# Maple integration test file: "3 Logarithms\3.2.1 (f+g x)^m (A+B log(e ((a+b x) over (c+d x))^n))^p.txt"

lst:=[

# Integrands of the form (f+g x)^m (A+B Log[e ((a+b x)/(c+d x))^n])^p

# Integrands of the form (f+g x)^m (A+B Log[e ((a+b x)/(c+d x))^n])^p when b f-a g=0

# Integrands of the form (f+g x)^m (A+B Log[e ((a+b x)/(c+d x))^n])^p and b f-a g=0

# p>0
[(a*g+b*g*x)^4*(A+B*log(e*((a+b*x)/(c+d*x))^n)),x,4,1/5*B*(b*c-a*d)^4*g^4*n*x/d^4-1/10*B*(b*c-a*d)^3*g^4*n*(a+b*x)^2/(b*d^3)+1/15*B*(b*c-a*d)^2*g^4*n*(a+b*x)^3/(b*d^2)-1/20*B*(b*c-a*d)*g^4*n*(a+b*x)^4/(b*d)+1/5*g^4*(a+b*x)^5*(A+B*log(e*((a+b*x)/(c+d*x))^n))/b-1/5*B*(b*c-a*d)^5*g^4*n*log(c+d*x)/(b*d^5)],
[(a*g+b*g*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n)),x,4,-1/4*B*(b*c-a*d)^3*g^3*n*x/d^3+1/8*B*(b*c-a*d)^2*g^3*n*(a+b*x)^2/(b*d^2)-1/12*B*(b*c-a*d)*g^3*n*(a+b*x)^3/(b*d)+1/4*g^3*(a+b*x)^4*(A+B*log(e*((a+b*x)/(c+d*x))^n))/b+1/4*B*(b*c-a*d)^4*g^3*n*log(c+d*x)/(b*d^4)],
[(a*g+b*g*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n)),x,4,1/3*B*(b*c-a*d)^2*g^2*n*x/d^2-1/6*B*(b*c-a*d)*g^2*n*(a+b*x)^2/(b*d)+1/3*g^2*(a+b*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))/b-1/3*B*(b*c-a*d)^3*g^2*n*log(c+d*x)/(b*d^3)],
[(a*g+b*g*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n)),x,4,-1/2*B*(b*c-a*d)*g*n*x/d+1/2*g*(a+b*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))/b+1/2*B*(b*c-a*d)^2*g*n*log(c+d*x)/(b*d^2)],
[(A+B*log(e*((a+b*x)/(c+d*x))^n))/(a*g+b*g*x),x,5,-log((-b*c+a*d)/(d*(a+b*x)))*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(b*g)+B*n*polylog(2,1+(b*c-a*d)/(d*(a+b*x)))/(b*g)],
[(A+B*log(e*((a+b*x)/(c+d*x))^n))/(a*g+b*g*x)^2,x,2,-B*n/(b*g^2*(a+b*x))-(c+d*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)*g^2*(a+b*x)),-B*n*(c+d*x)/((b*c-a*d)*g^2*(a+b*x))-(c+d*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)*g^2*(a+b*x))],
[(A+B*log(e*((a+b*x)/(c+d*x))^n))/(a*g+b*g*x)^3,x,4,-1/4*B*n/(b*g^3*(a+b*x)^2)+1/2*B*d*n/(b*(b*c-a*d)*g^3*(a+b*x))+1/2*B*d^2*n*log(a+b*x)/(b*(b*c-a*d)^2*g^3)+1/2*(-A-B*log(e*((a+b*x)/(c+d*x))^n))/(b*g^3*(a+b*x)^2)-1/2*B*d^2*n*log(c+d*x)/(b*(b*c-a*d)^2*g^3)],
[(A+B*log(e*((a+b*x)/(c+d*x))^n))/(a*g+b*g*x)^4,x,4,-1/9*B*n/(b*g^4*(a+b*x)^3)+1/6*B*d*n/(b*(b*c-a*d)*g^4*(a+b*x)^2)-1/3*B*d^2*n/(b*(b*c-a*d)^2*g^4*(a+b*x))-1/3*B*d^3*n*log(a+b*x)/(b*(b*c-a*d)^3*g^4)+1/3*(-A-B*log(e*((a+b*x)/(c+d*x))^n))/(b*g^4*(a+b*x)^3)+1/3*B*d^3*n*log(c+d*x)/(b*(b*c-a*d)^3*g^4)],
[(A+B*log(e*((a+b*x)/(c+d*x))^n))/(a*g+b*g*x)^5,x,4,-1/16*B*n/(b*g^5*(a+b*x)^4)+1/12*B*d*n/(b*(b*c-a*d)*g^5*(a+b*x)^3)-1/8*B*d^2*n/(b*(b*c-a*d)^2*g^5*(a+b*x)^2)+1/4*B*d^3*n/(b*(b*c-a*d)^3*g^5*(a+b*x))+1/4*B*d^4*n*log(a+b*x)/(b*(b*c-a*d)^4*g^5)+1/4*(-A-B*log(e*((a+b*x)/(c+d*x))^n))/(b*g^5*(a+b*x)^4)-1/4*B*d^4*n*log(c+d*x)/(b*(b*c-a*d)^4*g^5)],
[(a*g+b*g*x)^4*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2,x,8,-1/10*B*(b*c-a*d)*g^4*n*(a+b*x)^4*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(b*d)+1/5*g^4*(a+b*x)^5*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/b+1/30*B*(b*c-a*d)^2*g^4*n*(a+b*x)^3*(4*A+B*n+4*B*log(e*((a+b*x)/(c+d*x))^n))/(b*d^2)-1/60*B*(b*c-a*d)^3*g^4*n*(a+b*x)^2*(12*A+7*B*n+12*B*log(e*((a+b*x)/(c+d*x))^n))/(b*d^3)+1/30*B*(b*c-a*d)^4*g^4*n*(a+b*x)*(12*A+13*B*n+12*B*log(e*((a+b*x)/(c+d*x))^n))/(b*d^4)+1/30*B*(b*c-a*d)^5*g^4*n*(12*A+25*B*n+12*B*log(e*((a+b*x)/(c+d*x))^n))*log((b*c-a*d)/(b*(c+d*x)))/(b*d^5)+2/5*B^2*(b*c-a*d)^5*g^4*n^2*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(b*d^5)],
[(a*g+b*g*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2,x,7,-1/6*B*(b*c-a*d)*g^3*n*(a+b*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(b*d)+1/4*g^3*(a+b*x)^4*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/b+1/12*B*(b*c-a*d)^2*g^3*n*(a+b*x)^2*(3*A+B*n+3*B*log(e*((a+b*x)/(c+d*x))^n))/(b*d^2)-1/12*B*(b*c-a*d)^3*g^3*n*(a+b*x)*(6*A+5*B*n+6*B*log(e*((a+b*x)/(c+d*x))^n))/(b*d^3)-1/12*B*(b*c-a*d)^4*g^3*n*(6*A+11*B*n+6*B*log(e*((a+b*x)/(c+d*x))^n))*log((b*c-a*d)/(b*(c+d*x)))/(b*d^4)-1/2*B^2*(b*c-a*d)^4*g^3*n^2*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(b*d^4)],
[(a*g+b*g*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2,x,6,-1/3*B*(b*c-a*d)*g^2*n*(a+b*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(b*d)+1/3*g^2*(a+b*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/b+1/3*B*(b*c-a*d)^2*g^2*n*(a+b*x)*(2*A+B*n+2*B*log(e*((a+b*x)/(c+d*x))^n))/(b*d^2)+1/3*B*(b*c-a*d)^3*g^2*n*(2*A+3*B*n+2*B*log(e*((a+b*x)/(c+d*x))^n))*log((b*c-a*d)/(b*(c+d*x)))/(b*d^3)+2/3*B^2*(b*c-a*d)^3*g^2*n^2*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(b*d^3)],
[(a*g+b*g*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2,x,5,-B*(b*c-a*d)*g*n*(a+b*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(b*d)+1/2*g*(a+b*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/b-B*(b*c-a*d)^2*g*n*(A+B*n+B*log(e*((a+b*x)/(c+d*x))^n))*log((b*c-a*d)/(b*(c+d*x)))/(b*d^2)-B^2*(b*c-a*d)^2*g*n^2*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(b*d^2)],
[(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/(a*g+b*g*x),x,4,-(A+B*log(e*((a+b*x)/(c+d*x))^n))^2*log(1-b*(c+d*x)/(d*(a+b*x)))/(b*g)+2*B*n*(A+B*log(e*((a+b*x)/(c+d*x))^n))*polylog(2,b*(c+d*x)/(d*(a+b*x)))/(b*g)+2*B^2*n^2*polylog(3,b*(c+d*x)/(d*(a+b*x)))/(b*g)],
[(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/(a*g+b*g*x)^2,x,3,-2*B^2*n^2*(c+d*x)/((b*c-a*d)*g^2*(a+b*x))-2*B*n*(c+d*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)*g^2*(a+b*x))-(c+d*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/((b*c-a*d)*g^2*(a+b*x))],
[(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/(a*g+b*g*x)^3,x,7,2*B^2*d*n^2*(c+d*x)/((b*c-a*d)^2*g^3*(a+b*x))-1/4*b*B^2*n^2*(c+d*x)^2/((b*c-a*d)^2*g^3*(a+b*x)^2)+2*B*d*n*(c+d*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)^2*g^3*(a+b*x))-1/2*b*B*n*(c+d*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)^2*g^3*(a+b*x)^2)+d*(c+d*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/((b*c-a*d)^2*g^3*(a+b*x))-1/2*b*(c+d*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/((b*c-a*d)^2*g^3*(a+b*x)^2)],
[(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/(a*g+b*g*x)^4,x,9,-2*B^2*d^2*n^2*(c+d*x)/((b*c-a*d)^3*g^4*(a+b*x))+1/2*b*B^2*d*n^2*(c+d*x)^2/((b*c-a*d)^3*g^4*(a+b*x)^2)-2/27*b^2*B^2*n^2*(c+d*x)^3/((b*c-a*d)^3*g^4*(a+b*x)^3)-2*B*d^2*n*(c+d*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)^3*g^4*(a+b*x))+b*B*d*n*(c+d*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)^3*g^4*(a+b*x)^2)-2/9*b^2*B*n*(c+d*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)^3*g^4*(a+b*x)^3)-d^2*(c+d*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/((b*c-a*d)^3*g^4*(a+b*x))+b*d*(c+d*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/((b*c-a*d)^3*g^4*(a+b*x)^2)-1/3*b^2*(c+d*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/((b*c-a*d)^3*g^4*(a+b*x)^3)],
[(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/(a*g+b*g*x)^5,x,11,2*B^2*d^3*n^2*(c+d*x)/((b*c-a*d)^4*g^5*(a+b*x))-3/4*b*B^2*d^2*n^2*(c+d*x)^2/((b*c-a*d)^4*g^5*(a+b*x)^2)+2/9*b^2*B^2*d*n^2*(c+d*x)^3/((b*c-a*d)^4*g^5*(a+b*x)^3)-1/32*b^3*B^2*n^2*(c+d*x)^4/((b*c-a*d)^4*g^5*(a+b*x)^4)+2*B*d^3*n*(c+d*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)^4*g^5*(a+b*x))-3/2*b*B*d^2*n*(c+d*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)^4*g^5*(a+b*x)^2)+2/3*b^2*B*d*n*(c+d*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)^4*g^5*(a+b*x)^3)-1/8*b^3*B*n*(c+d*x)^4*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)^4*g^5*(a+b*x)^4)+d^3*(c+d*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/((b*c-a*d)^4*g^5*(a+b*x))-3/2*b*d^2*(c+d*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/((b*c-a*d)^4*g^5*(a+b*x)^2)+b^2*d*(c+d*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/((b*c-a*d)^4*g^5*(a+b*x)^3)-1/4*b^3*(c+d*x)^4*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/((b*c-a*d)^4*g^5*(a+b*x)^4)],

# p<0
[(a*g+b*g*x)^2/(A+B*log(e*((a+b*x)/(c+d*x))^n)),x,0,Unintegrable((a*g+b*g*x)^2/(A+B*log(e*((a+b*x)/(c+d*x))^n)),x)],
[(a*g+b*g*x)/(A+B*log(e*((a+b*x)/(c+d*x))^n)),x,0,Unintegrable((a*g+b*g*x)/(A+B*log(e*((a+b*x)/(c+d*x))^n)),x)],
[1/((a*g+b*g*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))),x,0,Unintegrable(1/((a*g+b*g*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))),x)],
[1/((a*g+b*g*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))),x,3,exp(A/(B*n))*(e*((a+b*x)/(c+d*x))^n)^(1/n)*(c+d*x)*Ei((-A-B*log(e*((a+b*x)/(c+d*x))^n))/(B*n))/(B*(b*c-a*d)*g^2*n*(a+b*x))],
[1/((a*g+b*g*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))),x,7,b*exp(2*A/(B*n))*(e*((a+b*x)/(c+d*x))^n)^(2/n)*(c+d*x)^2*Ei(-2*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(B*n))/(B*(b*c-a*d)^2*g^3*n*(a+b*x)^2)-d*exp(A/(B*n))*(e*((a+b*x)/(c+d*x))^n)^(1/n)*(c+d*x)*Ei((-A-B*log(e*((a+b*x)/(c+d*x))^n))/(B*n))/(B*(b*c-a*d)^2*g^3*n*(a+b*x))],
[(a*g+b*g*x)^2/(A+B*log(e*((a+b*x)/(c+d*x))^n))^2,x,0,Unintegrable((a*g+b*g*x)^2/(A+B*log(e*((a+b*x)/(c+d*x))^n))^2,x)],
[(a*g+b*g*x)/(A+B*log(e*((a+b*x)/(c+d*x))^n))^2,x,0,Unintegrable((a*g+b*g*x)/(A+B*log(e*((a+b*x)/(c+d*x))^n))^2,x)],
[1/((a*g+b*g*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2),x,0,Unintegrable(1/((a*g+b*g*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2),x)],
[1/((a*g+b*g*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2),x,4,-exp(A/(B*n))*(e*((a+b*x)/(c+d*x))^n)^(1/n)*(c+d*x)*Ei((-A-B*log(e*((a+b*x)/(c+d*x))^n))/(B*n))/(B^2*(b*c-a*d)*g^2*n^2*(a+b*x))+(-c-d*x)/(B*(b*c-a*d)*g^2*n*(a+b*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n)))],
[1/((a*g+b*g*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2),x,9,-2*b*exp(2*A/(B*n))*(e*((a+b*x)/(c+d*x))^n)^(2/n)*(c+d*x)^2*Ei(-2*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(B*n))/(B^2*(b*c-a*d)^2*g^3*n^2*(a+b*x)^2)+d*exp(A/(B*n))*(e*((a+b*x)/(c+d*x))^n)^(1/n)*(c+d*x)*Ei((-A-B*log(e*((a+b*x)/(c+d*x))^n))/(B*n))/(B^2*(b*c-a*d)^2*g^3*n^2*(a+b*x))+d*(c+d*x)/(B*(b*c-a*d)^2*g^3*n*(a+b*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n)))-b*(c+d*x)^2/(B*(b*c-a*d)^2*g^3*n*(a+b*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n)))],

# Integrands of the form (f+g x)^m (A+B Log[e ((a+b x)/(c+d x))^n])^p when d f-c g=0

# Integrands of the form (f+g x)^m (A+B Log[e ((a+b x)/(c+d x))^n])^p and d f-c g=0

# p>0
[(c*g+d*g*x)^4*(A+B*log(e*((a+b*x)/(c+d*x))^n)),x,4,-1/5*B*(b*c-a*d)^4*g^4*n*x/b^4-1/10*B*(b*c-a*d)^3*g^4*n*(c+d*x)^2/(b^3*d)-1/15*B*(b*c-a*d)^2*g^4*n*(c+d*x)^3/(b^2*d)-1/20*B*(b*c-a*d)*g^4*n*(c+d*x)^4/(b*d)-1/5*B*(b*c-a*d)^5*g^4*n*log(a+b*x)/(b^5*d)+1/5*g^4*(c+d*x)^5*(A+B*log(e*((a+b*x)/(c+d*x))^n))/d],
[(c*g+d*g*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n)),x,4,-1/4*B*(b*c-a*d)^3*g^3*n*x/b^3-1/8*B*(b*c-a*d)^2*g^3*n*(c+d*x)^2/(b^2*d)-1/12*B*(b*c-a*d)*g^3*n*(c+d*x)^3/(b*d)-1/4*B*(b*c-a*d)^4*g^3*n*log(a+b*x)/(b^4*d)+1/4*g^3*(c+d*x)^4*(A+B*log(e*((a+b*x)/(c+d*x))^n))/d],
[(c*g+d*g*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n)),x,4,-1/3*B*(b*c-a*d)^2*g^2*n*x/b^2-1/6*B*(b*c-a*d)*g^2*n*(c+d*x)^2/(b*d)-1/3*B*(b*c-a*d)^3*g^2*n*log(a+b*x)/(b^3*d)+1/3*g^2*(c+d*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))/d],
[(c*g+d*g*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n)),x,4,-1/2*B*(b*c-a*d)*g*n*x/b-1/2*B*(b*c-a*d)^2*g*n*log(a+b*x)/(b^2*d)+1/2*g*(c+d*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))/d],
[(A+B*log(e*((a+b*x)/(c+d*x))^n))/(c*g+d*g*x),x,5,-(A+B*log(e*((a+b*x)/(c+d*x))^n))*log((b*c-a*d)/(b*(c+d*x)))/(d*g)-B*n*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(d*g)],
[(A+B*log(e*((a+b*x)/(c+d*x))^n))/(c*g+d*g*x)^2,x,3,A*(a+b*x)/((b*c-a*d)*g^2*(c+d*x))-B*n*(a+b*x)/((b*c-a*d)*g^2*(c+d*x))+B*(a+b*x)*log(e*((a+b*x)/(c+d*x))^n)/((b*c-a*d)*g^2*(c+d*x))],
[(A+B*log(e*((a+b*x)/(c+d*x))^n))/(c*g+d*g*x)^3,x,4,1/4*B*n/(d*g^3*(c+d*x)^2)+1/2*b*B*n/(d*(b*c-a*d)*g^3*(c+d*x))+1/2*b^2*B*n*log(a+b*x)/(d*(b*c-a*d)^2*g^3)+1/2*(-A-B*log(e*((a+b*x)/(c+d*x))^n))/(d*g^3*(c+d*x)^2)-1/2*b^2*B*n*log(c+d*x)/(d*(b*c-a*d)^2*g^3)],
[(A+B*log(e*((a+b*x)/(c+d*x))^n))/(c*g+d*g*x)^4,x,4,1/9*B*n/(d*g^4*(c+d*x)^3)+1/6*b*B*n/(d*(b*c-a*d)*g^4*(c+d*x)^2)+1/3*b^2*B*n/(d*(b*c-a*d)^2*g^4*(c+d*x))+1/3*b^3*B*n*log(a+b*x)/(d*(b*c-a*d)^3*g^4)+1/3*(-A-B*log(e*((a+b*x)/(c+d*x))^n))/(d*g^4*(c+d*x)^3)-1/3*b^3*B*n*log(c+d*x)/(d*(b*c-a*d)^3*g^4)],
[(A+B*log(e*((a+b*x)/(c+d*x))^n))/(c*g+d*g*x)^5,x,4,1/16*B*n/(d*g^5*(c+d*x)^4)+1/12*b*B*n/(d*(b*c-a*d)*g^5*(c+d*x)^3)+1/8*b^2*B*n/(d*(b*c-a*d)^2*g^5*(c+d*x)^2)+1/4*b^3*B*n/(d*(b*c-a*d)^3*g^5*(c+d*x))+1/4*b^4*B*n*log(a+b*x)/(d*(b*c-a*d)^4*g^5)+1/4*(-A-B*log(e*((a+b*x)/(c+d*x))^n))/(d*g^5*(c+d*x)^4)-1/4*b^4*B*n*log(c+d*x)/(d*(b*c-a*d)^4*g^5)],
[(c*g+d*g*x)^4*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2,x,19,13/30*B^2*(b*c-a*d)^4*g^4*n^2*x/b^4+7/60*B^2*(b*c-a*d)^3*g^4*n^2*(c+d*x)^2/(b^3*d)+1/30*B^2*(b*c-a*d)^2*g^4*n^2*(c+d*x)^3/(b^2*d)-2/5*B*(b*c-a*d)^4*g^4*n*(a+b*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/b^5-1/5*B*(b*c-a*d)^3*g^4*n*(c+d*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(b^3*d)-2/15*B*(b*c-a*d)^2*g^4*n*(c+d*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(b^2*d)-1/10*B*(b*c-a*d)*g^4*n*(c+d*x)^4*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(b*d)+1/5*g^4*(c+d*x)^5*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/d+13/30*B^2*(b*c-a*d)^5*g^4*n^2*log((a+b*x)/(c+d*x))/(b^5*d)+5/6*B^2*(b*c-a*d)^5*g^4*n^2*log(c+d*x)/(b^5*d)+2/5*B*(b*c-a*d)^5*g^4*n*(A+B*log(e*((a+b*x)/(c+d*x))^n))*log(1-b*(c+d*x)/(d*(a+b*x)))/(b^5*d)-2/5*B^2*(b*c-a*d)^5*g^4*n^2*polylog(2,b*(c+d*x)/(d*(a+b*x)))/(b^5*d)],
[(c*g+d*g*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2,x,15,5/12*B^2*(b*c-a*d)^3*g^3*n^2*x/b^3+1/12*B^2*(b*c-a*d)^2*g^3*n^2*(c+d*x)^2/(b^2*d)-1/2*B*(b*c-a*d)^3*g^3*n*(a+b*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/b^4-1/4*B*(b*c-a*d)^2*g^3*n*(c+d*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(b^2*d)-1/6*B*(b*c-a*d)*g^3*n*(c+d*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(b*d)+1/4*g^3*(c+d*x)^4*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/d+5/12*B^2*(b*c-a*d)^4*g^3*n^2*log((a+b*x)/(c+d*x))/(b^4*d)+11/12*B^2*(b*c-a*d)^4*g^3*n^2*log(c+d*x)/(b^4*d)+1/2*B*(b*c-a*d)^4*g^3*n*(A+B*log(e*((a+b*x)/(c+d*x))^n))*log(1-b*(c+d*x)/(d*(a+b*x)))/(b^4*d)-1/2*B^2*(b*c-a*d)^4*g^3*n^2*polylog(2,b*(c+d*x)/(d*(a+b*x)))/(b^4*d)],
[(c*g+d*g*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2,x,11,1/3*B^2*(b*c-a*d)^2*g^2*n^2*x/b^2-2/3*B*(b*c-a*d)^2*g^2*n*(a+b*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/b^3-1/3*B*(b*c-a*d)*g^2*n*(c+d*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(b*d)+1/3*g^2*(c+d*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/d+1/3*B^2*(b*c-a*d)^3*g^2*n^2*log((a+b*x)/(c+d*x))/(b^3*d)+B^2*(b*c-a*d)^3*g^2*n^2*log(c+d*x)/(b^3*d)+2/3*B*(b*c-a*d)^3*g^2*n*(A+B*log(e*((a+b*x)/(c+d*x))^n))*log(1-b*(c+d*x)/(d*(a+b*x)))/(b^3*d)-2/3*B^2*(b*c-a*d)^3*g^2*n^2*polylog(2,b*(c+d*x)/(d*(a+b*x)))/(b^3*d)],
[(c*g+d*g*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2,x,7,-B*(b*c-a*d)*g*n*(a+b*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/b^2+1/2*g*(c+d*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/d+B^2*(b*c-a*d)^2*g*n^2*log(c+d*x)/(b^2*d)+B*(b*c-a*d)^2*g*n*(A+B*log(e*((a+b*x)/(c+d*x))^n))*log(1-b*(c+d*x)/(d*(a+b*x)))/(b^2*d)-B^2*(b*c-a*d)^2*g*n^2*polylog(2,b*(c+d*x)/(d*(a+b*x)))/(b^2*d)],
[(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/(c*g+d*g*x),x,4,-(A+B*log(e*((a+b*x)/(c+d*x))^n))^2*log((b*c-a*d)/(b*(c+d*x)))/(d*g)-2*B*n*(A+B*log(e*((a+b*x)/(c+d*x))^n))*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(d*g)+2*B^2*n^2*polylog(3,d*(a+b*x)/(b*(c+d*x)))/(d*g)],
[(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/(c*g+d*g*x)^2,x,4,-2*A*B*n*(a+b*x)/((b*c-a*d)*g^2*(c+d*x))+2*B^2*n^2*(a+b*x)/((b*c-a*d)*g^2*(c+d*x))-2*B^2*n*(a+b*x)*log(e*((a+b*x)/(c+d*x))^n)/((b*c-a*d)*g^2*(c+d*x))+(a+b*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/((b*c-a*d)*g^2*(c+d*x))],
[(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/(c*g+d*g*x)^3,x,8,-1/4*B^2*d*n^2*(a+b*x)^2/((b*c-a*d)^2*g^3*(c+d*x)^2)-2*A*b*B*n*(a+b*x)/((b*c-a*d)^2*g^3*(c+d*x))+2*b*B^2*n^2*(a+b*x)/((b*c-a*d)^2*g^3*(c+d*x))-2*b*B^2*n*(a+b*x)*log(e*((a+b*x)/(c+d*x))^n)/((b*c-a*d)^2*g^3*(c+d*x))+1/2*B*d*n*(a+b*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)^2*g^3*(c+d*x)^2)-1/2*d*(a+b*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/((b*c-a*d)^2*g^3*(c+d*x)^2)+b*(a+b*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/((b*c-a*d)^2*g^3*(c+d*x))],
[(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/(c*g+d*g*x)^4,x,6,2/27*B^2*d^2*n^2*(a+b*x)^3/((b*c-a*d)^3*g^4*(c+d*x)^3)-1/2*b*B^2*d*n^2*(a+b*x)^2/((b*c-a*d)^3*g^4*(c+d*x)^2)+2*b^2*B^2*n^2*(a+b*x)/((b*c-a*d)^3*g^4*(c+d*x))-2/9*B*d^2*n*(a+b*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)^3*g^4*(c+d*x)^3)+b*B*d*n*(a+b*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)^3*g^4*(c+d*x)^2)-2*b^2*B*n*(a+b*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)^3*g^4*(c+d*x))-1/3*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/(d*g^4*(c+d*x)^3)+2/3*b^3*B*n*(A+B*log(e*((a+b*x)/(c+d*x))^n))*log((a+b*x)/(c+d*x))/(d*(b*c-a*d)^3*g^4)-1/3*b^3*B^2*n^2*log((a+b*x)/(c+d*x))^2/(d*(b*c-a*d)^3*g^4)],
[(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/(c*g+d*g*x)^5,x,5,-1/32*B^2*d^3*n^2*(a+b*x)^4/((b*c-a*d)^4*g^5*(c+d*x)^4)+2/9*b*B^2*d^2*n^2*(a+b*x)^3/((b*c-a*d)^4*g^5*(c+d*x)^3)-3/4*b^2*B^2*d*n^2*(a+b*x)^2/((b*c-a*d)^4*g^5*(c+d*x)^2)+2*b^3*B^2*n^2*(a+b*x)/((b*c-a*d)^4*g^5*(c+d*x))+1/8*B*d^3*n*(a+b*x)^4*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)^4*g^5*(c+d*x)^4)-2/3*b*B*d^2*n*(a+b*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)^4*g^5*(c+d*x)^3)+3/2*b^2*B*d*n*(a+b*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)^4*g^5*(c+d*x)^2)-2*b^3*B*n*(a+b*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)^4*g^5*(c+d*x))-1/4*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/(d*g^5*(c+d*x)^4)+1/2*b^4*B*n*(A+B*log(e*((a+b*x)/(c+d*x))^n))*log((a+b*x)/(c+d*x))/(d*(b*c-a*d)^4*g^5)-1/4*b^4*B^2*n^2*log((a+b*x)/(c+d*x))^2/(d*(b*c-a*d)^4*g^5)],

