3*(7*b*B*d-6*A*b*e-a*B*e)*(a+b*x)^(5/2)*sqrt(d+e*x)/(e^2*(b*d-a*e))+5/8*(b*d-a*e)*(7*b*B*d-6*A*b*e-a*B*e)*sqrt(a+b*x)*sqrt(d+e*x)/e^4],
[(a+b*x)^(5/2)*(A+B*x)/(d+e*x)^(5/2),x,7,-2/3*(B*d-A*e)*(a+b*x)^(7/2)/(e*(b*d-a*e)*(d+e*x)^(3/2))+5/4*(b*d-a*e)*(7*b*B*d-4*A*b*e-3*a*B*e)*arctanh(sqrt(e)*sqrt(a+b*x)/(sqrt(b)*sqrt(d+e*x)))*sqrt(b)/e^(9/2)-2/3*(7*b*B*d-4*A*b*e-3*a*B*e)*(a+b*x)^(5/2)/(e^2*(b*d-a*e)*sqrt(d+e*x))+5/6*b*(7*b*B*d-4*A*b*e-3*a*B*e)*(a+b*x)^(3/2)*sqrt(d+e*x)/(e^3*(b*d-a*e))-5/4*b*(7*b*B*d-4*A*b*e-3*a*B*e)*sqrt(a+b*x)*sqrt(d+e*x)/e^4],
[(a+b*x)^(5/2)*(A+B*x)/(d+e*x)^(7/2),x,7,-2/5*(B*d-A*e)*(a+b*x)^(7/2)/(e*(b*d-a*e)*(d+e*x)^(5/2))-2/15*(7*b*B*d-2*A*b*e-5*a*B*e)*(a+b*x)^(5/2)/(e^2*(b*d-a*e)*(d+e*x)^(3/2))-b^(3/2)*(7*b*B*d-2*A*b*e-5*a*B*e)*arctanh(sqrt(e)*sqrt(a+b*x)/(sqrt(b)*sqrt(d+e*x)))/e^(9/2)-2/3*b*(7*b*B*d-2*A*b*e-5*a*B*e)*(a+b*x)^(3/2)/(e^3*(b*d-a*e)*sqrt(d+e*x))+b^2*(7*b*B*d-2*A*b*e-5*a*B*e)*sqrt(a+b*x)*sqrt(d+e*x)/(e^4*(b*d-a*e))],
[(a+b*x)^(5/2)*(A+B*x)/(d+e*x)^(9/2),x,7,-2/7*(B*d-A*e)*(a+b*x)^(7/2)/(e*(b*d-a*e)*(d+e*x)^(7/2))-2/5*B*(a+b*x)^(5/2)/(e^2*(d+e*x)^(5/2))-2/3*b*B*(a+b*x)^(3/2)/(e^3*(d+e*x)^(3/2))+2*b^(5/2)*B*arctanh(sqrt(e)*sqrt(a+b*x)/(sqrt(b)*sqrt(d+e*x)))/e^(9/2)-2*b^2*B*sqrt(a+b*x)/(e^4*sqrt(d+e*x))],
[(a+b*x)^(5/2)*(A+B*x)/(d+e*x)^(11/2),x,2,-2/9*(B*d-A*e)*(a+b*x)^(7/2)/(e*(b*d-a*e)*(d+e*x)^(9/2))+2/63*(7*b*B*d+2*A*b*e-9*a*B*e)*(a+b*x)^(7/2)/(e*(b*d-a*e)^2*(d+e*x)^(7/2))],
[(a+b*x)^(5/2)*(A+B*x)/(d+e*x)^(13/2),x,3,-2/11*(B*d-A*e)*(a+b*x)^(7/2)/(e*(b*d-a*e)*(d+e*x)^(11/2))+2/99*(7*b*B*d+4*A*b*e-11*a*B*e)*(a+b*x)^(7/2)/(e*(b*d-a*e)^2*(d+e*x)^(9/2))+4/693*b*(7*b*B*d+4*A*b*e-11*a*B*e)*(a+b*x)^(7/2)/(e*(b*d-a*e)^3*(d+e*x)^(7/2))],
[(a+b*x)^(5/2)*(A+B*x)/(d+e*x)^(15/2),x,4,-2/13*(B*d-A*e)*(a+b*x)^(7/2)/(e*(b*d-a*e)*(d+e*x)^(13/2))+2/143*(7*b*B*d+6*A*b*e-13*a*B*e)*(a+b*x)^(7/2)/(e*(b*d-a*e)^2*(d+e*x)^(11/2))+8/1287*b*(7*b*B*d+6*A*b*e-13*a*B*e)*(a+b*x)^(7/2)/(e*(b*d-a*e)^3*(d+e*x)^(9/2))+16/9009*b^2*(7*b*B*d+6*A*b*e-13*a*B*e)*(a+b*x)^(7/2)/(e*(b*d-a*e)^4*(d+e*x)^(7/2))],
[(a+b*x)^(5/2)*(A+B*x)/(d+e*x)^(17/2),x,5,-2/15*(B*d-A*e)*(a+b*x)^(7/2)/(e*(b*d-a*e)*(d+e*x)^(15/2))+2/195*(7*b*B*d+8*A*b*e-15*a*B*e)*(a+b*x)^(7/2)/(e*(b*d-a*e)^2*(d+e*x)^(13/2))+4/715*b*(7*b*B*d+8*A*b*e-15*a*B*e)*(a+b*x)^(7/2)/(e*(b*d-a*e)^3*(d+e*x)^(11/2))+16/6435*b^2*(7*b*B*d+8*A*b*e-15*a*B*e)*(a+b*x)^(7/2)/(e*(b*d-a*e)^4*(d+e*x)^(9/2))+32/45045*b^3*(7*b*B*d+8*A*b*e-15*a*B*e)*(a+b*x)^(7/2)/(e*(b*d-a*e)^5*(d+e*x)^(7/2))],
[(a+b*x)^(5/2)*(A+B*x)/(d+e*x)^(19/2),x,6,-2/17*(B*d-A*e)*(a+b*x)^(7/2)/(e*(b*d-a*e)*(d+e*x)^(17/2))+2/255*(7*b*B*d+10*A*b*e-17*a*B*e)*(a+b*x)^(7/2)/(e*(b*d-a*e)^2*(d+e*x)^(15/2))+16/3315*b*(7*b*B*d+10*A*b*e-17*a*B*e)*(a+b*x)^(7/2)/(e*(b*d-a*e)^3*(d+e*x)^(13/2))+32/12155*b^2*(7*b*B*d+10*A*b*e-17*a*B*e)*(a+b*x)^(7/2)/(e*(b*d-a*e)^4*(d+e*x)^(11/2))+128/109395*b^3*(7*b*B*d+10*A*b*e-17*a*B*e)*(a+b*x)^(7/2)/(e*(b*d-a*e)^5*(d+e*x)^(9/2))+256/765765*b^4*(7*b*B*d+10*A*b*e-17*a*B*e)*(a+b*x)^(7/2)/(e*(b*d-a*e)^6*(d+e*x)^(7/2))],

# m<0
[(A+B*x)*(d+e*x)^(5/2)/sqrt(a+b*x),x,7,-5/64*(b*d-a*e)^3*(b*B*d-8*A*b*e+7*a*B*e)*arctanh(sqrt(e)*sqrt(a+b*x)/(sqrt(b)*sqrt(d+e*x)))/(b^(9/2)*e^(3/2))-5/96*(b*d-a*e)*(b*B*d-8*A*b*e+7*a*B*e)*(d+e*x)^(3/2)*sqrt(a+b*x)/(b^3*e)-1/24*(b*B*d-8*A*b*e+7*a*B*e)*(d+e*x)^(5/2)*sqrt(a+b*x)/(b^2*e)+1/4*B*(d+e*x)^(7/2)*sqrt(a+b*x)/(b*e)-5/64*(b*d-a*e)^2*(b*B*d-8*A*b*e+7*a*B*e)*sqrt(a+b*x)*sqrt(d+e*x)/(b^4*e)],
[(A+B*x)*(d+e*x)^(3/2)/sqrt(a+b*x),x,6,-1/8*(b*d-a*e)^2*(b*B*d-6*A*b*e+5*a*B*e)*arctanh(sqrt(e)*sqrt(a+b*x)/(sqrt(b)*sqrt(d+e*x)))/(b^(7/2)*e^(3/2))-1/12*(b*B*d-6*A*b*e+5*a*B*e)*(d+e*x)^(3/2)*sqrt(a+b*x)/(b^2*e)+1/3*B*(d+e*x)^(5/2)*sqrt(a+b*x)/(b*e)-1/8*(b*d-a*e)*(b*B*d-6*A*b*e+5*a*B*e)*sqrt(a+b*x)*sqrt(d+e*x)/(b^3*e)],
[(A+B*x)*sqrt(d+e*x)/sqrt(a+b*x),x,5,-1/4*(b*d-a*e)*(b*B*d-4*A*b*e+3*a*B*e)*arctanh(sqrt(e)*sqrt(a+b*x)/(sqrt(b)*sqrt(d+e*x)))/(b^(5/2)*e^(3/2))+1/2*B*(d+e*x)^(3/2)*sqrt(a+b*x)/(b*e)-1/4*(b*B*d-4*A*b*e+3*a*B*e)*sqrt(a+b*x)*sqrt(d+e*x)/(b^2*e)],
[(A+B*x)/(sqrt(a+b*x)*sqrt(d+e*x)),x,4,(2*A*b*e-B*(b*d+a*e))*arctanh(sqrt(e)*sqrt(a+b*x)/(sqrt(b)*sqrt(d+e*x)))/(b^(3/2)*e^(3/2))+B*sqrt(a+b*x)*sqrt(d+e*x)/(b*e)],
[(A+B*x)/((d+e*x)^(3/2)*sqrt(a+b*x)),x,4,2*B*arctanh(sqrt(e)*sqrt(a+b*x)/(sqrt(b)*sqrt(d+e*x)))/(e^(3/2)*sqrt(b))-2*(B*d-A*e)*sqrt(a+b*x)/(e*(b*d-a*e)*sqrt(d+e*x))],
[(A+B*x)/((d+e*x)^(5/2)*sqrt(a+b*x)),x,2,-2/3*(B*d-A*e)*sqrt(a+b*x)/(e*(b*d-a*e)*(d+e*x)^(3/2))+2/3*(b*B*d+2*A*b*e-3*a*B*e)*sqrt(a+b*x)/(e*(b*d-a*e)^2*sqrt(d+e*x))],
[(A+B*x)/((d+e*x)^(7/2)*sqrt(a+b*x)),x,3,-2/5*(B*d-A*e)*sqrt(a+b*x)/(e*(b*d-a*e)*(d+e*x)^(5/2))+2/15*(b*B*d+4*A*b*e-5*a*B*e)*sqrt(a+b*x)/(e*(b*d-a*e)^2*(d+e*x)^(3/2))+4/15*b*(b*B*d+4*A*b*e-5*a*B*e)*sqrt(a+b*x)/(e*(b*d-a*e)^3*sqrt(d+e*x))],
[(A+B*x)/((d+e*x)^(9/2)*sqrt(a+b*x)),x,4,-2/7*(B*d-A*e)*sqrt(a+b*x)/(e*(b*d-a*e)*(d+e*x)^(7/2))+2/35*(b*B*d+6*A*b*e-7*a*B*e)*sqrt(a+b*x)/(e*(b*d-a*e)^2*(d+e*x)^(5/2))+8/105*b*(b*B*d+6*A*b*e-7*a*B*e)*sqrt(a+b*x)/(e*(b*d-a*e)^3*(d+e*x)^(3/2))+16/105*b^2*(b*B*d+6*A*b*e-7*a*B*e)*sqrt(a+b*x)/(e*(b*d-a*e)^4*sqrt(d+e*x))],
[(A+B*x)/((d+e*x)^(11/2)*sqrt(a+b*x)),x,5,-2/9*(B*d-A*e)*sqrt(a+b*x)/(e*(b*d-a*e)*(d+e*x)^(9/2))+2/63*(b*B*d+8*A*b*e-9*a*B*e)*sqrt(a+b*x)/(e*(b*d-a*e)^2*(d+e*x)^(7/2))+4/105*b*(b*B*d+8*A*b*e-9*a*B*e)*sqrt(a+b*x)/(e*(b*d-a*e)^3*(d+e*x)^(5/2))+16/315*b^2*(b*B*d+8*A*b*e-9*a*B*e)*sqrt(a+b*x)/(e*(b*d-a*e)^4*(d+e*x)^(3/2))+32/315*b^3*(b*B*d+8*A*b*e-9*a*B*e)*sqrt(a+b*x)/(e*(b*d-a*e)^5*sqrt(d+e*x))],
[(A+B*x)*(d+e*x)^(5/2)/(a+b*x)^(3/2),x,7,5/8*(b*d-a*e)^2*(b*B*d+6*A*b*e-7*a*B*e)*arctanh(sqrt(e)*sqrt(a+b*x)/(sqrt(b)*sqrt(d+e*x)))/(b^(9/2)*sqrt(e))-2*(A*b-a*B)*(d+e*x)^(7/2)/(b*(b*d-a*e)*sqrt(a+b*x))+5/12*(b*B*d+6*A*b*e-7*a*B*e)*(d+e*x)^(3/2)*sqrt(a+b*x)/b^3+1/3*(b*B*d+6*A*b*e-7*a*B*e)*(d+e*x)^(5/2)*sqrt(a+b*x)/(b^2*(b*d-a*e))+5/8*(b*d-a*e)*(b*B*d+6*A*b*e-7*a*B*e)*sqrt(a+b*x)*sqrt(d+e*x)/b^4],
[(A+B*x)*(d+e*x)^(3/2)/(a+b*x)^(3/2),x,6,3/4*(b*d-a*e)*(b*B*d+4*A*b*e-5*a*B*e)*arctanh(sqrt(e)*sqrt(a+b*x)/(sqrt(b)*sqrt(d+e*x)))/(b^(7/2)*sqrt(e))-2*(A*b-a*B)*(d+e*x)^(5/2)/(b*(b*d-a*e)*sqrt(a+b*x))+1/2*(b*B*d+4*A*b*e-5*a*B*e)*(d+e*x)^(3/2)*sqrt(a+b*x)/(b^2*(b*d-a*e))+3/4*(b*B*d+4*A*b*e-5*a*B*e)*sqrt(a+b*x)*sqrt(d+e*x)/b^3],
[(A+B*x)*sqrt(d+e*x)/(a+b*x)^(3/2),x,5,(b*B*d+2*A*b*e-3*a*B*e)*arctanh(sqrt(e)*sqrt(a+b*x)/(sqrt(b)*sqrt(d+e*x)))/(b^(5/2)*sqrt(e))-2*(A*b-a*B)*(d+e*x)^(3/2)/(b*(b*d-a*e)*sqrt(a+b*x))+(b*B*d+2*A*b*e-3*a*B*e)*sqrt(a+b*x)*sqrt(d+e*x)/(b^2*(b*d-a*e))],
[(A+B*x)/((a+b*x)^(3/2)*sqrt(d+e*x)),x,4,2*B*arctanh(sqrt(e)*sqrt(a+b*x)/(sqrt(b)*sqrt(d+e*x)))/(b^(3/2)*sqrt(e))-2*(A*b-a*B)*sqrt(d+e*x)/(b*(b*d-a*e)*sqrt(a+b*x))],
[(A+B*x)/((a+b*x)^(3/2)*(d+e*x)^(3/2)),x,2,-2*(B*d-A*e)/(e*(b*d-a*e)*sqrt(a+b*x)*sqrt(d+e*x))+2*(b*B*d-2*A*b*e+a*B*e)*sqrt(d+e*x)/(e*(b*d-a*e)^2*sqrt(a+b*x))],
[(A+B*x)/((a+b*x)^(3/2)*(d+e*x)^(5/2)),x,3,-2*(A*b-a*B)/(b*(b*d-a*e)*(d+e*x)^(3/2)*sqrt(a+b*x))+2/3*(b*B*d-4*A*b*e+3*a*B*e)*sqrt(a+b*x)/(b*(b*d-a*e)^2*(d+e*x)^(3/2))+4/3*(b*B*d-4*A*b*e+3*a*B*e)*sqrt(a+b*x)/((b*d-a*e)^3*sqrt(d+e*x))],
[(A+B*x)/((a+b*x)^(3/2)*(d+e*x)^(7/2)),x,4,-2*(A*b-a*B)/(b*(b*d-a*e)*(d+e*x)^(5/2)*sqrt(a+b*x))+2/5*(b*B*d-6*A*b*e+5*a*B*e)*sqrt(a+b*x)/(b*(b*d-a*e)^2*(d+e*x)^(5/2))+8/15*(b*B*d-6*A*b*e+5*a*B*e)*sqrt(a+b*x)/((b*d-a*e)^3*(d+e*x)^(3/2))+16/15*b*(b*B*d-6*A*b*e+5*a*B*e)*sqrt(a+b*x)/((b*d-a*e)^4*sqrt(d+e*x))],
[(A+B*x)/((a+b*x)^(3/2)*(d+e*x)^(9/2)),x,5,-2*(A*b-a*B)/(b*(b*d-a*e)*(d+e*x)^(7/2)*sqrt(a+b*x))+2/7*(b*B*d-8*A*b*e+7*a*B*e)*sqrt(a+b*x)/(b*(b*d-a*e)^2*(d+e*x)^(7/2))+12/35*(b*B*d-8*A*b*e+7*a*B*e)*sqrt(a+b*x)/((b*d-a*e)^3*(d+e*x)^(5/2))+16/35*b*(b*B*d-8*A*b*e+7*a*B*e)*sqrt(a+b*x)/((b*d-a*e)^4*(d+e*x)^(3/2))+32/35*b^2*(b*B*d-8*A*b*e+7*a*B*e)*sqrt(a+b*x)/((b*d-a*e)^5*sqrt(d+e*x))],
[(A+B*x)*(d+e*x)^(7/2)/(a+b*x)^(5/2),x,8,-2/3*(A*b-a*B)*(d+e*x)^(9/2)/(b*(b*d-a*e)*(a+b*x)^(3/2))+35/8*(b*d-a*e)^2*(b*B*d+2*A*b*e-3*a*B*e)*arctanh(sqrt(e)*sqrt(a+b*x)/(sqrt(b)*sqrt(d+e*x)))*sqrt(e)/b^(11/2)-2*(b*B*d+2*A*b*e-3*a*B*e)*(d+e*x)^(7/2)/(b^2*(b*d-a*e)*sqrt(a+b*x))+35/12*e*(b*B*d+2*A*b*e-3*a*B*e)*(d+e*x)^(3/2)*sqrt(a+b*x)/b^4+7/3*e*(b*B*d+2*A*b*e-3*a*B*e)*(d+e*x)^(5/2)*sqrt(a+b*x)/(b^3*(b*d-a*e))+35/8*e*(b*d-a*e)*(b*B*d+2*A*b*e-3*a*B*e)*sqrt(a+b*x)*sqrt(d+e*x)/b^5],
[(A+B*x)*(d+e*x)^(5/2)/(a+b*x)^(5/2),x,7,-2/3*(A*b-a*B)*(d+e*x)^(7/2)/(b*(b*d-a*e)*(a+b*x)^(3/2))+5/4*(b*d-a*e)*(3*b*B*d+4*A*b*e-7*a*B*e)*arctanh(sqrt(e)*sqrt(a+b*x)/(sqrt(b)*sqrt(d+e*x)))*sqrt(e)/b^(9/2)-2/3*(3*b*B*d+4*A*b*e-7*a*B*e)*(d+e*x)^(5/2)/(b^2*(b*d-a*e)*sqrt(a+b*x))+5/6*e*(3*b*B*d+4*A*b*e-7*a*B*e)*(d+e*x)^(3/2)*sqrt(a+b*x)/(b^3*(b*d-a*e))+5/4*e*(3*b*B*d+4*A*b*e-7*a*B*e)*sqrt(a+b*x)*sqrt(d+e*x)/b^4],
[(A+B*x)*(d+e*x)^(3/2)/(a+b*x)^(5/2),x,6,-2/3*(A*b-a*B)*(d+e*x)^(5/2)/(b*(b*d-a*e)*(a+b*x)^(3/2))+(3*b*B*d+2*A*b*e-5*a*B*e)*arctanh(sqrt(e)*sqrt(a+b*x)/(sqrt(b)*sqrt(d+e*x)))*sqrt(e)/b^(7/2)-2/3*(3*b*B*d+2*A*b*e-5*a*B*e)*(d+e*x)^(3/2)/(b^2*(b*d-a*e)*sqrt(a+b*x))+e*(3*b*B*d+2*A*b*e-5*a*B*e)*sqrt(a+b*x)*sqrt(d+e*x)/(b^3*(b*d-a*e))],
[(A+B*x)*sqrt(d+e*x)/(a+b*x)^(5/2),x,5,-2/3*(A*b-a*B)*(d+e*x)^(3/2)/(b*(b*d-a*e)*(a+b*x)^(3/2))+2*B*arctanh(sqrt(e)*sqrt(a+b*x)/(sqrt(b)*sqrt(d+e*x)))*sqrt(e)/b^(5/2)-2*B*sqrt(d+e*x)/(b^2*sqrt(a+b*x))],
[(A+B*x)/((a+b*x)^(5/2)*sqrt(d+e*x)),x,2,-2/3*(A*b-a*B)*sqrt(d+e*x)/(b*(b*d-a*e)*(a+b*x)^(3/2))-2/3*(3*b*B*d-2*A*b*e-a*B*e)*sqrt(d+e*x)/(b*(b*d-a*e)^2*sqrt(a+b*x))],
[(A+B*x)/((a+b*x)^(5/2)*(d+e*x)^(3/2)),x,3,-2*(B*d-A*e)/(e*(b*d-a*e)*(a+b*x)^(3/2)*sqrt(d+e*x))+2/3*(3*b*B*d-4*A*b*e+a*B*e)*sqrt(d+e*x)/(e*(b*d-a*e)^2*(a+b*x)^(3/2))-4/3*(3*b*B*d-4*A*b*e+a*B*e)*sqrt(d+e*x)/((b*d-a*e)^3*sqrt(a+b*x))],
[(A+B*x)/((a+b*x)^(5/2)*(d+e*x)^(5/2)),x,4,-2/3*(B*d-A*e)/(e*(b*d-a*e)*(a+b*x)^(3/2)*(d+e*x)^(3/2))+2/3*(b*B*d-2*A*b*e+a*B*e)/(e*(b*d-a*e)^2*(a+b*x)^(3/2)*sqrt(d+e*x))-8/3*(b*B*d-2*A*b*e+a*B*e)/((b*d-a*e)^3*sqrt(a+b*x)*sqrt(d+e*x))-16/3*e*(b*B*d-2*A*b*e+a*B*e)*sqrt(a+b*x)/((b*d-a*e)^4*sqrt(d+e*x))],
[(A+B*x)/((a+b*x)^(5/2)*(d+e*x)^(7/2)),x,5,-2/3*(A*b-a*B)/(b*(b*d-a*e)*(a+b*x)^(3/2)*(d+e*x)^(5/2))-2/3*(3*b*B*d-8*A*b*e+5*a*B*e)/(b*(b*d-a*e)^2*(d+e*x)^(5/2)*sqrt(a+b*x))-4/5*e*(3*b*B*d-8*A*b*e+5*a*B*e)*sqrt(a+b*x)/(b*(b*d-a*e)^3*(d+e*x)^(5/2))-16/15*e*(3*b*B*d-8*A*b*e+5*a*B*e)*sqrt(a+b*x)/((b*d-a*e)^4*(d+e*x)^(3/2))-32/15*b*e*(3*b*B*d-8*A*b*e+5*a*B*e)*sqrt(a+b*x)/((b*d-a*e)^5*sqrt(d+e*x))],
[(A+B*x)/((a+b*x)^(5/2)*(d+e*x)^(9/2)),x,6,-2/3*(A*b-a*B)/(b*(b*d-a*e)*(a+b*x)^(3/2)*(d+e*x)^(7/2))-2/3*(3*b*B*d-10*A*b*e+7*a*B*e)/(b*(b*d-a*e)^2*(d+e*x)^(7/2)*sqrt(a+b*x))-16/21*e*(3*b*B*d-10*A*b*e+7*a*B*e)*sqrt(a+b*x)/(b*(b*d-a*e)^3*(d+e*x)^(7/2))-32/35*e*(3*b*B*d-10*A*b*e+7*a*B*e)*sqrt(a+b*x)/((b*d-a*e)^4*(d+e*x)^(5/2))-128/105*b*e*(3*b*B*d-10*A*b*e+7*a*B*e)*sqrt(a+b*x)/((b*d-a*e)^5*(d+e*x)^(3/2))-256/105*b^2*e*(3*b*B*d-10*A*b*e+7*a*B*e)*sqrt(a+b*x)/((b*d-a*e)^6*sqrt(d+e*x))],

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

# n>0
[(2+3*x)^4*sqrt(1-2*x)*sqrt(3+5*x),x,7,-333/2000*(1-2*x)^(3/2)*(2+3*x)^2*(3+5*x)^(3/2)-1/20*(1-2*x)^(3/2)*(2+3*x)^3*(3+5*x)^(3/2)-7/640000*(1-2*x)^(3/2)*(3+5*x)^(3/2)*(231223+140652*x)+4122385421/51200000*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-34069301/5120000*(1-2*x)^(3/2)*sqrt(3+5*x)+374762311/51200000*sqrt(1-2*x)*sqrt(3+5*x)],
[(2+3*x)^3*sqrt(1-2*x)*sqrt(3+5*x),x,6,-3/50*(1-2*x)^(3/2)*(2+3*x)^2*(3+5*x)^(3/2)-21/16000*(1-2*x)^(3/2)*(3+5*x)^(3/2)*(731+444*x)+39142411/1280000*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-323491/128000*(1-2*x)^(3/2)*sqrt(3+5*x)+3558401/1280000*sqrt(1-2*x)*sqrt(3+5*x)],
[(2+3*x)^2*sqrt(1-2*x)*sqrt(3+5*x),x,6,-37/160*(1-2*x)^(3/2)*(3+5*x)^(3/2)-3/40*(1-2*x)^(3/2)*(2+3*x)*(3+5*x)^(3/2)+158873/12800*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-1313/1280*(1-2*x)^(3/2)*sqrt(3+5*x)+14443/12800*sqrt(1-2*x)*sqrt(3+5*x)],
[(2+3*x)*sqrt(1-2*x)*sqrt(3+5*x),x,5,-1/10*(1-2*x)^(3/2)*(3+5*x)^(3/2)+4477/800*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-37/80*(1-2*x)^(3/2)*sqrt(3+5*x)+407/800*sqrt(1-2*x)*sqrt(3+5*x)],
[sqrt(1-2*x)*sqrt(3+5*x),x,4,121/40*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-1/4*(1-2*x)^(3/2)*sqrt(3+5*x)+11/40*sqrt(1-2*x)*sqrt(3+5*x)],
[sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x),x,6,2/9*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))*sqrt(7)+37/9*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+1/3*sqrt(1-2*x)*sqrt(3+5*x)],
[sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2,x,6,-37/9*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)-2/9*arcsin(sqrt(2/11)*sqrt(3+5*x))*sqrt(10)-1/3*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)],
[sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3,x,4,-121/28*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)+1/2*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^2-11/28*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)],
[sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^4,x,5,1/7*(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^3-4477/392*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)+37/28*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^2-407/392*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)],
[sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^5,x,7,-794365/21952*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)-1/12*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^4+37/504*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+6005/14112*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+625115/197568*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)],
[sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^6,x,8,-5591773/43904*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)-1/15*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^5+37/840*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^4+403/1680*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+14023/9408*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+1466281/131712*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)],
[sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^7,x,9,-588912203/1229312*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)-1/18*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^6+37/1260*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^5+10921/70560*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^4+126799/141120*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+4429459/790272*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+463266973/11063808*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)],
[(2+3*x)^4*(3+5*x)^(3/2)*sqrt(1-2*x),x,8,-52760369/7680000*(1-2*x)^(3/2)*(3+5*x)^(3/2)-403/2800*(1-2*x)^(3/2)*(2+3*x)^2*(3+5*x)^(5/2)-3/70*(1-2*x)^(3/2)*(2+3*x)^3*(3+5*x)^(5/2)-1/640000*(1-2*x)^(3/2)*(3+5*x)^(5/2)*(1480103+874608*x)+70224051139/204800000*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-580364059/20480000*(1-2*x)^(3/2)*sqrt(3+5*x)+6384004649/204800000*sqrt(1-2*x)*sqrt(3+5*x)],
[(2+3*x)^3*(3+5*x)^(3/2)*sqrt(1-2*x),x,7,-953981/384000*(1-2*x)^(3/2)*(3+5*x)^(3/2)-1/20*(1-2*x)^(3/2)*(2+3*x)^2*(3+5*x)^(5/2)-7/32000*(1-2*x)^(3/2)*(3+5*x)^(5/2)*(3821+2256*x)+1269748711/10240000*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-10493791/1024000*(1-2*x)^(3/2)*sqrt(3+5*x)+115431701/10240000*sqrt(1-2*x)*sqrt(3+5*x)],
[(2+3*x)^2*(3+5*x)^(3/2)*sqrt(1-2*x),x,7,-9007/9600*(1-2*x)^(3/2)*(3+5*x)^(3/2)-153/800*(1-2*x)^(3/2)*(3+5*x)^(5/2)-3/50*(1-2*x)^(3/2)*(2+3*x)*(3+5*x)^(5/2)+11988317/256000*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-99077/25600*(1-2*x)^(3/2)*sqrt(3+5*x)+1089847/256000*sqrt(1-2*x)*sqrt(3+5*x)],
[(2+3*x)*(3+5*x)^(3/2)*sqrt(1-2*x),x,6,-181/480*(1-2*x)^(3/2)*(3+5*x)^(3/2)-3/40*(1-2*x)^(3/2)*(3+5*x)^(5/2)+240911/12800*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-1991/1280*(1-2*x)^(3/2)*sqrt(3+5*x)+21901/12800*sqrt(1-2*x)*sqrt(3+5*x)],
[(3+5*x)^(3/2)*sqrt(1-2*x),x,5,-1/6*(1-2*x)^(3/2)*(3+5*x)^(3/2)+1331/160*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-11/16*(1-2*x)^(3/2)*sqrt(3+5*x)+121/160*sqrt(1-2*x)*sqrt(3+5*x)],
[(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x),x,7,-2/27*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))*sqrt(7)+793/216*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+1/6*(3+5*x)^(3/2)*sqrt(1-2*x)-41/72*sqrt(1-2*x)*sqrt(3+5*x)],
[(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^2,x,7,41/27*arcsin(sqrt(2/11)*sqrt(3+5*x))*sqrt(5/2)+107/27*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)-1/3*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)+10/9*sqrt(1-2*x)*sqrt(3+5*x)],
[(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^3,x,7,-4091/756*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)-10/27*arcsin(sqrt(2/11)*sqrt(3+5*x))*sqrt(10)-1/6*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^2-107/252*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)],
[(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^4,x,5,-1331/392*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)-11/84*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^2+1/3*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^3-121/392*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)],
[(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^5,x,6,3/28*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^4-153065/21952*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)-1265/4704*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^2+115/168*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^3-13915/21952*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)],
[(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^6,x,8,-783959/43904*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)-1/15*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^5-107/2520*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^4+641/15120*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+17981/84672*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+1852307/1185408*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)],
[(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^7,x,9,-64645339/1229312*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)-1/18*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^6-107/3780*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^5+4619/211680*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^4+42461/423360*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+1460201/2370816*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+152571047/33191424*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)],
[(2+3*x)^4*(3+5*x)^(5/2)*sqrt(1-2*x),x,9,-1493993699/49152000*(1-2*x)^(3/2)*(3+5*x)^(3/2)-135817609/20480000*(1-2*x)^(3/2)*(3+5*x)^(5/2)-1419/11200*(1-2*x)^(3/2)*(2+3*x)^2*(3+5*x)^(7/2)-3/80*(1-2*x)^(3/2)*(2+3*x)^3*(3+5*x)^(7/2)-3/1280000*(1-2*x)^(3/2)*(3+5*x)^(7/2)*(899099+522420*x)+1988505613369/1310720000*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-16433930689/131072000*(1-2*x)^(3/2)*sqrt(3+5*x)+180773237579/1310720000*sqrt(1-2*x)*sqrt(3+5*x)],
[(2+3*x)^3*(3+5*x)^(5/2)*sqrt(1-2*x),x,8,-3262963/307200*(1-2*x)^(3/2)*(3+5*x)^(3/2)-296633/128000*(1-2*x)^(3/2)*(3+5*x)^(5/2)-3/70*(1-2*x)^(3/2)*(2+3*x)^2*(3+5*x)^(7/2)-3/8000*(1-2*x)^(3/2)*(3+5*x)^(7/2)*(1963+1140*x)+4343003753/8192000*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-35892593/819200*(1-2*x)^(3/2)*sqrt(3+5*x)+394818523/8192000*sqrt(1-2*x)*sqrt(3+5*x)],
[(2+3*x)^2*(3+5*x)^(5/2)*sqrt(1-2*x),x,8,-11759/3072*(1-2*x)^(3/2)*(3+5*x)^(3/2)-1069/1280*(1-2*x)^(3/2)*(3+5*x)^(5/2)-13/80*(1-2*x)^(3/2)*(3+5*x)^(7/2)-1/20*(1-2*x)^(3/2)*(2+3*x)*(3+5*x)^(7/2)+15651229/81920*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-129349/8192*(1-2*x)^(3/2)*sqrt(3+5*x)+1422839/81920*sqrt(1-2*x)*sqrt(3+5*x)],
[(2+3*x)*(3+5*x)^(5/2)*sqrt(1-2*x),x,7,-2761/1920*(1-2*x)^(3/2)*(3+5*x)^(3/2)-251/800*(1-2*x)^(3/2)*(3+5*x)^(5/2)-3/50*(1-2*x)^(3/2)*(3+5*x)^(7/2)+3674891/51200*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-30371/5120*(1-2*x)^(3/2)*sqrt(3+5*x)+334081/51200*sqrt(1-2*x)*sqrt(3+5*x)],
[(3+5*x)^(5/2)*sqrt(1-2*x),x,6,-55/96*(1-2*x)^(3/2)*(3+5*x)^(3/2)-1/8*(1-2*x)^(3/2)*(3+5*x)^(5/2)+14641/512*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-605/256*(1-2*x)^(3/2)*sqrt(3+5*x)+1331/512*sqrt(1-2*x)*sqrt(3+5*x)],
[(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x),x,8,6553/2592*arcsin(sqrt(2/11)*sqrt(3+5*x))*sqrt(5/2)+2/81*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))*sqrt(7)-5/24*(3+5*x)^(3/2)*sqrt(1-2*x)+1/9*(3+5*x)^(5/2)*sqrt(1-2*x)-925/864*sqrt(1-2*x)*sqrt(3+5*x)],
[(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^2,x,8,155/216*arcsin(sqrt(2/11)*sqrt(3+5*x))*sqrt(5/2)-59/27*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)+5/6*(3+5*x)^(3/2)*sqrt(1-2*x)-1/3*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)-95/72*sqrt(1-2*x)*sqrt(3+5*x)],
[(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^3,x,8,25/9*arcsin(sqrt(2/11)*sqrt(3+5*x))*sqrt(5/2)+2119/252*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)-59/84*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)-1/6*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^2+215/84*sqrt(1-2*x)*sqrt(3+5*x)],
[(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^4,x,8,-250433/31752*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)-50/81*arcsin(sqrt(2/11)*sqrt(3+5*x))*sqrt(10)-59/252*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^2-1/9*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^3-6401/10584*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)],
[(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^5,x,6,-73205/21952*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)-605/4704*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^2-11/168*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^3+1/4*(3+5*x)^(7/2)*sqrt(1-2*x)/(2+3*x)^4-6655/21952*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)],
[(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^6,x,7,3/35*(1-2*x)^(3/2)*(3+5*x)^(7/2)/(2+3*x)^5-248897/43904*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)-2057/9408*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^2-187/1680*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^3+17/40*(3+5*x)^(7/2)*sqrt(1-2*x)/(2+3*x)^4-22627/43904*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)],
[(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^7,x,9,-15036307/1229312*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)-59/1260*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^5-1/18*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^6-6533/211680*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^4+47279/1270080*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+1057139/7112448*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+106751933/99574272*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)],
[(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^8,x,10,-3735929329/120472576*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)-59/1764*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^6-1/21*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^7-6577/370440*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^5+369409/20744640*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^4+2524471/41489280*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+84539611/232339968*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+8818415317/3252759552*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)],
[sqrt(a+b*x)/((e+f*x)*sqrt(c+d*x)),x,7,2*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))*sqrt(b)/(f*sqrt(d))-2*arctanh(sqrt(d*e-c*f)*sqrt(a+b*x)/(sqrt(b*e-a*f)*sqrt(c+d*x)))*sqrt(b*e-a*f)/(f*sqrt(d*e-c*f))],
[sqrt(c+d*x)/((e+f*x)*sqrt(a+b*x)),x,7,2*arctanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))*sqrt(d)/(f*sqrt(b))-2*arctanh(sqrt(d*e-c*f)*sqrt(a+b*x)/(sqrt(b*e-a*f)*sqrt(c+d*x)))*sqrt(d*e-c*f)/(f*sqrt(b*e-a*f))],

# n<0
[(2+3*x)^3*sqrt(1-2*x)/sqrt(3+5*x),x,5,525371/64000*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-3/40*(1-2*x)^(3/2)*(2+3*x)^2*sqrt(3+5*x)-21/6400*(1-2*x)^(3/2)*(335+216*x)*sqrt(3+5*x)+47761/64000*sqrt(1-2*x)*sqrt(3+5*x)],
[(2+3*x)^2*sqrt(1-2*x)/sqrt(3+5*x),x,5,3047/800*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-23/80*(1-2*x)^(3/2)*sqrt(3+5*x)-1/10*(1-2*x)^(3/2)*(2+3*x)*sqrt(3+5*x)+277/800*sqrt(1-2*x)*sqrt(3+5*x)],
[(2+3*x)*sqrt(1-2*x)/sqrt(3+5*x),x,4,451/200*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-3/20*(1-2*x)^(3/2)*sqrt(3+5*x)+41/200*sqrt(1-2*x)*sqrt(3+5*x)],
[sqrt(1-2*x)/sqrt(3+5*x),x,3,11/5*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+1/5*sqrt(1-2*x)*sqrt(3+5*x)],
[sqrt(1-2*x)/((2+3*x)*sqrt(3+5*x)),x,6,-2/3*arcsin(sqrt(2/11)*sqrt(3+5*x))*sqrt(2/5)-2/3*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))*sqrt(7)],
[sqrt(1-2*x)/((2+3*x)^2*sqrt(3+5*x)),x,3,-11*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)+sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)],
[sqrt(1-2*x)/((2+3*x)^3*sqrt(3+5*x)),x,4,-1177/28*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)+3/14*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^2+107/28*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)],
[sqrt(1-2*x)/((2+3*x)^4*sqrt(3+5*x)),x,6,-68959/392*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)+1/3*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+173/84*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+18083/1176*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)],
[sqrt(1-2*x)/((2+3*x)^5*sqrt(3+5*x)),x,7,-16925425/21952*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)+1/4*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^4+81/56*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+14145/1568*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+1479375/21952*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)],
[(2+3*x)^3*sqrt(1-2*x)/(3+5*x)^(3/2),x,5,10409/4000*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-2/5*(2+3*x)^3*sqrt(1-2*x)/sqrt(3+5*x)-7/4000*(73-60*x)*sqrt(1-2*x)*sqrt(3+5*x)+7/25*(2+3*x)^2*sqrt(1-2*x)*sqrt(3+5*x)],
[(2+3*x)^2*sqrt(1-2*x)/(3+5*x)^(3/2),x,5,317/200*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-2/275*(1-2*x)^(3/2)/sqrt(3+5*x)-9/100*(1-2*x)^(3/2)*sqrt(3+5*x)+317/2200*sqrt(1-2*x)*sqrt(3+5*x)],
[(2+3*x)*sqrt(1-2*x)/(3+5*x)^(3/2),x,4,29/25*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-2/55*(1-2*x)^(3/2)/sqrt(3+5*x)+29/275*sqrt(1-2*x)*sqrt(3+5*x)],
[sqrt(1-2*x)/(3+5*x)^(3/2),x,3,-2/5*arcsin(sqrt(2/11)*sqrt(3+5*x))*sqrt(2/5)-2/5*sqrt(1-2*x)/sqrt(3+5*x)],
[sqrt(1-2*x)/((2+3*x)*(3+5*x)^(3/2)),x,3,2*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))*sqrt(7)-2*sqrt(1-2*x)/sqrt(3+5*x)],
[sqrt(1-2*x)/((2+3*x)^2*(3+5*x)^(3/2)),x,4,103*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)+3/7*(1-2*x)^(3/2)/((2+3*x)*sqrt(3+5*x))-103/7*sqrt(1-2*x)/sqrt(3+5*x)],
[sqrt(1-2*x)/((2+3*x)^3*(3+5*x)^(3/2)),x,6,17951/28*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)-2615/28*sqrt(1-2*x)/sqrt(3+5*x)+1/2*sqrt(1-2*x)/((2+3*x)^2*sqrt(3+5*x))+173/28*sqrt(1-2*x)/((2+3*x)*sqrt(3+5*x))],
[sqrt(1-2*x)/((2+3*x)^4*(3+5*x)^(3/2)),x,7,1463447/392*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)-639565/1176*sqrt(1-2*x)/sqrt(3+5*x)+1/3*sqrt(1-2*x)/((2+3*x)^3*sqrt(3+5*x))+81/28*sqrt(1-2*x)/((2+3*x)^2*sqrt(3+5*x))+14101/392*sqrt(1-2*x)/((2+3*x)*sqrt(3+5*x))],
[(2+3*x)^4*sqrt(1-2*x)/(3+5*x)^(5/2),x,6,35511/20000*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-2/15*(2+3*x)^4*sqrt(1-2*x)/(3+5*x)^(3/2)-524/825*(2+3*x)^3*sqrt(1-2*x)/sqrt(3+5*x)+623/1375*(2+3*x)^2*sqrt(1-2*x)*sqrt(3+5*x)+7/220000*(2563+8940*x)*sqrt(1-2*x)*sqrt(3+5*x)],
[(2+3*x)^3*sqrt(1-2*x)/(3+5*x)^(5/2),x,5,1071/1000*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-2/15*(2+3*x)^3*sqrt(1-2*x)/(3+5*x)^(3/2)-392/825*(2+3*x)^2*sqrt(1-2*x)/sqrt(3+5*x)+7/11000*(1243+1740*x)*sqrt(1-2*x)*sqrt(3+5*x)],
[(2+3*x)^2*sqrt(1-2*x)/(3+5*x)^(5/2),x,5,-2/825*(1-2*x)^(3/2)/(3+5*x)^(3/2)+3/5*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-12/275*(1-2*x)^(3/2)/sqrt(3+5*x)+3/55*sqrt(1-2*x)*sqrt(3+5*x)],
[(2+3*x)*sqrt(1-2*x)/(3+5*x)^(5/2),x,4,-2/165*(1-2*x)^(3/2)/(3+5*x)^(3/2)-6/25*arcsin(sqrt(2/11)*sqrt(3+5*x))*sqrt(2/5)-6/25*sqrt(1-2*x)/sqrt(3+5*x)],
[sqrt(1-2*x)/(3+5*x)^(5/2),x,1,-2/33*(1-2*x)^(3/2)/(3+5*x)^(3/2)],
[sqrt(1-2*x)/((2+3*x)*(3+5*x)^(5/2)),x,4,-10/33*(1-2*x)^(3/2)/(3+5*x)^(3/2)-6*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))*sqrt(7)+6*sqrt(1-2*x)/sqrt(3+5*x)],
[sqrt(1-2*x)/((2+3*x)^2*(3+5*x)^(5/2)),x,6,-519*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)-25/3*sqrt(1-2*x)/(3+5*x)^(3/2)+sqrt(1-2*x)/((2+3*x)*(3+5*x)^(3/2))+2495/33*sqrt(1-2*x)/sqrt(3+5*x)],
[sqrt(1-2*x)/((2+3*x)^3*(3+5*x)^(5/2)),x,7,-126513/28*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)-6095/84*sqrt(1-2*x)/(3+5*x)^(3/2)+1/2*sqrt(1-2*x)/((2+3*x)^2*(3+5*x)^(3/2))+243/28*sqrt(1-2*x)/((2+3*x)*(3+5*x)^(3/2))+608185/924*sqrt(1-2*x)/sqrt(3+5*x)],
[sqrt(1-2*x)/((2+3*x)^4*(3+5*x)^(5/2)),x,8,-13246251/392*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)-638165/1176*sqrt(1-2*x)/(3+5*x)^(3/2)+1/3*sqrt(1-2*x)/((2+3*x)^3*(3+5*x)^(3/2))+313/84*sqrt(1-2*x)/((2+3*x)^2*(3+5*x)^(3/2))+25441/392*sqrt(1-2*x)/((2+3*x)*(3+5*x)^(3/2))+63678595/12936*sqrt(1-2*x)/sqrt(3+5*x)],

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

# n>0
[(1-2*x)^(3/2)*(2+3*x)^3*sqrt(3+5*x),x,7,-1/20*(1-2*x)^(5/2)*(2+3*x)^2*(3+5*x)^(3/2)-1/160000*(1-2*x)^(5/2)*(3+5*x)^(3/2)*(88987+63120*x)+452517373/25600000*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+3739813/7680000*(1-2*x)^(3/2)*sqrt(3+5*x)-339983/384000*(1-2*x)^(5/2)*sqrt(3+5*x)+41137943/25600000*sqrt(1-2*x)*sqrt(3+5*x)],
[(1-2*x)^(3/2)*(2+3*x)^2*sqrt(3+5*x),x,7,-567/4000*(1-2*x)^(5/2)*(3+5*x)^(3/2)-3/50*(1-2*x)^(5/2)*(2+3*x)*(3+5*x)^(3/2)+5487713/640000*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+45353/192000*(1-2*x)^(3/2)*sqrt(3+5*x)-4123/9600*(1-2*x)^(5/2)*sqrt(3+5*x)+498883/640000*sqrt(1-2*x)*sqrt(3+5*x)],
[(1-2*x)^(3/2)*(2+3*x)*sqrt(3+5*x),x,6,-3/40*(1-2*x)^(5/2)*(3+5*x)^(3/2)+30613/6400*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+253/1920*(1-2*x)^(3/2)*sqrt(3+5*x)-23/96*(1-2*x)^(5/2)*sqrt(3+5*x)+2783/6400*sqrt(1-2*x)*sqrt(3+5*x)],
[(1-2*x)^(3/2)*sqrt(3+5*x),x,5,1331/400*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+11/120*(1-2*x)^(3/2)*sqrt(3+5*x)-1/6*(1-2*x)^(5/2)*sqrt(3+5*x)+121/400*sqrt(1-2*x)*sqrt(3+5*x)],
[(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x),x,7,14/27*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))*sqrt(7)+4091/540*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+1/6*(1-2*x)^(3/2)*sqrt(3+5*x)+107/180*sqrt(1-2*x)*sqrt(3+5*x)],
[(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^2,x,7,-107/27*arcsin(sqrt(2/11)*sqrt(3+5*x))*sqrt(2/5)-41/27*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))*sqrt(7)-1/3*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)-4/9*sqrt(1-2*x)*sqrt(3+5*x)],
[(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^3,x,7,-793/108*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)+4/27*arcsin(sqrt(2/11)*sqrt(3+5*x))*sqrt(10)-1/6*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^2+41/36*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)],
[(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^4,x,5,1/3*(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^3-1331/56*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)+11/4*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^2-121/56*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)],
[(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^5,x,6,3/28*(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^4+181/168*(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^3-240911/3136*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)+1991/224*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^2-21901/3136*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)],
[(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^6,x,8,-11988317/43904*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)-1/15*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^5+41/360*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^4+7723/15120*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+270463/84672*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+28291441/1185408*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)],
[(1-2*x)^(3/2)*(2+3*x)^3*(3+5*x)^(3/2),x,8,-141599/128000*(1-2*x)^(5/2)*(3+5*x)^(3/2)-3/70*(1-2*x)^(5/2)*(2+3*x)^2*(3+5*x)^(5/2)-3/280000*(1-2*x)^(5/2)*(3+5*x)^(5/2)*(49829+33300*x)+6219452877/102400000*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+17133479/10240000*(1-2*x)^(3/2)*sqrt(3+5*x)-1557589/512000*(1-2*x)^(5/2)*sqrt(3+5*x)+565404807/102400000*sqrt(1-2*x)*sqrt(3+5*x)],
[(1-2*x)^(3/2)*(2+3*x)^2*(3+5*x)^(3/2),x,8,-3101/6400*(1-2*x)^(5/2)*(3+5*x)^(3/2)-259/2000*(1-2*x)^(5/2)*(3+5*x)^(5/2)-1/20*(1-2*x)^(5/2)*(2+3*x)*(3+5*x)^(5/2)+136205223/5120000*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+375221/512000*(1-2*x)^(3/2)*sqrt(3+5*x)-34111/25600*(1-2*x)^(5/2)*sqrt(3+5*x)+12382293/5120000*sqrt(1-2*x)*sqrt(3+5*x)],
[(1-2*x)^(3/2)*(2+3*x)*(3+5*x)^(3/2),x,7,-37/160*(1-2*x)^(5/2)*(3+5*x)^(3/2)-3/50*(1-2*x)^(5/2)*(3+5*x)^(5/2)+1625151/128000*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+4477/12800*(1-2*x)^(3/2)*sqrt(3+5*x)-407/640*(1-2*x)^(5/2)*sqrt(3+5*x)+147741/128000*sqrt(1-2*x)*sqrt(3+5*x)],
[(1-2*x)^(3/2)*(3+5*x)^(3/2),x,6,-1/8*(1-2*x)^(5/2)*(3+5*x)^(3/2)+43923/6400*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+121/640*(1-2*x)^(3/2)*sqrt(3+5*x)-11/32*(1-2*x)^(5/2)*sqrt(3+5*x)+3993/6400*sqrt(1-2*x)*sqrt(3+5*x)],
[(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x),x,8,1/9*(1-2*x)^(3/2)*(3+5*x)^(3/2)-14/81*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))*sqrt(7)+19573/6480*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+37/180*(3+5*x)^(3/2)*sqrt(1-2*x)-1781/2160*sqrt(1-2*x)*sqrt(3+5*x)],
[(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^2,x,8,-1/3*(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)+37/27*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))*sqrt(7)+1649/108*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-1/3*(3+5*x)^(3/2)*sqrt(1-2*x)+107/36*sqrt(1-2*x)*sqrt(3+5*x)],
[(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^3,x,8,-1/6*(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^2-1649/108*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)-37/27*arcsin(sqrt(2/11)*sqrt(3+5*x))*sqrt(10)+37/12*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)-205/36*sqrt(1-2*x)*sqrt(3+5*x)],
[(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^4,x,8,-1/9*(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^3-19573/4536*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)+20/81*arcsin(sqrt(2/11)*sqrt(3+5*x))*sqrt(10)+37/36*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^2-661/1512*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)],
[(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^5,x,6,1/4*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^4-43923/3136*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)-121/224*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^2+11/8*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^3-3993/3136*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)],
[(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^6,x,7,3/35*(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^5+37/56*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^4-1625151/43904*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)-4477/3136*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^2+407/112*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^3-147741/43904*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)],
[(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^7,x,9,-1/18*(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^6-19457889/175616*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)+37/180*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^5-7591/30240*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^4+37333/181440*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+1316353/1016064*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+137752591/14224896*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)],
[(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^8,x,10,-1/21*(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^7-6219452877/17210368*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)+37/252*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^6-9901/52920*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^5+341917/2963520*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^4+4014523/5927040*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+140331343/33191424*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+14677525921/464679936*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)],
[(1-2*x)^(3/2)*(2+3*x)^3*(3+5*x)^(5/2),x,9,-3366319/819200*(1-2*x)^(5/2)*(3+5*x)^(3/2)-306029/256000*(1-2*x)^(5/2)*(3+5*x)^(5/2)-3/80*(1-2*x)^(5/2)*(2+3*x)^2*(3+5*x)^(7/2)-9/448000*(1-2*x)^(5/2)*(3+5*x)^(7/2)*(25043+16120*x)+147858829437/655360000*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+407324599/65536000*(1-2*x)^(3/2)*sqrt(3+5*x)-37029509/3276800*(1-2*x)^(5/2)*sqrt(3+5*x)+13441711767/655360000*sqrt(1-2*x)*sqrt(3+5*x)],
[(1-2*x)^(3/2)*(2+3*x)^2*(3+5*x)^(5/2),x,9,-8613/5120*(1-2*x)^(5/2)*(3+5*x)^(3/2)-783/1600*(1-2*x)^(5/2)*(3+5*x)^(5/2)-47/400*(1-2*x)^(5/2)*(3+5*x)^(7/2)-3/70*(1-2*x)^(5/2)*(2+3*x)*(3+5*x)^(7/2)+378308799/4096000*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+1042173/409600*(1-2*x)^(3/2)*sqrt(3+5*x)-94743/20480*(1-2*x)^(5/2)*sqrt(3+5*x)+34391709/4096000*sqrt(1-2*x)*sqrt(3+5*x)],
[(1-2*x)^(3/2)*(2+3*x)*(3+5*x)^(5/2),x,8,-187/256*(1-2*x)^(5/2)*(3+5*x)^(3/2)-17/80*(1-2*x)^(5/2)*(3+5*x)^(5/2)-1/20*(1-2*x)^(5/2)*(3+5*x)^(7/2)+8213601/204800*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+22627/20480*(1-2*x)^(3/2)*sqrt(3+5*x)-2057/1024*(1-2*x)^(5/2)*sqrt(3+5*x)+746691/204800*sqrt(1-2*x)*sqrt(3+5*x)],
[(1-2*x)^(3/2)*(3+5*x)^(5/2),x,7,-11/32*(1-2*x)^(5/2)*(3+5*x)^(3/2)-1/10*(1-2*x)^(5/2)*(3+5*x)^(5/2)+483153/25600*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+1331/2560*(1-2*x)^(3/2)*sqrt(3+5*x)-121/128*(1-2*x)^(5/2)*sqrt(3+5*x)+43923/25600*sqrt(1-2*x)*sqrt(3+5*x)],
[(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x),x,9,1/12*(1-2*x)^(3/2)*(3+5*x)^(5/2)+14/243*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))*sqrt(7)+648919/62208*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-53/192*(3+5*x)^(3/2)*sqrt(1-2*x)+23/216*(3+5*x)^(5/2)*sqrt(1-2*x)-15863/20736*sqrt(1-2*x)*sqrt(3+5*x)],
[(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^2,x,9,-1/3*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)-43/3888*arcsin(sqrt(2/11)*sqrt(3+5*x))*sqrt(5/2)-181/243*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))*sqrt(7)+25/12*(3+5*x)^(3/2)*sqrt(1-2*x)-8/27*(3+5*x)^(5/2)*sqrt(1-2*x)-3065/1296*sqrt(1-2*x)*sqrt(3+5*x)],
[(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^3,x,9,-1/6*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^2+1945/324*arcsin(sqrt(2/11)*sqrt(3+5*x))*sqrt(5/2)+6829/324*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)-35/4*(3+5*x)^(3/2)*sqrt(1-2*x)+181/36*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)+185/27*sqrt(1-2*x)*sqrt(3+5*x)],
[(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^4,x,9,-1/9*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^3-326717/13608*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)-575/243*arcsin(sqrt(2/11)*sqrt(3+5*x))*sqrt(10)+331/168*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)+181/108*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^2-39745/4536*sqrt(1-2*x)*sqrt(3+5*x)],
[(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^5,x,9,-1/12*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^4-1922677/762048*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)+100/243*arcsin(sqrt(2/11)*sqrt(3+5*x))*sqrt(10)-871/6048*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^2+181/216*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^3-77269/254016*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)],
[(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^6,x,7,1/5*(1-2*x)^(3/2)*(3+5*x)^(7/2)/(2+3*x)^5-483153/43904*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)-1331/3136*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^2-121/560*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^3+33/40*(3+5*x)^(7/2)*sqrt(1-2*x)/(2+3*x)^4-43923/43904*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)],
[(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^7,x,8,1/14*(1-2*x)^(5/2)*(3+5*x)^(7/2)/(2+3*x)^6+9/20*(1-2*x)^(3/2)*(3+5*x)^(7/2)/(2+3*x)^5-4348377/175616*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)-11979/12544*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^2-1089/2240*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^3+297/160*(3+5*x)^(7/2)*sqrt(1-2*x)/(2+3*x)^4-395307/175616*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)],
[(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^8,x,10,-1/21*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^7-1104970911/17210368*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)-12421/52920*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^5+181/756*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^6-1289227/8890560*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^4+6249601/53343360*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+224018941/298722816*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+23466191827/4182119424*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)],

# n<0
[(1-2*x)^(3/2)*(2+3*x)^3/sqrt(3+5*x),x,6,18648399/3200000*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+51373/320000*(1-2*x)^(3/2)*sqrt(3+5*x)-3/50*(1-2*x)^(5/2)*(2+3*x)^2*sqrt(3+5*x)-3/80000*(1-2*x)^(5/2)*(14629+11580*x)*sqrt(3+5*x)+1695309/3200000*sqrt(1-2*x)*sqrt(3+5*x)],
[(1-2*x)^(3/2)*(2+3*x)^2/sqrt(3+5*x),x,6,109263/32000*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+301/3200*(1-2*x)^(3/2)*sqrt(3+5*x)-119/800*(1-2*x)^(5/2)*sqrt(3+5*x)-3/40*(1-2*x)^(5/2)*(2+3*x)*sqrt(3+5*x)+9933/32000*sqrt(1-2*x)*sqrt(3+5*x)],
[(1-2*x)^(3/2)*(2+3*x)/sqrt(3+5*x),x,5,1089/400*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+3/40*(1-2*x)^(3/2)*sqrt(3+5*x)-1/10*(1-2*x)^(5/2)*sqrt(3+5*x)+99/400*sqrt(1-2*x)*sqrt(3+5*x)],
[(1-2*x)^(3/2)/sqrt(3+5*x),x,4,363/100*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+1/10*(1-2*x)^(3/2)*sqrt(3+5*x)+33/100*sqrt(1-2*x)*sqrt(3+5*x)],
[(1-2*x)^(3/2)/((2+3*x)*sqrt(3+5*x)),x,6,-103/45*arcsin(sqrt(2/11)*sqrt(3+5*x))*sqrt(2/5)-14/9*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))*sqrt(7)-2/15*sqrt(1-2*x)*sqrt(3+5*x)],
[(1-2*x)^(3/2)/((2+3*x)^2*sqrt(3+5*x)),x,6,4/9*arcsin(sqrt(2/11)*sqrt(3+5*x))*sqrt(2/5)-29/9*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))*sqrt(7)+7/3*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)],
[(1-2*x)^(3/2)/((2+3*x)^3*sqrt(3+5*x)),x,4,-363/4*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)+1/2*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^2+33/4*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)],
[(1-2*x)^(3/2)/((2+3*x)^4*sqrt(3+5*x)),x,5,-21417/56*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)+1/7*(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^3+59/28*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^2+1947/56*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)],
[(1-2*x)^(3/2)/((2+3*x)^5*sqrt(3+5*x)),x,7,-5274027/3136*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)+7/12*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^4+227/72*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+39667/2016*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+4148797/28224*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)],
[(1-2*x)^(3/2)/((2+3*x)^6*sqrt(3+5*x)),x,8,-333216939/43904*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)+7/15*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^5+293/120*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^4+23909/1680*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+835409/9408*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+87374783/131712*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)],
[(1-2*x)^(3/2)*(2+3*x)^3/(3+5*x)^(3/2),x,6,390621/160000*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-2/5*(1-2*x)^(3/2)*(2+3*x)^3/sqrt(3+5*x)-63/16000*(35-8*x)*(1-2*x)^(3/2)*sqrt(3+5*x)+27/100*(1-2*x)^(3/2)*(2+3*x)^2*sqrt(3+5*x)+35511/160000*sqrt(1-2*x)*sqrt(3+5*x)],
[(1-2*x)^(3/2)*(2+3*x)^2/(3+5*x)^(3/2),x,6,3927/2000*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-2/275*(1-2*x)^(5/2)/sqrt(3+5*x)+119/2200*(1-2*x)^(3/2)*sqrt(3+5*x)-3/50*(1-2*x)^(5/2)*sqrt(3+5*x)+357/2000*sqrt(1-2*x)*sqrt(3+5*x)],
[(1-2*x)^(3/2)*(2+3*x)/(3+5*x)^(3/2),x,5,33/20*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-2/55*(1-2*x)^(5/2)/sqrt(3+5*x)+1/22*(1-2*x)^(3/2)*sqrt(3+5*x)+3/20*sqrt(1-2*x)*sqrt(3+5*x)],
[(1-2*x)^(3/2)/(3+5*x)^(3/2),x,4,-33/25*arcsin(sqrt(2/11)*sqrt(3+5*x))*sqrt(2/5)-2/5*(1-2*x)^(3/2)/sqrt(3+5*x)-6/25*sqrt(1-2*x)*sqrt(3+5*x)],
[(1-2*x)^(3/2)/((2+3*x)*(3+5*x)^(3/2)),x,6,4/15*arcsin(sqrt(2/11)*sqrt(3+5*x))*sqrt(2/5)+14/3*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))*sqrt(7)-22/5*sqrt(1-2*x)/sqrt(3+5*x)],
[(1-2*x)^(3/2)/((2+3*x)^2*(3+5*x)^(3/2)),x,4,33*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))*sqrt(7)+(1-2*x)^(3/2)/((2+3*x)*sqrt(3+5*x))-33*sqrt(1-2*x)/sqrt(3+5*x)],
[(1-2*x)^(3/2)/((2+3*x)^3*(3+5*x)^(3/2)),x,5,5709/4*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)+3/14*(1-2*x)^(5/2)/((2+3*x)^2*sqrt(3+5*x))+173/28*(1-2*x)^(3/2)/((2+3*x)*sqrt(3+5*x))-5709/28*sqrt(1-2*x)/sqrt(3+5*x)],
[(1-2*x)^(3/2)/((2+3*x)^4*(3+5*x)^(3/2)),x,7,463881/56*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)-608185/504*sqrt(1-2*x)/sqrt(3+5*x)+7/9*sqrt(1-2*x)/((2+3*x)^3*sqrt(3+5*x))+77/12*sqrt(1-2*x)/((2+3*x)^2*sqrt(3+5*x))+13409/168*sqrt(1-2*x)/((2+3*x)*sqrt(3+5*x))],
[(1-2*x)^(3/2)/((2+3*x)^5*(3+5*x)^(3/2)),x,8,145708761/3136*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)-63678595/9408*sqrt(1-2*x)/sqrt(3+5*x)+7/12*sqrt(1-2*x)/((2+3*x)^4*sqrt(3+5*x))+33/8*sqrt(1-2*x)/((2+3*x)^3*sqrt(3+5*x))+8063/224*sqrt(1-2*x)/((2+3*x)^2*sqrt(3+5*x))+1403963/3136*sqrt(1-2*x)/((2+3*x)*sqrt(3+5*x))],
[(1-2*x)^(3/2)*(2+3*x)^3/(3+5*x)^(5/2),x,6,-2/15*(1-2*x)^(3/2)*(2+3*x)^3/(3+5*x)^(3/2)+13153/10000*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-128/25*(2+3*x)^3*sqrt(1-2*x)/sqrt(3+5*x)+378/125*(2+3*x)^2*sqrt(1-2*x)*sqrt(3+5*x)+21/10000*(853+1140*x)*sqrt(1-2*x)*sqrt(3+5*x)],
[(1-2*x)^(3/2)*(2+3*x)^2/(3+5*x)^(5/2),x,6,-2/825*(1-2*x)^(5/2)/(3+5*x)^(3/2)+343/500*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-388/9075*(1-2*x)^(5/2)/sqrt(3+5*x)+343/18150*(1-2*x)^(3/2)*sqrt(3+5*x)+343/5500*sqrt(1-2*x)*sqrt(3+5*x)],
[(1-2*x)^(3/2)*(2+3*x)/(3+5*x)^(5/2),x,5,-2/165*(1-2*x)^(5/2)/(3+5*x)^(3/2)-19/25*arcsin(sqrt(2/11)*sqrt(3+5*x))*sqrt(2/5)-38/165*(1-2*x)^(3/2)/sqrt(3+5*x)-38/275*sqrt(1-2*x)*sqrt(3+5*x)],
[(1-2*x)^(3/2)/(3+5*x)^(5/2),x,4,-2/15*(1-2*x)^(3/2)/(3+5*x)^(3/2)+4/25*arcsin(sqrt(2/11)*sqrt(3+5*x))*sqrt(2/5)+4/25*sqrt(1-2*x)/sqrt(3+5*x)],
[(1-2*x)^(3/2)/((2+3*x)*(3+5*x)^(5/2)),x,4,-2/3*(1-2*x)^(3/2)/(3+5*x)^(3/2)-14*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))*sqrt(7)+14*sqrt(1-2*x)/sqrt(3+5*x)],
[(1-2*x)^(3/2)/((2+3*x)^2*(3+5*x)^(5/2)),x,5,-169/21*(1-2*x)^(3/2)/(3+5*x)^(3/2)+3/7*(1-2*x)^(5/2)/((2+3*x)*(3+5*x)^(3/2))-169*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))*sqrt(7)+169*sqrt(1-2*x)/sqrt(3+5*x)],
[(1-2*x)^(3/2)/((2+3*x)^3*(3+5*x)^(5/2)),x,7,-40787/4*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)-655/4*sqrt(1-2*x)/(3+5*x)^(3/2)+7/6*sqrt(1-2*x)/((2+3*x)^2*(3+5*x)^(3/2))+235/12*sqrt(1-2*x)/((2+3*x)*(3+5*x)^(3/2))+17825/12*sqrt(1-2*x)/sqrt(3+5*x)],
[(1-2*x)^(3/2)/((2+3*x)^4*(3+5*x)^(5/2)),x,8,-4246733/56*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)-204595/168*sqrt(1-2*x)/(3+5*x)^(3/2)+7/9*sqrt(1-2*x)/((2+3*x)^3*(3+5*x)^(3/2))+301/36*sqrt(1-2*x)/((2+3*x)^2*(3+5*x)^(3/2))+24469/168*sqrt(1-2*x)/((2+3*x)*(3+5*x)^(3/2))+618645/56*sqrt(1-2*x)/sqrt(3+5*x)],

# Integrands of the form (a+b x)^m (c+d x)^(n/2) (e+f x)^(5/2)

# n>0
[(1-2*x)^(5/2)*(2+3*x)^3*sqrt(3+5*x),x,8,-3/70*(1-2*x)^(7/2)*(2+3*x)^2*(3+5*x)^(3/2)-3/280000*(1-2*x)^(7/2)*(3+5*x)^(3/2)*(33857+26700*x)+3735929329/256000000*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+30875449/76800000*(1-2*x)^(3/2)*sqrt(3+5*x)+2806859/19200000*(1-2*x)^(5/2)*sqrt(3+5*x)-255169/640000*(1-2*x)^(7/2)*sqrt(3+5*x)+339629939/256000000*sqrt(1-2*x)*sqrt(3+5*x)],
[(1-2*x)^(5/2)*(2+3*x)^2*sqrt(3+5*x),x,8,-193/2000*(1-2*x)^(7/2)*(3+5*x)^(3/2)-1/20*(1-2*x)^(7/2)*(2+3*x)*(3+5*x)^(3/2)+105254149/12800000*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+869869/3840000*(1-2*x)^(3/2)*sqrt(3+5*x)+79079/960000*(1-2*x)^(5/2)*sqrt(3+5*x)-7189/32000*(1-2*x)^(7/2)*sqrt(3+5*x)+9568559/12800000*sqrt(1-2*x)*sqrt(3+5*x)],
[(1-2*x)^(5/2)*(2+3*x)*sqrt(3+5*x),x,7,-3/50*(1-2*x)^(7/2)*(3+5*x)^(3/2)+1742279/320000*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+14399/96000*(1-2*x)^(3/2)*sqrt(3+5*x)+1309/24000*(1-2*x)^(5/2)*sqrt(3+5*x)-119/800*(1-2*x)^(7/2)*sqrt(3+5*x)+158389/320000*sqrt(1-2*x)*sqrt(3+5*x)],
[(1-2*x)^(5/2)*sqrt(3+5*x),x,6,14641/3200*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+121/960*(1-2*x)^(3/2)*sqrt(3+5*x)+11/240*(1-2*x)^(5/2)*sqrt(3+5*x)-1/8*(1-2*x)^(7/2)*sqrt(3+5*x)+1331/3200*sqrt(1-2*x)*sqrt(3+5*x)],
[(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x),x,8,98/81*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))*sqrt(7)+250433/16200*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+59/180*(1-2*x)^(3/2)*sqrt(3+5*x)+1/9*(1-2*x)^(5/2)*sqrt(3+5*x)+6401/5400*sqrt(1-2*x)*sqrt(3+5*x)],
[(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^2,x,8,-35/9*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))*sqrt(7)-2119/90*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-1/3*(1-2*x)^(3/2)*sqrt(3+5*x)-1/3*(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)-43/30*sqrt(1-2*x)*sqrt(3+5*x)],
[(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^3,x,8,118/27*arcsin(sqrt(2/11)*sqrt(3+5*x))*sqrt(2/5)-155/108*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))*sqrt(7)-1/6*(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^2+5/4*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)+19/18*sqrt(1-2*x)*sqrt(3+5*x)],
[(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^4,x,8,-32765/648*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)-8/81*arcsin(sqrt(2/11)*sqrt(3+5*x))*sqrt(10)-1/9*(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^3+5/12*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^2+925/216*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)],
[(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^5,x,6,1/4*(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^4+55/24*(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^3-73205/448*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)+605/32*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^2-6655/448*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)],
[(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^6,x,7,3/35*(1-2*x)^(7/2)*(3+5*x)^(3/2)/(2+3*x)^5+251/280*(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^4+2761/336*(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^3-3674891/6272*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)+30371/448*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^2-334081/6272*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)],
[(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^7,x,9,-391280725/175616*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)-1/18*(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^6+1/12*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^5+647/864*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^4+151621/36288*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+26486645/1016064*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+2770202075/14224896*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)],
[(1-2*x)^(5/2)*(2+3*x)^3*(3+5*x)^(3/2),x,9,-735439/1280000*(1-2*x)^(7/2)*(3+5*x)^(3/2)-3/80*(1-2*x)^(7/2)*(2+3*x)^2*(3+5*x)^(5/2)-9/448000*(1-2*x)^(7/2)*(3+5*x)^(5/2)*(18399+13480*x)+355329559167/8192000000*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+978869309/819200000*(1-2*x)^(3/2)*sqrt(3+5*x)+88988119/204800000*(1-2*x)^(5/2)*sqrt(3+5*x)-24269487/20480000*(1-2*x)^(7/2)*sqrt(3+5*x)+32302687197/8192000000*sqrt(1-2*x)*sqrt(3+5*x)],
[(1-2*x)^(5/2)*(2+3*x)^2*(3+5*x)^(3/2),x,9,-2287/8000*(1-2*x)^(7/2)*(3+5*x)^(3/2)-263/2800*(1-2*x)^(7/2)*(3+5*x)^(5/2)-3/70*(1-2*x)^(7/2)*(2+3*x)*(3+5*x)^(5/2)+1104970911/51200000*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+3043997/5120000*(1-2*x)^(3/2)*sqrt(3+5*x)+276727/1280000*(1-2*x)^(5/2)*sqrt(3+5*x)-75471/128000*(1-2*x)^(7/2)*sqrt(3+5*x)+100451901/51200000*sqrt(1-2*x)*sqrt(3+5*x)],
[(1-2*x)^(5/2)*(2+3*x)*(3+5*x)^(3/2),x,8,-63/400*(1-2*x)^(7/2)*(3+5*x)^(3/2)-1/20*(1-2*x)^(7/2)*(3+5*x)^(5/2)+30438639/2560000*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+83853/256000*(1-2*x)^(3/2)*sqrt(3+5*x)+7623/64000*(1-2*x)^(5/2)*sqrt(3+5*x)-2079/6400*(1-2*x)^(7/2)*sqrt(3+5*x)+2767149/2560000*sqrt(1-2*x)*sqrt(3+5*x)],
[(1-2*x)^(5/2)*(3+5*x)^(3/2),x,7,-1/10*(1-2*x)^(7/2)*(3+5*x)^(3/2)+483153/64000*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+1331/6400*(1-2*x)^(3/2)*sqrt(3+5*x)+121/1600*(1-2*x)^(5/2)*sqrt(3+5*x)-33/160*(1-2*x)^(7/2)*sqrt(3+5*x)+43923/64000*sqrt(1-2*x)*sqrt(3+5*x)],
[(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x),x,9,181/1080*(1-2*x)^(3/2)*(3+5*x)^(3/2)+1/12*(1-2*x)^(5/2)*(3+5*x)^(3/2)-98/243*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))*sqrt(7)+1922677/777600*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+7093/21600*(3+5*x)^(3/2)*sqrt(1-2*x)-390869/259200*sqrt(1-2*x)*sqrt(3+5*x)],
[(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^2,x,9,-8/27*(1-2*x)^(3/2)*(3+5*x)^(3/2)-1/3*(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)+805/243*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))*sqrt(7)+326717/9720*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-247/270*(3+5*x)^(3/2)*sqrt(1-2*x)+24251/3240*sqrt(1-2*x)*sqrt(3+5*x)],
[(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^3,x,9,-1/6*(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^2+115/36*(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)-1945/324*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))*sqrt(7)-6829/162*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+41/18*(3+5*x)^(3/2)*sqrt(1-2*x)-1649/108*sqrt(1-2*x)*sqrt(3+5*x)],
[(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^4,x,9,-1/9*(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^3+115/108*(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^2+215/1944*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)+362/243*arcsin(sqrt(2/11)*sqrt(3+5*x))*sqrt(10)+365/216*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)-845/648*sqrt(1-2*x)*sqrt(3+5*x)],
[(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^5,x,9,-1/12*(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^4+115/216*(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^3-3244595/108864*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)-40/243*arcsin(sqrt(2/11)*sqrt(3+5*x))*sqrt(10)+2675/864*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^2-97235/36288*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)],
[(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^6,x,7,1/5*(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^5+11/8*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^4-483153/6272*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)-1331/448*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^2+121/16*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^3-43923/6272*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)],
[(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^7,x,8,1/14*(1-2*x)^(7/2)*(3+5*x)^(5/2)/(2+3*x)^6+17/28*(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^5+935/224*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^4-41068005/175616*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)-113135/12544*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^2+10285/448*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^3-3733455/175616*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)],
[(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^8,x,10,-1/21*(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^7+115/756*(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^6-1891543995/2458624*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)+1921/1512*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^5-443563/254016*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^4+2199649/1524096*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+384136145/42674688*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+40175505215/597445632*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)],
[(1-2*x)^(5/2)*(2+3*x)^3*(3+5*x)^(5/2),x,10,-5787133/3072000*(1-2*x)^(7/2)*(3+5*x)^(3/2)-526103/768000*(1-2*x)^(7/2)*(3+5*x)^(5/2)-1/30*(1-2*x)^(7/2)*(2+3*x)^2*(3+5*x)^(7/2)-1/672000*(1-2*x)^(7/2)*(3+5*x)^(7/2)*(245011+170940*x)+932023556783/6553600000*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+7702674023/1966080000*(1-2*x)^(3/2)*sqrt(3+5*x)+700243093/491520000*(1-2*x)^(5/2)*sqrt(3+5*x)-63658463/16384000*(1-2*x)^(7/2)*sqrt(3+5*x)+84729414253/6553600000*sqrt(1-2*x)*sqrt(3+5*x)],
[(1-2*x)^(5/2)*(2+3*x)^2*(3+5*x)^(5/2),x,10,-132451/153600*(1-2*x)^(7/2)*(3+5*x)^(3/2)-12041/38400*(1-2*x)^(7/2)*(3+5*x)^(5/2)-999/11200*(1-2*x)^(7/2)*(3+5*x)^(7/2)-3/80*(1-2*x)^(7/2)*(2+3*x)*(3+5*x)^(7/2)+21331366001/327680000*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+176292281/98304000*(1-2*x)^(3/2)*sqrt(3+5*x)+16026571/24576000*(1-2*x)^(5/2)*sqrt(3+5*x)-1456961/819200*(1-2*x)^(7/2)*sqrt(3+5*x)+1939215091/327680000*sqrt(1-2*x)*sqrt(3+5*x)],
[(1-2*x)^(5/2)*(2+3*x)*(3+5*x)^(5/2),x,9,-407/960*(1-2*x)^(7/2)*(3+5*x)^(3/2)-37/240*(1-2*x)^(7/2)*(3+5*x)^(5/2)-3/70*(1-2*x)^(7/2)*(3+5*x)^(7/2)+65547757/2048000*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+541717/614400*(1-2*x)^(3/2)*sqrt(3+5*x)+49247/153600*(1-2*x)^(5/2)*sqrt(3+5*x)-4477/5120*(1-2*x)^(7/2)*sqrt(3+5*x)+5958887/2048000*sqrt(1-2*x)*sqrt(3+5*x)],
[(1-2*x)^(5/2)*(3+5*x)^(5/2),x,8,-11/48*(1-2*x)^(7/2)*(3+5*x)^(3/2)-1/12*(1-2*x)^(7/2)*(3+5*x)^(5/2)+1771561/102400*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+14641/30720*(1-2*x)^(3/2)*sqrt(3+5*x)+1331/7680*(1-2*x)^(5/2)*sqrt(3+5*x)-121/256*(1-2*x)^(7/2)*sqrt(3+5*x)+161051/102400*sqrt(1-2*x)*sqrt(3+5*x)],
[(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x),x,10,37/360*(1-2*x)^(3/2)*(3+5*x)^(5/2)+1/15*(1-2*x)^(5/2)*(3+5*x)^(5/2)+98/729*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))*sqrt(7)+109715471/9331200*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-14557/28800*(3+5*x)^(3/2)*sqrt(1-2*x)+4783/32400*(3+5*x)^(5/2)*sqrt(1-2*x)-1994287/3110400*sqrt(1-2*x)*sqrt(3+5*x)],
[(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^2,x,10,-5/18*(1-2*x)^(3/2)*(3+5*x)^(5/2)-1/3*(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)-1295/729*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))*sqrt(7)-660959/93312*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+1453/288*(3+5*x)^(3/2)*sqrt(1-2*x)-247/324*(3+5*x)^(5/2)*sqrt(1-2*x)-155777/31104*sqrt(1-2*x)*sqrt(3+5*x)],
[(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^3,x,10,-1/6*(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^2+185/36*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)+81733/5832*arcsin(sqrt(2/11)*sqrt(3+5*x))*sqrt(5/2)+21935/2916*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))*sqrt(7)-785/36*(3+5*x)^(3/2)*sqrt(1-2*x)+575/162*(3+5*x)^(5/2)*sqrt(1-2*x)+34145/1944*sqrt(1-2*x)*sqrt(3+5*x)],
[(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^4,x,10,-1/9*(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^3+185/108*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^2-21935/1458*arcsin(sqrt(2/11)*sqrt(3+5*x))*sqrt(5/2)-408665/5832*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)+2075/72*(3+5*x)^(3/2)*sqrt(1-2*x)-10385/648*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)-48625/1944*sqrt(1-2*x)*sqrt(3+5*x)],
[(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^5,x,10,-1/12*(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^4+185/216*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^3+3304795/326592*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)+1850/729*arcsin(sqrt(2/11)*sqrt(3+5*x))*sqrt(10)-3485/4032*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)+1165/2592*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^2+249575/108864*sqrt(1-2*x)*sqrt(3+5*x)],
[(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^6,x,10,-1/15*(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^5+37/72*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^4-109715471/4572288*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)-200/729*arcsin(sqrt(2/11)*sqrt(3+5*x))*sqrt(10)-32453/36288*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^2+2543/1296*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^3-3248687/1524096*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)],
[(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^7,x,8,1/6*(1-2*x)^(5/2)*(3+5*x)^(7/2)/(2+3*x)^6+11/12*(1-2*x)^(3/2)*(3+5*x)^(7/2)/(2+3*x)^5-8857805/175616*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)-73205/37632*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^2-1331/1344*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^3+121/32*(3+5*x)^(7/2)*sqrt(1-2*x)/(2+3*x)^4-805255/175616*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)],
[(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^8,x,9,3/49*(1-2*x)^(7/2)*(3+5*x)^(7/2)/(2+3*x)^7+37/84*(1-2*x)^(5/2)*(3+5*x)^(7/2)/(2+3*x)^6+407/168*(1-2*x)^(3/2)*(3+5*x)^(7/2)/(2+3*x)^5-327738785/2458624*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)-2708585/526848*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^2-49247/18816*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^3+4477/448*(3+5*x)^(7/2)*sqrt(1-2*x)/(2+3*x)^4-29794435/2458624*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)],
[(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^9,x,11,-1/24*(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^8+185/1008*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^7-106656830005/275365888*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)-720833/508032*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^5+47365/36288*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^6-75045071/85349376*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^4+372439373/512096256*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+64983635965/14338695168*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+6796051494355/200741732352*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)],

# n<0
[(1-2*x)^(5/2)*(2+3*x)^4/sqrt(3+5*x),x,8,12679836719/1280000000*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+104792039/384000000*(1-2*x)^(3/2)*sqrt(3+5*x)+9526549/96000000*(1-2*x)^(5/2)*sqrt(3+5*x)-271/2800*(1-2*x)^(7/2)*(2+3*x)^2*sqrt(3+5*x)-3/70*(1-2*x)^(7/2)*(2+3*x)^3*sqrt(3+5*x)-1/22400000*(1-2*x)^(7/2)*(12923401+11603280*x)*sqrt(3+5*x)+1152712429/1280000000*sqrt(1-2*x)*sqrt(3+5*x)],
[(1-2*x)^(5/2)*(2+3*x)^3/sqrt(3+5*x),x,7,368012183/64000000*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+3041423/19200000*(1-2*x)^(3/2)*sqrt(3+5*x)+276493/4800000*(1-2*x)^(5/2)*sqrt(3+5*x)-1/20*(1-2*x)^(7/2)*(2+3*x)^2*sqrt(3+5*x)-1/160000*(1-2*x)^(7/2)*(52951+47280*x)*sqrt(3+5*x)+33455653/64000000*sqrt(1-2*x)*sqrt(3+5*x)],
[(1-2*x)^(5/2)*(2+3*x)^2/sqrt(3+5*x),x,7,6531217/1600000*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+53977/480000*(1-2*x)^(3/2)*sqrt(3+5*x)+4907/120000*(1-2*x)^(5/2)*sqrt(3+5*x)-369/4000*(1-2*x)^(7/2)*sqrt(3+5*x)-3/50*(1-2*x)^(7/2)*(2+3*x)*sqrt(3+5*x)+593747/1600000*sqrt(1-2*x)*sqrt(3+5*x)],
[(1-2*x)^(5/2)*(2+3*x)/sqrt(3+5*x),x,6,65219/16000*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+539/4800*(1-2*x)^(3/2)*sqrt(3+5*x)+49/1200*(1-2*x)^(5/2)*sqrt(3+5*x)-3/40*(1-2*x)^(7/2)*sqrt(3+5*x)+5929/16000*sqrt(1-2*x)*sqrt(3+5*x)],
[(1-2*x)^(5/2)/sqrt(3+5*x),x,5,1331/200*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+11/60*(1-2*x)^(3/2)*sqrt(3+5*x)+1/15*(1-2*x)^(5/2)*sqrt(3+5*x)+121/200*sqrt(1-2*x)*sqrt(3+5*x)],
[(1-2*x)^(5/2)/((2+3*x)*sqrt(3+5*x)),x,7,-98/27*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))*sqrt(7)-17687/1350*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-1/15*(1-2*x)^(3/2)*sqrt(3+5*x)-239/450*sqrt(1-2*x)*sqrt(3+5*x)],
[(1-2*x)^(5/2)/((2+3*x)^2*sqrt(3+5*x)),x,7,346/135*arcsin(sqrt(2/11)*sqrt(3+5*x))*sqrt(2/5)-175/27*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))*sqrt(7)+7/3*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)+74/45*sqrt(1-2*x)*sqrt(3+5*x)],
[(1-2*x)^(5/2)/((2+3*x)^3*sqrt(3+5*x)),x,7,-8/27*arcsin(sqrt(2/11)*sqrt(3+5*x))*sqrt(2/5)-3035/108*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))*sqrt(7)+7/6*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^2+637/36*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)],
[(1-2*x)^(5/2)/((2+3*x)^4*sqrt(3+5*x)),x,5,-6655/8*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)+1/3*(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^3+55/12*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^2+605/8*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)],
[(1-2*x)^(5/2)/((2+3*x)^5*sqrt(3+5*x)),x,6,-1643785/448*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)+3/28*(1-2*x)^(7/2)*sqrt(3+5*x)/(2+3*x)^4+247/168*(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^3+13585/672*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^2+149435/448*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)],
[(1-2*x)^(5/2)/((2+3*x)^6*sqrt(3+5*x)),x,8,-104040277/6272*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)+7/15*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^5+2023/360*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^4+67187/2160*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+2347559/12096*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+245529161/169344*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)],
[(1-2*x)^(5/2)/((2+3*x)^7*sqrt(3+5*x)),x,9,-13391796605/175616*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)+7/18*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^6+497/108*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^5+21199/864*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^4+1729615/12096*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+302171615/338688*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+31603880465/4741632*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)],
[(1-2*x)^(5/2)*(2+3*x)^4/(3+5*x)^(3/2),x,8,1298595837/320000000*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-2/5*(1-2*x)^(5/2)*(2+3*x)^4/sqrt(3+5*x)+3577399/32000000*(1-2*x)^(3/2)*sqrt(3+5*x)+111/5000*(1-2*x)^(5/2)*(2+3*x)^2*sqrt(3+5*x)+13/50*(1-2*x)^(5/2)*(2+3*x)^3*sqrt(3+5*x)-1/8000000*(1-2*x)^(5/2)*(2725981+1990620*x)*sqrt(3+5*x)+118054167/320000000*sqrt(1-2*x)*sqrt(3+5*x)],
[(1-2*x)^(5/2)*(2+3*x)^3/(3+5*x)^(3/2),x,7,24319911/8000000*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-2/5*(1-2*x)^(5/2)*(2+3*x)^3/sqrt(3+5*x)+66997/800000*(1-2*x)^(3/2)*sqrt(3+5*x)-9/200000*(2127-460*x)*(1-2*x)^(5/2)*sqrt(3+5*x)+33/125*(1-2*x)^(5/2)*(2+3*x)^2*sqrt(3+5*x)+2210901/8000000*sqrt(1-2*x)*sqrt(3+5*x)],
[(1-2*x)^(5/2)*(2+3*x)^2/(3+5*x)^(3/2),x,7,236313/80000*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-2/275*(1-2*x)^(7/2)/sqrt(3+5*x)+651/8000*(1-2*x)^(3/2)*sqrt(3+5*x)+651/22000*(1-2*x)^(5/2)*sqrt(3+5*x)-9/200*(1-2*x)^(7/2)*sqrt(3+5*x)+21483/80000*sqrt(1-2*x)*sqrt(3+5*x)],
[(1-2*x)^(5/2)*(2+3*x)/(3+5*x)^(3/2),x,6,2541/1000*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-2/55*(1-2*x)^(7/2)/sqrt(3+5*x)+7/100*(1-2*x)^(3/2)*sqrt(3+5*x)+7/275*(1-2*x)^(5/2)*sqrt(3+5*x)+231/1000*sqrt(1-2*x)*sqrt(3+5*x)],
[(1-2*x)^(5/2)/(3+5*x)^(3/2),x,5,-363/50*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-2/5*(1-2*x)^(5/2)/sqrt(3+5*x)-1/5*(1-2*x)^(3/2)*sqrt(3+5*x)-33/50*sqrt(1-2*x)*sqrt(3+5*x)],
[(1-2*x)^(5/2)/((2+3*x)*(3+5*x)^(3/2)),x,7,338/225*arcsin(sqrt(2/11)*sqrt(3+5*x))*sqrt(2/5)+98/9*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))*sqrt(7)-22/5*(1-2*x)^(3/2)/sqrt(3+5*x)-128/75*sqrt(1-2*x)*sqrt(3+5*x)],
[(1-2*x)^(5/2)/((2+3*x)^2*(3+5*x)^(3/2)),x,7,-8/45*arcsin(sqrt(2/11)*sqrt(3+5*x))*sqrt(2/5)+665/9*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))*sqrt(7)+7/3*(1-2*x)^(3/2)/((2+3*x)*sqrt(3+5*x))-1111/15*sqrt(1-2*x)/sqrt(3+5*x)],
[(1-2*x)^(5/2)/((2+3*x)^3*(3+5*x)^(3/2)),x,5,1815/4*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))*sqrt(7)+1/2*(1-2*x)^(5/2)/((2+3*x)^2*sqrt(3+5*x))+55/4*(1-2*x)^(3/2)/((2+3*x)*sqrt(3+5*x))-1815/4*sqrt(1-2*x)/sqrt(3+5*x)],
[(1-2*x)^(5/2)/((2+3*x)^4*(3+5*x)^(3/2)),x,6,147015/8*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)+1/7*(1-2*x)^(7/2)/((2+3*x)^3*sqrt(3+5*x))+81/28*(1-2*x)^(5/2)/((2+3*x)^2*sqrt(3+5*x))+4455/56*(1-2*x)^(3/2)/((2+3*x)*sqrt(3+5*x))-147015/56*sqrt(1-2*x)/sqrt(3+5*x)],
[(1-2*x)^(5/2)/((2+3*x)^5*(3+5*x)^(3/2)),x,8,46095555/448*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)+7/12*(1-2*x)^(3/2)/((2+3*x)^4*sqrt(3+5*x))-181304825/12096*sqrt(1-2*x)/sqrt(3+5*x)+2051/216*sqrt(1-2*x)/((2+3*x)^3*sqrt(3+5*x))+22957/288*sqrt(1-2*x)/((2+3*x)^2*sqrt(3+5*x))+3997345/4032*sqrt(1-2*x)/((2+3*x)*sqrt(3+5*x))],
[(1-2*x)^(5/2)/((2+3*x)^6*(3+5*x)^(3/2)),x,9,3538809681/6272*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)+7/15*(1-2*x)^(3/2)/((2+3*x)^5*sqrt(3+5*x))-4639661185/56448*sqrt(1-2*x)/sqrt(3+5*x)+2513/360*sqrt(1-2*x)/((2+3*x)^4*sqrt(3+5*x))+12023/240*sqrt(1-2*x)/((2+3*x)^3*sqrt(3+5*x))+587477/1344*sqrt(1-2*x)/((2+3*x)^2*sqrt(3+5*x))+102293609/18816*sqrt(1-2*x)/((2+3*x)*sqrt(3+5*x))],
[(1-2*x)^(5/2)*(2+3*x)^4/(3+5*x)^(5/2),x,8,-2/15*(1-2*x)^(5/2)*(2+3*x)^4/(3+5*x)^(3/2)+88296593/40000000*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-508/75*(1-2*x)^(3/2)*(2+3*x)^4/sqrt(3+5*x)+23991/25000*(1-2*x)^(3/2)*(2+3*x)^2*sqrt(3+5*x)+2514/625*(1-2*x)^(3/2)*(2+3*x)^3*sqrt(3+5*x)+21/4000000*(1-2*x)^(3/2)*(64435+118392*x)*sqrt(3+5*x)+8026963/40000000*sqrt(1-2*x)*sqrt(3+5*x)],
[(1-2*x)^(5/2)*(2+3*x)^3/(3+5*x)^(5/2),x,7,-2/15*(1-2*x)^(5/2)*(2+3*x)^3/(3+5*x)^(3/2)+766843/400000*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-376/75*(1-2*x)^(3/2)*(2+3*x)^3/sqrt(3+5*x)+741/250*(1-2*x)^(3/2)*(2+3*x)^2*sqrt(3+5*x)+21/40000*(1-2*x)^(3/2)*(3185+4392*x)*sqrt(3+5*x)+69713/400000*sqrt(1-2*x)*sqrt(3+5*x)],
[(1-2*x)^(5/2)*(2+3*x)^2/(3+5*x)^(5/2),x,7,-2/825*(1-2*x)^(7/2)/(3+5*x)^(3/2)+3619/5000*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-76/1815*(1-2*x)^(7/2)/sqrt(3+5*x)+329/16500*(1-2*x)^(3/2)*sqrt(3+5*x)+329/45375*(1-2*x)^(5/2)*sqrt(3+5*x)+329/5000*sqrt(1-2*x)*sqrt(3+5*x)],
[(1-2*x)^(5/2)*(2+3*x)/(3+5*x)^(5/2),x,6,-2/165*(1-2*x)^(7/2)/(3+5*x)^(3/2)-1001/250*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-182/825*(1-2*x)^(5/2)/sqrt(3+5*x)-91/825*(1-2*x)^(3/2)*sqrt(3+5*x)-91/250*sqrt(1-2*x)*sqrt(3+5*x)],
[(1-2*x)^(5/2)/(3+5*x)^(5/2),x,5,-2/15*(1-2*x)^(5/2)/(3+5*x)^(3/2)+22/25*arcsin(sqrt(2/11)*sqrt(3+5*x))*sqrt(2/5)+4/15*(1-2*x)^(3/2)/sqrt(3+5*x)+4/25*sqrt(1-2*x)*sqrt(3+5*x)],
[(1-2*x)^(5/2)/((2+3*x)*(3+5*x)^(5/2)),x,7,-22/15*(1-2*x)^(3/2)/(3+5*x)^(3/2)-8/75*arcsin(sqrt(2/11)*sqrt(3+5*x))*sqrt(2/5)-98/3*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))*sqrt(7)+814/25*sqrt(1-2*x)/sqrt(3+5*x)],
[(1-2*x)^(5/2)/((2+3*x)^2*(3+5*x)^(5/2)),x,5,-55/3*(1-2*x)^(3/2)/(3+5*x)^(3/2)+(1-2*x)^(5/2)/((2+3*x)*(3+5*x)^(3/2))-385*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))*sqrt(7)+385*sqrt(1-2*x)/sqrt(3+5*x)],
[(1-2*x)^(5/2)/((2+3*x)^3*(3+5*x)^(5/2)),x,6,-13145/84*(1-2*x)^(3/2)/(3+5*x)^(3/2)+3/14*(1-2*x)^(7/2)/((2+3*x)^2*(3+5*x)^(3/2))+239/28*(1-2*x)^(5/2)/((2+3*x)*(3+5*x)^(3/2))-13145/4*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))*sqrt(7)+13145/4*sqrt(1-2*x)/sqrt(3+5*x)],
[(1-2*x)^(5/2)/((2+3*x)^4*(3+5*x)^(5/2)),x,8,7/9*(1-2*x)^(3/2)/((2+3*x)^3*(3+5*x)^(3/2))-1361195/8*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)-196735/72*sqrt(1-2*x)/(3+5*x)^(3/2)+77/4*sqrt(1-2*x)/((2+3*x)^2*(3+5*x)^(3/2))+7843/24*sqrt(1-2*x)/((2+3*x)*(3+5*x)^(3/2))+1784635/72*sqrt(1-2*x)/sqrt(3+5*x)],
[(1-2*x)^(5/2)/((2+3*x)^5*(3+5*x)^(5/2)),x,9,7/12*(1-2*x)^(3/2)/((2+3*x)^4*(3+5*x)^(3/2))-519421265/448*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)-25024175/1344*sqrt(1-2*x)/(3+5*x)^(3/2)+847/72*sqrt(1-2*x)/((2+3*x)^3*(3+5*x)^(3/2))+36817/288*sqrt(1-2*x)/((2+3*x)^2*(3+5*x)^(3/2))+2992825/1344*sqrt(1-2*x)/((2+3*x)*(3+5*x)^(3/2))+227000875/1344*sqrt(1-2*x)/sqrt(3+5*x)],
[(1-2*x)^(5/2)/((2+3*x)^6*(3+5*x)^(5/2)),x,10,7/15*(1-2*x)^(3/2)/((2+3*x)^5*(3+5*x)^(3/2))-46975917593/6272*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)-754386765/6272*sqrt(1-2*x)/(3+5*x)^(3/2)+1001/120*sqrt(1-2*x)/((2+3*x)^4*(3+5*x)^(3/2))+53009/720*sqrt(1-2*x)/((2+3*x)^3*(3+5*x)^(3/2))+3329689/4032*sqrt(1-2*x)/((2+3*x)^2*(3+5*x)^(3/2))+270667969/18816*sqrt(1-2*x)/((2+3*x)*(3+5*x)^(3/2))+20529722435/18816*sqrt(1-2*x)/sqrt(3+5*x)],

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

# n>0
[(2+3*x)^4*sqrt(3+5*x)/sqrt(1-2*x),x,6,1067352517/2560000*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-987/4000*(2+3*x)^2*(3+5*x)^(3/2)*sqrt(1-2*x)-3/50*(2+3*x)^3*(3+5*x)^(3/2)*sqrt(1-2*x)-21/640000*(3+5*x)^(3/2)*(194923+92040*x)*sqrt(1-2*x)-97032047/2560000*sqrt(1-2*x)*sqrt(3+5*x)],
[(2+3*x)^3*sqrt(3+5*x)/sqrt(1-2*x),x,5,677017/5120*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-3/40*(2+3*x)^2*(3+5*x)^(3/2)*sqrt(1-2*x)-3/1280*(3+5*x)^(3/2)*(865+408*x)*sqrt(1-2*x)-61547/5120*sqrt(1-2*x)*sqrt(3+5*x)],
[(2+3*x)^2*sqrt(3+5*x)/sqrt(1-2*x),x,5,68959/1600*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-181/400*(3+5*x)^(3/2)*sqrt(1-2*x)-1/10*(2+3*x)*(3+5*x)^(3/2)*sqrt(1-2*x)-6269/1600*sqrt(1-2*x)*sqrt(3+5*x)],
[(2+3*x)*sqrt(3+5*x)/sqrt(1-2*x),x,4,1177/80*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-3/20*(3+5*x)^(3/2)*sqrt(1-2*x)-107/80*sqrt(1-2*x)*sqrt(3+5*x)],
[sqrt(3+5*x)/sqrt(1-2*x),x,3,11/2*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-1/2*sqrt(1-2*x)*sqrt(3+5*x)],
[sqrt(3+5*x)/((2+3*x)*sqrt(1-2*x)),x,6,2/3*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)+1/3*arcsin(sqrt(2/11)*sqrt(3+5*x))*sqrt(10)],
[sqrt(3+5*x)/((2+3*x)^2*sqrt(1-2*x)),x,3,-11/7*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)-1/7*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)],
[sqrt(3+5*x)/((2+3*x)^3*sqrt(1-2*x)),x,4,-451/196*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)+3/14*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^2-41/196*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)],
[sqrt(3+5*x)/((2+3*x)^4*sqrt(1-2*x)),x,6,-15235/2744*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)-1/21*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+25/588*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+3895/8232*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)],
[sqrt(3+5*x)/((2+3*x)^5*sqrt(1-2*x)),x,7,-375265/21952*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)-1/28*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^4+1/56*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+305/1568*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+32735/21952*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)],
[(2+3*x)^3*(3+5*x)^(3/2)/sqrt(1-2*x),x,6,333216939/512000*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-917953/128000*(3+5*x)^(3/2)*sqrt(1-2*x)-3/50*(2+3*x)^2*(3+5*x)^(5/2)*sqrt(1-2*x)-3/16000*(3+5*x)^(5/2)*(7889+3900*x)*sqrt(1-2*x)-30292449/512000*sqrt(1-2*x)*sqrt(3+5*x)],
[(2+3*x)^2*(3+5*x)^(3/2)/sqrt(1-2*x),x,6,5274027/25600*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-14529/6400*(3+5*x)^(3/2)*sqrt(1-2*x)-251/800*(3+5*x)^(5/2)*sqrt(1-2*x)-3/40*(2+3*x)*(3+5*x)^(5/2)*sqrt(1-2*x)-479457/25600*sqrt(1-2*x)*sqrt(3+5*x)],
[(2+3*x)*(3+5*x)^(3/2)/sqrt(1-2*x),x,5,21417/320*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-59/80*(3+5*x)^(3/2)*sqrt(1-2*x)-1/10*(3+5*x)^(5/2)*sqrt(1-2*x)-1947/320*sqrt(1-2*x)*sqrt(3+5*x)],
[(3+5*x)^(3/2)/sqrt(1-2*x),x,4,363/16*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-1/4*(3+5*x)^(3/2)*sqrt(1-2*x)-33/16*sqrt(1-2*x)*sqrt(3+5*x)],
[(3+5*x)^(3/2)/((2+3*x)*sqrt(1-2*x)),x,6,29/18*arcsin(sqrt(2/11)*sqrt(3+5*x))*sqrt(5/2)-2/9*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)-5/6*sqrt(1-2*x)*sqrt(3+5*x)],
[(3+5*x)^(3/2)/((2+3*x)^2*sqrt(1-2*x)),x,6,103/63*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)+5/9*arcsin(sqrt(2/11)*sqrt(3+5*x))*sqrt(10)+1/21*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)],
[(3+5*x)^(3/2)/((2+3*x)^3*sqrt(1-2*x)),x,4,-363/196*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)-1/14*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^2-33/196*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)],
[(3+5*x)^(3/2)/((2+3*x)^4*sqrt(1-2*x)),x,5,-5445/2744*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)-15/196*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^2+1/7*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^3-495/2744*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)],
[(3+5*x)^(3/2)/((2+3*x)^5*sqrt(1-2*x)),x,7,-78045/21952*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)+1/84*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^4-43/504*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+85/14112*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+57595/197568*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)],
[(3+5*x)^(3/2)/((2+3*x)^6*sqrt(1-2*x)),x,8,-2664057/307328*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)+1/105*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^5-367/5880*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^4-73/11760*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+6107/65856*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+694229/921984*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)],
[(2+3*x)^3*(3+5*x)^(5/2)/sqrt(1-2*x),x,7,2678359321/819200*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-22135201/614400*(3+5*x)^(3/2)*sqrt(1-2*x)-2012291/384000*(3+5*x)^(5/2)*sqrt(1-2*x)-1/20*(2+3*x)^2*(3+5*x)^(7/2)*sqrt(1-2*x)-1/32000*(3+5*x)^(7/2)*(37439+18960*x)*sqrt(1-2*x)-243487211/819200*sqrt(1-2*x)*sqrt(3+5*x)],
[(2+3*x)^2*(3+5*x)^(5/2)/sqrt(1-2*x),x,7,104040277/102400*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-859837/76800*(3+5*x)^(3/2)*sqrt(1-2*x)-78167/48000*(3+5*x)^(5/2)*sqrt(1-2*x)-963/4000*(3+5*x)^(7/2)*sqrt(1-2*x)-3/50*(2+3*x)*(3+5*x)^(7/2)*sqrt(1-2*x)-9458207/102400*sqrt(1-2*x)*sqrt(3+5*x)],
[(2+3*x)*(3+5*x)^(5/2)/sqrt(1-2*x),x,6,328757/1024*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-2717/768*(3+5*x)^(3/2)*sqrt(1-2*x)-247/480*(3+5*x)^(5/2)*sqrt(1-2*x)-3/40*(3+5*x)^(7/2)*sqrt(1-2*x)-29887/1024*sqrt(1-2*x)*sqrt(3+5*x)],
[(3+5*x)^(5/2)/sqrt(1-2*x),x,5,1331/64*arcsin(sqrt(2/11)*sqrt(3+5*x))*sqrt(5/2)-55/48*(3+5*x)^(3/2)*sqrt(1-2*x)-1/6*(3+5*x)^(5/2)*sqrt(1-2*x)-605/64*sqrt(1-2*x)*sqrt(3+5*x)],
[(3+5*x)^(5/2)/((2+3*x)*sqrt(1-2*x)),x,7,3035/432*arcsin(sqrt(2/11)*sqrt(3+5*x))*sqrt(5/2)+2/27*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)-5/12*(3+5*x)^(3/2)*sqrt(1-2*x)-455/144*sqrt(1-2*x)*sqrt(3+5*x)],
[(3+5*x)^(5/2)/((2+3*x)^2*sqrt(1-2*x)),x,7,125/54*arcsin(sqrt(2/11)*sqrt(3+5*x))*sqrt(5/2)-173/189*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)+1/21*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)-185/126*sqrt(1-2*x)*sqrt(3+5*x)],
[(3+5*x)^(5/2)/((2+3*x)^3*sqrt(1-2*x)),x,7,17687/5292*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)+25/27*arcsin(sqrt(2/11)*sqrt(3+5*x))*sqrt(10)+1/42*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^2+239/1764*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)],
[(3+5*x)^(5/2)/((2+3*x)^4*sqrt(1-2*x)),x,5,-6655/2744*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)-55/588*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^2-1/21*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^3-605/2744*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)],
[(3+5*x)^(5/2)/((2+3*x)^5*sqrt(1-2*x)),x,6,-6655/3136*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)-55/672*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^2-1/24*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^3+3/28*(3+5*x)^(7/2)*sqrt(1-2*x)/(2+3*x)^4-605/3136*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)],
[(3+5*x)^(5/2)/((2+3*x)^6*sqrt(1-2*x)),x,8,-933031/307328*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)+1/105*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^5+437/17640*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^4-14831/105840*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3-12371/592704*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+1948963/8297856*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)],
[(3+5*x)^(5/2)/((2+3*x)^7*sqrt(1-2*x)),x,9,-52573169/8605184*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)+1/126*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^6+503/26460*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^5-149951/1481760*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^4-71369/2963520*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+958171/16595712*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+122343637/232339968*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)],

# n<0
[(2+3*x)^4/(sqrt(1-2*x)*sqrt(3+5*x)),x,5,10866247/128000*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-259/800*(2+3*x)^2*sqrt(1-2*x)*sqrt(3+5*x)-3/40*(2+3*x)^3*sqrt(1-2*x)*sqrt(3+5*x)-7/128000*(187559+77820*x)*sqrt(1-2*x)*sqrt(3+5*x)],
[(2+3*x)^3/(sqrt(1-2*x)*sqrt(3+5*x)),x,4,44437/1600*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-1/10*(2+3*x)^2*sqrt(1-2*x)*sqrt(3+5*x)-1/1600*(5363+2220*x)*sqrt(1-2*x)*sqrt(3+5*x)],
[(2+3*x)^2/(sqrt(1-2*x)*sqrt(3+5*x)),x,4,3827/400*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-333/400*sqrt(1-2*x)*sqrt(3+5*x)-3/20*(2+3*x)*sqrt(1-2*x)*sqrt(3+5*x)],
[(2+3*x)/(sqrt(1-2*x)*sqrt(3+5*x)),x,3,37/10*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-3/10*sqrt(1-2*x)*sqrt(3+5*x)],
[1/(sqrt(1-2*x)*sqrt(3+5*x)),x,2,arcsin(sqrt(2/11)*sqrt(3+5*x))*sqrt(2/5)],
[1/((2+3*x)*sqrt(1-2*x)*sqrt(3+5*x)),x,2,-2*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)],
[1/((2+3*x)^2*sqrt(1-2*x)*sqrt(3+5*x)),x,3,-37/7*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)+3/7*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)],
[1/((2+3*x)^3*sqrt(1-2*x)*sqrt(3+5*x)),x,5,-3827/196*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)+3/14*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+333/196*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)],
[1/((2+3*x)^4*sqrt(1-2*x)*sqrt(3+5*x)),x,6,-222185/2744*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)+1/7*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+185/196*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+19415/2744*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)],
[(2+3*x)^4/((3+5*x)^(3/2)*sqrt(1-2*x)),x,5,143283/8000*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-2/55*(2+3*x)^3*sqrt(1-2*x)/sqrt(3+5*x)-21/550*(2+3*x)^2*sqrt(1-2*x)*sqrt(3+5*x)-21/88000*(8987+3660*x)*sqrt(1-2*x)*sqrt(3+5*x)],
[(2+3*x)^3/((3+5*x)^(3/2)*sqrt(1-2*x)),x,4,2493/400*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-2/55*(2+3*x)^2*sqrt(1-2*x)/sqrt(3+5*x)-3/4400*(979+300*x)*sqrt(1-2*x)*sqrt(3+5*x)],
[(2+3*x)^2/((3+5*x)^(3/2)*sqrt(1-2*x)),x,4,123/50*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-2/275*sqrt(1-2*x)/sqrt(3+5*x)-9/50*sqrt(1-2*x)*sqrt(3+5*x)],
[(2+3*x)/((3+5*x)^(3/2)*sqrt(1-2*x)),x,3,3/5*arcsin(sqrt(2/11)*sqrt(3+5*x))*sqrt(2/5)-2/55*sqrt(1-2*x)/sqrt(3+5*x)],
[1/((3+5*x)^(3/2)*sqrt(1-2*x)),x,1,-2/11*sqrt(1-2*x)/sqrt(3+5*x)],
[1/((2+3*x)*(3+5*x)^(3/2)*sqrt(1-2*x)),x,3,6*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)-10/11*sqrt(1-2*x)/sqrt(3+5*x)],
[1/((2+3*x)^2*(3+5*x)^(3/2)*sqrt(1-2*x)),x,5,321/7*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)-515/77*sqrt(1-2*x)/sqrt(3+5*x)+3/7*sqrt(1-2*x)/((2+3*x)*sqrt(3+5*x))],
[1/((2+3*x)^3*(3+5*x)^(3/2)*sqrt(1-2*x)),x,6,56421/196*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)-90415/2156*sqrt(1-2*x)/sqrt(3+5*x)+3/14*sqrt(1-2*x)/((2+3*x)^2*sqrt(3+5*x))+543/196*sqrt(1-2*x)/((2+3*x)*sqrt(3+5*x))],
[1/((2+3*x)^4*(3+5*x)^(3/2)*sqrt(1-2*x)),x,7,4616025/2744*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)-7396875/30184*sqrt(1-2*x)/sqrt(3+5*x)+1/7*sqrt(1-2*x)/((2+3*x)^3*sqrt(3+5*x))+255/196*sqrt(1-2*x)/((2+3*x)^2*sqrt(3+5*x))+44475/2744*sqrt(1-2*x)/((2+3*x)*sqrt(3+5*x))],
[(2+3*x)^5/((3+5*x)^(5/2)*sqrt(1-2*x)),x,6,462357/40000*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-2/165*(2+3*x)^4*sqrt(1-2*x)/(3+5*x)^(3/2)-734/9075*(2+3*x)^3*sqrt(1-2*x)/sqrt(3+5*x)+511/30250*(2+3*x)^2*sqrt(1-2*x)*sqrt(3+5*x)-7/4840000*(938509+366420*x)*sqrt(1-2*x)*sqrt(3+5*x)],
[(2+3*x)^4/((3+5*x)^(5/2)*sqrt(1-2*x)),x,5,8127/2000*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-2/165*(2+3*x)^3*sqrt(1-2*x)/(3+5*x)^(3/2)-602/9075*(2+3*x)^2*sqrt(1-2*x)/sqrt(3+5*x)-7/242000*(12199+1020*x)*sqrt(1-2*x)*sqrt(3+5*x)],
[(2+3*x)^3/((3+5*x)^(5/2)*sqrt(1-2*x)),x,4,81/50*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-2/165*(2+3*x)^2*sqrt(1-2*x)/(3+5*x)^(3/2)-1/18150*(5831+9405*x)*sqrt(1-2*x)/sqrt(3+5*x)],
[(2+3*x)^2/((3+5*x)^(5/2)*sqrt(1-2*x)),x,4,9/25*arcsin(sqrt(2/11)*sqrt(3+5*x))*sqrt(2/5)-2/825*sqrt(1-2*x)/(3+5*x)^(3/2)-404/9075*sqrt(1-2*x)/sqrt(3+5*x)],
[(2+3*x)/((3+5*x)^(5/2)*sqrt(1-2*x)),x,2,-2/165*sqrt(1-2*x)/(3+5*x)^(3/2)-206/1815*sqrt(1-2*x)/sqrt(3+5*x)],
[1/((3+5*x)^(5/2)*sqrt(1-2*x)),x,2,-2/33*sqrt(1-2*x)/(3+5*x)^(3/2)-8/363*sqrt(1-2*x)/sqrt(3+5*x)],
[1/((2+3*x)*(3+5*x)^(5/2)*sqrt(1-2*x)),x,5,-18*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)-10/33*sqrt(1-2*x)/(3+5*x)^(3/2)+950/363*sqrt(1-2*x)/sqrt(3+5*x)],
[1/((2+3*x)^2*(3+5*x)^(5/2)*sqrt(1-2*x)),x,6,-1593/7*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)-845/231*sqrt(1-2*x)/(3+5*x)^(3/2)+3/7*sqrt(1-2*x)/((2+3*x)*(3+5*x)^(3/2))+84235/2541*sqrt(1-2*x)/sqrt(3+5*x)],
[1/((2+3*x)^3*(3+5*x)^(5/2)*sqrt(1-2*x)),x,7,-392283/196*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)-207895/6468*sqrt(1-2*x)/(3+5*x)^(3/2)+3/14*sqrt(1-2*x)/((2+3*x)^2*(3+5*x)^(3/2))+753/196*sqrt(1-2*x)/((2+3*x)*(3+5*x)^(3/2))+20743985/71148*sqrt(1-2*x)/sqrt(3+5*x)],
[1/((2+3*x)^4*(3+5*x)^(5/2)*sqrt(1-2*x)),x,8,-41307885/2744*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)-21891025/90552*sqrt(1-2*x)/(3+5*x)^(3/2)+1/7*sqrt(1-2*x)/((2+3*x)^3*(3+5*x)^(3/2))+325/196*sqrt(1-2*x)/((2+3*x)^2*(3+5*x)^(3/2))+79335/2744*sqrt(1-2*x)/((2+3*x)*(3+5*x)^(3/2))+2184369575/996072*sqrt(1-2*x)/sqrt(3+5*x)],
[1/((e+f*x)*sqrt(a+b*x)*sqrt(2*b*e-a*f+b*f*x)),x,2,arctan(sqrt(f)*sqrt(a+b*x)*sqrt(2*b*e-a*f+b*f*x)/(b*e-a*f))/((b*e-a*f)*sqrt(f))],