# p<0
[(c*g+d*g*x)^2/(A+B*log(e*((a+b*x)/(c+d*x))^n)),x,0,Unintegrable((c*g+d*g*x)^2/(A+B*log(e*((a+b*x)/(c+d*x))^n)),x)],
[(c*g+d*g*x)/(A+B*log(e*((a+b*x)/(c+d*x))^n)),x,0,Unintegrable((c*g+d*g*x)/(A+B*log(e*((a+b*x)/(c+d*x))^n)),x)],
[1/((c*g+d*g*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))),x,0,Unintegrable(1/((c*g+d*g*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))),x)],
[1/((c*g+d*g*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))),x,3,(a+b*x)*Ei((A+B*log(e*((a+b*x)/(c+d*x))^n))/(B*n))/(B*(b*c-a*d)*exp(A/(B*n))*g^2*n*(e*((a+b*x)/(c+d*x))^n)^(1/n)*(c+d*x))],
[1/((c*g+d*g*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))),x,7,b*(a+b*x)*Ei((A+B*log(e*((a+b*x)/(c+d*x))^n))/(B*n))/(B*(b*c-a*d)^2*exp(A/(B*n))*g^3*n*(e*((a+b*x)/(c+d*x))^n)^(1/n)*(c+d*x))-d*(a+b*x)^2*Ei(2*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(B*n))/(B*(b*c-a*d)^2*exp(2*A/(B*n))*g^3*n*(e*((a+b*x)/(c+d*x))^n)^(2/n)*(c+d*x)^2)],
[(c*g+d*g*x)^2/(A+B*log(e*((a+b*x)/(c+d*x))^n))^2,x,0,Unintegrable((c*g+d*g*x)^2/(A+B*log(e*((a+b*x)/(c+d*x))^n))^2,x)],
[(c*g+d*g*x)/(A+B*log(e*((a+b*x)/(c+d*x))^n))^2,x,0,Unintegrable((c*g+d*g*x)/(A+B*log(e*((a+b*x)/(c+d*x))^n))^2,x)],
[1/((c*g+d*g*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2),x,0,Unintegrable(1/((c*g+d*g*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2),x)],
[1/((c*g+d*g*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2),x,4,(a+b*x)*Ei((A+B*log(e*((a+b*x)/(c+d*x))^n))/(B*n))/(B^2*(b*c-a*d)*exp(A/(B*n))*g^2*n^2*(e*((a+b*x)/(c+d*x))^n)^(1/n)*(c+d*x))+(-a-b*x)/(B*(b*c-a*d)*g^2*n*(c+d*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n)))],
[1/((c*g+d*g*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2),x,10,b*(a+b*x)*Ei((A+B*log(e*((a+b*x)/(c+d*x))^n))/(B*n))/(B^2*(b*c-a*d)^2*exp(A/(B*n))*g^3*n^2*(e*((a+b*x)/(c+d*x))^n)^(1/n)*(c+d*x))-2*d*(a+b*x)^2*Ei(2*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(B*n))/(B^2*(b*c-a*d)^2*exp(2*A/(B*n))*g^3*n^2*(e*((a+b*x)/(c+d*x))^n)^(2/n)*(c+d*x)^2)+(-a-b*x)/(B*(b*c-a*d)*g^3*n*(c+d*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n)))],

# Integrands of the form (f+g x)^m (A+B Log[e ((a+b x)/(c+d x))^n])^p

# Integrands of the form (f+g x)^m (A+B Log[e ((a+b x)/(c+d x))^n])^p

# p>0
[(f+g*x)^4*(A+B*log(e*((a+b*x)/(c+d*x))^n)),x,3,1/5*B*(b*c-a*d)*g*(a^3*d^3*g^3-a^2*b*d^2*g^2*(5*d*f-c*g)+a*b^2*d*g*(10*d^2*f^2-5*c*d*f*g+c^2*g^2)-b^3*(10*d^3*f^3-10*c*d^2*f^2*g+5*c^2*d*f*g^2-c^3*g^3))*n*x/(b^4*d^4)-1/10*B*(b*c-a*d)*g^2*(a^2*d^2*g^2-a*b*d*g*(5*d*f-c*g)+b^2*(10*d^2*f^2-5*c*d*f*g+c^2*g^2))*n*x^2/(b^3*d^3)-1/15*B*(b*c-a*d)*g^3*(5*b*d*f-b*c*g-a*d*g)*n*x^3/(b^2*d^2)-1/20*B*(b*c-a*d)*g^4*n*x^4/(b*d)-1/5*B*(b*f-a*g)^5*n*log(a+b*x)/(b^5*g)+1/5*(f+g*x)^5*(A+B*log(e*((a+b*x)/(c+d*x))^n))/g+1/5*B*(d*f-c*g)^5*n*log(c+d*x)/(d^5*g)],
[(f+g*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n)),x,3,-1/4*B*(b*c-a*d)*g*(a^2*d^2*g^2-a*b*d*g*(4*d*f-c*g)+b^2*(6*d^2*f^2-4*c*d*f*g+c^2*g^2))*n*x/(b^3*d^3)-1/8*B*(b*c-a*d)*g^2*(4*b*d*f-b*c*g-a*d*g)*n*x^2/(b^2*d^2)-1/12*B*(b*c-a*d)*g^3*n*x^3/(b*d)-1/4*B*(b*f-a*g)^4*n*log(a+b*x)/(b^4*g)+1/4*(f+g*x)^4*(A+B*log(e*((a+b*x)/(c+d*x))^n))/g+1/4*B*(d*f-c*g)^4*n*log(c+d*x)/(d^4*g)],
[(f+g*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n)),x,3,-1/3*B*(b*c-a*d)*g*(3*b*d*f-b*c*g-a*d*g)*n*x/(b^2*d^2)-1/6*B*(b*c-a*d)*g^2*n*x^2/(b*d)-1/3*B*(b*f-a*g)^3*n*log(a+b*x)/(b^3*g)+1/3*(f+g*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))/g+1/3*B*(d*f-c*g)^3*n*log(c+d*x)/(d^3*g)],
[(f+g*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n)),x,3,-1/2*B*(b*c-a*d)*g*n*x/(b*d)-1/2*B*(b*f-a*g)^2*n*log(a+b*x)/(b^2*g)+1/2*(f+g*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))/g+1/2*B*(d*f-c*g)^2*n*log(c+d*x)/(d^2*g)],
[A+B*log(e*((a+b*x)/(c+d*x))^n),x,3,A*x+B*(a+b*x)*log(e*((a+b*x)/(c+d*x))^n)/b-B*(b*c-a*d)*n*log(c+d*x)/(b*d)],
[(A+B*log(e*((a+b*x)/(c+d*x))^n))/(f+g*x),x,7,-B*n*log(-g*(a+b*x)/(b*f-a*g))*log(f+g*x)/g+(A+B*log(e*((a+b*x)/(c+d*x))^n))*log(f+g*x)/g+B*n*log(-g*(c+d*x)/(d*f-c*g))*log(f+g*x)/g-B*n*polylog(2,b*(f+g*x)/(b*f-a*g))/g+B*n*polylog(2,d*(f+g*x)/(d*f-c*g))/g],
[(A+B*log(e*((a+b*x)/(c+d*x))^n))/(f+g*x)^2,x,3,(a+b*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*f-a*g)*(f+g*x))+B*(b*c-a*d)*n*log((f+g*x)/(c+d*x))/((b*f-a*g)*(d*f-c*g))],
[(A+B*log(e*((a+b*x)/(c+d*x))^n))/(f+g*x)^3,x,3,-1/2*B*(b*c-a*d)*n/((b*f-a*g)*(d*f-c*g)*(f+g*x))+1/2*b^2*B*n*log(a+b*x)/(g*(b*f-a*g)^2)+1/2*(-A-B*log(e*((a+b*x)/(c+d*x))^n))/(g*(f+g*x)^2)-1/2*B*d^2*n*log(c+d*x)/(g*(d*f-c*g)^2)+1/2*B*(b*c-a*d)*(2*b*d*f-b*c*g-a*d*g)*n*log(f+g*x)/((b*f-a*g)^2*(d*f-c*g)^2)],
[(A+B*log(e*((a+b*x)/(c+d*x))^n))/(f+g*x)^4,x,3,-1/6*B*(b*c-a*d)*n/((b*f-a*g)*(d*f-c*g)*(f+g*x)^2)-1/3*B*(b*c-a*d)*(2*b*d*f-b*c*g-a*d*g)*n/((b*f-a*g)^2*(d*f-c*g)^2*(f+g*x))+1/3*b^3*B*n*log(a+b*x)/(g*(b*f-a*g)^3)+1/3*(-A-B*log(e*((a+b*x)/(c+d*x))^n))/(g*(f+g*x)^3)-1/3*B*d^3*n*log(c+d*x)/(g*(d*f-c*g)^3)+1/3*B*(b*c-a*d)*(a^2*d^2*g^2-a*b*d*g*(3*d*f-c*g)+b^2*(3*d^2*f^2-3*c*d*f*g+c^2*g^2))*n*log(f+g*x)/((b*f-a*g)^3*(d*f-c*g)^3)],
[(A+B*log(e*((a+b*x)/(c+d*x))^n))/(f+g*x)^5,x,3,-1/12*B*(b*c-a*d)*n/((b*f-a*g)*(d*f-c*g)*(f+g*x)^3)-1/8*B*(b*c-a*d)*(2*b*d*f-b*c*g-a*d*g)*n/((b*f-a*g)^2*(d*f-c*g)^2*(f+g*x)^2)-1/4*B*(b*c-a*d)*(a^2*d^2*g^2-a*b*d*g*(3*d*f-c*g)+b^2*(3*d^2*f^2-3*c*d*f*g+c^2*g^2))*n/((b*f-a*g)^3*(d*f-c*g)^3*(f+g*x))+1/4*b^4*B*n*log(a+b*x)/(g*(b*f-a*g)^4)+1/4*(-A-B*log(e*((a+b*x)/(c+d*x))^n))/(g*(f+g*x)^4)-1/4*B*d^4*n*log(c+d*x)/(g*(d*f-c*g)^4)-1/4*B*(b*c-a*d)*(2*b*d*f-b*c*g-a*d*g)*(2*a*b*d^2*f*g-a^2*d^2*g^2-b^2*(2*d^2*f^2-2*c*d*f*g+c^2*g^2))*n*log(f+g*x)/((b*f-a*g)^4*(d*f-c*g)^4)],
[(f+g*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2,x,15,1/6*B^2*(b*c-a*d)^3*g^3*n^2*x/(b^3*d^3)+1/4*B^2*(b*c-a*d)^2*g^2*(4*b*d*f-3*b*c*g-a*d*g)*n^2*x/(b^3*d^3)+1/12*B^2*(b*c-a*d)^2*g^3*n^2*(c+d*x)^2/(b^2*d^4)-1/2*B*(b*c-a*d)*g*(a^2*d^2*g^2-2*a*b*d*g*(2*d*f-c*g)+b^2*(6*d^2*f^2-8*c*d*f*g+3*c^2*g^2))*n*(a+b*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(b^4*d^3)-1/4*B*(b*c-a*d)*g^2*(4*b*d*f-3*b*c*g-a*d*g)*n*(c+d*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(b^2*d^4)-1/6*B*(b*c-a*d)*g^3*n*(c+d*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(b*d^4)-1/4*(b*f-a*g)^4*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/(b^4*g)+1/4*(f+g*x)^4*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/g-1/2*B*(b*c-a*d)*(2*b*d*f-b*c*g-a*d*g)*(2*a*b*d^2*f*g-a^2*d^2*g^2-b^2*(2*d^2*f^2-2*c*d*f*g+c^2*g^2))*n*(A+B*log(e*((a+b*x)/(c+d*x))^n))*log((b*c-a*d)/(b*(c+d*x)))/(b^4*d^4)+1/6*B^2*(b*c-a*d)^4*g^3*n^2*log((a+b*x)/(c+d*x))/(b^4*d^4)+1/4*B^2*(b*c-a*d)^3*g^2*(4*b*d*f-3*b*c*g-a*d*g)*n^2*log((a+b*x)/(c+d*x))/(b^4*d^4)+1/6*B^2*(b*c-a*d)^4*g^3*n^2*log(c+d*x)/(b^4*d^4)+1/4*B^2*(b*c-a*d)^3*g^2*(4*b*d*f-3*b*c*g-a*d*g)*n^2*log(c+d*x)/(b^4*d^4)+1/2*B^2*(b*c-a*d)^2*g*(a^2*d^2*g^2-2*a*b*d*g*(2*d*f-c*g)+b^2*(6*d^2*f^2-8*c*d*f*g+3*c^2*g^2))*n^2*log(c+d*x)/(b^4*d^4)-1/2*B^2*(b*c-a*d)*(2*b*d*f-b*c*g-a*d*g)*(2*a*b*d^2*f*g-a^2*d^2*g^2-b^2*(2*d^2*f^2-2*c*d*f*g+c^2*g^2))*n^2*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(b^4*d^4)],
[(f+g*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2,x,12,1/3*B^2*(b*c-a*d)^2*g^2*n^2*x/(b^2*d^2)-2/3*B*(b*c-a*d)*g*(3*b*d*f-2*b*c*g-a*d*g)*n*(a+b*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(b^3*d^2)-1/3*B*(b*c-a*d)*g^2*n*(c+d*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(b*d^3)-1/3*(b*f-a*g)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/(b^3*g)+1/3*(f+g*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/g+2/3*B*(b*c-a*d)*(a^2*d^2*g^2-a*b*d*g*(3*d*f-c*g)+b^2*(3*d^2*f^2-3*c*d*f*g+c^2*g^2))*n*(A+B*log(e*((a+b*x)/(c+d*x))^n))*log((b*c-a*d)/(b*(c+d*x)))/(b^3*d^3)+1/3*B^2*(b*c-a*d)^3*g^2*n^2*log((a+b*x)/(c+d*x))/(b^3*d^3)+1/3*B^2*(b*c-a*d)^3*g^2*n^2*log(c+d*x)/(b^3*d^3)+2/3*B^2*(b*c-a*d)^2*g*(3*b*d*f-2*b*c*g-a*d*g)*n^2*log(c+d*x)/(b^3*d^3)+2/3*B^2*(b*c-a*d)*(a^2*d^2*g^2-a*b*d*g*(3*d*f-c*g)+b^2*(3*d^2*f^2-3*c*d*f*g+c^2*g^2))*n^2*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(b^3*d^3)],
[(f+g*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2,x,9,-B*(b*c-a*d)*g*n*(a+b*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(b^2*d)-1/2*(b*f-a*g)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/(b^2*g)+1/2*(f+g*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/g+B*(b*c-a*d)*(2*b*d*f-b*c*g-a*d*g)*n*(A+B*log(e*((a+b*x)/(c+d*x))^n))*log((b*c-a*d)/(b*(c+d*x)))/(b^2*d^2)+B^2*(b*c-a*d)^2*g*n^2*log(c+d*x)/(b^2*d^2)+B^2*(b*c-a*d)*(2*b*d*f-b*c*g-a*d*g)*n^2*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(b^2*d^2)],
[(A+B*log(e*((a+b*x)/(c+d*x))^n))^2,x,6,(a+b*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/b+2*B*(b*c-a*d)*n*(A+B*log(e*((a+b*x)/(c+d*x))^n))*log((b*c-a*d)/(b*(c+d*x)))/(b*d)+2*B^2*(b*c-a*d)*n^2*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(b*d)],
[(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/(f+g*x),x,9,-(A+B*log(e*((a+b*x)/(c+d*x))^n))^2*log((b*c-a*d)/(b*(c+d*x)))/g+(A+B*log(e*((a+b*x)/(c+d*x))^n))^2*log(1-(d*f-c*g)*(a+b*x)/((b*f-a*g)*(c+d*x)))/g-2*B*n*(A+B*log(e*((a+b*x)/(c+d*x))^n))*polylog(2,d*(a+b*x)/(b*(c+d*x)))/g+2*B*n*(A+B*log(e*((a+b*x)/(c+d*x))^n))*polylog(2,(d*f-c*g)*(a+b*x)/((b*f-a*g)*(c+d*x)))/g+2*B^2*n^2*polylog(3,d*(a+b*x)/(b*(c+d*x)))/g-2*B^2*n^2*polylog(3,(d*f-c*g)*(a+b*x)/((b*f-a*g)*(c+d*x)))/g],
[(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/(f+g*x)^2,x,4,(a+b*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/((b*f-a*g)*(f+g*x))+2*B*(b*c-a*d)*n*(A+B*log(e*((a+b*x)/(c+d*x))^n))*log(1-(d*f-c*g)*(a+b*x)/((b*f-a*g)*(c+d*x)))/((b*f-a*g)*(d*f-c*g))+2*B^2*(b*c-a*d)*n^2*polylog(2,(d*f-c*g)*(a+b*x)/((b*f-a*g)*(c+d*x)))/((b*f-a*g)*(d*f-c*g))],
[(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/(f+g*x)^3,x,9,B*(b*c-a*d)*g*n*(a+b*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*f-a*g)^2*(d*f-c*g)*(f+g*x))+1/2*b^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/(g*(b*f-a*g)^2)-1/2*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/(g*(f+g*x)^2)+B^2*(b*c-a*d)^2*g*n^2*log((f+g*x)/(c+d*x))/((b*f-a*g)^2*(d*f-c*g)^2)+B*(b*c-a*d)*(2*b*d*f-b*c*g-a*d*g)*n*(A+B*log(e*((a+b*x)/(c+d*x))^n))*log(1-(d*f-c*g)*(a+b*x)/((b*f-a*g)*(c+d*x)))/((b*f-a*g)^2*(d*f-c*g)^2)+B^2*(b*c-a*d)*(2*b*d*f-b*c*g-a*d*g)*n^2*polylog(2,(d*f-c*g)*(a+b*x)/((b*f-a*g)*(c+d*x)))/((b*f-a*g)^2*(d*f-c*g)^2)],
[(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/(f+g*x)^4,x,12,1/3*B^2*(b*c-a*d)^2*g^2*n^2*(c+d*x)/((b*f-a*g)^2*(d*f-c*g)^3*(f+g*x))-1/3*B*(b*c-a*d)*g^2*n*(c+d*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*f-a*g)*(d*f-c*g)^3*(f+g*x)^2)+2/3*B*(b*c-a*d)*g*(3*b*d*f-b*c*g-2*a*d*g)*n*(a+b*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*f-a*g)^3*(d*f-c*g)^2*(f+g*x))+1/3*b^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/(g*(b*f-a*g)^3)-1/3*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/(g*(f+g*x)^3)+1/3*B^2*(b*c-a*d)^3*g^2*n^2*log((a+b*x)/(c+d*x))/((b*f-a*g)^3*(d*f-c*g)^3)-1/3*B^2*(b*c-a*d)^3*g^2*n^2*log((f+g*x)/(c+d*x))/((b*f-a*g)^3*(d*f-c*g)^3)+2/3*B^2*(b*c-a*d)^2*g*(3*b*d*f-b*c*g-2*a*d*g)*n^2*log((f+g*x)/(c+d*x))/((b*f-a*g)^3*(d*f-c*g)^3)+2/3*B*(b*c-a*d)*(a^2*d^2*g^2-a*b*d*g*(3*d*f-c*g)+b^2*(3*d^2*f^2-3*c*d*f*g+c^2*g^2))*n*(A+B*log(e*((a+b*x)/(c+d*x))^n))*log(1-(d*f-c*g)*(a+b*x)/((b*f-a*g)*(c+d*x)))/((b*f-a*g)^3*(d*f-c*g)^3)+2/3*B^2*(b*c-a*d)*(a^2*d^2*g^2-a*b*d*g*(3*d*f-c*g)+b^2*(3*d^2*f^2-3*c*d*f*g+c^2*g^2))*n^2*polylog(2,(d*f-c*g)*(a+b*x)/((b*f-a*g)*(c+d*x)))/((b*f-a*g)^3*(d*f-c*g)^3)],
[(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/(f+g*x)^5,x,15,-1/12*B^2*(b*c-a*d)^2*g^3*n^2*(c+d*x)^2/((b*f-a*g)^2*(d*f-c*g)^4*(f+g*x)^2)-1/6*B^2*(b*c-a*d)^3*g^3*n^2*(c+d*x)/((b*f-a*g)^3*(d*f-c*g)^4*(f+g*x))+1/4*B^2*(b*c-a*d)^2*g^2*(4*b*d*f-b*c*g-3*a*d*g)*n^2*(c+d*x)/((b*f-a*g)^3*(d*f-c*g)^4*(f+g*x))+1/6*B*(b*c-a*d)*g^3*n*(c+d*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*f-a*g)*(d*f-c*g)^4*(f+g*x)^3)-1/4*B*(b*c-a*d)*g^2*(4*b*d*f-b*c*g-3*a*d*g)*n*(c+d*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*f-a*g)^2*(d*f-c*g)^4*(f+g*x)^2)+1/2*B*(b*c-a*d)*g*(3*a^2*d^2*g^2-2*a*b*d*g*(4*d*f-c*g)+b^2*(6*d^2*f^2-4*c*d*f*g+c^2*g^2))*n*(a+b*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*f-a*g)^4*(d*f-c*g)^3*(f+g*x))+1/4*b^4*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/(g*(b*f-a*g)^4)-1/4*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/(g*(f+g*x)^4)-1/6*B^2*(b*c-a*d)^4*g^3*n^2*log((a+b*x)/(c+d*x))/((b*f-a*g)^4*(d*f-c*g)^4)+1/4*B^2*(b*c-a*d)^3*g^2*(4*b*d*f-b*c*g-3*a*d*g)*n^2*log((a+b*x)/(c+d*x))/((b*f-a*g)^4*(d*f-c*g)^4)+1/6*B^2*(b*c-a*d)^4*g^3*n^2*log((f+g*x)/(c+d*x))/((b*f-a*g)^4*(d*f-c*g)^4)-1/4*B^2*(b*c-a*d)^3*g^2*(4*b*d*f-b*c*g-3*a*d*g)*n^2*log((f+g*x)/(c+d*x))/((b*f-a*g)^4*(d*f-c*g)^4)+1/2*B^2*(b*c-a*d)^2*g*(3*a^2*d^2*g^2-2*a*b*d*g*(4*d*f-c*g)+b^2*(6*d^2*f^2-4*c*d*f*g+c^2*g^2))*n^2*log((f+g*x)/(c+d*x))/((b*f-a*g)^4*(d*f-c*g)^4)-1/2*B*(b*c-a*d)*(2*b*d*f-b*c*g-a*d*g)*(2*a*b*d^2*f*g-a^2*d^2*g^2-b^2*(2*d^2*f^2-2*c*d*f*g+c^2*g^2))*n*(A+B*log(e*((a+b*x)/(c+d*x))^n))*log(1-(d*f-c*g)*(a+b*x)/((b*f-a*g)*(c+d*x)))/((b*f-a*g)^4*(d*f-c*g)^4)-1/2*B^2*(b*c-a*d)*(2*b*d*f-b*c*g-a*d*g)*(2*a*b*d^2*f*g-a^2*d^2*g^2-b^2*(2*d^2*f^2-2*c*d*f*g+c^2*g^2))*n^2*polylog(2,(d*f-c*g)*(a+b*x)/((b*f-a*g)*(c+d*x)))/((b*f-a*g)^4*(d*f-c*g)^4)],