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

# n>0
[(2+3*x)^5*sqrt(3+5*x)/(1-2*x)^(3/2),x,7,-35439958001/5120000*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+(2+3*x)^5*sqrt(3+5*x)/sqrt(1-2*x)+847637/32000*(2+3*x)^2*sqrt(1-2*x)*sqrt(3+5*x)+10389/1600*(2+3*x)^3*sqrt(1-2*x)*sqrt(3+5*x)+33/20*(2+3*x)^4*sqrt(1-2*x)*sqrt(3+5*x)+49/5120000*(87394471+36265980*x)*sqrt(1-2*x)*sqrt(3+5*x)],
[(2+3*x)^4*sqrt(3+5*x)/(1-2*x)^(3/2),x,6,-92108287/51200*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+(2+3*x)^4*sqrt(3+5*x)/sqrt(1-2*x)+2203/320*(2+3*x)^2*sqrt(1-2*x)*sqrt(3+5*x)+27/16*(2+3*x)^3*sqrt(1-2*x)*sqrt(3+5*x)+1/51200*(11129753+4618500*x)*sqrt(1-2*x)*sqrt(3+5*x)],
[(2+3*x)^3*sqrt(3+5*x)/(1-2*x)^(3/2),x,5,-1463447/3200*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+(2+3*x)^3*sqrt(3+5*x)/sqrt(1-2*x)+7/4*(2+3*x)^2*sqrt(1-2*x)*sqrt(3+5*x)+1/3200*(176833+73380*x)*sqrt(1-2*x)*sqrt(3+5*x)],
[(2+3*x)^2*sqrt(3+5*x)/(1-2*x)^(3/2),x,5,-17951/160*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+49/22*(3+5*x)^(3/2)/sqrt(1-2*x)+9/40*(3+5*x)^(3/2)*sqrt(1-2*x)+17951/1760*sqrt(1-2*x)*sqrt(3+5*x)],
[(2+3*x)*sqrt(3+5*x)/(1-2*x)^(3/2),x,4,-103/4*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+7/11*(3+5*x)^(3/2)/sqrt(1-2*x)+103/44*sqrt(1-2*x)*sqrt(3+5*x)],
[sqrt(3+5*x)/(1-2*x)^(3/2),x,3,-arcsin(sqrt(2/11)*sqrt(3+5*x))*sqrt(5/2)+sqrt(3+5*x)/sqrt(1-2*x)],
[sqrt(3+5*x)/((1-2*x)^(3/2)*(2+3*x)),x,3,2/7*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)+2/7*sqrt(3+5*x)/sqrt(1-2*x)],
[sqrt(3+5*x)/((1-2*x)^(3/2)*(2+3*x)^2),x,4,-29/49*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)+4/77*(3+5*x)^(3/2)/((2+3*x)*sqrt(1-2*x))-29/539*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)],
[sqrt(3+5*x)/((1-2*x)^(3/2)*(2+3*x)^3),x,6,-1585/1372*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)+2/7*sqrt(3+5*x)/((2+3*x)^2*sqrt(1-2*x))-15/98*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+15/1372*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)],
[sqrt(3+5*x)/((1-2*x)^(3/2)*(2+3*x)^4),x,7,-7435/2744*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)+2/7*sqrt(3+5*x)/((2+3*x)^3*sqrt(1-2*x))-1/7*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3-5/196*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+565/2744*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)],
[sqrt(3+5*x)/((1-2*x)^(3/2)*(2+3*x)^5),x,8,-1244755/153664*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)+2/7*sqrt(3+5*x)/((2+3*x)^4*sqrt(1-2*x))-27/196*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^4-13/392*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+835/10976*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+107245/153664*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)],
[(2+3*x)^4*(3+5*x)^(3/2)/(1-2*x)^(3/2),x,7,-11199264087/1024000*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+(2+3*x)^4*(3+5*x)^(3/2)/sqrt(1-2*x)+10377/1600*(2+3*x)^2*(3+5*x)^(3/2)*sqrt(1-2*x)+33/20*(2+3*x)^3*(3+5*x)^(3/2)*sqrt(1-2*x)+9/256000*(3+5*x)^(3/2)*(4772357+2253560*x)*sqrt(1-2*x)+1018114917/1024000*sqrt(1-2*x)*sqrt(3+5*x)],
[(2+3*x)^3*(3+5*x)^(3/2)/(1-2*x)^(3/2),x,6,-145708761/51200*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+(2+3*x)^3*(3+5*x)^(3/2)/sqrt(1-2*x)+27/16*(2+3*x)^2*(3+5*x)^(3/2)*sqrt(1-2*x)+9/12800*(3+5*x)^(3/2)*(62091+29320*x)*sqrt(1-2*x)+13246251/51200*sqrt(1-2*x)*sqrt(3+5*x)],
[(2+3*x)^2*(3+5*x)^(3/2)/(1-2*x)^(3/2),x,6,-463881/640*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+49/22*(3+5*x)^(5/2)/sqrt(1-2*x)+14057/1760*(3+5*x)^(3/2)*sqrt(1-2*x)+3/20*(3+5*x)^(5/2)*sqrt(1-2*x)+42171/640*sqrt(1-2*x)*sqrt(3+5*x)],
[(2+3*x)*(3+5*x)^(3/2)/(1-2*x)^(3/2),x,5,-5709/32*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+7/11*(3+5*x)^(5/2)/sqrt(1-2*x)+173/88*(3+5*x)^(3/2)*sqrt(1-2*x)+519/32*sqrt(1-2*x)*sqrt(3+5*x)],
[(3+5*x)^(3/2)/(1-2*x)^(3/2),x,4,-33/4*arcsin(sqrt(2/11)*sqrt(3+5*x))*sqrt(5/2)+(3+5*x)^(3/2)/sqrt(1-2*x)+15/4*sqrt(1-2*x)*sqrt(3+5*x)],
[(3+5*x)^(3/2)/((1-2*x)^(3/2)*(2+3*x)),x,6,-5/3*arcsin(sqrt(2/11)*sqrt(3+5*x))*sqrt(5/2)-2/21*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)+11/7*sqrt(3+5*x)/sqrt(1-2*x)],
[(3+5*x)^(3/2)/((1-2*x)^(3/2)*(2+3*x)^2),x,4,33/49*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)+2/7*(3+5*x)^(3/2)/((2+3*x)*sqrt(1-2*x))+3/49*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)],
[(3+5*x)^(3/2)/((1-2*x)^(3/2)*(2+3*x)^3),x,5,-825/1372*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)+4/77*(3+5*x)^(5/2)/((2+3*x)^2*sqrt(1-2*x))-25/1078*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^2-75/1372*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)],
[(3+5*x)^(3/2)/((1-2*x)^(3/2)*(2+3*x)^4),x,7,-2805/2744*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)+11/7*sqrt(3+5*x)/((2+3*x)^3*sqrt(1-2*x))-2/3*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3-145/588*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2-415/8232*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)],
[(3+5*x)^(3/2)/((1-2*x)^(3/2)*(2+3*x)^5),x,8,-279015/153664*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)+11/7*sqrt(3+5*x)/((2+3*x)^4*sqrt(1-2*x))-131/196*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^4-89/392*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3-745/10976*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+16985/153664*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)],
[(2+3*x)^4*(3+5*x)^(5/2)/(1-2*x)^(3/2),x,8,-107121749031/1638400*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+(2+3*x)^4*(3+5*x)^(5/2)/sqrt(1-2*x)+295101237/409600*(3+5*x)^(3/2)*sqrt(1-2*x)+999/160*(2+3*x)^2*(3+5*x)^(5/2)*sqrt(1-2*x)+13/8*(2+3*x)^3*(3+5*x)^(5/2)*sqrt(1-2*x)+1/51200*(3+5*x)^(5/2)*(7611023+3765060*x)*sqrt(1-2*x)+9738340821/1638400*sqrt(1-2*x)*sqrt(3+5*x)],
[(2+3*x)^3*(3+5*x)^(5/2)/(1-2*x)^(3/2),x,7,-3538809681/204800*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+(2+3*x)^3*(3+5*x)^(5/2)/sqrt(1-2*x)+9748787/51200*(3+5*x)^(3/2)*sqrt(1-2*x)+33/20*(2+3*x)^2*(3+5*x)^(5/2)*sqrt(1-2*x)+9/6400*(3+5*x)^(5/2)*(27937+13820*x)*sqrt(1-2*x)+321709971/204800*sqrt(1-2*x)*sqrt(3+5*x)],
[(2+3*x)^2*(3+5*x)^(5/2)/(1-2*x)^(3/2),x,7,-9219111/2048*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+49/22*(3+5*x)^(7/2)/sqrt(1-2*x)+25397/512*(3+5*x)^(3/2)*sqrt(1-2*x)+25397/3520*(3+5*x)^(5/2)*sqrt(1-2*x)+9/80*(3+5*x)^(7/2)*sqrt(1-2*x)+838101/2048*sqrt(1-2*x)*sqrt(3+5*x)],
[(2+3*x)*(3+5*x)^(5/2)/(1-2*x)^(3/2),x,6,-29403/128*arcsin(sqrt(2/11)*sqrt(3+5*x))*sqrt(5/2)+7/11*(3+5*x)^(7/2)/sqrt(1-2*x)+405/32*(3+5*x)^(3/2)*sqrt(1-2*x)+81/44*(3+5*x)^(5/2)*sqrt(1-2*x)+13365/128*sqrt(1-2*x)*sqrt(3+5*x)],
[(3+5*x)^(5/2)/(1-2*x)^(3/2),x,5,-1815/32*arcsin(sqrt(2/11)*sqrt(3+5*x))*sqrt(5/2)+(3+5*x)^(5/2)/sqrt(1-2*x)+25/8*(3+5*x)^(3/2)*sqrt(1-2*x)+825/32*sqrt(1-2*x)*sqrt(3+5*x)],
[(3+5*x)^(5/2)/((1-2*x)^(3/2)*(2+3*x)),x,7,-475/36*arcsin(sqrt(2/11)*sqrt(3+5*x))*sqrt(5/2)+2/63*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)+11/7*(3+5*x)^(3/2)/sqrt(1-2*x)+505/84*sqrt(1-2*x)*sqrt(3+5*x)],
[(3+5*x)^(5/2)/((1-2*x)^(3/2)*(2+3*x)^2),x,7,-25/9*arcsin(sqrt(2/11)*sqrt(3+5*x))*sqrt(5/2)-169/441*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)+11/7*(3+5*x)^(3/2)/((2+3*x)*sqrt(1-2*x))+32/147*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)],
[(3+5*x)^(5/2)/((1-2*x)^(3/2)*(2+3*x)^3),x,5,1815/1372*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)+2/7*(3+5*x)^(5/2)/((2+3*x)^2*sqrt(1-2*x))+5/98*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^2+165/1372*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)],
[(3+5*x)^(5/2)/((1-2*x)^(3/2)*(2+3*x)^4),x,6,-1815/2744*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)+4/77*(3+5*x)^(7/2)/((2+3*x)^3*sqrt(1-2*x))-5/196*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^2-1/77*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^3-165/2744*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)],
[(3+5*x)^(5/2)/((1-2*x)^(3/2)*(2+3*x)^5),x,8,-168795/153664*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)+11/7*(3+5*x)^(3/2)/((2+3*x)^4*sqrt(1-2*x))+131/588*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^4-3653/3528*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3-38365/98784*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2-167155/1382976*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)],
[(3+5*x)^(5/2)/((1-2*x)^(3/2)*(2+3*x)^6),x,9,-3474273/2151296*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)+11/7*(3+5*x)^(3/2)/((2+3*x)^5*sqrt(1-2*x))+164/735*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^5-42863/41160*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^4-29297/82320*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3-55277/460992*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+426781/6453888*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)],

# n<0
[(2+3*x)^5/((1-2*x)^(3/2)*sqrt(3+5*x)),x,6,-291096141/256000*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+7/11*(2+3*x)^4*sqrt(3+5*x)/sqrt(1-2*x)+76587/17600*(2+3*x)^2*sqrt(1-2*x)*sqrt(3+5*x)+939/880*(2+3*x)^3*sqrt(1-2*x)*sqrt(3+5*x)+21/2816000*(18424549+7645620*x)*sqrt(1-2*x)*sqrt(3+5*x)],
[(2+3*x)^4/((1-2*x)^(3/2)*sqrt(3+5*x)),x,5,-184641/640*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+7/11*(2+3*x)^3*sqrt(3+5*x)/sqrt(1-2*x)+243/220*(2+3*x)^2*sqrt(1-2*x)*sqrt(3+5*x)+9/7040*(27269+11316*x)*sqrt(1-2*x)*sqrt(3+5*x)],
[(2+3*x)^3/((1-2*x)^(3/2)*sqrt(3+5*x)),x,4,-56421/800*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+7/11*(2+3*x)^2*sqrt(3+5*x)/sqrt(1-2*x)+3/8800*(25003+10380*x)*sqrt(1-2*x)*sqrt(3+5*x)],
[(2+3*x)^2/((1-2*x)^(3/2)*sqrt(3+5*x)),x,4,-321/20*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+49/22*sqrt(3+5*x)/sqrt(1-2*x)+9/20*sqrt(1-2*x)*sqrt(3+5*x)],
[(2+3*x)/((1-2*x)^(3/2)*sqrt(3+5*x)),x,3,-3*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+7/11*sqrt(3+5*x)/sqrt(1-2*x)],
[1/((1-2*x)^(3/2)*sqrt(3+5*x)),x,1,2/11*sqrt(3+5*x)/sqrt(1-2*x)],
[1/((1-2*x)^(3/2)*(2+3*x)*sqrt(3+5*x)),x,3,-6/7*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)+4/77*sqrt(3+5*x)/sqrt(1-2*x)],
[1/((1-2*x)^(3/2)*(2+3*x)^2*sqrt(3+5*x)),x,5,-123/49*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)-58/539*sqrt(3+5*x)/sqrt(1-2*x)+3/7*sqrt(3+5*x)/((2+3*x)*sqrt(1-2*x))],
[1/((1-2*x)^(3/2)*(2+3*x)^3*sqrt(3+5*x)),x,6,-12465/1372*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)-3895/7546*sqrt(3+5*x)/sqrt(1-2*x)+3/14*sqrt(3+5*x)/((2+3*x)^2*sqrt(1-2*x))+345/196*sqrt(3+5*x)/((2+3*x)*sqrt(1-2*x))],
[1/((1-2*x)^(3/2)*(2+3*x)^4*sqrt(3+5*x)),x,7,-102345/2744*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)-32735/15092*sqrt(3+5*x)/sqrt(1-2*x)+1/7*sqrt(3+5*x)/((2+3*x)^3*sqrt(1-2*x))+27/28*sqrt(3+5*x)/((2+3*x)^2*sqrt(1-2*x))+2865/392*sqrt(3+5*x)/((2+3*x)*sqrt(1-2*x))],
[1/((1-2*x)^(3/2)*(2+3*x)^5*sqrt(3+5*x)),x,8,-24922335/153664*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)-7986105/845152*sqrt(3+5*x)/sqrt(1-2*x)+3/28*sqrt(3+5*x)/((2+3*x)^4*sqrt(1-2*x))+263/392*sqrt(3+5*x)/((2+3*x)^3*sqrt(1-2*x))+6621/1568*sqrt(3+5*x)/((2+3*x)^2*sqrt(1-2*x))+698295/21952*sqrt(3+5*x)/((2+3*x)*sqrt(1-2*x))],
[(2+3*x)^5/((1-2*x)^(3/2)*(3+5*x)^(3/2)),x,6,-2911419/16000*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+7/11*(2+3*x)^4/(sqrt(1-2*x)*sqrt(3+5*x))-37/605*(2+3*x)^3*sqrt(1-2*x)/sqrt(3+5*x)+8463/12100*(2+3*x)^2*sqrt(1-2*x)*sqrt(3+5*x)+21/1936000*(2027201+841380*x)*sqrt(1-2*x)*sqrt(3+5*x)],
[(2+3*x)^4/((1-2*x)^(3/2)*(3+5*x)^(3/2)),x,5,-35451/800*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+7/11*(2+3*x)^3/(sqrt(1-2*x)*sqrt(3+5*x))-37/605*(2+3*x)^2*sqrt(1-2*x)/sqrt(3+5*x)+3/96800*(173063+72060*x)*sqrt(1-2*x)*sqrt(3+5*x)],
[(2+3*x)^3/((1-2*x)^(3/2)*(3+5*x)^(3/2)),x,4,-999/100*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+7/11*(2+3*x)^2/(sqrt(1-2*x)*sqrt(3+5*x))+1/12100*(30443+50985*x)*sqrt(1-2*x)/sqrt(3+5*x)],
[(2+3*x)^2/((1-2*x)^(3/2)*(3+5*x)^(3/2)),x,4,-9/5*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+49/22/(sqrt(1-2*x)*sqrt(3+5*x))-1229/1210*sqrt(1-2*x)/sqrt(3+5*x)],
[(2+3*x)/((1-2*x)^(3/2)*(3+5*x)^(3/2)),x,2,(-2/55)/(sqrt(1-2*x)*sqrt(3+5*x))+74/605*sqrt(3+5*x)/sqrt(1-2*x)],
[1/((1-2*x)^(3/2)*(3+5*x)^(3/2)),x,2,2/11/(sqrt(1-2*x)*sqrt(3+5*x))-20/121*sqrt(1-2*x)/sqrt(3+5*x)],
[1/((1-2*x)^(3/2)*(2+3*x)*(3+5*x)^(3/2)),x,5,18/7*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)+4/77/(sqrt(1-2*x)*sqrt(3+5*x))-370/847*sqrt(1-2*x)/sqrt(3+5*x)],
[1/((1-2*x)^(3/2)*(2+3*x)^2*(3+5*x)^(3/2)),x,6,999/49*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)+(-58/539)/(sqrt(1-2*x)*sqrt(3+5*x))+3/7/((2+3*x)*sqrt(1-2*x)*sqrt(3+5*x))-17735/5929*sqrt(1-2*x)/sqrt(3+5*x)],
[1/((1-2*x)^(3/2)*(2+3*x)^3*(3+5*x)^(3/2)),x,7,177255/1372*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)+(-6205/7546)/(sqrt(1-2*x)*sqrt(3+5*x))+3/14/((2+3*x)^2*sqrt(1-2*x)*sqrt(3+5*x))+555/196/((2+3*x)*sqrt(1-2*x)*sqrt(3+5*x))-3125575/166012*sqrt(1-2*x)/sqrt(3+5*x)],
[1/((1-2*x)^(3/2)*(2+3*x)^4*(3+5*x)^(3/2)),x,8,2079585/2744*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)+(-73435/15092)/(sqrt(1-2*x)*sqrt(3+5*x))+1/7/((2+3*x)^3*sqrt(1-2*x)*sqrt(3+5*x))+37/28/((2+3*x)^2*sqrt(1-2*x)*sqrt(3+5*x))+6525/392/((2+3*x)*sqrt(1-2*x)*sqrt(3+5*x))-36657025/332024*sqrt(1-2*x)/sqrt(3+5*x)],
[(2+3*x)^5/((1-2*x)^(3/2)*(3+5*x)^(5/2)),x,6,-111321/4000*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+7/11*(2+3*x)^4/((3+5*x)^(3/2)*sqrt(1-2*x))-107/1815*(2+3*x)^3*sqrt(1-2*x)/(3+5*x)^(3/2)-4487/99825*(2+3*x)^2*sqrt(1-2*x)/sqrt(3+5*x)+7/5324000*(2571547+1078860*x)*sqrt(1-2*x)*sqrt(3+5*x)],
[(2+3*x)^4/((1-2*x)^(3/2)*(3+5*x)^(5/2)),x,5,-621/100*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+7/11*(2+3*x)^3/((3+5*x)^(3/2)*sqrt(1-2*x))-107/1815*(2+3*x)^2*sqrt(1-2*x)/(3+5*x)^(3/2)+1/399300*(627641+1051875*x)*sqrt(1-2*x)/sqrt(3+5*x)],
[(2+3*x)^3/((1-2*x)^(3/2)*(3+5*x)^(5/2)),x,4,-27/25*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+7/11*(2+3*x)^2/((3+5*x)^(3/2)*sqrt(1-2*x))-1/99825*(24439+38770*x)*sqrt(1-2*x)/(3+5*x)^(3/2)],
[(2+3*x)^2/((1-2*x)^(3/2)*(3+5*x)^(5/2)),x,3,49/22/((3+5*x)^(3/2)*sqrt(1-2*x))-3679/3630*sqrt(1-2*x)/(3+5*x)^(3/2)-4091/19965*sqrt(1-2*x)/sqrt(3+5*x)],
[(2+3*x)/((1-2*x)^(3/2)*(3+5*x)^(5/2)),x,3,7/11/((3+5*x)^(3/2)*sqrt(1-2*x))-107/363*sqrt(1-2*x)/(3+5*x)^(3/2)-428/3993*sqrt(1-2*x)/sqrt(3+5*x)],
[1/((1-2*x)^(3/2)*(3+5*x)^(5/2)),x,3,2/11/((3+5*x)^(3/2)*sqrt(1-2*x))-40/363*sqrt(1-2*x)/(3+5*x)^(3/2)-160/3993*sqrt(1-2*x)/sqrt(3+5*x)],
[1/((1-2*x)^(3/2)*(2+3*x)*(3+5*x)^(5/2)),x,6,-54/7*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)+4/77/((3+5*x)^(3/2)*sqrt(1-2*x))-410/2541*sqrt(1-2*x)/(3+5*x)^(3/2)+31030/27951*sqrt(1-2*x)/sqrt(3+5*x)],
[1/((1-2*x)^(3/2)*(2+3*x)^2*(3+5*x)^(5/2)),x,7,-4887/49*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)+(-58/539)/((3+5*x)^(3/2)*sqrt(1-2*x))+3/7/((2+3*x)*(3+5*x)^(3/2)*sqrt(1-2*x))-28705/17787*sqrt(1-2*x)/(3+5*x)^(3/2)+2841815/195657*sqrt(1-2*x)/sqrt(3+5*x)],
[1/((1-2*x)^(3/2)*(2+3*x)^3*(3+5*x)^(5/2)),x,8,-1215945/1372*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)+(-8515/7546)/((3+5*x)^(3/2)*sqrt(1-2*x))+3/14/((2+3*x)^2*(3+5*x)^(3/2)*sqrt(1-2*x))+765/196/((2+3*x)*(3+5*x)^(3/2)*sqrt(1-2*x))-7090175/498036*sqrt(1-2*x)/(3+5*x)^(3/2)+707286025/5478396*sqrt(1-2*x)/sqrt(3+5*x)],

# Integrands of the form (a+b x)^m (c+d x)^(n/2) / (e+f x)^(5/2)

# n>0
[(2+3*x)^4*sqrt(3+5*x)/(1-2*x)^(5/2),x,6,13246251/6400*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+1/3*(2+3*x)^4*sqrt(3+5*x)/(1-2*x)^(3/2)-299/66*(2+3*x)^3*sqrt(3+5*x)/sqrt(1-2*x)-697/88*(2+3*x)^2*sqrt(1-2*x)*sqrt(3+5*x)-1/70400*(17606479+7306140*x)*sqrt(1-2*x)*sqrt(3+5*x)],
[(2+3*x)^3*sqrt(3+5*x)/(1-2*x)^(5/2),x,5,126513/320*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+1/3*(2+3*x)^3*sqrt(3+5*x)/(1-2*x)^(3/2)-233/66*(2+3*x)^2*sqrt(3+5*x)/sqrt(1-2*x)-1/3520*(168157+69780*x)*sqrt(1-2*x)*sqrt(3+5*x)],
[(2+3*x)^2*sqrt(3+5*x)/(1-2*x)^(5/2),x,5,49/66*(3+5*x)^(3/2)/(1-2*x)^(3/2)+519/8*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-21/11*(3+5*x)^(3/2)/sqrt(1-2*x)-519/88*sqrt(1-2*x)*sqrt(3+5*x)],
[(2+3*x)*sqrt(3+5*x)/(1-2*x)^(5/2),x,4,7/33*(3+5*x)^(3/2)/(1-2*x)^(3/2)+3/2*arcsin(sqrt(2/11)*sqrt(3+5*x))*sqrt(5/2)-3/2*sqrt(3+5*x)/sqrt(1-2*x)],
[sqrt(3+5*x)/(1-2*x)^(5/2),x,1,2/33*(3+5*x)^(3/2)/(1-2*x)^(3/2)],
[sqrt(3+5*x)/((1-2*x)^(5/2)*(2+3*x)),x,4,4/231*(3+5*x)^(3/2)/(1-2*x)^(3/2)+6/49*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)+6/49*sqrt(3+5*x)/sqrt(1-2*x)],
[sqrt(3+5*x)/((1-2*x)^(5/2)*(2+3*x)^2),x,6,-75/343*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)+2/21*sqrt(3+5*x)/((1-2*x)^(3/2)*(2+3*x))+850/11319*sqrt(3+5*x)/sqrt(1-2*x)-5/49*sqrt(3+5*x)/((2+3*x)*sqrt(1-2*x))],
[sqrt(3+5*x)/((1-2*x)^(5/2)*(2+3*x)^3),x,7,-765/1372*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)+2/21*sqrt(3+5*x)/((1-2*x)^(3/2)*(2+3*x)^2)+415/22638*sqrt(3+5*x)/sqrt(1-2*x)-1/14*sqrt(3+5*x)/((2+3*x)^2*sqrt(1-2*x))+5/196*sqrt(3+5*x)/((2+3*x)*sqrt(1-2*x))],
[sqrt(3+5*x)/((1-2*x)^(5/2)*(2+3*x)^4),x,8,-25365/19208*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)+2/21*sqrt(3+5*x)/((1-2*x)^(3/2)*(2+3*x)^3)-16985/316932*sqrt(3+5*x)/sqrt(1-2*x)-3/49*sqrt(3+5*x)/((2+3*x)^3*sqrt(1-2*x))-1/196*sqrt(3+5*x)/((2+3*x)^2*sqrt(1-2*x))+605/2744*sqrt(3+5*x)/((2+3*x)*sqrt(1-2*x))],
[(2+3*x)^4*(3+5*x)^(3/2)/(1-2*x)^(5/2),x,7,1/3*(2+3*x)^4*(3+5*x)^(3/2)/(1-2*x)^(3/2)+1626211523/102400*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-123/22*(2+3*x)^3*(3+5*x)^(3/2)/sqrt(1-2*x)-3315/352*(2+3*x)^2*(3+5*x)^(3/2)*sqrt(1-2*x)-3/281600*(3+5*x)^(3/2)*(22868329+10798680*x)*sqrt(1-2*x)-1626211523/1126400*sqrt(1-2*x)*sqrt(3+5*x)],
[(2+3*x)^3*(3+5*x)^(3/2)/(1-2*x)^(5/2),x,6,1/3*(2+3*x)^3*(3+5*x)^(3/2)/(1-2*x)^(3/2)+4246733/1280*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-101/22*(2+3*x)^2*(3+5*x)^(3/2)/sqrt(1-2*x)-3/3520*(3+5*x)^(3/2)*(59719+28200*x)*sqrt(1-2*x)-4246733/14080*sqrt(1-2*x)*sqrt(3+5*x)],
[(2+3*x)^2*(3+5*x)^(3/2)/(1-2*x)^(5/2),x,6,49/66*(3+5*x)^(5/2)/(1-2*x)^(3/2)+40787/64*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-938/363*(3+5*x)^(5/2)/sqrt(1-2*x)-40787/5808*(3+5*x)^(3/2)*sqrt(1-2*x)-40787/704*sqrt(1-2*x)*sqrt(3+5*x)],
[(2+3*x)*(3+5*x)^(3/2)/(1-2*x)^(5/2),x,5,7/33*(3+5*x)^(5/2)/(1-2*x)^(3/2)+169/8*arcsin(sqrt(2/11)*sqrt(3+5*x))*sqrt(5/2)-169/66*(3+5*x)^(3/2)/sqrt(1-2*x)-845/88*sqrt(1-2*x)*sqrt(3+5*x)],
[(3+5*x)^(3/2)/(1-2*x)^(5/2),x,4,1/3*(3+5*x)^(3/2)/(1-2*x)^(3/2)+5/2*arcsin(sqrt(2/11)*sqrt(3+5*x))*sqrt(5/2)-5/2*sqrt(3+5*x)/sqrt(1-2*x)],
[(3+5*x)^(3/2)/((1-2*x)^(5/2)*(2+3*x)),x,4,2/21*(3+5*x)^(3/2)/(1-2*x)^(3/2)-2/49*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)-2/49*sqrt(3+5*x)/sqrt(1-2*x)],
[(3+5*x)^(3/2)/((1-2*x)^(5/2)*(2+3*x)^2),x,5,4/231*(3+5*x)^(5/2)/((1-2*x)^(3/2)*(2+3*x))+95/343*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)+190/1617*(3+5*x)^(3/2)/((2+3*x)*sqrt(1-2*x))+95/3773*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)],
[(3+5*x)^(3/2)/((1-2*x)^(5/2)*(2+3*x)^3),x,7,-5/28*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)+11/21*sqrt(3+5*x)/((1-2*x)^(3/2)*(2+3*x)^2)+5/42*sqrt(3+5*x)/sqrt(1-2*x)-3/14*sqrt(3+5*x)/((2+3*x)^2*sqrt(1-2*x))-5/28*sqrt(3+5*x)/((2+3*x)*sqrt(1-2*x))],
[(3+5*x)^(3/2)/((1-2*x)^(5/2)*(2+3*x)^4),x,8,-9395/19208*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)+11/21*sqrt(3+5*x)/((1-2*x)^(3/2)*(2+3*x)^3)+465/9604*sqrt(3+5*x)/sqrt(1-2*x)-32/147*sqrt(3+5*x)/((2+3*x)^3*sqrt(1-2*x))-23/196*sqrt(3+5*x)/((2+3*x)^2*sqrt(1-2*x))-85/2744*sqrt(3+5*x)/((2+3*x)*sqrt(1-2*x))],
[(2+3*x)^4*(3+5*x)^(5/2)/(1-2*x)^(5/2),x,8,1/3*(2+3*x)^4*(3+5*x)^(5/2)/(1-2*x)^(3/2)+46975917593/409600*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-439/66*(2+3*x)^3*(3+5*x)^(5/2)/sqrt(1-2*x)-4270537963/3379200*(3+5*x)^(3/2)*sqrt(1-2*x)-4819/440*(2+3*x)^2*(3+5*x)^(5/2)*sqrt(1-2*x)-1/140800*(3+5*x)^(5/2)*(36714139+18161940*x)*sqrt(1-2*x)-4270537963/409600*sqrt(1-2*x)*sqrt(3+5*x)],
[(2+3*x)^3*(3+5*x)^(5/2)/(1-2*x)^(5/2),x,7,1/3*(2+3*x)^3*(3+5*x)^(5/2)/(1-2*x)^(3/2)+103884253/4096*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-373/66*(2+3*x)^2*(3+5*x)^(5/2)/sqrt(1-2*x)-9444023/33792*(3+5*x)^(3/2)*sqrt(1-2*x)-1/1408*(3+5*x)^(5/2)*(81191+40164*x)*sqrt(1-2*x)-9444023/4096*sqrt(1-2*x)*sqrt(3+5*x)],
[(2+3*x)^2*(3+5*x)^(5/2)/(1-2*x)^(5/2),x,7,49/66*(3+5*x)^(7/2)/(1-2*x)^(3/2)+272239/256*arcsin(sqrt(2/11)*sqrt(3+5*x))*sqrt(5/2)-1183/363*(3+5*x)^(7/2)/sqrt(1-2*x)-123745/2112*(3+5*x)^(3/2)*sqrt(1-2*x)-24749/2904*(3+5*x)^(5/2)*sqrt(1-2*x)-123745/256*sqrt(1-2*x)*sqrt(3+5*x)],
[(2+3*x)*(3+5*x)^(5/2)/(1-2*x)^(5/2),x,6,7/33*(3+5*x)^(7/2)/(1-2*x)^(3/2)+13145/64*arcsin(sqrt(2/11)*sqrt(3+5*x))*sqrt(5/2)-239/66*(3+5*x)^(5/2)/sqrt(1-2*x)-5975/528*(3+5*x)^(3/2)*sqrt(1-2*x)-5975/64*sqrt(1-2*x)*sqrt(3+5*x)],
[(3+5*x)^(5/2)/(1-2*x)^(5/2),x,5,1/3*(3+5*x)^(5/2)/(1-2*x)^(3/2)+275/8*arcsin(sqrt(2/11)*sqrt(3+5*x))*sqrt(5/2)-25/6*(3+5*x)^(3/2)/sqrt(1-2*x)-125/8*sqrt(1-2*x)*sqrt(3+5*x)],
[(3+5*x)^(5/2)/((1-2*x)^(5/2)*(2+3*x)),x,7,11/21*(3+5*x)^(3/2)/(1-2*x)^(3/2)+25/6*arcsin(sqrt(2/11)*sqrt(3+5*x))*sqrt(5/2)+2/147*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)-407/98*sqrt(3+5*x)/sqrt(1-2*x)],
[(3+5*x)^(5/2)/((1-2*x)^(5/2)*(2+3*x)^2),x,5,2/21*(3+5*x)^(5/2)/((1-2*x)^(3/2)*(2+3*x))-55/343*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)-10/147*(3+5*x)^(3/2)/((2+3*x)*sqrt(1-2*x))-5/343*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)],
[(3+5*x)^(5/2)/((1-2*x)^(5/2)*(2+3*x)^3),x,6,4/231*(3+5*x)^(7/2)/((1-2*x)^(3/2)*(2+3*x)^2)+715/1372*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)+26/231*(3+5*x)^(5/2)/((2+3*x)^2*sqrt(1-2*x))+65/3234*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^2+65/1372*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)],
[(3+5*x)^(5/2)/((1-2*x)^(5/2)*(2+3*x)^4),x,8,11/21*(3+5*x)^(3/2)/((1-2*x)^(3/2)*(2+3*x)^3)-2585/19208*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)+15755/86436*sqrt(3+5*x)/sqrt(1-2*x)+32/441*sqrt(3+5*x)/((2+3*x)^3*sqrt(1-2*x))-187/588*sqrt(3+5*x)/((2+3*x)^2*sqrt(1-2*x))-2365/8232*sqrt(3+5*x)/((2+3*x)*sqrt(1-2*x))],
[(3+5*x)^(5/2)/((1-2*x)^(5/2)*(2+3*x)^5),x,9,11/21*(3+5*x)^(3/2)/((1-2*x)^(3/2)*(2+3*x)^4)-547745/1075648*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)+139745/1613472*sqrt(3+5*x)/sqrt(1-2*x)+43/588*sqrt(3+5*x)/((2+3*x)^4*sqrt(1-2*x))-2717/8232*sqrt(3+5*x)/((2+3*x)^3*sqrt(1-2*x))-2013/10976*sqrt(3+5*x)/((2+3*x)^2*sqrt(1-2*x))-14135/153664*sqrt(3+5*x)/((2+3*x)*sqrt(1-2*x))],

# n<0
[(2+3*x)^5/((1-2*x)^(5/2)*sqrt(3+5*x)),x,6,8261577/6400*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+7/33*(2+3*x)^4*sqrt(3+5*x)/(1-2*x)^(3/2)-2051/726*(2+3*x)^3*sqrt(3+5*x)/sqrt(1-2*x)-23909/4840*(2+3*x)^2*sqrt(1-2*x)*sqrt(3+5*x)-1/774400*(120791143+50124540*x)*sqrt(1-2*x)*sqrt(3+5*x)],
[(2+3*x)^4/((1-2*x)^(5/2)*sqrt(3+5*x)),x,5,392283/1600*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+7/33*(2+3*x)^3*sqrt(3+5*x)/(1-2*x)^(3/2)-1589/726*(2+3*x)^2*sqrt(3+5*x)/sqrt(1-2*x)-1/193600*(5735477+2380020*x)*sqrt(1-2*x)*sqrt(3+5*x)],
[(2+3*x)^3/((1-2*x)^(5/2)*sqrt(3+5*x)),x,4,1593/40*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+7/33*(2+3*x)^2*sqrt(3+5*x)/(1-2*x)^(3/2)-1/14520*(95621-33462*x)*sqrt(3+5*x)/sqrt(1-2*x)],
[(2+3*x)^2/((1-2*x)^(5/2)*sqrt(3+5*x)),x,4,9/2*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+49/66*sqrt(3+5*x)/(1-2*x)^(3/2)-448/363*sqrt(3+5*x)/sqrt(1-2*x)],
[(2+3*x)/((1-2*x)^(5/2)*sqrt(3+5*x)),x,2,7/33*sqrt(3+5*x)/(1-2*x)^(3/2)-29/363*sqrt(3+5*x)/sqrt(1-2*x)],
[1/((1-2*x)^(5/2)*sqrt(3+5*x)),x,2,2/33*sqrt(3+5*x)/(1-2*x)^(3/2)+20/363*sqrt(3+5*x)/sqrt(1-2*x)],
[1/((1-2*x)^(5/2)*(2+3*x)*sqrt(3+5*x)),x,5,-18/49*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)+4/231*sqrt(3+5*x)/(1-2*x)^(3/2)+676/17787*sqrt(3+5*x)/sqrt(1-2*x)],
[1/((1-2*x)^(5/2)*(2+3*x)^2*sqrt(3+5*x)),x,6,-405/343*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)-190/1617*sqrt(3+5*x)/(1-2*x)^(3/2)+3/7*sqrt(3+5*x)/((1-2*x)^(3/2)*(2+3*x))-4390/124509*sqrt(3+5*x)/sqrt(1-2*x)],
[1/((1-2*x)^(5/2)*(2+3*x)^3*sqrt(3+5*x)),x,7,-5805/1372*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)-1735/3234*sqrt(3+5*x)/(1-2*x)^(3/2)+3/14*sqrt(3+5*x)/((1-2*x)^(3/2)*(2+3*x)^2)+51/28*sqrt(3+5*x)/((1-2*x)^(3/2)*(2+3*x))-57595/249018*sqrt(3+5*x)/sqrt(1-2*x)],
[1/((1-2*x)^(5/2)*(2+3*x)^4*sqrt(3+5*x)),x,8,-330255/19208*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)-101485/45276*sqrt(3+5*x)/(1-2*x)^(3/2)+1/7*sqrt(3+5*x)/((1-2*x)^(3/2)*(2+3*x)^3)+193/196*sqrt(3+5*x)/((1-2*x)^(3/2)*(2+3*x)^2)+423/56*sqrt(3+5*x)/((1-2*x)^(3/2)*(2+3*x))-3471145/3486252*sqrt(3+5*x)/sqrt(1-2*x)],
[(2+3*x)^5/((1-2*x)^(5/2)*(3+5*x)^(3/2)),x,6,243189/1600*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+7/33*(2+3*x)^4/((1-2*x)^(3/2)*sqrt(3+5*x))-1561/726*(2+3*x)^3/(sqrt(1-2*x)*sqrt(3+5*x))+7723/39930*(2+3*x)^2*sqrt(1-2*x)/sqrt(3+5*x)-1/2129600*(39109961+16227780*x)*sqrt(1-2*x)*sqrt(3+5*x)],
[(2+3*x)^4/((1-2*x)^(5/2)*(3+5*x)^(3/2)),x,5,4887/200*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+7/33*(2+3*x)^3/((1-2*x)^(3/2)*sqrt(3+5*x))-1099/726*(2+3*x)^2/(sqrt(1-2*x)*sqrt(3+5*x))-1/798600*(4898747+8200665*x)*sqrt(1-2*x)/sqrt(3+5*x)],
[(2+3*x)^3/((1-2*x)^(5/2)*(3+5*x)^(3/2)),x,4,27/10*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+7/33*(2+3*x)^2/((1-2*x)^(3/2)*sqrt(3+5*x))+1/39930*(-66967-111311*x)/(sqrt(1-2*x)*sqrt(3+5*x))],
[(2+3*x)^2/((1-2*x)^(5/2)*(3+5*x)^(3/2)),x,3,49/66/((1-2*x)^(3/2)*sqrt(3+5*x))+(-1237/3630)/(sqrt(1-2*x)*sqrt(3+5*x))-793/19965*sqrt(3+5*x)/sqrt(1-2*x)],
[(2+3*x)/((1-2*x)^(5/2)*(3+5*x)^(3/2)),x,3,(-2/55)/((1-2*x)^(3/2)*sqrt(3+5*x))+82/1815*sqrt(3+5*x)/(1-2*x)^(3/2)+164/3993*sqrt(3+5*x)/sqrt(1-2*x)],
[1/((1-2*x)^(5/2)*(3+5*x)^(3/2)),x,3,2/33/((1-2*x)^(3/2)*sqrt(3+5*x))+40/363/(sqrt(1-2*x)*sqrt(3+5*x))-400/3993*sqrt(1-2*x)/sqrt(3+5*x)],
[1/((1-2*x)^(5/2)*(2+3*x)*(3+5*x)^(3/2)),x,6,54/49*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)+4/231/((1-2*x)^(3/2)*sqrt(3+5*x))+956/17787/(sqrt(1-2*x)*sqrt(3+5*x))-42230/195657*sqrt(1-2*x)/sqrt(3+5*x)],
[1/((1-2*x)^(5/2)*(2+3*x)^2*(3+5*x)^(3/2)),x,7,3105/343*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)+(-190/1617)/((1-2*x)^(3/2)*sqrt(3+5*x))+3/7/((1-2*x)^(3/2)*(2+3*x)*sqrt(3+5*x))+(-3830/124509)/(sqrt(1-2*x)*sqrt(3+5*x))-1840225/1369599*sqrt(1-2*x)/sqrt(3+5*x)],
[1/((1-2*x)^(5/2)*(2+3*x)^3*(3+5*x)^(3/2)),x,8,79515/1372*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)+(-2725/3234)/((1-2*x)^(3/2)*sqrt(3+5*x))+3/14/((1-2*x)^(3/2)*(2+3*x)^2*sqrt(3+5*x))+81/28/((1-2*x)^(3/2)*(2+3*x)*sqrt(3+5*x))+(-89945/249018)/(sqrt(1-2*x)*sqrt(3+5*x))-46307675/5478396*sqrt(1-2*x)/sqrt(3+5*x)],
[(2+3*x)^6/((1-2*x)^(5/2)*(3+5*x)^(5/2)),x,7,7/33*(2+3*x)^5/((1-2*x)^(3/2)*(3+5*x)^(3/2))+753543/8000*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-511/242*(2+3*x)^4/((3+5*x)^(3/2)*sqrt(1-2*x))+7591/39930*(2+3*x)^3*sqrt(1-2*x)/(3+5*x)^(3/2)+261331/2196150*(2+3*x)^2*sqrt(1-2*x)/sqrt(3+5*x)-7/117128000*(190406711+78981180*x)*sqrt(1-2*x)*sqrt(3+5*x)],
[(2+3*x)^5/((1-2*x)^(5/2)*(3+5*x)^(5/2)),x,6,7/33*(2+3*x)^4/((1-2*x)^(3/2)*(3+5*x)^(3/2))+2997/200*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-357/242*(2+3*x)^3/((3+5*x)^(3/2)*sqrt(1-2*x))+5281/39930*(2+3*x)^2*sqrt(1-2*x)/(3+5*x)^(3/2)-1/8784600*(33035947+55300905*x)*sqrt(1-2*x)/sqrt(3+5*x)],
[(2+3*x)^4/((1-2*x)^(5/2)*(3+5*x)^(5/2)),x,5,7/33*(2+3*x)^3/((1-2*x)^(3/2)*(3+5*x)^(3/2))+81/50*arcsin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-203/242*(2+3*x)^2/((3+5*x)^(3/2)*sqrt(1-2*x))+1/2196150*(627287+991010*x)*sqrt(1-2*x)/(3+5*x)^(3/2)],
[(2+3*x)^3/((1-2*x)^(5/2)*(3+5*x)^(5/2)),x,4,2/33*(2+3*x)^3/((1-2*x)^(3/2)*(3+5*x)^(3/2))+49/121/((3+5*x)^(3/2)*sqrt(1-2*x))-3679/19965*sqrt(1-2*x)/(3+5*x)^(3/2)-8182/219615*sqrt(1-2*x)/sqrt(3+5*x)],
[(2+3*x)^2/((1-2*x)^(5/2)*(3+5*x)^(5/2)),x,4,49/66/((1-2*x)^(3/2)*(3+5*x)^(3/2))+14/121/((3+5*x)^(3/2)*sqrt(1-2*x))-1649/7986*sqrt(1-2*x)/(3+5*x)^(3/2)-3298/43923*sqrt(1-2*x)/sqrt(3+5*x)],
[(2+3*x)/((1-2*x)^(5/2)*(3+5*x)^(5/2)),x,4,(-2/165)/((1-2*x)^(3/2)*(3+5*x)^(3/2))+74/1815/((1-2*x)^(3/2)*sqrt(3+5*x))+296/3993/(sqrt(1-2*x)*sqrt(3+5*x))-2960/43923*sqrt(1-2*x)/sqrt(3+5*x)],
[1/((1-2*x)^(5/2)*(3+5*x)^(5/2)),x,4,2/33/((1-2*x)^(3/2)*(3+5*x)^(3/2))+20/121/((3+5*x)^(3/2)*sqrt(1-2*x))-400/3993*sqrt(1-2*x)/(3+5*x)^(3/2)-1600/43923*sqrt(1-2*x)/sqrt(3+5*x)],
[1/((1-2*x)^(5/2)*(2+3*x)*(3+5*x)^(5/2)),x,7,4/231/((1-2*x)^(3/2)*(3+5*x)^(3/2))-162/49*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)+412/5929/((3+5*x)^(3/2)*sqrt(1-2*x))-19130/195657*sqrt(1-2*x)/(3+5*x)^(3/2)+1001590/2152227*sqrt(1-2*x)/sqrt(3+5*x)],
[1/((1-2*x)^(5/2)*(2+3*x)^2*(3+5*x)^(5/2)),x,8,(-190/1617)/((1-2*x)^(3/2)*(3+5*x)^(3/2))+3/7/((1-2*x)^(3/2)*(2+3*x)*(3+5*x)^(3/2))-14985/343*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)+(-1090/41503)/((3+5*x)^(3/2)*sqrt(1-2*x))-985525/1369599*sqrt(1-2*x)/(3+5*x)^(3/2)+95783075/15065589*sqrt(1-2*x)/sqrt(3+5*x)],
[1/((1-2*x)^(5/2)*(2+3*x)^3*(3+5*x)^(5/2)),x,9,(-3715/3234)/((1-2*x)^(3/2)*(3+5*x)^(3/2))+3/14/((1-2*x)^(3/2)*(2+3*x)^2*(3+5*x)^(3/2))+111/28/((1-2*x)^(3/2)*(2+3*x)*(3+5*x)^(3/2))-538245/1372*arctan(sqrt(1-2*x)/(sqrt(7)*sqrt(3+5*x)))/sqrt(7)+(-40765/83006)/((3+5*x)^(3/2)*sqrt(1-2*x))-34551425/5478396*sqrt(1-2*x)/(3+5*x)^(3/2)+3443814775/60262356*sqrt(1-2*x)/sqrt(3+5*x)],

# Integrands of the form (a+b x)^(m/2) (c+d x)^(n/2) (e+f x)^(p/2)
[1/(sqrt(a+b*x)*sqrt(c+b*(-1+c)*x/a)*sqrt(e+b*(-1+e)*x/a)),x,1,2*EllipticF(sqrt(1-c)*sqrt(a+b*x)/sqrt(a),sqrt((1-e)/(1-c)))*sqrt(a)/(b*sqrt(1-c))],
[1/(sqrt(a+b*x)*sqrt(c+d*x)*sqrt(e+b*(-1+e)*x/a)),x,2,2*EllipticF(sqrt(1-e)*sqrt(a+b*x)/sqrt(a),sqrt(-a*d/((b*c-a*d)*(1-e))))*sqrt(a)*sqrt(b*(c+d*x)/(b*c-a*d))/(b*sqrt(1-e)*sqrt(c+d*x))],
[1/(sqrt(a+b*x)*sqrt(c+d*x)*sqrt(e+f*x)),x,3,2*EllipticF(sqrt(d)*sqrt(a+b*x)/sqrt(-b*c+a*d),sqrt((b*c-a*d)*f/(d*(b*e-a*f))))*sqrt(-b*c+a*d)*sqrt(b*(c+d*x)/(b*c-a*d))*sqrt(b*(e+f*x)/(b*e-a*f))/(b*sqrt(d)*sqrt(c+d*x)*sqrt(e+f*x))],
[sqrt(e+b*(-1+e)*x/a)/(sqrt(a+b*x)*sqrt(c+b*(-1+c)*x/a)),x,1,2*EllipticE(sqrt(1-c)*sqrt(a+b*x)/sqrt(a),sqrt((1-e)/(1-c)))*sqrt(a)/(b*sqrt(1-c))],
[sqrt(c+d*x)/(sqrt(a+b*x)*sqrt(e+b*(-1+e)*x/a)),x,2,2*EllipticE(sqrt(1-e)*sqrt(a+b*x)/sqrt(a),sqrt(-a*d/((b*c-a*d)*(1-e))))*sqrt(a)*sqrt(c+d*x)/(b*sqrt(1-e)*sqrt(b*(c+d*x)/(b*c-a*d)))],
[sqrt(a+b*x)/(sqrt(c+b*(-1+c)*x/a)*sqrt(e+b*(-1+e)*x/a)),x,2,-2*a*EllipticE(sqrt(1-e)*sqrt(c-b*(1-c)*x/a)/sqrt(c-e),sqrt((c-e)/(1-e)))*sqrt(c-e)*sqrt(a+b*x)*sqrt(-(1-c)*(a*e-b*(1-e)*x)/(a*(c-e)))/(b*(1-c)*sqrt(1-e)*sqrt((1-c)*(a+b*x)/a)*sqrt(e-b*(1-e)*x/a))],
[sqrt(e+f*x)/(sqrt(a+b*x)*sqrt(c+d*x)),x,2,2*EllipticE(sqrt(d)*sqrt(a+b*x)/sqrt(-b*c+a*d),sqrt((b*c-a*d)*f/(d*(b*e-a*f))))*sqrt(-b*c+a*d)*sqrt(b*(c+d*x)/(b*c-a*d))*sqrt(e+f*x)/(b*sqrt(d)*sqrt(c+d*x)*sqrt(b*(e+f*x)/(b*e-a*f)))],

#  Caused infinite recursion for Rubi 4.14.9a 
[1/(sqrt(-c+d*x)*sqrt(c+d*x)*sqrt(e+f*x)),x,3,2*EllipticF(sqrt(c+d*x)/(sqrt(2)*sqrt(c)),sqrt(-2*c*f/(d*e-c*f)))*sqrt(c)*sqrt((c-d*x)/c)*sqrt(d*(e+f*x)/(d*e-c*f))/(d*sqrt(-c+d*x)*sqrt(e+f*x))],

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

# n>0
[(2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x),x,7,-2911577/590625*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-175111/1181250*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-23/1575*(2+3*x)^(3/2)*(3+5*x)^(3/2)*sqrt(1-2*x)+2/45*(2+3*x)^(5/2)*(3+5*x)^(3/2)*sqrt(1-2*x)-1244/13125*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-175111/236250*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x),x,6,-55019/26250*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-823/13125*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+2/35*(2+3*x)^(3/2)*(3+5*x)^(3/2)*sqrt(1-2*x)-27/875*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-823/2625*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x),x,5,-1159/1125*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-31/1125*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+2/25*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-31/225*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x),x,4,-37/45*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+2/45*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+2/9*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2),x,4,4/3*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-2/3*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-2/3*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)],
[sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2),x,5,-74/63*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+4/63*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-2/9*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+74/63*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)],
[sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(7/2),x,6,-4636/2205*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-124/2205*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-2/15*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)+74/315*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+4636/2205*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)],
[sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(9/2),x,7,-220076/36015*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-6584/36015*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-2/21*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(7/2)+74/735*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)+3184/5145*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+220076/36015*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)],
[(2+3*x)^(5/2)*(3+5*x)^(3/2)*sqrt(1-2*x),x,8,-1508889271/7087500*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-11346991/1771875*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-23/2475*(2+3*x)^(3/2)*(3+5*x)^(5/2)*sqrt(1-2*x)+2/55*(2+3*x)^(5/2)*(3+5*x)^(5/2)*sqrt(1-2*x)-342971/866250*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-543/9625*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)-11346991/3898125*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(2+3*x)^(3/2)*(3+5*x)^(3/2)*sqrt(1-2*x),x,7,-5327983/708750*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-160297/708750*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+2/45*(2+3*x)^(3/2)*(3+5*x)^(5/2)*sqrt(1-2*x)-1208/7875*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-3/175*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)-160297/141750*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x),x,6,-148831/47250*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-2252/23625*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-31/525*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)+2/35*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)-2252/4725*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(3+5*x)^(3/2)*sqrt(1-2*x)/sqrt(2+3*x),x,5,-974/675*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-41/675*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+2/15*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-41/135*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(3/2),x,5,-49/27*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+8/27*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-2/3*(3+5*x)^(3/2)*sqrt(1-2*x)/sqrt(2+3*x)+40/27*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(5/2),x,5,494/189*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-214/189*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-2/9*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(3/2)-214/189*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)],
[(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(7/2),x,6,-8314/6615*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+824/6615*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-2/15*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(5/2)-214/945*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+8314/6615*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)],
[(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(9/2),x,7,-475592/324135*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-10628/324135*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-2/21*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(7/2)-214/2205*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)+8578/46305*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+475592/324135*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)],
[(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(11/2),x,8,-22738708/6806835*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-673072/6806835*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-2/27*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(9/2)-214/3969*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(7/2)+8842/138915*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)+332372/972405*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+22738708/6806835*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)],
[(2+3*x)^(5/2)*(3+5*x)^(5/2)*sqrt(1-2*x),x,9,-16416987253/18427500*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-493825477/18427500*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-23/3575*(2+3*x)^(3/2)*(3+5*x)^(7/2)*sqrt(1-2*x)+2/65*(2+3*x)^(5/2)*(3+5*x)^(7/2)*sqrt(1-2*x)-1865989/1126125*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-564731/2252250*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)-2014/53625*(3+5*x)^(7/2)*sqrt(1-2*x)*sqrt(2+3*x)-493825477/40540500*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(2+3*x)^(3/2)*(3+5*x)^(5/2)*sqrt(1-2*x),x,8,-30926081/94500*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-465127/47250*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+2/55*(2+3*x)^(3/2)*(3+5*x)^(7/2)*sqrt(1-2*x)-7031/11550*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-177/1925*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)-3/275*(3+5*x)^(7/2)*sqrt(1-2*x)*sqrt(2+3*x)-465127/103950*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x),x,7,-488149/42525*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-29357/85050*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-223/945*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-31/945*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)+2/45*(3+5*x)^(7/2)*sqrt(1-2*x)*sqrt(2+3*x)-29357/17010*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(3+5*x)^(5/2)*sqrt(1-2*x)/sqrt(2+3*x),x,6,-9013/1890*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-131/945*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-1/7*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)+2/21*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)-131/189*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^(3/2),x,6,-1/5*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-3/5*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(33)-2/3*(3+5*x)^(5/2)*sqrt(1-2*x)/sqrt(2+3*x)+4/3*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^(5/2),x,6,-2209/567*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+494/567*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-2/9*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^(3/2)-118/63*(3+5*x)^(3/2)*sqrt(1-2*x)/sqrt(2+3*x)+2470/567*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^(7/2),x,6,31588/6615*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-12758/6615*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-118/315*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(3/2)-2/15*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^(5/2)-12758/6615*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)],
[(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^(9/2),x,7,-173482/108045*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+23612/108045*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-118/735*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(5/2)-2/21*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^(7/2)-4282/15435*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+173482/108045*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)],
[(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^(11/2),x,8,-27198452/20420505*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-442868/20420505*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-118/1323*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(7/2)-2/27*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^(9/2)-12934/138915*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)+568318/2917215*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+27198452/20420505*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)],
[(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^(13/2),x,9,-1305025844/47647845*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-37904696/47647845*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-118/2079*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(9/2)-2/33*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^(11/2)-13022/305613*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(7/2)+627806/10696455*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)+19417096/74875185*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+1305025844/524126295*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)],

# n<0
[sqrt(e+f*x)/(sqrt(a+b*x)*sqrt(c+d*x)),x,2,2*EllipticE(sqrt(d)*sqrt(a+b*x)/sqrt(-b*c+a*d),sqrt((b*c-a*d)*f/(d*(b*e-a*f))))*sqrt(-b*c+a*d)*sqrt(b*(c+d*x)/(b*c-a*d))*sqrt(e+f*x)/(b*sqrt(d)*sqrt(c+d*x)*sqrt(b*(e+f*x)/(b*e-a*f)))],
[sqrt(e+f*x)/((a+b*x)^(3/2)*sqrt(c+d*x)),x,4,-2*sqrt(c+d*x)*sqrt(e+f*x)/((b*c-a*d)*sqrt(a+b*x))+2*EllipticE(sqrt(f)*sqrt(a+b*x)/sqrt(-b*e+a*f),sqrt(d*(b*e-a*f)/((b*c-a*d)*f)))*sqrt(f)*sqrt(-b*e+a*f)*sqrt(c+d*x)*sqrt(b*(e+f*x)/(b*e-a*f))/(b*(b*c-a*d)*sqrt(b*(c+d*x)/(b*c-a*d))*sqrt(e+f*x))],
[sqrt(1-2*x)/(sqrt(-3-5*x)*sqrt(2+3*x)),x,1,2/3*EllipticE(sqrt(5)*sqrt(2+3*x),sqrt(2/35))*sqrt(7/5)],
[(2+3*x)^(5/2)*sqrt(1-2*x)/sqrt(3+5*x),x,6,-61151/43750*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-314/21875*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(33)-23/875*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+2/35*(2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x)-859/4375*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(2+3*x)^(3/2)*sqrt(1-2*x)/sqrt(3+5*x),x,5,-17/625*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-146/625*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(33)+2/25*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)-9/125*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x),x,4,-31/75*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-4/75*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+2/15*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[sqrt(1-2*x)/(sqrt(2+3*x)*sqrt(3+5*x)),x,2,2/3*EllipticE(sqrt(5)*sqrt(2+3*x),sqrt(2/35))*sqrt(7/5)*sqrt(-3-5*x)/sqrt(3+5*x)],
[sqrt(1-2*x)/((2+3*x)^(3/2)*sqrt(3+5*x)),x,3,-2*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+2*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)],
[sqrt(1-2*x)/((2+3*x)^(5/2)*sqrt(3+5*x)),x,5,-136/21*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-4/21*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+2/3*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+136/21*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)],
[sqrt(1-2*x)/((2+3*x)^(7/2)*sqrt(3+5*x)),x,6,-6388/245*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-64/245*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(33)+2/5*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)+92/35*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+6388/245*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)],
[(2+3*x)^(7/2)*sqrt(1-2*x)/(3+5*x)^(3/2),x,7,-203179/218750*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-38723/109375*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-2/5*(2+3*x)^(7/2)*sqrt(1-2*x)/sqrt(3+5*x)+183/4375*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+48/175*(2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x)-2486/21875*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(2+3*x)^(5/2)*sqrt(1-2*x)/(3+5*x)^(3/2),x,6,-1409/3125*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-1091/3125*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-2/5*(2+3*x)^(5/2)*sqrt(1-2*x)/sqrt(3+5*x)+36/125*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+13/625*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(2+3*x)^(3/2)*sqrt(1-2*x)/(3+5*x)^(3/2),x,5,-19/125*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-106/125*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-2/5*(2+3*x)^(3/2)*sqrt(1-2*x)/sqrt(3+5*x)+8/25*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2),x,4,-62/25*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+4/25*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(33)-2/5*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)],
[sqrt(1-2*x)/((3+5*x)^(3/2)*sqrt(2+3*x)),x,3,2*EllipticE(sqrt(5/11)*sqrt(1-2*x),sqrt(33/35))*sqrt(7/5)-2*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)],
[sqrt(1-2*x)/((2+3*x)^(3/2)*(3+5*x)^(3/2)),x,5,4*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+4*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(33)+2*sqrt(1-2*x)/(sqrt(2+3*x)*sqrt(3+5*x))-20*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)],
[sqrt(1-2*x)/((2+3*x)^(5/2)*(3+5*x)^(3/2)),x,6,556/7*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+184/7*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+2/3*sqrt(1-2*x)/((2+3*x)^(3/2)*sqrt(3+5*x))+92/7*sqrt(1-2*x)/(sqrt(2+3*x)*sqrt(3+5*x))-2780/21*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)],
[sqrt(1-2*x)/((2+3*x)^(7/2)*(3+5*x)^(3/2)),x,7,116464/245*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+38536/245*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+2/5*sqrt(1-2*x)/((2+3*x)^(5/2)*sqrt(3+5*x))+416/105*sqrt(1-2*x)/((2+3*x)^(3/2)*sqrt(3+5*x))+19268/245*sqrt(1-2*x)/(sqrt(2+3*x)*sqrt(3+5*x))-116464/147*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)],
[(2+3*x)^(9/2)*sqrt(1-2*x)/(3+5*x)^(5/2),x,8,-1473539/218750*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-31288/109375*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-2/15*(2+3*x)^(9/2)*sqrt(1-2*x)/(3+5*x)^(3/2)-118/165*(2+3*x)^(7/2)*sqrt(1-2*x)/sqrt(3+5*x)+5153/48125*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+958/1925*(2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x)-12601/240625*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(2+3*x)^(7/2)*sqrt(1-2*x)/(3+5*x)^(5/2),x,7,-523/15625*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-47342/15625*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-2/15*(2+3*x)^(7/2)*sqrt(1-2*x)/(3+5*x)^(3/2)-458/825*(2+3*x)^(5/2)*sqrt(1-2*x)/sqrt(3+5*x)+2818/6875*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+2719/34375*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(2+3*x)^(5/2)*sqrt(1-2*x)/(3+5*x)^(5/2),x,6,-169/625*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-496/625*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-2/15*(2+3*x)^(5/2)*sqrt(1-2*x)/(3+5*x)^(3/2)-326/825*(2+3*x)^(3/2)*sqrt(1-2*x)/sqrt(3+5*x)+458/1375*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(2+3*x)^(3/2)*sqrt(1-2*x)/(3+5*x)^(5/2),x,5,458/125*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-178/125*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-2/15*(2+3*x)^(3/2)*sqrt(1-2*x)/(3+5*x)^(3/2)-194/825*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)],
[sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(5/2),x,5,62/25*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+8/25*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-2/15*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)-62/165*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)],
[sqrt(1-2*x)/((3+5*x)^(5/2)*sqrt(2+3*x)),x,5,-136/5*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-4/5*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-2/3*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)+136/33*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)],
[sqrt(1-2*x)/((2+3*x)^(3/2)*(3+5*x)^(5/2)),x,6,-532*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-16*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+2*sqrt(1-2*x)/((3+5*x)^(3/2)*sqrt(2+3*x))-40/3*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)+2660/33*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)],
[sqrt(1-2*x)/((2+3*x)^(5/2)*(3+5*x)^(5/2)),x,7,-36968/7*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-1112/7*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+2/3*sqrt(1-2*x)/((2+3*x)^(3/2)*(3+5*x)^(3/2))+416/21*sqrt(1-2*x)/((3+5*x)^(3/2)*sqrt(2+3*x))-2780/21*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)+184840/231*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)],
[sqrt(1-2*x)/((2+3*x)^(7/2)*(3+5*x)^(5/2)),x,8,-10312712/245*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-310208/245*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+2/5*sqrt(1-2*x)/((2+3*x)^(5/2)*(3+5*x)^(3/2))+556/105*sqrt(1-2*x)/((2+3*x)^(3/2)*(3+5*x)^(3/2))+116044/735*sqrt(1-2*x)/((3+5*x)^(3/2)*sqrt(2+3*x))-155104/147*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)+10312712/1617*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)],

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

# n>0
[(1-2*x)^(3/2)*(2+3*x)^(5/2)*sqrt(3+5*x),x,8,2/55*(1-2*x)^(3/2)*(2+3*x)^(5/2)*(3+5*x)^(3/2)-604915631/17718750*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-18177329/17718750*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+1103/259875*(2+3*x)^(3/2)*(3+5*x)^(3/2)*sqrt(1-2*x)+178/7425*(2+3*x)^(5/2)*(3+5*x)^(3/2)*sqrt(1-2*x)-124891/2165625*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-18177329/38981250*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(1-2*x)^(3/2)*(2+3*x)^(3/2)*sqrt(3+5*x),x,7,2/45*(1-2*x)^(3/2)*(2+3*x)^(3/2)*(3+5*x)^(3/2)-5684677/3543750*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-84134/1771875*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+62/1575*(2+3*x)^(3/2)*(3+5*x)^(3/2)*sqrt(1-2*x)-347/39375*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-84134/354375*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(1-2*x)^(3/2)*sqrt(2+3*x)*sqrt(3+5*x),x,6,-118898/118125*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-2657/118125*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+2/35*(1-2*x)^(3/2)*(3+5*x)^(3/2)*sqrt(2+3*x)+194/2625*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-2657/23625*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(1-2*x)^(3/2)*sqrt(3+5*x)/sqrt(2+3*x),x,5,-4157/3375*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+412/3375*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+2/15*(1-2*x)^(3/2)*sqrt(2+3*x)*sqrt(3+5*x)+214/675*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^(3/2),x,5,494/135*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-214/135*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-2/3*(1-2*x)^(3/2)*sqrt(3+5*x)/sqrt(2+3*x)-16/27*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^(5/2),x,5,-98/27*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+16/27*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-2/9*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^(3/2)+82/27*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)],
[(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^(7/2),x,6,-3896/945*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-164/945*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-2/15*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^(5/2)+82/135*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+3896/945*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)],
[(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^(9/2),x,7,-595324/46305*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-18016/46305*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-2/21*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^(7/2)+82/315*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)+8516/6615*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+595324/46305*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)],
[(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^(11/2),x,8,-42623864/972405*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-1282376/972405*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-2/27*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^(9/2)+82/567*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(7/2)+13136/19845*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)+613276/138915*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+42623864/972405*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)],
[(1-2*x)^(3/2)*(2+3*x)^(5/2)*(3+5*x)^(3/2),x,9,2/65*(1-2*x)^(3/2)*(2+3*x)^(5/2)*(3+5*x)^(5/2)-51601293223/460687500*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-776112041/230343750*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+601/160875*(2+3*x)^(3/2)*(3+5*x)^(5/2)*sqrt(1-2*x)+178/10725*(2+3*x)^(5/2)*(3+5*x)^(5/2)*sqrt(1-2*x)-11725073/56306250*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-18034/625625*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)-776112041/506756250*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(1-2*x)^(3/2)*(2+3*x)^(3/2)*(3+5*x)^(3/2),x,8,2/55*(1-2*x)^(3/2)*(2+3*x)^(3/2)*(3+5*x)^(5/2)-90397364/1771875*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-5442127/3543750*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+62/2475*(2+3*x)^(3/2)*(3+5*x)^(5/2)*sqrt(1-2*x)-40703/433125*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-23/9625*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)-5442127/7796250*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(1-2*x)^(3/2)*(3+5*x)^(3/2)*sqrt(2+3*x),x,7,-4971289/2126250*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-76163/1063125*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+2/45*(1-2*x)^(3/2)*(3+5*x)^(5/2)*sqrt(2+3*x)-839/23625*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)+194/4725*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)-76163/212625*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(1-2*x)^(3/2)*(3+5*x)^(3/2)/sqrt(2+3*x),x,6,-29933/23625*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-1847/23625*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+2/21*(1-2*x)^(3/2)*(3+5*x)^(3/2)*sqrt(2+3*x)+74/525*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-1847/4725*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^(3/2),x,6,-2209/675*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+494/675*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-2/3*(1-2*x)^(3/2)*(3+5*x)^(3/2)/sqrt(2+3*x)-8/15*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)+494/135*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^(5/2),x,6,-2/9*(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^(3/2)+592/81*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-230/81*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+74/9*(3+5*x)^(3/2)*sqrt(1-2*x)/sqrt(2+3*x)-1150/81*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^(7/2),x,6,-2/15*(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^(5/2)-4418/945*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+988/945*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+74/45*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(3/2)+988/945*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)],
[(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^(9/2),x,7,-2/21*(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^(7/2)-119732/46305*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-7388/46305*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+74/105*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(5/2)-3632/6615*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+119732/46305*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)],
[(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^(11/2),x,8,-2/27*(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^(9/2)-19885156/2917215*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-609304/2917215*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+74/189*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(7/2)-8252/19845*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)+280904/416745*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+19885156/2917215*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)],
[(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^(13/2),x,9,-2/33*(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^(11/2)-1446357824/6806835*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-43537016/6806835*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+74/297*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(9/2)-12872/43659*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(7/2)+442076/1528065*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)+20799916/10696455*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+1446357824/74875185*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)],
[(1-2*x)^(3/2)*(2+3*x)^(5/2)*(3+5*x)^(5/2),x,10,2/75*(1-2*x)^(3/2)*(2+3*x)^(5/2)*(3+5*x)^(7/2)-836091184171/2073093750*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-50299451003/4146187500*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+2503/804375*(2+3*x)^(3/2)*(3+5*x)^(7/2)*sqrt(1-2*x)+178/14625*(2+3*x)^(5/2)*(3+5*x)^(7/2)*sqrt(1-2*x)-380132617/506756250*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-57509209/506756250*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)-199721/12065625*(3+5*x)^(7/2)*sqrt(1-2*x)*sqrt(2+3*x)-50299451003/9121612500*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(1-2*x)^(3/2)*(2+3*x)^(3/2)*(3+5*x)^(5/2),x,9,2/65*(1-2*x)^(3/2)*(2+3*x)^(3/2)*(3+5*x)^(7/2)-9380126059/55282500*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-70536439/13820625*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+62/3575*(2+3*x)^(3/2)*(3+5*x)^(7/2)*sqrt(1-2*x)-2133359/6756750*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-160084/3378375*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)-67/160875*(3+5*x)^(7/2)*sqrt(1-2*x)*sqrt(2+3*x)-70536439/30405375*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(1-2*x)^(3/2)*(3+5*x)^(5/2)*sqrt(2+3*x),x,8,-97540001/1275750*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-2930159/1275750*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+2/55*(1-2*x)^(3/2)*(3+5*x)^(7/2)*sqrt(2+3*x)-22576/155925*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-2377/155925*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)+194/7425*(3+5*x)^(7/2)*sqrt(1-2*x)*sqrt(2+3*x)-2930159/2806650*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(1-2*x)^(3/2)*(3+5*x)^(5/2)/sqrt(2+3*x),x,7,-886499/255150*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-11908/127575*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+2/27*(1-2*x)^(3/2)*(3+5*x)^(5/2)*sqrt(2+3*x)-499/2835*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)+46/567*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)-11908/25515*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(3/2),x,7,-2894/2835*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-1061/2835*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-2/3*(1-2*x)^(3/2)*(3+5*x)^(5/2)/sqrt(2+3*x)+202/63*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-32/63*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)-1061/567*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(5/2),x,7,-2/9*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(3/2)-9587/1215*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+2632/1215*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+362/27*(3+5*x)^(5/2)*sqrt(1-2*x)/sqrt(2+3*x)-614/27*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)+2632/243*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(7/2),x,7,-2/15*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(5/2)+116854/8505*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-43214/8505*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+362/135*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^(3/2)+9808/945*(3+5*x)^(3/2)*sqrt(1-2*x)/sqrt(2+3*x)-43214/1701*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(9/2),x,7,-2/21*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(7/2)-962678/138915*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+249448/138915*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+2108/6615*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(3/2)+362/315*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^(5/2)+249448/138915*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)],
[(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(11/2),x,8,-2/27*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(9/2)-17830424/8751645*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-1717916/8751645*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-1864/6615*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(5/2)+362/567*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^(7/2)-558524/1250235*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+17830424/8751645*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)],
[(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(13/2),x,9,-2/33*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(11/2)-3316711588/61261515*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-103970992/61261515*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-13292/43659*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(7/2)+362/891*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^(9/2)-1366496/4584195*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)+45748292/96268095*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+3316711588/673876665*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)],
[(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(15/2),x,10,-2/39*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(13/2)-245282464136/1858265955*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-7391549624/1858265955*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-20992/81081*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(9/2)+362/1287*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^(11/2)-2174468/11918907*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(7/2)+73596464/417161745*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)+3523482724/2920132215*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+245282464136/20440925505*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)],

# n<0
[(1-2*x)^(3/2)*(2+3*x)^(5/2)/sqrt(3+5*x),x,7,-6515539/5906250*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-104663/2953125*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+2/45*(1-2*x)^(3/2)*(2+3*x)^(5/2)*sqrt(3+5*x)+403/118125*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+178/4725*(2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x)-87476/590625*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(1-2*x)^(3/2)*(2+3*x)^(3/2)/sqrt(3+5*x),x,6,-46159/65625*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-2281/65625*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+2/35*(1-2*x)^(3/2)*(2+3*x)^(3/2)*sqrt(3+5*x)+62/875*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)-487/13125*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(1-2*x)^(3/2)*sqrt(2+3*x)/sqrt(3+5*x),x,5,-2797/5625*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-598/5625*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+2/25*(1-2*x)^(3/2)*sqrt(2+3*x)*sqrt(3+5*x)+194/1125*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(1-2*x)^(3/2)/(sqrt(2+3*x)*sqrt(3+5*x)),x,4,272/225*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-202/225*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-4/45*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(1-2*x)^(3/2)/((2+3*x)^(3/2)*sqrt(3+5*x)),x,4,-74/15*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+4/15*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+14/3*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)],
[(1-2*x)^(3/2)/((2+3*x)^(5/2)*sqrt(3+5*x)),x,5,-124/9*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-4/9*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+14/9*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+124/9*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)],
[(1-2*x)^(3/2)/((2+3*x)^(7/2)*sqrt(3+5*x)),x,6,-17804/315*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-536/315*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+14/15*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)+256/45*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+17804/315*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)],
[(1-2*x)^(3/2)/((2+3*x)^(9/2)*sqrt(3+5*x)),x,7,-1255552/5145*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-37768/5145*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+2/3*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(7/2)+388/105*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)+18068/735*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+1255552/5145*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)],
[(1-2*x)^(3/2)*(2+3*x)^(7/2)/(3+5*x)^(3/2),x,8,-1473539/1968750*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-31288/984375*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-2/5*(1-2*x)^(3/2)*(2+3*x)^(7/2)/sqrt(3+5*x)+5153/39375*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+958/1575*(2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x)-8/45*(2+3*x)^(7/2)*sqrt(1-2*x)*sqrt(3+5*x)-12601/196875*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(1-2*x)^(3/2)*(2+3*x)^(5/2)/(3+5*x)^(3/2),x,7,-47342/109375*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-5753/109375*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-2/5*(1-2*x)^(3/2)*(2+3*x)^(5/2)/sqrt(3+5*x)+2818/4375*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)-32/175*(2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x)+2719/21875*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(1-2*x)^(3/2)*(2+3*x)^(3/2)/(3+5*x)^(3/2),x,6,-169/3125*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-496/3125*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-2/5*(1-2*x)^(3/2)*(2+3*x)^(3/2)/sqrt(3+5*x)-24/125*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+458/625*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(1-2*x)^(3/2)*sqrt(2+3*x)/(3+5*x)^(3/2),x,5,458/375*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-178/375*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-2/5*(1-2*x)^(3/2)*sqrt(2+3*x)/sqrt(3+5*x)-16/75*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(1-2*x)^(3/2)/((3+5*x)^(3/2)*sqrt(2+3*x)),x,4,62/25*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+8/25*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-22/5*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)],
[(1-2*x)^(3/2)/((2+3*x)^(3/2)*(3+5*x)^(3/2)),x,5,136/5*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+4/5*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+14/3*sqrt(1-2*x)/(sqrt(2+3*x)*sqrt(3+5*x))-136/3*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)],
[(1-2*x)^(3/2)/((2+3*x)^(5/2)*(3+5*x)^(3/2)),x,6,532/3*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+16/3*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+14/9*sqrt(1-2*x)/((2+3*x)^(3/2)*sqrt(3+5*x))+88/3*sqrt(1-2*x)/(sqrt(2+3*x)*sqrt(3+5*x))-2660/9*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)],
[(1-2*x)^(3/2)/((2+3*x)^(7/2)*(3+5*x)^(3/2)),x,7,36968/35*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+1112/35*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+14/15*sqrt(1-2*x)/((2+3*x)^(5/2)*sqrt(3+5*x))+44/5*sqrt(1-2*x)/((2+3*x)^(3/2)*sqrt(3+5*x))+6116/35*sqrt(1-2*x)/(sqrt(2+3*x)*sqrt(3+5*x))-36968/21*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)],
[(1-2*x)^(3/2)/((2+3*x)^(9/2)*(3+5*x)^(3/2)),x,8,10312712/1715*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+310208/1715*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+2/3*sqrt(1-2*x)/((2+3*x)^(7/2)*sqrt(3+5*x))+176/35*sqrt(1-2*x)/((2+3*x)^(5/2)*sqrt(3+5*x))+12276/245*sqrt(1-2*x)/((2+3*x)^(3/2)*sqrt(3+5*x))+1706144/1715*sqrt(1-2*x)/(sqrt(2+3*x)*sqrt(3+5*x))-10312712/1029*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)],
[(1-2*x)^(3/2)*(2+3*x)^(7/2)/(3+5*x)^(5/2),x,8,-2/15*(1-2*x)^(3/2)*(2+3*x)^(7/2)/(3+5*x)^(3/2)-24369/109375*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(3/11)-25643/109375*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-6*(2+3*x)^(7/2)*sqrt(1-2*x)/sqrt(3+5*x)+3872/4375*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+622/175*(2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x)+4801/21875*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(1-2*x)^(3/2)*(2+3*x)^(5/2)/(3+5*x)^(5/2),x,7,-2/15*(1-2*x)^(3/2)*(2+3*x)^(5/2)/(3+5*x)^(3/2)-8366/15625*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(3/11)+1973/15625*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-106/25*(2+3*x)^(5/2)*sqrt(1-2*x)/sqrt(3+5*x)+1558/625*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+2264/3125*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(1-2*x)^(3/2)*(2+3*x)^(3/2)/(3+5*x)^(5/2),x,6,-2/15*(1-2*x)^(3/2)*(2+3*x)^(3/2)/(3+5*x)^(3/2)-582/625*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(3/11)+496/625*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-62/25*(2+3*x)^(3/2)*sqrt(1-2*x)/sqrt(3+5*x)+178/125*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(1-2*x)^(3/2)*sqrt(2+3*x)/(3+5*x)^(5/2),x,5,38/125*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+212/125*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-2/15*(1-2*x)^(3/2)*sqrt(2+3*x)/(3+5*x)^(3/2)-18/25*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)],
[(1-2*x)^(3/2)/((3+5*x)^(5/2)*sqrt(2+3*x)),x,5,-148/25*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-52/25*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-22/15*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)+148/15*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)],
[(1-2*x)^(3/2)/((2+3*x)^(3/2)*(3+5*x)^(5/2)),x,6,-556/5*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-184/5*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+14/3*sqrt(1-2*x)/((3+5*x)^(3/2)*sqrt(2+3*x))-92/3*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)+556/3*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)],
[(1-2*x)^(3/2)/((2+3*x)^(5/2)*(3+5*x)^(5/2)),x,7,-120*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(3/11)-1088*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+14/9*sqrt(1-2*x)/((2+3*x)^(3/2)*(3+5*x)^(3/2))+404/9*sqrt(1-2*x)/((3+5*x)^(3/2)*sqrt(2+3*x))-300*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)+5440/3*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)],
[(1-2*x)^(3/2)/((2+3*x)^(7/2)*(3+5*x)^(5/2)),x,8,-33232/35*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(3/11)-301304/35*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+14/15*sqrt(1-2*x)/((2+3*x)^(5/2)*(3+5*x)^(3/2))+536/45*sqrt(1-2*x)/((2+3*x)^(3/2)*(3+5*x)^(3/2))+111884/315*sqrt(1-2*x)/((3+5*x)^(3/2)*sqrt(2+3*x))-16616/7*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)+301304/21*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)],

# Integrands of the form (a+b x)^(m/2) (c+d x)^(n/2) (e+f x)^(5/2)

# n>0
[(1-2*x)^(5/2)*(2+3*x)^(5/2)*sqrt(3+5*x),x,9,62/2145*(1-2*x)^(3/2)*(2+3*x)^(5/2)*(3+5*x)^(3/2)+2/65*(1-2*x)^(5/2)*(2+3*x)^(5/2)*(3+5*x)^(3/2)-1163388067/38390625*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-69808931/76781250*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+32717/1126125*(2+3*x)^(3/2)*(3+5*x)^(3/2)*sqrt(1-2*x)+34/2475*(2+3*x)^(5/2)*(3+5*x)^(3/2)*sqrt(1-2*x)-445024/9384375*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-69808931/168918750*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(1-2*x)^(5/2)*(2+3*x)^(3/2)*sqrt(3+5*x),x,8,106/2475*(1-2*x)^(3/2)*(2+3*x)^(3/2)*(3+5*x)^(3/2)+2/55*(1-2*x)^(5/2)*(2+3*x)^(3/2)*(3+5*x)^(3/2)-326256461/17718750*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-4738087/8859375*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+2866/86625*(2+3*x)^(3/2)*(3+5*x)^(3/2)*sqrt(1-2*x)+38729/2165625*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-4738087/19490625*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(1-2*x)^(5/2)*sqrt(2+3*x)*sqrt(3+5*x),x,7,-6799613/5315625*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-110717/5315625*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+326/4725*(1-2*x)^(3/2)*(3+5*x)^(3/2)*sqrt(2+3*x)+2/45*(1-2*x)^(5/2)*(3+5*x)^(3/2)*sqrt(2+3*x)+10214/118125*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-110717/1063125*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(1-2*x)^(5/2)*sqrt(3+5*x)/sqrt(2+3*x),x,6,-86741/39375*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+11806/39375*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+118/525*(1-2*x)^(3/2)*sqrt(2+3*x)*sqrt(3+5*x)+2/21*(1-2*x)^(5/2)*sqrt(2+3*x)*sqrt(3+5*x)+4282/7875*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^(3/2),x,6,31588/3375*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-12758/3375*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-2/3*(1-2*x)^(5/2)*sqrt(3+5*x)/sqrt(2+3*x)-8/15*(1-2*x)^(3/2)*sqrt(2+3*x)*sqrt(3+5*x)-1076/675*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^(5/2),x,6,-4418/405*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+988/405*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-2/9*(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^(3/2)+10/3*(1-2*x)^(3/2)*sqrt(3+5*x)/sqrt(2+3*x)+196/81*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^(7/2),x,6,-4/5*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-12/5*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(33)-2/15*(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^(5/2)+2/3*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^(3/2)+8*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)],
[(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^(9/2),x,7,-36052/1323*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-1048/1323*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-2/21*(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^(7/2)+2/7*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^(5/2)+524/189*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+36052/1323*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)],
[(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^(11/2),x,8,-7810384/83349*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-234856/83349*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-2/27*(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^(9/2)+10/63*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^(7/2)+832/567*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)+112436/11907*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+7810384/83349*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)],
[(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^(13/2),x,9,-247408648/64827*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-7442032/64827*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-2/33*(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^(11/2)+10/99*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^(9/2)+1900/2079*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(7/2)+76492/14553*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)+3560432/101871*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+247408648/713097*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)],
[(1-2*x)^(5/2)*(2+3*x)^(5/2)*(3+5*x)^(3/2),x,10,62/2925*(1-2*x)^(3/2)*(2+3*x)^(5/2)*(3+5*x)^(5/2)+2/75*(1-2*x)^(5/2)*(2+3*x)^(5/2)*(3+5*x)^(5/2)-1764163292393/20730937500*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-13267820528/5182734375*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+142391/7239375*(2+3*x)^(3/2)*(3+5*x)^(5/2)*sqrt(1-2*x)+3698/482625*(2+3*x)^(5/2)*(3+5*x)^(5/2)*sqrt(1-2*x)-400516993/2533781250*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-569519/28153125*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)-13267820528/11402015625*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(1-2*x)^(5/2)*(2+3*x)^(3/2)*(3+5*x)^(3/2),x,9,106/3575*(1-2*x)^(3/2)*(2+3*x)^(3/2)*(3+5*x)^(5/2)+2/65*(1-2*x)^(5/2)*(2+3*x)^(3/2)*(3+5*x)^(5/2)-30660308017/691031250*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-923943703/691031250*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+8318/482625*(2+3*x)^(3/2)*(3+5*x)^(5/2)*sqrt(1-2*x)-6794792/84459375*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)+25603/1876875*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)-923943703/1520268750*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(1-2*x)^(5/2)*(3+5*x)^(3/2)*sqrt(2+3*x),x,8,-829177897/31893750*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-12996374/15946875*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+326/7425*(1-2*x)^(3/2)*(3+5*x)^(5/2)*sqrt(2+3*x)+2/55*(1-2*x)^(5/2)*(3+5*x)^(5/2)*sqrt(2+3*x)-78797/3898125*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)+30362/779625*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)-12996374/35083125*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(1-2*x)^(5/2)*(3+5*x)^(3/2)/sqrt(2+3*x),x,7,-4457606/3189375*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-429479/3189375*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+362/2835*(1-2*x)^(3/2)*(3+5*x)^(3/2)*sqrt(2+3*x)+2/27*(1-2*x)^(5/2)*(3+5*x)^(3/2)*sqrt(2+3*x)+14318/70875*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-429479/637875*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^(3/2),x,7,-481339/70875*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+124724/70875*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-2/3*(1-2*x)^(5/2)*(3+5*x)^(3/2)/sqrt(2+3*x)-32/63*(1-2*x)^(3/2)*(3+5*x)^(3/2)*sqrt(2+3*x)-2108/1575*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)+124724/14175*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^(5/2),x,7,-2/9*(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^(3/2)+116854/6075*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-43214/6075*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+230/27*(1-2*x)^(3/2)*(3+5*x)^(3/2)/sqrt(2+3*x)+788/135*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-43214/1215*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^(7/2),x,7,-2/15*(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^(5/2)+46/27*(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^(3/2)-19174/1215*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+5264/1215*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-316/27*(3+5*x)^(3/2)*sqrt(1-2*x)/sqrt(2+3*x)+5264/243*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^(9/2),x,7,-2/21*(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^(7/2)+46/63*(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^(5/2)-11576/3969*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-4244/3969*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+608/189*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(3/2)-4244/3969*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)],
[(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^(11/2),x,8,-2/27*(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^(9/2)+230/567*(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^(7/2)-3545996/250047*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-95264/250047*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+1532/567*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(5/2)-104036/35721*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+3545996/250047*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)],
[(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^(13/2),x,9,-2/33*(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^(11/2)+230/891*(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^(9/2)-780320008/1750329*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-23441272/1750329*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+12280/6237*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(7/2)-325796/130977*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)+11243972/2750517*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+780320008/19253619*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)],
[(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^(15/2),x,10,-2/39*(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^(13/2)+230/1287*(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^(11/2)-75041008472/53093313*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-2257166048/53093313*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+1300/891*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(9/2)-3347620/1702701*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(7/2)+23210828/11918907*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)+1079936248/83432349*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+75041008472/584026443*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)],
[(1-2*x)^(5/2)*(2+3*x)^(3/2)*(3+5*x)^(5/2),x,10,106/4875*(1-2*x)^(3/2)*(2+3*x)^(3/2)*(3+5*x)^(7/2)+2/75*(1-2*x)^(5/2)*(2+3*x)^(3/2)*(3+5*x)^(7/2)-1580201444291/12438562500*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-23763809947/6219281250*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+8038/804375*(2+3*x)^(3/2)*(3+5*x)^(7/2)*sqrt(1-2*x)-359748241/1520268750*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-26534891/760134375*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)+364267/36196875*(3+5*x)^(7/2)*sqrt(1-2*x)*sqrt(2+3*x)-23763809947/13682418750*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(1-2*x)^(5/2)*(3+5*x)^(5/2)*sqrt(2+3*x),x,9,-8120161139/124385625*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-486785077/248771250*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+326/10725*(1-2*x)^(3/2)*(3+5*x)^(7/2)*sqrt(2+3*x)+2/65*(1-2*x)^(5/2)*(3+5*x)^(7/2)*sqrt(2+3*x)-3872003/30405375*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-121031/30405375*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)+2314/111375*(3+5*x)^(7/2)*sqrt(1-2*x)*sqrt(2+3*x)-486785077/547296750*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(1-2*x)^(5/2)*(3+5*x)^(5/2)/sqrt(2+3*x),x,8,-146222113/3827250*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-1654421/1913625*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+74/891*(1-2*x)^(3/2)*(3+5*x)^(5/2)*sqrt(2+3*x)+2/33*(1-2*x)^(5/2)*(3+5*x)^(5/2)*sqrt(2+3*x)-146963/467775*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)+9698/93555*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)-1654421/4209975*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^(3/2),x,8,-25111/382725*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-310399/382725*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-2/3*(1-2*x)^(5/2)*(3+5*x)^(5/2)/sqrt(2+3*x)-40/81*(1-2*x)^(3/2)*(3+5*x)^(5/2)*sqrt(2+3*x)+64628/8505*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-2108/1701*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)-310399/76545*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^(5/2),x,8,-2/9*(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^(3/2)-452399/25515*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+135334/25515*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+370/27*(1-2*x)^(3/2)*(3+5*x)^(5/2)/sqrt(2+3*x)-31298/567*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)+5260/567*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)+135334/5103*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^(7/2),x,8,-2/15*(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^(5/2)+74/27*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(3/2)+136028/3645*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-48478/3645*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-6464/81*(3+5*x)^(5/2)*sqrt(1-2*x)/sqrt(2+3*x)+11036/81*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-48478/729*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^(9/2),x,8,-2/21*(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^(7/2)+74/63*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(5/2)-904798/35721*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+270668/35721*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-1844/567*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^(3/2)-62596/3969*(3+5*x)^(3/2)*sqrt(1-2*x)/sqrt(2+3*x)+1353340/35721*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^(11/2),x,8,-2/27*(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^(9/2)+370/567*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(7/2)-100444/750141*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-1241596/750141*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-13316/35721*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(3/2)+2776/1701*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^(5/2)-1241596/750141*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)],
[(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^(13/2),x,9,-2/33*(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^(11/2)+370/891*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(9/2)-584888452/5250987*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-13235368/5250987*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-55772/43659*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(5/2)+36980/18711*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^(7/2)-17089252/8251551*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+584888452/57760857*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)],
[(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^(15/2),x,10,-2/39*(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^(13/2)+370/1287*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(11/2)-129922578224/477839817*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-3894280616/477839817*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-2622980/1702701*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(7/2)+60080/34749*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^(9/2)-54281308/35756721*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)+1876198516/750891141*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+129922578224/5256237987*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)],
[(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^(17/2),x,11,-2/45*(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^(15/2)+74/351*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(13/2)-12641611554328/16724393595*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-380220959152/16724393595*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-1085156/729729*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(9/2)+16636/11583*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^(11/2)-112817764/107270163*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(7/2)+3914701972/3754455705*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)+181941877952/26281189935*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+12641611554328/183968329545*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)],

# n<0
[(1-2*x)^(5/2)*(2+3*x)^(5/2)/sqrt(3+5*x),x,8,-231061879/17718750*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-3963068/8859375*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+62/1485*(1-2*x)^(3/2)*(2+3*x)^(5/2)*sqrt(3+5*x)+2/55*(1-2*x)^(5/2)*(2+3*x)^(5/2)*sqrt(3+5*x)+181333/3898125*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+4258/155925*(2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x)-2865161/19490625*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(1-2*x)^(5/2)*(2+3*x)^(3/2)/sqrt(3+5*x),x,7,-8024546/8859375*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-509189/8859375*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+106/1575*(1-2*x)^(3/2)*(2+3*x)^(3/2)*sqrt(3+5*x)+2/45*(1-2*x)^(5/2)*(2+3*x)^(3/2)*sqrt(3+5*x)+8878/118125*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+21547/1771875*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(1-2*x)^(5/2)*sqrt(2+3*x)/sqrt(3+5*x),x,6,-408311/590625*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-132824/590625*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+326/2625*(1-2*x)^(3/2)*sqrt(2+3*x)*sqrt(3+5*x)+2/35*(1-2*x)^(5/2)*sqrt(2+3*x)*sqrt(3+5*x)+30922/118125*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(1-2*x)^(5/2)/(sqrt(2+3*x)*sqrt(3+5*x)),x,5,53194/16875*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-34154/16875*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-4/75*(1-2*x)^(3/2)*sqrt(2+3*x)*sqrt(3+5*x)-1088/3375*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(1-2*x)^(5/2)/((2+3*x)^(3/2)*sqrt(3+5*x)),x,5,-8314/675*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+824/675*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+14/3*(1-2*x)^(3/2)*sqrt(3+5*x)/sqrt(2+3*x)+428/135*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(1-2*x)^(5/2)/((2+3*x)^(5/2)*sqrt(3+5*x)),x,5,-3896/135*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-164/135*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+14/9*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^(3/2)+812/27*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)],
[(1-2*x)^(5/2)/((2+3*x)^(7/2)*sqrt(3+5*x)),x,6,-16564/135*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-496/135*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+14/15*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^(5/2)+1736/135*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+16564/135*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)],
[(1-2*x)^(5/2)/((2+3*x)^(9/2)*sqrt(3+5*x)),x,7,-703480/1323*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-21160/1323*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+2/3*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^(7/2)+76/9*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)+10124/189*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+703480/1323*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)],
[(1-2*x)^(5/2)/((2+3*x)^(11/2)*sqrt(3+5*x)),x,8,-66055016/27783*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-1986944/27783*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+14/27*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^(9/2)+512/81*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(7/2)+20420/567*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)+950584/3969*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+66055016/27783*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)],
[(1-2*x)^(5/2)/((2+3*x)^(13/2)*sqrt(3+5*x)),x,9,-23204503328/194481*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-697995152/194481*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+14/33*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^(11/2)+4508/891*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(9/2)+171004/6237*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(7/2)+7173272/43659*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)+333930952/305613*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+23204503328/2139291*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)],
[(1-2*x)^(5/2)*(2+3*x)^(7/2)/(3+5*x)^(3/2),x,9,-264260033/29531250*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-7261561/14765625*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-2/5*(1-2*x)^(5/2)*(2+3*x)^(7/2)/sqrt(3+5*x)-48/275*(1-2*x)^(3/2)*(2+3*x)^(7/2)*sqrt(3+5*x)+2020841/6496875*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+346636/259875*(2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x)-2972/7425*(2+3*x)^(7/2)*sqrt(1-2*x)*sqrt(3+5*x)-703672/32484375*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(1-2*x)^(5/2)*(2+3*x)^(5/2)/(3+5*x)^(3/2),x,8,-1509007/2953125*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-299863/2953125*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-2/5*(1-2*x)^(5/2)*(2+3*x)^(5/2)/sqrt(3+5*x)-8/45*(1-2*x)^(3/2)*(2+3*x)^(5/2)*sqrt(3+5*x)+167228/118125*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)-1972/4725*(2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x)+196499/590625*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(1-2*x)^(5/2)*(2+3*x)^(3/2)/(3+5*x)^(3/2),x,7,53279/328125*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-110014/328125*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-2/5*(1-2*x)^(5/2)*(2+3*x)^(3/2)/sqrt(3+5*x)-32/175*(1-2*x)^(3/2)*(2+3*x)^(3/2)*sqrt(3+5*x)-1972/4375*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+106772/65625*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(1-2*x)^(5/2)*sqrt(2+3*x)/(3+5*x)^(3/2),x,6,81164/28125*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-28174/28125*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-2/5*(1-2*x)^(5/2)*sqrt(2+3*x)/sqrt(3+5*x)-24/125*(1-2*x)^(3/2)*sqrt(2+3*x)*sqrt(3+5*x)-3028/5625*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(1-2*x)^(5/2)/((3+5*x)^(3/2)*sqrt(2+3*x)),x,5,5594/1125*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+1196/1125*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-22/5*(1-2*x)^(3/2)*sqrt(2+3*x)/sqrt(3+5*x)-388/225*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(1-2*x)^(5/2)/((2+3*x)^(3/2)*(3+5*x)^(3/2)),x,5,4636/75*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+124/75*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+14/3*(1-2*x)^(3/2)/(sqrt(2+3*x)*sqrt(3+5*x))-1496/15*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)],
[(1-2*x)^(5/2)/((2+3*x)^(5/2)*(3+5*x)^(3/2)),x,6,17804/45*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+536/45*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+14/9*(1-2*x)^(3/2)/((2+3*x)^(3/2)*sqrt(3+5*x))+1792/27*sqrt(1-2*x)/(sqrt(2+3*x)*sqrt(3+5*x))-17804/27*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)],
[(1-2*x)^(5/2)/((2+3*x)^(7/2)*(3+5*x)^(3/2)),x,7,105584/45*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+3176/45*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+14/15*(1-2*x)^(3/2)/((2+3*x)^(5/2)*sqrt(3+5*x))+2716/135*sqrt(1-2*x)/((2+3*x)^(3/2)*sqrt(3+5*x))+17468/45*sqrt(1-2*x)/(sqrt(2+3*x)*sqrt(3+5*x))-105584/27*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)],
[(1-2*x)^(5/2)/((2+3*x)^(9/2)*(3+5*x)^(3/2)),x,8,1959032/147*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+58928/147*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+2/3*(1-2*x)^(3/2)/((2+3*x)^(7/2)*sqrt(3+5*x))+104/9*sqrt(1-2*x)/((2+3*x)^(5/2)*sqrt(3+5*x))+2332/21*sqrt(1-2*x)/((2+3*x)^(3/2)*sqrt(3+5*x))+324104/147*sqrt(1-2*x)/(sqrt(2+3*x)*sqrt(3+5*x))-9795160/441*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)],
[(1-2*x)^(5/2)/((2+3*x)^(11/2)*(3+5*x)^(3/2)),x,9,683150096/9261*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+20549264/9261*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+14/27*(1-2*x)^(3/2)/((2+3*x)^(9/2)*sqrt(3+5*x))+652/81*sqrt(1-2*x)/((2+3*x)^(7/2)*sqrt(3+5*x))+11660/189*sqrt(1-2*x)/((2+3*x)^(5/2)*sqrt(3+5*x))+813208/1323*sqrt(1-2*x)/((2+3*x)^(3/2)*sqrt(3+5*x))+113020952/9261*sqrt(1-2*x)/(sqrt(2+3*x)*sqrt(3+5*x))-3415750480/27783*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)],
[(1-2*x)^(5/2)*(2+3*x)^(7/2)/(3+5*x)^(5/2),x,9,-2/15*(1-2*x)^(5/2)*(2+3*x)^(7/2)/(3+5*x)^(3/2)-1065118/4921875*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-595387/4921875*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-442/75*(1-2*x)^(3/2)*(2+3*x)^(7/2)/sqrt(3+5*x)+373022/196875*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+59662/7875*(2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x)-524/225*(2+3*x)^(7/2)*sqrt(1-2*x)*sqrt(3+5*x)+500501/984375*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(1-2*x)^(5/2)*(2+3*x)^(5/2)/(3+5*x)^(5/2),x,8,-2/15*(1-2*x)^(5/2)*(2+3*x)^(5/2)/(3+5*x)^(3/2)+49321/109375*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-32836/109375*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-62/15*(1-2*x)^(3/2)*(2+3*x)^(5/2)/sqrt(3+5*x)+22866/4375*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)-284/175*(2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x)+33778/21875*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(1-2*x)^(5/2)*(2+3*x)^(3/2)/(3+5*x)^(5/2),x,7,-2/15*(1-2*x)^(5/2)*(2+3*x)^(3/2)/(3+5*x)^(3/2)-7738/15625*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+9206/15625*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(33)-178/75*(1-2*x)^(3/2)*(2+3*x)^(3/2)/sqrt(3+5*x)-572/625*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+8874/3125*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(1-2*x)^(5/2)*sqrt(2+3*x)/(3+5*x)^(5/2),x,6,338/1875*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+992/1875*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-2/15*(1-2*x)^(5/2)*sqrt(2+3*x)/(3+5*x)^(3/2)-46/75*(1-2*x)^(3/2)*sqrt(2+3*x)/sqrt(3+5*x)-76/375*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(1-2*x)^(5/2)/((3+5*x)^(5/2)*sqrt(2+3*x)),x,5,-68/125*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-584/125*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(33)-22/15*(1-2*x)^(3/2)*sqrt(2+3*x)/(3+5*x)^(3/2)+572/25*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)],
[(1-2*x)^(5/2)/((2+3*x)^(3/2)*(3+5*x)^(5/2)),x,6,-6388/25*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-64/25*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(33)+14/3*(1-2*x)^(3/2)/((3+5*x)^(3/2)*sqrt(2+3*x))-1012/15*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)+6388/15*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)],
[(1-2*x)^(5/2)/((2+3*x)^(5/2)*(3+5*x)^(5/2)),x,7,14/9*(1-2*x)^(3/2)/((2+3*x)^(3/2)*(3+5*x)^(3/2))-36968/15*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-1112/15*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+308/3*sqrt(1-2*x)/((3+5*x)^(3/2)*sqrt(2+3*x))-6116/9*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)+36968/9*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)],
[(1-2*x)^(5/2)/((2+3*x)^(7/2)*(3+5*x)^(5/2)),x,8,14/15*(1-2*x)^(3/2)/((2+3*x)^(5/2)*(3+5*x)^(3/2))-96808/5*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-2912/5*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+1232/45*sqrt(1-2*x)/((2+3*x)^(3/2)*(3+5*x)^(3/2))+35948/45*sqrt(1-2*x)/((3+5*x)^(3/2)*sqrt(2+3*x))-16016/3*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)+96808/3*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)],
[(1-2*x)^(5/2)/((2+3*x)^(9/2)*(3+5*x)^(5/2)),x,9,2/3*(1-2*x)^(3/2)/((2+3*x)^(7/2)*(3+5*x)^(3/2))-201616/49*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-2234208/49*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(33)+44/3*sqrt(1-2*x)/((2+3*x)^(5/2)*(3+5*x)^(3/2))+11924/63*sqrt(1-2*x)/((2+3*x)^(3/2)*(3+5*x)^(3/2))+2488904/441*sqrt(1-2*x)/((3+5*x)^(3/2)*sqrt(2+3*x))-5544440/147*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)+11171040/49*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)],

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

# n>0
[(2+3*x)^(5/2)*sqrt(3+5*x)/sqrt(1-2*x),x,6,-5057/8750*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-56041/8750*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(33)-104/175*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)-1/7*(2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x)-4839/1750*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(2+3*x)^(3/2)*sqrt(3+5*x)/sqrt(1-2*x),x,5,-1597/250*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-8/125*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(33)-1/5*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)-23/25*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[sqrt(2+3*x)*sqrt(3+5*x)/sqrt(1-2*x),x,4,-34/15*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-1/15*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-1/3*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[sqrt(3+5*x)/(sqrt(1-2*x)*sqrt(2+3*x)),x,1,-EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)],
[sqrt(3+5*x)/((2+3*x)^(3/2)*sqrt(1-2*x)),x,4,2/3*EllipticE(sqrt(5)*sqrt(2+3*x),sqrt(2/35))*sqrt(5/7)*sqrt(-3-5*x)/sqrt(3+5*x)-2/7*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)],
[sqrt(3+5*x)/((2+3*x)^(5/2)*sqrt(1-2*x)),x,5,-62/147*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-8/147*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-2/21*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+62/147*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)],
[sqrt(3+5*x)/((2+3*x)^(7/2)*sqrt(1-2*x)),x,6,-68/1715*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-584/1715*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(33)-2/35*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)+18/245*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+1752/1715*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)],
[(2+3*x)^(5/2)*(3+5*x)^(3/2)/sqrt(1-2*x),x,7,-44109377/472500*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-663409/236250*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-137/315*(2+3*x)^(3/2)*(3+5*x)^(3/2)*sqrt(1-2*x)-1/9*(2+3*x)^(5/2)*(3+5*x)^(3/2)*sqrt(1-2*x)-9547/5250*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-663409/47250*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(2+3*x)^(3/2)*(3+5*x)^(3/2)/sqrt(1-2*x),x,6,-78472/2625*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-4721/5250*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-1/7*(2+3*x)^(3/2)*(3+5*x)^(3/2)*sqrt(1-2*x)-102/175*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-4721/1050*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(3+5*x)^(3/2)*sqrt(2+3*x)/sqrt(1-2*x),x,5,-4451/450*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-67/225*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-1/5*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-67/45*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(3+5*x)^(3/2)/(sqrt(1-2*x)*sqrt(2+3*x)),x,4,-31/9*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-1/9*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-5/9*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(3+5*x)^(3/2)/((2+3*x)^(3/2)*sqrt(1-2*x)),x,4,-37/21*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+2/21*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+2/21*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)],
[(3+5*x)^(3/2)/((2+3*x)^(5/2)*sqrt(1-2*x)),x,5,272/441*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-202/441*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+2/63*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)-272/441*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)],
[(3+5*x)^(3/2)/((2+3*x)^(7/2)*sqrt(1-2*x)),x,6,-5594/15435*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-1196/15435*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+2/105*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)-404/2205*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+5594/15435*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)],
[(3+5*x)^(3/2)/((2+3*x)^(9/2)*sqrt(1-2*x)),x,7,-184636/252105*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-9124/252105*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+2/147*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(7/2)-536/5145*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)+974/36015*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+184636/252105*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)],
[(2+3*x)^(7/2)*(3+5*x)^(5/2)/sqrt(1-2*x),x,9,-610627101631/36855000*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-2295970088/4606875*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-14303/12870*(2+3*x)^(3/2)*(3+5*x)^(5/2)*sqrt(1-2*x)-41/143*(2+3*x)^(5/2)*(3+5*x)^(5/2)*sqrt(1-2*x)-1/13*(2+3*x)^(7/2)*(3+5*x)^(5/2)*sqrt(1-2*x)-138809831/4504500*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-221673/50050*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)-2295970088/10135125*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(2+3*x)^(5/2)*(3+5*x)^(5/2)/sqrt(1-2*x),x,8,-725140729/141750*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-43624697/283500*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-34/99*(2+3*x)^(3/2)*(3+5*x)^(5/2)*sqrt(1-2*x)-1/11*(2+3*x)^(5/2)*(3+5*x)^(5/2)*sqrt(1-2*x)-329683/34650*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-1053/770*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)-43624697/623700*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(2+3*x)^(3/2)*(3+5*x)^(5/2)/sqrt(1-2*x),x,7,-8256877/56700*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-62092/14175*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-1/9*(2+3*x)^(3/2)*(3+5*x)^(5/2)*sqrt(1-2*x)-1877/630*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-3/7*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)-62092/2835*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(3+5*x)^(5/2)*sqrt(2+3*x)/sqrt(1-2*x),x,6,-17587/378*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-529/378*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-20/21*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-1/7*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)-2645/378*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(3+5*x)^(5/2)/(sqrt(1-2*x)*sqrt(2+3*x)),x,5,-4141/270*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-62/135*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-1/3*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-62/27*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(3+5*x)^(5/2)/((2+3*x)^(3/2)*sqrt(1-2*x)),x,5,-974/189*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-41/189*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+2/21*(3+5*x)^(3/2)*sqrt(1-2*x)/sqrt(2+3*x)-205/189*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(3+5*x)^(5/2)/((2+3*x)^(5/2)*sqrt(1-2*x)),x,5,-4157/1323*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+412/1323*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+2/63*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(3/2)+412/1323*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)],
[(3+5*x)^(5/2)/((2+3*x)^(7/2)*sqrt(1-2*x)),x,6,53194/46305*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-34154/46305*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+2/105*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(5/2)+544/6615*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)-53194/46305*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)],
[(3+5*x)^(5/2)/((2+3*x)^(9/2)*sqrt(1-2*x)),x,7,-816622/2268945*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-265648/2268945*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+2/147*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(7/2)+676/15435*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)-101902/324135*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+816622/2268945*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)],
[(3+5*x)^(5/2)/((2+3*x)^(11/2)*sqrt(1-2*x)),x,8,-32098184/47647845*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-2036756/47647845*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+2/189*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(9/2)+808/27783*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(7/2)-168034/972405*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)-43094/6806835*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+32098184/47647845*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)],
[(3+5*x)^(5/2)/((2+3*x)^(13/2)*sqrt(1-2*x)),x,9,-924247516/66706983*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-31704544/66706983*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+2/231*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(11/2)+940/43659*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(9/2)-251590/2139291*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(7/2)-362666/14975037*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)+11460644/104825259*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+924247516/733776813*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)],

# n<0
[1/(sqrt(1+x)*sqrt(2+x)*sqrt(3+x)),x,1,-2*EllipticF(1/sqrt(3+x),sqrt(2))],
[1/(sqrt(3-x)*sqrt(1+x)*sqrt(2+x)),x,1,2*EllipticF(1/2*sqrt(1+x),sqrt(-4))],
[1/(sqrt(2-x)*sqrt(1+x)*sqrt(3+x)),x,1,EllipticF(sqrt(1+x)/sqrt(3),sqrt(-3/2))*sqrt(2)],
[1/(sqrt(2-x)*sqrt(3-x)*sqrt(1+x)),x,1,EllipticF(sqrt(1+x)/sqrt(3),sqrt(3/4))],
[1/(sqrt(1-x)*sqrt(2+x)*sqrt(3+x)),x,1,2*EllipticF(sqrt(2+x)/sqrt(3),sqrt(-3))],
[1/(sqrt(1-x)*sqrt(3-x)*sqrt(2+x)),x,1,2*EllipticF(sqrt(2+x)/sqrt(3),sqrt(3/5))/sqrt(5)],
[1/(sqrt(1-x)*sqrt(2-x)*sqrt(3+x)),x,1,2*EllipticF(1/2*sqrt(3+x),sqrt(4/5))/sqrt(5)],
[1/(sqrt(1-x)*sqrt(2-x)*sqrt(3-x)),x,1,2*EllipticF(1/sqrt(3-x),sqrt(2))],
[1/(sqrt(-3+x)*sqrt(-2+x)*sqrt(-1+x)),x,1,-2*EllipticF(1/sqrt(-1+x),sqrt(2))],
[1/(sqrt(-3-x)*sqrt(-2+x)*sqrt(-1+x)),x,2,-EllipticF(2/sqrt(3+x),sqrt(5/4))*sqrt(3+x)/sqrt(-3-x)-I*EllipticK(-1/4)*sqrt(3+x)/sqrt(-3-x),-EllipticF(1/sqrt(3/4+1/4*x),sqrt(5/4))*sqrt(3+x)/sqrt(-3-x)],
[1/(sqrt(-2-x)*sqrt(-3+x)*sqrt(-1+x)),x,2,-2*EllipticF(1/sqrt(2/3+1/3*x),sqrt(5/3))*sqrt(2+x)/(sqrt(3)*sqrt(-2-x))],
[1/(sqrt(-3-x)*sqrt(-2-x)*sqrt(-1+x)),x,3,-2*I*EllipticK(4)*sqrt(2+x)/sqrt(-2-x)+EllipticK(3/4)*sqrt(3+x)/sqrt(-3-x)-EllipticF(2/sqrt(3+x),sqrt(1/4))*sqrt(2+x)*sqrt(3+x)/(sqrt(-3-x)*sqrt(-2-x)),-EllipticF(1/sqrt(3/4+1/4*x),sqrt(1/4))*sqrt(2+x)*sqrt(3+x)/(sqrt(-3-x)*sqrt(-2-x))],
[1/(sqrt(-1-x)*sqrt(-3+x)*sqrt(-2+x)),x,2,-2*EllipticF(1/sqrt(1/3+1/3*x),sqrt(4/3))*sqrt(1+x)/(sqrt(3)*sqrt(-1-x))],
[1/(sqrt(-3-x)*sqrt(-1-x)*sqrt(-2+x)),x,3,-2*EllipticF(1/sqrt(3/5+1/5*x),sqrt(2/5))*sqrt(1+x)*sqrt(3+x)/(sqrt(5)*sqrt(-3-x)*sqrt(-1-x))],
[1/(sqrt(-2-x)*sqrt(-1-x)*sqrt(-3+x)),x,3,-2*EllipticF(1/sqrt(2/5+1/5*x),sqrt(1/5))*sqrt(1+x)*sqrt(2+x)/(sqrt(5)*sqrt(-2-x)*sqrt(-1-x))],
[1/(sqrt(-3-x)*sqrt(-2-x)*sqrt(-1-x)),x,1,2*EllipticF(1/sqrt(-1-x),sqrt(2))],
[1/((a+b*x)^(3/2)*sqrt(c+d*x)*sqrt(e+f*x)),x,4,-2*b*sqrt(c+d*x)*sqrt(e+f*x)/((b*c-a*d)*(b*e-a*f)*sqrt(a+b*x))+2*EllipticE(sqrt(f)*sqrt(c+d*x)/sqrt(-d*e+c*f),sqrt(-b*(d*e-c*f)/((b*c-a*d)*f)))*sqrt(f)*sqrt(-d*e+c*f)*sqrt(a+b*x)*sqrt(d*(e+f*x)/(d*e-c*f))/((b*c-a*d)*(b*e-a*f)*sqrt(-d*(a+b*x)/(b*c-a*d))*sqrt(e+f*x))],
[1/((a+b*x)^(5/2)*sqrt(c+d*x)*sqrt(e+f*x)),x,8,-2/3*b*sqrt(c+d*x)*sqrt(e+f*x)/((b*c-a*d)*(b*e-a*f)*(a+b*x)^(3/2))+4/3*b*(b*d*e+b*c*f-2*a*d*f)*sqrt(c+d*x)*sqrt(e+f*x)/((b*c-a*d)^2*(b*e-a*f)^2*sqrt(a+b*x))-4/3*(b*d*e+b*c*f-2*a*d*f)*EllipticE(sqrt(d)*sqrt(a+b*x)/sqrt(-b*c+a*d),sqrt((b*c-a*d)*f/(d*(b*e-a*f))))*sqrt(d)*sqrt(b*(c+d*x)/(b*c-a*d))*sqrt(e+f*x)/((-b*c+a*d)^(3/2)*(b*e-a*f)^2*sqrt(c+d*x)*sqrt(b*(e+f*x)/(b*e-a*f)))+2/3*(2*b*d*e+b*c*f-3*a*d*f)*EllipticF(sqrt(d)*sqrt(a+b*x)/sqrt(-b*c+a*d),sqrt((b*c-a*d)*f/(d*(b*e-a*f))))*sqrt(d)*sqrt(b*(c+d*x)/(b*c-a*d))*sqrt(b*(e+f*x)/(b*e-a*f))/(b*(-b*c+a*d)^(3/2)*(b*e-a*f)*sqrt(c+d*x)*sqrt(e+f*x))],
[(2+3*x)^(7/2)/(sqrt(1-2*x)*sqrt(3+5*x)),x,6,-270248/21875*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-178879/43750*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-333/875*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)-3/35*(2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x)-15553/8750*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(2+3*x)^(5/2)/(sqrt(1-2*x)*sqrt(3+5*x)),x,5,-5161/1250*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-857/625*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-3/25*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)-74/125*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(2+3*x)^(3/2)/(sqrt(1-2*x)*sqrt(3+5*x)),x,4,-37/25*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-13/25*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-1/5*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[sqrt(2+3*x)/(sqrt(1-2*x)*sqrt(3+5*x)),x,1,-EllipticE(sqrt(5/11)*sqrt(1-2*x),sqrt(33/35))*sqrt(7/5)],
[1/(sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)),x,1,-2*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)],
[1/((2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)),x,3,-2*EllipticE(sqrt(5/11)*sqrt(1-2*x),sqrt(33/35))*sqrt(5/7)+6/7*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)],
[1/((2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x)),x,5,-148/49*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-52/49*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+2/7*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+148/49*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)],
[1/((2+3*x)^(7/2)*sqrt(1-2*x)*sqrt(3+5*x)),x,6,-20644/1715*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-6856/1715*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+6/35*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)+296/245*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+20644/1715*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)],
[(2+3*x)^(7/2)/((3+5*x)^(3/2)*sqrt(1-2*x)),x,6,-61151/6250*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(3/11)-942/3125*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(3/11)-2/55*(2+3*x)^(5/2)*sqrt(1-2*x)/sqrt(3+5*x)-69/1375*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)-2577/6875*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(2+3*x)^(5/2)/((3+5*x)^(3/2)*sqrt(1-2*x)),x,5,-438/125*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(3/11)-17/125*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(3/11)-2/55*(2+3*x)^(3/2)*sqrt(1-2*x)/sqrt(3+5*x)-27/275*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(2+3*x)^(3/2)/((3+5*x)^(3/2)*sqrt(1-2*x)),x,4,-31/25*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(3/11)-4/25*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(3/11)-2/55*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)],
[sqrt(2+3*x)/((3+5*x)^(3/2)*sqrt(1-2*x)),x,4,2/11*EllipticE(sqrt(5)*sqrt(2+3*x),sqrt(2/35))*sqrt(7/5)*sqrt(-3-5*x)/sqrt(3+5*x)-2/11*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)],
[1/((3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)),x,3,2*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(3/11)-10/11*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)],
[1/((2+3*x)^(3/2)*(3+5*x)^(3/2)*sqrt(1-2*x)),x,5,136/7*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(3/11)+4/7*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(3/11)+6/7*sqrt(1-2*x)/(sqrt(2+3*x)*sqrt(3+5*x))-680/77*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)],
[1/((2+3*x)^(5/2)*(3+5*x)^(3/2)*sqrt(1-2*x)),x,6,6388/49*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(3/11)+192/49*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(3/11)+2/7*sqrt(1-2*x)/((2+3*x)^(3/2)*sqrt(3+5*x))+288/49*sqrt(1-2*x)/(sqrt(2+3*x)*sqrt(3+5*x))-31940/539*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)],
[1/((2+3*x)^(7/2)*(3+5*x)^(3/2)*sqrt(1-2*x)),x,7,1344984/1715*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(3/11)+40456/1715*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(3/11)+6/35*sqrt(1-2*x)/((2+3*x)^(5/2)*sqrt(3+5*x))+436/245*sqrt(1-2*x)/((2+3*x)^(3/2)*sqrt(3+5*x))+60684/1715*sqrt(1-2*x)/(sqrt(2+3*x)*sqrt(3+5*x))-1344984/3773*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)],
[(2+3*x)^(9/2)/((3+5*x)^(5/2)*sqrt(1-2*x)),x,7,-6515539/343750*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-104663/171875*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-2/165*(2+3*x)^(7/2)*sqrt(1-2*x)/(3+5*x)^(3/2)-668/9075*(2+3*x)^(5/2)*sqrt(1-2*x)/sqrt(3+5*x)+403/75625*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)-87476/378125*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(2+3*x)^(7/2)/((3+5*x)^(5/2)*sqrt(1-2*x)),x,6,-46159/6875*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-2281/6875*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-2/165*(2+3*x)^(5/2)*sqrt(1-2*x)/(3+5*x)^(3/2)-536/9075*(2+3*x)^(3/2)*sqrt(1-2*x)/sqrt(3+5*x)-487/15125*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(2+3*x)^(5/2)/((3+5*x)^(5/2)*sqrt(1-2*x)),x,5,-2797/1375*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-598/1375*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-2/165*(2+3*x)^(3/2)*sqrt(1-2*x)/(3+5*x)^(3/2)-404/9075*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)],
[(2+3*x)^(3/2)/((3+5*x)^(5/2)*sqrt(1-2*x)),x,5,272/275*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-202/275*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-2/165*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)-272/1815*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)],
[sqrt(2+3*x)/((3+5*x)^(5/2)*sqrt(1-2*x)),x,5,74/55*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-4/55*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-2/33*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)-74/363*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)],
[1/((3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)),x,5,-124/11*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-4/11*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-10/33*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)+620/363*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)],
[1/((2+3*x)^(3/2)*(3+5*x)^(5/2)*sqrt(1-2*x)),x,6,-17804/77*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-536/77*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+6/7*sqrt(1-2*x)/((3+5*x)^(3/2)*sqrt(2+3*x))-1340/231*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)+89020/2541*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)],
[1/((2+3*x)^(5/2)*(3+5*x)^(5/2)*sqrt(1-2*x)),x,7,-1255552/539*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-37768/539*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+2/7*sqrt(1-2*x)/((2+3*x)^(3/2)*(3+5*x)^(3/2))+428/49*sqrt(1-2*x)/((3+5*x)^(3/2)*sqrt(2+3*x))-94420/1617*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)+6277760/17787*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)],
[1/((2+3*x)^(7/2)*(3+5*x)^(5/2)*sqrt(1-2*x)),x,8,-352875016/18865*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-10614544/18865*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+6/35*sqrt(1-2*x)/((2+3*x)^(5/2)*(3+5*x)^(3/2))+576/245*sqrt(1-2*x)/((2+3*x)^(3/2)*(3+5*x)^(3/2))+120324/1715*sqrt(1-2*x)/((3+5*x)^(3/2)*sqrt(2+3*x))-5307272/11319*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)+352875016/124509*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)],