# p<0
[(f+g*x)^2/(A+B*log(e*((a+b*x)/(c+d*x))^n)),x,0,Unintegrable((f+g*x)^2/(A+B*log(e*((a+b*x)/(c+d*x))^n)),x)],
[(f+g*x)/(A+B*log(e*((a+b*x)/(c+d*x))^n)),x,0,Unintegrable((f+g*x)/(A+B*log(e*((a+b*x)/(c+d*x))^n)),x)],
[1/(A+B*log(e*((a+b*x)/(c+d*x))^n)),x,0,Unintegrable(1/(A+B*log(e*((a+b*x)/(c+d*x))^n)),x)],
[1/((f+g*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))),x,0,Unintegrable(1/((f+g*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))),x)],
[1/((f+g*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))),x,0,Unintegrable(1/((f+g*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))),x)],
[1/((f+g*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))),x,0,Unintegrable(1/((f+g*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))),x)],
[(f+g*x)^2/(A+B*log(e*((a+b*x)/(c+d*x))^n))^2,x,0,Unintegrable((f+g*x)^2/(A+B*log(e*((a+b*x)/(c+d*x))^n))^2,x)],
[(f+g*x)/(A+B*log(e*((a+b*x)/(c+d*x))^n))^2,x,0,Unintegrable((f+g*x)/(A+B*log(e*((a+b*x)/(c+d*x))^n))^2,x)],
[1/(A+B*log(e*((a+b*x)/(c+d*x))^n))^2,x,0,Unintegrable(1/(A+B*log(e*((a+b*x)/(c+d*x))^n))^2,x)],
[1/((f+g*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2),x,0,Unintegrable(1/((f+g*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2),x)],
[1/((f+g*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2),x,0,Unintegrable(1/((f+g*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2),x)],
[1/((f+g*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2),x,0,Unintegrable(1/((f+g*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2),x)],

# Integrands of the form (f+g x)^m (A+B Log[e (a+b x)^n/(c+d x)^n])^p

# Integrands of the form (f+g x)^m (A+B Log[e (a+b x)^n/(c+d x)^n])^p when b f-a g=0

# Integrands of the form (f+g x)^m (A+B Log[e (a+b x)^1/(c+d x)^1])^p when b f-a g=0

# p>0
[(a*g+b*g*x)^4*(A+B*log(e*(a+b*x)/(c+d*x))),x,4,1/5*B*(b*c-a*d)^4*g^4*x/d^4-1/10*B*(b*c-a*d)^3*g^4*(a+b*x)^2/(b*d^3)+1/15*B*(b*c-a*d)^2*g^4*(a+b*x)^3/(b*d^2)-1/20*B*(b*c-a*d)*g^4*(a+b*x)^4/(b*d)+1/5*g^4*(a+b*x)^5*(A+B*log(e*(a+b*x)/(c+d*x)))/b-1/5*B*(b*c-a*d)^5*g^4*log(c+d*x)/(b*d^5)],
[(a*g+b*g*x)^3*(A+B*log(e*(a+b*x)/(c+d*x))),x,4,-1/4*B*(b*c-a*d)^3*g^3*x/d^3+1/8*B*(b*c-a*d)^2*g^3*(a+b*x)^2/(b*d^2)-1/12*B*(b*c-a*d)*g^3*(a+b*x)^3/(b*d)+1/4*g^3*(a+b*x)^4*(A+B*log(e*(a+b*x)/(c+d*x)))/b+1/4*B*(b*c-a*d)^4*g^3*log(c+d*x)/(b*d^4)],
[(a*g+b*g*x)^2*(A+B*log(e*(a+b*x)/(c+d*x))),x,4,1/3*B*(b*c-a*d)^2*g^2*x/d^2-1/6*B*(b*c-a*d)*g^2*(a+b*x)^2/(b*d)+1/3*g^2*(a+b*x)^3*(A+B*log(e*(a+b*x)/(c+d*x)))/b-1/3*B*(b*c-a*d)^3*g^2*log(c+d*x)/(b*d^3)],
[(a*g+b*g*x)*(A+B*log(e*(a+b*x)/(c+d*x))),x,4,-1/2*B*(b*c-a*d)*g*x/d+1/2*g*(a+b*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))/b+1/2*B*(b*c-a*d)^2*g*log(c+d*x)/(b*d^2)],
[(A+B*log(e*(a+b*x)/(c+d*x)))/(a*g+b*g*x),x,5,-log((-b*c+a*d)/(d*(a+b*x)))*(A+B*log(e*(a+b*x)/(c+d*x)))/(b*g)+B*polylog(2,1+(b*c-a*d)/(d*(a+b*x)))/(b*g)],
[(A+B*log(e*(a+b*x)/(c+d*x)))/(a*g+b*g*x)^2,x,2,-B/(b*g^2*(a+b*x))-(c+d*x)*(A+B*log(e*(a+b*x)/(c+d*x)))/((b*c-a*d)*g^2*(a+b*x)),-B*(c+d*x)/((b*c-a*d)*g^2*(a+b*x))-(c+d*x)*(A+B*log(e*(a+b*x)/(c+d*x)))/((b*c-a*d)*g^2*(a+b*x))],
[(A+B*log(e*(a+b*x)/(c+d*x)))/(a*g+b*g*x)^3,x,4,-1/4*B/(b*g^3*(a+b*x)^2)+1/2*B*d/(b*(b*c-a*d)*g^3*(a+b*x))+1/2*B*d^2*log(a+b*x)/(b*(b*c-a*d)^2*g^3)+1/2*(-A-B*log(e*(a+b*x)/(c+d*x)))/(b*g^3*(a+b*x)^2)-1/2*B*d^2*log(c+d*x)/(b*(b*c-a*d)^2*g^3)],
[(A+B*log(e*(a+b*x)/(c+d*x)))/(a*g+b*g*x)^4,x,4,-1/9*B/(b*g^4*(a+b*x)^3)+1/6*B*d/(b*(b*c-a*d)*g^4*(a+b*x)^2)-1/3*B*d^2/(b*(b*c-a*d)^2*g^4*(a+b*x))-1/3*B*d^3*log(a+b*x)/(b*(b*c-a*d)^3*g^4)+1/3*(-A-B*log(e*(a+b*x)/(c+d*x)))/(b*g^4*(a+b*x)^3)+1/3*B*d^3*log(c+d*x)/(b*(b*c-a*d)^3*g^4)],
[(A+B*log(e*(a+b*x)/(c+d*x)))/(a*g+b*g*x)^5,x,4,-1/16*B/(b*g^5*(a+b*x)^4)+1/12*B*d/(b*(b*c-a*d)*g^5*(a+b*x)^3)-1/8*B*d^2/(b*(b*c-a*d)^2*g^5*(a+b*x)^2)+1/4*B*d^3/(b*(b*c-a*d)^3*g^5*(a+b*x))+1/4*B*d^4*log(a+b*x)/(b*(b*c-a*d)^4*g^5)+1/4*(-A-B*log(e*(a+b*x)/(c+d*x)))/(b*g^5*(a+b*x)^4)-1/4*B*d^4*log(c+d*x)/(b*(b*c-a*d)^4*g^5)],
[(a*g+b*g*x)^4*(A+B*log(e*(a+b*x)/(c+d*x)))^2,x,8,-1/10*B*(b*c-a*d)*g^4*(a+b*x)^4*(A+B*log(e*(a+b*x)/(c+d*x)))/(b*d)+1/5*g^4*(a+b*x)^5*(A+B*log(e*(a+b*x)/(c+d*x)))^2/b+1/30*B*(b*c-a*d)^2*g^4*(a+b*x)^3*(4*A+B+4*B*log(e*(a+b*x)/(c+d*x)))/(b*d^2)-1/60*B*(b*c-a*d)^3*g^4*(a+b*x)^2*(12*A+7*B+12*B*log(e*(a+b*x)/(c+d*x)))/(b*d^3)+1/30*B*(b*c-a*d)^4*g^4*(a+b*x)*(12*A+13*B+12*B*log(e*(a+b*x)/(c+d*x)))/(b*d^4)+1/30*B*(b*c-a*d)^5*g^4*log((b*c-a*d)/(b*(c+d*x)))*(12*A+25*B+12*B*log(e*(a+b*x)/(c+d*x)))/(b*d^5)+2/5*B^2*(b*c-a*d)^5*g^4*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(b*d^5)],
[(a*g+b*g*x)^3*(A+B*log(e*(a+b*x)/(c+d*x)))^2,x,7,-1/6*B*(b*c-a*d)*g^3*(a+b*x)^3*(A+B*log(e*(a+b*x)/(c+d*x)))/(b*d)+1/4*g^3*(a+b*x)^4*(A+B*log(e*(a+b*x)/(c+d*x)))^2/b+1/12*B*(b*c-a*d)^2*g^3*(a+b*x)^2*(3*A+B+3*B*log(e*(a+b*x)/(c+d*x)))/(b*d^2)-1/12*B*(b*c-a*d)^3*g^3*(a+b*x)*(6*A+5*B+6*B*log(e*(a+b*x)/(c+d*x)))/(b*d^3)-1/12*B*(b*c-a*d)^4*g^3*log((b*c-a*d)/(b*(c+d*x)))*(6*A+11*B+6*B*log(e*(a+b*x)/(c+d*x)))/(b*d^4)-1/2*B^2*(b*c-a*d)^4*g^3*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(b*d^4)],
[(a*g+b*g*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))^2,x,6,-1/3*B*(b*c-a*d)*g^2*(a+b*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))/(b*d)+1/3*g^2*(a+b*x)^3*(A+B*log(e*(a+b*x)/(c+d*x)))^2/b+1/3*B*(b*c-a*d)^2*g^2*(a+b*x)*(2*A+B+2*B*log(e*(a+b*x)/(c+d*x)))/(b*d^2)+1/3*B*(b*c-a*d)^3*g^2*log((b*c-a*d)/(b*(c+d*x)))*(2*A+3*B+2*B*log(e*(a+b*x)/(c+d*x)))/(b*d^3)+2/3*B^2*(b*c-a*d)^3*g^2*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(b*d^3)],
[(a*g+b*g*x)*(A+B*log(e*(a+b*x)/(c+d*x)))^2,x,5,-B*(b*c-a*d)*g*(a+b*x)*(A+B*log(e*(a+b*x)/(c+d*x)))/(b*d)+1/2*g*(a+b*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))^2/b-B*(b*c-a*d)^2*g*log((b*c-a*d)/(b*(c+d*x)))*(A+B+B*log(e*(a+b*x)/(c+d*x)))/(b*d^2)-B^2*(b*c-a*d)^2*g*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(b*d^2)],
[(A+B*log(e*(a+b*x)/(c+d*x)))^2/(a*g+b*g*x),x,4,-(A+B*log(e*(a+b*x)/(c+d*x)))^2*log(1-b*(c+d*x)/(d*(a+b*x)))/(b*g)+2*B*(A+B*log(e*(a+b*x)/(c+d*x)))*polylog(2,b*(c+d*x)/(d*(a+b*x)))/(b*g)+2*B^2*polylog(3,b*(c+d*x)/(d*(a+b*x)))/(b*g)],
[(A+B*log(e*(a+b*x)/(c+d*x)))^2/(a*g+b*g*x)^2,x,3,-2*B^2*(c+d*x)/((b*c-a*d)*g^2*(a+b*x))-2*B*(c+d*x)*(A+B*log(e*(a+b*x)/(c+d*x)))/((b*c-a*d)*g^2*(a+b*x))-(c+d*x)*(A+B*log(e*(a+b*x)/(c+d*x)))^2/((b*c-a*d)*g^2*(a+b*x))],
[(A+B*log(e*(a+b*x)/(c+d*x)))^2/(a*g+b*g*x)^3,x,7,2*B^2*d*(c+d*x)/((b*c-a*d)^2*g^3*(a+b*x))-1/4*b*B^2*(c+d*x)^2/((b*c-a*d)^2*g^3*(a+b*x)^2)+2*B*d*(c+d*x)*(A+B*log(e*(a+b*x)/(c+d*x)))/((b*c-a*d)^2*g^3*(a+b*x))-1/2*b*B*(c+d*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))/((b*c-a*d)^2*g^3*(a+b*x)^2)+d*(c+d*x)*(A+B*log(e*(a+b*x)/(c+d*x)))^2/((b*c-a*d)^2*g^3*(a+b*x))-1/2*b*(c+d*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))^2/((b*c-a*d)^2*g^3*(a+b*x)^2)],
[(A+B*log(e*(a+b*x)/(c+d*x)))^2/(a*g+b*g*x)^4,x,9,-2*B^2*d^2*(c+d*x)/((b*c-a*d)^3*g^4*(a+b*x))+1/2*b*B^2*d*(c+d*x)^2/((b*c-a*d)^3*g^4*(a+b*x)^2)-2/27*b^2*B^2*(c+d*x)^3/((b*c-a*d)^3*g^4*(a+b*x)^3)-2*B*d^2*(c+d*x)*(A+B*log(e*(a+b*x)/(c+d*x)))/((b*c-a*d)^3*g^4*(a+b*x))+b*B*d*(c+d*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))/((b*c-a*d)^3*g^4*(a+b*x)^2)-2/9*b^2*B*(c+d*x)^3*(A+B*log(e*(a+b*x)/(c+d*x)))/((b*c-a*d)^3*g^4*(a+b*x)^3)-d^2*(c+d*x)*(A+B*log(e*(a+b*x)/(c+d*x)))^2/((b*c-a*d)^3*g^4*(a+b*x))+b*d*(c+d*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))^2/((b*c-a*d)^3*g^4*(a+b*x)^2)-1/3*b^2*(c+d*x)^3*(A+B*log(e*(a+b*x)/(c+d*x)))^2/((b*c-a*d)^3*g^4*(a+b*x)^3)],
[(A+B*log(e*(a+b*x)/(c+d*x)))^2/(a*g+b*g*x)^5,x,11,2*B^2*d^3*(c+d*x)/((b*c-a*d)^4*g^5*(a+b*x))-3/4*b*B^2*d^2*(c+d*x)^2/((b*c-a*d)^4*g^5*(a+b*x)^2)+2/9*b^2*B^2*d*(c+d*x)^3/((b*c-a*d)^4*g^5*(a+b*x)^3)-1/32*b^3*B^2*(c+d*x)^4/((b*c-a*d)^4*g^5*(a+b*x)^4)+2*B*d^3*(c+d*x)*(A+B*log(e*(a+b*x)/(c+d*x)))/((b*c-a*d)^4*g^5*(a+b*x))-3/2*b*B*d^2*(c+d*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))/((b*c-a*d)^4*g^5*(a+b*x)^2)+2/3*b^2*B*d*(c+d*x)^3*(A+B*log(e*(a+b*x)/(c+d*x)))/((b*c-a*d)^4*g^5*(a+b*x)^3)-1/8*b^3*B*(c+d*x)^4*(A+B*log(e*(a+b*x)/(c+d*x)))/((b*c-a*d)^4*g^5*(a+b*x)^4)+d^3*(c+d*x)*(A+B*log(e*(a+b*x)/(c+d*x)))^2/((b*c-a*d)^4*g^5*(a+b*x))-3/2*b*d^2*(c+d*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))^2/((b*c-a*d)^4*g^5*(a+b*x)^2)+b^2*d*(c+d*x)^3*(A+B*log(e*(a+b*x)/(c+d*x)))^2/((b*c-a*d)^4*g^5*(a+b*x)^3)-1/4*b^3*(c+d*x)^4*(A+B*log(e*(a+b*x)/(c+d*x)))^2/((b*c-a*d)^4*g^5*(a+b*x)^4)],
[log(d*(a+b*x)/(b*(c+d*x)))/(c*f+d*f*x),x,1,polylog(2,(b*c-a*d)/(b*(c+d*x)))/(d*f),polylog(2,1-d*(a+b*x)/(b*(c+d*x)))/(d*f)],
[log(1+1/(a+b*x))/(a+b*x),x,1,polylog(2,(-1)/(a+b*x))/b],
[log(1+(-1)/(a+b*x))/(a+b*x),x,1,polylog(2,1/(a+b*x))/b],

# p<0
[(a*g+b*g*x)^2/(A+B*log(e*(a+b*x)/(c+d*x))),x,0,Unintegrable((a*g+b*g*x)^2/(A+B*log(e*(a+b*x)/(c+d*x))),x)],
[(a*g+b*g*x)/(A+B*log(e*(a+b*x)/(c+d*x))),x,0,Unintegrable((a*g+b*g*x)/(A+B*log(e*(a+b*x)/(c+d*x))),x)],
[1/((a*g+b*g*x)*(A+B*log(e*(a+b*x)/(c+d*x)))),x,0,Unintegrable(1/((a*g+b*g*x)*(A+B*log(e*(a+b*x)/(c+d*x)))),x)],
[1/((a*g+b*g*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))),x,3,e*exp(A/B)*Ei((-A-B*log(e*(a+b*x)/(c+d*x)))/B)/(B*(b*c-a*d)*g^2)],
[1/((a*g+b*g*x)^3*(A+B*log(e*(a+b*x)/(c+d*x)))),x,7,b*e^2*exp(2*A/B)*Ei(-2*(A+B*log(e*(a+b*x)/(c+d*x)))/B)/(B*(b*c-a*d)^2*g^3)-d*e*exp(A/B)*Ei((-A-B*log(e*(a+b*x)/(c+d*x)))/B)/(B*(b*c-a*d)^2*g^3)],
[(a*g+b*g*x)^2/(A+B*log(e*(a+b*x)/(c+d*x)))^2,x,0,Unintegrable((a*g+b*g*x)^2/(A+B*log(e*(a+b*x)/(c+d*x)))^2,x)],
[(a*g+b*g*x)/(A+B*log(e*(a+b*x)/(c+d*x)))^2,x,0,Unintegrable((a*g+b*g*x)/(A+B*log(e*(a+b*x)/(c+d*x)))^2,x)],
[1/((a*g+b*g*x)*(A+B*log(e*(a+b*x)/(c+d*x)))^2),x,0,Unintegrable(1/((a*g+b*g*x)*(A+B*log(e*(a+b*x)/(c+d*x)))^2),x)],
[1/((a*g+b*g*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))^2),x,4,-e*exp(A/B)*Ei((-A-B*log(e*(a+b*x)/(c+d*x)))/B)/(B^2*(b*c-a*d)*g^2)+(-c-d*x)/(B*(b*c-a*d)*g^2*(a+b*x)*(A+B*log(e*(a+b*x)/(c+d*x))))],
[1/((a*g+b*g*x)^3*(A+B*log(e*(a+b*x)/(c+d*x)))^2),x,9,-2*b*e^2*exp(2*A/B)*Ei(-2*(A+B*log(e*(a+b*x)/(c+d*x)))/B)/(B^2*(b*c-a*d)^2*g^3)+d*e*exp(A/B)*Ei((-A-B*log(e*(a+b*x)/(c+d*x)))/B)/(B^2*(b*c-a*d)^2*g^3)+d*(c+d*x)/(B*(b*c-a*d)^2*g^3*(a+b*x)*(A+B*log(e*(a+b*x)/(c+d*x))))-b*(c+d*x)^2/(B*(b*c-a*d)^2*g^3*(a+b*x)^2*(A+B*log(e*(a+b*x)/(c+d*x))))],

# Integrands of the form (f+g x)^m (A+B Log[e (a+b x)^2/(c+d x)^2])^p when b f-a g=0

# p>0
[(a*g+b*g*x)^4*(A+B*log(e*(a+b*x)^2/(c+d*x)^2)),x,4,2/5*B*(b*c-a*d)^4*g^4*x/d^4-1/5*B*(b*c-a*d)^3*g^4*(a+b*x)^2/(b*d^3)+2/15*B*(b*c-a*d)^2*g^4*(a+b*x)^3/(b*d^2)-1/10*B*(b*c-a*d)*g^4*(a+b*x)^4/(b*d)+1/5*g^4*(a+b*x)^5*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))/b-2/5*B*(b*c-a*d)^5*g^4*log(c+d*x)/(b*d^5)],
[(a*g+b*g*x)^3*(A+B*log(e*(a+b*x)^2/(c+d*x)^2)),x,4,-1/2*B*(b*c-a*d)^3*g^3*x/d^3+1/4*B*(b*c-a*d)^2*g^3*(a+b*x)^2/(b*d^2)-1/6*B*(b*c-a*d)*g^3*(a+b*x)^3/(b*d)+1/4*g^3*(a+b*x)^4*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))/b+1/2*B*(b*c-a*d)^4*g^3*log(c+d*x)/(b*d^4)],
[(a*g+b*g*x)^2*(A+B*log(e*(a+b*x)^2/(c+d*x)^2)),x,4,2/3*B*(b*c-a*d)^2*g^2*x/d^2-1/3*B*(b*c-a*d)*g^2*(a+b*x)^2/(b*d)+1/3*g^2*(a+b*x)^3*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))/b-2/3*B*(b*c-a*d)^3*g^2*log(c+d*x)/(b*d^3)],
[(a*g+b*g*x)*(A+B*log(e*(a+b*x)^2/(c+d*x)^2)),x,4,-B*(b*c-a*d)*g*x/d+1/2*g*(a+b*x)^2*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))/b+B*(b*c-a*d)^2*g*log(c+d*x)/(b*d^2)],
[(A+B*log(e*(a+b*x)^2/(c+d*x)^2))/(a*g+b*g*x),x,5,-log((-b*c+a*d)/(d*(a+b*x)))*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))/(b*g)+2*B*polylog(2,1+(b*c-a*d)/(d*(a+b*x)))/(b*g)],
[(A+B*log(e*(a+b*x)^2/(c+d*x)^2))/(a*g+b*g*x)^2,x,2,-2*B/(b*g^2*(a+b*x))-(c+d*x)*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))/((b*c-a*d)*g^2*(a+b*x)),-2*B*(c+d*x)/((b*c-a*d)*g^2*(a+b*x))-(c+d*x)*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))/((b*c-a*d)*g^2*(a+b*x))],
[(A+B*log(e*(a+b*x)^2/(c+d*x)^2))/(a*g+b*g*x)^3,x,4,-1/2*B/(b*g^3*(a+b*x)^2)+B*d/(b*(b*c-a*d)*g^3*(a+b*x))+B*d^2*log(a+b*x)/(b*(b*c-a*d)^2*g^3)+1/2*(-A-B*log(e*(a+b*x)^2/(c+d*x)^2))/(b*g^3*(a+b*x)^2)-B*d^2*log(c+d*x)/(b*(b*c-a*d)^2*g^3)],
[(A+B*log(e*(a+b*x)^2/(c+d*x)^2))/(a*g+b*g*x)^4,x,4,-2/9*B/(b*g^4*(a+b*x)^3)+1/3*B*d/(b*(b*c-a*d)*g^4*(a+b*x)^2)-2/3*B*d^2/(b*(b*c-a*d)^2*g^4*(a+b*x))-2/3*B*d^3*log(a+b*x)/(b*(b*c-a*d)^3*g^4)+1/3*(-A-B*log(e*(a+b*x)^2/(c+d*x)^2))/(b*g^4*(a+b*x)^3)+2/3*B*d^3*log(c+d*x)/(b*(b*c-a*d)^3*g^4)],
[(A+B*log(e*(a+b*x)^2/(c+d*x)^2))/(a*g+b*g*x)^5,x,4,-1/8*B/(b*g^5*(a+b*x)^4)+1/6*B*d/(b*(b*c-a*d)*g^5*(a+b*x)^3)-1/4*B*d^2/(b*(b*c-a*d)^2*g^5*(a+b*x)^2)+1/2*B*d^3/(b*(b*c-a*d)^3*g^5*(a+b*x))+1/2*B*d^4*log(a+b*x)/(b*(b*c-a*d)^4*g^5)+1/4*(-A-B*log(e*(a+b*x)^2/(c+d*x)^2))/(b*g^5*(a+b*x)^4)-1/2*B*d^4*log(c+d*x)/(b*(b*c-a*d)^4*g^5)],
[(a*g+b*g*x)^4*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))^2,x,8,-1/5*B*(b*c-a*d)*g^4*(a+b*x)^4*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))/(b*d)+1/5*g^4*(a+b*x)^5*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))^2/b+2/15*B*(b*c-a*d)^2*g^4*(a+b*x)^3*(2*A+B+2*B*log(e*(a+b*x)^2/(c+d*x)^2))/(b*d^2)-1/15*B*(b*c-a*d)^3*g^4*(a+b*x)^2*(6*A+7*B+6*B*log(e*(a+b*x)^2/(c+d*x)^2))/(b*d^3)+2/15*B*(b*c-a*d)^4*g^4*(a+b*x)*(6*A+13*B+6*B*log(e*(a+b*x)^2/(c+d*x)^2))/(b*d^4)+2/15*B*(b*c-a*d)^5*g^4*(6*A+25*B+6*B*log(e*(a+b*x)^2/(c+d*x)^2))*log((b*c-a*d)/(b*(c+d*x)))/(b*d^5)+8/5*B^2*(b*c-a*d)^5*g^4*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(b*d^5)],
[(a*g+b*g*x)^3*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))^2,x,7,-1/3*B*(b*c-a*d)*g^3*(a+b*x)^3*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))/(b*d)+1/4*g^3*(a+b*x)^4*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))^2/b+1/6*B*(b*c-a*d)^2*g^3*(a+b*x)^2*(3*A+2*B+3*B*log(e*(a+b*x)^2/(c+d*x)^2))/(b*d^2)-1/3*B*(b*c-a*d)^3*g^3*(a+b*x)*(3*A+5*B+3*B*log(e*(a+b*x)^2/(c+d*x)^2))/(b*d^3)-1/3*B*(b*c-a*d)^4*g^3*(3*A+11*B+3*B*log(e*(a+b*x)^2/(c+d*x)^2))*log((b*c-a*d)/(b*(c+d*x)))/(b*d^4)-2*B^2*(b*c-a*d)^4*g^3*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(b*d^4)],
[(a*g+b*g*x)^2*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))^2,x,6,-2/3*B*(b*c-a*d)*g^2*(a+b*x)^2*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))/(b*d)+1/3*g^2*(a+b*x)^3*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))^2/b+4/3*B*(b*c-a*d)^2*g^2*(a+b*x)*(A+B+B*log(e*(a+b*x)^2/(c+d*x)^2))/(b*d^2)+4/3*B*(b*c-a*d)^3*g^2*(A+3*B+B*log(e*(a+b*x)^2/(c+d*x)^2))*log((b*c-a*d)/(b*(c+d*x)))/(b*d^3)+8/3*B^2*(b*c-a*d)^3*g^2*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(b*d^3)],
[(a*g+b*g*x)*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))^2,x,5,-2*B*(b*c-a*d)*g*(a+b*x)*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))/(b*d)+1/2*g*(a+b*x)^2*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))^2/b-2*B*(b*c-a*d)^2*g*(A+2*B+B*log(e*(a+b*x)^2/(c+d*x)^2))*log((b*c-a*d)/(b*(c+d*x)))/(b*d^2)-4*B^2*(b*c-a*d)^2*g*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(b*d^2)],
[(A+B*log(e*(a+b*x)^2/(c+d*x)^2))^2/(a*g+b*g*x),x,4,-(A+B*log(e*(a+b*x)^2/(c+d*x)^2))^2*log(1-b*(c+d*x)/(d*(a+b*x)))/(b*g)+4*B*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))*polylog(2,b*(c+d*x)/(d*(a+b*x)))/(b*g)+8*B^2*polylog(3,b*(c+d*x)/(d*(a+b*x)))/(b*g)],
[(A+B*log(e*(a+b*x)^2/(c+d*x)^2))^2/(a*g+b*g*x)^2,x,3,-8*B^2*(c+d*x)/((b*c-a*d)*g^2*(a+b*x))-4*B*(c+d*x)*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))/((b*c-a*d)*g^2*(a+b*x))-(c+d*x)*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))^2/((b*c-a*d)*g^2*(a+b*x))],
[(A+B*log(e*(a+b*x)^2/(c+d*x)^2))^2/(a*g+b*g*x)^3,x,7,8*B^2*d*(c+d*x)/((b*c-a*d)^2*g^3*(a+b*x))-b*B^2*(c+d*x)^2/((b*c-a*d)^2*g^3*(a+b*x)^2)+4*B*d*(c+d*x)*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))/((b*c-a*d)^2*g^3*(a+b*x))-b*B*(c+d*x)^2*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))/((b*c-a*d)^2*g^3*(a+b*x)^2)+d*(c+d*x)*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))^2/((b*c-a*d)^2*g^3*(a+b*x))-1/2*b*(c+d*x)^2*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))^2/((b*c-a*d)^2*g^3*(a+b*x)^2)],
[(A+B*log(e*(a+b*x)^2/(c+d*x)^2))^2/(a*g+b*g*x)^4,x,9,-8*B^2*d^2*(c+d*x)/((b*c-a*d)^3*g^4*(a+b*x))+2*b*B^2*d*(c+d*x)^2/((b*c-a*d)^3*g^4*(a+b*x)^2)-8/27*b^2*B^2*(c+d*x)^3/((b*c-a*d)^3*g^4*(a+b*x)^3)-4*B*d^2*(c+d*x)*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))/((b*c-a*d)^3*g^4*(a+b*x))+2*b*B*d*(c+d*x)^2*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))/((b*c-a*d)^3*g^4*(a+b*x)^2)-4/9*b^2*B*(c+d*x)^3*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))/((b*c-a*d)^3*g^4*(a+b*x)^3)-d^2*(c+d*x)*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))^2/((b*c-a*d)^3*g^4*(a+b*x))+b*d*(c+d*x)^2*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))^2/((b*c-a*d)^3*g^4*(a+b*x)^2)-1/3*b^2*(c+d*x)^3*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))^2/((b*c-a*d)^3*g^4*(a+b*x)^3)],
[(A+B*log(e*(a+b*x)^2/(c+d*x)^2))^2/(a*g+b*g*x)^5,x,11,8*B^2*d^3*(c+d*x)/((b*c-a*d)^4*g^5*(a+b*x))-3*b*B^2*d^2*(c+d*x)^2/((b*c-a*d)^4*g^5*(a+b*x)^2)+8/9*b^2*B^2*d*(c+d*x)^3/((b*c-a*d)^4*g^5*(a+b*x)^3)-1/8*b^3*B^2*(c+d*x)^4/((b*c-a*d)^4*g^5*(a+b*x)^4)+4*B*d^3*(c+d*x)*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))/((b*c-a*d)^4*g^5*(a+b*x))-3*b*B*d^2*(c+d*x)^2*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))/((b*c-a*d)^4*g^5*(a+b*x)^2)+4/3*b^2*B*d*(c+d*x)^3*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))/((b*c-a*d)^4*g^5*(a+b*x)^3)-1/4*b^3*B*(c+d*x)^4*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))/((b*c-a*d)^4*g^5*(a+b*x)^4)+d^3*(c+d*x)*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))^2/((b*c-a*d)^4*g^5*(a+b*x))-3/2*b*d^2*(c+d*x)^2*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))^2/((b*c-a*d)^4*g^5*(a+b*x)^2)+b^2*d*(c+d*x)^3*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))^2/((b*c-a*d)^4*g^5*(a+b*x)^3)-1/4*b^3*(c+d*x)^4*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))^2/((b*c-a*d)^4*g^5*(a+b*x)^4)],