#  Resulted in infinite recursion for Rubi versions prior to 4.5. 
[sqrt(x)/(sqrt(a+2*x)*sqrt(c+2*x)),x,3,EllipticE(sqrt(a+2*x)/sqrt(a-c),sqrt(1-c/a))*sqrt(a-c)*sqrt(x)*sqrt((-c-2*x)/(a-c))/(sqrt(2)*sqrt(-x/a)*sqrt(c+2*x))],

#  Following integrands are equal. 
[1/(sqrt(4-x)*sqrt(5-x)*sqrt(-3+x)),x,1,EllipticF(sqrt(-3+x),sqrt(1/2))*sqrt(2)],
[1/(sqrt(4-x)*sqrt((5-x)*(-3+x))),x,3,-2*EllipticF(sqrt(4-x),I)],
[1/(sqrt(4-x)*sqrt(-15+8*x-x^2)),x,2,-2*EllipticF(sqrt(4-x),I)],

#  Following integrands are equal. 
[1/(sqrt(6-x)*sqrt(-2+x)*sqrt(-1+x)),x,1,2*EllipticF(1/2*sqrt(-2+x),sqrt(-4))],
[1/(sqrt((6-x)*(-2+x))*sqrt(-1+x)),x,3,-2*EllipticF(1/2*sqrt(6-x),sqrt(4/5))/sqrt(5)],
[1/(sqrt(-1+x)*sqrt(-12+8*x-x^2)),x,2,-2*EllipticF(1/2*sqrt(6-x),sqrt(4/5))/sqrt(5)],

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

# n<0
[(2+3*x)^(7/2)*sqrt(3+5*x)/(1-2*x)^(3/2),x,7,4071079/17500*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+673523/8750*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+(2+3*x)^(7/2)*sqrt(3+5*x)/sqrt(1-2*x)+2517/350*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+12/7*(2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x)+29293/875*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(2+3*x)^(5/2)*sqrt(3+5*x)/(1-2*x)^(3/2),x,6,7279/125*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+4817/250*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+(2+3*x)^(5/2)*sqrt(3+5*x)/sqrt(1-2*x)+9/5*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+419/50*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(2+3*x)^(3/2)*sqrt(3+5*x)/(1-2*x)^(3/2),x,5,139/10*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+23/5*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+(2+3*x)^(3/2)*sqrt(3+5*x)/sqrt(1-2*x)+2*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[sqrt(2+3*x)*sqrt(3+5*x)/(1-2*x)^(3/2),x,4,EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(33)+sqrt(2+3*x)*sqrt(3+5*x)/sqrt(1-2*x)],
[sqrt(3+5*x)/((1-2*x)^(3/2)*sqrt(2+3*x)),x,3,EllipticE(sqrt(5/11)*sqrt(1-2*x),sqrt(33/35))*sqrt(5/7)+2/7*sqrt(2+3*x)*sqrt(3+5*x)/sqrt(1-2*x)],
[sqrt(3+5*x)/((1-2*x)^(3/2)*(2+3*x)^(3/2)),x,5,-62/49*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+4/49*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(33)+2/7*sqrt(3+5*x)/(sqrt(1-2*x)*sqrt(2+3*x))-12/49*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)],
[sqrt(3+5*x)/((1-2*x)^(3/2)*(2+3*x)^(5/2)),x,6,-38/343*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-212/343*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+2/7*sqrt(3+5*x)/((2+3*x)^(3/2)*sqrt(1-2*x))-8/49*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+38/343*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)],
[sqrt(3+5*x)/((1-2*x)^(3/2)*(2+3*x)^(7/2)),x,7,-5636/12005*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-4364/12005*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+2/7*sqrt(3+5*x)/((2+3*x)^(5/2)*sqrt(1-2*x))-36/245*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)-26/1715*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+5636/12005*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)],
[(2+3*x)^(7/2)*(3+5*x)^(3/2)/(1-2*x)^(3/2),x,8,112543103/78750*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+6770629/157500*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+(2+3*x)^(7/2)*(3+5*x)^(3/2)/sqrt(1-2*x)+1397/210*(2+3*x)^(3/2)*(3+5*x)^(3/2)*sqrt(1-2*x)+5/3*(2+3*x)^(5/2)*(3+5*x)^(3/2)*sqrt(1-2*x)+24358/875*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)+6770629/31500*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(2+3*x)^(5/2)*(3+5*x)^(3/2)/(1-2*x)^(3/2),x,7,1289089/3500*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+9694/875*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+(2+3*x)^(5/2)*(3+5*x)^(3/2)/sqrt(1-2*x)+12/7*(2+3*x)^(3/2)*(3+5*x)^(3/2)*sqrt(1-2*x)+2511/350*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)+9694/175*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(2+3*x)^(3/2)*(3+5*x)^(3/2)/(1-2*x)^(3/2),x,6,4621/50*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+139/50*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+(2+3*x)^(3/2)*(3+5*x)^(3/2)/sqrt(1-2*x)+9/5*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)+139/10*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(3+5*x)^(3/2)*sqrt(2+3*x)/(1-2*x)^(3/2),x,5,133/6*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+2/3*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+(3+5*x)^(3/2)*sqrt(2+3*x)/sqrt(1-2*x)+10/3*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(3+5*x)^(3/2)/((1-2*x)^(3/2)*sqrt(2+3*x)),x,4,34/7*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+1/7*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+11/7*sqrt(2+3*x)*sqrt(3+5*x)/sqrt(1-2*x)],
[(3+5*x)^(3/2)/((1-2*x)^(3/2)*(2+3*x)^(3/2)),x,5,31/49*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+4/49*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+11/7*sqrt(3+5*x)/(sqrt(1-2*x)*sqrt(2+3*x))-31/49*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)],
[(3+5*x)^(3/2)/((1-2*x)^(3/2)*(2+3*x)^(5/2)),x,6,458/1029*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-178/1029*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+11/7*sqrt(3+5*x)/((2+3*x)^(3/2)*sqrt(1-2*x))-97/147*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)-458/1029*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)],
[(3+5*x)^(3/2)/((1-2*x)^(3/2)*(2+3*x)^(7/2)),x,7,-338/12005*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-992/12005*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+11/7*sqrt(3+5*x)/((2+3*x)^(5/2)*sqrt(1-2*x))-163/245*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)-458/1715*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+338/12005*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)],
[(3+5*x)^(3/2)/((1-2*x)^(3/2)*(2+3*x)^(9/2)),x,8,-189368/588245*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-23012/588245*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+11/7*sqrt(3+5*x)/((2+3*x)^(7/2)*sqrt(1-2*x))-229/343*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(7/2)-2818/12005*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)-5438/84035*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+189368/588245*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)],
[(2+3*x)^(7/2)*(3+5*x)^(5/2)/(1-2*x)^(3/2),x,9,17888580643/189000*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+269045681/94500*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+(2+3*x)^(7/2)*(3+5*x)^(5/2)/sqrt(1-2*x)+419/66*(2+3*x)^(3/2)*(3+5*x)^(5/2)*sqrt(1-2*x)+18/11*(2+3*x)^(5/2)*(3+5*x)^(5/2)*sqrt(1-2*x)+4066493/23100*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)+9741/385*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)+269045681/207900*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(2+3*x)^(5/2)*(3+5*x)^(5/2)/(1-2*x)^(3/2),x,8,42696881/18900*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+1284329/18900*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+(2+3*x)^(5/2)*(3+5*x)^(5/2)/sqrt(1-2*x)+5/3*(2+3*x)^(3/2)*(3+5*x)^(5/2)*sqrt(1-2*x)+4853/105*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)+93/14*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)+1284329/3780*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(2+3*x)^(3/2)*(3+5*x)^(5/2)/(1-2*x)^(3/2),x,7,244879/420*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+3683/210*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+(2+3*x)^(3/2)*(3+5*x)^(5/2)/sqrt(1-2*x)+167/14*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)+12/7*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)+3683/42*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(3+5*x)^(5/2)*sqrt(2+3*x)/(1-2*x)^(3/2),x,6,6599/45*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+397/90*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+(3+5*x)^(5/2)*sqrt(2+3*x)/sqrt(1-2*x)+3*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)+397/18*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(3+5*x)^(5/2)/((1-2*x)^(3/2)*sqrt(2+3*x)),x,5,4451/126*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+67/63*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+11/7*(3+5*x)^(3/2)*sqrt(2+3*x)/sqrt(1-2*x)+335/63*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(3+5*x)^(5/2)/((1-2*x)^(3/2)*(2+3*x)^(3/2)),x,5,1159/147*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+31/147*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+11/7*(3+5*x)^(3/2)/(sqrt(1-2*x)*sqrt(2+3*x))+31/147*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)],
[(3+5*x)^(5/2)/((1-2*x)^(3/2)*(2+3*x)^(5/2)),x,6,2797/3087*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+598/3087*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+11/7*(3+5*x)^(3/2)/((2+3*x)^(3/2)*sqrt(1-2*x))+97/441*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)-2797/3087*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)],
[(3+5*x)^(5/2)/((1-2*x)^(3/2)*(2+3*x)^(7/2)),x,7,81164/108045*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-28174/108045*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+11/7*(3+5*x)^(3/2)/((2+3*x)^(5/2)*sqrt(1-2*x))+163/735*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)-15601/15435*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)-81164/108045*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)],
[(3+5*x)^(5/2)/((1-2*x)^(3/2)*(2+3*x)^(9/2)),x,8,106558/1764735*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-220028/1764735*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+11/7*(3+5*x)^(3/2)/((2+3*x)^(7/2)*sqrt(1-2*x))+229/1029*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(7/2)-37117/36015*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)-106772/252105*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)-106558/1764735*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)],
[(3+5*x)^(5/2)/((1-2*x)^(3/2)*(2+3*x)^(11/2)),x,9,-6036028/22235661*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-1199452/22235661*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+11/7*(3+5*x)^(3/2)/((2+3*x)^(9/2)*sqrt(1-2*x))+295/1323*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(9/2)-67345/64827*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(7/2)-167228/453789*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)-392998/3176523*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+6036028/22235661*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)],

# n>0
[(2+3*x)^(7/2)/((1-2*x)^(3/2)*sqrt(3+5*x)),x,6,168123/1250*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(3/11)+5057/1250*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(3/11)+7/11*(2+3*x)^(5/2)*sqrt(3+5*x)/sqrt(1-2*x)+312/275*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+14517/2750*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(2+3*x)^(5/2)/((1-2*x)^(3/2)*sqrt(3+5*x)),x,5,1597/50*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(3/11)+24/25*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(3/11)+7/11*(2+3*x)^(3/2)*sqrt(3+5*x)/sqrt(1-2*x)+69/55*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(2+3*x)^(3/2)/((1-2*x)^(3/2)*sqrt(3+5*x)),x,4,34/5*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(3/11)+1/5*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(3/11)+7/11*sqrt(2+3*x)*sqrt(3+5*x)/sqrt(1-2*x)],
[sqrt(2+3*x)/((1-2*x)^(3/2)*sqrt(3+5*x)),x,3,EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(3/11)+2/11*sqrt(2+3*x)*sqrt(3+5*x)/sqrt(1-2*x)],
[1/((1-2*x)^(3/2)*sqrt(2+3*x)*sqrt(3+5*x)),x,4,2/11*EllipticE(sqrt(5)*sqrt(2+3*x),sqrt(2/35))*sqrt(5/7)*sqrt(-3-5*x)/sqrt(3+5*x)+4/77*sqrt(2+3*x)*sqrt(3+5*x)/sqrt(1-2*x)],
[1/((1-2*x)^(3/2)*(2+3*x)^(3/2)*sqrt(3+5*x)),x,5,-62/49*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(3/11)-8/49*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(3/11)+4/77*sqrt(3+5*x)/(sqrt(1-2*x)*sqrt(2+3*x))+186/539*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)],
[1/((1-2*x)^(3/2)*(2+3*x)^(5/2)*sqrt(3+5*x)),x,6,-1752/343*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(3/11)-68/343*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(3/11)+4/77*sqrt(3+5*x)/((2+3*x)^(3/2)*sqrt(1-2*x))+54/539*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+5256/3773*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)],
[1/((1-2*x)^(3/2)*(2+3*x)^(7/2)*sqrt(3+5*x)),x,7,-244604/12005*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(3/11)-7536/12005*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(3/11)+4/77*sqrt(3+5*x)/((2+3*x)^(5/2)*sqrt(1-2*x))+138/2695*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)+10308/18865*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+733812/132055*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)],
[(2+3*x)^(9/2)/((1-2*x)^(3/2)*(3+5*x)^(3/2)),x,7,2911577/34375*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(3/11)+175111/68750*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(3/11)+7/11*(2+3*x)^(7/2)/(sqrt(1-2*x)*sqrt(3+5*x))-37/605*(2+3*x)^(5/2)*sqrt(1-2*x)/sqrt(3+5*x)+10851/15125*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+502941/151250*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(2+3*x)^(7/2)/((1-2*x)^(3/2)*(3+5*x)^(3/2)),x,6,55019/2750*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(3/11)+823/1375*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(3/11)+7/11*(2+3*x)^(5/2)/(sqrt(1-2*x)*sqrt(3+5*x))-37/605*(2+3*x)^(3/2)*sqrt(1-2*x)/sqrt(3+5*x)+2388/3025*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(2+3*x)^(5/2)/((1-2*x)^(3/2)*(3+5*x)^(3/2)),x,5,1159/275*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(3/11)+31/275*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(3/11)+7/11*(2+3*x)^(3/2)/(sqrt(1-2*x)*sqrt(3+5*x))-37/605*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)],
[(2+3*x)^(3/2)/((1-2*x)^(3/2)*(3+5*x)^(3/2)),x,5,37/55*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(3/11)-2/55*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(3/11)+7/11*sqrt(2+3*x)/(sqrt(1-2*x)*sqrt(3+5*x))-37/121*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)],
[sqrt(2+3*x)/((1-2*x)^(3/2)*(3+5*x)^(3/2)),x,5,4/11*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(3/11)-2/11*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(3/11)+2/11*sqrt(2+3*x)/(sqrt(1-2*x)*sqrt(3+5*x))-20/121*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)],
[1/((1-2*x)^(3/2)*(3+5*x)^(3/2)*sqrt(2+3*x)),x,5,74/77*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(3/11)-4/77*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(3/11)+4/77*sqrt(2+3*x)/(sqrt(1-2*x)*sqrt(3+5*x))-370/847*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)],
[1/((1-2*x)^(3/2)*(2+3*x)^(3/2)*(3+5*x)^(3/2)),x,6,4636/539*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(3/11)+124/539*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(3/11)+4/77/(sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x))+186/539*sqrt(1-2*x)/(sqrt(2+3*x)*sqrt(3+5*x))-23180/5929*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)],
[1/((1-2*x)^(3/2)*(2+3*x)^(5/2)*(3+5*x)^(3/2)),x,7,220076/3773*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(3/11)+6584/3773*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(3/11)+4/77/((2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x))+54/539*sqrt(1-2*x)/((2+3*x)^(3/2)*sqrt(3+5*x))+9876/3773*sqrt(1-2*x)/(sqrt(2+3*x)*sqrt(3+5*x))-1100380/41503*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)],
[1/((1-2*x)^(3/2)*(2+3*x)^(7/2)*(3+5*x)^(3/2)),x,8,46585232/132055*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(3/11)+1400888/132055*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(3/11)+4/77/((2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x))+138/2695*sqrt(1-2*x)/((2+3*x)^(5/2)*sqrt(3+5*x))+14928/18865*sqrt(1-2*x)/((2+3*x)^(3/2)*sqrt(3+5*x))+2101332/132055*sqrt(1-2*x)/(sqrt(2+3*x)*sqrt(3+5*x))-46585232/290521*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)],
[(2+3*x)^(11/2)/((1-2*x)^(3/2)*(3+5*x)^(5/2)),x,8,604915631/3781250*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+18177329/3781250*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+7/11*(2+3*x)^(9/2)/((3+5*x)^(3/2)*sqrt(1-2*x))-107/1815*(2+3*x)^(7/2)*sqrt(1-2*x)/(3+5*x)^(3/2)-4553/99825*(2+3*x)^(5/2)*sqrt(1-2*x)/sqrt(3+5*x)+380188/831875*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+17427983/8318750*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(2+3*x)^(9/2)/((1-2*x)^(3/2)*(3+5*x)^(5/2)),x,7,5684677/151250*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+84134/75625*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+7/11*(2+3*x)^(7/2)/((3+5*x)^(3/2)*sqrt(1-2*x))-107/1815*(2+3*x)^(5/2)*sqrt(1-2*x)/(3+5*x)^(3/2)-4421/99825*(2+3*x)^(3/2)*sqrt(1-2*x)/sqrt(3+5*x)+83093/166375*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(2+3*x)^(7/2)/((1-2*x)^(3/2)*(3+5*x)^(5/2)),x,6,118898/15125*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+2657/15125*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+7/11*(2+3*x)^(5/2)/((3+5*x)^(3/2)*sqrt(1-2*x))-107/1815*(2+3*x)^(3/2)*sqrt(1-2*x)/(3+5*x)^(3/2)-4289/99825*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)],
[(2+3*x)^(5/2)/((1-2*x)^(3/2)*(3+5*x)^(5/2)),x,6,4157/3025*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-412/3025*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+7/11*(2+3*x)^(3/2)/((3+5*x)^(3/2)*sqrt(1-2*x))-107/1815*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)-4157/19965*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)],
[(2+3*x)^(3/2)/((1-2*x)^(3/2)*(3+5*x)^(5/2)),x,6,494/605*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-214/605*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+7/11*sqrt(2+3*x)/((3+5*x)^(3/2)*sqrt(1-2*x))-107/363*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)-494/3993*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)],
[sqrt(2+3*x)/((1-2*x)^(3/2)*(3+5*x)^(5/2)),x,6,98/121*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-16/121*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+2/11*sqrt(2+3*x)/((3+5*x)^(3/2)*sqrt(1-2*x))-40/363*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)-490/3993*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)],
[1/((1-2*x)^(3/2)*(3+5*x)^(5/2)*sqrt(2+3*x)),x,6,-3896/847*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-164/847*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+4/77*sqrt(2+3*x)/((3+5*x)^(3/2)*sqrt(1-2*x))-410/2541*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)+19480/27951*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)],
[1/((1-2*x)^(3/2)*(2+3*x)^(3/2)*(3+5*x)^(5/2)),x,7,-595324/5929*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-18016/5929*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+4/77/((3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x))+186/539*sqrt(1-2*x)/((3+5*x)^(3/2)*sqrt(2+3*x))-45040/17787*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)+2976620/195657*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)],
[1/((1-2*x)^(3/2)*(2+3*x)^(5/2)*(3+5*x)^(5/2)),x,8,-42623864/41503*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-1282376/41503*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+4/77/((2+3*x)^(3/2)*(3+5*x)^(3/2)*sqrt(1-2*x))+54/539*sqrt(1-2*x)/((2+3*x)^(3/2)*(3+5*x)^(3/2))+14496/3773*sqrt(1-2*x)/((3+5*x)^(3/2)*sqrt(2+3*x))-3205940/124509*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)+213119320/1369599*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)],
[1/((1-2*x)^(3/2)*(2+3*x)^(7/2)*(3+5*x)^(5/2)),x,9,-12071114168/1452605*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-363103712/1452605*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+4/77/((2+3*x)^(5/2)*(3+5*x)^(3/2)*sqrt(1-2*x))+138/2695*sqrt(1-2*x)/((2+3*x)^(5/2)*(3+5*x)^(3/2))+19548/18865*sqrt(1-2*x)/((2+3*x)^(3/2)*(3+5*x)^(3/2))+4115652/132055*sqrt(1-2*x)/((3+5*x)^(3/2)*sqrt(2+3*x))-181551856/871563*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)+12071114168/9587193*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)],

# Integrands of the form (a+b x)^(m/2) (c+d x)^(n/2) / (e+f x)^(5/2)

# n<0
[(2+3*x)^(9/2)*sqrt(3+5*x)/(1-2*x)^(5/2),x,8,-112543103/8750*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-6770629/17500*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+1/3*(2+3*x)^(9/2)*sqrt(3+5*x)/(1-2*x)^(3/2)-166/33*(2+3*x)^(7/2)*sqrt(3+5*x)/sqrt(1-2*x)-139163/3850*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)-1327/154*(2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x)-6478333/38500*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(2+3*x)^(7/2)*sqrt(3+5*x)/(1-2*x)^(5/2),x,7,-1289089/500*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-9694/125*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+1/3*(2+3*x)^(7/2)*sqrt(3+5*x)/(1-2*x)^(3/2)-133/33*(2+3*x)^(5/2)*sqrt(3+5*x)/sqrt(1-2*x)-797/110*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)-18551/550*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(2+3*x)^(5/2)*sqrt(3+5*x)/(1-2*x)^(5/2),x,6,-4621/10*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-139/10*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+1/3*(2+3*x)^(5/2)*sqrt(3+5*x)/(1-2*x)^(3/2)-100/33*(2+3*x)^(3/2)*sqrt(3+5*x)/sqrt(1-2*x)-133/22*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(2+3*x)^(3/2)*sqrt(3+5*x)/(1-2*x)^(5/2),x,5,-133/2*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-2*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+1/3*(2+3*x)^(3/2)*sqrt(3+5*x)/(1-2*x)^(3/2)-67/33*sqrt(2+3*x)*sqrt(3+5*x)/sqrt(1-2*x)],
[sqrt(2+3*x)*sqrt(3+5*x)/(1-2*x)^(5/2),x,5,-34/7*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-1/7*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+1/3*sqrt(2+3*x)*sqrt(3+5*x)/(1-2*x)^(3/2)-68/231*sqrt(2+3*x)*sqrt(3+5*x)/sqrt(1-2*x)],
[sqrt(3+5*x)/((1-2*x)^(5/2)*sqrt(2+3*x)),x,5,31/49*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+4/49*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+2/21*sqrt(2+3*x)*sqrt(3+5*x)/(1-2*x)^(3/2)+62/1617*sqrt(2+3*x)*sqrt(3+5*x)/sqrt(1-2*x)],
[sqrt(3+5*x)/((1-2*x)^(5/2)*(2+3*x)^(3/2)),x,6,458/343*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-178/343*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+2/21*sqrt(3+5*x)/((1-2*x)^(3/2)*sqrt(2+3*x))+194/1617*sqrt(3+5*x)/(sqrt(1-2*x)*sqrt(2+3*x))-458/3773*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)],
[sqrt(3+5*x)/((1-2*x)^(5/2)*(2+3*x)^(5/2)),x,7,-338/2401*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-992/2401*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+2/21*sqrt(3+5*x)/((1-2*x)^(3/2)*(2+3*x)^(3/2))+326/1617*sqrt(3+5*x)/((2+3*x)^(3/2)*sqrt(1-2*x))-458/3773*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+338/26411*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)],
[sqrt(3+5*x)/((1-2*x)^(5/2)*(2+3*x)^(7/2)),x,8,-2092/84035*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-189368/84035*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+2/21*sqrt(3+5*x)/((1-2*x)^(3/2)*(2+3*x)^(5/2))+458/1617*sqrt(3+5*x)/((2+3*x)^(5/2)*sqrt(1-2*x))-2818/18865*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)-5438/132055*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+189368/924385*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)],
[(2+3*x)^(7/2)*(3+5*x)^(3/2)/(1-2*x)^(5/2),x,8,1/3*(2+3*x)^(7/2)*(3+5*x)^(3/2)/(1-2*x)^(3/2)-722133/3500*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(3/11)-6547351/3500*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-56/11*(2+3*x)^(5/2)*(3+5*x)^(3/2)/sqrt(1-2*x)-1341/154*(2+3*x)^(3/2)*(3+5*x)^(3/2)*sqrt(1-2*x)-140289/3850*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-2166399/7700*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(2+3*x)^(5/2)*(3+5*x)^(3/2)/(1-2*x)^(5/2),x,7,1/3*(2+3*x)^(5/2)*(3+5*x)^(3/2)/(1-2*x)^(3/2)-2077/50*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(3/11)-37663/100*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-45/11*(2+3*x)^(3/2)*(3+5*x)^(3/2)/sqrt(1-2*x)-807/110*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-6231/110*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(2+3*x)^(3/2)*(3+5*x)^(3/2)/(1-2*x)^(5/2),x,6,1/3*(2+3*x)^(3/2)*(3+5*x)^(3/2)/(1-2*x)^(3/2)-15/2*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(3/11)-68*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-34/11*(3+5*x)^(3/2)*sqrt(2+3*x)/sqrt(1-2*x)-225/22*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(3+5*x)^(3/2)*sqrt(2+3*x)/(1-2*x)^(5/2),x,5,-139/14*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-23/7*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+1/3*(3+5*x)^(3/2)*sqrt(2+3*x)/(1-2*x)^(3/2)-23/7*sqrt(2+3*x)*sqrt(3+5*x)/sqrt(1-2*x)],
[(3+5*x)^(3/2)/((1-2*x)^(5/2)*sqrt(2+3*x)),x,5,-37/49*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-13/49*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+11/21*sqrt(2+3*x)*sqrt(3+5*x)/(1-2*x)^(3/2)-74/147*sqrt(2+3*x)*sqrt(3+5*x)/sqrt(1-2*x)],
[(3+5*x)^(3/2)/((1-2*x)^(5/2)*(2+3*x)^(3/2)),x,6,19/343*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+106/343*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+11/21*sqrt(3+5*x)/((1-2*x)^(3/2)*sqrt(2+3*x))-8/147*sqrt(3+5*x)/(sqrt(1-2*x)*sqrt(2+3*x))-19/343*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)],
[(3+5*x)^(3/2)/((1-2*x)^(5/2)*(2+3*x)^(5/2)),x,7,-582/2401*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(3/11)+496/2401*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+11/21*sqrt(3+5*x)/((1-2*x)^(3/2)*(2+3*x)^(3/2))+58/147*sqrt(3+5*x)/((2+3*x)^(3/2)*sqrt(1-2*x))-89/343*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)-496/2401*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)],
[(3+5*x)^(3/2)/((1-2*x)^(5/2)*(2+3*x)^(7/2)),x,8,-16732/84035*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(3/11)+3946/84035*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+11/21*sqrt(3+5*x)/((1-2*x)^(3/2)*(2+3*x)^(5/2))+124/147*sqrt(3+5*x)/((2+3*x)^(5/2)*sqrt(1-2*x))-779/1715*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)-2264/12005*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)-3946/84035*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)],
[(2+3*x)^(7/2)*(3+5*x)^(5/2)/(1-2*x)^(5/2),x,9,1/3*(2+3*x)^(7/2)*(3+5*x)^(5/2)/(1-2*x)^(3/2)-174654791/12600*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-1313411/3150*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-203/33*(2+3*x)^(5/2)*(3+5*x)^(5/2)/sqrt(1-2*x)-225/22*(2+3*x)^(3/2)*(3+5*x)^(5/2)*sqrt(1-2*x)-1310203/4620*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-6277/154*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)-1313411/630*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(2+3*x)^(5/2)*(3+5*x)^(5/2)/(1-2*x)^(5/2),x,8,1/3*(2+3*x)^(5/2)*(3+5*x)^(5/2)/(1-2*x)^(3/2)-12601/140*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-69819/70*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(33)-170/33*(2+3*x)^(3/2)*(3+5*x)^(5/2)/sqrt(1-2*x)-28283/462*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-1355/154*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)-12601/28*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(2+3*x)^(3/2)*(3+5*x)^(5/2)/(1-2*x)^(5/2),x,7,1/3*(2+3*x)^(3/2)*(3+5*x)^(5/2)/(1-2*x)^(3/2)-12101/20*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-91/5*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-137/33*(3+5*x)^(5/2)*sqrt(2+3*x)/sqrt(1-2*x)-817/66*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-91*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(3+5*x)^(5/2)*sqrt(2+3*x)/(1-2*x)^(5/2),x,6,-4621/42*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-139/42*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+1/3*(3+5*x)^(5/2)*sqrt(2+3*x)/(1-2*x)^(3/2)-104/21*(3+5*x)^(3/2)*sqrt(2+3*x)/sqrt(1-2*x)-695/42*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(3+5*x)^(5/2)/((1-2*x)^(5/2)*sqrt(2+3*x)),x,5,-1597/98*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-8/49*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(33)+11/21*(3+5*x)^(3/2)*sqrt(2+3*x)/(1-2*x)^(3/2)-264/49*sqrt(2+3*x)*sqrt(3+5*x)/sqrt(1-2*x)],
[(3+5*x)^(5/2)/((1-2*x)^(5/2)*(2+3*x)^(3/2)),x,6,-17/343*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-146/343*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(33)+11/21*(3+5*x)^(3/2)/((1-2*x)^(3/2)*sqrt(2+3*x))-143/49*sqrt(3+5*x)/(sqrt(1-2*x)*sqrt(2+3*x))+438/343*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)],
[(3+5*x)^(5/2)/((1-2*x)^(5/2)*(2+3*x)^(5/2)),x,7,11/21*(3+5*x)^(3/2)/((1-2*x)^(3/2)*(2+3*x)^(3/2))+169/7203*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+496/7203*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-22/49*sqrt(3+5*x)/((2+3*x)^(3/2)*sqrt(1-2*x))+229/1029*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)-169/7203*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)],
[(3+5*x)^(5/2)/((1-2*x)^(5/2)*(2+3*x)^(7/2)),x,8,11/21*(3+5*x)^(3/2)/((1-2*x)^(3/2)*(2+3*x)^(5/2))-7738/84035*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+9206/84035*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(33)+99/49*sqrt(3+5*x)/((2+3*x)^(5/2)*sqrt(1-2*x))-1432/1715*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)-4437/12005*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)-27618/84035*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)],
[(3+5*x)^(5/2)/((1-2*x)^(5/2)*(2+3*x)^(9/2)),x,9,11/21*(3+5*x)^(3/2)/((1-2*x)^(3/2)*(2+3*x)^(7/2))+98642/823543*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)-65672/823543*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))*sqrt(11/3)+220/49*sqrt(3+5*x)/((2+3*x)^(7/2)*sqrt(1-2*x))-4545/2401*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(7/2)-11433/16807*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)-33778/117649*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)-98642/823543*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)],

# n>0
[(2+3*x)^(9/2)/((1-2*x)^(5/2)*sqrt(3+5*x)),x,7,-44109377/27500*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-663409/13750*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+7/33*(2+3*x)^(7/2)*sqrt(3+5*x)/(1-2*x)^(3/2)-910/363*(2+3*x)^(5/2)*sqrt(3+5*x)/sqrt(1-2*x)-27271/6050*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)-317384/15125*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(2+3*x)^(7/2)/((1-2*x)^(5/2)*sqrt(3+5*x)),x,6,-78472/275*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-4721/550*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+7/33*(2+3*x)^(5/2)*sqrt(3+5*x)/(1-2*x)^(3/2)-679/363*(2+3*x)^(3/2)*sqrt(3+5*x)/sqrt(1-2*x)-4517/1210*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(2+3*x)^(5/2)/((1-2*x)^(5/2)*sqrt(3+5*x)),x,5,-4451/110*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-67/55*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+7/33*(2+3*x)^(3/2)*sqrt(3+5*x)/(1-2*x)^(3/2)-448/363*sqrt(2+3*x)*sqrt(3+5*x)/sqrt(1-2*x)],
[(2+3*x)^(3/2)/((1-2*x)^(5/2)*sqrt(3+5*x)),x,5,-31/11*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-1/11*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+7/33*sqrt(2+3*x)*sqrt(3+5*x)/(1-2*x)^(3/2)-62/363*sqrt(2+3*x)*sqrt(3+5*x)/sqrt(1-2*x)],
[sqrt(2+3*x)/((1-2*x)^(5/2)*sqrt(3+5*x)),x,5,37/77*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-2/77*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+2/33*sqrt(2+3*x)*sqrt(3+5*x)/(1-2*x)^(3/2)+74/2541*sqrt(2+3*x)*sqrt(3+5*x)/sqrt(1-2*x)],
[1/((1-2*x)^(5/2)*sqrt(2+3*x)*sqrt(3+5*x)),x,5,272/539*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-202/539*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+4/231*sqrt(2+3*x)*sqrt(3+5*x)/(1-2*x)^(3/2)+544/17787*sqrt(2+3*x)*sqrt(3+5*x)/sqrt(1-2*x)],
[1/((1-2*x)^(5/2)*(2+3*x)^(3/2)*sqrt(3+5*x)),x,6,-5594/3773*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-1196/3773*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+4/231*sqrt(3+5*x)/((1-2*x)^(3/2)*sqrt(2+3*x))+808/17787*sqrt(3+5*x)/(sqrt(1-2*x)*sqrt(2+3*x))+5594/41503*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)],
[1/((1-2*x)^(5/2)*(2+3*x)^(5/2)*sqrt(3+5*x)),x,7,-184636/26411*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-9124/26411*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+4/231*sqrt(3+5*x)/((1-2*x)^(3/2)*(2+3*x)^(3/2))+1072/17787*sqrt(3+5*x)/((2+3*x)^(3/2)*sqrt(1-2*x))+974/41503*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+184636/290521*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)],
[1/((1-2*x)^(5/2)*(2+3*x)^(7/2)*sqrt(3+5*x)),x,8,-26062156/924385*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-837304/924385*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+4/231*sqrt(3+5*x)/((1-2*x)^(3/2)*(2+3*x)^(5/2))+1336/17787*sqrt(3+5*x)/((2+3*x)^(5/2)*sqrt(1-2*x))-806/207515*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)+349904/1452605*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+26062156/10168235*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)],
[(2+3*x)^(11/2)/((1-2*x)^(5/2)*(3+5*x)^(3/2)),x,8,-1508889271/1512500*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-11346991/378125*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+7/33*(2+3*x)^(9/2)/((1-2*x)^(3/2)*sqrt(3+5*x))-896/363*(2+3*x)^(7/2)/(sqrt(1-2*x)*sqrt(3+5*x))+4439/19965*(2+3*x)^(5/2)*sqrt(1-2*x)/sqrt(3+5*x)-932783/332750*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)-21713939/1663750*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(2+3*x)^(9/2)/((1-2*x)^(5/2)*(3+5*x)^(3/2)),x,7,-5327983/30250*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-160297/30250*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+7/33*(2+3*x)^(7/2)/((1-2*x)^(3/2)*sqrt(3+5*x))-665/363*(2+3*x)^(5/2)/(sqrt(1-2*x)*sqrt(3+5*x))+3284/19965*(2+3*x)^(3/2)*sqrt(1-2*x)/sqrt(3+5*x)-153319/66550*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(2+3*x)^(7/2)/((1-2*x)^(5/2)*(3+5*x)^(3/2)),x,6,-148831/6050*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-2252/3025*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+7/33*(2+3*x)^(5/2)/((1-2*x)^(3/2)*sqrt(3+5*x))-434/363*(2+3*x)^(3/2)/(sqrt(1-2*x)*sqrt(3+5*x))+2129/19965*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)],
[(2+3*x)^(5/2)/((1-2*x)^(5/2)*(3+5*x)^(3/2)),x,6,-974/605*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-41/605*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+7/33*(2+3*x)^(3/2)/((1-2*x)^(3/2)*sqrt(3+5*x))-203/363*sqrt(2+3*x)/(sqrt(1-2*x)*sqrt(3+5*x))+974/3993*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)],
[(2+3*x)^(3/2)/((1-2*x)^(5/2)*(3+5*x)^(3/2)),x,6,49/121*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-8/121*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+7/33*sqrt(2+3*x)/((1-2*x)^(3/2)*sqrt(3+5*x))+8/363*sqrt(2+3*x)/(sqrt(1-2*x)*sqrt(3+5*x))-245/3993*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)],
[sqrt(2+3*x)/((1-2*x)^(5/2)*(3+5*x)^(3/2)),x,6,494/847*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-214/847*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+2/33*sqrt(2+3*x)/((1-2*x)^(3/2)*sqrt(3+5*x))+214/2541*sqrt(2+3*x)/(sqrt(1-2*x)*sqrt(3+5*x))-2470/27951*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)],
[1/((1-2*x)^(5/2)*(3+5*x)^(3/2)*sqrt(2+3*x)),x,6,8314/5929*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-824/5929*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+4/231*sqrt(2+3*x)/((1-2*x)^(3/2)*sqrt(3+5*x))+824/17787*sqrt(2+3*x)/(sqrt(1-2*x)*sqrt(3+5*x))-41570/195657*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)],
[1/((1-2*x)^(5/2)*(2+3*x)^(3/2)*(3+5*x)^(3/2)),x,7,475592/41503*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+10628/41503*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+4/231/((1-2*x)^(3/2)*sqrt(2+3*x)*sqrt(3+5*x))+1088/17787/(sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x))+5314/41503*sqrt(1-2*x)/(sqrt(2+3*x)*sqrt(3+5*x))-2377960/1369599*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)],
[1/((1-2*x)^(5/2)*(2+3*x)^(5/2)*(3+5*x)^(3/2)),x,8,22738708/290521*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+673072/290521*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+4/231/((1-2*x)^(3/2)*(2+3*x)^(3/2)*sqrt(3+5*x))+1352/17787/((2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x))+694/41503*sqrt(1-2*x)/((2+3*x)^(3/2)*sqrt(3+5*x))+336536/290521*sqrt(1-2*x)/(sqrt(2+3*x)*sqrt(3+5*x))-113693540/9587193*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)],
[1/((1-2*x)^(5/2)*(2+3*x)^(7/2)*(3+5*x)^(3/2)),x,9,4839325048/10168235*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+145418632/10168235*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+4/231/((1-2*x)^(3/2)*(2+3*x)^(5/2)*sqrt(3+5*x))+1616/17787/((2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x))-2206/207515*sqrt(1-2*x)/((2+3*x)^(5/2)*sqrt(3+5*x))+499564/1452605*sqrt(1-2*x)/((2+3*x)^(3/2)*sqrt(3+5*x))+72709316/10168235*sqrt(1-2*x)/(sqrt(2+3*x)*sqrt(3+5*x))-4839325048/67110351*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)],
[(2+3*x)^(13/2)/((1-2*x)^(5/2)*(3+5*x)^(5/2)),x,9,7/33*(2+3*x)^(11/2)/((1-2*x)^(3/2)*(3+5*x)^(3/2))-51601293223/83187500*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-776112041/41593750*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-294/121*(2+3*x)^(9/2)/((3+5*x)^(3/2)*sqrt(1-2*x))+4373/19965*(2+3*x)^(7/2)*sqrt(1-2*x)/(3+5*x)^(3/2)+150812/1098075*(2+3*x)^(5/2)*sqrt(1-2*x)/sqrt(3+5*x)-31887029/18301250*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)-371279941/45753125*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(2+3*x)^(11/2)/((1-2*x)^(5/2)*(3+5*x)^(5/2)),x,8,7/33*(2+3*x)^(9/2)/((1-2*x)^(3/2)*(3+5*x)^(3/2))-90397364/831875*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-5442127/1663750*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-217/121*(2+3*x)^(7/2)/((3+5*x)^(3/2)*sqrt(1-2*x))+3218/19965*(2+3*x)^(5/2)*sqrt(1-2*x)/(3+5*x)^(3/2)+110519/1098075*(2+3*x)^(3/2)*sqrt(1-2*x)/sqrt(3+5*x)-5199979/3660250*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)],
[(2+3*x)^(9/2)/((1-2*x)^(5/2)*(3+5*x)^(5/2)),x,7,7/33*(2+3*x)^(7/2)/((1-2*x)^(3/2)*(3+5*x)^(3/2))-4971289/332750*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-76163/166375*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-140/121*(2+3*x)^(5/2)/((3+5*x)^(3/2)*sqrt(1-2*x))+2063/19965*(2+3*x)^(3/2)*sqrt(1-2*x)/(3+5*x)^(3/2)+70226/1098075*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)],
[(2+3*x)^(7/2)/((1-2*x)^(5/2)*(3+5*x)^(5/2)),x,7,7/33*(2+3*x)^(5/2)/((1-2*x)^(3/2)*(3+5*x)^(3/2))-29933/33275*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-1847/33275*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-63/121*(2+3*x)^(3/2)/((3+5*x)^(3/2)*sqrt(1-2*x))+908/19965*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)+29933/219615*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)],
[(2+3*x)^(5/2)/((1-2*x)^(5/2)*(3+5*x)^(5/2)),x,7,7/33*(2+3*x)^(3/2)/((1-2*x)^(3/2)*(3+5*x)^(3/2))+2209/6655*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-494/6655*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+14/121*sqrt(2+3*x)/((3+5*x)^(3/2)*sqrt(1-2*x))-247/3993*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)-2209/43923*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)],
[(2+3*x)^(3/2)/((1-2*x)^(5/2)*(3+5*x)^(5/2)),x,7,592/1331*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-230/1331*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+7/33*sqrt(2+3*x)/((1-2*x)^(3/2)*(3+5*x)^(3/2))+26/121*sqrt(2+3*x)/((3+5*x)^(3/2)*sqrt(1-2*x))-575/3993*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)-2960/43923*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)],
[sqrt(2+3*x)/((1-2*x)^(5/2)*(3+5*x)^(5/2)),x,7,4418/9317*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-988/9317*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+2/33*sqrt(2+3*x)/((1-2*x)^(3/2)*(3+5*x)^(3/2))+118/847*sqrt(2+3*x)/((3+5*x)^(3/2)*sqrt(1-2*x))-2470/27951*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)-22090/307461*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)],
[1/((1-2*x)^(5/2)*(3+5*x)^(5/2)*sqrt(2+3*x)),x,7,-119732/65219*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-7388/65219*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+4/231*sqrt(2+3*x)/((1-2*x)^(3/2)*(3+5*x)^(3/2))+368/5929*sqrt(2+3*x)/((3+5*x)^(3/2)*sqrt(1-2*x))-18470/195657*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)+598660/2152227*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)],
[1/((1-2*x)^(5/2)*(2+3*x)^(3/2)*(3+5*x)^(5/2)),x,8,-19885156/456533*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-609304/456533*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+4/231/((1-2*x)^(3/2)*(3+5*x)^(3/2)*sqrt(2+3*x))+456/5929/((3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x))+5034/41503*sqrt(1-2*x)/((3+5*x)^(3/2)*sqrt(2+3*x))-1523260/1369599*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)+99425780/15065589*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)],
[1/((1-2*x)^(5/2)*(2+3*x)^(5/2)*(3+5*x)^(5/2)),x,9,4/231/((1-2*x)^(3/2)*(2+3*x)^(3/2)*(3+5*x)^(3/2))-1446357824/3195731*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-43537016/3195731*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+544/5929/((2+3*x)^(3/2)*(3+5*x)^(3/2)*sqrt(1-2*x))+414/41503*sqrt(1-2*x)/((2+3*x)^(3/2)*(3+5*x)^(3/2))+488436/290521*sqrt(1-2*x)/((3+5*x)^(3/2)*sqrt(2+3*x))-108842540/9587193*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)+7231789120/105459123*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)],
[1/((1-2*x)^(5/2)*(2+3*x)^(7/2)*(3+5*x)^(5/2)),x,10,4/231/((1-2*x)^(3/2)*(2+3*x)^(5/2)*(3+5*x)^(3/2))-412810345784/111850585*EllipticE(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)-12417792656/111850585*EllipticF(sqrt(3/7)*sqrt(1-2*x),sqrt(35/33))/sqrt(33)+632/5929/((2+3*x)^(5/2)*(3+5*x)^(3/2)*sqrt(1-2*x))-3606/207515*sqrt(1-2*x)/((2+3*x)^(5/2)*(3+5*x)^(3/2))+649224/1452605*sqrt(1-2*x)/((2+3*x)^(3/2)*(3+5*x)^(3/2))+140700876/10168235*sqrt(1-2*x)/((3+5*x)^(3/2)*sqrt(2+3*x))-6208896328/67110351*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)+412810345784/738213861*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)],

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

# Integrands of the form (a+b x)^(1/3) (c+d x)^(n/3) (e+f x)^p

# n>0
[(a+b*x)^(1/3)*(c+d*x)^(2/3)*(e+f*x)^2,x,5,1/81*(b*c-a*d)*(10*a^2*d^2*f^2-10*a*b*d*f*(3*d*e-c*f)+b^2*(27*d^2*e^2-24*c*d*e*f+7*c^2*f^2))*(a+b*x)^(1/3)*(c+d*x)^(2/3)/(b^3*d^3)+1/54*(10*a^2*d^2*f^2-10*a*b*d*f*(3*d*e-c*f)+b^2*(27*d^2*e^2-24*c*d*e*f+7*c^2*f^2))*(a+b*x)^(4/3)*(c+d*x)^(2/3)/(b^3*d^2)+1/36*f*(15*b*d*e-7*b*c*f-8*a*d*f)*(a+b*x)^(4/3)*(c+d*x)^(5/3)/(b^2*d^2)+1/4*f*(a+b*x)^(4/3)*(c+d*x)^(5/3)*(e+f*x)/(b*d)+1/486*(b*c-a*d)^2*(10*a^2*d^2*f^2-10*a*b*d*f*(3*d*e-c*f)+b^2*(27*d^2*e^2-24*c*d*e*f+7*c^2*f^2))*log(a+b*x)/(b^(11/3)*d^(10/3))+1/162*(b*c-a*d)^2*(10*a^2*d^2*f^2-10*a*b*d*f*(3*d*e-c*f)+b^2*(27*d^2*e^2-24*c*d*e*f+7*c^2*f^2))*log(-1+b^(1/3)*(c+d*x)^(1/3)/(d^(1/3)*(a+b*x)^(1/3)))/(b^(11/3)*d^(10/3))+1/81*(b*c-a*d)^2*(10*a^2*d^2*f^2-10*a*b*d*f*(3*d*e-c*f)+b^2*(27*d^2*e^2-24*c*d*e*f+7*c^2*f^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^(11/3)*d^(10/3)*sqrt(3))],
[(a+b*x)^(1/3)*(c+d*x)^(2/3)*(e+f*x),x,4,1/27*(b*c-a*d)*(9*b*d*e-4*b*c*f-5*a*d*f)*(a+b*x)^(1/3)*(c+d*x)^(2/3)/(b^2*d^2)+1/18*(9*b*d*e-4*b*c*f-5*a*d*f)*(a+b*x)^(4/3)*(c+d*x)^(2/3)/(b^2*d)+1/3*f*(a+b*x)^(4/3)*(c+d*x)^(5/3)/(b*d)+1/162*(b*c-a*d)^2*(9*b*d*e-4*b*c*f-5*a*d*f)*log(a+b*x)/(b^(8/3)*d^(7/3))+1/54*(b*c-a*d)^2*(9*b*d*e-4*b*c*f-5*a*d*f)*log(-1+b^(1/3)*(c+d*x)^(1/3)/(d^(1/3)*(a+b*x)^(1/3)))/(b^(8/3)*d^(7/3))+1/27*(b*c-a*d)^2*(9*b*d*e-4*b*c*f-5*a*d*f)*arctan(1/sqrt(3)+2*b^(1/3)*(c+d*x)^(1/3)/(d^(1/3)*(a+b*x)^(1/3)*sqrt(3)))/(b^(8/3)*d^(7/3)*sqrt(3))],
[(a+b*x)^(1/3)*(c+d*x)^(2/3),x,3,1/3*(b*c-a*d)*(a+b*x)^(1/3)*(c+d*x)^(2/3)/(b*d)+1/2*(a+b*x)^(4/3)*(c+d*x)^(2/3)/b+1/18*(b*c-a*d)^2*log(a+b*x)/(b^(5/3)*d^(4/3))+1/6*(b*c-a*d)^2*log(-1+b^(1/3)*(c+d*x)^(1/3)/(d^(1/3)*(a+b*x)^(1/3)))/(b^(5/3)*d^(4/3))+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)))/(b^(5/3)*d^(4/3)*sqrt(3))],
[(a+b*x)^(1/3)*(c+d*x)^(2/3)/(e+f*x),x,4,(a+b*x)^(1/3)*(c+d*x)^(2/3)/f+1/6*(3*b*d*e-2*b*c*f-a*d*f)*log(a+b*x)/(b^(2/3)*d^(1/3)*f^2)+1/2*(b*e-a*f)^(1/3)*(d*e-c*f)^(2/3)*log(e+f*x)/f^2-3/2*(b*e-a*f)^(1/3)*(d*e-c*f)^(2/3)*log(-(a+b*x)^(1/3)+(b*e-a*f)^(1/3)*(c+d*x)^(1/3)/(d*e-c*f)^(1/3))/f^2+1/2*(3*b*d*e-2*b*c*f-a*d*f)*log(-1+b^(1/3)*(c+d*x)^(1/3)/(d^(1/3)*(a+b*x)^(1/3)))/(b^(2/3)*d^(1/3)*f^2)+(3*b*d*e-2*b*c*f-a*d*f)*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^(1/3)*f^2*sqrt(3))-(b*e-a*f)^(1/3)*(d*e-c*f)^(2/3)*arctan(1/sqrt(3)+2*(b*e-a*f)^(1/3)*(c+d*x)^(1/3)/((d*e-c*f)^(1/3)*(a+b*x)^(1/3)*sqrt(3)))*sqrt(3)/f^2],
[(a+b*x)^(1/3)*(c+d*x)^(2/3)/(e+f*x)^2,x,4,-(a+b*x)^(1/3)*(c+d*x)^(2/3)/(f*(e+f*x))-1/2*b^(1/3)*d^(2/3)*log(a+b*x)/f^2-1/6*(3*b*d*e-b*c*f-2*a*d*f)*log(e+f*x)/(f^2*(b*e-a*f)^(2/3)*(d*e-c*f)^(1/3))+1/2*(3*b*d*e-b*c*f-2*a*d*f)*log(-(a+b*x)^(1/3)+(b*e-a*f)^(1/3)*(c+d*x)^(1/3)/(d*e-c*f)^(1/3))/(f^2*(b*e-a*f)^(2/3)*(d*e-c*f)^(1/3))-3/2*b^(1/3)*d^(2/3)*log(-1+b^(1/3)*(c+d*x)^(1/3)/(d^(1/3)*(a+b*x)^(1/3)))/f^2+(3*b*d*e-b*c*f-2*a*d*f)*arctan(1/sqrt(3)+2*(b*e-a*f)^(1/3)*(c+d*x)^(1/3)/((d*e-c*f)^(1/3)*(a+b*x)^(1/3)*sqrt(3)))/(f^2*(b*e-a*f)^(2/3)*(d*e-c*f)^(1/3)*sqrt(3))-b^(1/3)*d^(2/3)*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)/f^2],
[(a+b*x)^(1/3)*(c+d*x)^(2/3)/(e+f*x)^3,x,3,1/2*(a+b*x)^(1/3)*(c+d*x)^(5/3)/((d*e-c*f)*(e+f*x)^2)-1/6*(b*c-a*d)*(a+b*x)^(1/3)*(c+d*x)^(2/3)/((b*e-a*f)*(d*e-c*f)*(e+f*x))-1/18*(b*c-a*d)^2*log(e+f*x)/((b*e-a*f)^(5/3)*(d*e-c*f)^(4/3))+1/6*(b*c-a*d)^2*log(-(a+b*x)^(1/3)+(b*e-a*f)^(1/3)*(c+d*x)^(1/3)/(d*e-c*f)^(1/3))/((b*e-a*f)^(5/3)*(d*e-c*f)^(4/3))+1/3*(b*c-a*d)^2*arctan(1/sqrt(3)+2*(b*e-a*f)^(1/3)*(c+d*x)^(1/3)/((d*e-c*f)^(1/3)*(a+b*x)^(1/3)*sqrt(3)))/((b*e-a*f)^(5/3)*(d*e-c*f)^(4/3)*sqrt(3))],
[(a+b*x)^(1/3)*(c+d*x)^(2/3)/(e+f*x)^4,x,4,-1/3*f*(a+b*x)^(4/3)*(c+d*x)^(5/3)/((b*e-a*f)*(d*e-c*f)*(e+f*x)^3)+1/18*(9*b*d*e-5*b*c*f-4*a*d*f)*(a+b*x)^(1/3)*(c+d*x)^(5/3)/((b*e-a*f)*(d*e-c*f)^2*(e+f*x)^2)-1/54*(b*c-a*d)*(9*b*d*e-5*b*c*f-4*a*d*f)*(a+b*x)^(1/3)*(c+d*x)^(2/3)/((b*e-a*f)^2*(d*e-c*f)^2*(e+f*x))-1/162*(b*c-a*d)^2*(9*b*d*e-5*b*c*f-4*a*d*f)*log(e+f*x)/((b*e-a*f)^(8/3)*(d*e-c*f)^(7/3))+1/54*(b*c-a*d)^2*(9*b*d*e-5*b*c*f-4*a*d*f)*log(-(a+b*x)^(1/3)+(b*e-a*f)^(1/3)*(c+d*x)^(1/3)/(d*e-c*f)^(1/3))/((b*e-a*f)^(8/3)*(d*e-c*f)^(7/3))+1/27*(b*c-a*d)^2*(9*b*d*e-5*b*c*f-4*a*d*f)*arctan(1/sqrt(3)+2*(b*e-a*f)^(1/3)*(c+d*x)^(1/3)/((d*e-c*f)^(1/3)*(a+b*x)^(1/3)*sqrt(3)))/((b*e-a*f)^(8/3)*(d*e-c*f)^(7/3)*sqrt(3))],

# n<0
[(a+b*x)^(1/3)*(e+f*x)^2/(c+d*x)^(1/3),x,4,1/27*(5*a^2*d^2*f^2-2*a*b*d*f*(9*d*e-4*c*f)+b^2*(27*d^2*e^2-36*c*d*e*f+14*c^2*f^2))*(a+b*x)^(1/3)*(c+d*x)^(2/3)/(b^2*d^3)+1/18*f*(12*b*d*e-7*b*c*f-5*a*d*f)*(a+b*x)^(4/3)*(c+d*x)^(2/3)/(b^2*d^2)+1/3*f*(a+b*x)^(4/3)*(c+d*x)^(2/3)*(e+f*x)/(b*d)+1/162*(b*c-a*d)*(5*a^2*d^2*f^2-2*a*b*d*f*(9*d*e-4*c*f)+b^2*(27*d^2*e^2-36*c*d*e*f+14*c^2*f^2))*log(a+b*x)/(b^(8/3)*d^(10/3))+1/54*(b*c-a*d)*(5*a^2*d^2*f^2-2*a*b*d*f*(9*d*e-4*c*f)+b^2*(27*d^2*e^2-36*c*d*e*f+14*c^2*f^2))*log(-1+b^(1/3)*(c+d*x)^(1/3)/(d^(1/3)*(a+b*x)^(1/3)))/(b^(8/3)*d^(10/3))+1/27*(b*c-a*d)*(5*a^2*d^2*f^2-2*a*b*d*f*(9*d*e-4*c*f)+b^2*(27*d^2*e^2-36*c*d*e*f+14*c^2*f^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^(8/3)*d^(10/3)*sqrt(3))],
[(a+b*x)^(1/3)*(e+f*x)/(c+d*x)^(1/3),x,3,1/3*(3*b*d*e-2*b*c*f-a*d*f)*(a+b*x)^(1/3)*(c+d*x)^(2/3)/(b*d^2)+1/2*f*(a+b*x)^(4/3)*(c+d*x)^(2/3)/(b*d)+1/18*(b*c-a*d)*(3*b*d*e-2*b*c*f-a*d*f)*log(a+b*x)/(b^(5/3)*d^(7/3))+1/6*(b*c-a*d)*(3*b*d*e-2*b*c*f-a*d*f)*log(-1+b^(1/3)*(c+d*x)^(1/3)/(d^(1/3)*(a+b*x)^(1/3)))/(b^(5/3)*d^(7/3))+1/3*(b*c-a*d)*(3*b*d*e-2*b*c*f-a*d*f)*arctan(1/sqrt(3)+2*b^(1/3)*(c+d*x)^(1/3)/(d^(1/3)*(a+b*x)^(1/3)*sqrt(3)))/(b^(5/3)*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))],
[(a+b*x)^(1/3)/((c+d*x)^(1/3)*(e+f*x)),x,4,-1/2*b^(1/3)*log(a+b*x)/(d^(1/3)*f)-1/2*(b*e-a*f)^(1/3)*log(e+f*x)/(f*(d*e-c*f)^(1/3))+3/2*(b*e-a*f)^(1/3)*log(-(a+b*x)^(1/3)+(b*e-a*f)^(1/3)*(c+d*x)^(1/3)/(d*e-c*f)^(1/3))/(f*(d*e-c*f)^(1/3))-3/2*b^(1/3)*log(-1+b^(1/3)*(c+d*x)^(1/3)/(d^(1/3)*(a+b*x)^(1/3)))/(d^(1/3)*f)-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^(1/3)*f)+(b*e-a*f)^(1/3)*arctan(1/sqrt(3)+2*(b*e-a*f)^(1/3)*(c+d*x)^(1/3)/((d*e-c*f)^(1/3)*(a+b*x)^(1/3)*sqrt(3)))*sqrt(3)/(f*(d*e-c*f)^(1/3))],
[(a+b*x)^(1/3)/((c+d*x)^(1/3)*(e+f*x)^2),x,2,(a+b*x)^(1/3)*(c+d*x)^(2/3)/((d*e-c*f)*(e+f*x))-1/6*(b*c-a*d)*log(e+f*x)/((b*e-a*f)^(2/3)*(d*e-c*f)^(4/3))+1/2*(b*c-a*d)*log(-(a+b*x)^(1/3)+(b*e-a*f)^(1/3)*(c+d*x)^(1/3)/(d*e-c*f)^(1/3))/((b*e-a*f)^(2/3)*(d*e-c*f)^(4/3))+(b*c-a*d)*arctan(1/sqrt(3)+2*(b*e-a*f)^(1/3)*(c+d*x)^(1/3)/((d*e-c*f)^(1/3)*(a+b*x)^(1/3)*sqrt(3)))/((b*e-a*f)^(2/3)*(d*e-c*f)^(4/3)*sqrt(3))],
[(a+b*x)^(1/3)/((c+d*x)^(1/3)*(e+f*x)^3),x,3,-1/2*f*(a+b*x)^(4/3)*(c+d*x)^(2/3)/((b*e-a*f)*(d*e-c*f)*(e+f*x)^2)+1/3*(3*b*d*e-b*c*f-2*a*d*f)*(a+b*x)^(1/3)*(c+d*x)^(2/3)/((b*e-a*f)*(d*e-c*f)^2*(e+f*x))-1/18*(b*c-a*d)*(3*b*d*e-b*c*f-2*a*d*f)*log(e+f*x)/((b*e-a*f)^(5/3)*(d*e-c*f)^(7/3))+1/6*(b*c-a*d)*(3*b*d*e-b*c*f-2*a*d*f)*log(-(a+b*x)^(1/3)+(b*e-a*f)^(1/3)*(c+d*x)^(1/3)/(d*e-c*f)^(1/3))/((b*e-a*f)^(5/3)*(d*e-c*f)^(7/3))+1/3*(b*c-a*d)*(3*b*d*e-b*c*f-2*a*d*f)*arctan(1/sqrt(3)+2*(b*e-a*f)^(1/3)*(c+d*x)^(1/3)/((d*e-c*f)^(1/3)*(a+b*x)^(1/3)*sqrt(3)))/((b*e-a*f)^(5/3)*(d*e-c*f)^(7/3)*sqrt(3))],
[(a+b*x)^(1/3)/((c+d*x)^(1/3)*(e+f*x)^4),x,5,1/3*(a+b*x)^(1/3)*(c+d*x)^(2/3)/((d*e-c*f)*(e+f*x)^3)+1/18*(6*b*d*e+b*c*f-7*a*d*f)*(a+b*x)^(1/3)*(c+d*x)^(2/3)/((b*e-a*f)*(d*e-c*f)^2*(e+f*x)^2)+1/54*(28*a^2*d^2*f^2-a*b*d*f*(51*d*e+5*c*f)+b^2*(18*d^2*e^2+15*c*d*e*f-5*c^2*f^2))*(a+b*x)^(1/3)*(c+d*x)^(2/3)/((b*e-a*f)^2*(d*e-c*f)^3*(e+f*x))-1/162*(b*c-a*d)*(14*a^2*d^2*f^2-4*a*b*d*f*(9*d*e-2*c*f)+b^2*(27*d^2*e^2-18*c*d*e*f+5*c^2*f^2))*log(e+f*x)/((b*e-a*f)^(8/3)*(d*e-c*f)^(10/3))+1/54*(b*c-a*d)*(14*a^2*d^2*f^2-4*a*b*d*f*(9*d*e-2*c*f)+b^2*(27*d^2*e^2-18*c*d*e*f+5*c^2*f^2))*log(-(a+b*x)^(1/3)+(b*e-a*f)^(1/3)*(c+d*x)^(1/3)/(d*e-c*f)^(1/3))/((b*e-a*f)^(8/3)*(d*e-c*f)^(10/3))+1/27*(b*c-a*d)*(14*a^2*d^2*f^2-4*a*b*d*f*(9*d*e-2*c*f)+b^2*(27*d^2*e^2-18*c*d*e*f+5*c^2*f^2))*arctan(1/sqrt(3)+2*(b*e-a*f)^(1/3)*(c+d*x)^(1/3)/((d*e-c*f)^(1/3)*(a+b*x)^(1/3)*sqrt(3)))/((b*e-a*f)^(8/3)*(d*e-c*f)^(10/3)*sqrt(3))],

# Integrands of the form 1 / (a+b x)^(1/3) (c+d x)^(n/3) (e+f x)^p

# n>0

# n<0
[(e+f*x)^3/((a+b*x)^(1/3)*(c+d*x)^(2/3)),x,3,1/3*f*(a+b*x)^(2/3)*(c+d*x)^(1/3)*(e+f*x)^2/(b*d)+1/54*f*(a+b*x)^(2/3)*(c+d*x)^(1/3)*(28*a^2*d^2*f^2-a*b*d*f*(108*d*e-31*c*f)+b^2*(144*d^2*e^2-135*c*d*e*f+40*c^2*f^2)+3*b*d*f*(15*b*d*e-8*b*c*f-7*a*d*f)*x)/(b^3*d^3)+1/162*(14*a^3*d^3*f^3-6*a^2*b*d^2*f^2*(9*d*e-2*c*f)+3*a*b^2*d*f*(27*d^2*e^2-18*c*d*e*f+5*c^2*f^2)-b^3*(81*d^3*e^3-162*c*d^2*e^2*f+135*c^2*d*e*f^2-40*c^3*f^3))*log(c+d*x)/(b^(10/3)*d^(11/3))+1/54*(14*a^3*d^3*f^3-6*a^2*b*d^2*f^2*(9*d*e-2*c*f)+3*a*b^2*d*f*(27*d^2*e^2-18*c*d*e*f+5*c^2*f^2)-b^3*(81*d^3*e^3-162*c*d^2*e^2*f+135*c^2*d*e*f^2-40*c^3*f^3))*log(-1+d^(1/3)*(a+b*x)^(1/3)/(b^(1/3)*(c+d*x)^(1/3)))/(b^(10/3)*d^(11/3))+1/27*(14*a^3*d^3*f^3-6*a^2*b*d^2*f^2*(9*d*e-2*c*f)+3*a*b^2*d*f*(27*d^2*e^2-18*c*d*e*f+5*c^2*f^2)-b^3*(81*d^3*e^3-162*c*d^2*e^2*f+135*c^2*d*e*f^2-40*c^3*f^3))*arctan(1/sqrt(3)+2*d^(1/3)*(a+b*x)^(1/3)/(b^(1/3)*(c+d*x)^(1/3)*sqrt(3)))/(b^(10/3)*d^(11/3)*sqrt(3))],
[(e+f*x)^2/((a+b*x)^(1/3)*(c+d*x)^(2/3)),x,3,1/6*f*(9*b*d*e-5*b*c*f-4*a*d*f)*(a+b*x)^(2/3)*(c+d*x)^(1/3)/(b^2*d^2)+1/2*f*(a+b*x)^(2/3)*(c+d*x)^(1/3)*(e+f*x)/(b*d)-1/18*(2*a^2*d^2*f^2-2*a*b*d*f*(3*d*e-c*f)+b^2*(9*d^2*e^2-12*c*d*e*f+5*c^2*f^2))*log(c+d*x)/(b^(7/3)*d^(8/3))-1/6*(2*a^2*d^2*f^2-2*a*b*d*f*(3*d*e-c*f)+b^2*(9*d^2*e^2-12*c*d*e*f+5*c^2*f^2))*log(-1+d^(1/3)*(a+b*x)^(1/3)/(b^(1/3)*(c+d*x)^(1/3)))/(b^(7/3)*d^(8/3))-1/3*(2*a^2*d^2*f^2-2*a*b*d*f*(3*d*e-c*f)+b^2*(9*d^2*e^2-12*c*d*e*f+5*c^2*f^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^(7/3)*d^(8/3)*sqrt(3))],
[(e+f*x)/((a+b*x)^(1/3)*(c+d*x)^(2/3)),x,2,f*(a+b*x)^(2/3)*(c+d*x)^(1/3)/(b*d)-1/6*(3*b*d*e-2*b*c*f-a*d*f)*log(c+d*x)/(b^(4/3)*d^(5/3))-1/2*(3*b*d*e-2*b*c*f-a*d*f)*log(-1+d^(1/3)*(a+b*x)^(1/3)/(b^(1/3)*(c+d*x)^(1/3)))/(b^(4/3)*d^(5/3))-(3*b*d*e-2*b*c*f-a*d*f)*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))],
[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)^(1/3)*(c+d*x)^(2/3)*(e+f*x)),x,1,1/2*log(e+f*x)/((b*e-a*f)^(1/3)*(d*e-c*f)^(2/3))-3/2*log((d*e-c*f)^(1/3)*(a+b*x)^(1/3)/(b*e-a*f)^(1/3)-(c+d*x)^(1/3))/((b*e-a*f)^(1/3)*(d*e-c*f)^(2/3))-arctan(1/sqrt(3)+2*(d*e-c*f)^(1/3)*(a+b*x)^(1/3)/((b*e-a*f)^(1/3)*(c+d*x)^(1/3)*sqrt(3)))*sqrt(3)/((b*e-a*f)^(1/3)*(d*e-c*f)^(2/3))],
[1/((a+b*x)^(1/3)*(c+d*x)^(2/3)*(e+f*x)^2),x,2,-f*(a+b*x)^(2/3)*(c+d*x)^(1/3)/((b*e-a*f)*(d*e-c*f)*(e+f*x))+1/6*(3*b*d*e-b*c*f-2*a*d*f)*log(e+f*x)/((b*e-a*f)^(4/3)*(d*e-c*f)^(5/3))-1/2*(3*b*d*e-b*c*f-2*a*d*f)*log((d*e-c*f)^(1/3)*(a+b*x)^(1/3)/(b*e-a*f)^(1/3)-(c+d*x)^(1/3))/((b*e-a*f)^(4/3)*(d*e-c*f)^(5/3))-(3*b*d*e-b*c*f-2*a*d*f)*arctan(1/sqrt(3)+2*(d*e-c*f)^(1/3)*(a+b*x)^(1/3)/((b*e-a*f)^(1/3)*(c+d*x)^(1/3)*sqrt(3)))/((b*e-a*f)^(4/3)*(d*e-c*f)^(5/3)*sqrt(3))],
[1/((a+b*x)^(1/3)*(c+d*x)^(2/3)*(e+f*x)^3),x,4,-1/2*f*(a+b*x)^(2/3)*(c+d*x)^(1/3)/((b*e-a*f)*(d*e-c*f)*(e+f*x)^2)-1/6*f*(9*b*d*e-4*b*c*f-5*a*d*f)*(a+b*x)^(2/3)*(c+d*x)^(1/3)/((b*e-a*f)^2*(d*e-c*f)^2*(e+f*x))+1/18*(5*a^2*d^2*f^2-2*a*b*d*f*(6*d*e-c*f)+b^2*(9*d^2*e^2-6*c*d*e*f+2*c^2*f^2))*log(e+f*x)/((b*e-a*f)^(7/3)*(d*e-c*f)^(8/3))-1/6*(5*a^2*d^2*f^2-2*a*b*d*f*(6*d*e-c*f)+b^2*(9*d^2*e^2-6*c*d*e*f+2*c^2*f^2))*log((d*e-c*f)^(1/3)*(a+b*x)^(1/3)/(b*e-a*f)^(1/3)-(c+d*x)^(1/3))/((b*e-a*f)^(7/3)*(d*e-c*f)^(8/3))-1/3*(5*a^2*d^2*f^2-2*a*b*d*f*(6*d*e-c*f)+b^2*(9*d^2*e^2-6*c*d*e*f+2*c^2*f^2))*arctan(1/sqrt(3)+2*(d*e-c*f)^(1/3)*(a+b*x)^(1/3)/((b*e-a*f)^(1/3)*(c+d*x)^(1/3)*sqrt(3)))/((b*e-a*f)^(7/3)*(d*e-c*f)^(8/3)*sqrt(3))],

# Integrands of the form (a+b x)^m / ((c+d x)^(1/3) (e+f x)^(n/3)) with 2 b d e-b c f-a d f=0

# n>0

# n<0
[(a+b*x)^3/((c+d*x)^(1/3)*(b*c+a*d+2*b*d*x)^(1/3)),x,7,3/20*(a+b*x)^2*(c+d*x)^(2/3)*(b*c+a*d+2*b*d*x)^(2/3)/d^2+9/560*(b*c-a*d)*(c+d*x)^(2/3)*(23*b*c-39*a*d-16*b*d*x)*(b*c+a*d+2*b*d*x)^(2/3)/d^4-81/112*(b*c-a*d)^3*((c+d*x)*(b*c+a*d+2*b*d*x))^(1/3)*sqrt(d^2*(3*b*c+a*d+4*b*d*x)^2)*sqrt((d*(3*b*c+a*d)+4*b*d^2*x)^2)/(b^(2/3)*d^6*(c+d*x)^(1/3)*(b*c+a*d+2*b*d*x)^(1/3)*(3*b*c+a*d+4*b*d*x)*(2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3))))-27/56*3^(3/4)*(b*c-a*d)^(11/3)*((c+d*x)*(b*c+a*d+2*b*d*x))^(1/3)*((b*c-a*d)^(2/3)+2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3))*EllipticF((2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+(b*c-a*d)^(2/3)*(1-sqrt(3)))/(2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt((d*(3*b*c+a*d)+4*b*d^2*x)^2)*sqrt(((b*c-a*d)^(4/3)-2*b^(1/3)*(b*c-a*d)^(2/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+4*b^(2/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(2/3))/(2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2)/(b^(2/3)*d^4*(c+d*x)^(1/3)*(b*c+a*d+2*b*d*x)^(1/3)*(3*b*c+a*d+4*b*d*x)*sqrt(2)*sqrt(d^2*(3*b*c+a*d+4*b*d*x)^2)*sqrt((b*c-a*d)^(2/3)*((b*c-a*d)^(2/3)+2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3))/(2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2))+81/224*3^(1/4)*(b*c-a*d)^(11/3)*((c+d*x)*(b*c+a*d+2*b*d*x))^(1/3)*((b*c-a*d)^(2/3)+2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3))*EllipticE((2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+(b*c-a*d)^(2/3)*(1-sqrt(3)))/(2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt((d*(3*b*c+a*d)+4*b*d^2*x)^2)*sqrt(2-sqrt(3))*sqrt(((b*c-a*d)^(4/3)-2*b^(1/3)*(b*c-a*d)^(2/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+4*b^(2/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(2/3))/(2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2)/(b^(2/3)*d^4*(c+d*x)^(1/3)*(b*c+a*d+2*b*d*x)^(1/3)*(3*b*c+a*d+4*b*d*x)*sqrt(d^2*(3*b*c+a*d+4*b*d*x)^2)*sqrt((b*c-a*d)^(2/3)*((b*c-a*d)^(2/3)+2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3))/(2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2))],
[(a+b*x)^2/((c+d*x)^(1/3)*(b*c+a*d+2*b*d*x)^(1/3)),x,7,-45/112*(b*c-a*d)*(c+d*x)^(2/3)*(b*c+a*d+2*b*d*x)^(2/3)/d^3+3/14*(a+b*x)*(c+d*x)^(2/3)*(b*c+a*d+2*b*d*x)^(2/3)/d^2+99/112*(b*c-a*d)^2*((c+d*x)*(b*c+a*d+2*b*d*x))^(1/3)*sqrt(d^2*(3*b*c+a*d+4*b*d*x)^2)*sqrt((d*(3*b*c+a*d)+4*b*d^2*x)^2)/(b^(2/3)*d^5*(c+d*x)^(1/3)*(b*c+a*d+2*b*d*x)^(1/3)*(3*b*c+a*d+4*b*d*x)*(2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3))))+33/56*3^(3/4)*(b*c-a*d)^(8/3)*((c+d*x)*(b*c+a*d+2*b*d*x))^(1/3)*((b*c-a*d)^(2/3)+2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3))*EllipticF((2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+(b*c-a*d)^(2/3)*(1-sqrt(3)))/(2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt((d*(3*b*c+a*d)+4*b*d^2*x)^2)*sqrt(((b*c-a*d)^(4/3)-2*b^(1/3)*(b*c-a*d)^(2/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+4*b^(2/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(2/3))/(2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2)/(b^(2/3)*d^3*(c+d*x)^(1/3)*(b*c+a*d+2*b*d*x)^(1/3)*(3*b*c+a*d+4*b*d*x)*sqrt(2)*sqrt(d^2*(3*b*c+a*d+4*b*d*x)^2)*sqrt((b*c-a*d)^(2/3)*((b*c-a*d)^(2/3)+2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3))/(2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2))-99/224*3^(1/4)*(b*c-a*d)^(8/3)*((c+d*x)*(b*c+a*d+2*b*d*x))^(1/3)*((b*c-a*d)^(2/3)+2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3))*EllipticE((2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+(b*c-a*d)^(2/3)*(1-sqrt(3)))/(2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt((d*(3*b*c+a*d)+4*b*d^2*x)^2)*sqrt(2-sqrt(3))*sqrt(((b*c-a*d)^(4/3)-2*b^(1/3)*(b*c-a*d)^(2/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+4*b^(2/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(2/3))/(2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2)/(b^(2/3)*d^3*(c+d*x)^(1/3)*(b*c+a*d+2*b*d*x)^(1/3)*(3*b*c+a*d+4*b*d*x)*sqrt(d^2*(3*b*c+a*d+4*b*d*x)^2)*sqrt((b*c-a*d)^(2/3)*((b*c-a*d)^(2/3)+2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3))/(2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2))],
[(a+b*x)/((c+d*x)^(1/3)*(b*c+a*d+2*b*d*x)^(1/3)),x,6,3/8*(c+d*x)^(2/3)*(b*c+a*d+2*b*d*x)^(2/3)/d^2-9/8*(b*c-a*d)*((c+d*x)*(b*c+a*d+2*b*d*x))^(1/3)*sqrt(d^2*(3*b*c+a*d+4*b*d*x)^2)*sqrt((d*(3*b*c+a*d)+4*b*d^2*x)^2)/(b^(2/3)*d^4*(c+d*x)^(1/3)*(b*c+a*d+2*b*d*x)^(1/3)*(3*b*c+a*d+4*b*d*x)*(2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3))))-3/4*3^(3/4)*(b*c-a*d)^(5/3)*((c+d*x)*(b*c+a*d+2*b*d*x))^(1/3)*((b*c-a*d)^(2/3)+2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3))*EllipticF((2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+(b*c-a*d)^(2/3)*(1-sqrt(3)))/(2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt((d*(3*b*c+a*d)+4*b*d^2*x)^2)*sqrt(((b*c-a*d)^(4/3)-2*b^(1/3)*(b*c-a*d)^(2/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+4*b^(2/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(2/3))/(2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2)/(b^(2/3)*d^2*(c+d*x)^(1/3)*(b*c+a*d+2*b*d*x)^(1/3)*(3*b*c+a*d+4*b*d*x)*sqrt(2)*sqrt(d^2*(3*b*c+a*d+4*b*d*x)^2)*sqrt((b*c-a*d)^(2/3)*((b*c-a*d)^(2/3)+2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3))/(2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2))+9/16*3^(1/4)*(b*c-a*d)^(5/3)*((c+d*x)*(b*c+a*d+2*b*d*x))^(1/3)*((b*c-a*d)^(2/3)+2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3))*EllipticE((2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+(b*c-a*d)^(2/3)*(1-sqrt(3)))/(2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt((d*(3*b*c+a*d)+4*b*d^2*x)^2)*sqrt(2-sqrt(3))*sqrt(((b*c-a*d)^(4/3)-2*b^(1/3)*(b*c-a*d)^(2/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+4*b^(2/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(2/3))/(2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2)/(b^(2/3)*d^2*(c+d*x)^(1/3)*(b*c+a*d+2*b*d*x)^(1/3)*(3*b*c+a*d+4*b*d*x)*sqrt(d^2*(3*b*c+a*d+4*b*d*x)^2)*sqrt((b*c-a*d)^(2/3)*((b*c-a*d)^(2/3)+2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3))/(2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2))],
[1/((c+d*x)^(1/3)*(b*c+a*d+2*b*d*x)^(1/3)),x,5,3/2*((c+d*x)*(b*c+a*d+2*b*d*x))^(1/3)*sqrt(d^2*(3*b*c+a*d+4*b*d*x)^2)*sqrt((d*(3*b*c+a*d)+4*b*d^2*x)^2)/(b^(2/3)*d^3*(c+d*x)^(1/3)*(b*c+a*d+2*b*d*x)^(1/3)*(3*b*c+a*d+4*b*d*x)*(2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3))))+3^(3/4)*(b*c-a*d)^(2/3)*((c+d*x)*(b*c+a*d+2*b*d*x))^(1/3)*((b*c-a*d)^(2/3)+2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3))*EllipticF((2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+(b*c-a*d)^(2/3)*(1-sqrt(3)))/(2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt((d*(3*b*c+a*d)+4*b*d^2*x)^2)*sqrt(((b*c-a*d)^(4/3)-2*b^(1/3)*(b*c-a*d)^(2/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+4*b^(2/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(2/3))/(2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2)/(b^(2/3)*d*(c+d*x)^(1/3)*(b*c+a*d+2*b*d*x)^(1/3)*(3*b*c+a*d+4*b*d*x)*sqrt(2)*sqrt(d^2*(3*b*c+a*d+4*b*d*x)^2)*sqrt((b*c-a*d)^(2/3)*((b*c-a*d)^(2/3)+2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3))/(2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2))-3/4*3^(1/4)*(b*c-a*d)^(2/3)*((c+d*x)*(b*c+a*d+2*b*d*x))^(1/3)*((b*c-a*d)^(2/3)+2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3))*EllipticE((2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+(b*c-a*d)^(2/3)*(1-sqrt(3)))/(2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt((d*(3*b*c+a*d)+4*b*d^2*x)^2)*sqrt(2-sqrt(3))*sqrt(((b*c-a*d)^(4/3)-2*b^(1/3)*(b*c-a*d)^(2/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+4*b^(2/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(2/3))/(2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2)/(b^(2/3)*d*(c+d*x)^(1/3)*(b*c+a*d+2*b*d*x)^(1/3)*(3*b*c+a*d+4*b*d*x)*sqrt(d^2*(3*b*c+a*d+4*b*d*x)^2)*sqrt((b*c-a*d)^(2/3)*((b*c-a*d)^(2/3)+2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3))/(2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2))],
[1/((a+b*x)*(c+d*x)^(1/3)*(b*c+a*d+2*b*d*x)^(1/3)),x,1,-1/2*log(a+b*x)/(b^(2/3)*(b*c-a*d)^(2/3))+3/4*log(b^(2/3)*(c+d*x)^(2/3)/(b*c-a*d)^(1/3)-(b*c+a*d+2*b*d*x)^(1/3))/(b^(2/3)*(b*c-a*d)^(2/3))-1/2*arctan(1/sqrt(3)+2*b^(2/3)*(c+d*x)^(2/3)/((b*c-a*d)^(1/3)*(b*c+a*d+2*b*d*x)^(1/3)*sqrt(3)))*sqrt(3)/(b^(2/3)*(b*c-a*d)^(2/3))],
[1/((a+b*x)^2*(c+d*x)^(1/3)*(b*c+a*d+2*b*d*x)^(1/3)),x,8,-(c+d*x)^(2/3)*(b*c+a*d+2*b*d*x)^(2/3)/((b*c-a*d)^2*(a+b*x))+1/2*d*log(a+b*x)/(b^(2/3)*(b*c-a*d)^(5/3))-3/4*d*log(b^(2/3)*(c+d*x)^(2/3)/(b*c-a*d)^(1/3)-(b*c+a*d+2*b*d*x)^(1/3))/(b^(2/3)*(b*c-a*d)^(5/3))+1/2*d*arctan(1/sqrt(3)+2*b^(2/3)*(c+d*x)^(2/3)/((b*c-a*d)^(1/3)*(b*c+a*d+2*b*d*x)^(1/3)*sqrt(3)))*sqrt(3)/(b^(2/3)*(b*c-a*d)^(5/3))+((c+d*x)*(b*c+a*d+2*b*d*x))^(1/3)*sqrt(d^2*(3*b*c+a*d+4*b*d*x)^2)*sqrt((d*(3*b*c+a*d)+4*b*d^2*x)^2)/(b^(2/3)*d*(b*c-a*d)^2*(c+d*x)^(1/3)*(b*c+a*d+2*b*d*x)^(1/3)*(3*b*c+a*d+4*b*d*x)*(2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3))))+d*((c+d*x)*(b*c+a*d+2*b*d*x))^(1/3)*((b*c-a*d)^(2/3)+2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3))*EllipticF((2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+(b*c-a*d)^(2/3)*(1-sqrt(3)))/(2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2)*sqrt((d*(3*b*c+a*d)+4*b*d^2*x)^2)*sqrt(((b*c-a*d)^(4/3)-2*b^(1/3)*(b*c-a*d)^(2/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+4*b^(2/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(2/3))/(2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2)/(3^(1/4)*b^(2/3)*(b*c-a*d)^(4/3)*(c+d*x)^(1/3)*(b*c+a*d+2*b*d*x)^(1/3)*(3*b*c+a*d+4*b*d*x)*sqrt(d^2*(3*b*c+a*d+4*b*d*x)^2)*sqrt((b*c-a*d)^(2/3)*((b*c-a*d)^(2/3)+2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3))/(2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2))-1/2*3^(1/4)*d*((c+d*x)*(b*c+a*d+2*b*d*x))^(1/3)*((b*c-a*d)^(2/3)+2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3))*EllipticE((2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+(b*c-a*d)^(2/3)*(1-sqrt(3)))/(2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt((d*(3*b*c+a*d)+4*b*d^2*x)^2)*sqrt(2-sqrt(3))*sqrt(((b*c-a*d)^(4/3)-2*b^(1/3)*(b*c-a*d)^(2/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+4*b^(2/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(2/3))/(2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2)/(b^(2/3)*(b*c-a*d)^(4/3)*(c+d*x)^(1/3)*(b*c+a*d+2*b*d*x)^(1/3)*(3*b*c+a*d+4*b*d*x)*sqrt(d^2*(3*b*c+a*d+4*b*d*x)^2)*sqrt((b*c-a*d)^(2/3)*((b*c-a*d)^(2/3)+2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3))/(2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2))],
[1/((a+b*x)^3*(c+d*x)^(1/3)*(b*c+a*d+2*b*d*x)^(1/3)),x,9,-1/2*(c+d*x)^(2/3)*(b*c+a*d+2*b*d*x)^(2/3)/((b*c-a*d)^2*(a+b*x)^2)+2*d*(c+d*x)^(2/3)*(b*c+a*d+2*b*d*x)^(2/3)/((b*c-a*d)^3*(a+b*x))-2/3*d^2*log(a+b*x)/(b^(2/3)*(b*c-a*d)^(8/3))+d^2*log(b^(2/3)*(c+d*x)^(2/3)/(b*c-a*d)^(1/3)-(b*c+a*d+2*b*d*x)^(1/3))/(b^(2/3)*(b*c-a*d)^(8/3))-2*d^2*arctan(1/sqrt(3)+2*b^(2/3)*(c+d*x)^(2/3)/((b*c-a*d)^(1/3)*(b*c+a*d+2*b*d*x)^(1/3)*sqrt(3)))/(b^(2/3)*(b*c-a*d)^(8/3)*sqrt(3))-2*((c+d*x)*(b*c+a*d+2*b*d*x))^(1/3)*sqrt(d^2*(3*b*c+a*d+4*b*d*x)^2)*sqrt((d*(3*b*c+a*d)+4*b*d^2*x)^2)/(b^(2/3)*(b*c-a*d)^3*(c+d*x)^(1/3)*(b*c+a*d+2*b*d*x)^(1/3)*(3*b*c+a*d+4*b*d*x)*(2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3))))-2*d^2*((c+d*x)*(b*c+a*d+2*b*d*x))^(1/3)*((b*c-a*d)^(2/3)+2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3))*EllipticF((2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+(b*c-a*d)^(2/3)*(1-sqrt(3)))/(2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt(2)*sqrt((d*(3*b*c+a*d)+4*b*d^2*x)^2)*sqrt(((b*c-a*d)^(4/3)-2*b^(1/3)*(b*c-a*d)^(2/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+4*b^(2/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(2/3))/(2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2)/(3^(1/4)*b^(2/3)*(b*c-a*d)^(7/3)*(c+d*x)^(1/3)*(b*c+a*d+2*b*d*x)^(1/3)*(3*b*c+a*d+4*b*d*x)*sqrt(d^2*(3*b*c+a*d+4*b*d*x)^2)*sqrt((b*c-a*d)^(2/3)*((b*c-a*d)^(2/3)+2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3))/(2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2))+3^(1/4)*d^2*((c+d*x)*(b*c+a*d+2*b*d*x))^(1/3)*((b*c-a*d)^(2/3)+2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3))*EllipticE((2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+(b*c-a*d)^(2/3)*(1-sqrt(3)))/(2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt((d*(3*b*c+a*d)+4*b*d^2*x)^2)*sqrt(2-sqrt(3))*sqrt(((b*c-a*d)^(4/3)-2*b^(1/3)*(b*c-a*d)^(2/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+4*b^(2/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(2/3))/(2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2)/(b^(2/3)*(b*c-a*d)^(7/3)*(c+d*x)^(1/3)*(b*c+a*d+2*b*d*x)^(1/3)*(3*b*c+a*d+4*b*d*x)*sqrt(d^2*(3*b*c+a*d+4*b*d*x)^2)*sqrt((b*c-a*d)^(2/3)*((b*c-a*d)^(2/3)+2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3))/(2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2))],
[(a+b*x)^3/((c+d*x)^(1/3)*(b*c+a*d+2*b*d*x)^(4/3)),x,7,3/14*(a+b*x)^2*(c+d*x)^(2/3)/(d^2*(b*c+a*d+2*b*d*x)^(1/3))+9/112*(b*c-a*d)*(c+d*x)^(2/3)*(b*c-7*a*d-6*b*d*x)/(d^4*(b*c+a*d+2*b*d*x)^(1/3))+81/112*(b*c-a*d)^2*((c+d*x)*(b*c+a*d+2*b*d*x))^(1/3)*sqrt(d^2*(3*b*c+a*d+4*b*d*x)^2)*sqrt((d*(3*b*c+a*d)+4*b*d^2*x)^2)/(b^(2/3)*d^6*(c+d*x)^(1/3)*(b*c+a*d+2*b*d*x)^(1/3)*(3*b*c+a*d+4*b*d*x)*(2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3))))+27/56*3^(3/4)*(b*c-a*d)^(8/3)*((c+d*x)*(b*c+a*d+2*b*d*x))^(1/3)*((b*c-a*d)^(2/3)+2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3))*EllipticF((2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+(b*c-a*d)^(2/3)*(1-sqrt(3)))/(2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt((d*(3*b*c+a*d)+4*b*d^2*x)^2)*sqrt(((b*c-a*d)^(4/3)-2*b^(1/3)*(b*c-a*d)^(2/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+4*b^(2/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(2/3))/(2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2)/(b^(2/3)*d^4*(c+d*x)^(1/3)*(b*c+a*d+2*b*d*x)^(1/3)*(3*b*c+a*d+4*b*d*x)*sqrt(2)*sqrt(d^2*(3*b*c+a*d+4*b*d*x)^2)*sqrt((b*c-a*d)^(2/3)*((b*c-a*d)^(2/3)+2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3))/(2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2))-81/224*3^(1/4)*(b*c-a*d)^(8/3)*((c+d*x)*(b*c+a*d+2*b*d*x))^(1/3)*((b*c-a*d)^(2/3)+2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3))*EllipticE((2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+(b*c-a*d)^(2/3)*(1-sqrt(3)))/(2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt((d*(3*b*c+a*d)+4*b*d^2*x)^2)*sqrt(2-sqrt(3))*sqrt(((b*c-a*d)^(4/3)-2*b^(1/3)*(b*c-a*d)^(2/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+4*b^(2/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(2/3))/(2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2)/(b^(2/3)*d^4*(c+d*x)^(1/3)*(b*c+a*d+2*b*d*x)^(1/3)*(3*b*c+a*d+4*b*d*x)*sqrt(d^2*(3*b*c+a*d+4*b*d*x)^2)*sqrt((b*c-a*d)^(2/3)*((b*c-a*d)^(2/3)+2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3))/(2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2))],
[(a+b*x)^2/((c+d*x)^(1/3)*(b*c+a*d+2*b*d*x)^(4/3)),x,7,-3/4*(b*c-a*d)*(c+d*x)^(2/3)/(d^3*(b*c+a*d+2*b*d*x)^(1/3))+3/16*(c+d*x)^(2/3)*(b*c+a*d+2*b*d*x)^(2/3)/d^3-9/16*(b*c-a*d)*((c+d*x)*(b*c+a*d+2*b*d*x))^(1/3)*sqrt(d^2*(3*b*c+a*d+4*b*d*x)^2)*sqrt((d*(3*b*c+a*d)+4*b*d^2*x)^2)/(b^(2/3)*d^5*(c+d*x)^(1/3)*(b*c+a*d+2*b*d*x)^(1/3)*(3*b*c+a*d+4*b*d*x)*(2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3))))-3/8*3^(3/4)*(b*c-a*d)^(5/3)*((c+d*x)*(b*c+a*d+2*b*d*x))^(1/3)*((b*c-a*d)^(2/3)+2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3))*EllipticF((2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+(b*c-a*d)^(2/3)*(1-sqrt(3)))/(2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt((d*(3*b*c+a*d)+4*b*d^2*x)^2)*sqrt(((b*c-a*d)^(4/3)-2*b^(1/3)*(b*c-a*d)^(2/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+4*b^(2/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(2/3))/(2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2)/(b^(2/3)*d^3*(c+d*x)^(1/3)*(b*c+a*d+2*b*d*x)^(1/3)*(3*b*c+a*d+4*b*d*x)*sqrt(2)*sqrt(d^2*(3*b*c+a*d+4*b*d*x)^2)*sqrt((b*c-a*d)^(2/3)*((b*c-a*d)^(2/3)+2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3))/(2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2))+9/32*3^(1/4)*(b*c-a*d)^(5/3)*((c+d*x)*(b*c+a*d+2*b*d*x))^(1/3)*((b*c-a*d)^(2/3)+2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3))*EllipticE((2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+(b*c-a*d)^(2/3)*(1-sqrt(3)))/(2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt((d*(3*b*c+a*d)+4*b*d^2*x)^2)*sqrt(2-sqrt(3))*sqrt(((b*c-a*d)^(4/3)-2*b^(1/3)*(b*c-a*d)^(2/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+4*b^(2/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(2/3))/(2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2)/(b^(2/3)*d^3*(c+d*x)^(1/3)*(b*c+a*d+2*b*d*x)^(1/3)*(3*b*c+a*d+4*b*d*x)*sqrt(d^2*(3*b*c+a*d+4*b*d*x)^2)*sqrt((b*c-a*d)^(2/3)*((b*c-a*d)^(2/3)+2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3))/(2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2))],
[(a+b*x)/((c+d*x)^(1/3)*(b*c+a*d+2*b*d*x)^(4/3)),x,1,3/2*(c+d*x)^(2/3)/(d^2*(b*c+a*d+2*b*d*x)^(1/3))],
[1/((c+d*x)^(1/3)*(b*c+a*d+2*b*d*x)^(4/3)),x,6,-3*(c+d*x)^(2/3)/(d*(b*c-a*d)*(b*c+a*d+2*b*d*x)^(1/3))+3/2*((c+d*x)*(b*c+a*d+2*b*d*x))^(1/3)*sqrt(d^2*(3*b*c+a*d+4*b*d*x)^2)*sqrt((d*(3*b*c+a*d)+4*b*d^2*x)^2)/(b^(2/3)*d^3*(b*c-a*d)*(c+d*x)^(1/3)*(b*c+a*d+2*b*d*x)^(1/3)*(3*b*c+a*d+4*b*d*x)*(2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3))))+3^(3/4)*((c+d*x)*(b*c+a*d+2*b*d*x))^(1/3)*((b*c-a*d)^(2/3)+2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3))*EllipticF((2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+(b*c-a*d)^(2/3)*(1-sqrt(3)))/(2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt((d*(3*b*c+a*d)+4*b*d^2*x)^2)*sqrt(((b*c-a*d)^(4/3)-2*b^(1/3)*(b*c-a*d)^(2/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+4*b^(2/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(2/3))/(2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2)/(b^(2/3)*d*(b*c-a*d)^(1/3)*(c+d*x)^(1/3)*(b*c+a*d+2*b*d*x)^(1/3)*(3*b*c+a*d+4*b*d*x)*sqrt(2)*sqrt(d^2*(3*b*c+a*d+4*b*d*x)^2)*sqrt((b*c-a*d)^(2/3)*((b*c-a*d)^(2/3)+2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3))/(2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2))-3/4*3^(1/4)*((c+d*x)*(b*c+a*d+2*b*d*x))^(1/3)*((b*c-a*d)^(2/3)+2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3))*EllipticE((2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+(b*c-a*d)^(2/3)*(1-sqrt(3)))/(2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3))),sqrt(-7-4*sqrt(3)))*sqrt((d*(3*b*c+a*d)+4*b*d^2*x)^2)*sqrt(2-sqrt(3))*sqrt(((b*c-a*d)^(4/3)-2*b^(1/3)*(b*c-a*d)^(2/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+4*b^(2/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(2/3))/(2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2)/(b^(2/3)*d*(b*c-a*d)^(1/3)*(c+d*x)^(1/3)*(b*c+a*d+2*b*d*x)^(1/3)*(3*b*c+a*d+4*b*d*x)*sqrt(d^2*(3*b*c+a*d+4*b*d*x)^2)*sqrt((b*c-a*d)^(2/3)*((b*c-a*d)^(2/3)+2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3))/(2*b^(1/3)*((c+d*x)*(a*d+b*(c+2*d*x)))^(1/3)+(b*c-a*d)^(2/3)*(1+sqrt(3)))^2))],
[1/((a+b*x)*(c+d*x)^(1/3)*(b*c+a*d+2*b*d*x)^(4/3)),x,2,3/2*(c+d*x)^(2/3)*((-b*c-a*d-2*b*d*x)/(b*c-a*d))^(1/3)*AppellF1(2/3,4/3,1,5/3,2*b*(c+d*x)/(b*c-a*d),b*(c+d*x)/(b*c-a*d))/((b*c-a*d)^2*(b*c+a*d+2*b*d*x)^(1/3))],
[1/((a+b*x)^2*(c+d*x)^(1/3)*(b*c+a*d+2*b*d*x)^(4/3)),x,2,-3/2*d*(c+d*x)^(2/3)*((-b*c-a*d-2*b*d*x)/(b*c-a*d))^(1/3)*AppellF1(2/3,4/3,2,5/3,2*b*(c+d*x)/(b*c-a*d),b*(c+d*x)/(b*c-a*d))/((b*c-a*d)^3*(b*c+a*d+2*b*d*x)^(1/3))],
[1/((a+b*x)^3*(c+d*x)^(1/3)*(b*c+a*d+2*b*d*x)^(4/3)),x,2,3/2*d^2*(c+d*x)^(2/3)*((-b*c-a*d-2*b*d*x)/(b*c-a*d))^(1/3)*AppellF1(2/3,4/3,3,5/3,2*b*(c+d*x)/(b*c-a*d),b*(c+d*x)/(b*c-a*d))/((b*c-a*d)^4*(b*c+a*d+2*b*d*x)^(1/3))],
[1/((d-3*e*x)^(1/3)*(d+e*x)*(d+3*e*x)^(1/3)),x,1,1/4*log(d+e*x)/(d^(2/3)*e)-3/8*log(-1/2*(d-3*e*x)^(2/3)/d^(1/3)-(d+3*e*x)^(1/3))/(d^(2/3)*e)+1/4*arctan(1/sqrt(3)-(d-3*e*x)^(2/3)/(d^(1/3)*(d+3*e*x)^(1/3)*sqrt(3)))*sqrt(3)/(d^(2/3)*e)],

# Integrands of the form (a+b x)^(4/3) (c+d x)^(n/3) (e+f x)^p

# n>0

# n<0
[(a+b*x)^(4/3)*(e+f*x)^2/(c+d*x)^(4/3),x,5,3*(d*e-c*f)^2*(a+b*x)^(7/3)/(d^2*(b*c-a*d)*(c+d*x)^(1/3))-4/27*(a^2*d^2*f^2-a*b*d*f*(9*d*e-7*c*f)-b^2*(27*d^2*e^2-63*c*d*e*f+35*c^2*f^2))*(a+b*x)^(1/3)*(c+d*x)^(2/3)/(b*d^4)+1/9*(a^2*d^2*f^2-a*b*d*f*(9*d*e-7*c*f)-b^2*(27*d^2*e^2-63*c*d*e*f+35*c^2*f^2))*(a+b*x)^(4/3)*(c+d*x)^(2/3)/(b*d^3*(b*c-a*d))+1/3*f^2*(a+b*x)^(7/3)*(c+d*x)^(2/3)/(b*d^2)-2/81*(b*c-a*d)*(a^2*d^2*f^2-a*b*d*f*(9*d*e-7*c*f)-b^2*(27*d^2*e^2-63*c*d*e*f+35*c^2*f^2))*log(a+b*x)/(b^(5/3)*d^(13/3))-2/27*(b*c-a*d)*(a^2*d^2*f^2-a*b*d*f*(9*d*e-7*c*f)-b^2*(27*d^2*e^2-63*c*d*e*f+35*c^2*f^2))*log(-1+b^(1/3)*(c+d*x)^(1/3)/(d^(1/3)*(a+b*x)^(1/3)))/(b^(5/3)*d^(13/3))-4/27*(b*c-a*d)*(a^2*d^2*f^2-a*b*d*f*(9*d*e-7*c*f)-b^2*(27*d^2*e^2-63*c*d*e*f+35*c^2*f^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^(5/3)*d^(13/3)*sqrt(3))],
[(a+b*x)^(4/3)*(e+f*x)/(c+d*x)^(4/3),x,4,3*(d*e-c*f)*(a+b*x)^(7/3)/(d*(b*c-a*d)*(c+d*x)^(1/3))+2/3*(6*b*d*e-7*b*c*f+a*d*f)*(a+b*x)^(1/3)*(c+d*x)^(2/3)/d^3-1/2*(6*b*d*e-7*b*c*f+a*d*f)*(a+b*x)^(4/3)*(c+d*x)^(2/3)/(d^2*(b*c-a*d))+1/9*(b*c-a*d)*(6*b*d*e-7*b*c*f+a*d*f)*log(a+b*x)/(b^(2/3)*d^(10/3))+1/3*(b*c-a*d)*(6*b*d*e-7*b*c*f+a*d*f)*log(-1+b^(1/3)*(c+d*x)^(1/3)/(d^(1/3)*(a+b*x)^(1/3)))/(b^(2/3)*d^(10/3))+2/3*(b*c-a*d)*(6*b*d*e-7*b*c*f+a*d*f)*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^(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)^(4/3)/((c+d*x)^(4/3)*(e+f*x)),x,4,3*(b*c-a*d)*(a+b*x)^(1/3)/(d*(d*e-c*f)*(c+d*x)^(1/3))-1/2*b^(4/3)*log(a+b*x)/(d^(4/3)*f)-1/2*(b*e-a*f)^(4/3)*log(e+f*x)/(f*(d*e-c*f)^(4/3))+3/2*(b*e-a*f)^(4/3)*log(-(a+b*x)^(1/3)+(b*e-a*f)^(1/3)*(c+d*x)^(1/3)/(d*e-c*f)^(1/3))/(f*(d*e-c*f)^(4/3))-3/2*b^(4/3)*log(-1+b^(1/3)*(c+d*x)^(1/3)/(d^(1/3)*(a+b*x)^(1/3)))/(d^(4/3)*f)-b^(4/3)*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)*f)+(b*e-a*f)^(4/3)*arctan(1/sqrt(3)+2*(b*e-a*f)^(1/3)*(c+d*x)^(1/3)/((d*e-c*f)^(1/3)*(a+b*x)^(1/3)*sqrt(3)))*sqrt(3)/(f*(d*e-c*f)^(4/3))],
[(a+b*x)^(4/3)/((c+d*x)^(4/3)*(e+f*x)^2),x,3,-3*(a+b*x)^(4/3)/((d*e-c*f)*(c+d*x)^(1/3)*(e+f*x))+4*(b*e-a*f)*(a+b*x)^(1/3)*(c+d*x)^(2/3)/((d*e-c*f)^2*(e+f*x))-2/3*(b*c-a*d)*(b*e-a*f)^(1/3)*log(e+f*x)/(d*e-c*f)^(7/3)+2*(b*c-a*d)*(b*e-a*f)^(1/3)*log(-(a+b*x)^(1/3)+(b*e-a*f)^(1/3)*(c+d*x)^(1/3)/(d*e-c*f)^(1/3))/(d*e-c*f)^(7/3)+4*(b*c-a*d)*(b*e-a*f)^(1/3)*arctan(1/sqrt(3)+2*(b*e-a*f)^(1/3)*(c+d*x)^(1/3)/((d*e-c*f)^(1/3)*(a+b*x)^(1/3)*sqrt(3)))/((d*e-c*f)^(7/3)*sqrt(3))],
[(a+b*x)^(4/3)/((c+d*x)^(4/3)*(e+f*x)^3),x,4,3*d*(a+b*x)^(7/3)/((b*c-a*d)*(d*e-c*f)*(c+d*x)^(1/3)*(e+f*x)^2)-1/2*(6*b*d*e+b*c*f-7*a*d*f)*(a+b*x)^(4/3)*(c+d*x)^(2/3)/((b*c-a*d)*(d*e-c*f)^2*(e+f*x)^2)+2/3*(6*b*d*e+b*c*f-7*a*d*f)*(a+b*x)^(1/3)*(c+d*x)^(2/3)/((d*e-c*f)^3*(e+f*x))-1/9*(b*c-a*d)*(6*b*d*e+b*c*f-7*a*d*f)*log(e+f*x)/((b*e-a*f)^(2/3)*(d*e-c*f)^(10/3))+1/3*(b*c-a*d)*(6*b*d*e+b*c*f-7*a*d*f)*log(-(a+b*x)^(1/3)+(b*e-a*f)^(1/3)*(c+d*x)^(1/3)/(d*e-c*f)^(1/3))/((b*e-a*f)^(2/3)*(d*e-c*f)^(10/3))+2/3*(b*c-a*d)*(6*b*d*e+b*c*f-7*a*d*f)*arctan(1/sqrt(3)+2*(b*e-a*f)^(1/3)*(c+d*x)^(1/3)/((d*e-c*f)^(1/3)*(a+b*x)^(1/3)*sqrt(3)))/((b*e-a*f)^(2/3)*(d*e-c*f)^(10/3)*sqrt(3))],
[(a+b*x)^(4/3)/((c+d*x)^(4/3)*(e+f*x)^4),x,6,3*(b*c-a*d)*(a+b*x)^(1/3)/(d*(d*e-c*f)*(c+d*x)^(1/3)*(e+f*x)^3)+1/3*(b*d*e+9*b*c*f-10*a*d*f)*(a+b*x)^(1/3)*(c+d*x)^(2/3)/(d*(d*e-c*f)^2*(e+f*x)^3)+1/9*(3*b*d*e+32*b*c*f-35*a*d*f)*(a+b*x)^(1/3)*(c+d*x)^(2/3)/((d*e-c*f)^3*(e+f*x)^2)+1/27*(140*a^2*d^2*f^2-7*a*b*d*f*(21*d*e+19*c*f)+b^2*(9*d^2*e^2+129*c*d*e*f+2*c^2*f^2))*(a+b*x)^(1/3)*(c+d*x)^(2/3)/((b*e-a*f)*(d*e-c*f)^4*(e+f*x))-2/81*(b*c-a*d)*(35*a^2*d^2*f^2-7*a*b*d*f*(9*d*e+c*f)+b^2*(27*d^2*e^2+9*c*d*e*f-c^2*f^2))*log(e+f*x)/((b*e-a*f)^(5/3)*(d*e-c*f)^(13/3))+2/27*(b*c-a*d)*(35*a^2*d^2*f^2-7*a*b*d*f*(9*d*e+c*f)+b^2*(27*d^2*e^2+9*c*d*e*f-c^2*f^2))*log(-(a+b*x)^(1/3)+(b*e-a*f)^(1/3)*(c+d*x)^(1/3)/(d*e-c*f)^(1/3))/((b*e-a*f)^(5/3)*(d*e-c*f)^(13/3))+4/27*(b*c-a*d)*(35*a^2*d^2*f^2-7*a*b*d*f*(9*d*e+c*f)+b^2*(27*d^2*e^2+9*c*d*e*f-c^2*f^2))*arctan(1/sqrt(3)+2*(b*e-a*f)^(1/3)*(c+d*x)^(1/3)/((d*e-c*f)^(1/3)*(a+b*x)^(1/3)*sqrt(3)))/((b*e-a*f)^(5/3)*(d*e-c*f)^(13/3)*sqrt(3))],

# Integrands of the form (a+b x)^m (c+d x)^(n/2) (e+f x)^(p/4)
[1/((a+b*x)*(e+f*x)^(1/4)*sqrt(c+d*x)),x,5,2*(d*e-c*f)^(1/4)*EllipticPi(d^(1/4)*(e+f*x)^(1/4)/(d*e-c*f)^(1/4),-sqrt(b)*sqrt(d*e-c*f)/(sqrt(d)*sqrt(b*e-a*f)),I)*sqrt(-f*(c+d*x)/(d*e-c*f))/(d^(1/4)*sqrt(b)*sqrt(b*e-a*f)*sqrt(c+d*x))-2*(d*e-c*f)^(1/4)*EllipticPi(d^(1/4)*(e+f*x)^(1/4)/(d*e-c*f)^(1/4),sqrt(b)*sqrt(d*e-c*f)/(sqrt(d)*sqrt(b*e-a*f)),I)*sqrt(-f*(c+d*x)/(d*e-c*f))/(d^(1/4)*sqrt(b)*sqrt(b*e-a*f)*sqrt(c+d*x))],
[1/((a+b*x)*(e+f*x)^(3/4)*sqrt(c+d*x)),x,5,-2*(d*e-c*f)^(1/4)*EllipticPi(d^(1/4)*(e+f*x)^(1/4)/(d*e-c*f)^(1/4),-sqrt(b)*sqrt(d*e-c*f)/(sqrt(d)*sqrt(b*e-a*f)),I)*sqrt(-f*(c+d*x)/(d*e-c*f))/(d^(1/4)*(b*e-a*f)*sqrt(c+d*x))-2*(d*e-c*f)^(1/4)*EllipticPi(d^(1/4)*(e+f*x)^(1/4)/(d*e-c*f)^(1/4),sqrt(b)*sqrt(d*e-c*f)/(sqrt(d)*sqrt(b*e-a*f)),I)*sqrt(-f*(c+d*x)/(d*e-c*f))/(d^(1/4)*(b*e-a*f)*sqrt(c+d*x))],

# Integrands of the form (a+b x)^m (c+d x)^n (e+f x)^p with m, n and/or p symbolic

# Integrands of the form (a+b x)^m (A+B x) (d+e x)^p
[(a+b*x)^p*(A+B*x)*(d+e*x)^(-2-p),x,3,-(B*d-A*e)*(a+b*x)^(1+p)*(d+e*x)^(-1-p)/(e*(b*d-a*e)*(1+p))-B*(a+b*x)^p*hypergeom([-p,-p],[1-p],b*(d+e*x)/(b*d-a*e))/(e^2*p*(-e*(a+b*x)/(b*d-a*e))^p*(d+e*x)^p)],
[(a+b*x)*(c+d*x)^n/(e+f*x)^n,x,3,1/2*b*(c+d*x)^(1+n)*(e+f*x)^(1-n)/(d*f)+1/2*(2*a*d*f-b*(c*f*(1-n)+d*e*(1+n)))*(c+d*x)^(1+n)*(d*(e+f*x)/(d*e-c*f))^n*hypergeom([n,1+n],[2+n],-f*(c+d*x)/(d*e-c*f))/(d^2*f*(1+n)*(e+f*x)^n)],
[(a+b*x)*(c+d*x)^(-1+n)/(e+f*x)^n,x,3,-(b*c-a*d)*(c+d*x)^n*(e+f*x)^(1-n)/(d*(d*e-c*f)*n)-(a*d*f-b*(c*f*(1-n)+d*e*n))*(c+d*x)^(1+n)*(d*(e+f*x)/(d*e-c*f))^n*hypergeom([n,1+n],[2+n],-f*(c+d*x)/(d*e-c*f))/(d^2*(d*e-c*f)*n*(1+n)*(e+f*x)^n)],
[(a+b*x)*(c+d*x)^(-2+n)/(e+f*x)^n,x,3,(b*c-a*d)*(c+d*x)^(-1+n)*(e+f*x)^(1-n)/(d*(d*e-c*f)*(1-n))+b*(c+d*x)^n*(d*(e+f*x)/(d*e-c*f))^n*hypergeom([n,n],[1+n],-f*(c+d*x)/(d*e-c*f))/(d^2*n*(e+f*x)^n)],
[(a+b*x)*(c+d*x)^(-3+n)/(e+f*x)^n,x,2,(b*c-a*d)*(c+d*x)^(-2+n)*(e+f*x)^(1-n)/(d*(d*e-c*f)*(2-n))+(a*d*f+b*(c*f*(1-n)-d*e*(2-n)))*(c+d*x)^(-1+n)*(e+f*x)^(1-n)/(d*(d*e-c*f)^2*(1-n)*(2-n))],
[(a+b*x)*(c+d*x)^(-4+n)/(e+f*x)^n,x,3,(b*c-a*d)*(c+d*x)^(-3+n)*(e+f*x)^(1-n)/(d*(d*e-c*f)*(3-n))+(2*a*d*f+b*(c*f*(1-n)-d*e*(3-n)))*(c+d*x)^(-2+n)*(e+f*x)^(1-n)/(d*(d*e-c*f)^2*(2-n)*(3-n))-f*(2*a*d*f+b*(c*f*(1-n)-d*e*(3-n)))*(c+d*x)^(-1+n)*(e+f*x)^(1-n)/(d*(d*e-c*f)^3*(1-n)*(2-n)*(3-n))],
[(a+b*x)*(c+d*x)^(-5+n)/(e+f*x)^n,x,4,(b*c-a*d)*(c+d*x)^(-4+n)*(e+f*x)^(1-n)/(d*(d*e-c*f)*(4-n))+(3*a*d*f+b*(c*f*(1-n)-d*e*(4-n)))*(c+d*x)^(-3+n)*(e+f*x)^(1-n)/(d*(d*e-c*f)^2*(3-n)*(4-n))-2*f*(3*a*d*f+b*(c*f*(1-n)-d*e*(4-n)))*(c+d*x)^(-2+n)*(e+f*x)^(1-n)/(d*(d*e-c*f)^3*(2-n)*(3-n)*(4-n))+2*f^2*(3*a*d*f+b*(c*f*(1-n)-d*e*(4-n)))*(c+d*x)^(-1+n)*(e+f*x)^(1-n)/(d*(d*e-c*f)^4*(1-n)*(2-n)*(3-n)*(4-n))],
[(c+d*x)*(e+f*x)^n/(a+b*x)^n,x,3,1/2*d*(a+b*x)^(1-n)*(e+f*x)^(1+n)/(b*f)+1/2*(b*(2*c*f-d*e*(1-n))-a*d*f*(1+n))*(-f*(a+b*x)/(b*e-a*f))^n*(e+f*x)^(1+n)*hypergeom([n,1+n],[2+n],b*(e+f*x)/(b*e-a*f))/(b*f^2*(1+n)*(a+b*x)^n)],
[(c+d*x)*(e+f*x)^(-1+n)/(a+b*x)^n,x,3,(d*e-c*f)*(a+b*x)^(1-n)*(e+f*x)^n/(f*(b*e-a*f)*n)+(b*(c*f-d*e*(1-n))-a*d*f*n)*(-f*(a+b*x)/(b*e-a*f))^n*(e+f*x)^(1+n)*hypergeom([n,1+n],[2+n],b*(e+f*x)/(b*e-a*f))/(f^2*(b*e-a*f)*n*(1+n)*(a+b*x)^n)],
[(c+d*x)*(e+f*x)^(-2+n)/(a+b*x)^n,x,3,-(d*e-c*f)*(a+b*x)^(1-n)*(e+f*x)^(-1+n)/(f*(b*e-a*f)*(1-n))+d*(-f*(a+b*x)/(b*e-a*f))^n*(e+f*x)^n*hypergeom([n,n],[1+n],b*(e+f*x)/(b*e-a*f))/(f^2*n*(a+b*x)^n)],
[(c+d*x)*(e+f*x)^(-3+n)/(a+b*x)^n,x,2,-(d*e-c*f)*(a+b*x)^(1-n)*(e+f*x)^(-2+n)/(f*(b*e-a*f)*(2-n))-(a*d*f*(2-n)-b*(c*f+d*(e-e*n)))*(a+b*x)^(1-n)*(e+f*x)^(-1+n)/(f*(b*e-a*f)^2*(1-n)*(2-n))],
[(c+d*x)*(e+f*x)^(-4+n)/(a+b*x)^n,x,3,-(d*e-c*f)*(a+b*x)^(1-n)*(e+f*x)^(-3+n)/(f*(b*e-a*f)*(3-n))+(b*(2*c*f+d*e*(1-n))-a*d*f*(3-n))*(a+b*x)^(1-n)*(e+f*x)^(-2+n)/(f*(b*e-a*f)^2*(2-n)*(3-n))+b*(b*(2*c*f+d*e*(1-n))-a*d*f*(3-n))*(a+b*x)^(1-n)*(e+f*x)^(-1+n)/(f*(b*e-a*f)^3*(1-n)*(2-n)*(3-n))],
[(c+d*x)*(e+f*x)^(-5+n)/(a+b*x)^n,x,4,-(d*e-c*f)*(a+b*x)^(1-n)*(e+f*x)^(-4+n)/(f*(b*e-a*f)*(4-n))+(b*(3*c*f+d*e*(1-n))-a*d*f*(4-n))*(a+b*x)^(1-n)*(e+f*x)^(-3+n)/(f*(b*e-a*f)^2*(3-n)*(4-n))+2*b*(b*(3*c*f+d*e*(1-n))-a*d*f*(4-n))*(a+b*x)^(1-n)*(e+f*x)^(-2+n)/(f*(b*e-a*f)^3*(2-n)*(3-n)*(4-n))+2*b^2*(b*(3*c*f+d*e*(1-n))-a*d*f*(4-n))*(a+b*x)^(1-n)*(e+f*x)^(-1+n)/(f*(b*e-a*f)^4*(1-n)*(2-n)*(3-n)*(4-n))],