# p<0
[(a*g+b*g*x)^2/(A+B*log(e*(a+b*x)^2/(c+d*x)^2)),x,0,Unintegrable((a*g+b*g*x)^2/(A+B*log(e*(a+b*x)^2/(c+d*x)^2)),x)],
[(a*g+b*g*x)/(A+B*log(e*(a+b*x)^2/(c+d*x)^2)),x,0,Unintegrable((a*g+b*g*x)/(A+B*log(e*(a+b*x)^2/(c+d*x)^2)),x)],
[1/((a*g+b*g*x)*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))),x,0,Unintegrable(1/((a*g+b*g*x)*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))),x)],
[1/((a*g+b*g*x)^2*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))),x,3,1/2*exp(1/2*A/B)*(c+d*x)*Ei(1/2*(-A-B*log(e*(a+b*x)^2/(c+d*x)^2))/B)*sqrt(e*(a+b*x)^2/(c+d*x)^2)/(B*(b*c-a*d)*g^2*(a+b*x))],
[1/((a*g+b*g*x)^3*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))),x,7,1/2*b*e*exp(A/B)*Ei((-A-B*log(e*(a+b*x)^2/(c+d*x)^2))/B)/(B*(b*c-a*d)^2*g^3)-1/2*d*exp(1/2*A/B)*(c+d*x)*Ei(1/2*(-A-B*log(e*(a+b*x)^2/(c+d*x)^2))/B)*sqrt(e*(a+b*x)^2/(c+d*x)^2)/(B*(b*c-a*d)^2*g^3*(a+b*x))],
[(a*g+b*g*x)^2/(A+B*log(e*(a+b*x)^2/(c+d*x)^2))^2,x,0,Unintegrable((a*g+b*g*x)^2/(A+B*log(e*(a+b*x)^2/(c+d*x)^2))^2,x)],
[(a*g+b*g*x)/(A+B*log(e*(a+b*x)^2/(c+d*x)^2))^2,x,0,Unintegrable((a*g+b*g*x)/(A+B*log(e*(a+b*x)^2/(c+d*x)^2))^2,x)],
[1/((a*g+b*g*x)*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))^2),x,0,Unintegrable(1/((a*g+b*g*x)*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))^2),x)],
[1/((a*g+b*g*x)^2*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))^2),x,4,1/2*(-c-d*x)/(B*(b*c-a*d)*g^2*(a+b*x)*(A+B*log(e*(a+b*x)^2/(c+d*x)^2)))-1/4*exp(1/2*A/B)*(c+d*x)*Ei(1/2*(-A-B*log(e*(a+b*x)^2/(c+d*x)^2))/B)*sqrt(e*(a+b*x)^2/(c+d*x)^2)/(B^2*(b*c-a*d)*g^2*(a+b*x))],
[1/((a*g+b*g*x)^3*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))^2),x,9,-1/2*b*e*exp(A/B)*Ei((-A-B*log(e*(a+b*x)^2/(c+d*x)^2))/B)/(B^2*(b*c-a*d)^2*g^3)+1/2*d*(c+d*x)/(B*(b*c-a*d)^2*g^3*(a+b*x)*(A+B*log(e*(a+b*x)^2/(c+d*x)^2)))-1/2*b*(c+d*x)^2/(B*(b*c-a*d)^2*g^3*(a+b*x)^2*(A+B*log(e*(a+b*x)^2/(c+d*x)^2)))+1/4*d*exp(1/2*A/B)*(c+d*x)*Ei(1/2*(-A-B*log(e*(a+b*x)^2/(c+d*x)^2))/B)*sqrt(e*(a+b*x)^2/(c+d*x)^2)/(B^2*(b*c-a*d)^2*g^3*(a+b*x))],

# Integrands of the form (f+g x)^m (A+B Log[e (a+b x)^n/(c+d x)^n])^p when b f-a g=0

# p>0
[(a+b*x)^4*(A+B*log(e*(a+b*x)^n/(c+d*x)^n)),x,3,1/5*B*(b*c-a*d)^4*n*x/d^4-1/10*B*(b*c-a*d)^3*n*(a+b*x)^2/(b*d^3)+1/15*B*(b*c-a*d)^2*n*(a+b*x)^3/(b*d^2)-1/20*B*(b*c-a*d)*n*(a+b*x)^4/(b*d)-1/5*B*(b*c-a*d)^5*n*log(c+d*x)/(b*d^5)+1/5*(a+b*x)^5*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))/b],
[(a+b*x)^3*(A+B*log(e*(a+b*x)^n/(c+d*x)^n)),x,3,-1/4*B*(b*c-a*d)^3*n*x/d^3+1/8*B*(b*c-a*d)^2*n*(a+b*x)^2/(b*d^2)-1/12*B*(b*c-a*d)*n*(a+b*x)^3/(b*d)+1/4*B*(b*c-a*d)^4*n*log(c+d*x)/(b*d^4)+1/4*(a+b*x)^4*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))/b],
[(a+b*x)^2*(A+B*log(e*(a+b*x)^n/(c+d*x)^n)),x,3,1/3*B*(b*c-a*d)^2*n*x/d^2-1/6*B*(b*c-a*d)*n*(a+b*x)^2/(b*d)-1/3*B*(b*c-a*d)^3*n*log(c+d*x)/(b*d^3)+1/3*(a+b*x)^3*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))/b],
[(a+b*x)*(A+B*log(e*(a+b*x)^n/(c+d*x)^n)),x,3,-1/2*B*(b*c-a*d)*n*x/d+1/2*B*(b*c-a*d)^2*n*log(c+d*x)/(b*d^2)+1/2*(a+b*x)^2*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))/b],
[(A+B*log(e*(a+b*x)^n/(c+d*x)^n))/(a+b*x),x,5,-log((-b*c+a*d)/(d*(a+b*x)))*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))/b+B*n*polylog(2,1+(b*c-a*d)/(d*(a+b*x)))/b],
[(A+B*log(e*(a+b*x)^n/(c+d*x)^n))/(a+b*x)^2,x,3,-B*n/(b*(a+b*x))-B*d*n*log(a+b*x)/(b*(b*c-a*d))+B*d*n*log(c+d*x)/(b*(b*c-a*d))+(-A-B*log(e*(a+b*x)^n/(c+d*x)^n))/(b*(a+b*x))],
[(A+B*log(e*(a+b*x)^n/(c+d*x)^n))/(a+b*x)^3,x,3,-1/4*B*n/(b*(a+b*x)^2)+1/2*B*d*n/(b*(b*c-a*d)*(a+b*x))+1/2*B*d^2*n*log(a+b*x)/(b*(b*c-a*d)^2)-1/2*B*d^2*n*log(c+d*x)/(b*(b*c-a*d)^2)+1/2*(-A-B*log(e*(a+b*x)^n/(c+d*x)^n))/(b*(a+b*x)^2)],
[(A+B*log(e*(a+b*x)^n/(c+d*x)^n))/(a+b*x)^4,x,3,-1/9*B*n/(b*(a+b*x)^3)+1/6*B*d*n/(b*(b*c-a*d)*(a+b*x)^2)-1/3*B*d^2*n/(b*(b*c-a*d)^2*(a+b*x))-1/3*B*d^3*n*log(a+b*x)/(b*(b*c-a*d)^3)+1/3*B*d^3*n*log(c+d*x)/(b*(b*c-a*d)^3)+1/3*(-A-B*log(e*(a+b*x)^n/(c+d*x)^n))/(b*(a+b*x)^3)],
[(A+B*log(e*(a+b*x)^n/(c+d*x)^n))/(a+b*x)^5,x,3,-1/16*B*n/(b*(a+b*x)^4)+1/12*B*d*n/(b*(b*c-a*d)*(a+b*x)^3)-1/8*B*d^2*n/(b*(b*c-a*d)^2*(a+b*x)^2)+1/4*B*d^3*n/(b*(b*c-a*d)^3*(a+b*x))+1/4*B*d^4*n*log(a+b*x)/(b*(b*c-a*d)^4)-1/4*B*d^4*n*log(c+d*x)/(b*(b*c-a*d)^4)+1/4*(-A-B*log(e*(a+b*x)^n/(c+d*x)^n))/(b*(a+b*x)^4)],
[(a+b*x)^3*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^2,x,8,-1/6*B*(b*c-a*d)*n*(a+b*x)^3*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))/(b*d)+1/4*(a+b*x)^4*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^2/b+1/12*B*(b*c-a*d)^2*n*(a+b*x)^2*(3*A+B*n+3*B*log(e*(a+b*x)^n/(c+d*x)^n))/(b*d^2)-1/12*B*(b*c-a*d)^3*n*(a+b*x)*(6*A+5*B*n+6*B*log(e*(a+b*x)^n/(c+d*x)^n))/(b*d^3)-1/12*B*(b*c-a*d)^4*n*log((b*c-a*d)/(b*(c+d*x)))*(6*A+11*B*n+6*B*log(e*(a+b*x)^n/(c+d*x)^n))/(b*d^4)-1/2*B^2*(b*c-a*d)^4*n^2*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(b*d^4)],
[(a+b*x)^2*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^2,x,7,-1/3*B*(b*c-a*d)*n*(a+b*x)^2*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))/(b*d)+1/3*(a+b*x)^3*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^2/b+1/3*B*(b*c-a*d)^2*n*(a+b*x)*(2*A+B*n+2*B*log(e*(a+b*x)^n/(c+d*x)^n))/(b*d^2)+1/3*B*(b*c-a*d)^3*n*log((b*c-a*d)/(b*(c+d*x)))*(2*A+3*B*n+2*B*log(e*(a+b*x)^n/(c+d*x)^n))/(b*d^3)+2/3*B^2*(b*c-a*d)^3*n^2*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(b*d^3)],
[(a+b*x)*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^2,x,6,-B*(b*c-a*d)*n*(a+b*x)*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))/(b*d)+1/2*(a+b*x)^2*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^2/b-B*(b*c-a*d)^2*n*log((b*c-a*d)/(b*(c+d*x)))*(A+B*n+B*log(e*(a+b*x)^n/(c+d*x)^n))/(b*d^2)-B^2*(b*c-a*d)^2*n^2*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(b*d^2)],
[(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^2/(a+b*x),x,5,-(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^2*log(1-b*(c+d*x)/(d*(a+b*x)))/b+2*B*n*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))*polylog(2,b*(c+d*x)/(d*(a+b*x)))/b+2*B^2*n^2*polylog(3,b*(c+d*x)/(d*(a+b*x)))/b],
[(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^2/(a+b*x)^2,x,4,-2*B^2*n^2*(c+d*x)/((b*c-a*d)*(a+b*x))-2*B*n*(c+d*x)*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))/((b*c-a*d)*(a+b*x))-(c+d*x)*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^2/((b*c-a*d)*(a+b*x))],
[(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^2/(a+b*x)^3,x,8,2*B^2*d*n^2*(c+d*x)/((b*c-a*d)^2*(a+b*x))-1/4*b*B^2*n^2*(c+d*x)^2/((b*c-a*d)^2*(a+b*x)^2)+2*B*d*n*(c+d*x)*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))/((b*c-a*d)^2*(a+b*x))-1/2*b*B*n*(c+d*x)^2*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))/((b*c-a*d)^2*(a+b*x)^2)+d*(c+d*x)*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^2/((b*c-a*d)^2*(a+b*x))-1/2*b*(c+d*x)^2*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^2/((b*c-a*d)^2*(a+b*x)^2)],
[(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^2/(a+b*x)^4,x,10,-2*B^2*d^2*n^2*(c+d*x)/((b*c-a*d)^3*(a+b*x))+1/2*b*B^2*d*n^2*(c+d*x)^2/((b*c-a*d)^3*(a+b*x)^2)-2/27*b^2*B^2*n^2*(c+d*x)^3/((b*c-a*d)^3*(a+b*x)^3)-2*B*d^2*n*(c+d*x)*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))/((b*c-a*d)^3*(a+b*x))+b*B*d*n*(c+d*x)^2*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))/((b*c-a*d)^3*(a+b*x)^2)-2/9*b^2*B*n*(c+d*x)^3*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))/((b*c-a*d)^3*(a+b*x)^3)-d^2*(c+d*x)*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^2/((b*c-a*d)^3*(a+b*x))+b*d*(c+d*x)^2*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^2/((b*c-a*d)^3*(a+b*x)^2)-1/3*b^2*(c+d*x)^3*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^2/((b*c-a*d)^3*(a+b*x)^3)],
[(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^2/(a+b*x)^5,x,12,2*B^2*d^3*n^2*(c+d*x)/((b*c-a*d)^4*(a+b*x))-3/4*b*B^2*d^2*n^2*(c+d*x)^2/((b*c-a*d)^4*(a+b*x)^2)+2/9*b^2*B^2*d*n^2*(c+d*x)^3/((b*c-a*d)^4*(a+b*x)^3)-1/32*b^3*B^2*n^2*(c+d*x)^4/((b*c-a*d)^4*(a+b*x)^4)+2*B*d^3*n*(c+d*x)*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))/((b*c-a*d)^4*(a+b*x))-3/2*b*B*d^2*n*(c+d*x)^2*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))/((b*c-a*d)^4*(a+b*x)^2)+2/3*b^2*B*d*n*(c+d*x)^3*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))/((b*c-a*d)^4*(a+b*x)^3)-1/8*b^3*B*n*(c+d*x)^4*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))/((b*c-a*d)^4*(a+b*x)^4)+d^3*(c+d*x)*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^2/((b*c-a*d)^4*(a+b*x))-3/2*b*d^2*(c+d*x)^2*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^2/((b*c-a*d)^4*(a+b*x)^2)+b^2*d*(c+d*x)^3*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^2/((b*c-a*d)^4*(a+b*x)^3)-1/4*b^3*(c+d*x)^4*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^2/((b*c-a*d)^4*(a+b*x)^4)],
[(a+b*x)^3*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^3,x,27,-1/4*B^3*(b*c-a*d)^3*n^3*x/d^3-1/4*B^3*(b*c-a*d)^4*n^3*log((a+b*x)/(c+d*x))/(b*d^4)+3/2*B^3*(b*c-a*d)^4*n^3*log(c+d*x)/(b*d^4)-7/4*B^2*(b*c-a*d)^3*n^2*(a+b*x)*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))/(b*d^3)+1/4*b*B^2*(b*c-a*d)^2*n^2*(c+d*x)^2*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))/d^4-9/2*B^2*(b*c-a*d)^4*n^2*log((b*c-a*d)/(b*(c+d*x)))*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))/(b*d^4)-9/4*B*(b*c-a*d)^3*n*(a+b*x)*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^2/(b*d^3)+9/8*b*B*(b*c-a*d)^2*n*(c+d*x)^2*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^2/d^4-1/4*b^2*B*(b*c-a*d)*n*(c+d*x)^3*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^2/d^4-3/4*B*(b*c-a*d)^4*n*log((b*c-a*d)/(b*(c+d*x)))*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^2/(b*d^4)+1/4*(a+b*x)^4*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^3/b+7/4*B^2*(b*c-a*d)^4*n^2*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))*log(1-b*(c+d*x)/(d*(a+b*x)))/(b*d^4)-9/2*B^3*(b*c-a*d)^4*n^3*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(b*d^4)-3/2*B^2*(b*c-a*d)^4*n^2*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(b*d^4)-7/4*B^3*(b*c-a*d)^4*n^3*polylog(2,b*(c+d*x)/(d*(a+b*x)))/(b*d^4)+3/2*B^3*(b*c-a*d)^4*n^3*polylog(3,d*(a+b*x)/(b*(c+d*x)))/(b*d^4)],
[(a+b*x)^2*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^3,x,17,-B^3*(b*c-a*d)^3*n^3*log(c+d*x)/(b*d^3)+B^2*(b*c-a*d)^2*n^2*(a+b*x)*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))/(b*d^2)+4*B^2*(b*c-a*d)^3*n^2*log((b*c-a*d)/(b*(c+d*x)))*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))/(b*d^3)+2*B*(b*c-a*d)^2*n*(a+b*x)*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^2/(b*d^2)-1/2*b*B*(b*c-a*d)*n*(c+d*x)^2*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^2/d^3+B*(b*c-a*d)^3*n*log((b*c-a*d)/(b*(c+d*x)))*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^2/(b*d^3)+1/3*(a+b*x)^3*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^3/b-B^2*(b*c-a*d)^3*n^2*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))*log(1-b*(c+d*x)/(d*(a+b*x)))/(b*d^3)+4*B^3*(b*c-a*d)^3*n^3*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(b*d^3)+2*B^2*(b*c-a*d)^3*n^2*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(b*d^3)+B^3*(b*c-a*d)^3*n^3*polylog(2,b*(c+d*x)/(d*(a+b*x)))/(b*d^3)-2*B^3*(b*c-a*d)^3*n^3*polylog(3,d*(a+b*x)/(b*(c+d*x)))/(b*d^3)],
[(a+b*x)*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^3,x,11,-3*B^2*(b*c-a*d)^2*n^2*log((b*c-a*d)/(b*(c+d*x)))*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))/(b*d^2)-3/2*B*(b*c-a*d)*n*(a+b*x)*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^2/(b*d)-3/2*B*(b*c-a*d)^2*n*log((b*c-a*d)/(b*(c+d*x)))*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^2/(b*d^2)+1/2*(a+b*x)^2*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^3/b-3*B^3*(b*c-a*d)^2*n^3*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(b*d^2)-3*B^2*(b*c-a*d)^2*n^2*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(b*d^2)+3*B^3*(b*c-a*d)^2*n^3*polylog(3,d*(a+b*x)/(b*(c+d*x)))/(b*d^2)],
[(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^3/(a+b*x),x,6,-(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^3*log(1-b*(c+d*x)/(d*(a+b*x)))/b+3*B*n*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^2*polylog(2,b*(c+d*x)/(d*(a+b*x)))/b+6*B^2*n^2*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))*polylog(3,b*(c+d*x)/(d*(a+b*x)))/b+6*B^3*n^3*polylog(4,b*(c+d*x)/(d*(a+b*x)))/b],
[(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^3/(a+b*x)^2,x,5,-6*B^3*n^3*(c+d*x)/((b*c-a*d)*(a+b*x))-6*B^2*n^2*(c+d*x)*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))/((b*c-a*d)*(a+b*x))-3*B*n*(c+d*x)*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^2/((b*c-a*d)*(a+b*x))-(c+d*x)*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^3/((b*c-a*d)*(a+b*x))],
[(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^3/(a+b*x)^3,x,10,6*B^3*d*n^3*(c+d*x)/((b*c-a*d)^2*(a+b*x))-3/8*b*B^3*n^3*(c+d*x)^2/((b*c-a*d)^2*(a+b*x)^2)+6*B^2*d*n^2*(c+d*x)*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))/((b*c-a*d)^2*(a+b*x))-3/4*b*B^2*n^2*(c+d*x)^2*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))/((b*c-a*d)^2*(a+b*x)^2)+3*B*d*n*(c+d*x)*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^2/((b*c-a*d)^2*(a+b*x))-3/4*b*B*n*(c+d*x)^2*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^2/((b*c-a*d)^2*(a+b*x)^2)+d*(c+d*x)*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^3/((b*c-a*d)^2*(a+b*x))-1/2*b*(c+d*x)^2*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^3/((b*c-a*d)^2*(a+b*x)^2)],
[(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^3/(a+b*x)^4,x,13,-6*B^3*d^2*n^3*(c+d*x)/((b*c-a*d)^3*(a+b*x))+3/4*b*B^3*d*n^3*(c+d*x)^2/((b*c-a*d)^3*(a+b*x)^2)-2/27*b^2*B^3*n^3*(c+d*x)^3/((b*c-a*d)^3*(a+b*x)^3)-6*B^2*d^2*n^2*(c+d*x)*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))/((b*c-a*d)^3*(a+b*x))+3/2*b*B^2*d*n^2*(c+d*x)^2*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))/((b*c-a*d)^3*(a+b*x)^2)-2/9*b^2*B^2*n^2*(c+d*x)^3*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))/((b*c-a*d)^3*(a+b*x)^3)-3*B*d^2*n*(c+d*x)*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^2/((b*c-a*d)^3*(a+b*x))+3/2*b*B*d*n*(c+d*x)^2*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^2/((b*c-a*d)^3*(a+b*x)^2)-1/3*b^2*B*n*(c+d*x)^3*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^2/((b*c-a*d)^3*(a+b*x)^3)-d^2*(c+d*x)*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^3/((b*c-a*d)^3*(a+b*x))+b*d*(c+d*x)^2*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^3/((b*c-a*d)^3*(a+b*x)^2)-1/3*b^2*(c+d*x)^3*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^3/((b*c-a*d)^3*(a+b*x)^3)],
[(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^3/(a+b*x)^5,x,16,6*B^3*d^3*n^3*(c+d*x)/((b*c-a*d)^4*(a+b*x))-9/8*b*B^3*d^2*n^3*(c+d*x)^2/((b*c-a*d)^4*(a+b*x)^2)+2/9*b^2*B^3*d*n^3*(c+d*x)^3/((b*c-a*d)^4*(a+b*x)^3)-3/128*b^3*B^3*n^3*(c+d*x)^4/((b*c-a*d)^4*(a+b*x)^4)+6*B^2*d^3*n^2*(c+d*x)*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))/((b*c-a*d)^4*(a+b*x))-9/4*b*B^2*d^2*n^2*(c+d*x)^2*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))/((b*c-a*d)^4*(a+b*x)^2)+2/3*b^2*B^2*d*n^2*(c+d*x)^3*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))/((b*c-a*d)^4*(a+b*x)^3)-3/32*b^3*B^2*n^2*(c+d*x)^4*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))/((b*c-a*d)^4*(a+b*x)^4)+3*B*d^3*n*(c+d*x)*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^2/((b*c-a*d)^4*(a+b*x))-9/4*b*B*d^2*n*(c+d*x)^2*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^2/((b*c-a*d)^4*(a+b*x)^2)+b^2*B*d*n*(c+d*x)^3*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^2/((b*c-a*d)^4*(a+b*x)^3)-3/16*b^3*B*n*(c+d*x)^4*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^2/((b*c-a*d)^4*(a+b*x)^4)+d^3*(c+d*x)*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^3/((b*c-a*d)^4*(a+b*x))-3/2*b*d^2*(c+d*x)^2*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^3/((b*c-a*d)^4*(a+b*x)^2)+b^2*d*(c+d*x)^3*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^3/((b*c-a*d)^4*(a+b*x)^3)-1/4*b^3*(c+d*x)^4*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^3/((b*c-a*d)^4*(a+b*x)^4)],

# p<0
[1/((a*g+b*g*x)^2*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))),x,4,exp(A/(B*n))*(c+d*x)*(e*(a+b*x)^n/(c+d*x)^n)^(1/n)*Ei((-A-B*log(e*(a+b*x)^n/(c+d*x)^n))/(B*n))/(B*(b*c-a*d)*g^2*n*(a+b*x))],

# Integrands of the form (f+g x)^m (A+B Log[e (a+b x)^n/(c+d x)^n])^p when d f-c g=0

# Integrands of the form (f+g x)^m (A+B Log[e (a+b x)^1/(c+d x)^1])^p when d f-c g=0

# p>0
[(a*g+b*g*x)^4*(A+B*log(e*(c+d*x)/(a+b*x))),x,4,-1/5*B*(b*c-a*d)^4*g^4*x/d^4+1/10*B*(b*c-a*d)^3*g^4*(a+b*x)^2/(b*d^3)-1/15*B*(b*c-a*d)^2*g^4*(a+b*x)^3/(b*d^2)+1/20*B*(b*c-a*d)*g^4*(a+b*x)^4/(b*d)+1/5*B*(b*c-a*d)^5*g^4*log(c+d*x)/(b*d^5)+1/5*g^4*(a+b*x)^5*(A+B*log(e*(c+d*x)/(a+b*x)))/b],
[(a*g+b*g*x)^3*(A+B*log(e*(c+d*x)/(a+b*x))),x,4,1/4*B*(b*c-a*d)^3*g^3*x/d^3-1/8*B*(b*c-a*d)^2*g^3*(a+b*x)^2/(b*d^2)+1/12*B*(b*c-a*d)*g^3*(a+b*x)^3/(b*d)-1/4*B*(b*c-a*d)^4*g^3*log(c+d*x)/(b*d^4)+1/4*g^3*(a+b*x)^4*(A+B*log(e*(c+d*x)/(a+b*x)))/b],
[(a*g+b*g*x)^2*(A+B*log(e*(c+d*x)/(a+b*x))),x,4,-1/3*B*(b*c-a*d)^2*g^2*x/d^2+1/6*B*(b*c-a*d)*g^2*(a+b*x)^2/(b*d)+1/3*B*(b*c-a*d)^3*g^2*log(c+d*x)/(b*d^3)+1/3*g^2*(a+b*x)^3*(A+B*log(e*(c+d*x)/(a+b*x)))/b],
[(a*g+b*g*x)*(A+B*log(e*(c+d*x)/(a+b*x))),x,4,1/2*B*(b*c-a*d)*g*x/d-1/2*B*(b*c-a*d)^2*g*log(c+d*x)/(b*d^2)+1/2*g*(a+b*x)^2*(A+B*log(e*(c+d*x)/(a+b*x)))/b],
[(A+B*log(e*(c+d*x)/(a+b*x)))/(a*g+b*g*x),x,5,-log((-b*c+a*d)/(d*(a+b*x)))*(A+B*log(e*(c+d*x)/(a+b*x)))/(b*g)-B*polylog(2,1+(b*c-a*d)/(d*(a+b*x)))/(b*g)],
[(A+B*log(e*(c+d*x)/(a+b*x)))/(a*g+b*g*x)^2,x,3,(-A+B)/(b*g^2*(a+b*x))-B*(c+d*x)*log(e*(c+d*x)/(a+b*x))/((b*c-a*d)*g^2*(a+b*x)),-A*(c+d*x)/((b*c-a*d)*g^2*(a+b*x))+B*(c+d*x)/((b*c-a*d)*g^2*(a+b*x))-B*(c+d*x)*log(e*(c+d*x)/(a+b*x))/((b*c-a*d)*g^2*(a+b*x))],
[(A+B*log(e*(c+d*x)/(a+b*x)))/(a*g+b*g*x)^3,x,4,1/4*B/(b*g^3*(a+b*x)^2)-1/2*B*d/(b*(b*c-a*d)*g^3*(a+b*x))-1/2*B*d^2*log(a+b*x)/(b*(b*c-a*d)^2*g^3)+1/2*B*d^2*log(c+d*x)/(b*(b*c-a*d)^2*g^3)+1/2*(-A-B*log(e*(c+d*x)/(a+b*x)))/(b*g^3*(a+b*x)^2)],
[(A+B*log(e*(c+d*x)/(a+b*x)))/(a*g+b*g*x)^4,x,4,1/9*B/(b*g^4*(a+b*x)^3)-1/6*B*d/(b*(b*c-a*d)*g^4*(a+b*x)^2)+1/3*B*d^2/(b*(b*c-a*d)^2*g^4*(a+b*x))+1/3*B*d^3*log(a+b*x)/(b*(b*c-a*d)^3*g^4)-1/3*B*d^3*log(c+d*x)/(b*(b*c-a*d)^3*g^4)+1/3*(-A-B*log(e*(c+d*x)/(a+b*x)))/(b*g^4*(a+b*x)^3)],
[(A+B*log(e*(c+d*x)/(a+b*x)))/(a*g+b*g*x)^5,x,4,1/16*B/(b*g^5*(a+b*x)^4)-1/12*B*d/(b*(b*c-a*d)*g^5*(a+b*x)^3)+1/8*B*d^2/(b*(b*c-a*d)^2*g^5*(a+b*x)^2)-1/4*B*d^3/(b*(b*c-a*d)^3*g^5*(a+b*x))-1/4*B*d^4*log(a+b*x)/(b*(b*c-a*d)^4*g^5)+1/4*B*d^4*log(c+d*x)/(b*(b*c-a*d)^4*g^5)+1/4*(-A-B*log(e*(c+d*x)/(a+b*x)))/(b*g^5*(a+b*x)^4)],
[(a*g+b*g*x)^4*(A+B*log(e*(c+d*x)/(a+b*x)))^2,x,19,13/30*B^2*(b*c-a*d)^4*g^4*x/d^4-7/60*B^2*(b*c-a*d)^3*g^4*(a+b*x)^2/(b*d^3)+1/30*B^2*(b*c-a*d)^2*g^4*(a+b*x)^3/(b*d^2)-5/6*B^2*(b*c-a*d)^5*g^4*log(a+b*x)/(b*d^5)-13/30*B^2*(b*c-a*d)^5*g^4*log((c+d*x)/(a+b*x))/(b*d^5)+1/5*B*(b*c-a*d)^3*g^4*(a+b*x)^2*(A+B*log(e*(c+d*x)/(a+b*x)))/(b*d^3)-2/15*B*(b*c-a*d)^2*g^4*(a+b*x)^3*(A+B*log(e*(c+d*x)/(a+b*x)))/(b*d^2)+1/10*B*(b*c-a*d)*g^4*(a+b*x)^4*(A+B*log(e*(c+d*x)/(a+b*x)))/(b*d)-2/5*B*(b*c-a*d)^4*g^4*(c+d*x)*(A+B*log(e*(c+d*x)/(a+b*x)))/d^5+1/5*g^4*(a+b*x)^5*(A+B*log(e*(c+d*x)/(a+b*x)))^2/b-2/5*B*(b*c-a*d)^5*g^4*(A+B*log(e*(c+d*x)/(a+b*x)))*log(1-d*(a+b*x)/(b*(c+d*x)))/(b*d^5)+2/5*B^2*(b*c-a*d)^5*g^4*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(b*d^5)],
[(a*g+b*g*x)^3*(A+B*log(e*(c+d*x)/(a+b*x)))^2,x,15,-5/12*B^2*(b*c-a*d)^3*g^3*x/d^3+1/12*B^2*(b*c-a*d)^2*g^3*(a+b*x)^2/(b*d^2)+11/12*B^2*(b*c-a*d)^4*g^3*log(a+b*x)/(b*d^4)+5/12*B^2*(b*c-a*d)^4*g^3*log((c+d*x)/(a+b*x))/(b*d^4)-1/4*B*(b*c-a*d)^2*g^3*(a+b*x)^2*(A+B*log(e*(c+d*x)/(a+b*x)))/(b*d^2)+1/6*B*(b*c-a*d)*g^3*(a+b*x)^3*(A+B*log(e*(c+d*x)/(a+b*x)))/(b*d)+1/2*B*(b*c-a*d)^3*g^3*(c+d*x)*(A+B*log(e*(c+d*x)/(a+b*x)))/d^4+1/4*g^3*(a+b*x)^4*(A+B*log(e*(c+d*x)/(a+b*x)))^2/b+1/2*B*(b*c-a*d)^4*g^3*(A+B*log(e*(c+d*x)/(a+b*x)))*log(1-d*(a+b*x)/(b*(c+d*x)))/(b*d^4)-1/2*B^2*(b*c-a*d)^4*g^3*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(b*d^4)],
[(a*g+b*g*x)^2*(A+B*log(e*(c+d*x)/(a+b*x)))^2,x,11,1/3*B^2*(b*c-a*d)^2*g^2*x/d^2-B^2*(b*c-a*d)^3*g^2*log(a+b*x)/(b*d^3)-1/3*B^2*(b*c-a*d)^3*g^2*log((c+d*x)/(a+b*x))/(b*d^3)+1/3*B*(b*c-a*d)*g^2*(a+b*x)^2*(A+B*log(e*(c+d*x)/(a+b*x)))/(b*d)-2/3*B*(b*c-a*d)^2*g^2*(c+d*x)*(A+B*log(e*(c+d*x)/(a+b*x)))/d^3+1/3*g^2*(a+b*x)^3*(A+B*log(e*(c+d*x)/(a+b*x)))^2/b-2/3*B*(b*c-a*d)^3*g^2*(A+B*log(e*(c+d*x)/(a+b*x)))*log(1-d*(a+b*x)/(b*(c+d*x)))/(b*d^3)+2/3*B^2*(b*c-a*d)^3*g^2*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(b*d^3)],
[(a*g+b*g*x)*(A+B*log(e*(c+d*x)/(a+b*x)))^2,x,7,B^2*(b*c-a*d)^2*g*log(a+b*x)/(b*d^2)+B*(b*c-a*d)*g*(c+d*x)*(A+B*log(e*(c+d*x)/(a+b*x)))/d^2+1/2*g*(a+b*x)^2*(A+B*log(e*(c+d*x)/(a+b*x)))^2/b+B*(b*c-a*d)^2*g*(A+B*log(e*(c+d*x)/(a+b*x)))*log(1-d*(a+b*x)/(b*(c+d*x)))/(b*d^2)-B^2*(b*c-a*d)^2*g*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(b*d^2)],
[(A+B*log(e*(c+d*x)/(a+b*x)))^2/(a*g+b*g*x),x,4,-log((-b*c+a*d)/(d*(a+b*x)))*(A+B*log(e*(c+d*x)/(a+b*x)))^2/(b*g)-2*B*(A+B*log(e*(c+d*x)/(a+b*x)))*polylog(2,b*(c+d*x)/(d*(a+b*x)))/(b*g)+2*B^2*polylog(3,b*(c+d*x)/(d*(a+b*x)))/(b*g)],
[(A+B*log(e*(c+d*x)/(a+b*x)))^2/(a*g+b*g*x)^2,x,4,2*A*B*(c+d*x)/((b*c-a*d)*g^2*(a+b*x))-2*B^2*(c+d*x)/((b*c-a*d)*g^2*(a+b*x))+2*B^2*(c+d*x)*log(e*(c+d*x)/(a+b*x))/((b*c-a*d)*g^2*(a+b*x))-(c+d*x)*(A+B*log(e*(c+d*x)/(a+b*x)))^2/((b*c-a*d)*g^2*(a+b*x))],
[(A+B*log(e*(c+d*x)/(a+b*x)))^2/(a*g+b*g*x)^3,x,8,-2*A*B*d*(c+d*x)/((b*c-a*d)^2*g^3*(a+b*x))+2*B^2*d*(c+d*x)/((b*c-a*d)^2*g^3*(a+b*x))-1/4*b*B^2*(c+d*x)^2/((b*c-a*d)^2*g^3*(a+b*x)^2)-2*B^2*d*(c+d*x)*log(e*(c+d*x)/(a+b*x))/((b*c-a*d)^2*g^3*(a+b*x))+1/2*b*B*(c+d*x)^2*(A+B*log(e*(c+d*x)/(a+b*x)))/((b*c-a*d)^2*g^3*(a+b*x)^2)+d*(c+d*x)*(A+B*log(e*(c+d*x)/(a+b*x)))^2/((b*c-a*d)^2*g^3*(a+b*x))-1/2*b*(c+d*x)^2*(A+B*log(e*(c+d*x)/(a+b*x)))^2/((b*c-a*d)^2*g^3*(a+b*x)^2)],
[(A+B*log(e*(c+d*x)/(a+b*x)))^2/(a*g+b*g*x)^4,x,6,-2*B^2*d^2*(c+d*x)/((b*c-a*d)^3*g^4*(a+b*x))+1/2*b*B^2*d*(c+d*x)^2/((b*c-a*d)^3*g^4*(a+b*x)^2)-2/27*b^2*B^2*(c+d*x)^3/((b*c-a*d)^3*g^4*(a+b*x)^3)+1/3*B^2*d^3*log((c+d*x)/(a+b*x))^2/(b*(b*c-a*d)^3*g^4)+2*B*d^2*(c+d*x)*(A+B*log(e*(c+d*x)/(a+b*x)))/((b*c-a*d)^3*g^4*(a+b*x))-b*B*d*(c+d*x)^2*(A+B*log(e*(c+d*x)/(a+b*x)))/((b*c-a*d)^3*g^4*(a+b*x)^2)+2/9*b^2*B*(c+d*x)^3*(A+B*log(e*(c+d*x)/(a+b*x)))/((b*c-a*d)^3*g^4*(a+b*x)^3)-2/3*B*d^3*log((c+d*x)/(a+b*x))*(A+B*log(e*(c+d*x)/(a+b*x)))/(b*(b*c-a*d)^3*g^4)-1/3*(A+B*log(e*(c+d*x)/(a+b*x)))^2/(b*g^4*(a+b*x)^3)],
[(A+B*log(e*(c+d*x)/(a+b*x)))^2/(a*g+b*g*x)^5,x,5,2*B^2*d^3*(c+d*x)/((b*c-a*d)^4*g^5*(a+b*x))-3/4*b*B^2*d^2*(c+d*x)^2/((b*c-a*d)^4*g^5*(a+b*x)^2)+2/9*b^2*B^2*d*(c+d*x)^3/((b*c-a*d)^4*g^5*(a+b*x)^3)-1/32*b^3*B^2*(c+d*x)^4/((b*c-a*d)^4*g^5*(a+b*x)^4)-1/4*B^2*d^4*log((c+d*x)/(a+b*x))^2/(b*(b*c-a*d)^4*g^5)-2*B*d^3*(c+d*x)*(A+B*log(e*(c+d*x)/(a+b*x)))/((b*c-a*d)^4*g^5*(a+b*x))+3/2*b*B*d^2*(c+d*x)^2*(A+B*log(e*(c+d*x)/(a+b*x)))/((b*c-a*d)^4*g^5*(a+b*x)^2)-2/3*b^2*B*d*(c+d*x)^3*(A+B*log(e*(c+d*x)/(a+b*x)))/((b*c-a*d)^4*g^5*(a+b*x)^3)+1/8*b^3*B*(c+d*x)^4*(A+B*log(e*(c+d*x)/(a+b*x)))/((b*c-a*d)^4*g^5*(a+b*x)^4)+1/2*B*d^4*log((c+d*x)/(a+b*x))*(A+B*log(e*(c+d*x)/(a+b*x)))/(b*(b*c-a*d)^4*g^5)-1/4*(A+B*log(e*(c+d*x)/(a+b*x)))^2/(b*g^5*(a+b*x)^4)],

# p<0
[(a*g+b*g*x)^2/(A+B*log(e*(c+d*x)/(a+b*x))),x,0,Unintegrable((a*g+b*g*x)^2/(A+B*log(e*(c+d*x)/(a+b*x))),x)],
[(a*g+b*g*x)/(A+B*log(e*(c+d*x)/(a+b*x))),x,0,Unintegrable((a*g+b*g*x)/(A+B*log(e*(c+d*x)/(a+b*x))),x)],
[1/((a*g+b*g*x)*(A+B*log(e*(c+d*x)/(a+b*x)))),x,0,Unintegrable(1/((a*g+b*g*x)*(A+B*log(e*(c+d*x)/(a+b*x)))),x)],
[1/((a*g+b*g*x)^2*(A+B*log(e*(c+d*x)/(a+b*x)))),x,3,-Ei((A+B*log(e*(c+d*x)/(a+b*x)))/B)/(B*(b*c-a*d)*e*exp(A/B)*g^2)],
[1/((a*g+b*g*x)^3*(A+B*log(e*(c+d*x)/(a+b*x)))),x,7,d*Ei((A+B*log(e*(c+d*x)/(a+b*x)))/B)/(B*(b*c-a*d)^2*e*exp(A/B)*g^3)-b*Ei(2*(A+B*log(e*(c+d*x)/(a+b*x)))/B)/(B*(b*c-a*d)^2*e^2*exp(2*A/B)*g^3)],
[(a*g+b*g*x)^2/(A+B*log(e*(c+d*x)/(a+b*x)))^2,x,0,Unintegrable((a*g+b*g*x)^2/(A+B*log(e*(c+d*x)/(a+b*x)))^2,x)],
[(a*g+b*g*x)/(A+B*log(e*(c+d*x)/(a+b*x)))^2,x,0,Unintegrable((a*g+b*g*x)/(A+B*log(e*(c+d*x)/(a+b*x)))^2,x)],
[1/((a*g+b*g*x)*(A+B*log(e*(c+d*x)/(a+b*x)))^2),x,0,Unintegrable(1/((a*g+b*g*x)*(A+B*log(e*(c+d*x)/(a+b*x)))^2),x)],
[1/((a*g+b*g*x)^2*(A+B*log(e*(c+d*x)/(a+b*x)))^2),x,4,-Ei((A+B*log(e*(c+d*x)/(a+b*x)))/B)/(B^2*(b*c-a*d)*e*exp(A/B)*g^2)+(c+d*x)/(B*(b*c-a*d)*g^2*(a+b*x)*(A+B*log(e*(c+d*x)/(a+b*x))))],
[1/((a*g+b*g*x)^3*(A+B*log(e*(c+d*x)/(a+b*x)))^2),x,10,d*Ei((A+B*log(e*(c+d*x)/(a+b*x)))/B)/(B^2*(b*c-a*d)^2*e*exp(A/B)*g^3)-2*b*Ei(2*(A+B*log(e*(c+d*x)/(a+b*x)))/B)/(B^2*(b*c-a*d)^2*e^2*exp(2*A/B)*g^3)+(c+d*x)/(B*(b*c-a*d)*g^3*(a+b*x)^2*(A+B*log(e*(c+d*x)/(a+b*x))))],

# Integrands of the form (f+g x)^m (A+B Log[e (a+b x)^2/(c+d x)^2])^p when d f-c g=0

# p>0
[(a*g+b*g*x)^4*(A+B*log(e*(c+d*x)^2/(a+b*x)^2)),x,4,-2/5*B*(b*c-a*d)^4*g^4*x/d^4+1/5*B*(b*c-a*d)^3*g^4*(a+b*x)^2/(b*d^3)-2/15*B*(b*c-a*d)^2*g^4*(a+b*x)^3/(b*d^2)+1/10*B*(b*c-a*d)*g^4*(a+b*x)^4/(b*d)+2/5*B*(b*c-a*d)^5*g^4*log(c+d*x)/(b*d^5)+1/5*g^4*(a+b*x)^5*(A+B*log(e*(c+d*x)^2/(a+b*x)^2))/b],
[(a*g+b*g*x)^3*(A+B*log(e*(c+d*x)^2/(a+b*x)^2)),x,4,1/2*B*(b*c-a*d)^3*g^3*x/d^3-1/4*B*(b*c-a*d)^2*g^3*(a+b*x)^2/(b*d^2)+1/6*B*(b*c-a*d)*g^3*(a+b*x)^3/(b*d)-1/2*B*(b*c-a*d)^4*g^3*log(c+d*x)/(b*d^4)+1/4*g^3*(a+b*x)^4*(A+B*log(e*(c+d*x)^2/(a+b*x)^2))/b],
[(a*g+b*g*x)^2*(A+B*log(e*(c+d*x)^2/(a+b*x)^2)),x,4,-2/3*B*(b*c-a*d)^2*g^2*x/d^2+1/3*B*(b*c-a*d)*g^2*(a+b*x)^2/(b*d)+2/3*B*(b*c-a*d)^3*g^2*log(c+d*x)/(b*d^3)+1/3*g^2*(a+b*x)^3*(A+B*log(e*(c+d*x)^2/(a+b*x)^2))/b],
[(a*g+b*g*x)*(A+B*log(e*(c+d*x)^2/(a+b*x)^2)),x,4,B*(b*c-a*d)*g*x/d-B*(b*c-a*d)^2*g*log(c+d*x)/(b*d^2)+1/2*g*(a+b*x)^2*(A+B*log(e*(c+d*x)^2/(a+b*x)^2))/b],
[(A+B*log(e*(c+d*x)^2/(a+b*x)^2))/(a*g+b*g*x),x,5,-log((-b*c+a*d)/(d*(a+b*x)))*(A+B*log(e*(c+d*x)^2/(a+b*x)^2))/(b*g)-2*B*polylog(2,1+(b*c-a*d)/(d*(a+b*x)))/(b*g)],
[(A+B*log(e*(c+d*x)^2/(a+b*x)^2))/(a*g+b*g*x)^2,x,3,-A*(c+d*x)/((b*c-a*d)*g^2*(a+b*x))+2*B*(c+d*x)/((b*c-a*d)*g^2*(a+b*x))-B*(c+d*x)*log(e*(c+d*x)^2/(a+b*x)^2)/((b*c-a*d)*g^2*(a+b*x))],
[(A+B*log(e*(c+d*x)^2/(a+b*x)^2))/(a*g+b*g*x)^3,x,4,1/2*B/(b*g^3*(a+b*x)^2)-B*d/(b*(b*c-a*d)*g^3*(a+b*x))-B*d^2*log(a+b*x)/(b*(b*c-a*d)^2*g^3)+B*d^2*log(c+d*x)/(b*(b*c-a*d)^2*g^3)+1/2*(-A-B*log(e*(c+d*x)^2/(a+b*x)^2))/(b*g^3*(a+b*x)^2)],
[(A+B*log(e*(c+d*x)^2/(a+b*x)^2))/(a*g+b*g*x)^4,x,4,2/9*B/(b*g^4*(a+b*x)^3)-1/3*B*d/(b*(b*c-a*d)*g^4*(a+b*x)^2)+2/3*B*d^2/(b*(b*c-a*d)^2*g^4*(a+b*x))+2/3*B*d^3*log(a+b*x)/(b*(b*c-a*d)^3*g^4)-2/3*B*d^3*log(c+d*x)/(b*(b*c-a*d)^3*g^4)+1/3*(-A-B*log(e*(c+d*x)^2/(a+b*x)^2))/(b*g^4*(a+b*x)^3)],
[(A+B*log(e*(c+d*x)^2/(a+b*x)^2))/(a*g+b*g*x)^5,x,4,1/8*B/(b*g^5*(a+b*x)^4)-1/6*B*d/(b*(b*c-a*d)*g^5*(a+b*x)^3)+1/4*B*d^2/(b*(b*c-a*d)^2*g^5*(a+b*x)^2)-1/2*B*d^3/(b*(b*c-a*d)^3*g^5*(a+b*x))-1/2*B*d^4*log(a+b*x)/(b*(b*c-a*d)^4*g^5)+1/2*B*d^4*log(c+d*x)/(b*(b*c-a*d)^4*g^5)+1/4*(-A-B*log(e*(c+d*x)^2/(a+b*x)^2))/(b*g^5*(a+b*x)^4)],
[(a*g+b*g*x)^4*(A+B*log(e*(c+d*x)^2/(a+b*x)^2))^2,x,19,26/15*B^2*(b*c-a*d)^4*g^4*x/d^4-7/15*B^2*(b*c-a*d)^3*g^4*(a+b*x)^2/(b*d^3)+2/15*B^2*(b*c-a*d)^2*g^4*(a+b*x)^3/(b*d^2)-10/3*B^2*(b*c-a*d)^5*g^4*log(a+b*x)/(b*d^5)-26/15*B^2*(b*c-a*d)^5*g^4*log((c+d*x)/(a+b*x))/(b*d^5)+2/5*B*(b*c-a*d)^3*g^4*(a+b*x)^2*(A+B*log(e*(c+d*x)^2/(a+b*x)^2))/(b*d^3)-4/15*B*(b*c-a*d)^2*g^4*(a+b*x)^3*(A+B*log(e*(c+d*x)^2/(a+b*x)^2))/(b*d^2)+1/5*B*(b*c-a*d)*g^4*(a+b*x)^4*(A+B*log(e*(c+d*x)^2/(a+b*x)^2))/(b*d)-4/5*B*(b*c-a*d)^4*g^4*(c+d*x)*(A+B*log(e*(c+d*x)^2/(a+b*x)^2))/d^5+1/5*g^4*(a+b*x)^5*(A+B*log(e*(c+d*x)^2/(a+b*x)^2))^2/b-4/5*B*(b*c-a*d)^5*g^4*(A+B*log(e*(c+d*x)^2/(a+b*x)^2))*log(1-d*(a+b*x)/(b*(c+d*x)))/(b*d^5)+8/5*B^2*(b*c-a*d)^5*g^4*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(b*d^5)],
[(a*g+b*g*x)^3*(A+B*log(e*(c+d*x)^2/(a+b*x)^2))^2,x,15,-5/3*B^2*(b*c-a*d)^3*g^3*x/d^3+1/3*B^2*(b*c-a*d)^2*g^3*(a+b*x)^2/(b*d^2)+11/3*B^2*(b*c-a*d)^4*g^3*log(a+b*x)/(b*d^4)+5/3*B^2*(b*c-a*d)^4*g^3*log((c+d*x)/(a+b*x))/(b*d^4)-1/2*B*(b*c-a*d)^2*g^3*(a+b*x)^2*(A+B*log(e*(c+d*x)^2/(a+b*x)^2))/(b*d^2)+1/3*B*(b*c-a*d)*g^3*(a+b*x)^3*(A+B*log(e*(c+d*x)^2/(a+b*x)^2))/(b*d)+B*(b*c-a*d)^3*g^3*(c+d*x)*(A+B*log(e*(c+d*x)^2/(a+b*x)^2))/d^4+1/4*g^3*(a+b*x)^4*(A+B*log(e*(c+d*x)^2/(a+b*x)^2))^2/b+B*(b*c-a*d)^4*g^3*(A+B*log(e*(c+d*x)^2/(a+b*x)^2))*log(1-d*(a+b*x)/(b*(c+d*x)))/(b*d^4)-2*B^2*(b*c-a*d)^4*g^3*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(b*d^4)],
[(a*g+b*g*x)^2*(A+B*log(e*(c+d*x)^2/(a+b*x)^2))^2,x,11,4/3*B^2*(b*c-a*d)^2*g^2*x/d^2-4*B^2*(b*c-a*d)^3*g^2*log(a+b*x)/(b*d^3)-4/3*B^2*(b*c-a*d)^3*g^2*log((c+d*x)/(a+b*x))/(b*d^3)+2/3*B*(b*c-a*d)*g^2*(a+b*x)^2*(A+B*log(e*(c+d*x)^2/(a+b*x)^2))/(b*d)-4/3*B*(b*c-a*d)^2*g^2*(c+d*x)*(A+B*log(e*(c+d*x)^2/(a+b*x)^2))/d^3+1/3*g^2*(a+b*x)^3*(A+B*log(e*(c+d*x)^2/(a+b*x)^2))^2/b-4/3*B*(b*c-a*d)^3*g^2*(A+B*log(e*(c+d*x)^2/(a+b*x)^2))*log(1-d*(a+b*x)/(b*(c+d*x)))/(b*d^3)+8/3*B^2*(b*c-a*d)^3*g^2*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(b*d^3)],
[(a*g+b*g*x)*(A+B*log(e*(c+d*x)^2/(a+b*x)^2))^2,x,7,4*B^2*(b*c-a*d)^2*g*log(a+b*x)/(b*d^2)+2*B*(b*c-a*d)*g*(c+d*x)*(A+B*log(e*(c+d*x)^2/(a+b*x)^2))/d^2+1/2*g*(a+b*x)^2*(A+B*log(e*(c+d*x)^2/(a+b*x)^2))^2/b+2*B*(b*c-a*d)^2*g*(A+B*log(e*(c+d*x)^2/(a+b*x)^2))*log(1-d*(a+b*x)/(b*(c+d*x)))/(b*d^2)-4*B^2*(b*c-a*d)^2*g*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(b*d^2)],
[(A+B*log(e*(c+d*x)^2/(a+b*x)^2))^2/(a*g+b*g*x),x,4,-log((-b*c+a*d)/(d*(a+b*x)))*(A+B*log(e*(c+d*x)^2/(a+b*x)^2))^2/(b*g)-4*B*(A+B*log(e*(c+d*x)^2/(a+b*x)^2))*polylog(2,b*(c+d*x)/(d*(a+b*x)))/(b*g)+8*B^2*polylog(3,b*(c+d*x)/(d*(a+b*x)))/(b*g)],
[(A+B*log(e*(c+d*x)^2/(a+b*x)^2))^2/(a*g+b*g*x)^2,x,4,4*A*B*(c+d*x)/((b*c-a*d)*g^2*(a+b*x))-8*B^2*(c+d*x)/((b*c-a*d)*g^2*(a+b*x))+4*B^2*(c+d*x)*log(e*(c+d*x)^2/(a+b*x)^2)/((b*c-a*d)*g^2*(a+b*x))-(c+d*x)*(A+B*log(e*(c+d*x)^2/(a+b*x)^2))^2/((b*c-a*d)*g^2*(a+b*x))],
[(A+B*log(e*(c+d*x)^2/(a+b*x)^2))^2/(a*g+b*g*x)^3,x,8,-4*A*B*d*(c+d*x)/((b*c-a*d)^2*g^3*(a+b*x))+8*B^2*d*(c+d*x)/((b*c-a*d)^2*g^3*(a+b*x))-b*B^2*(c+d*x)^2/((b*c-a*d)^2*g^3*(a+b*x)^2)-4*B^2*d*(c+d*x)*log(e*(c+d*x)^2/(a+b*x)^2)/((b*c-a*d)^2*g^3*(a+b*x))+b*B*(c+d*x)^2*(A+B*log(e*(c+d*x)^2/(a+b*x)^2))/((b*c-a*d)^2*g^3*(a+b*x)^2)+d*(c+d*x)*(A+B*log(e*(c+d*x)^2/(a+b*x)^2))^2/((b*c-a*d)^2*g^3*(a+b*x))-1/2*b*(c+d*x)^2*(A+B*log(e*(c+d*x)^2/(a+b*x)^2))^2/((b*c-a*d)^2*g^3*(a+b*x)^2)],
[(A+B*log(e*(c+d*x)^2/(a+b*x)^2))^2/(a*g+b*g*x)^4,x,6,-8*B^2*d^2*(c+d*x)/((b*c-a*d)^3*g^4*(a+b*x))+2*b*B^2*d*(c+d*x)^2/((b*c-a*d)^3*g^4*(a+b*x)^2)-8/27*b^2*B^2*(c+d*x)^3/((b*c-a*d)^3*g^4*(a+b*x)^3)+4/3*B^2*d^3*log((c+d*x)/(a+b*x))^2/(b*(b*c-a*d)^3*g^4)+4*B*d^2*(c+d*x)*(A+B*log(e*(c+d*x)^2/(a+b*x)^2))/((b*c-a*d)^3*g^4*(a+b*x))-2*b*B*d*(c+d*x)^2*(A+B*log(e*(c+d*x)^2/(a+b*x)^2))/((b*c-a*d)^3*g^4*(a+b*x)^2)+4/9*b^2*B*(c+d*x)^3*(A+B*log(e*(c+d*x)^2/(a+b*x)^2))/((b*c-a*d)^3*g^4*(a+b*x)^3)-4/3*B*d^3*log((c+d*x)/(a+b*x))*(A+B*log(e*(c+d*x)^2/(a+b*x)^2))/(b*(b*c-a*d)^3*g^4)-1/3*(A+B*log(e*(c+d*x)^2/(a+b*x)^2))^2/(b*g^4*(a+b*x)^3)],
[(A+B*log(e*(c+d*x)^2/(a+b*x)^2))^2/(a*g+b*g*x)^5,x,5,8*B^2*d^3*(c+d*x)/((b*c-a*d)^4*g^5*(a+b*x))-3*b*B^2*d^2*(c+d*x)^2/((b*c-a*d)^4*g^5*(a+b*x)^2)+8/9*b^2*B^2*d*(c+d*x)^3/((b*c-a*d)^4*g^5*(a+b*x)^3)-1/8*b^3*B^2*(c+d*x)^4/((b*c-a*d)^4*g^5*(a+b*x)^4)-B^2*d^4*log((c+d*x)/(a+b*x))^2/(b*(b*c-a*d)^4*g^5)-4*B*d^3*(c+d*x)*(A+B*log(e*(c+d*x)^2/(a+b*x)^2))/((b*c-a*d)^4*g^5*(a+b*x))+3*b*B*d^2*(c+d*x)^2*(A+B*log(e*(c+d*x)^2/(a+b*x)^2))/((b*c-a*d)^4*g^5*(a+b*x)^2)-4/3*b^2*B*d*(c+d*x)^3*(A+B*log(e*(c+d*x)^2/(a+b*x)^2))/((b*c-a*d)^4*g^5*(a+b*x)^3)+1/4*b^3*B*(c+d*x)^4*(A+B*log(e*(c+d*x)^2/(a+b*x)^2))/((b*c-a*d)^4*g^5*(a+b*x)^4)+B*d^4*log((c+d*x)/(a+b*x))*(A+B*log(e*(c+d*x)^2/(a+b*x)^2))/(b*(b*c-a*d)^4*g^5)-1/4*(A+B*log(e*(c+d*x)^2/(a+b*x)^2))^2/(b*g^5*(a+b*x)^4)],

# p<0
[(a*g+b*g*x)^2/(A+B*log(e*(c+d*x)^2/(a+b*x)^2)),x,0,Unintegrable((a*g+b*g*x)^2/(A+B*log(e*(c+d*x)^2/(a+b*x)^2)),x)],
[(a*g+b*g*x)/(A+B*log(e*(c+d*x)^2/(a+b*x)^2)),x,0,Unintegrable((a*g+b*g*x)/(A+B*log(e*(c+d*x)^2/(a+b*x)^2)),x)],
[1/((a*g+b*g*x)*(A+B*log(e*(c+d*x)^2/(a+b*x)^2))),x,0,Unintegrable(1/((a*g+b*g*x)*(A+B*log(e*(c+d*x)^2/(a+b*x)^2))),x)],
[1/((a*g+b*g*x)^2*(A+B*log(e*(c+d*x)^2/(a+b*x)^2))),x,3,-1/2*(c+d*x)*Ei(1/2*(A+B*log(e*(c+d*x)^2/(a+b*x)^2))/B)/(B*(b*c-a*d)*exp(1/2*A/B)*g^2*(a+b*x)*sqrt(e*(c+d*x)^2/(a+b*x)^2))],
[1/((a*g+b*g*x)^3*(A+B*log(e*(c+d*x)^2/(a+b*x)^2))),x,7,-1/2*b*Ei((A+B*log(e*(c+d*x)^2/(a+b*x)^2))/B)/(B*(b*c-a*d)^2*e*exp(A/B)*g^3)+1/2*d*(c+d*x)*Ei(1/2*(A+B*log(e*(c+d*x)^2/(a+b*x)^2))/B)/(B*(b*c-a*d)^2*exp(1/2*A/B)*g^3*(a+b*x)*sqrt(e*(c+d*x)^2/(a+b*x)^2))],
[(a*g+b*g*x)^2/(A+B*log(e*(c+d*x)^2/(a+b*x)^2))^2,x,0,Unintegrable((a*g+b*g*x)^2/(A+B*log(e*(c+d*x)^2/(a+b*x)^2))^2,x)],
[(a*g+b*g*x)/(A+B*log(e*(c+d*x)^2/(a+b*x)^2))^2,x,0,Unintegrable((a*g+b*g*x)/(A+B*log(e*(c+d*x)^2/(a+b*x)^2))^2,x)],
[1/((a*g+b*g*x)*(A+B*log(e*(c+d*x)^2/(a+b*x)^2))^2),x,0,Unintegrable(1/((a*g+b*g*x)*(A+B*log(e*(c+d*x)^2/(a+b*x)^2))^2),x)],
[1/((a*g+b*g*x)^2*(A+B*log(e*(c+d*x)^2/(a+b*x)^2))^2),x,4,1/2*(c+d*x)/(B*(b*c-a*d)*g^2*(a+b*x)*(A+B*log(e*(c+d*x)^2/(a+b*x)^2)))-1/4*(c+d*x)*Ei(1/2*(A+B*log(e*(c+d*x)^2/(a+b*x)^2))/B)/(B^2*(b*c-a*d)*exp(1/2*A/B)*g^2*(a+b*x)*sqrt(e*(c+d*x)^2/(a+b*x)^2))],
[1/((a*g+b*g*x)^3*(A+B*log(e*(c+d*x)^2/(a+b*x)^2))^2),x,10,-1/2*b*Ei((A+B*log(e*(c+d*x)^2/(a+b*x)^2))/B)/(B^2*(b*c-a*d)^2*e*exp(A/B)*g^3)+1/2*(c+d*x)/(B*(b*c-a*d)*g^3*(a+b*x)^2*(A+B*log(e*(c+d*x)^2/(a+b*x)^2)))+1/4*d*(c+d*x)*Ei(1/2*(A+B*log(e*(c+d*x)^2/(a+b*x)^2))/B)/(B^2*(b*c-a*d)^2*exp(1/2*A/B)*g^3*(a+b*x)*sqrt(e*(c+d*x)^2/(a+b*x)^2))],

# Integrands of the form (f+g x)^m (A+B Log[e (a+b x)^n/(c+d x)^n])^p when d f-c g=0

# p>0

# p<0
[1/((a*g+b*g*x)^2*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))),x,4,exp(A/(B*n))*(c+d*x)*(e*(a+b*x)^n/(c+d*x)^n)^(1/n)*Ei((-A-B*log(e*(a+b*x)^n/(c+d*x)^n))/(B*n))/(B*(b*c-a*d)*g^2*n*(a+b*x))],

# Integrands of the form (f+g x)^m (A+B Log[e (a+b x)^n/(c+d x)^n])^p

# Integrands of the form (f+g x)^m (A+B Log[e (a+b x)^1/(c+d x)^1])^p

# p>0
[(f+g*x)^4*(A+B*log(e*(a+b*x)/(c+d*x))),x,3,1/5*B*(b*c-a*d)*g*(a^3*d^3*g^3-a^2*b*d^2*g^2*(5*d*f-c*g)+a*b^2*d*g*(10*d^2*f^2-5*c*d*f*g+c^2*g^2)-b^3*(10*d^3*f^3-10*c*d^2*f^2*g+5*c^2*d*f*g^2-c^3*g^3))*x/(b^4*d^4)-1/10*B*(b*c-a*d)*g^2*(a^2*d^2*g^2-a*b*d*g*(5*d*f-c*g)+b^2*(10*d^2*f^2-5*c*d*f*g+c^2*g^2))*x^2/(b^3*d^3)-1/15*B*(b*c-a*d)*g^3*(5*b*d*f-b*c*g-a*d*g)*x^3/(b^2*d^2)-1/20*B*(b*c-a*d)*g^4*x^4/(b*d)-1/5*B*(b*f-a*g)^5*log(a+b*x)/(b^5*g)+1/5*(f+g*x)^5*(A+B*log(e*(a+b*x)/(c+d*x)))/g+1/5*B*(d*f-c*g)^5*log(c+d*x)/(d^5*g)],
[(f+g*x)^3*(A+B*log(e*(a+b*x)/(c+d*x))),x,3,-1/4*B*(b*c-a*d)*g*(a^2*d^2*g^2-a*b*d*g*(4*d*f-c*g)+b^2*(6*d^2*f^2-4*c*d*f*g+c^2*g^2))*x/(b^3*d^3)-1/8*B*(b*c-a*d)*g^2*(4*b*d*f-b*c*g-a*d*g)*x^2/(b^2*d^2)-1/12*B*(b*c-a*d)*g^3*x^3/(b*d)-1/4*B*(b*f-a*g)^4*log(a+b*x)/(b^4*g)+1/4*(f+g*x)^4*(A+B*log(e*(a+b*x)/(c+d*x)))/g+1/4*B*(d*f-c*g)^4*log(c+d*x)/(d^4*g)],
[(f+g*x)^2*(A+B*log(e*(a+b*x)/(c+d*x))),x,3,-1/3*B*(b*c-a*d)*g*(3*b*d*f-b*c*g-a*d*g)*x/(b^2*d^2)-1/6*B*(b*c-a*d)*g^2*x^2/(b*d)-1/3*B*(b*f-a*g)^3*log(a+b*x)/(b^3*g)+1/3*(f+g*x)^3*(A+B*log(e*(a+b*x)/(c+d*x)))/g+1/3*B*(d*f-c*g)^3*log(c+d*x)/(d^3*g)],
[(f+g*x)*(A+B*log(e*(a+b*x)/(c+d*x))),x,3,-1/2*B*(b*c-a*d)*g*x/(b*d)-1/2*B*(b*f-a*g)^2*log(a+b*x)/(b^2*g)+1/2*(f+g*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))/g+1/2*B*(d*f-c*g)^2*log(c+d*x)/(d^2*g)],
[A+B*log(e*(a+b*x)/(c+d*x)),x,3,A*x+B*(a+b*x)*log(e*(a+b*x)/(c+d*x))/b-B*(b*c-a*d)*log(c+d*x)/(b*d)],
[(A+B*log(e*(a+b*x)/(c+d*x)))/(f+g*x),x,7,-B*log(-g*(a+b*x)/(b*f-a*g))*log(f+g*x)/g+(A+B*log(e*(a+b*x)/(c+d*x)))*log(f+g*x)/g+B*log(-g*(c+d*x)/(d*f-c*g))*log(f+g*x)/g-B*polylog(2,b*(f+g*x)/(b*f-a*g))/g+B*polylog(2,d*(f+g*x)/(d*f-c*g))/g],
[(A+B*log(e*(a+b*x)/(c+d*x)))/(f+g*x)^2,x,3,(a+b*x)*(A+B*log(e*(a+b*x)/(c+d*x)))/((b*f-a*g)*(f+g*x))+B*(b*c-a*d)*log((f+g*x)/(c+d*x))/((b*f-a*g)*(d*f-c*g))],
[(A+B*log(e*(a+b*x)/(c+d*x)))/(f+g*x)^3,x,3,-1/2*B*(b*c-a*d)/((b*f-a*g)*(d*f-c*g)*(f+g*x))+1/2*b^2*B*log(a+b*x)/(g*(b*f-a*g)^2)+1/2*(-A-B*log(e*(a+b*x)/(c+d*x)))/(g*(f+g*x)^2)-1/2*B*d^2*log(c+d*x)/(g*(d*f-c*g)^2)+1/2*B*(b*c-a*d)*(2*b*d*f-b*c*g-a*d*g)*log(f+g*x)/((b*f-a*g)^2*(d*f-c*g)^2)],
[(A+B*log(e*(a+b*x)/(c+d*x)))/(f+g*x)^4,x,3,-1/6*B*(b*c-a*d)/((b*f-a*g)*(d*f-c*g)*(f+g*x)^2)-1/3*B*(b*c-a*d)*(2*b*d*f-b*c*g-a*d*g)/((b*f-a*g)^2*(d*f-c*g)^2*(f+g*x))+1/3*b^3*B*log(a+b*x)/(g*(b*f-a*g)^3)+1/3*(-A-B*log(e*(a+b*x)/(c+d*x)))/(g*(f+g*x)^3)-1/3*B*d^3*log(c+d*x)/(g*(d*f-c*g)^3)+1/3*B*(b*c-a*d)*(a^2*d^2*g^2-a*b*d*g*(3*d*f-c*g)+b^2*(3*d^2*f^2-3*c*d*f*g+c^2*g^2))*log(f+g*x)/((b*f-a*g)^3*(d*f-c*g)^3)],
[(A+B*log(e*(a+b*x)/(c+d*x)))/(f+g*x)^5,x,3,-1/12*B*(b*c-a*d)/((b*f-a*g)*(d*f-c*g)*(f+g*x)^3)-1/8*B*(b*c-a*d)*(2*b*d*f-b*c*g-a*d*g)/((b*f-a*g)^2*(d*f-c*g)^2*(f+g*x)^2)-1/4*B*(b*c-a*d)*(a^2*d^2*g^2-a*b*d*g*(3*d*f-c*g)+b^2*(3*d^2*f^2-3*c*d*f*g+c^2*g^2))/((b*f-a*g)^3*(d*f-c*g)^3*(f+g*x))+1/4*b^4*B*log(a+b*x)/(g*(b*f-a*g)^4)+1/4*(-A-B*log(e*(a+b*x)/(c+d*x)))/(g*(f+g*x)^4)-1/4*B*d^4*log(c+d*x)/(g*(d*f-c*g)^4)-1/4*B*(b*c-a*d)*(2*b*d*f-b*c*g-a*d*g)*(2*a*b*d^2*f*g-a^2*d^2*g^2-b^2*(2*d^2*f^2-2*c*d*f*g+c^2*g^2))*log(f+g*x)/((b*f-a*g)^4*(d*f-c*g)^4)],
[(f+g*x)^3*(A+B*log(e*(a+b*x)/(c+d*x)))^2,x,15,1/6*B^2*(b*c-a*d)^3*g^3*x/(b^3*d^3)+1/4*B^2*(b*c-a*d)^2*g^2*(4*b*d*f-3*b*c*g-a*d*g)*x/(b^3*d^3)+1/12*B^2*(b*c-a*d)^2*g^3*(c+d*x)^2/(b^2*d^4)+1/6*B^2*(b*c-a*d)^4*g^3*log((a+b*x)/(c+d*x))/(b^4*d^4)+1/4*B^2*(b*c-a*d)^3*g^2*(4*b*d*f-3*b*c*g-a*d*g)*log((a+b*x)/(c+d*x))/(b^4*d^4)-1/2*B*(b*c-a*d)*g*(a^2*d^2*g^2-2*a*b*d*g*(2*d*f-c*g)+b^2*(6*d^2*f^2-8*c*d*f*g+3*c^2*g^2))*(a+b*x)*(A+B*log(e*(a+b*x)/(c+d*x)))/(b^4*d^3)-1/4*B*(b*c-a*d)*g^2*(4*b*d*f-3*b*c*g-a*d*g)*(c+d*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))/(b^2*d^4)-1/6*B*(b*c-a*d)*g^3*(c+d*x)^3*(A+B*log(e*(a+b*x)/(c+d*x)))/(b*d^4)-1/2*B*(b*c-a*d)*(2*b*d*f-b*c*g-a*d*g)*(2*a*b*d^2*f*g-a^2*d^2*g^2-b^2*(2*d^2*f^2-2*c*d*f*g+c^2*g^2))*log((b*c-a*d)/(b*(c+d*x)))*(A+B*log(e*(a+b*x)/(c+d*x)))/(b^4*d^4)-1/4*(b*f-a*g)^4*(A+B*log(e*(a+b*x)/(c+d*x)))^2/(b^4*g)+1/4*(f+g*x)^4*(A+B*log(e*(a+b*x)/(c+d*x)))^2/g+1/6*B^2*(b*c-a*d)^4*g^3*log(c+d*x)/(b^4*d^4)+1/4*B^2*(b*c-a*d)^3*g^2*(4*b*d*f-3*b*c*g-a*d*g)*log(c+d*x)/(b^4*d^4)+1/2*B^2*(b*c-a*d)^2*g*(a^2*d^2*g^2-2*a*b*d*g*(2*d*f-c*g)+b^2*(6*d^2*f^2-8*c*d*f*g+3*c^2*g^2))*log(c+d*x)/(b^4*d^4)-1/2*B^2*(b*c-a*d)*(2*b*d*f-b*c*g-a*d*g)*(2*a*b*d^2*f*g-a^2*d^2*g^2-b^2*(2*d^2*f^2-2*c*d*f*g+c^2*g^2))*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(b^4*d^4)],
[(f+g*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))^2,x,12,1/3*B^2*(b*c-a*d)^2*g^2*x/(b^2*d^2)+1/3*B^2*(b*c-a*d)^3*g^2*log((a+b*x)/(c+d*x))/(b^3*d^3)-2/3*B*(b*c-a*d)*g*(3*b*d*f-2*b*c*g-a*d*g)*(a+b*x)*(A+B*log(e*(a+b*x)/(c+d*x)))/(b^3*d^2)-1/3*B*(b*c-a*d)*g^2*(c+d*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))/(b*d^3)+2/3*B*(b*c-a*d)*(a^2*d^2*g^2-a*b*d*g*(3*d*f-c*g)+b^2*(3*d^2*f^2-3*c*d*f*g+c^2*g^2))*log((b*c-a*d)/(b*(c+d*x)))*(A+B*log(e*(a+b*x)/(c+d*x)))/(b^3*d^3)-1/3*(b*f-a*g)^3*(A+B*log(e*(a+b*x)/(c+d*x)))^2/(b^3*g)+1/3*(f+g*x)^3*(A+B*log(e*(a+b*x)/(c+d*x)))^2/g+1/3*B^2*(b*c-a*d)^3*g^2*log(c+d*x)/(b^3*d^3)+2/3*B^2*(b*c-a*d)^2*g*(3*b*d*f-2*b*c*g-a*d*g)*log(c+d*x)/(b^3*d^3)+2/3*B^2*(b*c-a*d)*(a^2*d^2*g^2-a*b*d*g*(3*d*f-c*g)+b^2*(3*d^2*f^2-3*c*d*f*g+c^2*g^2))*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(b^3*d^3)],
[(f+g*x)*(A+B*log(e*(a+b*x)/(c+d*x)))^2,x,9,-B*(b*c-a*d)*g*(a+b*x)*(A+B*log(e*(a+b*x)/(c+d*x)))/(b^2*d)+B*(b*c-a*d)*(2*b*d*f-b*c*g-a*d*g)*log((b*c-a*d)/(b*(c+d*x)))*(A+B*log(e*(a+b*x)/(c+d*x)))/(b^2*d^2)-1/2*(b*f-a*g)^2*(A+B*log(e*(a+b*x)/(c+d*x)))^2/(b^2*g)+1/2*(f+g*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))^2/g+B^2*(b*c-a*d)^2*g*log(c+d*x)/(b^2*d^2)+B^2*(b*c-a*d)*(2*b*d*f-b*c*g-a*d*g)*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(b^2*d^2)],
[(A+B*log(e*(a+b*x)/(c+d*x)))^2,x,6,2*B*(b*c-a*d)*log((b*c-a*d)/(b*(c+d*x)))*(A+B*log(e*(a+b*x)/(c+d*x)))/(b*d)+(a+b*x)*(A+B*log(e*(a+b*x)/(c+d*x)))^2/b+2*B^2*(b*c-a*d)*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(b*d)],
[(A+B*log(e*(a+b*x)/(c+d*x)))^2/(f+g*x),x,9,-log((b*c-a*d)/(b*(c+d*x)))*(A+B*log(e*(a+b*x)/(c+d*x)))^2/g+(A+B*log(e*(a+b*x)/(c+d*x)))^2*log(1-(d*f-c*g)*(a+b*x)/((b*f-a*g)*(c+d*x)))/g-2*B*(A+B*log(e*(a+b*x)/(c+d*x)))*polylog(2,d*(a+b*x)/(b*(c+d*x)))/g+2*B*(A+B*log(e*(a+b*x)/(c+d*x)))*polylog(2,(d*f-c*g)*(a+b*x)/((b*f-a*g)*(c+d*x)))/g+2*B^2*polylog(3,d*(a+b*x)/(b*(c+d*x)))/g-2*B^2*polylog(3,(d*f-c*g)*(a+b*x)/((b*f-a*g)*(c+d*x)))/g],
[(A+B*log(e*(a+b*x)/(c+d*x)))^2/(f+g*x)^2,x,4,(a+b*x)*(A+B*log(e*(a+b*x)/(c+d*x)))^2/((b*f-a*g)*(f+g*x))+2*B*(b*c-a*d)*(A+B*log(e*(a+b*x)/(c+d*x)))*log(1-(d*f-c*g)*(a+b*x)/((b*f-a*g)*(c+d*x)))/((b*f-a*g)*(d*f-c*g))+2*B^2*(b*c-a*d)*polylog(2,(d*f-c*g)*(a+b*x)/((b*f-a*g)*(c+d*x)))/((b*f-a*g)*(d*f-c*g))],
[(A+B*log(e*(a+b*x)/(c+d*x)))^2/(f+g*x)^3,x,9,B*(b*c-a*d)*g*(a+b*x)*(A+B*log(e*(a+b*x)/(c+d*x)))/((b*f-a*g)^2*(d*f-c*g)*(f+g*x))+1/2*b^2*(A+B*log(e*(a+b*x)/(c+d*x)))^2/(g*(b*f-a*g)^2)-1/2*(A+B*log(e*(a+b*x)/(c+d*x)))^2/(g*(f+g*x)^2)+B^2*(b*c-a*d)^2*g*log((f+g*x)/(c+d*x))/((b*f-a*g)^2*(d*f-c*g)^2)+B*(b*c-a*d)*(2*b*d*f-b*c*g-a*d*g)*(A+B*log(e*(a+b*x)/(c+d*x)))*log(1-(d*f-c*g)*(a+b*x)/((b*f-a*g)*(c+d*x)))/((b*f-a*g)^2*(d*f-c*g)^2)+B^2*(b*c-a*d)*(2*b*d*f-b*c*g-a*d*g)*polylog(2,(d*f-c*g)*(a+b*x)/((b*f-a*g)*(c+d*x)))/((b*f-a*g)^2*(d*f-c*g)^2)],
[(A+B*log(e*(a+b*x)/(c+d*x)))^2/(f+g*x)^4,x,12,1/3*B^2*(b*c-a*d)^2*g^2*(c+d*x)/((b*f-a*g)^2*(d*f-c*g)^3*(f+g*x))+1/3*B^2*(b*c-a*d)^3*g^2*log((a+b*x)/(c+d*x))/((b*f-a*g)^3*(d*f-c*g)^3)-1/3*B*(b*c-a*d)*g^2*(c+d*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))/((b*f-a*g)*(d*f-c*g)^3*(f+g*x)^2)+2/3*B*(b*c-a*d)*g*(3*b*d*f-b*c*g-2*a*d*g)*(a+b*x)*(A+B*log(e*(a+b*x)/(c+d*x)))/((b*f-a*g)^3*(d*f-c*g)^2*(f+g*x))+1/3*b^3*(A+B*log(e*(a+b*x)/(c+d*x)))^2/(g*(b*f-a*g)^3)-1/3*(A+B*log(e*(a+b*x)/(c+d*x)))^2/(g*(f+g*x)^3)-1/3*B^2*(b*c-a*d)^3*g^2*log((f+g*x)/(c+d*x))/((b*f-a*g)^3*(d*f-c*g)^3)+2/3*B^2*(b*c-a*d)^2*g*(3*b*d*f-b*c*g-2*a*d*g)*log((f+g*x)/(c+d*x))/((b*f-a*g)^3*(d*f-c*g)^3)+2/3*B*(b*c-a*d)*(a^2*d^2*g^2-a*b*d*g*(3*d*f-c*g)+b^2*(3*d^2*f^2-3*c*d*f*g+c^2*g^2))*(A+B*log(e*(a+b*x)/(c+d*x)))*log(1-(d*f-c*g)*(a+b*x)/((b*f-a*g)*(c+d*x)))/((b*f-a*g)^3*(d*f-c*g)^3)+2/3*B^2*(b*c-a*d)*(a^2*d^2*g^2-a*b*d*g*(3*d*f-c*g)+b^2*(3*d^2*f^2-3*c*d*f*g+c^2*g^2))*polylog(2,(d*f-c*g)*(a+b*x)/((b*f-a*g)*(c+d*x)))/((b*f-a*g)^3*(d*f-c*g)^3)],
[(A+B*log(e*(a+b*x)/(c+d*x)))^2/(f+g*x)^5,x,15,-1/12*B^2*(b*c-a*d)^2*g^3*(c+d*x)^2/((b*f-a*g)^2*(d*f-c*g)^4*(f+g*x)^2)-1/6*B^2*(b*c-a*d)^3*g^3*(c+d*x)/((b*f-a*g)^3*(d*f-c*g)^4*(f+g*x))+1/4*B^2*(b*c-a*d)^2*g^2*(4*b*d*f-b*c*g-3*a*d*g)*(c+d*x)/((b*f-a*g)^3*(d*f-c*g)^4*(f+g*x))-1/6*B^2*(b*c-a*d)^4*g^3*log((a+b*x)/(c+d*x))/((b*f-a*g)^4*(d*f-c*g)^4)+1/4*B^2*(b*c-a*d)^3*g^2*(4*b*d*f-b*c*g-3*a*d*g)*log((a+b*x)/(c+d*x))/((b*f-a*g)^4*(d*f-c*g)^4)+1/6*B*(b*c-a*d)*g^3*(c+d*x)^3*(A+B*log(e*(a+b*x)/(c+d*x)))/((b*f-a*g)*(d*f-c*g)^4*(f+g*x)^3)-1/4*B*(b*c-a*d)*g^2*(4*b*d*f-b*c*g-3*a*d*g)*(c+d*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))/((b*f-a*g)^2*(d*f-c*g)^4*(f+g*x)^2)+1/2*B*(b*c-a*d)*g*(3*a^2*d^2*g^2-2*a*b*d*g*(4*d*f-c*g)+b^2*(6*d^2*f^2-4*c*d*f*g+c^2*g^2))*(a+b*x)*(A+B*log(e*(a+b*x)/(c+d*x)))/((b*f-a*g)^4*(d*f-c*g)^3*(f+g*x))+1/4*b^4*(A+B*log(e*(a+b*x)/(c+d*x)))^2/(g*(b*f-a*g)^4)-1/4*(A+B*log(e*(a+b*x)/(c+d*x)))^2/(g*(f+g*x)^4)+1/6*B^2*(b*c-a*d)^4*g^3*log((f+g*x)/(c+d*x))/((b*f-a*g)^4*(d*f-c*g)^4)-1/4*B^2*(b*c-a*d)^3*g^2*(4*b*d*f-b*c*g-3*a*d*g)*log((f+g*x)/(c+d*x))/((b*f-a*g)^4*(d*f-c*g)^4)+1/2*B^2*(b*c-a*d)^2*g*(3*a^2*d^2*g^2-2*a*b*d*g*(4*d*f-c*g)+b^2*(6*d^2*f^2-4*c*d*f*g+c^2*g^2))*log((f+g*x)/(c+d*x))/((b*f-a*g)^4*(d*f-c*g)^4)-1/2*B*(b*c-a*d)*(2*b*d*f-b*c*g-a*d*g)*(2*a*b*d^2*f*g-a^2*d^2*g^2-b^2*(2*d^2*f^2-2*c*d*f*g+c^2*g^2))*(A+B*log(e*(a+b*x)/(c+d*x)))*log(1-(d*f-c*g)*(a+b*x)/((b*f-a*g)*(c+d*x)))/((b*f-a*g)^4*(d*f-c*g)^4)-1/2*B^2*(b*c-a*d)*(2*b*d*f-b*c*g-a*d*g)*(2*a*b*d^2*f*g-a^2*d^2*g^2-b^2*(2*d^2*f^2-2*c*d*f*g+c^2*g^2))*polylog(2,(d*f-c*g)*(a+b*x)/((b*f-a*g)*(c+d*x)))/((b*f-a*g)^4*(d*f-c*g)^4)],
[log((1+x)/(-1+x))/x^2,x,3,2*log(-x/(1-x))-(1+x)*log((-1-x)/(1-x))/x],

# p<0
[(f+g*x)^2/(A+B*log(e*(a+b*x)/(c+d*x))),x,0,Unintegrable((f+g*x)^2/(A+B*log(e*(a+b*x)/(c+d*x))),x)],
[(f+g*x)/(A+B*log(e*(a+b*x)/(c+d*x))),x,0,Unintegrable((f+g*x)/(A+B*log(e*(a+b*x)/(c+d*x))),x)],
[1/(A+B*log(e*(a+b*x)/(c+d*x))),x,0,Unintegrable(1/(A+B*log(e*(a+b*x)/(c+d*x))),x)],
[1/((f+g*x)*(A+B*log(e*(a+b*x)/(c+d*x)))),x,0,Unintegrable(1/((f+g*x)*(A+B*log(e*(a+b*x)/(c+d*x)))),x)],
[1/((f+g*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))),x,0,Unintegrable(1/((f+g*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))),x)],
[1/((f+g*x)^3*(A+B*log(e*(a+b*x)/(c+d*x)))),x,0,Unintegrable(1/((f+g*x)^3*(A+B*log(e*(a+b*x)/(c+d*x)))),x)],
[(f+g*x)^2/(A+B*log(e*(a+b*x)/(c+d*x)))^2,x,0,Unintegrable((f+g*x)^2/(A+B*log(e*(a+b*x)/(c+d*x)))^2,x)],
[(f+g*x)/(A+B*log(e*(a+b*x)/(c+d*x)))^2,x,0,Unintegrable((f+g*x)/(A+B*log(e*(a+b*x)/(c+d*x)))^2,x)],
[1/(A+B*log(e*(a+b*x)/(c+d*x)))^2,x,0,Unintegrable(1/(A+B*log(e*(a+b*x)/(c+d*x)))^2,x)],
[1/((f+g*x)*(A+B*log(e*(a+b*x)/(c+d*x)))^2),x,0,Unintegrable(1/((f+g*x)*(A+B*log(e*(a+b*x)/(c+d*x)))^2),x)],
[1/((f+g*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))^2),x,0,Unintegrable(1/((f+g*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))^2),x)],
[1/((f+g*x)^3*(A+B*log(e*(a+b*x)/(c+d*x)))^2),x,0,Unintegrable(1/((f+g*x)^3*(A+B*log(e*(a+b*x)/(c+d*x)))^2),x)],

# Integrands of the form (f+g x)^m (A+B Log[e (a+b x)^2/(c+d x)^2])^p

# p>0
[(f+g*x)^4*(A+B*log(e*(a+b*x)^2/(c+d*x)^2)),x,3,2/5*B*(b*c-a*d)*g*(a^3*d^3*g^3-a^2*b*d^2*g^2*(5*d*f-c*g)+a*b^2*d*g*(10*d^2*f^2-5*c*d*f*g+c^2*g^2)-b^3*(10*d^3*f^3-10*c*d^2*f^2*g+5*c^2*d*f*g^2-c^3*g^3))*x/(b^4*d^4)-1/5*B*(b*c-a*d)*g^2*(a^2*d^2*g^2-a*b*d*g*(5*d*f-c*g)+b^2*(10*d^2*f^2-5*c*d*f*g+c^2*g^2))*x^2/(b^3*d^3)-2/15*B*(b*c-a*d)*g^3*(5*b*d*f-b*c*g-a*d*g)*x^3/(b^2*d^2)-1/10*B*(b*c-a*d)*g^4*x^4/(b*d)-2/5*B*(b*f-a*g)^5*log(a+b*x)/(b^5*g)+1/5*(f+g*x)^5*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))/g+2/5*B*(d*f-c*g)^5*log(c+d*x)/(d^5*g)],
[(f+g*x)^3*(A+B*log(e*(a+b*x)^2/(c+d*x)^2)),x,3,-1/2*B*(b*c-a*d)*g*(a^2*d^2*g^2-a*b*d*g*(4*d*f-c*g)+b^2*(6*d^2*f^2-4*c*d*f*g+c^2*g^2))*x/(b^3*d^3)-1/4*B*(b*c-a*d)*g^2*(4*b*d*f-b*c*g-a*d*g)*x^2/(b^2*d^2)-1/6*B*(b*c-a*d)*g^3*x^3/(b*d)-1/2*B*(b*f-a*g)^4*log(a+b*x)/(b^4*g)+1/4*(f+g*x)^4*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))/g+1/2*B*(d*f-c*g)^4*log(c+d*x)/(d^4*g)],
[(f+g*x)^2*(A+B*log(e*(a+b*x)^2/(c+d*x)^2)),x,3,-2/3*B*(b*c-a*d)*g*(3*b*d*f-b*c*g-a*d*g)*x/(b^2*d^2)-1/3*B*(b*c-a*d)*g^2*x^2/(b*d)-2/3*B*(b*f-a*g)^3*log(a+b*x)/(b^3*g)+1/3*(f+g*x)^3*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))/g+2/3*B*(d*f-c*g)^3*log(c+d*x)/(d^3*g)],
[(f+g*x)*(A+B*log(e*(a+b*x)^2/(c+d*x)^2)),x,3,-B*(b*c-a*d)*g*x/(b*d)-B*(b*f-a*g)^2*log(a+b*x)/(b^2*g)+1/2*(f+g*x)^2*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))/g+B*(d*f-c*g)^2*log(c+d*x)/(d^2*g)],
[A+B*log(e*(a+b*x)^2/(c+d*x)^2),x,3,A*x+B*(a+b*x)*log(e*(a+b*x)^2/(c+d*x)^2)/b-2*B*(b*c-a*d)*log(c+d*x)/(b*d)],
[(A+B*log(e*(a+b*x)^2/(c+d*x)^2))/(f+g*x),x,7,-2*B*log(-g*(a+b*x)/(b*f-a*g))*log(f+g*x)/g+(A+B*log(e*(a+b*x)^2/(c+d*x)^2))*log(f+g*x)/g+2*B*log(-g*(c+d*x)/(d*f-c*g))*log(f+g*x)/g-2*B*polylog(2,b*(f+g*x)/(b*f-a*g))/g+2*B*polylog(2,d*(f+g*x)/(d*f-c*g))/g],
[(A+B*log(e*(a+b*x)^2/(c+d*x)^2))/(f+g*x)^2,x,3,(a+b*x)*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))/((b*f-a*g)*(f+g*x))+2*B*(b*c-a*d)*log((f+g*x)/(c+d*x))/((b*f-a*g)*(d*f-c*g))],
[(A+B*log(e*(a+b*x)^2/(c+d*x)^2))/(f+g*x)^3,x,3,-B*(b*c-a*d)/((b*f-a*g)*(d*f-c*g)*(f+g*x))+b^2*B*log(a+b*x)/(g*(b*f-a*g)^2)+1/2*(-A-B*log(e*(a+b*x)^2/(c+d*x)^2))/(g*(f+g*x)^2)-B*d^2*log(c+d*x)/(g*(d*f-c*g)^2)+B*(b*c-a*d)*(2*b*d*f-b*c*g-a*d*g)*log(f+g*x)/((b*f-a*g)^2*(d*f-c*g)^2)],
[(A+B*log(e*(a+b*x)^2/(c+d*x)^2))/(f+g*x)^4,x,3,-1/3*B*(b*c-a*d)/((b*f-a*g)*(d*f-c*g)*(f+g*x)^2)-2/3*B*(b*c-a*d)*(2*b*d*f-b*c*g-a*d*g)/((b*f-a*g)^2*(d*f-c*g)^2*(f+g*x))+2/3*b^3*B*log(a+b*x)/(g*(b*f-a*g)^3)+1/3*(-A-B*log(e*(a+b*x)^2/(c+d*x)^2))/(g*(f+g*x)^3)-2/3*B*d^3*log(c+d*x)/(g*(d*f-c*g)^3)+2/3*B*(b*c-a*d)*(a^2*d^2*g^2-a*b*d*g*(3*d*f-c*g)+b^2*(3*d^2*f^2-3*c*d*f*g+c^2*g^2))*log(f+g*x)/((b*f-a*g)^3*(d*f-c*g)^3)],
[(A+B*log(e*(a+b*x)^2/(c+d*x)^2))/(f+g*x)^5,x,3,-1/6*B*(b*c-a*d)/((b*f-a*g)*(d*f-c*g)*(f+g*x)^3)-1/4*B*(b*c-a*d)*(2*b*d*f-b*c*g-a*d*g)/((b*f-a*g)^2*(d*f-c*g)^2*(f+g*x)^2)-1/2*B*(b*c-a*d)*(a^2*d^2*g^2-a*b*d*g*(3*d*f-c*g)+b^2*(3*d^2*f^2-3*c*d*f*g+c^2*g^2))/((b*f-a*g)^3*(d*f-c*g)^3*(f+g*x))+1/2*b^4*B*log(a+b*x)/(g*(b*f-a*g)^4)+1/4*(-A-B*log(e*(a+b*x)^2/(c+d*x)^2))/(g*(f+g*x)^4)-1/2*B*d^4*log(c+d*x)/(g*(d*f-c*g)^4)-1/2*B*(b*c-a*d)*(2*b*d*f-b*c*g-a*d*g)*(2*a*b*d^2*f*g-a^2*d^2*g^2-b^2*(2*d^2*f^2-2*c*d*f*g+c^2*g^2))*log(f+g*x)/((b*f-a*g)^4*(d*f-c*g)^4)],
[(f+g*x)^3*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))^2,x,15,2/3*B^2*(b*c-a*d)^3*g^3*x/(b^3*d^3)+B^2*(b*c-a*d)^2*g^2*(4*b*d*f-3*b*c*g-a*d*g)*x/(b^3*d^3)+1/3*B^2*(b*c-a*d)^2*g^3*(c+d*x)^2/(b^2*d^4)-B*(b*c-a*d)*g*(a^2*d^2*g^2-2*a*b*d*g*(2*d*f-c*g)+b^2*(6*d^2*f^2-8*c*d*f*g+3*c^2*g^2))*(a+b*x)*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))/(b^4*d^3)-1/2*B*(b*c-a*d)*g^2*(4*b*d*f-3*b*c*g-a*d*g)*(c+d*x)^2*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))/(b^2*d^4)-1/3*B*(b*c-a*d)*g^3*(c+d*x)^3*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))/(b*d^4)-1/4*(b*f-a*g)^4*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))^2/(b^4*g)+1/4*(f+g*x)^4*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))^2/g-B*(b*c-a*d)*(2*b*d*f-b*c*g-a*d*g)*(2*a*b*d^2*f*g-a^2*d^2*g^2-b^2*(2*d^2*f^2-2*c*d*f*g+c^2*g^2))*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))*log((b*c-a*d)/(b*(c+d*x)))/(b^4*d^4)+2/3*B^2*(b*c-a*d)^4*g^3*log((a+b*x)/(c+d*x))/(b^4*d^4)+B^2*(b*c-a*d)^3*g^2*(4*b*d*f-3*b*c*g-a*d*g)*log((a+b*x)/(c+d*x))/(b^4*d^4)+2/3*B^2*(b*c-a*d)^4*g^3*log(c+d*x)/(b^4*d^4)+B^2*(b*c-a*d)^3*g^2*(4*b*d*f-3*b*c*g-a*d*g)*log(c+d*x)/(b^4*d^4)+2*B^2*(b*c-a*d)^2*g*(a^2*d^2*g^2-2*a*b*d*g*(2*d*f-c*g)+b^2*(6*d^2*f^2-8*c*d*f*g+3*c^2*g^2))*log(c+d*x)/(b^4*d^4)-2*B^2*(b*c-a*d)*(2*b*d*f-b*c*g-a*d*g)*(2*a*b*d^2*f*g-a^2*d^2*g^2-b^2*(2*d^2*f^2-2*c*d*f*g+c^2*g^2))*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(b^4*d^4)],
[(f+g*x)^2*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))^2,x,12,4/3*B^2*(b*c-a*d)^2*g^2*x/(b^2*d^2)-4/3*B*(b*c-a*d)*g*(3*b*d*f-2*b*c*g-a*d*g)*(a+b*x)*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))/(b^3*d^2)-2/3*B*(b*c-a*d)*g^2*(c+d*x)^2*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))/(b*d^3)-1/3*(b*f-a*g)^3*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))^2/(b^3*g)+1/3*(f+g*x)^3*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))^2/g+4/3*B*(b*c-a*d)*(a^2*d^2*g^2-a*b*d*g*(3*d*f-c*g)+b^2*(3*d^2*f^2-3*c*d*f*g+c^2*g^2))*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))*log((b*c-a*d)/(b*(c+d*x)))/(b^3*d^3)+4/3*B^2*(b*c-a*d)^3*g^2*log((a+b*x)/(c+d*x))/(b^3*d^3)+4/3*B^2*(b*c-a*d)^3*g^2*log(c+d*x)/(b^3*d^3)+8/3*B^2*(b*c-a*d)^2*g*(3*b*d*f-2*b*c*g-a*d*g)*log(c+d*x)/(b^3*d^3)+8/3*B^2*(b*c-a*d)*(a^2*d^2*g^2-a*b*d*g*(3*d*f-c*g)+b^2*(3*d^2*f^2-3*c*d*f*g+c^2*g^2))*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(b^3*d^3)],
[(f+g*x)*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))^2,x,9,-2*B*(b*c-a*d)*g*(a+b*x)*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))/(b^2*d)-1/2*(b*f-a*g)^2*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))^2/(b^2*g)+1/2*(f+g*x)^2*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))^2/g+2*B*(b*c-a*d)*(2*b*d*f-b*c*g-a*d*g)*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))*log((b*c-a*d)/(b*(c+d*x)))/(b^2*d^2)+4*B^2*(b*c-a*d)^2*g*log(c+d*x)/(b^2*d^2)+4*B^2*(b*c-a*d)*(2*b*d*f-b*c*g-a*d*g)*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(b^2*d^2)],
[(A+B*log(e*(a+b*x)^2/(c+d*x)^2))^2,x,6,(a+b*x)*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))^2/b+4*B*(b*c-a*d)*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))*log((b*c-a*d)/(b*(c+d*x)))/(b*d)+8*B^2*(b*c-a*d)*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(b*d)],
[(A+B*log(e*(a+b*x)^2/(c+d*x)^2))^2/(f+g*x),x,9,-(A+B*log(e*(a+b*x)^2/(c+d*x)^2))^2*log((b*c-a*d)/(b*(c+d*x)))/g+(A+B*log(e*(a+b*x)^2/(c+d*x)^2))^2*log(1-(d*f-c*g)*(a+b*x)/((b*f-a*g)*(c+d*x)))/g-4*B*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))*polylog(2,d*(a+b*x)/(b*(c+d*x)))/g+4*B*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))*polylog(2,(d*f-c*g)*(a+b*x)/((b*f-a*g)*(c+d*x)))/g+8*B^2*polylog(3,d*(a+b*x)/(b*(c+d*x)))/g-8*B^2*polylog(3,(d*f-c*g)*(a+b*x)/((b*f-a*g)*(c+d*x)))/g],
[(A+B*log(e*(a+b*x)^2/(c+d*x)^2))^2/(f+g*x)^2,x,4,(a+b*x)*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))^2/((b*f-a*g)*(f+g*x))+4*B*(b*c-a*d)*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))*log(1-(d*f-c*g)*(a+b*x)/((b*f-a*g)*(c+d*x)))/((b*f-a*g)*(d*f-c*g))+8*B^2*(b*c-a*d)*polylog(2,(d*f-c*g)*(a+b*x)/((b*f-a*g)*(c+d*x)))/((b*f-a*g)*(d*f-c*g))],
[(A+B*log(e*(a+b*x)^2/(c+d*x)^2))^2/(f+g*x)^3,x,9,2*B*(b*c-a*d)*g*(a+b*x)*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))/((b*f-a*g)^2*(d*f-c*g)*(f+g*x))+1/2*b^2*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))^2/(g*(b*f-a*g)^2)-1/2*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))^2/(g*(f+g*x)^2)+4*B^2*(b*c-a*d)^2*g*log((f+g*x)/(c+d*x))/((b*f-a*g)^2*(d*f-c*g)^2)+2*B*(b*c-a*d)*(2*b*d*f-b*c*g-a*d*g)*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))*log(1-(d*f-c*g)*(a+b*x)/((b*f-a*g)*(c+d*x)))/((b*f-a*g)^2*(d*f-c*g)^2)+4*B^2*(b*c-a*d)*(2*b*d*f-b*c*g-a*d*g)*polylog(2,(d*f-c*g)*(a+b*x)/((b*f-a*g)*(c+d*x)))/((b*f-a*g)^2*(d*f-c*g)^2)],
[(A+B*log(e*(a+b*x)^2/(c+d*x)^2))^2/(f+g*x)^4,x,12,4/3*B^2*(b*c-a*d)^2*g^2*(c+d*x)/((b*f-a*g)^2*(d*f-c*g)^3*(f+g*x))-2/3*B*(b*c-a*d)*g^2*(c+d*x)^2*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))/((b*f-a*g)*(d*f-c*g)^3*(f+g*x)^2)+4/3*B*(b*c-a*d)*g*(3*b*d*f-b*c*g-2*a*d*g)*(a+b*x)*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))/((b*f-a*g)^3*(d*f-c*g)^2*(f+g*x))+1/3*b^3*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))^2/(g*(b*f-a*g)^3)-1/3*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))^2/(g*(f+g*x)^3)+4/3*B^2*(b*c-a*d)^3*g^2*log((a+b*x)/(c+d*x))/((b*f-a*g)^3*(d*f-c*g)^3)-4/3*B^2*(b*c-a*d)^3*g^2*log((f+g*x)/(c+d*x))/((b*f-a*g)^3*(d*f-c*g)^3)+8/3*B^2*(b*c-a*d)^2*g*(3*b*d*f-b*c*g-2*a*d*g)*log((f+g*x)/(c+d*x))/((b*f-a*g)^3*(d*f-c*g)^3)+4/3*B*(b*c-a*d)*(a^2*d^2*g^2-a*b*d*g*(3*d*f-c*g)+b^2*(3*d^2*f^2-3*c*d*f*g+c^2*g^2))*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))*log(1-(d*f-c*g)*(a+b*x)/((b*f-a*g)*(c+d*x)))/((b*f-a*g)^3*(d*f-c*g)^3)+8/3*B^2*(b*c-a*d)*(a^2*d^2*g^2-a*b*d*g*(3*d*f-c*g)+b^2*(3*d^2*f^2-3*c*d*f*g+c^2*g^2))*polylog(2,(d*f-c*g)*(a+b*x)/((b*f-a*g)*(c+d*x)))/((b*f-a*g)^3*(d*f-c*g)^3)],
[(A+B*log(e*(a+b*x)^2/(c+d*x)^2))^2/(f+g*x)^5,x,15,-1/3*B^2*(b*c-a*d)^2*g^3*(c+d*x)^2/((b*f-a*g)^2*(d*f-c*g)^4*(f+g*x)^2)-2/3*B^2*(b*c-a*d)^3*g^3*(c+d*x)/((b*f-a*g)^3*(d*f-c*g)^4*(f+g*x))+B^2*(b*c-a*d)^2*g^2*(4*b*d*f-b*c*g-3*a*d*g)*(c+d*x)/((b*f-a*g)^3*(d*f-c*g)^4*(f+g*x))+1/3*B*(b*c-a*d)*g^3*(c+d*x)^3*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))/((b*f-a*g)*(d*f-c*g)^4*(f+g*x)^3)-1/2*B*(b*c-a*d)*g^2*(4*b*d*f-b*c*g-3*a*d*g)*(c+d*x)^2*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))/((b*f-a*g)^2*(d*f-c*g)^4*(f+g*x)^2)+B*(b*c-a*d)*g*(3*a^2*d^2*g^2-2*a*b*d*g*(4*d*f-c*g)+b^2*(6*d^2*f^2-4*c*d*f*g+c^2*g^2))*(a+b*x)*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))/((b*f-a*g)^4*(d*f-c*g)^3*(f+g*x))+1/4*b^4*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))^2/(g*(b*f-a*g)^4)-1/4*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))^2/(g*(f+g*x)^4)-2/3*B^2*(b*c-a*d)^4*g^3*log((a+b*x)/(c+d*x))/((b*f-a*g)^4*(d*f-c*g)^4)+B^2*(b*c-a*d)^3*g^2*(4*b*d*f-b*c*g-3*a*d*g)*log((a+b*x)/(c+d*x))/((b*f-a*g)^4*(d*f-c*g)^4)+2/3*B^2*(b*c-a*d)^4*g^3*log((f+g*x)/(c+d*x))/((b*f-a*g)^4*(d*f-c*g)^4)-B^2*(b*c-a*d)^3*g^2*(4*b*d*f-b*c*g-3*a*d*g)*log((f+g*x)/(c+d*x))/((b*f-a*g)^4*(d*f-c*g)^4)+2*B^2*(b*c-a*d)^2*g*(3*a^2*d^2*g^2-2*a*b*d*g*(4*d*f-c*g)+b^2*(6*d^2*f^2-4*c*d*f*g+c^2*g^2))*log((f+g*x)/(c+d*x))/((b*f-a*g)^4*(d*f-c*g)^4)-B*(b*c-a*d)*(2*b*d*f-b*c*g-a*d*g)*(2*a*b*d^2*f*g-a^2*d^2*g^2-b^2*(2*d^2*f^2-2*c*d*f*g+c^2*g^2))*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))*log(1-(d*f-c*g)*(a+b*x)/((b*f-a*g)*(c+d*x)))/((b*f-a*g)^4*(d*f-c*g)^4)-2*B^2*(b*c-a*d)*(2*b*d*f-b*c*g-a*d*g)*(2*a*b*d^2*f*g-a^2*d^2*g^2-b^2*(2*d^2*f^2-2*c*d*f*g+c^2*g^2))*polylog(2,(d*f-c*g)*(a+b*x)/((b*f-a*g)*(c+d*x)))/((b*f-a*g)^4*(d*f-c*g)^4)],

# p<0
[(f+g*x)^2/(A+B*log(e*(a+b*x)^2/(c+d*x)^2)),x,0,Unintegrable((f+g*x)^2/(A+B*log(e*(a+b*x)^2/(c+d*x)^2)),x)],
[(f+g*x)/(A+B*log(e*(a+b*x)^2/(c+d*x)^2)),x,0,Unintegrable((f+g*x)/(A+B*log(e*(a+b*x)^2/(c+d*x)^2)),x)],
[1/(A+B*log(e*(a+b*x)^2/(c+d*x)^2)),x,0,Unintegrable(1/(A+B*log(e*(a+b*x)^2/(c+d*x)^2)),x)],
[1/((f+g*x)*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))),x,0,Unintegrable(1/((f+g*x)*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))),x)],
[1/((f+g*x)^2*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))),x,0,Unintegrable(1/((f+g*x)^2*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))),x)],
[1/((f+g*x)^3*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))),x,0,Unintegrable(1/((f+g*x)^3*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))),x)],
[(f+g*x)^2/(A+B*log(e*(a+b*x)^2/(c+d*x)^2))^2,x,0,Unintegrable((f+g*x)^2/(A+B*log(e*(a+b*x)^2/(c+d*x)^2))^2,x)],
[(f+g*x)/(A+B*log(e*(a+b*x)^2/(c+d*x)^2))^2,x,0,Unintegrable((f+g*x)/(A+B*log(e*(a+b*x)^2/(c+d*x)^2))^2,x)],
[1/(A+B*log(e*(a+b*x)^2/(c+d*x)^2))^2,x,0,Unintegrable(1/(A+B*log(e*(a+b*x)^2/(c+d*x)^2))^2,x)],
[1/((f+g*x)*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))^2),x,0,Unintegrable(1/((f+g*x)*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))^2),x)],
[1/((f+g*x)^2*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))^2),x,0,Unintegrable(1/((f+g*x)^2*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))^2),x)],
[1/((f+g*x)^3*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))^2),x,0,Unintegrable(1/((f+g*x)^3*(A+B*log(e*(a+b*x)^2/(c+d*x)^2))^2),x)],

# Integrands of the form (f+g x)^m (A+B Log[e (a+b x)^n/(c+d x)^n])^p

# p>0
[(g+h*x)^4*(A+B*log(e*(a+b*x)^n/(c+d*x)^n)),x,3,1/5*B*(b*c-a*d)*h*(a^3*d^3*h^3-a^2*b*d^2*h^2*(5*d*g-c*h)+a*b^2*d*h*(10*d^2*g^2-5*c*d*g*h+c^2*h^2)-b^3*(10*d^3*g^3-10*c*d^2*g^2*h+5*c^2*d*g*h^2-c^3*h^3))*n*x/(b^4*d^4)-1/10*B*(b*c-a*d)*h^2*(a^2*d^2*h^2-a*b*d*h*(5*d*g-c*h)+b^2*(10*d^2*g^2-5*c*d*g*h+c^2*h^2))*n*x^2/(b^3*d^3)-1/15*B*(b*c-a*d)*h^3*(5*b*d*g-b*c*h-a*d*h)*n*x^3/(b^2*d^2)-1/20*B*(b*c-a*d)*h^4*n*x^4/(b*d)-1/5*B*(b*g-a*h)^5*n*log(a+b*x)/(b^5*h)+1/5*B*(d*g-c*h)^5*n*log(c+d*x)/(d^5*h)+1/5*(g+h*x)^5*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))/h],
[(g+h*x)^3*(A+B*log(e*(a+b*x)^n/(c+d*x)^n)),x,3,-1/4*B*(b*c-a*d)*h*(a^2*d^2*h^2-a*b*d*h*(4*d*g-c*h)+b^2*(6*d^2*g^2-4*c*d*g*h+c^2*h^2))*n*x/(b^3*d^3)-1/8*B*(b*c-a*d)*h^2*(4*b*d*g-b*c*h-a*d*h)*n*x^2/(b^2*d^2)-1/12*B*(b*c-a*d)*h^3*n*x^3/(b*d)-1/4*B*(b*g-a*h)^4*n*log(a+b*x)/(b^4*h)+1/4*B*(d*g-c*h)^4*n*log(c+d*x)/(d^4*h)+1/4*(g+h*x)^4*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))/h],
[(g+h*x)^2*(A+B*log(e*(a+b*x)^n/(c+d*x)^n)),x,3,-1/3*B*(b*c-a*d)*h*(3*b*d*g-b*c*h-a*d*h)*n*x/(b^2*d^2)-1/6*B*(b*c-a*d)*h^2*n*x^2/(b*d)-1/3*B*(b*g-a*h)^3*n*log(a+b*x)/(b^3*h)+1/3*B*(d*g-c*h)^3*n*log(c+d*x)/(d^3*h)+1/3*(g+h*x)^3*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))/h],
[(g+h*x)*(A+B*log(e*(a+b*x)^n/(c+d*x)^n)),x,3,-1/2*B*(b*c-a*d)*h*n*x/(b*d)-1/2*B*(b*g-a*h)^2*n*log(a+b*x)/(b^2*h)+1/2*B*(d*g-c*h)^2*n*log(c+d*x)/(d^2*h)+1/2*(g+h*x)^2*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))/h],
[A+B*log(e*(a+b*x)^n/(c+d*x)^n),x,3,A*x-B*(b*c-a*d)*n*log(c+d*x)/(b*d)+B*(a+b*x)*log(e*(a+b*x)^n/(c+d*x)^n)/b],
[(A+B*log(e*(a+b*x)^n/(c+d*x)^n))/(g+h*x),x,7,-B*n*log(-h*(a+b*x)/(b*g-a*h))*log(g+h*x)/h+B*n*log(-h*(c+d*x)/(d*g-c*h))*log(g+h*x)/h+(A+B*log(e*(a+b*x)^n/(c+d*x)^n))*log(g+h*x)/h-B*n*polylog(2,b*(g+h*x)/(b*g-a*h))/h+B*n*polylog(2,d*(g+h*x)/(d*g-c*h))/h],
[(A+B*log(e*(a+b*x)^n/(c+d*x)^n))/(g+h*x)^2,x,3,b*B*n*log(a+b*x)/(h*(b*g-a*h))-B*d*n*log(c+d*x)/(h*(d*g-c*h))+(-A-B*log(e*(a+b*x)^n/(c+d*x)^n))/(h*(g+h*x))+B*(b*c-a*d)*n*log(g+h*x)/((b*g-a*h)*(d*g-c*h))],
[(A+B*log(e*(a+b*x)^n/(c+d*x)^n))/(g+h*x)^3,x,3,-1/2*B*(b*c-a*d)*n/((b*g-a*h)*(d*g-c*h)*(g+h*x))+1/2*b^2*B*n*log(a+b*x)/(h*(b*g-a*h)^2)-1/2*B*d^2*n*log(c+d*x)/(h*(d*g-c*h)^2)+1/2*(-A-B*log(e*(a+b*x)^n/(c+d*x)^n))/(h*(g+h*x)^2)+1/2*B*(b*c-a*d)*(2*b*d*g-b*c*h-a*d*h)*n*log(g+h*x)/((b*g-a*h)^2*(d*g-c*h)^2)],
[(A+B*log(e*(a+b*x)^n/(c+d*x)^n))/(g+h*x)^4,x,3,-1/6*B*(b*c-a*d)*n/((b*g-a*h)*(d*g-c*h)*(g+h*x)^2)-1/3*B*(b*c-a*d)*(2*b*d*g-b*c*h-a*d*h)*n/((b*g-a*h)^2*(d*g-c*h)^2*(g+h*x))+1/3*b^3*B*n*log(a+b*x)/(h*(b*g-a*h)^3)-1/3*B*d^3*n*log(c+d*x)/(h*(d*g-c*h)^3)+1/3*(-A-B*log(e*(a+b*x)^n/(c+d*x)^n))/(h*(g+h*x)^3)+1/3*B*(b*c-a*d)*(a^2*d^2*h^2-a*b*d*h*(3*d*g-c*h)+b^2*(3*d^2*g^2-3*c*d*g*h+c^2*h^2))*n*log(g+h*x)/((b*g-a*h)^3*(d*g-c*h)^3)],
[(A+B*log(e*(a+b*x)^n/(c+d*x)^n))/(g+h*x)^5,x,3,-1/12*B*(b*c-a*d)*n/((b*g-a*h)*(d*g-c*h)*(g+h*x)^3)-1/8*B*(b*c-a*d)*(2*b*d*g-b*c*h-a*d*h)*n/((b*g-a*h)^2*(d*g-c*h)^2*(g+h*x)^2)-1/4*B*(b*c-a*d)*(a^2*d^2*h^2-a*b*d*h*(3*d*g-c*h)+b^2*(3*d^2*g^2-3*c*d*g*h+c^2*h^2))*n/((b*g-a*h)^3*(d*g-c*h)^3*(g+h*x))+1/4*b^4*B*n*log(a+b*x)/(h*(b*g-a*h)^4)-1/4*B*d^4*n*log(c+d*x)/(h*(d*g-c*h)^4)+1/4*(-A-B*log(e*(a+b*x)^n/(c+d*x)^n))/(h*(g+h*x)^4)-1/4*B*(b*c-a*d)*(2*b*d*g-b*c*h-a*d*h)*(2*a*b*d^2*g*h-a^2*d^2*h^2-b^2*(2*d^2*g^2-2*c*d*g*h+c^2*h^2))*n*log(g+h*x)/((b*g-a*h)^4*(d*g-c*h)^4)],
[(g+h*x)^2*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^2,x,13,1/3*B^2*(b*c-a*d)^2*h^2*n^2*x/(b^2*d^2)+1/3*B^2*(b*c-a*d)^3*h^2*n^2*log((a+b*x)/(c+d*x))/(b^3*d^3)+1/3*B^2*(b*c-a*d)^3*h^2*n^2*log(c+d*x)/(b^3*d^3)+2/3*B^2*(b*c-a*d)^2*h*(3*b*d*g-2*b*c*h-a*d*h)*n^2*log(c+d*x)/(b^3*d^3)-2/3*B*(b*c-a*d)*h*(3*b*d*g-2*b*c*h-a*d*h)*n*(a+b*x)*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))/(b^3*d^2)-1/3*B*(b*c-a*d)*h^2*n*(c+d*x)^2*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))/(b*d^3)+2/3*B*(b*c-a*d)*(a^2*d^2*h^2-a*b*d*h*(3*d*g-c*h)+b^2*(3*d^2*g^2-3*c*d*g*h+c^2*h^2))*n*log((b*c-a*d)/(b*(c+d*x)))*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))/(b^3*d^3)-1/3*(b*g-a*h)^3*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^2/(b^3*h)+1/3*(g+h*x)^3*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^2/h+2/3*B^2*(b*c-a*d)*(a^2*d^2*h^2-a*b*d*h*(3*d*g-c*h)+b^2*(3*d^2*g^2-3*c*d*g*h+c^2*h^2))*n^2*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(b^3*d^3)],
[(g+h*x)*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^2,x,10,B^2*(b*c-a*d)^2*h*n^2*log(c+d*x)/(b^2*d^2)-B*(b*c-a*d)*h*n*(a+b*x)*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))/(b^2*d)+B*(b*c-a*d)*(2*b*d*g-b*c*h-a*d*h)*n*log((b*c-a*d)/(b*(c+d*x)))*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))/(b^2*d^2)-1/2*(b*g-a*h)^2*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^2/(b^2*h)+1/2*(g+h*x)^2*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^2/h+B^2*(b*c-a*d)*(2*b*d*g-b*c*h-a*d*h)*n^2*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(b^2*d^2)],
[(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^2,x,6,2*B*(b*c-a*d)*n*log((b*c-a*d)/(b*(c+d*x)))*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))/(b*d)+(a+b*x)*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^2/b+2*B^2*(b*c-a*d)*n^2*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(b*d)],
[(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^2/(g+h*x),x,10,-log((b*c-a*d)/(b*(c+d*x)))*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^2/h+(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^2*log(1-(d*g-c*h)*(a+b*x)/((b*g-a*h)*(c+d*x)))/h-2*B*n*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))*polylog(2,d*(a+b*x)/(b*(c+d*x)))/h+2*B*n*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))*polylog(2,(d*g-c*h)*(a+b*x)/((b*g-a*h)*(c+d*x)))/h+2*B^2*n^2*polylog(3,d*(a+b*x)/(b*(c+d*x)))/h-2*B^2*n^2*polylog(3,(d*g-c*h)*(a+b*x)/((b*g-a*h)*(c+d*x)))/h],
[(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^2/(g+h*x)^2,x,5,(a+b*x)*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^2/((b*g-a*h)*(g+h*x))+2*B*(b*c-a*d)*n*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))*log(1-(d*g-c*h)*(a+b*x)/((b*g-a*h)*(c+d*x)))/((b*g-a*h)*(d*g-c*h))+2*B^2*(b*c-a*d)*n^2*polylog(2,(d*g-c*h)*(a+b*x)/((b*g-a*h)*(c+d*x)))/((b*g-a*h)*(d*g-c*h))],
[(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^2/(g+h*x)^3,x,10,B*(b*c-a*d)*h*n*(a+b*x)*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))/((b*g-a*h)^2*(d*g-c*h)*(g+h*x))+1/2*b^2*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^2/(h*(b*g-a*h)^2)-1/2*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^2/(h*(g+h*x)^2)+B^2*(b*c-a*d)^2*h*n^2*log((g+h*x)/(c+d*x))/((b*g-a*h)^2*(d*g-c*h)^2)+B*(b*c-a*d)*(2*b*d*g-b*c*h-a*d*h)*n*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))*log(1-(d*g-c*h)*(a+b*x)/((b*g-a*h)*(c+d*x)))/((b*g-a*h)^2*(d*g-c*h)^2)+B^2*(b*c-a*d)*(2*b*d*g-b*c*h-a*d*h)*n^2*polylog(2,(d*g-c*h)*(a+b*x)/((b*g-a*h)*(c+d*x)))/((b*g-a*h)^2*(d*g-c*h)^2)],
[(g+h*x)^2*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^3,x,19,-B^3*(b*c-a*d)^3*h^2*n^3*log(c+d*x)/(b^3*d^3)+B^2*(b*c-a*d)^2*h^2*n^2*(a+b*x)*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))/(b^3*d^2)-2*B^2*(b*c-a*d)^2*h*(3*b*d*g-2*b*c*h-a*d*h)*n^2*log((b*c-a*d)/(b*(c+d*x)))*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))/(b^3*d^3)-B*(b*c-a*d)*h*(3*b*d*g-2*b*c*h-a*d*h)*n*(a+b*x)*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^2/(b^3*d^2)-1/2*B*(b*c-a*d)*h^2*n*(c+d*x)^2*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^2/(b*d^3)+B*(b*c-a*d)*(a^2*d^2*h^2-a*b*d*h*(3*d*g-c*h)+b^2*(3*d^2*g^2-3*c*d*g*h+c^2*h^2))*n*log((b*c-a*d)/(b*(c+d*x)))*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^2/(b^3*d^3)-1/3*(b*g-a*h)^3*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^3/(b^3*h)+1/3*(g+h*x)^3*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^3/h-B^2*(b*c-a*d)^3*h^2*n^2*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))*log(1-b*(c+d*x)/(d*(a+b*x)))/(b^3*d^3)-2*B^3*(b*c-a*d)^2*h*(3*b*d*g-2*b*c*h-a*d*h)*n^3*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(b^3*d^3)+2*B^2*(b*c-a*d)*(a^2*d^2*h^2-a*b*d*h*(3*d*g-c*h)+b^2*(3*d^2*g^2-3*c*d*g*h+c^2*h^2))*n^2*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(b^3*d^3)+B^3*(b*c-a*d)^3*h^2*n^3*polylog(2,b*(c+d*x)/(d*(a+b*x)))/(b^3*d^3)-2*B^3*(b*c-a*d)*(a^2*d^2*h^2-a*b*d*h*(3*d*g-c*h)+b^2*(3*d^2*g^2-3*c*d*g*h+c^2*h^2))*n^3*polylog(3,d*(a+b*x)/(b*(c+d*x)))/(b^3*d^3)],
[(g+h*x)*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^3,x,13,-3*B^2*(b*c-a*d)^2*h*n^2*log((b*c-a*d)/(b*(c+d*x)))*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))/(b^2*d^2)-3/2*B*(b*c-a*d)*h*n*(a+b*x)*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^2/(b^2*d)+3/2*B*(b*c-a*d)*(2*b*d*g-b*c*h-a*d*h)*n*log((b*c-a*d)/(b*(c+d*x)))*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^2/(b^2*d^2)-1/2*(b*g-a*h)^2*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^3/(b^2*h)+1/2*(g+h*x)^2*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^3/h-3*B^3*(b*c-a*d)^2*h*n^3*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(b^2*d^2)+3*B^2*(b*c-a*d)*(2*b*d*g-b*c*h-a*d*h)*n^2*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(b^2*d^2)-3*B^3*(b*c-a*d)*(2*b*d*g-b*c*h-a*d*h)*n^3*polylog(3,d*(a+b*x)/(b*(c+d*x)))/(b^2*d^2)],
[(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^3,x,6,3*B*(b*c-a*d)*n*log((b*c-a*d)/(b*(c+d*x)))*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^2/(b*d)+(a+b*x)*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^3/b+6*B^2*(b*c-a*d)*n^2*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(b*d)-6*B^3*(b*c-a*d)*n^3*polylog(3,d*(a+b*x)/(b*(c+d*x)))/(b*d)],
[(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^3/(g+h*x),x,12,-log((b*c-a*d)/(b*(c+d*x)))*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^3/h+(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^3*log(1-(d*g-c*h)*(a+b*x)/((b*g-a*h)*(c+d*x)))/h-3*B*n*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^2*polylog(2,d*(a+b*x)/(b*(c+d*x)))/h+3*B*n*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^2*polylog(2,(d*g-c*h)*(a+b*x)/((b*g-a*h)*(c+d*x)))/h+6*B^2*n^2*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))*polylog(3,d*(a+b*x)/(b*(c+d*x)))/h-6*B^2*n^2*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))*polylog(3,(d*g-c*h)*(a+b*x)/((b*g-a*h)*(c+d*x)))/h-6*B^3*n^3*polylog(4,d*(a+b*x)/(b*(c+d*x)))/h+6*B^3*n^3*polylog(4,(d*g-c*h)*(a+b*x)/((b*g-a*h)*(c+d*x)))/h],
[(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^3/(g+h*x)^2,x,6,(a+b*x)*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^3/((b*g-a*h)*(g+h*x))+3*B*(b*c-a*d)*n*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^2*log(1-(d*g-c*h)*(a+b*x)/((b*g-a*h)*(c+d*x)))/((b*g-a*h)*(d*g-c*h))+6*B^2*(b*c-a*d)*n^2*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))*polylog(2,(d*g-c*h)*(a+b*x)/((b*g-a*h)*(c+d*x)))/((b*g-a*h)*(d*g-c*h))-6*B^3*(b*c-a*d)*n^3*polylog(3,(d*g-c*h)*(a+b*x)/((b*g-a*h)*(c+d*x)))/((b*g-a*h)*(d*g-c*h))],
[(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^3/(g+h*x)^3,x,13,3/2*B*(b*c-a*d)*h*n*(a+b*x)*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^2/((b*g-a*h)^2*(d*g-c*h)*(g+h*x))+1/2*b^2*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^3/(h*(b*g-a*h)^2)-1/2*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^3/(h*(g+h*x)^2)+3*B^2*(b*c-a*d)^2*h*n^2*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))*log(1-(d*g-c*h)*(a+b*x)/((b*g-a*h)*(c+d*x)))/((b*g-a*h)^2*(d*g-c*h)^2)+3/2*B*(b*c-a*d)*(2*b*d*g-b*c*h-a*d*h)*n*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^2*log(1-(d*g-c*h)*(a+b*x)/((b*g-a*h)*(c+d*x)))/((b*g-a*h)^2*(d*g-c*h)^2)+3*B^3*(b*c-a*d)^2*h*n^3*polylog(2,(d*g-c*h)*(a+b*x)/((b*g-a*h)*(c+d*x)))/((b*g-a*h)^2*(d*g-c*h)^2)+3*B^2*(b*c-a*d)*(2*b*d*g-b*c*h-a*d*h)*n^2*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))*polylog(2,(d*g-c*h)*(a+b*x)/((b*g-a*h)*(c+d*x)))/((b*g-a*h)^2*(d*g-c*h)^2)-3*B^3*(b*c-a*d)*(2*b*d*g-b*c*h-a*d*h)*n^3*polylog(3,(d*g-c*h)*(a+b*x)/((b*g-a*h)*(c+d*x)))/((b*g-a*h)^2*(d*g-c*h)^2)]]:

# p<0