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

# n=0
[(a+b*x)^m*(e+f*x)^p/(c+d*x)^m,x,3,(a+b*x)^(1+m)*(b*(c+d*x)/(b*c-a*d))^m*(e+f*x)^p*AppellF1(1+m,m,-p,2+m,-d*(a+b*x)/(b*c-a*d),-f*(a+b*x)/(b*e-a*f))/(b*(1+m)*(c+d*x)^m*(b*(e+f*x)/(b*e-a*f))^p)],
[(5-4*x)^4*(2+3*x)^m/(1+2*x)^m,x,4,-1/45*(88-m)*(5-4*x)^2*(1+2*x)^(1-m)*(2+3*x)^(1+m)-2/15*(5-4*x)^3*(1+2*x)^(1-m)*(2+3*x)^(1+m)-1/1215*(1+2*x)^(1-m)*(2+3*x)^(1+m)*(386850-25441*m+426*m^2-2*m^3-24*(4359-154*m+m^2)*x)+1/1215*2^(-1-m)*(3528363-639760*m+29050*m^2-440*m^3+2*m^4)*(1+2*x)^(1-m)*hypergeom([1-m,-m],[2-m],-3*(1+2*x))/(1-m)],
[(a+b*x)^m*(e+f*x)^3/(c+d*x)^m,x,4,1/4*f*(a+b*x)^(1+m)*(c+d*x)^(1-m)*(e+f*x)^2/(b*d)+1/24*f*(a+b*x)^(1+m)*(c+d*x)^(1-m)*(a^2*d^2*f^2*(6-5*m+m^2)-2*a*b*d*f*(6*d*e*(2-m)-c*f*(3-m^2))+b^2*(30*d^2*e^2-12*c*d*e*f*(2+m)+c^2*f^2*(6+5*m+m^2))-2*b*d*f*(a*d*f*(3-m)-b*(6*d*e-c*f*(3+m)))*x)/(b^3*d^3)-1/24*(a^3*d^3*f^3*(6-11*m+6*m^2-m^3)-3*a^2*b*d^2*f^2*(2-3*m+m^2)*(4*d*e-c*f*(1+m))+3*a*b^2*d*f*(1-m)*(12*d^2*e^2-8*c*d*e*f*(1+m)+c^2*f^2*(2+3*m+m^2))-b^3*(24*d^3*e^3-36*c*d^2*e^2*f*(1+m)+12*c^2*d*e*f^2*(2+3*m+m^2)-c^3*f^3*(6+11*m+6*m^2+m^3)))*(a+b*x)^(1+m)*(b*(c+d*x)/(b*c-a*d))^m*hypergeom([m,1+m],[2+m],-d*(a+b*x)/(b*c-a*d))/(b^4*d^3*(1+m)*(c+d*x)^m)],
[(a+b*x)^m*(e+f*x)^2/(c+d*x)^m,x,4,-1/6*f*(a*d*f*(2-m)-b*(4*d*e-c*f*(2+m)))*(a+b*x)^(1+m)*(c+d*x)^(1-m)/(b^2*d^2)+1/3*f*(a+b*x)^(1+m)*(c+d*x)^(1-m)*(e+f*x)/(b*d)+1/6*(a^2*d^2*f^2*(2-3*m+m^2)-2*a*b*d*f*(1-m)*(3*d*e-c*f*(1+m))+b^2*(6*d^2*e^2-6*c*d*e*f*(1+m)+c^2*f^2*(2+3*m+m^2)))*(a+b*x)^(1+m)*(b*(c+d*x)/(b*c-a*d))^m*hypergeom([m,1+m],[2+m],-d*(a+b*x)/(b*c-a*d))/(b^3*d^2*(1+m)*(c+d*x)^m)],
[(a+b*x)^m*(e+f*x)/(c+d*x)^m,x,3,1/2*f*(a+b*x)^(1+m)*(c+d*x)^(1-m)/(b*d)-1/2*(a*d*f*(1-m)-b*(2*d*e-c*f*(1+m)))*(a+b*x)^(1+m)*(b*(c+d*x)/(b*c-a*d))^m*hypergeom([m,1+m],[2+m],-d*(a+b*x)/(b*c-a*d))/(b^2*d*(1+m)*(c+d*x)^m)],
[(a+b*x)^m/(c+d*x)^m,x,2,(a+b*x)^(1+m)*(b*(c+d*x)/(b*c-a*d))^m*hypergeom([m,1+m],[2+m],-d*(a+b*x)/(b*c-a*d))/(b*(1+m)*(c+d*x)^m)],
[(a+b*x)^m/((c+d*x)^m*(e+f*x)),x,5,-(a+b*x)^m*hypergeom([1,m],[1+m],(d*e-c*f)*(a+b*x)/((b*e-a*f)*(c+d*x)))/(f*m*(c+d*x)^m)+(a+b*x)^m*(b*(c+d*x)/(b*c-a*d))^m*hypergeom([m,m],[1+m],-d*(a+b*x)/(b*c-a*d))/(f*m*(c+d*x)^m)],
[(a+b*x)^m/((c+d*x)^m*(e+f*x)^2),x,1,(b*c-a*d)*(a+b*x)^(1+m)*(c+d*x)^(-1-m)*hypergeom([2,1+m],[2+m],(d*e-c*f)*(a+b*x)/((b*e-a*f)*(c+d*x)))/((b*e-a*f)^2*(1+m))],
[(a+b*x)^m/((c+d*x)^m*(e+f*x)^3),x,2,-1/2*f*(a+b*x)^(1+m)*(c+d*x)^(1-m)/((b*e-a*f)*(d*e-c*f)*(e+f*x)^2)+1/2*(b*c-a*d)*(b*(2*d*e-c*f*(1-m))-a*d*f*(1+m))*(a+b*x)^(1+m)*(c+d*x)^(-1-m)*hypergeom([2,1+m],[2+m],(d*e-c*f)*(a+b*x)/((b*e-a*f)*(c+d*x)))/((b*e-a*f)^3*(d*e-c*f)*(1+m))],
[(a+b*x)^m/((c+d*x)^m*(e+f*x)^4),x,4,-1/3*f*(a+b*x)^(1+m)*(c+d*x)^(1-m)/((b*e-a*f)*(d*e-c*f)*(e+f*x)^3)-1/6*f*(b*(4*d*e-c*f*(2-m))-a*d*f*(2+m))*(a+b*x)^(1+m)*(c+d*x)^(1-m)/((b*e-a*f)^2*(d*e-c*f)^2*(e+f*x)^2)-1/6*(b*c-a*d)*(2*a*b*d*f*(3*d*e-c*f*(1-m))*(1+m)-a^2*d^2*f^2*(2+3*m+m^2)-b^2*(6*d^2*e^2-6*c*d*e*f*(1-m)+c^2*f^2*(2-3*m+m^2)))*(a+b*x)^(1+m)*(c+d*x)^(-1-m)*hypergeom([2,1+m],[2+m],(d*e-c*f)*(a+b*x)/((b*e-a*f)*(c+d*x)))/((b*e-a*f)^4*(d*e-c*f)^2*(1+m))],
[(2+3*x)^m/((5-4*x)^5*(1+2*x)^m),x,5,1/322*(1+2*x)^(1-m)*(2+3*x)^(1+m)/(5-4*x)^4+1/77763*(66+m)*(1+2*x)^(1-m)*(2+3*x)^(1+m)/(5-4*x)^3+1/25039686*(4359+220*m+2*m^2)*(1+2*x)^(1-m)*(2+3*x)^(1+m)/(5-4*x)^2+1/2453889228*(32010+4358*m+132*m^2+m^3)*(1+2*x)^(1-m)*(2+3*x)^(-1+m)*hypergeom([2,1-m],[2-m],23/14*(1+2*x)/(2+3*x))/(1-m)],

# n>0
[(a+b*x)^m*(c+d*x)^(-1-m)*(e+f*x)^p,x,3,(a+b*x)^(1+m)*(b*(c+d*x)/(b*c-a*d))^m*(e+f*x)^p*AppellF1(1+m,1+m,-p,2+m,-d*(a+b*x)/(b*c-a*d),-f*(a+b*x)/(b*e-a*f))/((b*c-a*d)*(1+m)*(c+d*x)^m*(b*(e+f*x)/(b*e-a*f))^p)],
[(5-4*x)^3*(1+2*x)^(-1-m)*(2+3*x)^m,x,3,-2/9*(5-4*x)^2*(2+3*x)^(1+m)/(1+2*x)^m-1/27*(2+3*x)^(1+m)*(9261-512*m+4*m^2-4*(109-2*m)*m*x)/(m*(1+2*x)^m)+1/27*2^(-1-m)*(27783-8324*m+390*m^2-4*m^3)*(1+2*x)^(1-m)*hypergeom([1-m,-m],[2-m],-3*(1+2*x))/((1-m)*m)],
[(5-4*x)^2*(1+2*x)^(-1-m)*(2+3*x)^m,x,3,-7/3*(21-m)*(2+3*x)^(1+m)/(m*(1+2*x)^m)-1/3*(5-4*x)*(2+3*x)^(1+m)/(1+2*x)^m+1/3*2^(-1-m)*(441-86*m+2*m^2)*(1+2*x)^(1-m)*hypergeom([1-m,-m],[2-m],-3*(1+2*x))/((1-m)*m)],
[(a+b*x)^m*(c+d*x)^(-1-m)*(e+f*x),x,3,(d*e-c*f)*(a+b*x)^(1+m)/(d*(b*c-a*d)*m*(c+d*x)^m)-(a*d*f*m+b*(d*e-c*f*(1+m)))*(a+b*x)^(1+m)*(b*(c+d*x)/(b*c-a*d))^m*hypergeom([m,1+m],[2+m],-d*(a+b*x)/(b*c-a*d))/(b*d*(b*c-a*d)*m*(1+m)*(c+d*x)^m)],
[(a+b*x)^m*(c+d*x)^(-1-m),x,2,-(a+b*x)^m*hypergeom([-m,-m],[1-m],b*(c+d*x)/(b*c-a*d))/(d*m*(-d*(a+b*x)/(b*c-a*d))^m*(c+d*x)^m)],
[(a+b*x)^m*(c+d*x)^(-1-m)/(e+f*x),x,1,-(a+b*x)^m*hypergeom([1,-m],[1-m],(b*e-a*f)*(c+d*x)/((d*e-c*f)*(a+b*x)))/((d*e-c*f)*m*(c+d*x)^m)],
[(a+b*x)^m*(c+d*x)^(-1-m)/(e+f*x)^2,x,2,d*(a+b*x)^(1+m)/((b*c-a*d)*(d*e-c*f)*m*(c+d*x)^m*(e+f*x))+(a*d*f*(1+m)-b*(d*e+c*f*m))*(a+b*x)^(1+m)*(c+d*x)^(-1-m)*hypergeom([2,1+m],[2+m],(d*e-c*f)*(a+b*x)/((b*e-a*f)*(c+d*x)))/((b*e-a*f)^2*(d*e-c*f)*m*(1+m))],
[(a+b*x)^m*(c+d*x)^(-1-m)/(e+f*x)^3,x,4,-1/2*f*(a+b*x)^(1+m)/((b*e-a*f)*(d*e-c*f)*(c+d*x)^m*(e+f*x)^2)-1/2*f*(b*(3*d*e-c*f*(1-m))-a*d*f*(2+m))*(a+b*x)^(1+m)/((b*e-a*f)^2*(d*e-c*f)^2*(c+d*x)^m*(e+f*x))+1/2*(2*a*b*d*f*(1+m)*(2*d*e+c*f*m)-b^2*(2*d^2*e^2+4*c*d*e*f*m-c^2*f^2*(1-m)*m)-a^2*d^2*f^2*(2+3*m+m^2))*(a+b*x)^m*hypergeom([1,-m],[1-m],(b*e-a*f)*(c+d*x)/((d*e-c*f)*(a+b*x)))/((b*e-a*f)^2*(d*e-c*f)^3*m*(c+d*x)^m)],
[(a+b*x)^m*(c+d*x)^(-1-m)/(e+f*x)^4,x,5,-1/3*f*(a+b*x)^(1+m)/((b*e-a*f)*(d*e-c*f)*(c+d*x)^m*(e+f*x)^3)-1/6*f*(b*(5*d*e-c*f*(2-m))-a*d*f*(3+m))*(a+b*x)^(1+m)/((b*e-a*f)^2*(d*e-c*f)^2*(c+d*x)^m*(e+f*x)^2)-1/6*f*(a^2*d^2*f^2*(6+5*m+m^2)-a*b*d*f*(d*e*(15+8*m)-c*f*(3-2*m-2*m^2))+b^2*(11*d^2*e^2-c*d*e*f*(7-8*m)+c^2*f^2*(2-3*m+m^2)))*(a+b*x)^(1+m)/((b*e-a*f)^3*(d*e-c*f)^3*(c+d*x)^m*(e+f*x))+1/6*(3*a*b^2*d*f*(1+m)*(6*d^2*e^2+6*c*d*e*f*m-c^2*f^2*(1-m)*m)-3*a^2*b*d^2*f^2*(3*d*e+c*f*m)*(2+3*m+m^2)+a^3*d^3*f^3*(6+11*m+6*m^2+m^3)-b^3*(6*d^3*e^3+18*c*d^2*e^2*f*m-9*c^2*d*e*f^2*(1-m)*m+c^3*f^3*m*(2-3*m+m^2)))*(a+b*x)^m*hypergeom([1,-m],[1-m],(b*e-a*f)*(c+d*x)/((d*e-c*f)*(a+b*x)))/((b*e-a*f)^3*(d*e-c*f)^4*m*(c+d*x)^m)],
[(a+b*x)^m*(c+d*x)^(-2-m)*(e+f*x)^p,x,3,b*(a+b*x)^(1+m)*(b*(c+d*x)/(b*c-a*d))^m*(e+f*x)^p*AppellF1(1+m,2+m,-p,2+m,-d*(a+b*x)/(b*c-a*d),-f*(a+b*x)/(b*e-a*f))/((b*c-a*d)^2*(1+m)*(c+d*x)^m*(b*(e+f*x)/(b*e-a*f))^p)],
[(5-4*x)^3*(1+2*x)^(-2-m)*(2+3*x)^m,x,3,-1/3*(5-4*x)^2*(1+2*x)^(-1-m)*(2+3*x)^(1+m)-1/9*(1+2*x)^(-1-m)*(2+3*x)^(1+m)*(2768-315*m+4*m^2-8*(43-m)*(1+m)*x)/(1+m)+1/9*(1323-128*m+2*m^2)*hypergeom([-m,-m],[1-m],-3*(1+2*x))/(2^m*m*(1+2*x)^m)],
[(a+b*x)^m*(c+d*x)^(-2-m)*(e+f*x)^2,x,4,(d*e-c*f)*(a*d*f*(1+m)+b*(d*e-c*f*(2+m)))*(a+b*x)^(1+m)*(c+d*x)^(-1-m)/(b*d^2*(b*c-a*d)*(1+m))+f*(a+b*x)^(1+m)*(c+d*x)^(-1-m)*(e+f*x)/(b*d)-f*(a*d*f*m+b*(2*d*e-c*f*(2+m)))*(a+b*x)^m*hypergeom([-m,-m],[1-m],b*(c+d*x)/(b*c-a*d))/(b*d^3*m*(-d*(a+b*x)/(b*c-a*d))^m*(c+d*x)^m)],
[(a+b*x)^m*(c+d*x)^(-2-m)*(e+f*x),x,3,(d*e-c*f)*(a+b*x)^(1+m)*(c+d*x)^(-1-m)/(d*(b*c-a*d)*(1+m))-f*(a+b*x)^m*hypergeom([-m,-m],[1-m],b*(c+d*x)/(b*c-a*d))/(d^2*m*(-d*(a+b*x)/(b*c-a*d))^m*(c+d*x)^m)],
[(a+b*x)^m*(c+d*x)^(-2-m),x,1,(a+b*x)^(1+m)*(c+d*x)^(-1-m)/((b*c-a*d)*(1+m))],
[(a+b*x)^m*(c+d*x)^(-2-m)/(e+f*x),x,2,d*(a+b*x)^(1+m)*(c+d*x)^(-1-m)/((b*c-a*d)*(d*e-c*f)*(1+m))+f*(a+b*x)^m*hypergeom([1,-m],[1-m],(b*e-a*f)*(c+d*x)/((d*e-c*f)*(a+b*x)))/((d*e-c*f)^2*m*(c+d*x)^m)],
[(a+b*x)^m*(c+d*x)^(-2-m)/(e+f*x)^2,x,4,-d*(a*d*f*(2+m)-b*(d*e+c*f*(1+m)))*(a+b*x)^(1+m)*(c+d*x)^(-1-m)/((b*c-a*d)*(b*e-a*f)*(d*e-c*f)^2*(1+m))-f*(a+b*x)^(1+m)*(c+d*x)^(-1-m)/((b*e-a*f)*(d*e-c*f)*(e+f*x))-f*(a*d*f*(2+m)-b*(2*d*e+c*f*m))*(a+b*x)^m*hypergeom([1,-m],[1-m],(b*e-a*f)*(c+d*x)/((d*e-c*f)*(a+b*x)))/((b*e-a*f)*(d*e-c*f)^3*m*(c+d*x)^m)],
[(a+b*x)^m*(c+d*x)^(-2-m)/(e+f*x)^3,x,5,1/2*d*(a^2*d^2*f^2*(6+5*m+m^2)+b^2*(2*d^2*e^2+5*c*d*e*f*(1+m)-c^2*f^2*(1-m^2))-a*b*d*f*(d*e*(9+5*m)+c*f*(3+5*m+2*m^2)))*(a+b*x)^(1+m)*(c+d*x)^(-1-m)/((b*c-a*d)*(b*e-a*f)^2*(d*e-c*f)^3*(1+m))-1/2*f*(a+b*x)^(1+m)*(c+d*x)^(-1-m)/((b*e-a*f)*(d*e-c*f)*(e+f*x)^2)-1/2*f*(b*(4*d*e-c*f*(1-m))-a*d*f*(3+m))*(a+b*x)^(1+m)*(c+d*x)^(-1-m)/((b*e-a*f)^2*(d*e-c*f)^2*(e+f*x))-1/2*f*(2*a*b*d*f*(2+m)*(3*d*e+c*f*m)-b^2*(6*d^2*e^2+6*c*d*e*f*m-c^2*f^2*(1-m)*m)-a^2*d^2*f^2*(6+5*m+m^2))*(a+b*x)^m*hypergeom([1,-m],[1-m],(b*e-a*f)*(c+d*x)/((d*e-c*f)*(a+b*x)))/((b*e-a*f)^2*(d*e-c*f)^4*m*(c+d*x)^m)],
[(a+b*x)^m*(c+d*x)^(-3-m)*(e+f*x)^p,x,3,b^2*(a+b*x)^(1+m)*(b*(c+d*x)/(b*c-a*d))^m*(e+f*x)^p*AppellF1(1+m,3+m,-p,2+m,-d*(a+b*x)/(b*c-a*d),-f*(a+b*x)/(b*e-a*f))/((b*c-a*d)^3*(1+m)*(c+d*x)^m*(b*(e+f*x)/(b*e-a*f))^p)],
[(5-4*x)^4*(1+2*x)^(-3-m)*(2+3*x)^m,x,4,-1/9*(107-2*m)*(5-4*x)^2*(1+2*x)^(-2-m)*(2+3*x)^(1+m)-1/3*(5-4*x)^3*(1+2*x)^(-2-m)*(2+3*x)^(1+m)+7/9*(1+2*x)^(-2-m)*(2+3*x)^(1+m)*(3*(4638+485*m+108*m^2-2*m^3)+2*(15209+1882*m-530*m^2+8*m^3)*x)/(2+3*m+m^2)-1/9*2^(2-m)*(1323-85*m+m^2)*hypergeom([-m,-m],[1-m],-3*(1+2*x))/(m*(1+2*x)^m)],
[(5-4*x)^3*(1+2*x)^(-3-m)*(2+3*x)^m,x,3,-2/3*(5-4*x)^2*(1+2*x)^(-2-m)*(2+3*x)^(1+m)+7/3*(1+2*x)^(-2-m)*(2+3*x)^(1+m)*(3*(186-m+2*m^2)+2*(677+102*m-8*m^2)*x)/(2+3*m+m^2)-1/3*2^(1-m)*(63-2*m)*hypergeom([-m,-m],[1-m],-3*(1+2*x))/(m*(1+2*x)^m)],
[(a+b*x)^m*(c+d*x)^(-3-m)*(e+f*x)^2,x,4,(d*e-c*f)^2*(a+b*x)^(1+m)*(c+d*x)^(-2-m)/(d^2*(b*c-a*d)*(2+m))-(d*e-c*f)*(2*a*d*f*(2+m)-b*(d*e+c*f*(3+2*m)))*(a+b*x)^(1+m)*(c+d*x)^(-1-m)/(d^2*(b*c-a*d)^2*(1+m)*(2+m))-f^2*(a+b*x)^m*hypergeom([-m,-m],[1-m],b*(c+d*x)/(b*c-a*d))/(d^3*m*(-d*(a+b*x)/(b*c-a*d))^m*(c+d*x)^m)],
[(a+b*x)^m*(c+d*x)^(-3-m)*(e+f*x),x,2,(d*e-c*f)*(a+b*x)^(1+m)*(c+d*x)^(-2-m)/(d*(b*c-a*d)*(2+m))-(a*d*f*(2+m)-b*(d*e+c*f*(1+m)))*(a+b*x)^(1+m)*(c+d*x)^(-1-m)/(d*(b*c-a*d)^2*(1+m)*(2+m))],
[(a+b*x)^m*(c+d*x)^(-3-m),x,2,(a+b*x)^(1+m)*(c+d*x)^(-2-m)/((b*c-a*d)*(2+m))+b*(a+b*x)^(1+m)*(c+d*x)^(-1-m)/((b*c-a*d)^2*(1+m)*(2+m))],
[(a+b*x)^m*(c+d*x)^(-3-m)/(e+f*x),x,4,d*(a+b*x)^(1+m)*(c+d*x)^(-2-m)/((b*c-a*d)*(d*e-c*f)*(2+m))+d*(a*d*f*(2+m)+b*(d*e-c*f*(3+m)))*(a+b*x)^(1+m)*(c+d*x)^(-1-m)/((b*c-a*d)^2*(d*e-c*f)^2*(1+m)*(2+m))-f^2*(a+b*x)^m*hypergeom([1,-m],[1-m],(b*e-a*f)*(c+d*x)/((d*e-c*f)*(a+b*x)))/((d*e-c*f)^3*m*(c+d*x)^m)],
[(a+b*x)^m*(c+d*x)^(-3-m)/(e+f*x)^2,x,5,-d*(a*d*f*(3+m)-b*(d*e+c*f*(2+m)))*(a+b*x)^(1+m)*(c+d*x)^(-2-m)/((b*c-a*d)*(b*e-a*f)*(d*e-c*f)^2*(2+m))-d*(a^2*d^2*f^2*(6+5*m+m^2)-b^2*(d^2*e^2-c*d*e*f*(5+2*m)-c^2*f^2*(2+3*m+m^2))-a*b*d*f*(d*e*(3+2*m)+c*f*(9+8*m+2*m^2)))*(a+b*x)^(1+m)*(c+d*x)^(-1-m)/((b*c-a*d)^2*(b*e-a*f)*(d*e-c*f)^3*(1+m)*(2+m))-f*(a+b*x)^(1+m)*(c+d*x)^(-2-m)/((b*e-a*f)*(d*e-c*f)*(e+f*x))+f^2*(a*d*f*(3+m)-b*(3*d*e+c*f*m))*(a+b*x)^m*hypergeom([1,-m],[1-m],(b*e-a*f)*(c+d*x)/((d*e-c*f)*(a+b*x)))/((b*e-a*f)*(d*e-c*f)^4*m*(c+d*x)^m)],
[(a+b*x)^m*(c+d*x)^(-4-m)*(e+f*x)^p,x,3,b^3*(a+b*x)^(1+m)*(b*(c+d*x)/(b*c-a*d))^m*(e+f*x)^p*AppellF1(1+m,4+m,-p,2+m,-d*(a+b*x)/(b*c-a*d),-f*(a+b*x)/(b*e-a*f))/((b*c-a*d)^4*(1+m)*(c+d*x)^m*(b*(e+f*x)/(b*e-a*f))^p)],
[(5-4*x)^4*(1+2*x)^(-4-m)*(2+3*x)^m,x,9,-49/9*(15-2*m)*(27+2*m)*(1+2*x)^(-3-m)*(2+3*x)^(1+m)/(3+m)+14/9*(15-2*m)*(5-4*x)*(1+2*x)^(-3-m)*(2+3*x)^(1+m)-2/3*(5-4*x)^3*(1+2*x)^(-3-m)*(2+3*x)^(1+m)+196/3*(42-m)*(1+2*x)^(-2-m)*(2+3*x)^(1+m)/(2+m)+14/9*(15-2*m)*(579+52*m+2*m^2)*(1+2*x)^(-2-m)*(2+3*x)^(1+m)/(6+5*m+m^2)-28/3*(42-m)*(29+4*m)*(1+2*x)^(-1-m)*(2+3*x)^(1+m)/(2+3*m+m^2)-14/3*(15-2*m)*(579+52*m+2*m^2)*(1+2*x)^(-1-m)*(2+3*x)^(1+m)/(6+11*m+6*m^2+m^3)+1/3*2^(3-m)*(42-m)*hypergeom([-m,-m],[1-m],-3*(1+2*x))/(m*(1+2*x)^m)],
[(a+b*x)^m*(c+d*x)^(-4-m)*(e+f*x)^3,x,10,(d*e-c*f)^3*(a+b*x)^(1+m)*(c+d*x)^(-3-m)/(d^3*(b*c-a*d)*(3+m))+3*f*(d*e-c*f)^2*(a+b*x)^(1+m)*(c+d*x)^(-2-m)/(d^3*(b*c-a*d)*(2+m))+2*b*(d*e-c*f)^3*(a+b*x)^(1+m)*(c+d*x)^(-2-m)/(d^3*(b*c-a*d)^2*(2+m)*(3+m))+3*f^2*(d*e-c*f)*(a+b*x)^(1+m)*(c+d*x)^(-1-m)/(d^3*(b*c-a*d)*(1+m))+3*b*f*(d*e-c*f)^2*(a+b*x)^(1+m)*(c+d*x)^(-1-m)/(d^3*(b*c-a*d)^2*(1+m)*(2+m))+2*b^2*(d*e-c*f)^3*(a+b*x)^(1+m)*(c+d*x)^(-1-m)/(d^3*(b*c-a*d)^3*(1+m)*(2+m)*(3+m))-f^3*(a+b*x)^m*hypergeom([-m,-m],[1-m],b*(c+d*x)/(b*c-a*d))/(d^4*m*(-d*(a+b*x)/(b*c-a*d))^m*(c+d*x)^m)],
[(a+b*x)^m*(c+d*x)^(-4-m)*(e+f*x)^2,x,4,-(d*e-c*f)*(a*d*f*(3+m)-b*(d*e+c*f*(2+m)))*(a+b*x)^(1+m)*(c+d*x)^(-3-m)/(b*d^2*(b*c-a*d)*(3+m))+(a^2*d^2*f^2*(6+5*m+m^2)-2*a*b*d*f*(3+m)*(d*e+c*f*(1+m))+b^2*(2*d^2*e^2+2*c*d*e*f*(1+m)+c^2*f^2*(2+3*m+m^2)))*(a+b*x)^(1+m)*(c+d*x)^(-2-m)/(b*d^2*(b*c-a*d)^2*(2+m)*(3+m))+(a^2*d^2*f^2*(6+5*m+m^2)-2*a*b*d*f*(3+m)*(d*e+c*f*(1+m))+b^2*(2*d^2*e^2+2*c*d*e*f*(1+m)+c^2*f^2*(2+3*m+m^2)))*(a+b*x)^(1+m)*(c+d*x)^(-1-m)/(d^2*(b*c-a*d)^3*(1+m)*(2+m)*(3+m))-f*(a+b*x)^(1+m)*(c+d*x)^(-3-m)*(e+f*x)/(b*d)],
[(a+b*x)^m*(c+d*x)^(-4-m)*(e+f*x),x,3,(d*e-c*f)*(a+b*x)^(1+m)*(c+d*x)^(-3-m)/(d*(b*c-a*d)*(3+m))-(a*d*f*(3+m)-b*(2*d*e+c*f*(1+m)))*(a+b*x)^(1+m)*(c+d*x)^(-2-m)/(d*(b*c-a*d)^2*(2+m)*(3+m))-b*(a*d*f*(3+m)-b*(2*d*e+c*f*(1+m)))*(a+b*x)^(1+m)*(c+d*x)^(-1-m)/(d*(b*c-a*d)^3*(1+m)*(2+m)*(3+m))],
[(a+b*x)^m*(c+d*x)^(-4-m),x,3,(a+b*x)^(1+m)*(c+d*x)^(-3-m)/((b*c-a*d)*(3+m))+2*b*(a+b*x)^(1+m)*(c+d*x)^(-2-m)/((b*c-a*d)^2*(2+m)*(3+m))+2*b^2*(a+b*x)^(1+m)*(c+d*x)^(-1-m)/((b*c-a*d)^3*(1+m)*(2+m)*(3+m))],
[(a+b*x)^m*(c+d*x)^(-4-m)/(e+f*x),x,5,d*(a+b*x)^(1+m)*(c+d*x)^(-3-m)/((b*c-a*d)*(d*e-c*f)*(3+m))+d*(a*d*f*(3+m)+b*(2*d*e-c*f*(5+m)))*(a+b*x)^(1+m)*(c+d*x)^(-2-m)/((b*c-a*d)^2*(d*e-c*f)^2*(2+m)*(3+m))+d*(a^2*d^2*f^2*(6+5*m+m^2)+a*b*d*f*(3+m)*(d*e-c*f*(5+2*m))+b^2*(2*d^2*e^2-c*d*e*f*(7+m)+c^2*f^2*(11+6*m+m^2)))*(a+b*x)^(1+m)*(c+d*x)^(-1-m)/((b*c-a*d)^3*(d*e-c*f)^3*(1+m)*(2+m)*(3+m))+f^3*(a+b*x)^m*hypergeom([1,-m],[1-m],(b*e-a*f)*(c+d*x)/((d*e-c*f)*(a+b*x)))/((d*e-c*f)^4*m*(c+d*x)^m)],
[(a+b*x)^m*(c+d*x)^(-4-m)/(e+f*x)^2,x,6,-d*(a*d*f*(4+m)-b*(d*e+c*f*(3+m)))*(a+b*x)^(1+m)*(c+d*x)^(-3-m)/((b*c-a*d)*(b*e-a*f)*(d*e-c*f)^2*(3+m))-d*(a^2*d^2*f^2*(12+7*m+m^2)-b^2*(2*d^2*e^2-2*c*d*e*f*(4+m)-c^2*f^2*(6+5*m+m^2))-2*a*b*d*f*(d*e*(2+m)+c*f*(10+6*m+m^2)))*(a+b*x)^(1+m)*(c+d*x)^(-2-m)/((b*c-a*d)^2*(b*e-a*f)*(d*e-c*f)^3*(2+m)*(3+m))-d*(a^3*d^3*f^3*(24+26*m+9*m^2+m^3)-a^2*b*d^2*f^2*(3+m)*(d*e*(4+3*m)+c*f*(20+15*m+3*m^2))-b^3*(2*d^3*e^3-2*c*d^2*e^2*f*(5+m)+c^2*d*e*f^2*(26+17*m+3*m^2)+c^3*f^3*(6+11*m+6*m^2+m^3))-a*b^2*d*f*(2*d^2*e^2*(2+m)-2*c*d*e*f*(16+15*m+3*m^2)-c^2*f^2*(44+50*m+21*m^2+3*m^3)))*(a+b*x)^(1+m)*(c+d*x)^(-1-m)/((b*c-a*d)^3*(b*e-a*f)*(d*e-c*f)^4*(1+m)*(2+m)*(3+m))-f*(a+b*x)^(1+m)*(c+d*x)^(-3-m)/((b*e-a*f)*(d*e-c*f)*(e+f*x))-f^3*(a*d*f*(4+m)-b*(4*d*e+c*f*m))*(a+b*x)^m*hypergeom([1,-m],[1-m],(b*e-a*f)*(c+d*x)/((d*e-c*f)*(a+b*x)))/((b*e-a*f)*(d*e-c*f)^5*m*(c+d*x)^m)],
[(a+b*x)^m*(c+d*x)^(-5-m)*(e+f*x)^p,x,3,b^4*(a+b*x)^(1+m)*(b*(c+d*x)/(b*c-a*d))^m*(e+f*x)^p*AppellF1(1+m,5+m,-p,2+m,-d*(a+b*x)/(b*c-a*d),-f*(a+b*x)/(b*e-a*f))/((b*c-a*d)^5*(1+m)*(c+d*x)^m*(b*(e+f*x)/(b*e-a*f))^p)],
[(5-4*x)^5*(1+2*x)^(-5-m)*(2+3*x)^m,x,16,-7/3*(13-2*m)*(5-4*x)^3*(1+2*x)^(-4-m)*(2+3*x)^(1+m)/(4+m)-2/3*(5-4*x)^4*(1+2*x)^(-4-m)*(2+3*x)^(1+m)+24334/81*(105-2*m)*(1+2*x)^(-3-m)*(2+3*x)^(1+m)/(3+m)+1127/3*(13-2*m)*(27+2*m)*(1+2*x)^(-3-m)*(2+3*x)^(1+m)/(12+7*m+m^2)-322/3*(13-2*m)*(5-4*x)*(1+2*x)^(-3-m)*(2+3*x)^(1+m)/(4+m)-48668/27*(105-2*m)*(1+2*x)^(-2-m)*(2+3*x)^(1+m)/(6+5*m+m^2)-322/3*(13-2*m)*(579+52*m+2*m^2)*(1+2*x)^(-2-m)*(2+3*x)^(1+m)/(24+26*m+9*m^2+m^3)+48668/9*(105-2*m)*(1+2*x)^(-1-m)*(2+3*x)^(1+m)/(6+11*m+6*m^2+m^3)+322*(13-2*m)*(579+52*m+2*m^2)*(1+2*x)^(-1-m)*(2+3*x)^(1+m)/(24+50*m+35*m^2+10*m^3+m^4)-4232/27*(105-2*m)*(1+2*x)^(-3-m)*(2+3*x)^(2+m)/(3+m)+4232/9*(105-2*m)*(1+2*x)^(-2-m)*(2+3*x)^(2+m)/(6+5*m+m^2)+736/27*(105-2*m)*(1+2*x)^(-3-m)*(2+3*x)^(3+m)/(3+m)-1/81*2^(3-m)*(105-2*m)*(1+2*x)^(-3-m)*hypergeom([-3-m,-3-m],[-2-m],-3*(1+2*x))/(3+m)],
[(a+b*x)^m*(c+d*x)^(-5-m)*(e+f*x)^4,x,14,(d*e-c*f)^4*(a+b*x)^(1+m)*(c+d*x)^(-4-m)/(d^4*(b*c-a*d)*(4+m))+4*f*(d*e-c*f)^3*(a+b*x)^(1+m)*(c+d*x)^(-3-m)/(d^4*(b*c-a*d)*(3+m))+3*b*(d*e-c*f)^4*(a+b*x)^(1+m)*(c+d*x)^(-3-m)/(d^4*(b*c-a*d)^2*(3+m)*(4+m))+6*f^2*(d*e-c*f)^2*(a+b*x)^(1+m)*(c+d*x)^(-2-m)/(d^4*(b*c-a*d)*(2+m))+8*b*f*(d*e-c*f)^3*(a+b*x)^(1+m)*(c+d*x)^(-2-m)/(d^4*(b*c-a*d)^2*(2+m)*(3+m))+6*b^2*(d*e-c*f)^4*(a+b*x)^(1+m)*(c+d*x)^(-2-m)/(d^4*(b*c-a*d)^3*(2+m)*(3+m)*(4+m))+4*f^3*(d*e-c*f)*(a+b*x)^(1+m)*(c+d*x)^(-1-m)/(d^4*(b*c-a*d)*(1+m))+6*b*f^2*(d*e-c*f)^2*(a+b*x)^(1+m)*(c+d*x)^(-1-m)/(d^4*(b*c-a*d)^2*(1+m)*(2+m))+8*b^2*f*(d*e-c*f)^3*(a+b*x)^(1+m)*(c+d*x)^(-1-m)/(d^4*(b*c-a*d)^3*(1+m)*(2+m)*(3+m))+6*b^3*(d*e-c*f)^4*(a+b*x)^(1+m)*(c+d*x)^(-1-m)/(d^4*(b*c-a*d)^4*(1+m)*(2+m)*(3+m)*(4+m))-f^4*(a+b*x)^m*hypergeom([-m,-m],[1-m],b*(c+d*x)/(b*c-a*d))/(d^5*m*(-d*(a+b*x)/(b*c-a*d))^m*(c+d*x)^m)],
[(a+b*x)^m*(c+d*x)^(-5-m)*(e+f*x)^3,x,5,-3*(b*e-a*f)*(d*e-c*f)*(a*d*f*(3+m)-b*(d*e+c*f*(2+m)))*(a+b*x)^(1+m)*(c+d*x)^(-3-m)/(b*d^2*(b*c-a*d)^2*(3+m)*(4+m))+3*(b*e-a*f)*(a^2*d^2*f^2*(6+5*m+m^2)-2*a*b*d*f*(3+m)*(d*e+c*f*(1+m))+b^2*(2*d^2*e^2+2*c*d*e*f*(1+m)+c^2*f^2*(2+3*m+m^2)))*(a+b*x)^(1+m)*(c+d*x)^(-2-m)/(b*d^2*(b*c-a*d)^3*(2+m)*(3+m)*(4+m))+3*(b*e-a*f)*(a^2*d^2*f^2*(6+5*m+m^2)-2*a*b*d*f*(3+m)*(d*e+c*f*(1+m))+b^2*(2*d^2*e^2+2*c*d*e*f*(1+m)+c^2*f^2*(2+3*m+m^2)))*(a+b*x)^(1+m)*(c+d*x)^(-1-m)/(d^2*(b*c-a*d)^4*(1+m)*(2+m)*(3+m)*(4+m))-3*f*(b*e-a*f)*(a+b*x)^(1+m)*(c+d*x)^(-3-m)*(e+f*x)/(b*d*(b*c-a*d)*(4+m))+(a+b*x)^(1+m)*(c+d*x)^(-4-m)*(e+f*x)^3/((b*c-a*d)*(4+m))],
[(a+b*x)^m*(c+d*x)^(-5-m)*(e+f*x)^2,x,5,-1/2*(d*e-c*f)*(a*d*f*(4+m)-b*(2*d*e+c*f*(2+m)))*(a+b*x)^(1+m)*(c+d*x)^(-4-m)/(b*d^2*(b*c-a*d)*(4+m))+1/2*(a^2*d^2*f^2*(12+7*m+m^2)-2*a*b*d*f*(4+m)*(2*d*e+c*f*(1+m))+b^2*(6*d^2*e^2+4*c*d*e*f*(1+m)+c^2*f^2*(2+3*m+m^2)))*(a+b*x)^(1+m)*(c+d*x)^(-3-m)/(b*d^2*(b*c-a*d)^2*(3+m)*(4+m))+(a^2*d^2*f^2*(12+7*m+m^2)-2*a*b*d*f*(4+m)*(2*d*e+c*f*(1+m))+b^2*(6*d^2*e^2+4*c*d*e*f*(1+m)+c^2*f^2*(2+3*m+m^2)))*(a+b*x)^(1+m)*(c+d*x)^(-2-m)/(d^2*(b*c-a*d)^3*(2+m)*(3+m)*(4+m))+b*(a^2*d^2*f^2*(12+7*m+m^2)-2*a*b*d*f*(4+m)*(2*d*e+c*f*(1+m))+b^2*(6*d^2*e^2+4*c*d*e*f*(1+m)+c^2*f^2*(2+3*m+m^2)))*(a+b*x)^(1+m)*(c+d*x)^(-1-m)/(d^2*(b*c-a*d)^4*(1+m)*(2+m)*(3+m)*(4+m))-1/2*f*(a+b*x)^(1+m)*(c+d*x)^(-4-m)*(e+f*x)/(b*d)],
[(a+b*x)^m*(c+d*x)^(-5-m)*(e+f*x),x,4,(d*e-c*f)*(a+b*x)^(1+m)*(c+d*x)^(-4-m)/(d*(b*c-a*d)*(4+m))-(a*d*f*(4+m)-b*(3*d*e+c*f*(1+m)))*(a+b*x)^(1+m)*(c+d*x)^(-3-m)/(d*(b*c-a*d)^2*(3+m)*(4+m))-2*b*(a*d*f*(4+m)-b*(3*d*e+c*f*(1+m)))*(a+b*x)^(1+m)*(c+d*x)^(-2-m)/(d*(b*c-a*d)^3*(2+m)*(3+m)*(4+m))-2*b^2*(a*d*f*(4+m)-b*(3*d*e+c*f*(1+m)))*(a+b*x)^(1+m)*(c+d*x)^(-1-m)/(d*(b*c-a*d)^4*(1+m)*(2+m)*(3+m)*(4+m))],
[(a+b*x)^m*(c+d*x)^(-5-m),x,4,(a+b*x)^(1+m)*(c+d*x)^(-4-m)/((b*c-a*d)*(4+m))+3*b*(a+b*x)^(1+m)*(c+d*x)^(-3-m)/((b*c-a*d)^2*(3+m)*(4+m))+6*b^2*(a+b*x)^(1+m)*(c+d*x)^(-2-m)/((b*c-a*d)^3*(2+m)*(3+m)*(4+m))+6*b^3*(a+b*x)^(1+m)*(c+d*x)^(-1-m)/((b*c-a*d)^4*(1+m)*(2+m)*(3+m)*(4+m))],
[(a+b*x)^m*(c+d*x)^(-5-m)/(e+f*x),x,6,d*(a+b*x)^(1+m)*(c+d*x)^(-4-m)/((b*c-a*d)*(d*e-c*f)*(4+m))+d*(a*d*f*(4+m)+b*(3*d*e-c*f*(7+m)))*(a+b*x)^(1+m)*(c+d*x)^(-3-m)/((b*c-a*d)^2*(d*e-c*f)^2*(3+m)*(4+m))+d*(a^2*d^2*f^2*(12+7*m+m^2)+2*a*b*d*f*(4+m)*(d*e-c*f*(4+m))+b^2*(6*d^2*e^2-2*c*d*e*f*(10+m)+c^2*f^2*(26+9*m+m^2)))*(a+b*x)^(1+m)*(c+d*x)^(-2-m)/((b*c-a*d)^3*(d*e-c*f)^3*(2+m)*(3+m)*(4+m))+d*(a^3*d^3*f^3*(24+26*m+9*m^2+m^3)+a^2*b*d^2*f^2*(12+7*m+m^2)*(d*e-c*f*(7+3*m))+a*b^2*d*f*(4+m)*(2*d^2*e^2-2*c*d*e*f*(5+m)+c^2*f^2*(26+17*m+3*m^2))+b^3*(6*d^3*e^3-2*c*d^2*e^2*f*(13+m)+c^2*d*e*f^2*(46+11*m+m^2)-c^3*f^3*(50+35*m+10*m^2+m^3)))*(a+b*x)^(1+m)*(c+d*x)^(-1-m)/((b*c-a*d)^4*(d*e-c*f)^4*(1+m)*(2+m)*(3+m)*(4+m))-f^4*(a+b*x)^m*hypergeom([1,-m],[1-m],(b*e-a*f)*(c+d*x)/((d*e-c*f)*(a+b*x)))/((d*e-c*f)^5*m*(c+d*x)^m)],

#  {(a + b*x)^m/(c + d*x)^(m + 5)/(e + f*x)^2, x, 7, -((d*(a*d*f*(5 + m) - b*(d*e + c*f*(4 + m)))*(a + b*x)^(1 + m)*(c + d*x)^(-4 - m))/((b*c - a*d)*(b*e - a*f)*(d*e - c*f)^2*(4 + m))) - (d*(a^2*d^2*f^2*(20 + 9*m + m^2) - b^2*(3*d^2*e^2 - c*d*e*f*(11 + 2*m) - c^2*f^2*(12 + 7*m + m^2)) - a*b*d*f*(d*e*(5 + 2*m) + c*f*(35 + 16*m + 2*m^2)))*(a + b*x)^(1 + m)*(c + d*x)^(-3 - m))/((b*c - a*d)^2*(b*e - a*f)*(d*e - c*f)^3*(3 + m)*(4 + m)) - (d*(a^3*d^3*f^3*(60 + 47*m + 12*m^2 + m^3) - a^2*b*d^2*f^2*(4 + m)*(d*e*(5 + 3*m) + c*f*(40 + 21*m + 3*m^2)) - b^3*(6*d^3*e^3 - 4*c*d^2*e^2*f*(7 + m) + c^2*d*e*f^2*(58 + 25*m + 3*m^2) + c^3*f^3*(24 + 26*m + 9*m^2 + m^3)) - a*b^2*d*f*(2*d^2*e^2*(5 + 2*m) - 6*c*d*e*f*(10 + 7*m + m^2) - c^2*f^2*(130 + 103*m + 30*m^2 + 3*m^3)))*(a + b*x)^(1 + m)*(c + d*x)^(-2 - m))/((b*c - a*d)^3*(b*e - a*f)*(d*e - c*f)^4*(2 + m)*(3 + m)*(4 + m)) - (d*(a^4*d^4*f^4*(120 + 154*m + 71*m^2 + 14*m^3 + m^4) - a^3*b*d^3*f^3*(12 + 7*m + m^2)*(d*e*(5 + 4*m) + c*f*(35 + 24*m + 4*m^2)) - a^2*b^2*d^2*f^2*(4 + m)*(d^2*e^2*(5 + 3*m) - c*d*e*f*(55 + 57*m + 12*m^2) - 2*c^2*f^2*(65 + 66*m + 24*m^2 + 3*m^3)) - b^4*(6*d^4*e^4 - 2*c*d^3*e^3*f*(17 + 2*m) + c^2*d^2*e^2*f^2*(86 + 29*m + 3*m^2) - c^3*d*e*f^3*(154 + 129*m + 39*m^2 + 4*m^3) - c^4*f^4*(24 + 50*m + 35*m^2 + 10*m^3 + m^4)) - a*b^3*d*f*(2*d^3*e^3*(5 + 2*m) - 2*c*d^2*e^2*f*(35 + 23*m + 3*m^2) + c^2*d*e*f^2*(290 + 329*m + 111*m^2 + 12*m^3) + c^3*f^3*(250 + 329*m + 179*m^2 + 44*m^3 + 4*m^4)))*(a + b*x)^(1 + m)*(c + d*x)^(-1 - m))/((b*c - a*d)^4*(b*e - a*f)*(d*e - c*f)^5*(1 + m)*(2 + m)*(3 + m)*(4 + m)) - (f*(a + b*x)^(1 + m)*(c + d*x)^(-4 - m))/((b*e - a*f)*(d*e - c*f)*(e + f*x)) + (f^4*(a*d*f*(5 + m) - b*(5*d*e + c*f*m))*(a + b*x)^m*Hypergeometric2F1[1, -m, 1 - m, ((b*e - a*f)*(c + d*x))/((d*e - c*f)*(a + b*x))])/((c + d*x)^m*((b*e - a*f)*(d*e - c*f)^6*m))} 

# n<0
[(a+b*x)^m*(c+d*x)^(1-m)*(e+f*x)^p,x,3,(b*c-a*d)*(a+b*x)^(1+m)*(b*(c+d*x)/(b*c-a*d))^m*(e+f*x)^p*AppellF1(1+m,-1+m,-p,2+m,-d*(a+b*x)/(b*c-a*d),-f*(a+b*x)/(b*e-a*f))/(b^2*(1+m)*(c+d*x)^m*(b*(e+f*x)/(b*e-a*f))^p)],
[(a+b*x)^m*(c+d*x)^(1-m)*(e+f*x)^3,x,4,1/5*f*(a+b*x)^(1+m)*(c+d*x)^(2-m)*(e+f*x)^2/(b*d)+1/60*f*(a+b*x)^(1+m)*(c+d*x)^(2-m)*(a^2*d^2*f^2*(12-7*m+m^2)-a*b*d*f*(15*d*e*(3-m)-c*f*(9+2*m-2*m^2))+b^2*(48*d^2*e^2-15*c*d*e*f*(2+m)+c^2*f^2*(6+5*m+m^2))-3*b*d*f*(a*d*f*(4-m)-b*(7*d*e-c*f*(3+m)))*x)/(b^3*d^3)-1/60*(b*c-a*d)*(a^3*d^3*f^3*(24-26*m+9*m^2-m^3)-3*a^2*b*d^2*f^2*(6-5*m+m^2)*(5*d*e-c*f*(1+m))+3*a*b^2*d*f*(2-m)*(20*d^2*e^2-10*c*d*e*f*(1+m)+c^2*f^2*(2+3*m+m^2))-b^3*(60*d^3*e^3-60*c*d^2*e^2*f*(1+m)+15*c^2*d*e*f^2*(2+3*m+m^2)-c^3*f^3*(6+11*m+6*m^2+m^3)))*(a+b*x)^(1+m)*(b*(c+d*x)/(b*c-a*d))^m*hypergeom([-1+m,1+m],[2+m],-d*(a+b*x)/(b*c-a*d))/(b^5*d^3*(1+m)*(c+d*x)^m)],
[(a+b*x)^m*(c+d*x)^(1-m)*(e+f*x)^2,x,4,-1/12*f*(a*d*f*(3-m)-b*(5*d*e-c*f*(2+m)))*(a+b*x)^(1+m)*(c+d*x)^(2-m)/(b^2*d^2)+1/4*f*(a+b*x)^(1+m)*(c+d*x)^(2-m)*(e+f*x)/(b*d)+1/12*(b*c-a*d)*(a^2*d^2*f^2*(6-5*m+m^2)-2*a*b*d*f*(2-m)*(4*d*e-c*f*(1+m))+b^2*(12*d^2*e^2-8*c*d*e*f*(1+m)+c^2*f^2*(2+3*m+m^2)))*(a+b*x)^(1+m)*(b*(c+d*x)/(b*c-a*d))^m*hypergeom([-1+m,1+m],[2+m],-d*(a+b*x)/(b*c-a*d))/(b^4*d^2*(1+m)*(c+d*x)^m)],
[(a+b*x)^m*(c+d*x)^(1-m)*(e+f*x),x,3,1/3*f*(a+b*x)^(1+m)*(c+d*x)^(2-m)/(b*d)-1/3*(b*c-a*d)*(a*d*f*(2-m)-b*(3*d*e-c*f*(1+m)))*(a+b*x)^(1+m)*(b*(c+d*x)/(b*c-a*d))^m*hypergeom([-1+m,1+m],[2+m],-d*(a+b*x)/(b*c-a*d))/(b^3*d*(1+m)*(c+d*x)^m)],
[(a+b*x)^m*(c+d*x)^(1-m),x,2,(b*c-a*d)*(a+b*x)^(1+m)*(b*(c+d*x)/(b*c-a*d))^m*hypergeom([-1+m,1+m],[2+m],-d*(a+b*x)/(b*c-a*d))/(b^2*(1+m)*(c+d*x)^m)],
[(a+b*x)^m*(c+d*x)^(1-m)/(e+f*x),x,6,-d*(d*e-c*f)*(a+b*x)^(1+m)/((b*c-a*d)*f^2*m*(c+d*x)^m)-(d*e-c*f)*(a+b*x)^m*hypergeom([1,-m],[1-m],(b*e-a*f)*(c+d*x)/((d*e-c*f)*(a+b*x)))/(f^2*m*(c+d*x)^m)+d*(b*(d*e-c*f*(1-m))-a*d*f*m)*(a+b*x)^(1+m)*(b*(c+d*x)/(b*c-a*d))^m*hypergeom([m,1+m],[2+m],-d*(a+b*x)/(b*c-a*d))/(b*(b*c-a*d)*f^2*m*(1+m)*(c+d*x)^m)],
[(a+b*x)^m*(c+d*x)^(1-m)/(e+f*x)^2,x,6,-(a+b*x)^m*(c+d*x)^(1-m)/(f*(e+f*x))+(a*d*f*(1-m)-b*(d*e-c*f*m))*(a+b*x)^m*hypergeom([1,m],[1+m],(d*e-c*f)*(a+b*x)/((b*e-a*f)*(c+d*x)))/(f^2*(b*e-a*f)*m*(c+d*x)^m)+d*(a+b*x)^m*(b*(c+d*x)/(b*c-a*d))^m*hypergeom([m,m],[1+m],-d*(a+b*x)/(b*c-a*d))/(f^2*m*(c+d*x)^m)],
[(a+b*x)^m*(c+d*x)^(1-m)/(e+f*x)^3,x,1,(b*c-a*d)^2*(a+b*x)^(1+m)*(c+d*x)^(-1-m)*hypergeom([3,1+m],[2+m],(d*e-c*f)*(a+b*x)/((b*e-a*f)*(c+d*x)))/((b*e-a*f)^3*(1+m))],
[(a+b*x)^m*(c+d*x)^(1-m)/(e+f*x)^4,x,2,-1/3*f*(a+b*x)^(1+m)*(c+d*x)^(2-m)/((b*e-a*f)*(d*e-c*f)*(e+f*x)^3)+1/3*(b*c-a*d)^2*(b*(3*d*e-c*f*(2-m))-a*d*f*(1+m))*(a+b*x)^(1+m)*(c+d*x)^(-1-m)*hypergeom([3,1+m],[2+m],(d*e-c*f)*(a+b*x)/((b*e-a*f)*(c+d*x)))/((b*e-a*f)^4*(d*e-c*f)*(1+m))],
[(a+b*x)^m*(c+d*x)^(1-m)/(e+f*x)^5,x,4,-1/4*f*(a+b*x)^(1+m)*(c+d*x)^(2-m)/((b*e-a*f)*(d*e-c*f)*(e+f*x)^4)-1/12*f*(b*(5*d*e-c*f*(3-m))-a*d*f*(2+m))*(a+b*x)^(1+m)*(c+d*x)^(2-m)/((b*e-a*f)^2*(d*e-c*f)^2*(e+f*x)^3)-1/12*(b*c-a*d)^2*(2*a*b*d*f*(4*d*e-c*f*(2-m))*(1+m)-a^2*d^2*f^2*(2+3*m+m^2)-b^2*(12*d^2*e^2-8*c*d*e*f*(2-m)+c^2*f^2*(6-5*m+m^2)))*(a+b*x)^(1+m)*(c+d*x)^(-1-m)*hypergeom([3,1+m],[2+m],(d*e-c*f)*(a+b*x)/((b*e-a*f)*(c+d*x)))/((b*e-a*f)^5*(d*e-c*f)^2*(1+m))],
[(a+b*x)^m*(c+d*x)^(1-m)/(e+f*x)^6,x,5,-1/5*f*(a+b*x)^(1+m)*(c+d*x)^(2-m)/((b*e-a*f)*(d*e-c*f)*(e+f*x)^5)-1/20*f*(b*(7*d*e-c*f*(4-m))-a*d*f*(3+m))*(a+b*x)^(1+m)*(c+d*x)^(2-m)/((b*e-a*f)^2*(d*e-c*f)^2*(e+f*x)^4)-1/60*f*(a^2*d^2*f^2*(6+5*m+m^2)-a*b*d*f*(3*d*e*(7+4*m)-c*f*(9+2*m-2*m^2))+b^2*(27*d^2*e^2-3*c*d*e*f*(11-4*m)+c^2*f^2*(12-7*m+m^2)))*(a+b*x)^(1+m)*(c+d*x)^(2-m)/((b*e-a*f)^3*(d*e-c*f)^3*(e+f*x)^3)+1/60*(b*c-a*d)^2*(3*a^2*b*d^2*f^2*(5*d*e-c*f*(2-m))*(2+3*m+m^2)-a^3*d^3*f^3*(6+11*m+6*m^2+m^3)-3*a*b^2*d*f*(1+m)*(20*d^2*e^2-10*c*d*e*f*(2-m)+c^2*f^2*(6-5*m+m^2))+b^3*(60*d^3*e^3-60*c*d^2*e^2*f*(2-m)+15*c^2*d*e*f^2*(6-5*m+m^2)-c^3*f^3*(24-26*m+9*m^2-m^3)))*(a+b*x)^(1+m)*(c+d*x)^(-1-m)*hypergeom([3,1+m],[2+m],(d*e-c*f)*(a+b*x)/((b*e-a*f)*(c+d*x)))/((b*e-a*f)^6*(d*e-c*f)^3*(1+m))],
[(a+b*x)^m*(c+d*x)^(2-m)*(e+f*x)^p,x,3,(b*c-a*d)^2*(a+b*x)^(1+m)*(b*(c+d*x)/(b*c-a*d))^m*(e+f*x)^p*AppellF1(1+m,-2+m,-p,2+m,-d*(a+b*x)/(b*c-a*d),-f*(a+b*x)/(b*e-a*f))/(b^3*(1+m)*(c+d*x)^m*(b*(e+f*x)/(b*e-a*f))^p)],
[(a+b*x)^m*(c+d*x)^(2-m)*(e+f*x)^3,x,4,1/6*f*(a+b*x)^(1+m)*(c+d*x)^(3-m)*(e+f*x)^2/(b*d)+1/120*f*(a+b*x)^(1+m)*(c+d*x)^(3-m)*(a^2*d^2*f^2*(20-9*m+m^2)-2*a*b*d*f*(9*d*e*(4-m)-c*f*(6+2*m-m^2))+b^2*(70*d^2*e^2-18*c*d*e*f*(2+m)+c^2*f^2*(6+5*m+m^2))-4*b*d*f*(a*d*f*(5-m)-b*(8*d*e-c*f*(3+m)))*x)/(b^3*d^3)-1/120*(b*c-a*d)^2*(a^3*d^3*f^3*(60-47*m+12*m^2-m^3)-3*a^2*b*d^2*f^2*(12-7*m+m^2)*(6*d*e-c*f*(1+m))+3*a*b^2*d*f*(3-m)*(30*d^2*e^2-12*c*d*e*f*(1+m)+c^2*f^2*(2+3*m+m^2))-b^3*(120*d^3*e^3-90*c*d^2*e^2*f*(1+m)+18*c^2*d*e*f^2*(2+3*m+m^2)-c^3*f^3*(6+11*m+6*m^2+m^3)))*(a+b*x)^(1+m)*(b*(c+d*x)/(b*c-a*d))^m*hypergeom([-2+m,1+m],[2+m],-d*(a+b*x)/(b*c-a*d))/(b^6*d^3*(1+m)*(c+d*x)^m)],
[(a+b*x)^m*(c+d*x)^(2-m)*(e+f*x)^2,x,4,-1/20*f*(a*d*f*(4-m)-b*(6*d*e-c*f*(2+m)))*(a+b*x)^(1+m)*(c+d*x)^(3-m)/(b^2*d^2)+1/5*f*(a+b*x)^(1+m)*(c+d*x)^(3-m)*(e+f*x)/(b*d)+1/20*(b*c-a*d)^2*(a^2*d^2*f^2*(12-7*m+m^2)-2*a*b*d*f*(3-m)*(5*d*e-c*f*(1+m))+b^2*(20*d^2*e^2-10*c*d*e*f*(1+m)+c^2*f^2*(2+3*m+m^2)))*(a+b*x)^(1+m)*(b*(c+d*x)/(b*c-a*d))^m*hypergeom([-2+m,1+m],[2+m],-d*(a+b*x)/(b*c-a*d))/(b^5*d^2*(1+m)*(c+d*x)^m)],
[(a+b*x)^m*(c+d*x)^(2-m)*(e+f*x),x,3,1/4*f*(a+b*x)^(1+m)*(c+d*x)^(3-m)/(b*d)-1/4*(b*c-a*d)^2*(a*d*f*(3-m)-b*(4*d*e-c*f*(1+m)))*(a+b*x)^(1+m)*(b*(c+d*x)/(b*c-a*d))^m*hypergeom([-2+m,1+m],[2+m],-d*(a+b*x)/(b*c-a*d))/(b^4*d*(1+m)*(c+d*x)^m)],
[(a+b*x)^m*(c+d*x)^(2-m),x,2,(b*c-a*d)^2*(a+b*x)^(1+m)*(b*(c+d*x)/(b*c-a*d))^m*hypergeom([-2+m,1+m],[2+m],-d*(a+b*x)/(b*c-a*d))/(b^3*(1+m)*(c+d*x)^m)],
[(a+b*x)^m*(c+d*x)^(2-m)/(e+f*x),x,6,-1/2*d*(2*a*b*c*d*f^2*m-a^2*d^2*f^2*m-b^2*(2*d^2*e^2-4*c*d*e*f+c^2*f^2*(2+m)))*(a+b*x)^(1+m)/(b^2*(b*c-a*d)*f^3*m*(c+d*x)^m)+1/2*d^2*(a+b*x)^(2+m)/(b^2*f*(c+d*x)^m)+(d*e-c*f)^2*(a+b*x)^m*hypergeom([1,-m],[1-m],(b*e-a*f)*(c+d*x)/((d*e-c*f)*(a+b*x)))/(f^3*m*(c+d*x)^m)+1/2*d*(2*a*b*d*f*(d*e-c*f*(2-m))*m+a^2*d^2*f^2*(1-m)*m-b^2*(2*d^2*e^2-2*c*d*e*f*(2-m)+c^2*f^2*(2-3*m+m^2)))*(a+b*x)^(1+m)*(b*(c+d*x)/(b*c-a*d))^m*hypergeom([m,1+m],[2+m],-d*(a+b*x)/(b*c-a*d))/(b^2*(b*c-a*d)*f^3*m*(1+m)*(c+d*x)^m)],
[(a+b*x)^m*(c+d*x)^(2-m)/(e+f*x)^2,x,7,-2*d^2*(d*e-c*f)*(a+b*x)^(1+m)/((b*c-a*d)*f^3*m*(c+d*x)^m)+(d*e-c*f)^2*(a+b*x)^(1+m)/(f^2*(b*e-a*f)*(c+d*x)^m*(e+f*x))+(d*e-c*f)*(a*d*f*(2-m)-b*(2*d*e-c*f*m))*(a+b*x)^m*hypergeom([1,-m],[1-m],(b*e-a*f)*(c+d*x)/((d*e-c*f)*(a+b*x)))/(f^3*(b*e-a*f)*m*(c+d*x)^m)+d^2*(b*(2*d*e-c*f*(2-m))-a*d*f*m)*(a+b*x)^(1+m)*(b*(c+d*x)/(b*c-a*d))^m*hypergeom([m,1+m],[2+m],-d*(a+b*x)/(b*c-a*d))/(b*(b*c-a*d)*f^3*m*(1+m)*(c+d*x)^m)],
[(a+b*x)^m*(c+d*x)^(2-m)/(e+f*x)^3,x,7,1/2*(b*e-a*f)*(a+b*x)^(-1+m)*(c+d*x)^(2-m)/(f^2*(e+f*x)^2)+1/2*(a*d*f*(2-m)-b*(3*d*e-c*f*(1+m)))*(a+b*x)^(-1+m)*(c+d*x)^(2-m)/(f^2*(d*e-c*f)*(e+f*x))-1/2*(2*a*b*d*f*(2-m)*(d*e-c*f*m)-b^2*(2*d^2*e^2-2*c*d*e*f*m-c^2*f^2*(1-m)*m)-a^2*d^2*f^2*(2-3*m+m^2))*(a+b*x)^(-1+m)*(c+d*x)^(1-m)*hypergeom([1,-1+m],[m],(d*e-c*f)*(a+b*x)/((b*e-a*f)*(c+d*x)))/(f^3*(b*e-a*f)*(d*e-c*f)*(1-m))-d*(b*c-a*d)*(a+b*x)^(-1+m)*(b*(c+d*x)/(b*c-a*d))^m*hypergeom([-1+m,-1+m],[m],-d*(a+b*x)/(b*c-a*d))/(f^3*(1-m)*(c+d*x)^m)],
[(a+b*x)^m*(c+d*x)^(2-m)/(e+f*x)^4,x,1,(b*c-a*d)^3*(a+b*x)^(1+m)*(c+d*x)^(-1-m)*hypergeom([4,1+m],[2+m],(d*e-c*f)*(a+b*x)/((b*e-a*f)*(c+d*x)))/((b*e-a*f)^4*(1+m))],
[(a+b*x)^m*(c+d*x)^(2-m)/(e+f*x)^5,x,2,-1/4*f*(a+b*x)^(1+m)*(c+d*x)^(3-m)/((b*e-a*f)*(d*e-c*f)*(e+f*x)^4)+1/4*(b*c-a*d)^3*(b*(4*d*e-c*f*(3-m))-a*d*f*(1+m))*(a+b*x)^(1+m)*(c+d*x)^(-1-m)*hypergeom([4,1+m],[2+m],(d*e-c*f)*(a+b*x)/((b*e-a*f)*(c+d*x)))/((b*e-a*f)^5*(d*e-c*f)*(1+m))],
[(a+b*x)^m*(c+d*x)^(2-m)/(e+f*x)^6,x,4,-1/5*f*(a+b*x)^(1+m)*(c+d*x)^(3-m)/((b*e-a*f)*(d*e-c*f)*(e+f*x)^5)-1/20*f*(b*(6*d*e-c*f*(4-m))-a*d*f*(2+m))*(a+b*x)^(1+m)*(c+d*x)^(3-m)/((b*e-a*f)^2*(d*e-c*f)^2*(e+f*x)^4)-1/20*(b*c-a*d)^3*(2*a*b*d*f*(5*d*e-c*f*(3-m))*(1+m)-a^2*d^2*f^2*(2+3*m+m^2)-b^2*(20*d^2*e^2-10*c*d*e*f*(3-m)+c^2*f^2*(12-7*m+m^2)))*(a+b*x)^(1+m)*(c+d*x)^(-1-m)*hypergeom([4,1+m],[2+m],(d*e-c*f)*(a+b*x)/((b*e-a*f)*(c+d*x)))/((b*e-a*f)^6*(d*e-c*f)^2*(1+m))],
[(a+b*x)^m*(c+d*x)^(2-m)/(e+f*x)^7,x,5,-1/6*f*(a+b*x)^(1+m)*(c+d*x)^(3-m)/((b*e-a*f)*(d*e-c*f)*(e+f*x)^6)-1/30*f*(b*(8*d*e-c*f*(5-m))-a*d*f*(3+m))*(a+b*x)^(1+m)*(c+d*x)^(3-m)/((b*e-a*f)^2*(d*e-c*f)^2*(e+f*x)^5)-1/120*f*(a^2*d^2*f^2*(6+5*m+m^2)-2*a*b*d*f*(d*e*(12+7*m)-c*f*(6+2*m-m^2))+b^2*(38*d^2*e^2-2*c*d*e*f*(26-7*m)+c^2*f^2*(20-9*m+m^2)))*(a+b*x)^(1+m)*(c+d*x)^(3-m)/((b*e-a*f)^3*(d*e-c*f)^3*(e+f*x)^4)+1/120*(b*c-a*d)^3*(3*a^2*b*d^2*f^2*(6*d*e-c*f*(3-m))*(2+3*m+m^2)-a^3*d^3*f^3*(6+11*m+6*m^2+m^3)-3*a*b^2*d*f*(1+m)*(30*d^2*e^2-12*c*d*e*f*(3-m)+c^2*f^2*(12-7*m+m^2))+b^3*(120*d^3*e^3-90*c*d^2*e^2*f*(3-m)+18*c^2*d*e*f^2*(12-7*m+m^2)-c^3*f^3*(60-47*m+12*m^2-m^3)))*(a+b*x)^(1+m)*(c+d*x)^(-1-m)*hypergeom([4,1+m],[2+m],(d*e-c*f)*(a+b*x)/((b*e-a*f)*(c+d*x)))/((b*e-a*f)^7*(d*e-c*f)^3*(1+m))],
[(a+b*x)^m*(c+d*x)^(3-m)/(e+f*x),x,7,b*(b*e-a*f)^3*(a+b*x)^(-3+m)*(c+d*x)^(4-m)/((b*c-a*d)*f^4*(3-m))-1/6*b*(b*(3*d*e-c*f*(1-m))-a*d*f*(2+m))*(a+b*x)^(-2+m)*(c+d*x)^(4-m)/(d^2*f^2)+1/3*b*(a+b*x)^(-1+m)*(c+d*x)^(4-m)/(d*f)-(b*e-a*f)^3*(a+b*x)^(-3+m)*(c+d*x)^(3-m)*hypergeom([1,-3+m],[-2+m],(d*e-c*f)*(a+b*x)/((b*e-a*f)*(c+d*x)))/(f^4*(3-m))-1/6*(b*c-a*d)^2*(3*a^2*b*d^2*f^2*(d*e-c*f*(3-m))*(1-m)*m+a^3*d^3*f^3*m*(2-3*m+m^2)+3*a*b^2*d*f*m*(2*d^2*e^2-2*c*d*e*f*(3-m)+c^2*f^2*(6-5*m+m^2))-b^3*(6*d^3*e^3-6*c*d^2*e^2*f*(3-m)+3*c^2*d*e*f^2*(6-5*m+m^2)-c^3*f^3*(6-11*m+6*m^2-m^3)))*(a+b*x)^(-2+m)*(b*(c+d*x)/(b*c-a*d))^m*hypergeom([-3+m,-2+m],[-1+m],-d*(a+b*x)/(b*c-a*d))/(b^3*d^2*f^4*(2-m)*(3-m)*(c+d*x)^m),-1/6*d*(3*a^2*b*d^2*f^2*(d*e-c*f*(5-m))*m-3*a*b^2*c*d*f^2*(2*d*e-c*f*(6-m))*m+a^3*d^3*f^3*(4-m)*m+b^3*(6*d^3*e^3-18*c*d^2*e^2*f+3*c^2*d*e*f^2*(6+m)-c^3*f^3*(6+7*m-m^2)))*(a+b*x)^(1+m)/(b^3*(b*c-a*d)*f^4*m*(c+d*x)^m)-1/6*d^2*(b*(3*d*e-c*f*(9-m))+a*d*f*(6-m))*(a+b*x)^(2+m)/(b^3*f^2*(c+d*x)^m)+1/3*d^3*(a+b*x)^(3+m)/(b^3*f*(c+d*x)^m)-(d*e-c*f)^3*(a+b*x)^m*hypergeom([1,-m],[1-m],(b*e-a*f)*(c+d*x)/((d*e-c*f)*(a+b*x)))/(f^4*m*(c+d*x)^m)-1/6*d*(3*a^2*b*d^2*f^2*(d*e-c*f*(3-m))*(1-m)*m+a^3*d^3*f^3*m*(2-3*m+m^2)+3*a*b^2*d*f*m*(2*d^2*e^2-2*c*d*e*f*(3-m)+c^2*f^2*(6-5*m+m^2))-b^3*(6*d^3*e^3-6*c*d^2*e^2*f*(3-m)+3*c^2*d*e*f^2*(6-5*m+m^2)-c^3*f^3*(6-11*m+6*m^2-m^3)))*(a+b*x)^(1+m)*(b*(c+d*x)/(b*c-a*d))^m*hypergeom([m,1+m],[2+m],-d*(a+b*x)/(b*c-a*d))/(b^3*(b*c-a*d)*f^4*m*(1+m)*(c+d*x)^m)],
[(a+b*x)^m*(c+d*x)^(3-m)/(e+f*x)^2,x,2,3*b*d*(d*e-c*f)^2*(a+b*x)^m*(c+d*x)^(1-m)/((b*c-a*d)*f^4*m)+1/2*d^2*(a+b*x)^(1+m)*(c+d*x)^(1-m)/(b*f^2)-(d*e-c*f)^2*(a+b*x)^m*(c+d*x)^(1-m)/(f^3*(e+f*x))+(d*e-c*f)^2*(a*d*f*(3-m)-b*(3*d*e-c*f*m))*(a+b*x)^m*hypergeom([1,m],[1+m],(d*e-c*f)*(a+b*x)/((b*e-a*f)*(c+d*x)))/(f^4*(b*e-a*f)*m*(c+d*x)^m)+1/2*d^2*(2*a*b*d*f*(2*d*e-c*f*(3-m))*m+a^2*d^2*f^2*(1-m)*m-b^2*(6*d^2*e^2-4*c*d*e*f*(3-m)+c^2*f^2*(6-5*m+m^2)))*(a+b*x)^(1+m)*(b*(c+d*x)/(b*c-a*d))^m*hypergeom([m,1+m],[2+m],-d*(a+b*x)/(b*c-a*d))/(b^2*(b*c-a*d)*f^4*m*(1+m)*(c+d*x)^m),(b*c-a*d)^3*(a+b*x)^(1+m)*(b*(c+d*x)/(b*c-a*d))^m*AppellF1(1+m,-3+m,2,2+m,-d*(a+b*x)/(b*c-a*d),-f*(a+b*x)/(b*e-a*f))/(b^2*(b*e-a*f)^2*(1+m)*(c+d*x)^m)],
[(a+b*x)^m*(c+d*x)^(3-m)/(e+f*x)^3,x,8,-3*d^3*(d*e-c*f)*(a+b*x)^(1+m)/((b*c-a*d)*f^4*m*(c+d*x)^m)-1/2*(d*e-c*f)^3*(a+b*x)^(1+m)/(f^3*(b*e-a*f)*(c+d*x)^m*(e+f*x)^2)+1/2*(d*e-c*f)^2*(b*(5*d*e+c*f*(1-m))-a*d*f*(6-m))*(a+b*x)^(1+m)/(f^3*(b*e-a*f)^2*(c+d*x)^m*(e+f*x))+1/2*(d*e-c*f)*(2*a*b*d*f*(3-m)*(2*d*e-c*f*m)-b^2*(6*d^2*e^2-4*c*d*e*f*m-c^2*f^2*(1-m)*m)-a^2*d^2*f^2*(6-5*m+m^2))*(a+b*x)^m*hypergeom([1,-m],[1-m],(b*e-a*f)*(c+d*x)/((d*e-c*f)*(a+b*x)))/(f^4*(b*e-a*f)^2*m*(c+d*x)^m)+d^3*(b*(3*d*e-c*f*(3-m))-a*d*f*m)*(a+b*x)^(1+m)*(b*(c+d*x)/(b*c-a*d))^m*hypergeom([m,1+m],[2+m],-d*(a+b*x)/(b*c-a*d))/(b*(b*c-a*d)*f^4*m*(1+m)*(c+d*x)^m)],
[(a+b*x)^(1-n)*(c+d*x)^(1+n)/(b*c+a*d+2*b*d*x),x,6,1/8*(b*c-a*d)*(3-2*n)*(a+b*x)^(2-n)*(c+d*x)^(-1+n)/(b^3*(1-n))+1/4*d*(a+b*x)^(3-n)*(c+d*x)^(-1+n)/b^3+1/8*(b*c-a*d)^2*(a+b*x)^(1-n)*(c+d*x)^(-1+n)*hypergeom([1,-1+n],[n],-b*(c+d*x)/(d*(a+b*x)))/(b^3*d*(1-n))-1/8*(b*c-a*d)^2*(1-2*n^2)*(-d*(a+b*x)/(b*c-a*d))^n*(c+d*x)^n*hypergeom([-1+n,n],[1+n],b*(c+d*x)/(b*c-a*d))/(b^2*d^2*(1-n)*n*(a+b*x)^n)],
[(a+b*x)^(1-n)*(c+d*x)^(1+n)/(b*c+a*d+2*b*d*x)^2,x,4,-1/4*(b*c-a*d)*(a+b*x)^(1-n)*(c+d*x)^(-1+n)*hypergeom([2,1-n],[2-n],-d*(a+b*x)/(b*(c+d*x)))/(b^3*d*(1-n))+1/4*(-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))/(b*d^2*(1+n)*(a+b*x)^n)],
[(a+b*x)^(1-n)*(c+d*x)^(1+n)/(b*c+a*d+2*b*d*x)^3,x,7,-1/8*(b*c-a*d)*(a+b*x)^(1-n)*(c+d*x)^n/(b^2*d*(b*c+a*d+2*b*d*x)^2)-1/8*(1+2*n)*(a+b*x)^(1-n)*(c+d*x)^n/(b^2*d*(b*c+a*d+2*b*d*x))-1/8*(1-2*n^2)*(c+d*x)^n*hypergeom([1,n],[1+n],-b*(c+d*x)/(d*(a+b*x)))/(b^2*d^2*n*(a+b*x)^n)+1/8*(-d*(a+b*x)/(b*c-a*d))^n*(c+d*x)^n*hypergeom([n,n],[1+n],b*(c+d*x)/(b*c-a*d))/(b^2*d^2*n*(a+b*x)^n)],
[(a+b*x)^(1-n)*(c+d*x)^(1+n)/(b*c+a*d+2*b*d*x)^4,x,1,(a+b*x)^(2-n)*(c+d*x)^(-2+n)*hypergeom([4,2-n],[3-n],-d*(a+b*x)/(b*(c+d*x)))/(b^4*(b*c-a*d)*(2-n))],
[(a+b*x)^m*(c+d*x)^(2-m)/(b*c+a*d+2*b*d*x),x,6,1/8*(b*c-a*d)*(1+2*m)*(a+b*x)^(1+m)/(b^3*m*(c+d*x)^m)+1/4*d*(a+b*x)^(2+m)/(b^3*(c+d*x)^m)+1/8*(b*c-a*d)^2*(a+b*x)^m*hypergeom([1,-m],[1-m],-b*(c+d*x)/(d*(a+b*x)))/(b^3*d*m*(c+d*x)^m)-1/8*(b*c-a*d)*(1-4*m+2*m^2)*(a+b*x)^(1+m)*(b*(c+d*x)/(b*c-a*d))^m*hypergeom([m,1+m],[2+m],-d*(a+b*x)/(b*c-a*d))/(b^3*m*(1+m)*(c+d*x)^m)],
[(a+b*x)^m*(c+d*x)^(2-m)/(b*c+a*d+2*b*d*x)^2,x,4,-1/4*(b*c-a*d)*(a+b*x)^m*hypergeom([2,m],[1+m],-d*(a+b*x)/(b*(c+d*x)))/(b^3*d*m*(c+d*x)^m)+1/4*(b*c-a*d)*(a+b*x)^m*(b*(c+d*x)/(b*c-a*d))^m*hypergeom([-1+m,m],[1+m],-d*(a+b*x)/(b*c-a*d))/(b^3*d*m*(c+d*x)^m)],
[(a+b*x)^m*(c+d*x)^(2-m)/(b*c+a*d+2*b*d*x)^3,x,7,1/8*(b*c-a*d)*(a+b*x)^(-1+m)*(c+d*x)^(2-m)/(b*d^2*(b*c+a*d+2*b*d*x)^2)+1/8*(1-2*m)*(a+b*x)^(-1+m)*(c+d*x)^(2-m)/(b*d^2*(b*c+a*d+2*b*d*x))-1/8*(1-4*m+2*m^2)*(a+b*x)^(-1+m)*(c+d*x)^(1-m)*hypergeom([1,-1+m],[m],-d*(a+b*x)/(b*(c+d*x)))/(b^2*d^2*(1-m))-1/8*(b*c-a*d)*(a+b*x)^(-1+m)*(b*(c+d*x)/(b*c-a*d))^m*hypergeom([-1+m,-1+m],[m],-d*(a+b*x)/(b*c-a*d))/(b^3*d^2*(1-m)*(c+d*x)^m)],
[(a+b*x)^m*(c+d*x)^(2-m)/(b*c+a*d+2*b*d*x)^4,x,1,(a+b*x)^(1+m)*(c+d*x)^(-1-m)*hypergeom([4,1+m],[2+m],-d*(a+b*x)/(b*(c+d*x)))/(b^4*(b*c-a*d)*(1+m))],

# n symbolic
[(a+b*x)^m*(c+d*x)^(-m-n)*(e+f*x)^(n+p),x,3,(a+b*x)^(1+m)*(c+d*x)^(-m-n)*(b*(c+d*x)/(b*c-a*d))^(m+n)*(e+f*x)^(n+p)*(b*(e+f*x)/(b*e-a*f))^(-n-p)*AppellF1(1+m,m+n,-n-p,2+m,-d*(a+b*x)/(b*c-a*d),-f*(a+b*x)/(b*e-a*f))/(b*(1+m))],
[(a+b*x)^m*(c+d*x)^(-m-n)*(e+f*x)^(1+n),x,3,(b*e-a*f)*(a+b*x)^(1+m)*(c+d*x)^(-m-n)*(b*(c+d*x)/(b*c-a*d))^(m+n)*(e+f*x)^n*AppellF1(1+m,m+n,-1-n,2+m,-d*(a+b*x)/(b*c-a*d),-f*(a+b*x)/(b*e-a*f))/(b^2*(1+m)*(b*(e+f*x)/(b*e-a*f))^n)],
[(a+b*x)^m*(c+d*x)^(-m-n)*(e+f*x)^n,x,3,(a+b*x)^(1+m)*(c+d*x)^(-m-n)*(b*(c+d*x)/(b*c-a*d))^(m+n)*(e+f*x)^n*AppellF1(1+m,m+n,-n,2+m,-d*(a+b*x)/(b*c-a*d),-f*(a+b*x)/(b*e-a*f))/(b*(1+m)*(b*(e+f*x)/(b*e-a*f))^n)],
[(a+b*x)^m*(c+d*x)^(-m-n)*(e+f*x)^(-1+n),x,3,(a+b*x)^(1+m)*(c+d*x)^(-m-n)*(b*(c+d*x)/(b*c-a*d))^(m+n)*(e+f*x)^n*AppellF1(1+m,m+n,1-n,2+m,-d*(a+b*x)/(b*c-a*d),-f*(a+b*x)/(b*e-a*f))/((b*e-a*f)*(1+m)*(b*(e+f*x)/(b*e-a*f))^n)],
[(a+b*x)^m*(c+d*x)^(-m-n)*(e+f*x)^(-2+n),x,1,(a+b*x)^(1+m)*(c+d*x)^(-m-n)*((b*e-a*f)*(c+d*x)/((b*c-a*d)*(e+f*x)))^(m+n)*(e+f*x)^(-1+n)*hypergeom([1+m,m+n],[2+m],-(d*e-c*f)*(a+b*x)/((b*c-a*d)*(e+f*x)))/((b*e-a*f)*(1+m))],
[(a+b*x)^m*(c+d*x)^(-m-n)*(e+f*x)^(-3+n),x,2,-f*(a+b*x)^(1+m)*(c+d*x)^(1-m-n)*(e+f*x)^(-2+n)/((b*e-a*f)*(d*e-c*f)*(2-n))-(a*d*f*(1+m)-b*(d*e*(2-n)-c*f*(1-m-n)))*(a+b*x)^(1+m)*(c+d*x)^(-m-n)*((b*e-a*f)*(c+d*x)/((b*c-a*d)*(e+f*x)))^(m+n)*(e+f*x)^(-1+n)*hypergeom([1+m,m+n],[2+m],-(d*e-c*f)*(a+b*x)/((b*c-a*d)*(e+f*x)))/((b*e-a*f)^2*(d*e-c*f)*(1+m)*(2-n))],
[(a+b*x)^m*(c+d*x)^(-m-n)*(e+f*x)^(-4+n),x,4,-f*(a+b*x)^(1+m)*(c+d*x)^(1-m-n)*(e+f*x)^(-3+n)/((b*e-a*f)*(d*e-c*f)*(3-n))+f*(a*d*f*(2+m)-b*(d*e*(4-n)-c*f*(2-m-n)))*(a+b*x)^(1+m)*(c+d*x)^(1-m-n)*(e+f*x)^(-2+n)/((b*e-a*f)^2*(d*e-c*f)^2*(2-n)*(3-n))+(a^2*d^2*f^2*(2+3*m+m^2)-2*a*b*d*f*(1+m)*(d*e*(3-n)-c*f*(1-m-n))-b^2*(2*c*d*e*f*(3-n)*(1-m-n)-d^2*e^2*(6-5*n+n^2)-c^2*f^2*(2+m^2-m*(3-2*n)-3*n+n^2)))*(a+b*x)^(1+m)*(c+d*x)^(-m-n)*((b*e-a*f)*(c+d*x)/((b*c-a*d)*(e+f*x)))^(m+n)*(e+f*x)^(-1+n)*hypergeom([1+m,m+n],[2+m],-(d*e-c*f)*(a+b*x)/((b*c-a*d)*(e+f*x)))/((b*e-a*f)^3*(d*e-c*f)^2*(1+m)*(2-n)*(3-n))],

#  {(a + b*x)^m/(c + d*x)^(m + n)*(e + f*x)^(n - 5), x, 5, -((f*(a + b*x)^(1 + m)*(c + d*x)^(1 - m - n)*(e + f*x)^(-4 + n))/((b*e - a*f)*(d*e - c*f)*(4 - n))) + (f*(a*d*f*(3 + m) - b*(d*e*(6 - n) - c*f*(3 - m - n)))*(a + b*x)^(1 + m)*(c + d*x)^(1 - m - n)*(e + f*x)^(-3 + n))/((b*e - a*f)^2*(d*e - c*f)^2*(3 - n)*(4 - n)) - (1/((b*e - a*f)^3*(d*e - c*f)^3*(2 - n)*(3 - n)*(4 - n)))*(f*(a^2*d^2*f^2*(6 + 5*m + m^2) - a*b*d*f*(d*e*(2*m*(5 - n) + 3*(6 - n)) - c*f*(6 - 2*m^2 - 3*n - 2*m*n)) + b^2*(d^2*e^2*(18 - 8*n + n^2) + c^2*f^2*(6 + m^2 - m*(5 - 2*n) - 5*n + n^2) - c*d*e*f*(18 - 2*m*(5 - n) - 13*n + 2*n^2)))*(a + b*x)^(1 + m)*(c + d*x)^(1 - m - n)*(e + f*x)^(-2 + n)) - ((a^3*d^3*f^3*(6 + 11*m + 6*m^2 + m^3) - 3*a^2*b*d^2*f^2*(2 + 3*m + m^2)*(d*e*(4 - n) - c*f*(1 - m - n)) - 3*a*b^2*d*f*(1 + m)*(2*c*d*e*f*(4 - n)*(1 - m - n) - d^2*e^2*(12 - 7*n + n^2) - c^2*f^2*(2 + m^2 - m*(3 - 2*n) - 3*n + n^2)) + b^3*(3*c*d^2*e^2*f*(1 - m - n)*(12 - 7*n + n^2) - 3*c^2*d*e*f^2*(4 - n)*(2 + m^2 - m*(3 - 2*n) - 3*n + n^2) - d^3*e^3*(24 - 26*n + 9*n^2 - n^3) + c^3*f^3*(6 - m^3 + 3*m^2*(2 - n) - 11*n + 6*n^2 - n^3 - m*(11 - 12*n + 3*n^2))))*(a + b*x)^(1 + m)*(c + d*x)^(-m - n)*(((b*e - a*f)*(c + d*x))/((b*c - a*d)*(e + f*x)))^(m + n)*(e + f*x)^(-1 + n)*Hypergeometric2F1[1 + m, m + n, 2 + m, -(((d*e - c*f)*(a + b*x))/((b*c - a*d)*(e + f*x)))])/((b*e - a*f)^4*(d*e - c*f)^3*(1 + m)*(2 - n)*(3 - n)*(4 - n))} 

# Integrands of the form (a+b x)^m (c+d x)^n (e+f x)^p
[(a+b*x)^m*(c+d*x)^n*((b*c*f+a*d*f+a*d*f*m+b*c*f*n)/(b*d*(2+m+n))+f*x)^(-3-m-n),x,1,b*d*(2+m+n)*(a+b*x)^(1+m)*(c+d*x)^(1+n)*(f*(a*d*(1+m)+b*c*(1+n))/(b*d*(2+m+n))+f*x)^(-2-m-n)/((b*c-a*d)^2*f*(1+m)*(1+n))],
[(a+b*x)^m*(c+d*x)^(-1-d*(b*e-a*f)*(1+m)/(b*(d*e-c*f)))*(e+f*x)^(-1+(b*c-a*d)*f*(1+m)/(b*(d*e-c*f))),x,1,b*(a+b*x)^(1+m)*(e+f*x)^((b*c-a*d)*f*(1+m)/(b*(d*e-c*f)))/((b*c-a*d)*(b*e-a*f)*(1+m)*(c+d*x)^(d*(b*e-a*f)*(1+m)/(b*(d*e-c*f))))],
[(a+b*x)^m*(c+d*x)^n*(e+f*x)^(-m-n),x,3,(a+b*x)^(1+m)*(c+d*x)^n*(e+f*x)^(-m-n)*(b*(e+f*x)/(b*e-a*f))^(m+n)*AppellF1(1+m,-n,m+n,2+m,-d*(a+b*x)/(b*c-a*d),-f*(a+b*x)/(b*e-a*f))/(b*(1+m)*(b*(c+d*x)/(b*c-a*d))^n)],
[(a+b*x)^m*(c+d*x)^n*(e+f*x)^(-1-m-n),x,3,(a+b*x)^(1+m)*(c+d*x)^n*(e+f*x)^(-m-n)*(b*(e+f*x)/(b*e-a*f))^(m+n)*AppellF1(1+m,-n,1+m+n,2+m,-d*(a+b*x)/(b*c-a*d),-f*(a+b*x)/(b*e-a*f))/((b*e-a*f)*(1+m)*(b*(c+d*x)/(b*c-a*d))^n)],
[(a+b*x)^m*(c+d*x)^n*(e+f*x)^(-2-m-n),x,1,(a+b*x)^(1+m)*(c+d*x)^n*(e+f*x)^(-1-m-n)*hypergeom([1+m,-n],[2+m],-(d*e-c*f)*(a+b*x)/((b*c-a*d)*(e+f*x)))/((b*e-a*f)*(1+m)*((b*e-a*f)*(c+d*x)/((b*c-a*d)*(e+f*x)))^n)],
[(a+b*x)^m*(c+d*x)^n*(e+f*x)^(-3-m-n),x,2,-f*(a+b*x)^(1+m)*(c+d*x)^(1+n)*(e+f*x)^(-2-m-n)/((b*e-a*f)*(d*e-c*f)*(2+m+n))-(a*d*f*(1+m)+b*(c*f*(1+n)-d*e*(2+m+n)))*(a+b*x)^(1+m)*(c+d*x)^n*(e+f*x)^(-1-m-n)*hypergeom([1+m,-n],[2+m],-(d*e-c*f)*(a+b*x)/((b*c-a*d)*(e+f*x)))/((b*e-a*f)^2*(d*e-c*f)*(1+m)*(2+m+n)*((b*e-a*f)*(c+d*x)/((b*c-a*d)*(e+f*x)))^n)],
[(a+b*x)^m*(c+d*x)^n*(e+f*x)^(-4-m-n),x,4,-f*(a+b*x)^(1+m)*(c+d*x)^(1+n)*(e+f*x)^(-3-m-n)/((b*e-a*f)*(d*e-c*f)*(3+m+n))+f*(a*d*f*(2+m)+b*(c*f*(2+n)-d*e*(4+m+n)))*(a+b*x)^(1+m)*(c+d*x)^(1+n)*(e+f*x)^(-2-m-n)/((b*e-a*f)^2*(d*e-c*f)^2*(2+m+n)*(3+m+n))+(a^2*d^2*f^2*(2+3*m+m^2)+2*a*b*d*f*(1+m)*(c*f*(1+n)-d*e*(3+m+n))-b^2*(2*c*d*e*f*(1+n)*(3+m+n)-c^2*f^2*(2+3*n+n^2)-d^2*e^2*(6+m^2+5*n+n^2+m*(5+2*n))))*(a+b*x)^(1+m)*(c+d*x)^n*(e+f*x)^(-1-m-n)*hypergeom([1+m,-n],[2+m],-(d*e-c*f)*(a+b*x)/((b*c-a*d)*(e+f*x)))/((b*e-a*f)^3*(d*e-c*f)^2*(1+m)*(2+m+n)*(3+m+n)*((b*e-a*f)*(c+d*x)/((b*c-a*d)*(e+f*x)))^n)],

#  {(a + b*x)^m*(c + d*x)^n/(e + f*x)^(m + n + 5), x, 5, -((f*(a + b*x)^(1 + m)*(c + d*x)^(1 + n)*(e + f*x)^(-4 - m - n))/((b*e - a*f)*(d*e - c*f)*(4 + m + n))) + (f*(a*d*f*(3 + m) + b*(c*f*(3 + n) - d*e*(6 + m + n)))*(a + b*x)^(1 + m)*(c + d*x)^(1 + n)*(e + f*x)^(-3 - m - n))/((b*e - a*f)^2*(d*e - c*f)^2*(3 + m + n)*(4 + m + n)) - (f*(a^2*d^2*f^2*(6 + 5*m + m^2) + b^2*(c^2*f^2*(6 + 5*n + n^2) + d^2*e^2*(18 + m^2 + 8*n + n^2 + 2*m*(4 + n)) - c*d*e*f*(18 + 13*n + 2*n^2 + m*(3 + 2*n))) + a*b*d*f*(c*f*(6 + 3*m + 3*n + 2*m*n) - d*e*(2*m^2 + 3*(6 + n) + m*(13 + 2*n))))*(a + b*x)^(1 + m)*(c + d*x)^(1 + n)*(e + f*x)^(-2 - m - n))/((b*e - a*f)^3*(d*e - c*f)^3*(2 + m + n)*(3 + m + n)*(4 + m + n)) + (1/((b*e - a*f)^4*(d*e - c*f)^3*(1 + m)*(2 + m + n)*(3 + m + n)*(4 + m + n)))*(((f*(b*c*(1 + m) + a*d*(1 + n))*(a^2*d^2*f^2*(6 + 5*m + m^2) + b^2*(c^2*f^2*(6 + 5*n + n^2) + d^2*e^2*(18 + m^2 + 8*n + n^2 + 2*m*(4 + n)) - c*d*e*f*(18 + 13*n + 2*n^2 + m*(3 + 2*n))) + a*b*d*f*(c*f*(6 + 3*m + 3*n + 2*m*n) - d*e*(2*m^2 + 3*(6 + n) + m*(13 + 2*n)))) + (2 + m + n)*(a*b*c*d*f^2*(a*d*f*(3 + m) + b*(c*f*(3 + n) - d*e*(6 + m + n))) - b*d*e*(f*(b*c*(1 + m) + a*d*(1 + n))*(a*d*f*(3 + m) + b*(c*f*(3 + n) - d*e*(6 + m + n))) + (3 + m + n)*(2*a*b*c*d*f^2 + b*d*e*(a*d*f*(3 + m) + b*(c*f*(3 + n) - d*e*(4 + m + n))) - (b*c + a*d)*f*(a*d*f*(3 + m) + b*(c*f*(3 + n) - d*e*(4 + m + n))))) + (b*c + a*d)*f*(f*(b*c*(1 + m) + a*d*(1 + n))*(a*d*f*(3 + m) + b*(c*f*(3 + n) - d*e*(6 + m + n))) + (3 + m + n)*(2*a*b*c*d*f^2 + b*d*e*(a*d*f*(3 + m) + b*(c*f*(3 + n) - d*e*(4 + m + n))) - (b*c + a*d)*f*(a*d*f*(3 + m) + b*(c*f*(3 + n) - d*e*(4 + m + n)))))))*(a + b*x)^(1 + m)*(c + d*x)^n*(e + f*x)^(-1 - m - n)*Hypergeometric2F1[1 + m, -n, 2 + m, -(((d*e - c*f)*(a + b*x))/((b*c - a*d)*(e + f*x)))])/(((b*e - a*f)*(c + d*x))/((b*c - a*d)*(e + f*x)))^n)} 
[(a+b*x)^m*(c+d*x)^n*(e+f*x)^p,x,3,(a+b*x)^(1+m)*(c+d*x)^n*(e+f*x)^p*AppellF1(1+m,-n,-p,2+m,-d*(a+b*x)/(b*c-a*d),-f*(a+b*x)/(b*e-a*f))/(b*(1+m)*(b*(c+d*x)/(b*c-a*d))^n*(b*(e+f*x)/(b*e-a*f))^p)],
[(a+b*x)^m*(c+d*x)^n*(e+f*x)^2,x,4,f*(b*d*e*(4+m+n)-f*(b*c*(2+m)+a*d*(2+n)))*(a+b*x)^(1+m)*(c+d*x)^(1+n)/(b^2*d^2*(2+m+n)*(3+m+n))+f*(a+b*x)^(1+m)*(c+d*x)^(1+n)*(e+f*x)/(b*d*(3+m+n))+(f*(b*c*(1+m)+a*d*(1+n))*(b*d*e*(4+m+n)-f*(b*c*(2+m)+a*d*(2+n)))+b*d*(2+m+n)*(a*f*(c*f+d*e*(1+n))+b*e*(c*f*(1+m)-d*e*(3+m+n))))*(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^2*d^2*(b*c-a*d)*(1+n)*(2+m+n)*(3+m+n)),f*(b*d*e*(4+m+n)-f*(b*c*(2+m)+a*d*(2+n)))*(a+b*x)^(1+m)*(c+d*x)^(1+n)/(b^2*d^2*(2+m+n)*(3+m+n))+f*(a+b*x)^(1+m)*(c+d*x)^(1+n)*(e+f*x)/(b*d*(3+m+n))-(f*(b*c*(1+m)+a*d*(1+n))*(b*d*e*(4+m+n)-f*(b*c*(2+m)+a*d*(2+n)))+b*d*(2+m+n)*(a*f*(c*f+d*e*(1+n))+b*e*(c*f*(1+m)-d*e*(3+m+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^3*d^2*(1+m)*(2+m+n)*(3+m+n)*(b*(c+d*x)/(b*c-a*d))^n)],
[(a+b*x)^m*(c+d*x)^n*(e+f*x),x,3,f*(a+b*x)^(1+m)*(c+d*x)^(1+n)/(b*d*(2+m+n))-(b*d*e*(2+m+n)-f*(b*c*(1+m)+a*d*(1+n)))*(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*d*(b*c-a*d)*(1+n)*(2+m+n)),f*(a+b*x)^(1+m)*(c+d*x)^(1+n)/(b*d*(2+m+n))+(b*d*e*(2+m+n)-f*(b*c*(1+m)+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^2*d*(1+m)*(2+m+n)*(b*(c+d*x)/(b*c-a*d))^n)],
[(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)^n/(e+f*x),x,2,(a+b*x)^(1+m)*(c+d*x)^n*AppellF1(1+m,-n,1,2+m,-d*(a+b*x)/(b*c-a*d),-f*(a+b*x)/(b*e-a*f))/((b*e-a*f)*(1+m)*(b*(c+d*x)/(b*c-a*d))^n)],
[(a+b*x)^m*(c+d*x)^n/(e+f*x)^2,x,2,b*(a+b*x)^(1+m)*(c+d*x)^n*AppellF1(1+m,-n,2,2+m,-d*(a+b*x)/(b*c-a*d),-f*(a+b*x)/(b*e-a*f))/((b*e-a*f)^2*(1+m)*(b*(c+d*x)/(b*c-a*d))^n)],
[(a+b*x)^m*(c+d*x)^n/(e+f*x)^3,x,2,b^2*(a+b*x)^(1+m)*(c+d*x)^n*AppellF1(1+m,-n,3,2+m,-d*(a+b*x)/(b*c-a*d),-f*(a+b*x)/(b*e-a*f))/((b*e-a*f)^3*(1+m)*(b*(c+d*x)/(b*c-a*d))^n)],
[(3+4*x)^n/(sqrt(1-x)*sqrt(1+x)),x,1,-7^n*AppellF1(1/2,1/2,-n,3/2,1/2*(1-x),4/7*(1-x))*sqrt(2)*sqrt(1-x)],
[(3-4*x)^n/(sqrt(1-x)*sqrt(1+x)),x,1,7^n*AppellF1(1/2,-n,1/2,3/2,4/7*(1+x),1/2*(1+x))*sqrt(2)*sqrt(1+x)],
[(-3+4*x)^n/(sqrt(1-x)*sqrt(1+x)),x,1,-AppellF1(1/2,1/2,-n,3/2,1/2*(1-x),4*(1-x))*sqrt(2)*sqrt(1-x)],
[(-3-4*x)^n/(sqrt(1-x)*sqrt(1+x)),x,1,AppellF1(1/2,-n,1/2,3/2,4*(1+x),1/2*(1+x))*sqrt(2)*sqrt(1+x)],
[(a+b*x)^(4/3)/((e+f*x)*sqrt(c+d*x)),x,2,3/7*(a+b*x)^(7/3)*AppellF1(7/3,1/2,1,10/3,-d*(a+b*x)/(b*c-a*d),-f*(a+b*x)/(b*e-a*f))*sqrt(b*(c+d*x)/(b*c-a*d))/((b*e-a*f)*sqrt(c+d*x))],
[(c+d*x)^(2/5)*(e+f*x)^(3/5)/sqrt(a+b*x),x,3,2*(c+d*x)^(2/5)*(e+f*x)^(3/5)*AppellF1(1/2,-2/5,-3/5,3/2,-d*(a+b*x)/(b*c-a*d),-f*(a+b*x)/(b*e-a*f))*sqrt(a+b*x)/(b*(b*(c+d*x)/(b*c-a*d))^(2/5)*(b*(e+f*x)/(b*e-a*f))^(3/5))],
[(e+f*x)^n*sqrt(a+b*x)/sqrt(c+d*x),x,3,2/3*(a+b*x)^(3/2)*(e+f*x)^n*AppellF1(3/2,1/2,-n,5/2,-d*(a+b*x)/(b*c-a*d),-f*(a+b*x)/(b*e-a*f))*sqrt(b*(c+d*x)/(b*c-a*d))/(b*(b*(e+f*x)/(b*e-a*f))^n*sqrt(c+d*x))],
[(e+f*x)^n*sqrt(c+d*x)/sqrt(a+b*x),x,3,2*(e+f*x)^n*AppellF1(1/2,-1/2,-n,3/2,-d*(a+b*x)/(b*c-a*d),-f*(a+b*x)/(b*e-a*f))*sqrt(a+b*x)*sqrt(c+d*x)/(b*(b*(e+f*x)/(b*e-a*f))^n*sqrt(b*(c+d*x)/(b*c-a*d)))],
[(e+f*x)^n/((c+d*x)^(3/2)*sqrt(a+b*x)),x,3,2*(e+f*x)^n*AppellF1(1/2,3/2,-n,3/2,-d*(a+b*x)/(b*c-a*d),-f*(a+b*x)/(b*e-a*f))*sqrt(a+b*x)*sqrt(b*(c+d*x)/(b*c-a*d))/((b*c-a*d)*(b*(e+f*x)/(b*e-a*f))^n*sqrt(c+d*x))],
[(e+f*x)^n/((a+b*x)^(3/2)*sqrt(c+d*x)),x,3,-2*(e+f*x)^n*AppellF1(-1/2,1/2,-n,1/2,-d*(a+b*x)/(b*c-a*d),-f*(a+b*x)/(b*e-a*f))*sqrt(b*(c+d*x)/(b*c-a*d))/(b*(b*(e+f*x)/(b*e-a*f))^n*sqrt(a+b*x)*sqrt(c+d*x))],
[(a+b*x)^(1/2)*(c+d*x)^(1/3)/(e+f*x),x,2,2/3*(a+b*x)^(3/2)*(c+d*x)^(1/3)*AppellF1(3/2,-1/3,1,5/2,-d*(a+b*x)/(b*c-a*d),-f*(a+b*x)/(b*e-a*f))/((b*e-a*f)*(b*(c+d*x)/(b*c-a*d))^(1/3))],
[(a+b*x)^(1/3)*(c+d*x)^(1/2)/(e+f*x),x,2,3/4*(a+b*x)^(4/3)*AppellF1(4/3,-1/2,1,7/3,-d*(a+b*x)/(b*c-a*d),-f*(a+b*x)/(b*e-a*f))*sqrt(c+d*x)/((b*e-a*f)*sqrt(b*(c+d*x)/(b*c-a*d)))],
[(a+b*x)^(1/2)*(c+d*x)^(1/3)*(e+f*x)^(1/4),x,3,2/3*(a+b*x)^(3/2)*(c+d*x)^(1/3)*(e+f*x)^(1/4)*AppellF1(3/2,-1/3,-1/4,5/2,-d*(a+b*x)/(b*c-a*d),-f*(a+b*x)/(b*e-a*f))/(b*(b*(c+d*x)/(b*c-a*d))^(1/3)*(b*(e+f*x)/(b*e-a*f))^(1/4))],
[(a+b*x)^(1/3)*(c+d*x)^(1/2)*(e+f*x)^(1/4),x,3,3/4*(a+b*x)^(4/3)*(e+f*x)^(1/4)*AppellF1(4/3,-1/2,-1/4,7/3,-d*(a+b*x)/(b*c-a*d),-f*(a+b*x)/(b*e-a*f))*sqrt(c+d*x)/(b*(b*(e+f*x)/(b*e-a*f))^(1/4)*sqrt(b*(c+d*x)/(b*c-a*d)))],
[(a+b*x)^4*(A+B*x)*(d+e*x)^m,x,2,-(b*d-a*e)^4*(B*d-A*e)*(d+e*x)^(1+m)/(e^6*(1+m))+(b*d-a*e)^3*(5*b*B*d-4*A*b*e-a*B*e)*(d+e*x)^(2+m)/(e^6*(2+m))-2*b*(b*d-a*e)^2*(5*b*B*d-3*A*b*e-2*a*B*e)*(d+e*x)^(3+m)/(e^6*(3+m))+2*b^2*(b*d-a*e)*(5*b*B*d-2*A*b*e-3*a*B*e)*(d+e*x)^(4+m)/(e^6*(4+m))-b^3*(5*b*B*d-A*b*e-4*a*B*e)*(d+e*x)^(5+m)/(e^6*(5+m))+b^4*B*(d+e*x)^(6+m)/(e^6*(6+m))],
[(a+b*x)^3*(A+B*x)*(d+e*x)^m,x,2,(b*d-a*e)^3*(B*d-A*e)*(d+e*x)^(1+m)/(e^5*(1+m))-(b*d-a*e)^2*(4*b*B*d-3*A*b*e-a*B*e)*(d+e*x)^(2+m)/(e^5*(2+m))+3*b*(b*d-a*e)*(2*b*B*d-A*b*e-a*B*e)*(d+e*x)^(3+m)/(e^5*(3+m))-b^2*(4*b*B*d-A*b*e-3*a*B*e)*(d+e*x)^(4+m)/(e^5*(4+m))+b^3*B*(d+e*x)^(5+m)/(e^5*(5+m))],
[(a+b*x)^2*(A+B*x)*(d+e*x)^m,x,2,-(b*d-a*e)^2*(B*d-A*e)*(d+e*x)^(1+m)/(e^4*(1+m))+(b*d-a*e)*(3*b*B*d-2*A*b*e-a*B*e)*(d+e*x)^(2+m)/(e^4*(2+m))-b*(3*b*B*d-A*b*e-2*a*B*e)*(d+e*x)^(3+m)/(e^4*(3+m))+b^2*B*(d+e*x)^(4+m)/(e^4*(4+m))],
[(a+b*x)*(A+B*x)*(d+e*x)^m,x,2,(b*d-a*e)*(B*d-A*e)*(d+e*x)^(1+m)/(e^3*(1+m))-(2*b*B*d-A*b*e-a*B*e)*(d+e*x)^(2+m)/(e^3*(2+m))+b*B*(d+e*x)^(3+m)/(e^3*(3+m))],
[(A+B*x)*(d+e*x)^m,x,2,-(B*d-A*e)*(d+e*x)^(1+m)/(e^2*(1+m))+B*(d+e*x)^(2+m)/(e^2*(2+m))],
[(A+B*x)*(d+e*x)^m/(a+b*x),x,2,B*(d+e*x)^(1+m)/(b*e*(1+m))-(A*b-a*B)*(d+e*x)^(1+m)*hypergeom([1,1+m],[2+m],b*(d+e*x)/(b*d-a*e))/(b*(b*d-a*e)*(1+m))],
[(A+B*x)*(d+e*x)^m/(a+b*x)^2,x,2,-(A*b-a*B)*(d+e*x)^(1+m)/(b*(b*d-a*e)*(a+b*x))+(a*B*e*(1+m)-b*(B*d+A*e*m))*(d+e*x)^(1+m)*hypergeom([1,1+m],[2+m],b*(d+e*x)/(b*d-a*e))/(b*(b*d-a*e)^2*(1+m))],
[(1-2*x)*(2+3*x)^m*(3+5*x)^3,x,2,-7/243*(2+3*x)^(1+m)/(1+m)+107/243*(2+3*x)^(2+m)/(2+m)-185/81*(2+3*x)^(3+m)/(3+m)+1025/243*(2+3*x)^(4+m)/(4+m)-250/243*(2+3*x)^(5+m)/(5+m)],
[(1-2*x)*(2+3*x)^m*(3+5*x)^2,x,2,7/81*(2+3*x)^(1+m)/(1+m)-8/9*(2+3*x)^(2+m)/(2+m)+65/27*(2+3*x)^(3+m)/(3+m)-50/81*(2+3*x)^(4+m)/(4+m)],
[(1-2*x)*(2+3*x)^m*(3+5*x),x,2,-7/27*(2+3*x)^(1+m)/(1+m)+37/27*(2+3*x)^(2+m)/(2+m)-10/27*(2+3*x)^(3+m)/(3+m)],
[(1-2*x)*(2+3*x)^m/(3+5*x),x,2,-2/15*(2+3*x)^(1+m)/(1+m)-11/5*(2+3*x)^(1+m)*hypergeom([1,1+m],[2+m],5*(2+3*x))/(1+m)],
[(1-2*x)*(2+3*x)^m/(3+5*x)^2,x,2,-11/5*(2+3*x)^(1+m)/(3+5*x)+1/5*(2-33*m)*(2+3*x)^(1+m)*hypergeom([1,1+m],[2+m],5*(2+3*x))/(1+m)],
[(1-2*x)*(2+3*x)^m/(3+5*x)^3,x,2,-11/10*(2+3*x)^(1+m)/(3+5*x)^2-3/10*(37-33*m)*(2+3*x)^(1+m)*hypergeom([2,1+m],[2+m],5*(2+3*x))/(1+m)],
[(2+3*x)^m*(3+5*x)^3/(1-2*x),x,3,-5135/216*(2+3*x)^(1+m)/(1+m)-725/108*(2+3*x)^(2+m)/(2+m)-125/54*(2+3*x)^(3+m)/(3+m)+1331/56*(2+3*x)^(1+m)*hypergeom([1,1+m],[2+m],2/7*(2+3*x))/(1+m)],
[(2+3*x)^m*(3+5*x)^2/(1-2*x),x,3,-155/36*(2+3*x)^(1+m)/(1+m)-25/18*(2+3*x)^(2+m)/(2+m)+121/28*(2+3*x)^(1+m)*hypergeom([1,1+m],[2+m],2/7*(2+3*x))/(1+m)],
[(2+3*x)^m*(3+5*x)/(1-2*x),x,2,-5/6*(2+3*x)^(1+m)/(1+m)+11/14*(2+3*x)^(1+m)*hypergeom([1,1+m],[2+m],2/7*(2+3*x))/(1+m)],
[(2+3*x)^m/((1-2*x)*(3+5*x)),x,3,2/77*(2+3*x)^(1+m)*hypergeom([1,1+m],[2+m],2/7*(2+3*x))/(1+m)-5/11*(2+3*x)^(1+m)*hypergeom([1,1+m],[2+m],5*(2+3*x))/(1+m)],
[(2+3*x)^m/((1-2*x)*(3+5*x)^2),x,4,-5/11*(2+3*x)^(1+m)/(3+5*x)+4/847*(2+3*x)^(1+m)*hypergeom([1,1+m],[2+m],2/7*(2+3*x))/(1+m)-5/121*(2+33*m)*(2+3*x)^(1+m)*hypergeom([1,1+m],[2+m],5*(2+3*x))/(1+m)],
[(2+3*x)^m/((1-2*x)*(3+5*x)^3),x,5,-5/22*(2+3*x)^(1+m)/(3+5*x)^2+5/242*(29-33*m)*(2+3*x)^(1+m)/(3+5*x)+8/9317*(2+3*x)^(1+m)*hypergeom([1,1+m],[2+m],2/7*(2+3*x))/(1+m)-5/2662*(8-957*m+1089*m^2)*(2+3*x)^(1+m)*hypergeom([1,1+m],[2+m],5*(2+3*x))/(1+m)],

#  Mathematica 8 cannot get these. 
[(a+b*x)^m/(e+f*x)^2,x,1,b*(a+b*x)^(1+m)*hypergeom([2,1+m],[2+m],-f*(a+b*x)/(b*e-a*f))/((b*e-a*f)^2*(1+m))],
[(a+b*x)^m/((c+d*x)*(e+f*x)^2),x,4,-f*(a+b*x)^(1+m)/((b*e-a*f)*(d*e-c*f)*(e+f*x))+d^2*(a+b*x)^(1+m)*hypergeom([1,1+m],[2+m],-d*(a+b*x)/(b*c-a*d))/((b*c-a*d)*(d*e-c*f)^2*(1+m))+f*(a*d*f-b*(d*e*(1-m)+c*f*m))*(a+b*x)^(1+m)*hypergeom([1,1+m],[2+m],-f*(a+b*x)/(b*e-a*f))/((b*e-a*f)^2*(d*e-c*f)^2*(1+m))],
[(a+b*x)^m/((c+d*x)^2*(e+f*x)^2),x,5,f*(b*d*e+b*c*f-2*a*d*f)*(a+b*x)^(1+m)/((b*c-a*d)*(b*e-a*f)*(d*e-c*f)^2*(e+f*x))+d*(a+b*x)^(1+m)/((b*c-a*d)*(d*e-c*f)*(c+d*x)*(e+f*x))+d^2*(2*a*d*f-b*(c*f*(2-m)+d*e*m))*(a+b*x)^(1+m)*hypergeom([1,1+m],[2+m],-d*(a+b*x)/(b*c-a*d))/((b*c-a*d)^2*(d*e-c*f)^3*(1+m))-f^2*(2*a*d*f-b*(d*e*(2-m)+c*f*m))*(a+b*x)^(1+m)*hypergeom([1,1+m],[2+m],-f*(a+b*x)/(b*e-a*f))/((b*e-a*f)^2*(d*e-c*f)^3*(1+m))]]:
