# Maple integration test file: "3 Logarithms\3.2.2 (f+g x)^m (h+i x)^q (A+B log(e ((a+b x) over (c+d x))^n))^p.txt"

lst:=[

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

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

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

# q>0
[(a*g+b*g*x)^3*(c*i+d*i*x)*(A+B*log(e*(a+b*x)/(c+d*x))),x,5,-1/20*B*(b*c-a*d)^4*g^3*i*x/(b*d^3)+1/40*B*(b*c-a*d)^3*g^3*i*(a+b*x)^2/(b^2*d^2)-1/60*B*(b*c-a*d)^2*g^3*i*(a+b*x)^3/(b^2*d)+1/5*g^3*i*(a+b*x)^4*(c+d*x)*(A+B*log(e*(a+b*x)/(c+d*x)))/b+1/20*(b*c-a*d)*g^3*i*(a+b*x)^4*(A-B+B*log(e*(a+b*x)/(c+d*x)))/b^2+1/20*B*(b*c-a*d)^5*g^3*i*log(c+d*x)/(b^2*d^4)],
[(a*g+b*g*x)^2*(c*i+d*i*x)*(A+B*log(e*(a+b*x)/(c+d*x))),x,5,1/12*B*(b*c-a*d)^3*g^2*i*x/(b*d^2)-1/24*B*(b*c-a*d)^2*g^2*i*(a+b*x)^2/(b^2*d)+1/4*g^2*i*(a+b*x)^3*(c+d*x)*(A+B*log(e*(a+b*x)/(c+d*x)))/b+1/12*(b*c-a*d)*g^2*i*(a+b*x)^3*(A-B+B*log(e*(a+b*x)/(c+d*x)))/b^2-1/12*B*(b*c-a*d)^4*g^2*i*log(c+d*x)/(b^2*d^3)],
[(a*g+b*g*x)*(c*i+d*i*x)*(A+B*log(e*(a+b*x)/(c+d*x))),x,5,-1/6*B*(b*c-a*d)^2*g*i*x/(b*d)+1/3*g*i*(a+b*x)^2*(c+d*x)*(A+B*log(e*(a+b*x)/(c+d*x)))/b+1/6*(b*c-a*d)*g*i*(a+b*x)^2*(A-B+B*log(e*(a+b*x)/(c+d*x)))/b^2+1/6*B*(b*c-a*d)^3*g*i*log(c+d*x)/(b^2*d^2)],
[(c*i+d*i*x)*(A+B*log(e*(a+b*x)/(c+d*x))),x,4,-1/2*B*(b*c-a*d)*i*x/b-1/2*B*(b*c-a*d)^2*i*log(a+b*x)/(b^2*d)+1/2*i*(c+d*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))/d],
[(c*i+d*i*x)*(A+B*log(e*(a+b*x)/(c+d*x)))/(a*g+b*g*x),x,6,i*(c+d*x)*(A+B*log(e*(a+b*x)/(c+d*x)))/(b*g)-(b*c-a*d)*i*log((-b*c+a*d)/(d*(a+b*x)))*(A-B+B*log(e*(a+b*x)/(c+d*x)))/(b^2*g)+B*(b*c-a*d)*i*polylog(2,1+(b*c-a*d)/(d*(a+b*x)))/(b^2*g)],
[(c*i+d*i*x)*(A+B*log(e*(a+b*x)/(c+d*x)))/(a*g+b*g*x)^2,x,5,-B*i*(c+d*x)/(b*g^2*(a+b*x))-i*(c+d*x)*(A+B*log(e*(a+b*x)/(c+d*x)))/(b*g^2*(a+b*x))-d*i*(A+B*log(e*(a+b*x)/(c+d*x)))*log(1-b*(c+d*x)/(d*(a+b*x)))/(b^2*g^2)+B*d*i*polylog(2,b*(c+d*x)/(d*(a+b*x)))/(b^2*g^2)],
[(c*i+d*i*x)*(A+B*log(e*(a+b*x)/(c+d*x)))/(a*g+b*g*x)^3,x,2,-1/4*B*i*(c+d*x)^2/((b*c-a*d)*g^3*(a+b*x)^2)-1/2*i*(c+d*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))/((b*c-a*d)*g^3*(a+b*x)^2)],
[(c*i+d*i*x)*(A+B*log(e*(a+b*x)/(c+d*x)))/(a*g+b*g*x)^4,x,5,1/4*B*d*i*(c+d*x)^2/((b*c-a*d)^2*g^4*(a+b*x)^2)-1/9*b*B*i*(c+d*x)^3/((b*c-a*d)^2*g^4*(a+b*x)^3)+1/2*d*i*(c+d*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))/((b*c-a*d)^2*g^4*(a+b*x)^2)-1/3*b*i*(c+d*x)^3*(A+B*log(e*(a+b*x)/(c+d*x)))/((b*c-a*d)^2*g^4*(a+b*x)^3)],
[(c*i+d*i*x)*(A+B*log(e*(a+b*x)/(c+d*x)))/(a*g+b*g*x)^5,x,5,-1/4*B*d^2*i*(c+d*x)^2/((b*c-a*d)^3*g^5*(a+b*x)^2)+2/9*b*B*d*i*(c+d*x)^3/((b*c-a*d)^3*g^5*(a+b*x)^3)-1/16*b^2*B*i*(c+d*x)^4/((b*c-a*d)^3*g^5*(a+b*x)^4)-1/2*d^2*i*(c+d*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))/((b*c-a*d)^3*g^5*(a+b*x)^2)+2/3*b*d*i*(c+d*x)^3*(A+B*log(e*(a+b*x)/(c+d*x)))/((b*c-a*d)^3*g^5*(a+b*x)^3)-1/4*b^2*i*(c+d*x)^4*(A+B*log(e*(a+b*x)/(c+d*x)))/((b*c-a*d)^3*g^5*(a+b*x)^4)],
[(a*g+b*g*x)^3*(c*i+d*i*x)^2*(A+B*log(e*(a+b*x)/(c+d*x))),x,5,1/60*B*(b*c-a*d)^5*g^3*i^2*x/(b^2*d^3)+1/120*B*(b*c-a*d)^4*g^3*i^2*(c+d*x)^2/(b*d^4)-19/180*B*(b*c-a*d)^3*g^3*i^2*(c+d*x)^3/d^4+13/120*b*B*(b*c-a*d)^2*g^3*i^2*(c+d*x)^4/d^4-1/30*b^2*B*(b*c-a*d)*g^3*i^2*(c+d*x)^5/d^4+1/60*B*(b*c-a*d)^6*g^3*i^2*log((a+b*x)/(c+d*x))/(b^3*d^4)-1/3*(b*c-a*d)^3*g^3*i^2*(c+d*x)^3*(A+B*log(e*(a+b*x)/(c+d*x)))/d^4+3/4*b*(b*c-a*d)^2*g^3*i^2*(c+d*x)^4*(A+B*log(e*(a+b*x)/(c+d*x)))/d^4-3/5*b^2*(b*c-a*d)*g^3*i^2*(c+d*x)^5*(A+B*log(e*(a+b*x)/(c+d*x)))/d^4+1/6*b^3*g^3*i^2*(c+d*x)^6*(A+B*log(e*(a+b*x)/(c+d*x)))/d^4+1/60*B*(b*c-a*d)^6*g^3*i^2*log(c+d*x)/(b^3*d^4)],
[(a*g+b*g*x)^2*(c*i+d*i*x)^2*(A+B*log(e*(a+b*x)/(c+d*x))),x,5,-1/30*B*(b*c-a*d)^4*g^2*i^2*x/(b^2*d^2)-1/60*B*(b*c-a*d)^3*g^2*i^2*(c+d*x)^2/(b*d^3)+1/10*B*(b*c-a*d)^2*g^2*i^2*(c+d*x)^3/d^3-1/20*b*B*(b*c-a*d)*g^2*i^2*(c+d*x)^4/d^3-1/30*B*(b*c-a*d)^5*g^2*i^2*log((a+b*x)/(c+d*x))/(b^3*d^3)+1/3*(b*c-a*d)^2*g^2*i^2*(c+d*x)^3*(A+B*log(e*(a+b*x)/(c+d*x)))/d^3-1/2*b*(b*c-a*d)*g^2*i^2*(c+d*x)^4*(A+B*log(e*(a+b*x)/(c+d*x)))/d^3+1/5*b^2*g^2*i^2*(c+d*x)^5*(A+B*log(e*(a+b*x)/(c+d*x)))/d^3-1/30*B*(b*c-a*d)^5*g^2*i^2*log(c+d*x)/(b^3*d^3)],
[(a*g+b*g*x)*(c*i+d*i*x)^2*(A+B*log(e*(a+b*x)/(c+d*x))),x,5,1/12*B*(b*c-a*d)^3*g*i^2*x/(b^2*d)+1/24*B*(b*c-a*d)^2*g*i^2*(c+d*x)^2/(b*d^2)-1/12*B*(b*c-a*d)*g*i^2*(c+d*x)^3/d^2+1/12*B*(b*c-a*d)^4*g*i^2*log((a+b*x)/(c+d*x))/(b^3*d^2)-1/3*(b*c-a*d)*g*i^2*(c+d*x)^3*(A+B*log(e*(a+b*x)/(c+d*x)))/d^2+1/4*b*g*i^2*(c+d*x)^4*(A+B*log(e*(a+b*x)/(c+d*x)))/d^2+1/12*B*(b*c-a*d)^4*g*i^2*log(c+d*x)/(b^3*d^2)],
[(c*i+d*i*x)^2*(A+B*log(e*(a+b*x)/(c+d*x))),x,4,-1/3*B*(b*c-a*d)^2*i^2*x/b^2-1/6*B*(b*c-a*d)*i^2*(c+d*x)^2/(b*d)-1/3*B*(b*c-a*d)^3*i^2*log(a+b*x)/(b^3*d)+1/3*i^2*(c+d*x)^3*(A+B*log(e*(a+b*x)/(c+d*x)))/d],
[(c*i+d*i*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))/(a*g+b*g*x),x,10,-1/2*B*d*(b*c-a*d)*i^2*x/(b^2*g)-1/2*B*(b*c-a*d)^2*i^2*log((a+b*x)/(c+d*x))/(b^3*g)+d*(b*c-a*d)*i^2*(a+b*x)*(A+B*log(e*(a+b*x)/(c+d*x)))/(b^3*g)+1/2*i^2*(c+d*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))/(b*g)-3/2*B*(b*c-a*d)^2*i^2*log(c+d*x)/(b^3*g)-(b*c-a*d)^2*i^2*(A+B*log(e*(a+b*x)/(c+d*x)))*log(1-b*(c+d*x)/(d*(a+b*x)))/(b^3*g)+B*(b*c-a*d)^2*i^2*polylog(2,b*(c+d*x)/(d*(a+b*x)))/(b^3*g)],
[(c*i+d*i*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))/(a*g+b*g*x)^2,x,8,-B*(b*c-a*d)*i^2*(c+d*x)/(b^2*g^2*(a+b*x))+d^2*i^2*(a+b*x)*(A+B*log(e*(a+b*x)/(c+d*x)))/(b^3*g^2)-(b*c-a*d)*i^2*(c+d*x)*(A+B*log(e*(a+b*x)/(c+d*x)))/(b^2*g^2*(a+b*x))-B*d*(b*c-a*d)*i^2*log(c+d*x)/(b^3*g^2)-2*d*(b*c-a*d)*i^2*(A+B*log(e*(a+b*x)/(c+d*x)))*log(1-b*(c+d*x)/(d*(a+b*x)))/(b^3*g^2)+2*B*d*(b*c-a*d)*i^2*polylog(2,b*(c+d*x)/(d*(a+b*x)))/(b^3*g^2)],
[(c*i+d*i*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))/(a*g+b*g*x)^3,x,7,-B*d*i^2*(c+d*x)/(b^2*g^3*(a+b*x))-1/4*B*i^2*(c+d*x)^2/(b*g^3*(a+b*x)^2)-d*i^2*(c+d*x)*(A+B*log(e*(a+b*x)/(c+d*x)))/(b^2*g^3*(a+b*x))-1/2*i^2*(c+d*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))/(b*g^3*(a+b*x)^2)-d^2*i^2*(A+B*log(e*(a+b*x)/(c+d*x)))*log(1-b*(c+d*x)/(d*(a+b*x)))/(b^3*g^3)+B*d^2*i^2*polylog(2,b*(c+d*x)/(d*(a+b*x)))/(b^3*g^3)],
[(c*i+d*i*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))/(a*g+b*g*x)^4,x,2,-1/9*B*i^2*(c+d*x)^3/((b*c-a*d)*g^4*(a+b*x)^3)-1/3*i^2*(c+d*x)^3*(A+B*log(e*(a+b*x)/(c+d*x)))/((b*c-a*d)*g^4*(a+b*x)^3)],
[(c*i+d*i*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))/(a*g+b*g*x)^5,x,5,1/9*B*d*i^2*(c+d*x)^3/((b*c-a*d)^2*g^5*(a+b*x)^3)-1/16*b*B*i^2*(c+d*x)^4/((b*c-a*d)^2*g^5*(a+b*x)^4)+1/3*d*i^2*(c+d*x)^3*(A+B*log(e*(a+b*x)/(c+d*x)))/((b*c-a*d)^2*g^5*(a+b*x)^3)-1/4*b*i^2*(c+d*x)^4*(A+B*log(e*(a+b*x)/(c+d*x)))/((b*c-a*d)^2*g^5*(a+b*x)^4)],
[(c*i+d*i*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))/(a*g+b*g*x)^6,x,5,-1/9*B*d^2*i^2*(c+d*x)^3/((b*c-a*d)^3*g^6*(a+b*x)^3)+1/8*b*B*d*i^2*(c+d*x)^4/((b*c-a*d)^3*g^6*(a+b*x)^4)-1/25*b^2*B*i^2*(c+d*x)^5/((b*c-a*d)^3*g^6*(a+b*x)^5)-1/3*d^2*i^2*(c+d*x)^3*(A+B*log(e*(a+b*x)/(c+d*x)))/((b*c-a*d)^3*g^6*(a+b*x)^3)+1/2*b*d*i^2*(c+d*x)^4*(A+B*log(e*(a+b*x)/(c+d*x)))/((b*c-a*d)^3*g^6*(a+b*x)^4)-1/5*b^2*i^2*(c+d*x)^5*(A+B*log(e*(a+b*x)/(c+d*x)))/((b*c-a*d)^3*g^6*(a+b*x)^5)],
[(a*g+b*g*x)^3*(c*i+d*i*x)^3*(A+B*log(e*(a+b*x)/(c+d*x))),x,5,1/140*B*(b*c-a*d)^6*g^3*i^3*x/(b^3*d^3)+1/280*B*(b*c-a*d)^5*g^3*i^3*(c+d*x)^2/(b^2*d^4)+1/420*B*(b*c-a*d)^4*g^3*i^3*(c+d*x)^3/(b*d^4)-17/280*B*(b*c-a*d)^3*g^3*i^3*(c+d*x)^4/d^4+1/14*b*B*(b*c-a*d)^2*g^3*i^3*(c+d*x)^5/d^4-1/42*b^2*B*(b*c-a*d)*g^3*i^3*(c+d*x)^6/d^4+1/140*B*(b*c-a*d)^7*g^3*i^3*log((a+b*x)/(c+d*x))/(b^4*d^4)-1/4*(b*c-a*d)^3*g^3*i^3*(c+d*x)^4*(A+B*log(e*(a+b*x)/(c+d*x)))/d^4+3/5*b*(b*c-a*d)^2*g^3*i^3*(c+d*x)^5*(A+B*log(e*(a+b*x)/(c+d*x)))/d^4-1/2*b^2*(b*c-a*d)*g^3*i^3*(c+d*x)^6*(A+B*log(e*(a+b*x)/(c+d*x)))/d^4+1/7*b^3*g^3*i^3*(c+d*x)^7*(A+B*log(e*(a+b*x)/(c+d*x)))/d^4+1/140*B*(b*c-a*d)^7*g^3*i^3*log(c+d*x)/(b^4*d^4)],
[(a*g+b*g*x)^2*(c*i+d*i*x)^3*(A+B*log(e*(a+b*x)/(c+d*x))),x,5,-1/60*B*(b*c-a*d)^5*g^2*i^3*x/(b^3*d^2)-1/120*B*(b*c-a*d)^4*g^2*i^3*(c+d*x)^2/(b^2*d^3)-1/180*B*(b*c-a*d)^3*g^2*i^3*(c+d*x)^3/(b*d^3)+7/120*B*(b*c-a*d)^2*g^2*i^3*(c+d*x)^4/d^3-1/30*b*B*(b*c-a*d)*g^2*i^3*(c+d*x)^5/d^3-1/60*B*(b*c-a*d)^6*g^2*i^3*log((a+b*x)/(c+d*x))/(b^4*d^3)+1/4*(b*c-a*d)^2*g^2*i^3*(c+d*x)^4*(A+B*log(e*(a+b*x)/(c+d*x)))/d^3-2/5*b*(b*c-a*d)*g^2*i^3*(c+d*x)^5*(A+B*log(e*(a+b*x)/(c+d*x)))/d^3+1/6*b^2*g^2*i^3*(c+d*x)^6*(A+B*log(e*(a+b*x)/(c+d*x)))/d^3-1/60*B*(b*c-a*d)^6*g^2*i^3*log(c+d*x)/(b^4*d^3)],
[(a*g+b*g*x)*(c*i+d*i*x)^3*(A+B*log(e*(a+b*x)/(c+d*x))),x,5,1/20*B*(b*c-a*d)^4*g*i^3*x/(b^3*d)+1/40*B*(b*c-a*d)^3*g*i^3*(c+d*x)^2/(b^2*d^2)+1/60*B*(b*c-a*d)^2*g*i^3*(c+d*x)^3/(b*d^2)-1/20*B*(b*c-a*d)*g*i^3*(c+d*x)^4/d^2+1/20*B*(b*c-a*d)^5*g*i^3*log((a+b*x)/(c+d*x))/(b^4*d^2)-1/4*(b*c-a*d)*g*i^3*(c+d*x)^4*(A+B*log(e*(a+b*x)/(c+d*x)))/d^2+1/5*b*g*i^3*(c+d*x)^5*(A+B*log(e*(a+b*x)/(c+d*x)))/d^2+1/20*B*(b*c-a*d)^5*g*i^3*log(c+d*x)/(b^4*d^2)],
[(c*i+d*i*x)^3*(A+B*log(e*(a+b*x)/(c+d*x))),x,4,-1/4*B*(b*c-a*d)^3*i^3*x/b^3-1/8*B*(b*c-a*d)^2*i^3*(c+d*x)^2/(b^2*d)-1/12*B*(b*c-a*d)*i^3*(c+d*x)^3/(b*d)-1/4*B*(b*c-a*d)^4*i^3*log(a+b*x)/(b^4*d)+1/4*i^3*(c+d*x)^4*(A+B*log(e*(a+b*x)/(c+d*x)))/d],
[(c*i+d*i*x)^3*(A+B*log(e*(a+b*x)/(c+d*x)))/(a*g+b*g*x),x,14,-5/6*B*d*(b*c-a*d)^2*i^3*x/(b^3*g)-1/6*B*(b*c-a*d)*i^3*(c+d*x)^2/(b^2*g)-5/6*B*(b*c-a*d)^3*i^3*log((a+b*x)/(c+d*x))/(b^4*g)+d*(b*c-a*d)^2*i^3*(a+b*x)*(A+B*log(e*(a+b*x)/(c+d*x)))/(b^4*g)+1/2*(b*c-a*d)*i^3*(c+d*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))/(b^2*g)+1/3*i^3*(c+d*x)^3*(A+B*log(e*(a+b*x)/(c+d*x)))/(b*g)-11/6*B*(b*c-a*d)^3*i^3*log(c+d*x)/(b^4*g)-(b*c-a*d)^3*i^3*(A+B*log(e*(a+b*x)/(c+d*x)))*log(1-b*(c+d*x)/(d*(a+b*x)))/(b^4*g)+B*(b*c-a*d)^3*i^3*polylog(2,b*(c+d*x)/(d*(a+b*x)))/(b^4*g)],
[(c*i+d*i*x)^3*(A+B*log(e*(a+b*x)/(c+d*x)))/(a*g+b*g*x)^2,x,11,-1/2*B*d^2*(b*c-a*d)*i^3*x/(b^3*g^2)-B*(b*c-a*d)^2*i^3*(c+d*x)/(b^3*g^2*(a+b*x))-1/2*B*d*(b*c-a*d)^2*i^3*log((a+b*x)/(c+d*x))/(b^4*g^2)+2*d^2*(b*c-a*d)*i^3*(a+b*x)*(A+B*log(e*(a+b*x)/(c+d*x)))/(b^4*g^2)-(b*c-a*d)^2*i^3*(c+d*x)*(A+B*log(e*(a+b*x)/(c+d*x)))/(b^3*g^2*(a+b*x))+1/2*d*i^3*(c+d*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))/(b^2*g^2)-5/2*B*d*(b*c-a*d)^2*i^3*log(c+d*x)/(b^4*g^2)-3*d*(b*c-a*d)^2*i^3*(A+B*log(e*(a+b*x)/(c+d*x)))*log(1-b*(c+d*x)/(d*(a+b*x)))/(b^4*g^2)+3*B*d*(b*c-a*d)^2*i^3*polylog(2,b*(c+d*x)/(d*(a+b*x)))/(b^4*g^2)],
[(c*i+d*i*x)^3*(A+B*log(e*(a+b*x)/(c+d*x)))/(a*g+b*g*x)^3,x,9,-2*B*d*(b*c-a*d)*i^3*(c+d*x)/(b^3*g^3*(a+b*x))-1/4*B*(b*c-a*d)*i^3*(c+d*x)^2/(b^2*g^3*(a+b*x)^2)+d^3*i^3*(a+b*x)*(A+B*log(e*(a+b*x)/(c+d*x)))/(b^4*g^3)-2*d*(b*c-a*d)*i^3*(c+d*x)*(A+B*log(e*(a+b*x)/(c+d*x)))/(b^3*g^3*(a+b*x))-1/2*(b*c-a*d)*i^3*(c+d*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))/(b^2*g^3*(a+b*x)^2)-B*d^2*(b*c-a*d)*i^3*log(c+d*x)/(b^4*g^3)-3*d^2*(b*c-a*d)*i^3*(A+B*log(e*(a+b*x)/(c+d*x)))*log(1-b*(c+d*x)/(d*(a+b*x)))/(b^4*g^3)+3*B*d^2*(b*c-a*d)*i^3*polylog(2,b*(c+d*x)/(d*(a+b*x)))/(b^4*g^3)],
[(c*i+d*i*x)^3*(A+B*log(e*(a+b*x)/(c+d*x)))/(a*g+b*g*x)^4,x,9,-B*d^2*i^3*(c+d*x)/(b^3*g^4*(a+b*x))-1/4*B*d*i^3*(c+d*x)^2/(b^2*g^4*(a+b*x)^2)-1/9*B*i^3*(c+d*x)^3/(b*g^4*(a+b*x)^3)-d^2*i^3*(c+d*x)*(A+B*log(e*(a+b*x)/(c+d*x)))/(b^3*g^4*(a+b*x))-1/2*d*i^3*(c+d*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))/(b^2*g^4*(a+b*x)^2)-1/3*i^3*(c+d*x)^3*(A+B*log(e*(a+b*x)/(c+d*x)))/(b*g^4*(a+b*x)^3)-d^3*i^3*(A+B*log(e*(a+b*x)/(c+d*x)))*log(1-b*(c+d*x)/(d*(a+b*x)))/(b^4*g^4)+B*d^3*i^3*polylog(2,b*(c+d*x)/(d*(a+b*x)))/(b^4*g^4)],
[(c*i+d*i*x)^3*(A+B*log(e*(a+b*x)/(c+d*x)))/(a*g+b*g*x)^5,x,2,-1/16*B*i^3*(c+d*x)^4/((b*c-a*d)*g^5*(a+b*x)^4)-1/4*i^3*(c+d*x)^4*(A+B*log(e*(a+b*x)/(c+d*x)))/((b*c-a*d)*g^5*(a+b*x)^4)],
[(c*i+d*i*x)^3*(A+B*log(e*(a+b*x)/(c+d*x)))/(a*g+b*g*x)^6,x,5,1/16*B*d*i^3*(c+d*x)^4/((b*c-a*d)^2*g^6*(a+b*x)^4)-1/25*b*B*i^3*(c+d*x)^5/((b*c-a*d)^2*g^6*(a+b*x)^5)+1/4*d*i^3*(c+d*x)^4*(A+B*log(e*(a+b*x)/(c+d*x)))/((b*c-a*d)^2*g^6*(a+b*x)^4)-1/5*b*i^3*(c+d*x)^5*(A+B*log(e*(a+b*x)/(c+d*x)))/((b*c-a*d)^2*g^6*(a+b*x)^5)],
[(c*i+d*i*x)^3*(A+B*log(e*(a+b*x)/(c+d*x)))/(a*g+b*g*x)^7,x,5,-1/16*B*d^2*i^3*(c+d*x)^4/((b*c-a*d)^3*g^7*(a+b*x)^4)+2/25*b*B*d*i^3*(c+d*x)^5/((b*c-a*d)^3*g^7*(a+b*x)^5)-1/36*b^2*B*i^3*(c+d*x)^6/((b*c-a*d)^3*g^7*(a+b*x)^6)-1/4*d^2*i^3*(c+d*x)^4*(A+B*log(e*(a+b*x)/(c+d*x)))/((b*c-a*d)^3*g^7*(a+b*x)^4)+2/5*b*d*i^3*(c+d*x)^5*(A+B*log(e*(a+b*x)/(c+d*x)))/((b*c-a*d)^3*g^7*(a+b*x)^5)-1/6*b^2*i^3*(c+d*x)^6*(A+B*log(e*(a+b*x)/(c+d*x)))/((b*c-a*d)^3*g^7*(a+b*x)^6)],

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

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

# q>0
[(a*g+b*g*x)^3*(c*i+d*i*x)*(A+B*log(e*(a+b*x)/(c+d*x)))^2,x,11,3/10*B^2*(b*c-a*d)^4*g^3*i*x/(b*d^3)-3/20*B^2*(b*c-a*d)^3*g^3*i*(c+d*x)^2/d^4+1/30*b*B^2*(b*c-a*d)^2*g^3*i*(c+d*x)^3/d^4-1/30*B*(b*c-a*d)^2*g^3*i*(a+b*x)^3*(A+B*log(e*(a+b*x)/(c+d*x)))/(b^2*d)-1/10*B*(b*c-a*d)*g^3*i*(a+b*x)^4*(A+B*log(e*(a+b*x)/(c+d*x)))/b^2+1/20*(b*c-a*d)*g^3*i*(a+b*x)^4*(A+B*log(e*(a+b*x)/(c+d*x)))^2/b^2+1/5*g^3*i*(a+b*x)^4*(c+d*x)*(A+B*log(e*(a+b*x)/(c+d*x)))^2/b+1/60*B*(b*c-a*d)^3*g^3*i*(a+b*x)^2*(3*A+B+3*B*log(e*(a+b*x)/(c+d*x)))/(b^2*d^2)-1/60*B*(b*c-a*d)^4*g^3*i*(a+b*x)*(6*A+5*B+6*B*log(e*(a+b*x)/(c+d*x)))/(b^2*d^3)-1/60*B*(b*c-a*d)^5*g^3*i*log((b*c-a*d)/(b*(c+d*x)))*(6*A+11*B+6*B*log(e*(a+b*x)/(c+d*x)))/(b^2*d^4)-1/10*B^2*(b*c-a*d)^5*g^3*i*log(c+d*x)/(b^2*d^4)-1/10*B^2*(b*c-a*d)^5*g^3*i*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(b^2*d^4)],
[(a*g+b*g*x)^2*(c*i+d*i*x)*(A+B*log(e*(a+b*x)/(c+d*x)))^2,x,10,-1/3*B^2*(b*c-a*d)^3*g^2*i*x/(b*d^2)+1/12*B^2*(b*c-a*d)^2*g^2*i*(c+d*x)^2/d^3-1/12*B*(b*c-a*d)^2*g^2*i*(a+b*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))/(b^2*d)-1/6*B*(b*c-a*d)*g^2*i*(a+b*x)^3*(A+B*log(e*(a+b*x)/(c+d*x)))/b^2+1/12*(b*c-a*d)*g^2*i*(a+b*x)^3*(A+B*log(e*(a+b*x)/(c+d*x)))^2/b^2+1/4*g^2*i*(a+b*x)^3*(c+d*x)*(A+B*log(e*(a+b*x)/(c+d*x)))^2/b+1/12*B*(b*c-a*d)^3*g^2*i*(a+b*x)*(2*A+B+2*B*log(e*(a+b*x)/(c+d*x)))/(b^2*d^2)+1/12*B*(b*c-a*d)^4*g^2*i*log((b*c-a*d)/(b*(c+d*x)))*(2*A+3*B+2*B*log(e*(a+b*x)/(c+d*x)))/(b^2*d^3)+1/6*B^2*(b*c-a*d)^4*g^2*i*log(c+d*x)/(b^2*d^3)+1/6*B^2*(b*c-a*d)^4*g^2*i*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(b^2*d^3)],
[(a*g+b*g*x)*(c*i+d*i*x)*(A+B*log(e*(a+b*x)/(c+d*x)))^2,x,9,1/3*B^2*(b*c-a*d)^2*g*i*x/(b*d)-1/3*B*(b*c-a*d)^2*g*i*(a+b*x)*(A+B*log(e*(a+b*x)/(c+d*x)))/(b^2*d)-1/3*B*(b*c-a*d)*g*i*(a+b*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))/b^2+1/6*(b*c-a*d)*g*i*(a+b*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))^2/b^2+1/3*g*i*(a+b*x)^2*(c+d*x)*(A+B*log(e*(a+b*x)/(c+d*x)))^2/b-1/3*B*(b*c-a*d)^3*g*i*log((b*c-a*d)/(b*(c+d*x)))*(A+B+B*log(e*(a+b*x)/(c+d*x)))/(b^2*d^2)-1/3*B^2*(b*c-a*d)^3*g*i*log(c+d*x)/(b^2*d^2)-1/3*B^2*(b*c-a*d)^3*g*i*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(b^2*d^2)],
[(c*i+d*i*x)*(A+B*log(e*(a+b*x)/(c+d*x)))^2,x,7,-B*(b*c-a*d)*i*(a+b*x)*(A+B*log(e*(a+b*x)/(c+d*x)))/b^2+1/2*i*(c+d*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))^2/d+B^2*(b*c-a*d)^2*i*log(c+d*x)/(b^2*d)+B*(b*c-a*d)^2*i*(A+B*log(e*(a+b*x)/(c+d*x)))*log(1-b*(c+d*x)/(d*(a+b*x)))/(b^2*d)-B^2*(b*c-a*d)^2*i*polylog(2,b*(c+d*x)/(d*(a+b*x)))/(b^2*d)],
[(c*i+d*i*x)*(A+B*log(e*(a+b*x)/(c+d*x)))^2/(a*g+b*g*x),x,8,2*B*(b*c-a*d)*i*log((b*c-a*d)/(b*(c+d*x)))*(A+B*log(e*(a+b*x)/(c+d*x)))/(b^2*g)+d*i*(a+b*x)*(A+B*log(e*(a+b*x)/(c+d*x)))^2/(b^2*g)-(b*c-a*d)*i*(A+B*log(e*(a+b*x)/(c+d*x)))^2*log(1-b*(c+d*x)/(d*(a+b*x)))/(b^2*g)+2*B^2*(b*c-a*d)*i*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(b^2*g)+2*B*(b*c-a*d)*i*(A+B*log(e*(a+b*x)/(c+d*x)))*polylog(2,b*(c+d*x)/(d*(a+b*x)))/(b^2*g)+2*B^2*(b*c-a*d)*i*polylog(3,b*(c+d*x)/(d*(a+b*x)))/(b^2*g)],
[(c*i+d*i*x)*(A+B*log(e*(a+b*x)/(c+d*x)))^2/(a*g+b*g*x)^2,x,7,-2*B^2*i*(c+d*x)/(b*g^2*(a+b*x))-2*B*i*(c+d*x)*(A+B*log(e*(a+b*x)/(c+d*x)))/(b*g^2*(a+b*x))-i*(c+d*x)*(A+B*log(e*(a+b*x)/(c+d*x)))^2/(b*g^2*(a+b*x))-d*i*(A+B*log(e*(a+b*x)/(c+d*x)))^2*log(1-b*(c+d*x)/(d*(a+b*x)))/(b^2*g^2)+2*B*d*i*(A+B*log(e*(a+b*x)/(c+d*x)))*polylog(2,b*(c+d*x)/(d*(a+b*x)))/(b^2*g^2)+2*B^2*d*i*polylog(3,b*(c+d*x)/(d*(a+b*x)))/(b^2*g^2)],
[(c*i+d*i*x)*(A+B*log(e*(a+b*x)/(c+d*x)))^2/(a*g+b*g*x)^3,x,3,-1/4*B^2*i*(c+d*x)^2/((b*c-a*d)*g^3*(a+b*x)^2)-1/2*B*i*(c+d*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))/((b*c-a*d)*g^3*(a+b*x)^2)-1/2*i*(c+d*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))^2/((b*c-a*d)*g^3*(a+b*x)^2)],
[(c*i+d*i*x)*(A+B*log(e*(a+b*x)/(c+d*x)))^2/(a*g+b*g*x)^4,x,7,1/4*B^2*d*i*(c+d*x)^2/((b*c-a*d)^2*g^4*(a+b*x)^2)-2/27*b*B^2*i*(c+d*x)^3/((b*c-a*d)^2*g^4*(a+b*x)^3)+1/2*B*d*i*(c+d*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))/((b*c-a*d)^2*g^4*(a+b*x)^2)-2/9*b*B*i*(c+d*x)^3*(A+B*log(e*(a+b*x)/(c+d*x)))/((b*c-a*d)^2*g^4*(a+b*x)^3)+1/2*d*i*(c+d*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))^2/((b*c-a*d)^2*g^4*(a+b*x)^2)-1/3*b*i*(c+d*x)^3*(A+B*log(e*(a+b*x)/(c+d*x)))^2/((b*c-a*d)^2*g^4*(a+b*x)^3)],
[(c*i+d*i*x)*(A+B*log(e*(a+b*x)/(c+d*x)))^2/(a*g+b*g*x)^5,x,9,-1/4*B^2*d^2*i*(c+d*x)^2/((b*c-a*d)^3*g^5*(a+b*x)^2)+4/27*b*B^2*d*i*(c+d*x)^3/((b*c-a*d)^3*g^5*(a+b*x)^3)-1/32*b^2*B^2*i*(c+d*x)^4/((b*c-a*d)^3*g^5*(a+b*x)^4)-1/2*B*d^2*i*(c+d*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))/((b*c-a*d)^3*g^5*(a+b*x)^2)+4/9*b*B*d*i*(c+d*x)^3*(A+B*log(e*(a+b*x)/(c+d*x)))/((b*c-a*d)^3*g^5*(a+b*x)^3)-1/8*b^2*B*i*(c+d*x)^4*(A+B*log(e*(a+b*x)/(c+d*x)))/((b*c-a*d)^3*g^5*(a+b*x)^4)-1/2*d^2*i*(c+d*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))^2/((b*c-a*d)^3*g^5*(a+b*x)^2)+2/3*b*d*i*(c+d*x)^3*(A+B*log(e*(a+b*x)/(c+d*x)))^2/((b*c-a*d)^3*g^5*(a+b*x)^3)-1/4*b^2*i*(c+d*x)^4*(A+B*log(e*(a+b*x)/(c+d*x)))^2/((b*c-a*d)^3*g^5*(a+b*x)^4)],
[(a*g+b*g*x)^3*(c*i+d*i*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))^2,x,17,3/20*B^2*(b*c-a*d)^5*g^3*i^2*x/(b^2*d^3)+1/60*B^2*(b*c-a*d)^2*g^3*i^2*(a+b*x)^4/b^3-3/40*B^2*(b*c-a*d)^4*g^3*i^2*(c+d*x)^2/(b*d^4)+1/60*B^2*(b*c-a*d)^3*g^3*i^2*(c+d*x)^3/d^4-1/90*B*(b*c-a*d)^3*g^3*i^2*(a+b*x)^3*(A+B*log(e*(a+b*x)/(c+d*x)))/(b^3*d)-1/20*B*(b*c-a*d)^2*g^3*i^2*(a+b*x)^4*(A+B*log(e*(a+b*x)/(c+d*x)))/b^3-1/15*B*(b*c-a*d)*g^3*i^2*(a+b*x)^4*(c+d*x)*(A+B*log(e*(a+b*x)/(c+d*x)))/b^2+1/60*(b*c-a*d)^2*g^3*i^2*(a+b*x)^4*(A+B*log(e*(a+b*x)/(c+d*x)))^2/b^3+1/15*(b*c-a*d)*g^3*i^2*(a+b*x)^4*(c+d*x)*(A+B*log(e*(a+b*x)/(c+d*x)))^2/b^2+1/6*g^3*i^2*(a+b*x)^4*(c+d*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))^2/b+1/180*B*(b*c-a*d)^4*g^3*i^2*(a+b*x)^2*(3*A+B+3*B*log(e*(a+b*x)/(c+d*x)))/(b^3*d^2)-1/180*B*(b*c-a*d)^5*g^3*i^2*(a+b*x)*(6*A+5*B+6*B*log(e*(a+b*x)/(c+d*x)))/(b^3*d^3)-1/180*B*(b*c-a*d)^6*g^3*i^2*log((b*c-a*d)/(b*(c+d*x)))*(6*A+11*B+6*B*log(e*(a+b*x)/(c+d*x)))/(b^3*d^4)-1/20*B^2*(b*c-a*d)^6*g^3*i^2*log(c+d*x)/(b^3*d^4)-1/30*B^2*(b*c-a*d)^6*g^3*i^2*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(b^3*d^4)],
[(a*g+b*g*x)^2*(c*i+d*i*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))^2,x,15,-1/10*B^2*(b*c-a*d)^4*g^2*i^2*x/(b^2*d^2)-1/20*B^2*(b*c-a*d)^3*g^2*i^2*(c+d*x)^2/(b*d^3)+1/30*B^2*(b*c-a*d)^2*g^2*i^2*(c+d*x)^3/d^3+1/30*B^2*(b*c-a*d)^5*g^2*i^2*log((a+b*x)/(c+d*x))/(b^3*d^3)-1/30*B*(b*c-a*d)^3*g^2*i^2*(a+b*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))/(b^3*d)-1/15*B*(b*c-a*d)^2*g^2*i^2*(a+b*x)^3*(A+B*log(e*(a+b*x)/(c+d*x)))/b^3-1/5*B*(b*c-a*d)^3*g^2*i^2*(c+d*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))/(b*d^3)+4/15*B*(b*c-a*d)^2*g^2*i^2*(c+d*x)^3*(A+B*log(e*(a+b*x)/(c+d*x)))/d^3-1/10*b*B*(b*c-a*d)*g^2*i^2*(c+d*x)^4*(A+B*log(e*(a+b*x)/(c+d*x)))/d^3+1/30*(b*c-a*d)^2*g^2*i^2*(a+b*x)^3*(A+B*log(e*(a+b*x)/(c+d*x)))^2/b^3+1/10*(b*c-a*d)*g^2*i^2*(a+b*x)^3*(c+d*x)*(A+B*log(e*(a+b*x)/(c+d*x)))^2/b^2+1/5*g^2*i^2*(a+b*x)^3*(c+d*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))^2/b+1/30*B*(b*c-a*d)^4*g^2*i^2*(a+b*x)*(2*A+B+2*B*log(e*(a+b*x)/(c+d*x)))/(b^3*d^2)+1/30*B*(b*c-a*d)^5*g^2*i^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^3*d^3)+1/10*B^2*(b*c-a*d)^5*g^2*i^2*log(c+d*x)/(b^3*d^3)+1/15*B^2*(b*c-a*d)^5*g^2*i^2*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(b^3*d^3)],
[(a*g+b*g*x)*(c*i+d*i*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))^2,x,14,1/12*B^2*(b*c-a*d)^3*g*i^2*x/(b^2*d)+1/12*B^2*(b*c-a*d)^2*g*i^2*(c+d*x)^2/(b*d^2)-1/12*B^2*(b*c-a*d)^4*g*i^2*log((a+b*x)/(c+d*x))/(b^3*d^2)-1/6*B*(b*c-a*d)^3*g*i^2*(a+b*x)*(A+B*log(e*(a+b*x)/(c+d*x)))/(b^3*d)-1/6*B*(b*c-a*d)^2*g*i^2*(a+b*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))/b^3+1/4*B*(b*c-a*d)^2*g*i^2*(c+d*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))/(b*d^2)-1/6*B*(b*c-a*d)*g*i^2*(c+d*x)^3*(A+B*log(e*(a+b*x)/(c+d*x)))/d^2+1/12*(b*c-a*d)^2*g*i^2*(a+b*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))^2/b^3+1/6*(b*c-a*d)*g*i^2*(a+b*x)^2*(c+d*x)*(A+B*log(e*(a+b*x)/(c+d*x)))^2/b^2+1/4*g*i^2*(a+b*x)^2*(c+d*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))^2/b-1/6*B*(b*c-a*d)^4*g*i^2*log((b*c-a*d)/(b*(c+d*x)))*(A+B+B*log(e*(a+b*x)/(c+d*x)))/(b^3*d^2)-1/4*B^2*(b*c-a*d)^4*g*i^2*log(c+d*x)/(b^3*d^2)-1/6*B^2*(b*c-a*d)^4*g*i^2*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(b^3*d^2)],
[(c*i+d*i*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))^2,x,11,1/3*B^2*(b*c-a*d)^2*i^2*x/b^2+1/3*B^2*(b*c-a*d)^3*i^2*log((a+b*x)/(c+d*x))/(b^3*d)-2/3*B*(b*c-a*d)^2*i^2*(a+b*x)*(A+B*log(e*(a+b*x)/(c+d*x)))/b^3-1/3*B*(b*c-a*d)*i^2*(c+d*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))/(b*d)+1/3*i^2*(c+d*x)^3*(A+B*log(e*(a+b*x)/(c+d*x)))^2/d+B^2*(b*c-a*d)^3*i^2*log(c+d*x)/(b^3*d)+2/3*B*(b*c-a*d)^3*i^2*(A+B*log(e*(a+b*x)/(c+d*x)))*log(1-b*(c+d*x)/(d*(a+b*x)))/(b^3*d)-2/3*B^2*(b*c-a*d)^3*i^2*polylog(2,b*(c+d*x)/(d*(a+b*x)))/(b^3*d)],
[(c*i+d*i*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))^2/(a*g+b*g*x),x,15,-B*d*(b*c-a*d)*i^2*(a+b*x)*(A+B*log(e*(a+b*x)/(c+d*x)))/(b^3*g)+2*B*(b*c-a*d)^2*i^2*log((b*c-a*d)/(b*(c+d*x)))*(A+B*log(e*(a+b*x)/(c+d*x)))/(b^3*g)+d*(b*c-a*d)*i^2*(a+b*x)*(A+B*log(e*(a+b*x)/(c+d*x)))^2/(b^3*g)+1/2*i^2*(c+d*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))^2/(b*g)+B^2*(b*c-a*d)^2*i^2*log(c+d*x)/(b^3*g)+B*(b*c-a*d)^2*i^2*(A+B*log(e*(a+b*x)/(c+d*x)))*log(1-b*(c+d*x)/(d*(a+b*x)))/(b^3*g)-(b*c-a*d)^2*i^2*(A+B*log(e*(a+b*x)/(c+d*x)))^2*log(1-b*(c+d*x)/(d*(a+b*x)))/(b^3*g)+2*B^2*(b*c-a*d)^2*i^2*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(b^3*g)-B^2*(b*c-a*d)^2*i^2*polylog(2,b*(c+d*x)/(d*(a+b*x)))/(b^3*g)+2*B*(b*c-a*d)^2*i^2*(A+B*log(e*(a+b*x)/(c+d*x)))*polylog(2,b*(c+d*x)/(d*(a+b*x)))/(b^3*g)+2*B^2*(b*c-a*d)^2*i^2*polylog(3,b*(c+d*x)/(d*(a+b*x)))/(b^3*g)],
[(c*i+d*i*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))^2/(a*g+b*g*x)^2,x,11,-2*B^2*(b*c-a*d)*i^2*(c+d*x)/(b^2*g^2*(a+b*x))-2*B*(b*c-a*d)*i^2*(c+d*x)*(A+B*log(e*(a+b*x)/(c+d*x)))/(b^2*g^2*(a+b*x))+2*B*d*(b*c-a*d)*i^2*log((b*c-a*d)/(b*(c+d*x)))*(A+B*log(e*(a+b*x)/(c+d*x)))/(b^3*g^2)+d^2*i^2*(a+b*x)*(A+B*log(e*(a+b*x)/(c+d*x)))^2/(b^3*g^2)-(b*c-a*d)*i^2*(c+d*x)*(A+B*log(e*(a+b*x)/(c+d*x)))^2/(b^2*g^2*(a+b*x))-2*d*(b*c-a*d)*i^2*(A+B*log(e*(a+b*x)/(c+d*x)))^2*log(1-b*(c+d*x)/(d*(a+b*x)))/(b^3*g^2)+2*B^2*d*(b*c-a*d)*i^2*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(b^3*g^2)+4*B*d*(b*c-a*d)*i^2*(A+B*log(e*(a+b*x)/(c+d*x)))*polylog(2,b*(c+d*x)/(d*(a+b*x)))/(b^3*g^2)+4*B^2*d*(b*c-a*d)*i^2*polylog(3,b*(c+d*x)/(d*(a+b*x)))/(b^3*g^2)],
[(c*i+d*i*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))^2/(a*g+b*g*x)^3,x,10,-2*B^2*d*i^2*(c+d*x)/(b^2*g^3*(a+b*x))-1/4*B^2*i^2*(c+d*x)^2/(b*g^3*(a+b*x)^2)-2*B*d*i^2*(c+d*x)*(A+B*log(e*(a+b*x)/(c+d*x)))/(b^2*g^3*(a+b*x))-1/2*B*i^2*(c+d*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))/(b*g^3*(a+b*x)^2)-d*i^2*(c+d*x)*(A+B*log(e*(a+b*x)/(c+d*x)))^2/(b^2*g^3*(a+b*x))-1/2*i^2*(c+d*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))^2/(b*g^3*(a+b*x)^2)-d^2*i^2*(A+B*log(e*(a+b*x)/(c+d*x)))^2*log(1-b*(c+d*x)/(d*(a+b*x)))/(b^3*g^3)+2*B*d^2*i^2*(A+B*log(e*(a+b*x)/(c+d*x)))*polylog(2,b*(c+d*x)/(d*(a+b*x)))/(b^3*g^3)+2*B^2*d^2*i^2*polylog(3,b*(c+d*x)/(d*(a+b*x)))/(b^3*g^3)],
[(c*i+d*i*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))^2/(a*g+b*g*x)^4,x,3,-2/27*B^2*i^2*(c+d*x)^3/((b*c-a*d)*g^4*(a+b*x)^3)-2/9*B*i^2*(c+d*x)^3*(A+B*log(e*(a+b*x)/(c+d*x)))/((b*c-a*d)*g^4*(a+b*x)^3)-1/3*i^2*(c+d*x)^3*(A+B*log(e*(a+b*x)/(c+d*x)))^2/((b*c-a*d)*g^4*(a+b*x)^3)],
[(c*i+d*i*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))^2/(a*g+b*g*x)^5,x,7,2/27*B^2*d*i^2*(c+d*x)^3/((b*c-a*d)^2*g^5*(a+b*x)^3)-1/32*b*B^2*i^2*(c+d*x)^4/((b*c-a*d)^2*g^5*(a+b*x)^4)+2/9*B*d*i^2*(c+d*x)^3*(A+B*log(e*(a+b*x)/(c+d*x)))/((b*c-a*d)^2*g^5*(a+b*x)^3)-1/8*b*B*i^2*(c+d*x)^4*(A+B*log(e*(a+b*x)/(c+d*x)))/((b*c-a*d)^2*g^5*(a+b*x)^4)+1/3*d*i^2*(c+d*x)^3*(A+B*log(e*(a+b*x)/(c+d*x)))^2/((b*c-a*d)^2*g^5*(a+b*x)^3)-1/4*b*i^2*(c+d*x)^4*(A+B*log(e*(a+b*x)/(c+d*x)))^2/((b*c-a*d)^2*g^5*(a+b*x)^4)],
[(c*i+d*i*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))^2/(a*g+b*g*x)^6,x,9,-2/27*B^2*d^2*i^2*(c+d*x)^3/((b*c-a*d)^3*g^6*(a+b*x)^3)+1/16*b*B^2*d*i^2*(c+d*x)^4/((b*c-a*d)^3*g^6*(a+b*x)^4)-2/125*b^2*B^2*i^2*(c+d*x)^5/((b*c-a*d)^3*g^6*(a+b*x)^5)-2/9*B*d^2*i^2*(c+d*x)^3*(A+B*log(e*(a+b*x)/(c+d*x)))/((b*c-a*d)^3*g^6*(a+b*x)^3)+1/4*b*B*d*i^2*(c+d*x)^4*(A+B*log(e*(a+b*x)/(c+d*x)))/((b*c-a*d)^3*g^6*(a+b*x)^4)-2/25*b^2*B*i^2*(c+d*x)^5*(A+B*log(e*(a+b*x)/(c+d*x)))/((b*c-a*d)^3*g^6*(a+b*x)^5)-1/3*d^2*i^2*(c+d*x)^3*(A+B*log(e*(a+b*x)/(c+d*x)))^2/((b*c-a*d)^3*g^6*(a+b*x)^3)+1/2*b*d*i^2*(c+d*x)^4*(A+B*log(e*(a+b*x)/(c+d*x)))^2/((b*c-a*d)^3*g^6*(a+b*x)^4)-1/5*b^2*i^2*(c+d*x)^5*(A+B*log(e*(a+b*x)/(c+d*x)))^2/((b*c-a*d)^3*g^6*(a+b*x)^5)],
[(a*g+b*g*x)^3*(c*i+d*i*x)^3*(A+B*log(e*(a+b*x)/(c+d*x)))^2,x,22,5/84*B^2*(b*c-a*d)^6*g^3*i^3*x/(b^3*d^3)+1/140*B^2*(b*c-a*d)^3*g^3*i^3*(a+b*x)^4/b^4-29/840*B^2*(b*c-a*d)^5*g^3*i^3*(c+d*x)^2/(b^2*d^4)+47/1260*B^2*(b*c-a*d)^4*g^3*i^3*(c+d*x)^3/(b*d^4)-13/420*B^2*(b*c-a*d)^3*g^3*i^3*(c+d*x)^4/d^4+1/105*b*B^2*(b*c-a*d)^2*g^3*i^3*(c+d*x)^5/d^4-1/210*B^2*(b*c-a*d)^7*g^3*i^3*log((a+b*x)/(c+d*x))/(b^4*d^4)-1/210*B*(b*c-a*d)^4*g^3*i^3*(a+b*x)^3*(A+B*log(e*(a+b*x)/(c+d*x)))/(b^4*d)-3/140*B*(b*c-a*d)^3*g^3*i^3*(a+b*x)^4*(A+B*log(e*(a+b*x)/(c+d*x)))/b^4-1/35*B*(b*c-a*d)^2*g^3*i^3*(a+b*x)^4*(c+d*x)*(A+B*log(e*(a+b*x)/(c+d*x)))/b^3+2/21*B*(b*c-a*d)^4*g^3*i^3*(c+d*x)^3*(A+B*log(e*(a+b*x)/(c+d*x)))/(b*d^4)-3/14*B*(b*c-a*d)^3*g^3*i^3*(c+d*x)^4*(A+B*log(e*(a+b*x)/(c+d*x)))/d^4+6/35*b*B*(b*c-a*d)^2*g^3*i^3*(c+d*x)^5*(A+B*log(e*(a+b*x)/(c+d*x)))/d^4-1/21*b^2*B*(b*c-a*d)*g^3*i^3*(c+d*x)^6*(A+B*log(e*(a+b*x)/(c+d*x)))/d^4+1/140*(b*c-a*d)^3*g^3*i^3*(a+b*x)^4*(A+B*log(e*(a+b*x)/(c+d*x)))^2/b^4+1/35*(b*c-a*d)^2*g^3*i^3*(a+b*x)^4*(c+d*x)*(A+B*log(e*(a+b*x)/(c+d*x)))^2/b^3+1/14*(b*c-a*d)*g^3*i^3*(a+b*x)^4*(c+d*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))^2/b^2+1/7*g^3*i^3*(a+b*x)^4*(c+d*x)^3*(A+B*log(e*(a+b*x)/(c+d*x)))^2/b+1/420*B*(b*c-a*d)^5*g^3*i^3*(a+b*x)^2*(3*A+B+3*B*log(e*(a+b*x)/(c+d*x)))/(b^4*d^2)-1/420*B*(b*c-a*d)^6*g^3*i^3*(a+b*x)*(6*A+5*B+6*B*log(e*(a+b*x)/(c+d*x)))/(b^4*d^3)-1/420*B*(b*c-a*d)^7*g^3*i^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^4*d^4)-11/420*B^2*(b*c-a*d)^7*g^3*i^3*log(c+d*x)/(b^4*d^4)-1/70*B^2*(b*c-a*d)^7*g^3*i^3*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(b^4*d^4)],
[(a*g+b*g*x)^2*(c*i+d*i*x)^3*(A+B*log(e*(a+b*x)/(c+d*x)))^2,x,20,-7/180*B^2*(b*c-a*d)^5*g^2*i^3*x/(b^3*d^2)-7/360*B^2*(b*c-a*d)^4*g^2*i^3*(c+d*x)^2/(b^2*d^3)-1/60*B^2*(b*c-a*d)^3*g^2*i^3*(c+d*x)^3/(b*d^3)+1/60*B^2*(b*c-a*d)^2*g^2*i^3*(c+d*x)^4/d^3+1/36*B^2*(b*c-a*d)^6*g^2*i^3*log((a+b*x)/(c+d*x))/(b^4*d^3)-1/60*B*(b*c-a*d)^4*g^2*i^3*(a+b*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))/(b^4*d)-1/30*B*(b*c-a*d)^3*g^2*i^3*(a+b*x)^3*(A+B*log(e*(a+b*x)/(c+d*x)))/b^4-1/10*B*(b*c-a*d)^4*g^2*i^3*(c+d*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))/(b^2*d^3)+1/45*B*(b*c-a*d)^3*g^2*i^3*(c+d*x)^3*(A+B*log(e*(a+b*x)/(c+d*x)))/(b*d^3)+7/60*B*(b*c-a*d)^2*g^2*i^3*(c+d*x)^4*(A+B*log(e*(a+b*x)/(c+d*x)))/d^3-1/15*b*B*(b*c-a*d)*g^2*i^3*(c+d*x)^5*(A+B*log(e*(a+b*x)/(c+d*x)))/d^3+1/60*(b*c-a*d)^3*g^2*i^3*(a+b*x)^3*(A+B*log(e*(a+b*x)/(c+d*x)))^2/b^4+1/20*(b*c-a*d)^2*g^2*i^3*(a+b*x)^3*(c+d*x)*(A+B*log(e*(a+b*x)/(c+d*x)))^2/b^3+1/10*(b*c-a*d)*g^2*i^3*(a+b*x)^3*(c+d*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))^2/b^2+1/6*g^2*i^3*(a+b*x)^3*(c+d*x)^3*(A+B*log(e*(a+b*x)/(c+d*x)))^2/b+1/60*B*(b*c-a*d)^5*g^2*i^3*(a+b*x)*(2*A+B+2*B*log(e*(a+b*x)/(c+d*x)))/(b^4*d^2)+1/60*B*(b*c-a*d)^6*g^2*i^3*log((b*c-a*d)/(b*(c+d*x)))*(2*A+3*B+2*B*log(e*(a+b*x)/(c+d*x)))/(b^4*d^3)+11/180*B^2*(b*c-a*d)^6*g^2*i^3*log(c+d*x)/(b^4*d^3)+1/30*B^2*(b*c-a*d)^6*g^2*i^3*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(b^4*d^3)],
[(a*g+b*g*x)*(c*i+d*i*x)^3*(A+B*log(e*(a+b*x)/(c+d*x)))^2,x,19,1/60*B^2*(b*c-a*d)^4*g*i^3*x/(b^3*d)+1/30*B^2*(b*c-a*d)^3*g*i^3*(c+d*x)^2/(b^2*d^2)+1/30*B^2*(b*c-a*d)^2*g*i^3*(c+d*x)^3/(b*d^2)-1/12*B^2*(b*c-a*d)^5*g*i^3*log((a+b*x)/(c+d*x))/(b^4*d^2)-1/10*B*(b*c-a*d)^4*g*i^3*(a+b*x)*(A+B*log(e*(a+b*x)/(c+d*x)))/(b^4*d)-1/10*B*(b*c-a*d)^3*g*i^3*(a+b*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))/b^4+3/20*B*(b*c-a*d)^3*g*i^3*(c+d*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))/(b^2*d^2)+1/30*B*(b*c-a*d)^2*g*i^3*(c+d*x)^3*(A+B*log(e*(a+b*x)/(c+d*x)))/(b*d^2)-1/10*B*(b*c-a*d)*g*i^3*(c+d*x)^4*(A+B*log(e*(a+b*x)/(c+d*x)))/d^2+1/20*(b*c-a*d)^3*g*i^3*(a+b*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))^2/b^4+1/10*(b*c-a*d)^2*g*i^3*(a+b*x)^2*(c+d*x)*(A+B*log(e*(a+b*x)/(c+d*x)))^2/b^3+3/20*(b*c-a*d)*g*i^3*(a+b*x)^2*(c+d*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))^2/b^2+1/5*g*i^3*(a+b*x)^2*(c+d*x)^3*(A+B*log(e*(a+b*x)/(c+d*x)))^2/b-1/10*B*(b*c-a*d)^5*g*i^3*log((b*c-a*d)/(b*(c+d*x)))*(A+B+B*log(e*(a+b*x)/(c+d*x)))/(b^4*d^2)-11/60*B^2*(b*c-a*d)^5*g*i^3*log(c+d*x)/(b^4*d^2)-1/10*B^2*(b*c-a*d)^5*g*i^3*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(b^4*d^2)],
[(c*i+d*i*x)^3*(A+B*log(e*(a+b*x)/(c+d*x)))^2,x,15,5/12*B^2*(b*c-a*d)^3*i^3*x/b^3+1/12*B^2*(b*c-a*d)^2*i^3*(c+d*x)^2/(b^2*d)+5/12*B^2*(b*c-a*d)^4*i^3*log((a+b*x)/(c+d*x))/(b^4*d)-1/2*B*(b*c-a*d)^3*i^3*(a+b*x)*(A+B*log(e*(a+b*x)/(c+d*x)))/b^4-1/4*B*(b*c-a*d)^2*i^3*(c+d*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))/(b^2*d)-1/6*B*(b*c-a*d)*i^3*(c+d*x)^3*(A+B*log(e*(a+b*x)/(c+d*x)))/(b*d)+1/4*i^3*(c+d*x)^4*(A+B*log(e*(a+b*x)/(c+d*x)))^2/d+11/12*B^2*(b*c-a*d)^4*i^3*log(c+d*x)/(b^4*d)+1/2*B*(b*c-a*d)^4*i^3*(A+B*log(e*(a+b*x)/(c+d*x)))*log(1-b*(c+d*x)/(d*(a+b*x)))/(b^4*d)-1/2*B^2*(b*c-a*d)^4*i^3*polylog(2,b*(c+d*x)/(d*(a+b*x)))/(b^4*d)],
[(c*i+d*i*x)^3*(A+B*log(e*(a+b*x)/(c+d*x)))^2/(a*g+b*g*x),x,26,1/3*B^2*d*(b*c-a*d)^2*i^3*x/(b^3*g)+1/3*B^2*(b*c-a*d)^3*i^3*log((a+b*x)/(c+d*x))/(b^4*g)-5/3*B*d*(b*c-a*d)^2*i^3*(a+b*x)*(A+B*log(e*(a+b*x)/(c+d*x)))/(b^4*g)-1/3*B*(b*c-a*d)*i^3*(c+d*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))/(b^2*g)+2*B*(b*c-a*d)^3*i^3*log((b*c-a*d)/(b*(c+d*x)))*(A+B*log(e*(a+b*x)/(c+d*x)))/(b^4*g)+d*(b*c-a*d)^2*i^3*(a+b*x)*(A+B*log(e*(a+b*x)/(c+d*x)))^2/(b^4*g)+1/2*(b*c-a*d)*i^3*(c+d*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))^2/(b^2*g)+1/3*i^3*(c+d*x)^3*(A+B*log(e*(a+b*x)/(c+d*x)))^2/(b*g)+2*B^2*(b*c-a*d)^3*i^3*log(c+d*x)/(b^4*g)+5/3*B*(b*c-a*d)^3*i^3*(A+B*log(e*(a+b*x)/(c+d*x)))*log(1-b*(c+d*x)/(d*(a+b*x)))/(b^4*g)-(b*c-a*d)^3*i^3*(A+B*log(e*(a+b*x)/(c+d*x)))^2*log(1-b*(c+d*x)/(d*(a+b*x)))/(b^4*g)+2*B^2*(b*c-a*d)^3*i^3*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(b^4*g)-5/3*B^2*(b*c-a*d)^3*i^3*polylog(2,b*(c+d*x)/(d*(a+b*x)))/(b^4*g)+2*B*(b*c-a*d)^3*i^3*(A+B*log(e*(a+b*x)/(c+d*x)))*polylog(2,b*(c+d*x)/(d*(a+b*x)))/(b^4*g)+2*B^2*(b*c-a*d)^3*i^3*polylog(3,b*(c+d*x)/(d*(a+b*x)))/(b^4*g)],
[(c*i+d*i*x)^3*(A+B*log(e*(a+b*x)/(c+d*x)))^2/(a*g+b*g*x)^2,x,17,-2*B^2*(b*c-a*d)^2*i^3*(c+d*x)/(b^3*g^2*(a+b*x))-B*d^2*(b*c-a*d)*i^3*(a+b*x)*(A+B*log(e*(a+b*x)/(c+d*x)))/(b^4*g^2)-2*B*(b*c-a*d)^2*i^3*(c+d*x)*(A+B*log(e*(a+b*x)/(c+d*x)))/(b^3*g^2*(a+b*x))+4*B*d*(b*c-a*d)^2*i^3*log((b*c-a*d)/(b*(c+d*x)))*(A+B*log(e*(a+b*x)/(c+d*x)))/(b^4*g^2)+2*d^2*(b*c-a*d)*i^3*(a+b*x)*(A+B*log(e*(a+b*x)/(c+d*x)))^2/(b^4*g^2)-(b*c-a*d)^2*i^3*(c+d*x)*(A+B*log(e*(a+b*x)/(c+d*x)))^2/(b^3*g^2*(a+b*x))+1/2*d*i^3*(c+d*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))^2/(b^2*g^2)+B^2*d*(b*c-a*d)^2*i^3*log(c+d*x)/(b^4*g^2)+B*d*(b*c-a*d)^2*i^3*(A+B*log(e*(a+b*x)/(c+d*x)))*log(1-b*(c+d*x)/(d*(a+b*x)))/(b^4*g^2)-3*d*(b*c-a*d)^2*i^3*(A+B*log(e*(a+b*x)/(c+d*x)))^2*log(1-b*(c+d*x)/(d*(a+b*x)))/(b^4*g^2)+4*B^2*d*(b*c-a*d)^2*i^3*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(b^4*g^2)-B^2*d*(b*c-a*d)^2*i^3*polylog(2,b*(c+d*x)/(d*(a+b*x)))/(b^4*g^2)+6*B*d*(b*c-a*d)^2*i^3*(A+B*log(e*(a+b*x)/(c+d*x)))*polylog(2,b*(c+d*x)/(d*(a+b*x)))/(b^4*g^2)+6*B^2*d*(b*c-a*d)^2*i^3*polylog(3,b*(c+d*x)/(d*(a+b*x)))/(b^4*g^2)],
[(c*i+d*i*x)^3*(A+B*log(e*(a+b*x)/(c+d*x)))^2/(a*g+b*g*x)^3,x,13,-4*B^2*d*(b*c-a*d)*i^3*(c+d*x)/(b^3*g^3*(a+b*x))-1/4*B^2*(b*c-a*d)*i^3*(c+d*x)^2/(b^2*g^3*(a+b*x)^2)-4*B*d*(b*c-a*d)*i^3*(c+d*x)*(A+B*log(e*(a+b*x)/(c+d*x)))/(b^3*g^3*(a+b*x))-1/2*B*(b*c-a*d)*i^3*(c+d*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))/(b^2*g^3*(a+b*x)^2)+2*B*d^2*(b*c-a*d)*i^3*log((b*c-a*d)/(b*(c+d*x)))*(A+B*log(e*(a+b*x)/(c+d*x)))/(b^4*g^3)+d^3*i^3*(a+b*x)*(A+B*log(e*(a+b*x)/(c+d*x)))^2/(b^4*g^3)-2*d*(b*c-a*d)*i^3*(c+d*x)*(A+B*log(e*(a+b*x)/(c+d*x)))^2/(b^3*g^3*(a+b*x))-1/2*(b*c-a*d)*i^3*(c+d*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))^2/(b^2*g^3*(a+b*x)^2)-3*d^2*(b*c-a*d)*i^3*(A+B*log(e*(a+b*x)/(c+d*x)))^2*log(1-b*(c+d*x)/(d*(a+b*x)))/(b^4*g^3)+2*B^2*d^2*(b*c-a*d)*i^3*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(b^4*g^3)+6*B*d^2*(b*c-a*d)*i^3*(A+B*log(e*(a+b*x)/(c+d*x)))*polylog(2,b*(c+d*x)/(d*(a+b*x)))/(b^4*g^3)+6*B^2*d^2*(b*c-a*d)*i^3*polylog(3,b*(c+d*x)/(d*(a+b*x)))/(b^4*g^3)],
[(c*i+d*i*x)^3*(A+B*log(e*(a+b*x)/(c+d*x)))^2/(a*g+b*g*x)^5,x,3,-1/32*B^2*i^3*(c+d*x)^4/((b*c-a*d)*g^5*(a+b*x)^4)-1/8*B*i^3*(c+d*x)^4*(A+B*log(e*(a+b*x)/(c+d*x)))/((b*c-a*d)*g^5*(a+b*x)^4)-1/4*i^3*(c+d*x)^4*(A+B*log(e*(a+b*x)/(c+d*x)))^2/((b*c-a*d)*g^5*(a+b*x)^4)],
[(c*i+d*i*x)^3*(A+B*log(e*(a+b*x)/(c+d*x)))^2/(a*g+b*g*x)^6,x,7,1/32*B^2*d*i^3*(c+d*x)^4/((b*c-a*d)^2*g^6*(a+b*x)^4)-2/125*b*B^2*i^3*(c+d*x)^5/((b*c-a*d)^2*g^6*(a+b*x)^5)+1/8*B*d*i^3*(c+d*x)^4*(A+B*log(e*(a+b*x)/(c+d*x)))/((b*c-a*d)^2*g^6*(a+b*x)^4)-2/25*b*B*i^3*(c+d*x)^5*(A+B*log(e*(a+b*x)/(c+d*x)))/((b*c-a*d)^2*g^6*(a+b*x)^5)+1/4*d*i^3*(c+d*x)^4*(A+B*log(e*(a+b*x)/(c+d*x)))^2/((b*c-a*d)^2*g^6*(a+b*x)^4)-1/5*b*i^3*(c+d*x)^5*(A+B*log(e*(a+b*x)/(c+d*x)))^2/((b*c-a*d)^2*g^6*(a+b*x)^5)],
[(c*i+d*i*x)^3*(A+B*log(e*(a+b*x)/(c+d*x)))^2/(a*g+b*g*x)^7,x,9,-1/32*B^2*d^2*i^3*(c+d*x)^4/((b*c-a*d)^3*g^7*(a+b*x)^4)+4/125*b*B^2*d*i^3*(c+d*x)^5/((b*c-a*d)^3*g^7*(a+b*x)^5)-1/108*b^2*B^2*i^3*(c+d*x)^6/((b*c-a*d)^3*g^7*(a+b*x)^6)-1/8*B*d^2*i^3*(c+d*x)^4*(A+B*log(e*(a+b*x)/(c+d*x)))/((b*c-a*d)^3*g^7*(a+b*x)^4)+4/25*b*B*d*i^3*(c+d*x)^5*(A+B*log(e*(a+b*x)/(c+d*x)))/((b*c-a*d)^3*g^7*(a+b*x)^5)-1/18*b^2*B*i^3*(c+d*x)^6*(A+B*log(e*(a+b*x)/(c+d*x)))/((b*c-a*d)^3*g^7*(a+b*x)^6)-1/4*d^2*i^3*(c+d*x)^4*(A+B*log(e*(a+b*x)/(c+d*x)))^2/((b*c-a*d)^3*g^7*(a+b*x)^4)+2/5*b*d*i^3*(c+d*x)^5*(A+B*log(e*(a+b*x)/(c+d*x)))^2/((b*c-a*d)^3*g^7*(a+b*x)^5)-1/6*b^2*i^3*(c+d*x)^6*(A+B*log(e*(a+b*x)/(c+d*x)))^2/((b*c-a*d)^3*g^7*(a+b*x)^6)],

# q<0
[(a*g+b*g*x)^3*(A+B*log(e*(a+b*x)/(c+d*x)))^2/(c*i+d*i*x),x,25,1/3*b*B^2*(b*c-a*d)^2*g^3*x/(d^3*i)+1/3*B^2*(b*c-a*d)^3*g^3*log((a+b*x)/(c+d*x))/(d^4*i)+7/3*B*(b*c-a*d)^2*g^3*(a+b*x)*(A+B*log(e*(a+b*x)/(c+d*x)))/(d^3*i)-1/3*b^2*B*(b*c-a*d)*g^3*(c+d*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))/(d^4*i)+6*B*(b*c-a*d)^3*g^3*log((b*c-a*d)/(b*(c+d*x)))*(A+B*log(e*(a+b*x)/(c+d*x)))/(d^4*i)+3*(b*c-a*d)^2*g^3*(a+b*x)*(A+B*log(e*(a+b*x)/(c+d*x)))^2/(d^3*i)-3/2*b^2*(b*c-a*d)*g^3*(c+d*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))^2/(d^4*i)+1/3*b^3*g^3*(c+d*x)^3*(A+B*log(e*(a+b*x)/(c+d*x)))^2/(d^4*i)+(b*c-a*d)^3*g^3*log((b*c-a*d)/(b*(c+d*x)))*(A+B*log(e*(a+b*x)/(c+d*x)))^2/(d^4*i)-2*B^2*(b*c-a*d)^3*g^3*log(c+d*x)/(d^4*i)-7/3*B*(b*c-a*d)^3*g^3*(A+B*log(e*(a+b*x)/(c+d*x)))*log(1-b*(c+d*x)/(d*(a+b*x)))/(d^4*i)+6*B^2*(b*c-a*d)^3*g^3*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(d^4*i)+2*B*(b*c-a*d)^3*g^3*(A+B*log(e*(a+b*x)/(c+d*x)))*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(d^4*i)+7/3*B^2*(b*c-a*d)^3*g^3*polylog(2,b*(c+d*x)/(d*(a+b*x)))/(d^4*i)-2*B^2*(b*c-a*d)^3*g^3*polylog(3,d*(a+b*x)/(b*(c+d*x)))/(d^4*i)],
[(a*g+b*g*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))^2/(c*i+d*i*x),x,15,-B*(b*c-a*d)*g^2*(a+b*x)*(A+B*log(e*(a+b*x)/(c+d*x)))/(d^2*i)-4*B*(b*c-a*d)^2*g^2*log((b*c-a*d)/(b*(c+d*x)))*(A+B*log(e*(a+b*x)/(c+d*x)))/(d^3*i)-2*(b*c-a*d)*g^2*(a+b*x)*(A+B*log(e*(a+b*x)/(c+d*x)))^2/(d^2*i)+1/2*b^2*g^2*(c+d*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))^2/(d^3*i)-(b*c-a*d)^2*g^2*log((b*c-a*d)/(b*(c+d*x)))*(A+B*log(e*(a+b*x)/(c+d*x)))^2/(d^3*i)+B^2*(b*c-a*d)^2*g^2*log(c+d*x)/(d^3*i)+B*(b*c-a*d)^2*g^2*(A+B*log(e*(a+b*x)/(c+d*x)))*log(1-b*(c+d*x)/(d*(a+b*x)))/(d^3*i)-4*B^2*(b*c-a*d)^2*g^2*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(d^3*i)-2*B*(b*c-a*d)^2*g^2*(A+B*log(e*(a+b*x)/(c+d*x)))*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(d^3*i)-B^2*(b*c-a*d)^2*g^2*polylog(2,b*(c+d*x)/(d*(a+b*x)))/(d^3*i)+2*B^2*(b*c-a*d)^2*g^2*polylog(3,d*(a+b*x)/(b*(c+d*x)))/(d^3*i)],
[(a*g+b*g*x)*(A+B*log(e*(a+b*x)/(c+d*x)))^2/(c*i+d*i*x),x,9,2*B*(b*c-a*d)*g*log((b*c-a*d)/(b*(c+d*x)))*(A+B*log(e*(a+b*x)/(c+d*x)))/(d^2*i)+g*(a+b*x)*(A+B*log(e*(a+b*x)/(c+d*x)))^2/(d*i)+(b*c-a*d)*g*log((b*c-a*d)/(b*(c+d*x)))*(A+B*log(e*(a+b*x)/(c+d*x)))^2/(d^2*i)+2*B^2*(b*c-a*d)*g*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(d^2*i)+2*B*(b*c-a*d)*g*(A+B*log(e*(a+b*x)/(c+d*x)))*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(d^2*i)-2*B^2*(b*c-a*d)*g*polylog(3,d*(a+b*x)/(b*(c+d*x)))/(d^2*i)],
[(A+B*log(e*(a+b*x)/(c+d*x)))^2/(c*i+d*i*x),x,4,-log((b*c-a*d)/(b*(c+d*x)))*(A+B*log(e*(a+b*x)/(c+d*x)))^2/(d*i)-2*B*(A+B*log(e*(a+b*x)/(c+d*x)))*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(d*i)+2*B^2*polylog(3,d*(a+b*x)/(b*(c+d*x)))/(d*i)],
[(A+B*log(e*(a+b*x)/(c+d*x)))^2/((a*g+b*g*x)*(c*i+d*i*x)),x,3,1/3*(A+B*log(e*(a+b*x)/(c+d*x)))^3/(B*(b*c-a*d)*g*i)],
[(A+B*log(e*(a+b*x)/(c+d*x)))^2/((a*g+b*g*x)^2*(c*i+d*i*x)),x,7,-2*b*B^2*(c+d*x)/((b*c-a*d)^2*g^2*i*(a+b*x))-2*b*B*(c+d*x)*(A+B*log(e*(a+b*x)/(c+d*x)))/((b*c-a*d)^2*g^2*i*(a+b*x))-b*(c+d*x)*(A+B*log(e*(a+b*x)/(c+d*x)))^2/((b*c-a*d)^2*g^2*i*(a+b*x))-1/3*d*(A+B*log(e*(a+b*x)/(c+d*x)))^3/(B*(b*c-a*d)^2*g^2*i)],
[(A+B*log(e*(a+b*x)/(c+d*x)))^2/((a*g+b*g*x)^3*(c*i+d*i*x)),x,9,4*b*B^2*d*(c+d*x)/((b*c-a*d)^3*g^3*i*(a+b*x))-1/4*b^2*B^2*(c+d*x)^2/((b*c-a*d)^3*g^3*i*(a+b*x)^2)+4*b*B*d*(c+d*x)*(A+B*log(e*(a+b*x)/(c+d*x)))/((b*c-a*d)^3*g^3*i*(a+b*x))-1/2*b^2*B*(c+d*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))/((b*c-a*d)^3*g^3*i*(a+b*x)^2)+2*b*d*(c+d*x)*(A+B*log(e*(a+b*x)/(c+d*x)))^2/((b*c-a*d)^3*g^3*i*(a+b*x))-1/2*b^2*(c+d*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))^2/((b*c-a*d)^3*g^3*i*(a+b*x)^2)+1/3*d^2*(A+B*log(e*(a+b*x)/(c+d*x)))^3/(B*(b*c-a*d)^3*g^3*i)],
[(A+B*log(e*(a+b*x)/(c+d*x)))^2/((a*g+b*g*x)^4*(c*i+d*i*x)),x,11,-6*b*B^2*d^2*(c+d*x)/((b*c-a*d)^4*g^4*i*(a+b*x))+3/4*b^2*B^2*d*(c+d*x)^2/((b*c-a*d)^4*g^4*i*(a+b*x)^2)-2/27*b^3*B^2*(c+d*x)^3/((b*c-a*d)^4*g^4*i*(a+b*x)^3)-6*b*B*d^2*(c+d*x)*(A+B*log(e*(a+b*x)/(c+d*x)))/((b*c-a*d)^4*g^4*i*(a+b*x))+3/2*b^2*B*d*(c+d*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))/((b*c-a*d)^4*g^4*i*(a+b*x)^2)-2/9*b^3*B*(c+d*x)^3*(A+B*log(e*(a+b*x)/(c+d*x)))/((b*c-a*d)^4*g^4*i*(a+b*x)^3)-3*b*d^2*(c+d*x)*(A+B*log(e*(a+b*x)/(c+d*x)))^2/((b*c-a*d)^4*g^4*i*(a+b*x))+3/2*b^2*d*(c+d*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))^2/((b*c-a*d)^4*g^4*i*(a+b*x)^2)-1/3*b^3*(c+d*x)^3*(A+B*log(e*(a+b*x)/(c+d*x)))^2/((b*c-a*d)^4*g^4*i*(a+b*x)^3)-1/3*d^3*(A+B*log(e*(a+b*x)/(c+d*x)))^3/(B*(b*c-a*d)^4*g^4*i)],
[(a*g+b*g*x)^3*(A+B*log(e*(a+b*x)/(c+d*x)))^2/(c*i+d*i*x)^2,x,18,2*A*B*(b*c-a*d)^2*g^3*(a+b*x)/(d^3*i^2*(c+d*x))-2*B^2*(b*c-a*d)^2*g^3*(a+b*x)/(d^3*i^2*(c+d*x))+2*B^2*(b*c-a*d)^2*g^3*(a+b*x)*log(e*(a+b*x)/(c+d*x))/(d^3*i^2*(c+d*x))-b*B*(b*c-a*d)*g^3*(a+b*x)*(A+B*log(e*(a+b*x)/(c+d*x)))/(d^3*i^2)-6*b*B*(b*c-a*d)^2*g^3*log((b*c-a*d)/(b*(c+d*x)))*(A+B*log(e*(a+b*x)/(c+d*x)))/(d^4*i^2)-3*b*(b*c-a*d)*g^3*(a+b*x)*(A+B*log(e*(a+b*x)/(c+d*x)))^2/(d^3*i^2)-(b*c-a*d)^2*g^3*(a+b*x)*(A+B*log(e*(a+b*x)/(c+d*x)))^2/(d^3*i^2*(c+d*x))+1/2*b^3*g^3*(c+d*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))^2/(d^4*i^2)-3*b*(b*c-a*d)^2*g^3*log((b*c-a*d)/(b*(c+d*x)))*(A+B*log(e*(a+b*x)/(c+d*x)))^2/(d^4*i^2)+b*B^2*(b*c-a*d)^2*g^3*log(c+d*x)/(d^4*i^2)+b*B*(b*c-a*d)^2*g^3*(A+B*log(e*(a+b*x)/(c+d*x)))*log(1-b*(c+d*x)/(d*(a+b*x)))/(d^4*i^2)-6*b*B^2*(b*c-a*d)^2*g^3*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(d^4*i^2)-6*b*B*(b*c-a*d)^2*g^3*(A+B*log(e*(a+b*x)/(c+d*x)))*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(d^4*i^2)-b*B^2*(b*c-a*d)^2*g^3*polylog(2,b*(c+d*x)/(d*(a+b*x)))/(d^4*i^2)+6*b*B^2*(b*c-a*d)^2*g^3*polylog(3,d*(a+b*x)/(b*(c+d*x)))/(d^4*i^2)],
[(a*g+b*g*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))^2/(c*i+d*i*x)^2,x,12,-2*A*B*(b*c-a*d)*g^2*(a+b*x)/(d^2*i^2*(c+d*x))+2*B^2*(b*c-a*d)*g^2*(a+b*x)/(d^2*i^2*(c+d*x))-2*B^2*(b*c-a*d)*g^2*(a+b*x)*log(e*(a+b*x)/(c+d*x))/(d^2*i^2*(c+d*x))+2*b*B*(b*c-a*d)*g^2*log((b*c-a*d)/(b*(c+d*x)))*(A+B*log(e*(a+b*x)/(c+d*x)))/(d^3*i^2)+b*g^2*(a+b*x)*(A+B*log(e*(a+b*x)/(c+d*x)))^2/(d^2*i^2)+(b*c-a*d)*g^2*(a+b*x)*(A+B*log(e*(a+b*x)/(c+d*x)))^2/(d^2*i^2*(c+d*x))+2*b*(b*c-a*d)*g^2*log((b*c-a*d)/(b*(c+d*x)))*(A+B*log(e*(a+b*x)/(c+d*x)))^2/(d^3*i^2)+2*b*B^2*(b*c-a*d)*g^2*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(d^3*i^2)+4*b*B*(b*c-a*d)*g^2*(A+B*log(e*(a+b*x)/(c+d*x)))*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(d^3*i^2)-4*b*B^2*(b*c-a*d)*g^2*polylog(3,d*(a+b*x)/(b*(c+d*x)))/(d^3*i^2)],
[(a*g+b*g*x)*(A+B*log(e*(a+b*x)/(c+d*x)))^2/(c*i+d*i*x)^2,x,9,2*A*B*g*(a+b*x)/(d*i^2*(c+d*x))-2*B^2*g*(a+b*x)/(d*i^2*(c+d*x))+2*B^2*g*(a+b*x)*log(e*(a+b*x)/(c+d*x))/(d*i^2*(c+d*x))-g*(a+b*x)*(A+B*log(e*(a+b*x)/(c+d*x)))^2/(d*i^2*(c+d*x))-b*g*log((b*c-a*d)/(b*(c+d*x)))*(A+B*log(e*(a+b*x)/(c+d*x)))^2/(d^2*i^2)-2*b*B*g*(A+B*log(e*(a+b*x)/(c+d*x)))*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(d^2*i^2)+2*b*B^2*g*polylog(3,d*(a+b*x)/(b*(c+d*x)))/(d^2*i^2)],
[(A+B*log(e*(a+b*x)/(c+d*x)))^2/(c*i+d*i*x)^2,x,4,-2*A*B*(a+b*x)/((b*c-a*d)*i^2*(c+d*x))+2*B^2*(a+b*x)/((b*c-a*d)*i^2*(c+d*x))-2*B^2*(a+b*x)*log(e*(a+b*x)/(c+d*x))/((b*c-a*d)*i^2*(c+d*x))+(a+b*x)*(A+B*log(e*(a+b*x)/(c+d*x)))^2/((b*c-a*d)*i^2*(c+d*x))],
[(A+B*log(e*(a+b*x)/(c+d*x)))^2/((a*g+b*g*x)*(c*i+d*i*x)^2),x,7,2*A*B*d*(a+b*x)/((b*c-a*d)^2*g*i^2*(c+d*x))-2*B^2*d*(a+b*x)/((b*c-a*d)^2*g*i^2*(c+d*x))+2*B^2*d*(a+b*x)*log(e*(a+b*x)/(c+d*x))/((b*c-a*d)^2*g*i^2*(c+d*x))-d*(a+b*x)*(A+B*log(e*(a+b*x)/(c+d*x)))^2/((b*c-a*d)^2*g*i^2*(c+d*x))+1/3*b*(A+B*log(e*(a+b*x)/(c+d*x)))^3/(B*(b*c-a*d)^2*g*i^2)],
[(A+B*log(e*(a+b*x)/(c+d*x)))^2/((a*g+b*g*x)^2*(c*i+d*i*x)^2),x,10,-2*A*B*d^2*(a+b*x)/((b*c-a*d)^3*g^2*i^2*(c+d*x))+2*B^2*d^2*(a+b*x)/((b*c-a*d)^3*g^2*i^2*(c+d*x))-2*b^2*B^2*(c+d*x)/((b*c-a*d)^3*g^2*i^2*(a+b*x))-2*B^2*d^2*(a+b*x)*log(e*(a+b*x)/(c+d*x))/((b*c-a*d)^3*g^2*i^2*(c+d*x))-2*b^2*B*(c+d*x)*(A+B*log(e*(a+b*x)/(c+d*x)))/((b*c-a*d)^3*g^2*i^2*(a+b*x))+d^2*(a+b*x)*(A+B*log(e*(a+b*x)/(c+d*x)))^2/((b*c-a*d)^3*g^2*i^2*(c+d*x))-b^2*(c+d*x)*(A+B*log(e*(a+b*x)/(c+d*x)))^2/((b*c-a*d)^3*g^2*i^2*(a+b*x))-2/3*b*d*(A+B*log(e*(a+b*x)/(c+d*x)))^3/(B*(b*c-a*d)^3*g^2*i^2)],
[(A+B*log(e*(a+b*x)/(c+d*x)))^2/((a*g+b*g*x)^3*(c*i+d*i*x)^2),x,12,2*A*B*d^3*(a+b*x)/((b*c-a*d)^4*g^3*i^2*(c+d*x))-2*B^2*d^3*(a+b*x)/((b*c-a*d)^4*g^3*i^2*(c+d*x))+6*b^2*B^2*d*(c+d*x)/((b*c-a*d)^4*g^3*i^2*(a+b*x))-1/4*b^3*B^2*(c+d*x)^2/((b*c-a*d)^4*g^3*i^2*(a+b*x)^2)+2*B^2*d^3*(a+b*x)*log(e*(a+b*x)/(c+d*x))/((b*c-a*d)^4*g^3*i^2*(c+d*x))+6*b^2*B*d*(c+d*x)*(A+B*log(e*(a+b*x)/(c+d*x)))/((b*c-a*d)^4*g^3*i^2*(a+b*x))-1/2*b^3*B*(c+d*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))/((b*c-a*d)^4*g^3*i^2*(a+b*x)^2)-d^3*(a+b*x)*(A+B*log(e*(a+b*x)/(c+d*x)))^2/((b*c-a*d)^4*g^3*i^2*(c+d*x))+3*b^2*d*(c+d*x)*(A+B*log(e*(a+b*x)/(c+d*x)))^2/((b*c-a*d)^4*g^3*i^2*(a+b*x))-1/2*b^3*(c+d*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))^2/((b*c-a*d)^4*g^3*i^2*(a+b*x)^2)+b*d^2*(A+B*log(e*(a+b*x)/(c+d*x)))^3/(B*(b*c-a*d)^4*g^3*i^2)],
[(A+B*log(e*(a+b*x)/(c+d*x)))^2/((a*g+b*g*x)^4*(c*i+d*i*x)^2),x,14,-2*A*B*d^4*(a+b*x)/((b*c-a*d)^5*g^4*i^2*(c+d*x))+2*B^2*d^4*(a+b*x)/((b*c-a*d)^5*g^4*i^2*(c+d*x))-12*b^2*B^2*d^2*(c+d*x)/((b*c-a*d)^5*g^4*i^2*(a+b*x))+b^3*B^2*d*(c+d*x)^2/((b*c-a*d)^5*g^4*i^2*(a+b*x)^2)-2/27*b^4*B^2*(c+d*x)^3/((b*c-a*d)^5*g^4*i^2*(a+b*x)^3)-2*B^2*d^4*(a+b*x)*log(e*(a+b*x)/(c+d*x))/((b*c-a*d)^5*g^4*i^2*(c+d*x))-12*b^2*B*d^2*(c+d*x)*(A+B*log(e*(a+b*x)/(c+d*x)))/((b*c-a*d)^5*g^4*i^2*(a+b*x))+2*b^3*B*d*(c+d*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))/((b*c-a*d)^5*g^4*i^2*(a+b*x)^2)-2/9*b^4*B*(c+d*x)^3*(A+B*log(e*(a+b*x)/(c+d*x)))/((b*c-a*d)^5*g^4*i^2*(a+b*x)^3)+d^4*(a+b*x)*(A+B*log(e*(a+b*x)/(c+d*x)))^2/((b*c-a*d)^5*g^4*i^2*(c+d*x))-6*b^2*d^2*(c+d*x)*(A+B*log(e*(a+b*x)/(c+d*x)))^2/((b*c-a*d)^5*g^4*i^2*(a+b*x))+2*b^3*d*(c+d*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))^2/((b*c-a*d)^5*g^4*i^2*(a+b*x)^2)-1/3*b^4*(c+d*x)^3*(A+B*log(e*(a+b*x)/(c+d*x)))^2/((b*c-a*d)^5*g^4*i^2*(a+b*x)^3)-4/3*b*d^3*(A+B*log(e*(a+b*x)/(c+d*x)))^3/(B*(b*c-a*d)^5*g^4*i^2)],
[(a*g+b*g*x)^3*(A+B*log(e*(a+b*x)/(c+d*x)))^2/(c*i+d*i*x)^3,x,14,1/4*B^2*(b*c-a*d)*g^3*(a+b*x)^2/(d^2*i^3*(c+d*x)^2)-4*A*b*B*(b*c-a*d)*g^3*(a+b*x)/(d^3*i^3*(c+d*x))+4*b*B^2*(b*c-a*d)*g^3*(a+b*x)/(d^3*i^3*(c+d*x))-4*b*B^2*(b*c-a*d)*g^3*(a+b*x)*log(e*(a+b*x)/(c+d*x))/(d^3*i^3*(c+d*x))-1/2*B*(b*c-a*d)*g^3*(a+b*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))/(d^2*i^3*(c+d*x)^2)+2*b^2*B*(b*c-a*d)*g^3*log((b*c-a*d)/(b*(c+d*x)))*(A+B*log(e*(a+b*x)/(c+d*x)))/(d^4*i^3)+b^2*g^3*(a+b*x)*(A+B*log(e*(a+b*x)/(c+d*x)))^2/(d^3*i^3)+1/2*(b*c-a*d)*g^3*(a+b*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))^2/(d^2*i^3*(c+d*x)^2)+2*b*(b*c-a*d)*g^3*(a+b*x)*(A+B*log(e*(a+b*x)/(c+d*x)))^2/(d^3*i^3*(c+d*x))+3*b^2*(b*c-a*d)*g^3*log((b*c-a*d)/(b*(c+d*x)))*(A+B*log(e*(a+b*x)/(c+d*x)))^2/(d^4*i^3)+2*b^2*B^2*(b*c-a*d)*g^3*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(d^4*i^3)+6*b^2*B*(b*c-a*d)*g^3*(A+B*log(e*(a+b*x)/(c+d*x)))*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(d^4*i^3)-6*b^2*B^2*(b*c-a*d)*g^3*polylog(3,d*(a+b*x)/(b*(c+d*x)))/(d^4*i^3)],
[(a*g+b*g*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))^2/(c*i+d*i*x)^3,x,11,-1/4*B^2*g^2*(a+b*x)^2/(d*i^3*(c+d*x)^2)+2*A*b*B*g^2*(a+b*x)/(d^2*i^3*(c+d*x))-2*b*B^2*g^2*(a+b*x)/(d^2*i^3*(c+d*x))+2*b*B^2*g^2*(a+b*x)*log(e*(a+b*x)/(c+d*x))/(d^2*i^3*(c+d*x))+1/2*B*g^2*(a+b*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))/(d*i^3*(c+d*x)^2)-1/2*g^2*(a+b*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))^2/(d*i^3*(c+d*x)^2)-b*g^2*(a+b*x)*(A+B*log(e*(a+b*x)/(c+d*x)))^2/(d^2*i^3*(c+d*x))-b^2*g^2*log((b*c-a*d)/(b*(c+d*x)))*(A+B*log(e*(a+b*x)/(c+d*x)))^2/(d^3*i^3)-2*b^2*B*g^2*(A+B*log(e*(a+b*x)/(c+d*x)))*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(d^3*i^3)+2*b^2*B^2*g^2*polylog(3,d*(a+b*x)/(b*(c+d*x)))/(d^3*i^3)],
[(a*g+b*g*x)*(A+B*log(e*(a+b*x)/(c+d*x)))^2/(c*i+d*i*x)^3,x,3,1/4*B^2*g*(a+b*x)^2/((b*c-a*d)*i^3*(c+d*x)^2)-1/2*B*g*(a+b*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))/((b*c-a*d)*i^3*(c+d*x)^2)+1/2*g*(a+b*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))^2/((b*c-a*d)*i^3*(c+d*x)^2)],
[(A+B*log(e*(a+b*x)/(c+d*x)))^2/(c*i+d*i*x)^3,x,8,-1/4*B^2*d*(a+b*x)^2/((b*c-a*d)^2*i^3*(c+d*x)^2)-2*A*b*B*(a+b*x)/((b*c-a*d)^2*i^3*(c+d*x))+2*b*B^2*(a+b*x)/((b*c-a*d)^2*i^3*(c+d*x))-2*b*B^2*(a+b*x)*log(e*(a+b*x)/(c+d*x))/((b*c-a*d)^2*i^3*(c+d*x))+1/2*B*d*(a+b*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))/((b*c-a*d)^2*i^3*(c+d*x)^2)-1/2*d*(a+b*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))^2/((b*c-a*d)^2*i^3*(c+d*x)^2)+b*(a+b*x)*(A+B*log(e*(a+b*x)/(c+d*x)))^2/((b*c-a*d)^2*i^3*(c+d*x))],
[(A+B*log(e*(a+b*x)/(c+d*x)))^2/((a*g+b*g*x)*(c*i+d*i*x)^3),x,15,1/4*B^2*d^2*(a+b*x)^2/((b*c-a*d)^3*g*i^3*(c+d*x)^2)+4*A*b*B*d*(a+b*x)/((b*c-a*d)^3*g*i^3*(c+d*x))-4*b*B^2*d*(a+b*x)/((b*c-a*d)^3*g*i^3*(c+d*x))+4*b*B^2*d*(a+b*x)*log(e*(a+b*x)/(c+d*x))/((b*c-a*d)^3*g*i^3*(c+d*x))-1/2*B*d^2*(a+b*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))/((b*c-a*d)^3*g*i^3*(c+d*x)^2)+1/2*d^2*(a+b*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))^2/((b*c-a*d)^3*g*i^3*(c+d*x)^2)-2*b*d*(a+b*x)*(A+B*log(e*(a+b*x)/(c+d*x)))^2/((b*c-a*d)^3*g*i^3*(c+d*x))+1/3*b^2*(A+B*log(e*(a+b*x)/(c+d*x)))^3/(B*(b*c-a*d)^3*g*i^3)],
[(A+B*log(e*(a+b*x)/(c+d*x)))^2/((a*g+b*g*x)^2*(c*i+d*i*x)^3),x,12,-1/4*B^2*d^3*(a+b*x)^2/((b*c-a*d)^4*g^2*i^3*(c+d*x)^2)-6*A*b*B*d^2*(a+b*x)/((b*c-a*d)^4*g^2*i^3*(c+d*x))+6*b*B^2*d^2*(a+b*x)/((b*c-a*d)^4*g^2*i^3*(c+d*x))-2*b^3*B^2*(c+d*x)/((b*c-a*d)^4*g^2*i^3*(a+b*x))-6*b*B^2*d^2*(a+b*x)*log(e*(a+b*x)/(c+d*x))/((b*c-a*d)^4*g^2*i^3*(c+d*x))+1/2*B*d^3*(a+b*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))/((b*c-a*d)^4*g^2*i^3*(c+d*x)^2)-2*b^3*B*(c+d*x)*(A+B*log(e*(a+b*x)/(c+d*x)))/((b*c-a*d)^4*g^2*i^3*(a+b*x))-1/2*d^3*(a+b*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))^2/((b*c-a*d)^4*g^2*i^3*(c+d*x)^2)+3*b*d^2*(a+b*x)*(A+B*log(e*(a+b*x)/(c+d*x)))^2/((b*c-a*d)^4*g^2*i^3*(c+d*x))-b^3*(c+d*x)*(A+B*log(e*(a+b*x)/(c+d*x)))^2/((b*c-a*d)^4*g^2*i^3*(a+b*x))-b^2*d*(A+B*log(e*(a+b*x)/(c+d*x)))^3/(B*(b*c-a*d)^4*g^2*i^3)],
[(A+B*log(e*(a+b*x)/(c+d*x)))^2/((a*g+b*g*x)^3*(c*i+d*i*x)^3),x,14,1/4*B^2*d^4*(a+b*x)^2/((b*c-a*d)^5*g^3*i^3*(c+d*x)^2)+8*A*b*B*d^3*(a+b*x)/((b*c-a*d)^5*g^3*i^3*(c+d*x))-8*b*B^2*d^3*(a+b*x)/((b*c-a*d)^5*g^3*i^3*(c+d*x))+8*b^3*B^2*d*(c+d*x)/((b*c-a*d)^5*g^3*i^3*(a+b*x))-1/4*b^4*B^2*(c+d*x)^2/((b*c-a*d)^5*g^3*i^3*(a+b*x)^2)+8*b*B^2*d^3*(a+b*x)*log(e*(a+b*x)/(c+d*x))/((b*c-a*d)^5*g^3*i^3*(c+d*x))-1/2*B*d^4*(a+b*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))/((b*c-a*d)^5*g^3*i^3*(c+d*x)^2)+8*b^3*B*d*(c+d*x)*(A+B*log(e*(a+b*x)/(c+d*x)))/((b*c-a*d)^5*g^3*i^3*(a+b*x))-1/2*b^4*B*(c+d*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))/((b*c-a*d)^5*g^3*i^3*(a+b*x)^2)+1/2*d^4*(a+b*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))^2/((b*c-a*d)^5*g^3*i^3*(c+d*x)^2)-4*b*d^3*(a+b*x)*(A+B*log(e*(a+b*x)/(c+d*x)))^2/((b*c-a*d)^5*g^3*i^3*(c+d*x))+4*b^3*d*(c+d*x)*(A+B*log(e*(a+b*x)/(c+d*x)))^2/((b*c-a*d)^5*g^3*i^3*(a+b*x))-1/2*b^4*(c+d*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))^2/((b*c-a*d)^5*g^3*i^3*(a+b*x)^2)+2*b^2*d^2*(A+B*log(e*(a+b*x)/(c+d*x)))^3/(B*(b*c-a*d)^5*g^3*i^3)],
[(A+B*log(e*(a+b*x)/(c+d*x)))^2/((a*g+b*g*x)^4*(c*i+d*i*x)^3),x,16,-1/4*B^2*d^5*(a+b*x)^2/((b*c-a*d)^6*g^4*i^3*(c+d*x)^2)-10*A*b*B*d^4*(a+b*x)/((b*c-a*d)^6*g^4*i^3*(c+d*x))+10*b*B^2*d^4*(a+b*x)/((b*c-a*d)^6*g^4*i^3*(c+d*x))-20*b^3*B^2*d^2*(c+d*x)/((b*c-a*d)^6*g^4*i^3*(a+b*x))+5/4*b^4*B^2*d*(c+d*x)^2/((b*c-a*d)^6*g^4*i^3*(a+b*x)^2)-2/27*b^5*B^2*(c+d*x)^3/((b*c-a*d)^6*g^4*i^3*(a+b*x)^3)-10*b*B^2*d^4*(a+b*x)*log(e*(a+b*x)/(c+d*x))/((b*c-a*d)^6*g^4*i^3*(c+d*x))+1/2*B*d^5*(a+b*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))/((b*c-a*d)^6*g^4*i^3*(c+d*x)^2)-20*b^3*B*d^2*(c+d*x)*(A+B*log(e*(a+b*x)/(c+d*x)))/((b*c-a*d)^6*g^4*i^3*(a+b*x))+5/2*b^4*B*d*(c+d*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))/((b*c-a*d)^6*g^4*i^3*(a+b*x)^2)-2/9*b^5*B*(c+d*x)^3*(A+B*log(e*(a+b*x)/(c+d*x)))/((b*c-a*d)^6*g^4*i^3*(a+b*x)^3)-1/2*d^5*(a+b*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))^2/((b*c-a*d)^6*g^4*i^3*(c+d*x)^2)+5*b*d^4*(a+b*x)*(A+B*log(e*(a+b*x)/(c+d*x)))^2/((b*c-a*d)^6*g^4*i^3*(c+d*x))-10*b^3*d^2*(c+d*x)*(A+B*log(e*(a+b*x)/(c+d*x)))^2/((b*c-a*d)^6*g^4*i^3*(a+b*x))+5/2*b^4*d*(c+d*x)^2*(A+B*log(e*(a+b*x)/(c+d*x)))^2/((b*c-a*d)^6*g^4*i^3*(a+b*x)^2)-1/3*b^5*(c+d*x)^3*(A+B*log(e*(a+b*x)/(c+d*x)))^2/((b*c-a*d)^6*g^4*i^3*(a+b*x)^3)-10/3*b^2*d^3*(A+B*log(e*(a+b*x)/(c+d*x)))^3/(B*(b*c-a*d)^6*g^4*i^3)],

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

# q>0
[(a*g+b*g*x)^3*(c*i+d*i*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n)),x,5,-1/20*B*(b*c-a*d)^4*g^3*i*n*x/(b*d^3)+1/40*B*(b*c-a*d)^3*g^3*i*n*(a+b*x)^2/(b^2*d^2)-1/60*B*(b*c-a*d)^2*g^3*i*n*(a+b*x)^3/(b^2*d)+1/5*g^3*i*(a+b*x)^4*(c+d*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/b+1/20*(b*c-a*d)*g^3*i*(a+b*x)^4*(A-B*n+B*log(e*((a+b*x)/(c+d*x))^n))/b^2+1/20*B*(b*c-a*d)^5*g^3*i*n*log(c+d*x)/(b^2*d^4)],
[(a*g+b*g*x)^2*(c*i+d*i*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n)),x,5,1/12*B*(b*c-a*d)^3*g^2*i*n*x/(b*d^2)-1/24*B*(b*c-a*d)^2*g^2*i*n*(a+b*x)^2/(b^2*d)+1/4*g^2*i*(a+b*x)^3*(c+d*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/b+1/12*(b*c-a*d)*g^2*i*(a+b*x)^3*(A-B*n+B*log(e*((a+b*x)/(c+d*x))^n))/b^2-1/12*B*(b*c-a*d)^4*g^2*i*n*log(c+d*x)/(b^2*d^3)],
[(a*g+b*g*x)*(c*i+d*i*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n)),x,5,-1/6*B*(b*c-a*d)^2*g*i*n*x/(b*d)+1/3*g*i*(a+b*x)^2*(c+d*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/b+1/6*(b*c-a*d)*g*i*(a+b*x)^2*(A-B*n+B*log(e*((a+b*x)/(c+d*x))^n))/b^2+1/6*B*(b*c-a*d)^3*g*i*n*log(c+d*x)/(b^2*d^2)],
[(c*i+d*i*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n)),x,4,-1/2*B*(b*c-a*d)*i*n*x/b-1/2*B*(b*c-a*d)^2*i*n*log(a+b*x)/(b^2*d)+1/2*i*(c+d*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))/d],
[(c*i+d*i*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(a*g+b*g*x),x,6,i*(c+d*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(b*g)-(b*c-a*d)*i*log((-b*c+a*d)/(d*(a+b*x)))*(A-B*n+B*log(e*((a+b*x)/(c+d*x))^n))/(b^2*g)+B*(b*c-a*d)*i*n*polylog(2,1+(b*c-a*d)/(d*(a+b*x)))/(b^2*g)],
[(c*i+d*i*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(a*g+b*g*x)^2,x,5,-B*i*n*(c+d*x)/(b*g^2*(a+b*x))-i*(c+d*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(b*g^2*(a+b*x))-d*i*(A+B*log(e*((a+b*x)/(c+d*x))^n))*log(1-b*(c+d*x)/(d*(a+b*x)))/(b^2*g^2)+B*d*i*n*polylog(2,b*(c+d*x)/(d*(a+b*x)))/(b^2*g^2)],
[(c*i+d*i*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(a*g+b*g*x)^3,x,2,-1/4*B*i*n*(c+d*x)^2/((b*c-a*d)*g^3*(a+b*x)^2)-1/2*i*(c+d*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)*g^3*(a+b*x)^2)],
[(c*i+d*i*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(a*g+b*g*x)^4,x,5,1/4*B*d*i*n*(c+d*x)^2/((b*c-a*d)^2*g^4*(a+b*x)^2)-1/9*b*B*i*n*(c+d*x)^3/((b*c-a*d)^2*g^4*(a+b*x)^3)+1/2*d*i*(c+d*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)^2*g^4*(a+b*x)^2)-1/3*b*i*(c+d*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)^2*g^4*(a+b*x)^3)],
[(c*i+d*i*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(a*g+b*g*x)^5,x,5,-1/4*B*d^2*i*n*(c+d*x)^2/((b*c-a*d)^3*g^5*(a+b*x)^2)+2/9*b*B*d*i*n*(c+d*x)^3/((b*c-a*d)^3*g^5*(a+b*x)^3)-1/16*b^2*B*i*n*(c+d*x)^4/((b*c-a*d)^3*g^5*(a+b*x)^4)-1/2*d^2*i*(c+d*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)^3*g^5*(a+b*x)^2)+2/3*b*d*i*(c+d*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)^3*g^5*(a+b*x)^3)-1/4*b^2*i*(c+d*x)^4*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)^3*g^5*(a+b*x)^4)],
[(a*g+b*g*x)^3*(c*i+d*i*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n)),x,5,1/60*B*(b*c-a*d)^5*g^3*i^2*n*x/(b^2*d^3)+1/120*B*(b*c-a*d)^4*g^3*i^2*n*(c+d*x)^2/(b*d^4)-19/180*B*(b*c-a*d)^3*g^3*i^2*n*(c+d*x)^3/d^4+13/120*b*B*(b*c-a*d)^2*g^3*i^2*n*(c+d*x)^4/d^4-1/30*b^2*B*(b*c-a*d)*g^3*i^2*n*(c+d*x)^5/d^4-1/3*(b*c-a*d)^3*g^3*i^2*(c+d*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))/d^4+3/4*b*(b*c-a*d)^2*g^3*i^2*(c+d*x)^4*(A+B*log(e*((a+b*x)/(c+d*x))^n))/d^4-3/5*b^2*(b*c-a*d)*g^3*i^2*(c+d*x)^5*(A+B*log(e*((a+b*x)/(c+d*x))^n))/d^4+1/6*b^3*g^3*i^2*(c+d*x)^6*(A+B*log(e*((a+b*x)/(c+d*x))^n))/d^4+1/60*B*(b*c-a*d)^6*g^3*i^2*n*log((a+b*x)/(c+d*x))/(b^3*d^4)+1/60*B*(b*c-a*d)^6*g^3*i^2*n*log(c+d*x)/(b^3*d^4)],
[(a*g+b*g*x)^2*(c*i+d*i*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n)),x,5,-1/30*B*(b*c-a*d)^4*g^2*i^2*n*x/(b^2*d^2)-1/60*B*(b*c-a*d)^3*g^2*i^2*n*(c+d*x)^2/(b*d^3)+1/10*B*(b*c-a*d)^2*g^2*i^2*n*(c+d*x)^3/d^3-1/20*b*B*(b*c-a*d)*g^2*i^2*n*(c+d*x)^4/d^3+1/3*(b*c-a*d)^2*g^2*i^2*(c+d*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))/d^3-1/2*b*(b*c-a*d)*g^2*i^2*(c+d*x)^4*(A+B*log(e*((a+b*x)/(c+d*x))^n))/d^3+1/5*b^2*g^2*i^2*(c+d*x)^5*(A+B*log(e*((a+b*x)/(c+d*x))^n))/d^3-1/30*B*(b*c-a*d)^5*g^2*i^2*n*log((a+b*x)/(c+d*x))/(b^3*d^3)-1/30*B*(b*c-a*d)^5*g^2*i^2*n*log(c+d*x)/(b^3*d^3)],
[(a*g+b*g*x)*(c*i+d*i*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n)),x,5,1/12*B*(b*c-a*d)^3*g*i^2*n*x/(b^2*d)+1/24*B*(b*c-a*d)^2*g*i^2*n*(c+d*x)^2/(b*d^2)-1/12*B*(b*c-a*d)*g*i^2*n*(c+d*x)^3/d^2-1/3*(b*c-a*d)*g*i^2*(c+d*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))/d^2+1/4*b*g*i^2*(c+d*x)^4*(A+B*log(e*((a+b*x)/(c+d*x))^n))/d^2+1/12*B*(b*c-a*d)^4*g*i^2*n*log((a+b*x)/(c+d*x))/(b^3*d^2)+1/12*B*(b*c-a*d)^4*g*i^2*n*log(c+d*x)/(b^3*d^2)],
[(c*i+d*i*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n)),x,4,-1/3*B*(b*c-a*d)^2*i^2*n*x/b^2-1/6*B*(b*c-a*d)*i^2*n*(c+d*x)^2/(b*d)-1/3*B*(b*c-a*d)^3*i^2*n*log(a+b*x)/(b^3*d)+1/3*i^2*(c+d*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))/d],
[(c*i+d*i*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(a*g+b*g*x),x,10,-1/2*B*d*(b*c-a*d)*i^2*n*x/(b^2*g)+d*(b*c-a*d)*i^2*(a+b*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(b^3*g)+1/2*i^2*(c+d*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(b*g)-1/2*B*(b*c-a*d)^2*i^2*n*log((a+b*x)/(c+d*x))/(b^3*g)-3/2*B*(b*c-a*d)^2*i^2*n*log(c+d*x)/(b^3*g)-(b*c-a*d)^2*i^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))*log(1-b*(c+d*x)/(d*(a+b*x)))/(b^3*g)+B*(b*c-a*d)^2*i^2*n*polylog(2,b*(c+d*x)/(d*(a+b*x)))/(b^3*g)],
[(c*i+d*i*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(a*g+b*g*x)^2,x,8,-B*(b*c-a*d)*i^2*n*(c+d*x)/(b^2*g^2*(a+b*x))+d^2*i^2*(a+b*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(b^3*g^2)-(b*c-a*d)*i^2*(c+d*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(b^2*g^2*(a+b*x))-B*d*(b*c-a*d)*i^2*n*log(c+d*x)/(b^3*g^2)-2*d*(b*c-a*d)*i^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))*log(1-b*(c+d*x)/(d*(a+b*x)))/(b^3*g^2)+2*B*d*(b*c-a*d)*i^2*n*polylog(2,b*(c+d*x)/(d*(a+b*x)))/(b^3*g^2)],
[(c*i+d*i*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(a*g+b*g*x)^3,x,7,-B*d*i^2*n*(c+d*x)/(b^2*g^3*(a+b*x))-1/4*B*i^2*n*(c+d*x)^2/(b*g^3*(a+b*x)^2)-d*i^2*(c+d*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(b^2*g^3*(a+b*x))-1/2*i^2*(c+d*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(b*g^3*(a+b*x)^2)-d^2*i^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))*log(1-b*(c+d*x)/(d*(a+b*x)))/(b^3*g^3)+B*d^2*i^2*n*polylog(2,b*(c+d*x)/(d*(a+b*x)))/(b^3*g^3)],
[(c*i+d*i*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(a*g+b*g*x)^4,x,2,-1/9*B*i^2*n*(c+d*x)^3/((b*c-a*d)*g^4*(a+b*x)^3)-1/3*i^2*(c+d*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)*g^4*(a+b*x)^3)],
[(c*i+d*i*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(a*g+b*g*x)^5,x,5,1/9*B*d*i^2*n*(c+d*x)^3/((b*c-a*d)^2*g^5*(a+b*x)^3)-1/16*b*B*i^2*n*(c+d*x)^4/((b*c-a*d)^2*g^5*(a+b*x)^4)+1/3*d*i^2*(c+d*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)^2*g^5*(a+b*x)^3)-1/4*b*i^2*(c+d*x)^4*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)^2*g^5*(a+b*x)^4)],
[(c*i+d*i*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(a*g+b*g*x)^6,x,5,-1/9*B*d^2*i^2*n*(c+d*x)^3/((b*c-a*d)^3*g^6*(a+b*x)^3)+1/8*b*B*d*i^2*n*(c+d*x)^4/((b*c-a*d)^3*g^6*(a+b*x)^4)-1/25*b^2*B*i^2*n*(c+d*x)^5/((b*c-a*d)^3*g^6*(a+b*x)^5)-1/3*d^2*i^2*(c+d*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)^3*g^6*(a+b*x)^3)+1/2*b*d*i^2*(c+d*x)^4*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)^3*g^6*(a+b*x)^4)-1/5*b^2*i^2*(c+d*x)^5*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)^3*g^6*(a+b*x)^5)],
[(a*g+b*g*x)^3*(c*i+d*i*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n)),x,5,1/140*B*(b*c-a*d)^6*g^3*i^3*n*x/(b^3*d^3)+1/280*B*(b*c-a*d)^5*g^3*i^3*n*(c+d*x)^2/(b^2*d^4)+1/420*B*(b*c-a*d)^4*g^3*i^3*n*(c+d*x)^3/(b*d^4)-17/280*B*(b*c-a*d)^3*g^3*i^3*n*(c+d*x)^4/d^4+1/14*b*B*(b*c-a*d)^2*g^3*i^3*n*(c+d*x)^5/d^4-1/42*b^2*B*(b*c-a*d)*g^3*i^3*n*(c+d*x)^6/d^4-1/4*(b*c-a*d)^3*g^3*i^3*(c+d*x)^4*(A+B*log(e*((a+b*x)/(c+d*x))^n))/d^4+3/5*b*(b*c-a*d)^2*g^3*i^3*(c+d*x)^5*(A+B*log(e*((a+b*x)/(c+d*x))^n))/d^4-1/2*b^2*(b*c-a*d)*g^3*i^3*(c+d*x)^6*(A+B*log(e*((a+b*x)/(c+d*x))^n))/d^4+1/7*b^3*g^3*i^3*(c+d*x)^7*(A+B*log(e*((a+b*x)/(c+d*x))^n))/d^4+1/140*B*(b*c-a*d)^7*g^3*i^3*n*log((a+b*x)/(c+d*x))/(b^4*d^4)+1/140*B*(b*c-a*d)^7*g^3*i^3*n*log(c+d*x)/(b^4*d^4)],
[(a*g+b*g*x)^2*(c*i+d*i*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n)),x,5,-1/60*B*(b*c-a*d)^5*g^2*i^3*n*x/(b^3*d^2)-1/120*B*(b*c-a*d)^4*g^2*i^3*n*(c+d*x)^2/(b^2*d^3)-1/180*B*(b*c-a*d)^3*g^2*i^3*n*(c+d*x)^3/(b*d^3)+7/120*B*(b*c-a*d)^2*g^2*i^3*n*(c+d*x)^4/d^3-1/30*b*B*(b*c-a*d)*g^2*i^3*n*(c+d*x)^5/d^3+1/4*(b*c-a*d)^2*g^2*i^3*(c+d*x)^4*(A+B*log(e*((a+b*x)/(c+d*x))^n))/d^3-2/5*b*(b*c-a*d)*g^2*i^3*(c+d*x)^5*(A+B*log(e*((a+b*x)/(c+d*x))^n))/d^3+1/6*b^2*g^2*i^3*(c+d*x)^6*(A+B*log(e*((a+b*x)/(c+d*x))^n))/d^3-1/60*B*(b*c-a*d)^6*g^2*i^3*n*log((a+b*x)/(c+d*x))/(b^4*d^3)-1/60*B*(b*c-a*d)^6*g^2*i^3*n*log(c+d*x)/(b^4*d^3)],
[(a*g+b*g*x)*(c*i+d*i*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n)),x,5,1/20*B*(b*c-a*d)^4*g*i^3*n*x/(b^3*d)+1/40*B*(b*c-a*d)^3*g*i^3*n*(c+d*x)^2/(b^2*d^2)+1/60*B*(b*c-a*d)^2*g*i^3*n*(c+d*x)^3/(b*d^2)-1/20*B*(b*c-a*d)*g*i^3*n*(c+d*x)^4/d^2-1/4*(b*c-a*d)*g*i^3*(c+d*x)^4*(A+B*log(e*((a+b*x)/(c+d*x))^n))/d^2+1/5*b*g*i^3*(c+d*x)^5*(A+B*log(e*((a+b*x)/(c+d*x))^n))/d^2+1/20*B*(b*c-a*d)^5*g*i^3*n*log((a+b*x)/(c+d*x))/(b^4*d^2)+1/20*B*(b*c-a*d)^5*g*i^3*n*log(c+d*x)/(b^4*d^2)],
[(c*i+d*i*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n)),x,4,-1/4*B*(b*c-a*d)^3*i^3*n*x/b^3-1/8*B*(b*c-a*d)^2*i^3*n*(c+d*x)^2/(b^2*d)-1/12*B*(b*c-a*d)*i^3*n*(c+d*x)^3/(b*d)-1/4*B*(b*c-a*d)^4*i^3*n*log(a+b*x)/(b^4*d)+1/4*i^3*(c+d*x)^4*(A+B*log(e*((a+b*x)/(c+d*x))^n))/d],
[(c*i+d*i*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(a*g+b*g*x),x,14,-5/6*B*d*(b*c-a*d)^2*i^3*n*x/(b^3*g)-1/6*B*(b*c-a*d)*i^3*n*(c+d*x)^2/(b^2*g)+d*(b*c-a*d)^2*i^3*(a+b*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(b^4*g)+1/2*(b*c-a*d)*i^3*(c+d*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(b^2*g)+1/3*i^3*(c+d*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(b*g)-5/6*B*(b*c-a*d)^3*i^3*n*log((a+b*x)/(c+d*x))/(b^4*g)-11/6*B*(b*c-a*d)^3*i^3*n*log(c+d*x)/(b^4*g)-(b*c-a*d)^3*i^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))*log(1-b*(c+d*x)/(d*(a+b*x)))/(b^4*g)+B*(b*c-a*d)^3*i^3*n*polylog(2,b*(c+d*x)/(d*(a+b*x)))/(b^4*g)],
[(c*i+d*i*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(a*g+b*g*x)^2,x,11,-1/2*B*d^2*(b*c-a*d)*i^3*n*x/(b^3*g^2)-B*(b*c-a*d)^2*i^3*n*(c+d*x)/(b^3*g^2*(a+b*x))+2*d^2*(b*c-a*d)*i^3*(a+b*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(b^4*g^2)-(b*c-a*d)^2*i^3*(c+d*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(b^3*g^2*(a+b*x))+1/2*d*i^3*(c+d*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(b^2*g^2)-1/2*B*d*(b*c-a*d)^2*i^3*n*log((a+b*x)/(c+d*x))/(b^4*g^2)-5/2*B*d*(b*c-a*d)^2*i^3*n*log(c+d*x)/(b^4*g^2)-3*d*(b*c-a*d)^2*i^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))*log(1-b*(c+d*x)/(d*(a+b*x)))/(b^4*g^2)+3*B*d*(b*c-a*d)^2*i^3*n*polylog(2,b*(c+d*x)/(d*(a+b*x)))/(b^4*g^2)],
[(c*i+d*i*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(a*g+b*g*x)^3,x,9,-2*B*d*(b*c-a*d)*i^3*n*(c+d*x)/(b^3*g^3*(a+b*x))-1/4*B*(b*c-a*d)*i^3*n*(c+d*x)^2/(b^2*g^3*(a+b*x)^2)+d^3*i^3*(a+b*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(b^4*g^3)-2*d*(b*c-a*d)*i^3*(c+d*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(b^3*g^3*(a+b*x))-1/2*(b*c-a*d)*i^3*(c+d*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(b^2*g^3*(a+b*x)^2)-B*d^2*(b*c-a*d)*i^3*n*log(c+d*x)/(b^4*g^3)-3*d^2*(b*c-a*d)*i^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))*log(1-b*(c+d*x)/(d*(a+b*x)))/(b^4*g^3)+3*B*d^2*(b*c-a*d)*i^3*n*polylog(2,b*(c+d*x)/(d*(a+b*x)))/(b^4*g^3)],
[(c*i+d*i*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(a*g+b*g*x)^4,x,9,-B*d^2*i^3*n*(c+d*x)/(b^3*g^4*(a+b*x))-1/4*B*d*i^3*n*(c+d*x)^2/(b^2*g^4*(a+b*x)^2)-1/9*B*i^3*n*(c+d*x)^3/(b*g^4*(a+b*x)^3)-d^2*i^3*(c+d*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(b^3*g^4*(a+b*x))-1/2*d*i^3*(c+d*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(b^2*g^4*(a+b*x)^2)-1/3*i^3*(c+d*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(b*g^4*(a+b*x)^3)-d^3*i^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))*log(1-b*(c+d*x)/(d*(a+b*x)))/(b^4*g^4)+B*d^3*i^3*n*polylog(2,b*(c+d*x)/(d*(a+b*x)))/(b^4*g^4)],

# q<0
[(a*g+b*g*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(c*i+d*i*x),x,6,1/3*g^3*(a+b*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(d*i)-1/6*(b*c-a*d)*g^3*(a+b*x)^2*(3*A+B*n+3*B*log(e*((a+b*x)/(c+d*x))^n))/(d^2*i)+1/6*(b*c-a*d)^2*g^3*(a+b*x)*(6*A+5*B*n+6*B*log(e*((a+b*x)/(c+d*x))^n))/(d^3*i)+1/6*(b*c-a*d)^3*g^3*(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)))/(d^4*i)+B*(b*c-a*d)^3*g^3*n*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(d^4*i)],
[(a*g+b*g*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(c*i+d*i*x),x,5,1/2*g^2*(a+b*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(d*i)-1/2*(b*c-a*d)*g^2*(a+b*x)*(2*A+B*n+2*B*log(e*((a+b*x)/(c+d*x))^n))/(d^2*i)-1/2*(b*c-a*d)^2*g^2*(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)))/(d^3*i)-B*(b*c-a*d)^2*g^2*n*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(d^3*i)],
[(a*g+b*g*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(c*i+d*i*x),x,4,g*(a+b*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(d*i)+(b*c-a*d)*g*(A+B*n+B*log(e*((a+b*x)/(c+d*x))^n))*log((b*c-a*d)/(b*(c+d*x)))/(d^2*i)+B*(b*c-a*d)*g*n*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(d^2*i)],
[(A+B*log(e*((a+b*x)/(c+d*x))^n))/(c*i+d*i*x),x,5,-(A+B*log(e*((a+b*x)/(c+d*x))^n))*log((b*c-a*d)/(b*(c+d*x)))/(d*i)-B*n*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(d*i)],
[(A+B*log(e*((a+b*x)/(c+d*x))^n))/((a*g+b*g*x)*(c*i+d*i*x)),x,2,1/2*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/(B*(b*c-a*d)*g*i*n)],
[(A+B*log(e*((a+b*x)/(c+d*x))^n))/((a*g+b*g*x)^2*(c*i+d*i*x)),x,5,-b*B*n*(c+d*x)/((b*c-a*d)^2*g^2*i*(a+b*x))-b*(c+d*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)^2*g^2*i*(a+b*x))-d*(A+B*log(e*((a+b*x)/(c+d*x))^n))*log((a+b*x)/(c+d*x))/((b*c-a*d)^2*g^2*i)+1/2*B*d*n*log((a+b*x)/(c+d*x))^2/((b*c-a*d)^2*g^2*i)],
[(A+B*log(e*((a+b*x)/(c+d*x))^n))/((a*g+b*g*x)^3*(c*i+d*i*x)),x,7,-1/4*B*n*(c+d*x)^2*(b-4*d*(a+b*x)/(c+d*x))^2/((b*c-a*d)^3*g^3*i*(a+b*x)^2)+2*b*d*(c+d*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)^3*g^3*i*(a+b*x))-1/2*b^2*(c+d*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)^3*g^3*i*(a+b*x)^2)+d^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))*log((a+b*x)/(c+d*x))/((b*c-a*d)^3*g^3*i)-1/2*B*d^2*n*log((a+b*x)/(c+d*x))^2/((b*c-a*d)^3*g^3*i)],
[(A+B*log(e*((a+b*x)/(c+d*x))^n))/((a*g+b*g*x)^4*(c*i+d*i*x)),x,8,-3*b*B*d^2*n*(c+d*x)/((b*c-a*d)^4*g^4*i*(a+b*x))+3/4*b^2*B*d*n*(c+d*x)^2/((b*c-a*d)^4*g^4*i*(a+b*x)^2)-1/9*b^3*B*n*(c+d*x)^3/((b*c-a*d)^4*g^4*i*(a+b*x)^3)-3*b*d^2*(c+d*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)^4*g^4*i*(a+b*x))+3/2*b^2*d*(c+d*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)^4*g^4*i*(a+b*x)^2)-1/3*b^3*(c+d*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)^4*g^4*i*(a+b*x)^3)-d^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))*log((a+b*x)/(c+d*x))/((b*c-a*d)^4*g^4*i)+1/2*B*d^3*n*log((a+b*x)/(c+d*x))^2/((b*c-a*d)^4*g^4*i)],
[(a*g+b*g*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(c*i+d*i*x)^2,x,9,3*B*(b*c-a*d)^2*g^3*n*(a+b*x)/(d^3*i^2*(c+d*x))-1/2*(b*c-a*d)^2*g^3*(6*A+5*B*n)*(a+b*x)/(d^3*i^2*(c+d*x))-3*B*(b*c-a*d)^2*g^3*(a+b*x)*log(e*((a+b*x)/(c+d*x))^n)/(d^3*i^2*(c+d*x))+1/2*g^3*(a+b*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(d*i^2*(c+d*x))-1/2*(b*c-a*d)*g^3*(a+b*x)^2*(3*A+B*n+3*B*log(e*((a+b*x)/(c+d*x))^n))/(d^2*i^2*(c+d*x))-1/2*b*(b*c-a*d)^2*g^3*(6*A+5*B*n+6*B*log(e*((a+b*x)/(c+d*x))^n))*log((b*c-a*d)/(b*(c+d*x)))/(d^4*i^2)-3*b*B*(b*c-a*d)^2*g^3*n*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(d^4*i^2)],
[(a*g+b*g*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(c*i+d*i*x)^2,x,8,-2*B*(b*c-a*d)*g^2*n*(a+b*x)/(d^2*i^2*(c+d*x))+(b*c-a*d)*g^2*(2*A+B*n)*(a+b*x)/(d^2*i^2*(c+d*x))+2*B*(b*c-a*d)*g^2*(a+b*x)*log(e*((a+b*x)/(c+d*x))^n)/(d^2*i^2*(c+d*x))+g^2*(a+b*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(d*i^2*(c+d*x))+b*(b*c-a*d)*g^2*(2*A+B*n+2*B*log(e*((a+b*x)/(c+d*x))^n))*log((b*c-a*d)/(b*(c+d*x)))/(d^3*i^2)+2*b*B*(b*c-a*d)*g^2*n*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(d^3*i^2)],
[(a*g+b*g*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(c*i+d*i*x)^2,x,7,-A*g*(a+b*x)/(d*i^2*(c+d*x))+B*g*n*(a+b*x)/(d*i^2*(c+d*x))-B*g*(a+b*x)*log(e*((a+b*x)/(c+d*x))^n)/(d*i^2*(c+d*x))-b*g*(A+B*log(e*((a+b*x)/(c+d*x))^n))*log((b*c-a*d)/(b*(c+d*x)))/(d^2*i^2)-b*B*g*n*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(d^2*i^2)],
[(A+B*log(e*((a+b*x)/(c+d*x))^n))/(c*i+d*i*x)^2,x,3,A*(a+b*x)/((b*c-a*d)*i^2*(c+d*x))-B*n*(a+b*x)/((b*c-a*d)*i^2*(c+d*x))+B*(a+b*x)*log(e*((a+b*x)/(c+d*x))^n)/((b*c-a*d)*i^2*(c+d*x))],
[(A+B*log(e*((a+b*x)/(c+d*x))^n))/((a*g+b*g*x)*(c*i+d*i*x)^2),x,5,-A*d*(a+b*x)/((b*c-a*d)^2*g*i^2*(c+d*x))+B*d*n*(a+b*x)/((b*c-a*d)^2*g*i^2*(c+d*x))-B*d*(a+b*x)*log(e*((a+b*x)/(c+d*x))^n)/((b*c-a*d)^2*g*i^2*(c+d*x))+1/2*b*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/(B*(b*c-a*d)^2*g*i^2*n)],
[(A+B*log(e*((a+b*x)/(c+d*x))^n))/((a*g+b*g*x)^2*(c*i+d*i*x)^2),x,4,-B*d^2*n*(a+b*x)/((b*c-a*d)^3*g^2*i^2*(c+d*x))-b^2*B*n*(c+d*x)/((b*c-a*d)^3*g^2*i^2*(a+b*x))+d^2*(a+b*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)^3*g^2*i^2*(c+d*x))-b^2*(c+d*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)^3*g^2*i^2*(a+b*x))-2*b*d*(A+B*log(e*((a+b*x)/(c+d*x))^n))*log((a+b*x)/(c+d*x))/((b*c-a*d)^3*g^2*i^2)+b*B*d*n*log((a+b*x)/(c+d*x))^2/((b*c-a*d)^3*g^2*i^2)],
[(A+B*log(e*((a+b*x)/(c+d*x))^n))/((a*g+b*g*x)^3*(c*i+d*i*x)^2),x,8,B*d^3*n*(a+b*x)/((b*c-a*d)^4*g^3*i^2*(c+d*x))+3*b^2*B*d*n*(c+d*x)/((b*c-a*d)^4*g^3*i^2*(a+b*x))-1/4*b^3*B*n*(c+d*x)^2/((b*c-a*d)^4*g^3*i^2*(a+b*x)^2)-d^3*(a+b*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)^4*g^3*i^2*(c+d*x))+3*b^2*d*(c+d*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)^4*g^3*i^2*(a+b*x))-1/2*b^3*(c+d*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)^4*g^3*i^2*(a+b*x)^2)+3*b*d^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))*log((a+b*x)/(c+d*x))/((b*c-a*d)^4*g^3*i^2)-3/2*b*B*d^2*n*log((a+b*x)/(c+d*x))^2/((b*c-a*d)^4*g^3*i^2)],
[(A+B*log(e*((a+b*x)/(c+d*x))^n))/((a*g+b*g*x)^4*(c*i+d*i*x)^2),x,4,-B*d^4*n*(a+b*x)/((b*c-a*d)^5*g^4*i^2*(c+d*x))-6*b^2*B*d^2*n*(c+d*x)/((b*c-a*d)^5*g^4*i^2*(a+b*x))+b^3*B*d*n*(c+d*x)^2/((b*c-a*d)^5*g^4*i^2*(a+b*x)^2)-1/9*b^4*B*n*(c+d*x)^3/((b*c-a*d)^5*g^4*i^2*(a+b*x)^3)+d^4*(a+b*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)^5*g^4*i^2*(c+d*x))-6*b^2*d^2*(c+d*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)^5*g^4*i^2*(a+b*x))+2*b^3*d*(c+d*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)^5*g^4*i^2*(a+b*x)^2)-1/3*b^4*(c+d*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)^5*g^4*i^2*(a+b*x)^3)-4*b*d^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))*log((a+b*x)/(c+d*x))/((b*c-a*d)^5*g^4*i^2)+2*b*B*d^3*n*log((a+b*x)/(c+d*x))^2/((b*c-a*d)^5*g^4*i^2)],
[(a*g+b*g*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(c*i+d*i*x)^3,x,9,-3/4*B*(b*c-a*d)*g^3*n*(a+b*x)^2/(d^2*i^3*(c+d*x)^2)-3*b*B*(b*c-a*d)*g^3*n*(a+b*x)/(d^3*i^3*(c+d*x))+b*(b*c-a*d)*g^3*(3*A+B*n)*(a+b*x)/(d^3*i^3*(c+d*x))+3*b*B*(b*c-a*d)*g^3*(a+b*x)*log(e*((a+b*x)/(c+d*x))^n)/(d^3*i^3*(c+d*x))+g^3*(a+b*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(d*i^3*(c+d*x)^2)+1/2*(b*c-a*d)*g^3*(a+b*x)^2*(3*A+B*n+3*B*log(e*((a+b*x)/(c+d*x))^n))/(d^2*i^3*(c+d*x)^2)+b^2*(b*c-a*d)*g^3*(3*A+B*n+3*B*log(e*((a+b*x)/(c+d*x))^n))*log((b*c-a*d)/(b*(c+d*x)))/(d^4*i^3)+3*b^2*B*(b*c-a*d)*g^3*n*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(d^4*i^3)],
[(a*g+b*g*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(c*i+d*i*x)^3,x,8,1/4*B*g^2*n*(a+b*x)^2/(d*i^3*(c+d*x)^2)-A*b*g^2*(a+b*x)/(d^2*i^3*(c+d*x))+b*B*g^2*n*(a+b*x)/(d^2*i^3*(c+d*x))-b*B*g^2*(a+b*x)*log(e*((a+b*x)/(c+d*x))^n)/(d^2*i^3*(c+d*x))-1/2*g^2*(a+b*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(d*i^3*(c+d*x)^2)-b^2*g^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))*log((b*c-a*d)/(b*(c+d*x)))/(d^3*i^3)-b^2*B*g^2*n*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(d^3*i^3)],
[(a*g+b*g*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(c*i+d*i*x)^3,x,2,-1/4*B*g*n*(a+b*x)^2/((b*c-a*d)*i^3*(c+d*x)^2)+1/2*g*(a+b*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)*i^3*(c+d*x)^2)],
[(A+B*log(e*((a+b*x)/(c+d*x))^n))/(c*i+d*i*x)^3,x,4,1/4*B*n/(d*i^3*(c+d*x)^2)+1/2*b*B*n/(d*(b*c-a*d)*i^3*(c+d*x))+1/2*b^2*B*n*log(a+b*x)/(d*(b*c-a*d)^2*i^3)+1/2*(-A-B*log(e*((a+b*x)/(c+d*x))^n))/(d*i^3*(c+d*x)^2)-1/2*b^2*B*n*log(c+d*x)/(d*(b*c-a*d)^2*i^3)],
[(A+B*log(e*((a+b*x)/(c+d*x))^n))/((a*g+b*g*x)*(c*i+d*i*x)^3),x,4,-1/4*B*n*(4*b-d*(a+b*x)/(c+d*x))^2/((b*c-a*d)^3*g*i^3)+1/2*d^2*(a+b*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)^3*g*i^3*(c+d*x)^2)-2*b*d*(a+b*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)^3*g*i^3*(c+d*x))+b^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))*log((a+b*x)/(c+d*x))/((b*c-a*d)^3*g*i^3)-1/2*b^2*B*n*log((a+b*x)/(c+d*x))^2/((b*c-a*d)^3*g*i^3)],
[(A+B*log(e*((a+b*x)/(c+d*x))^n))/((a*g+b*g*x)^2*(c*i+d*i*x)^3),x,4,1/4*B*d^3*n*(a+b*x)^2/((b*c-a*d)^4*g^2*i^3*(c+d*x)^2)-3*b*B*d^2*n*(a+b*x)/((b*c-a*d)^4*g^2*i^3*(c+d*x))-b^3*B*n*(c+d*x)/((b*c-a*d)^4*g^2*i^3*(a+b*x))-1/2*d^3*(a+b*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)^4*g^2*i^3*(c+d*x)^2)+3*b*d^2*(a+b*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)^4*g^2*i^3*(c+d*x))-b^3*(c+d*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)^4*g^2*i^3*(a+b*x))-3*b^2*d*(A+B*log(e*((a+b*x)/(c+d*x))^n))*log((a+b*x)/(c+d*x))/((b*c-a*d)^4*g^2*i^3)+3/2*b^2*B*d*n*log((a+b*x)/(c+d*x))^2/((b*c-a*d)^4*g^2*i^3)],
[(A+B*log(e*((a+b*x)/(c+d*x))^n))/((a*g+b*g*x)^3*(c*i+d*i*x)^3),x,5,-1/4*B*d^4*n*(a+b*x)^2/((b*c-a*d)^5*g^3*i^3*(c+d*x)^2)+4*b*B*d^3*n*(a+b*x)/((b*c-a*d)^5*g^3*i^3*(c+d*x))+4*b^3*B*d*n*(c+d*x)/((b*c-a*d)^5*g^3*i^3*(a+b*x))-1/4*b^4*B*n*(c+d*x)^2/((b*c-a*d)^5*g^3*i^3*(a+b*x)^2)+1/2*d^4*(a+b*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)^5*g^3*i^3*(c+d*x)^2)-4*b*d^3*(a+b*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)^5*g^3*i^3*(c+d*x))+4*b^3*d*(c+d*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)^5*g^3*i^3*(a+b*x))-1/2*b^4*(c+d*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)^5*g^3*i^3*(a+b*x)^2)+6*b^2*d^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))*log((a+b*x)/(c+d*x))/((b*c-a*d)^5*g^3*i^3)-3*b^2*B*d^2*n*log((a+b*x)/(c+d*x))^2/((b*c-a*d)^5*g^3*i^3)],
[(A+B*log(e*((a+b*x)/(c+d*x))^n))/((a*g+b*g*x)^4*(c*i+d*i*x)^3),x,8,1/4*B*d^5*n*(a+b*x)^2/((b*c-a*d)^6*g^4*i^3*(c+d*x)^2)-5*b*B*d^4*n*(a+b*x)/((b*c-a*d)^6*g^4*i^3*(c+d*x))-10*b^3*B*d^2*n*(c+d*x)/((b*c-a*d)^6*g^4*i^3*(a+b*x))+5/4*b^4*B*d*n*(c+d*x)^2/((b*c-a*d)^6*g^4*i^3*(a+b*x)^2)-1/9*b^5*B*n*(c+d*x)^3/((b*c-a*d)^6*g^4*i^3*(a+b*x)^3)-1/2*d^5*(a+b*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)^6*g^4*i^3*(c+d*x)^2)+5*b*d^4*(a+b*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)^6*g^4*i^3*(c+d*x))-10*b^3*d^2*(c+d*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)^6*g^4*i^3*(a+b*x))+5/2*b^4*d*(c+d*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)^6*g^4*i^3*(a+b*x)^2)-1/3*b^5*(c+d*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)^6*g^4*i^3*(a+b*x)^3)-10*b^2*d^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))*log((a+b*x)/(c+d*x))/((b*c-a*d)^6*g^4*i^3)+5*b^2*B*d^3*n*log((a+b*x)/(c+d*x))^2/((b*c-a*d)^6*g^4*i^3)],

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

# q>0
[(a*g+b*g*x)^3*(c*i+d*i*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2,x,11,3/10*B^2*(b*c-a*d)^4*g^3*i*n^2*x/(b*d^3)-3/20*B^2*(b*c-a*d)^3*g^3*i*n^2*(c+d*x)^2/d^4+1/30*b*B^2*(b*c-a*d)^2*g^3*i*n^2*(c+d*x)^3/d^4-1/30*B*(b*c-a*d)^2*g^3*i*n*(a+b*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(b^2*d)-1/10*B*(b*c-a*d)*g^3*i*n*(a+b*x)^4*(A+B*log(e*((a+b*x)/(c+d*x))^n))/b^2+1/20*(b*c-a*d)*g^3*i*(a+b*x)^4*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/b^2+1/5*g^3*i*(a+b*x)^4*(c+d*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/b+1/60*B*(b*c-a*d)^3*g^3*i*n*(a+b*x)^2*(3*A+B*n+3*B*log(e*((a+b*x)/(c+d*x))^n))/(b^2*d^2)-1/60*B*(b*c-a*d)^4*g^3*i*n*(a+b*x)*(6*A+5*B*n+6*B*log(e*((a+b*x)/(c+d*x))^n))/(b^2*d^3)-1/60*B*(b*c-a*d)^5*g^3*i*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^2*d^4)-1/10*B^2*(b*c-a*d)^5*g^3*i*n^2*log(c+d*x)/(b^2*d^4)-1/10*B^2*(b*c-a*d)^5*g^3*i*n^2*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(b^2*d^4)],
[(a*g+b*g*x)^2*(c*i+d*i*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2,x,10,-1/3*B^2*(b*c-a*d)^3*g^2*i*n^2*x/(b*d^2)+1/12*B^2*(b*c-a*d)^2*g^2*i*n^2*(c+d*x)^2/d^3-1/12*B*(b*c-a*d)^2*g^2*i*n*(a+b*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(b^2*d)-1/6*B*(b*c-a*d)*g^2*i*n*(a+b*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))/b^2+1/12*(b*c-a*d)*g^2*i*(a+b*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/b^2+1/4*g^2*i*(a+b*x)^3*(c+d*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/b+1/12*B*(b*c-a*d)^3*g^2*i*n*(a+b*x)*(2*A+B*n+2*B*log(e*((a+b*x)/(c+d*x))^n))/(b^2*d^2)+1/12*B*(b*c-a*d)^4*g^2*i*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^2*d^3)+1/6*B^2*(b*c-a*d)^4*g^2*i*n^2*log(c+d*x)/(b^2*d^3)+1/6*B^2*(b*c-a*d)^4*g^2*i*n^2*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(b^2*d^3)],
[(a*g+b*g*x)*(c*i+d*i*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2,x,9,1/3*B^2*(b*c-a*d)^2*g*i*n^2*x/(b*d)-1/3*B*(b*c-a*d)^2*g*i*n*(a+b*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(b^2*d)-1/3*B*(b*c-a*d)*g*i*n*(a+b*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))/b^2+1/6*(b*c-a*d)*g*i*(a+b*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/b^2+1/3*g*i*(a+b*x)^2*(c+d*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/b-1/3*B*(b*c-a*d)^3*g*i*n*(A+B*n+B*log(e*((a+b*x)/(c+d*x))^n))*log((b*c-a*d)/(b*(c+d*x)))/(b^2*d^2)-1/3*B^2*(b*c-a*d)^3*g*i*n^2*log(c+d*x)/(b^2*d^2)-1/3*B^2*(b*c-a*d)^3*g*i*n^2*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(b^2*d^2)],
[(c*i+d*i*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2,x,7,-B*(b*c-a*d)*i*n*(a+b*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/b^2+1/2*i*(c+d*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/d+B^2*(b*c-a*d)^2*i*n^2*log(c+d*x)/(b^2*d)+B*(b*c-a*d)^2*i*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*i*n^2*polylog(2,b*(c+d*x)/(d*(a+b*x)))/(b^2*d)],
[(c*i+d*i*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/(a*g+b*g*x),x,8,d*i*(a+b*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/(b^2*g)+2*B*(b*c-a*d)*i*n*(A+B*log(e*((a+b*x)/(c+d*x))^n))*log((b*c-a*d)/(b*(c+d*x)))/(b^2*g)-(b*c-a*d)*i*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2*log(1-b*(c+d*x)/(d*(a+b*x)))/(b^2*g)+2*B^2*(b*c-a*d)*i*n^2*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(b^2*g)+2*B*(b*c-a*d)*i*n*(A+B*log(e*((a+b*x)/(c+d*x))^n))*polylog(2,b*(c+d*x)/(d*(a+b*x)))/(b^2*g)+2*B^2*(b*c-a*d)*i*n^2*polylog(3,b*(c+d*x)/(d*(a+b*x)))/(b^2*g)],
[(c*i+d*i*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/(a*g+b*g*x)^2,x,7,-2*B^2*i*n^2*(c+d*x)/(b*g^2*(a+b*x))-2*B*i*n*(c+d*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(b*g^2*(a+b*x))-i*(c+d*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/(b*g^2*(a+b*x))-d*i*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2*log(1-b*(c+d*x)/(d*(a+b*x)))/(b^2*g^2)+2*B*d*i*n*(A+B*log(e*((a+b*x)/(c+d*x))^n))*polylog(2,b*(c+d*x)/(d*(a+b*x)))/(b^2*g^2)+2*B^2*d*i*n^2*polylog(3,b*(c+d*x)/(d*(a+b*x)))/(b^2*g^2)],
[(c*i+d*i*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/(a*g+b*g*x)^3,x,3,-1/4*B^2*i*n^2*(c+d*x)^2/((b*c-a*d)*g^3*(a+b*x)^2)-1/2*B*i*n*(c+d*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)*g^3*(a+b*x)^2)-1/2*i*(c+d*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/((b*c-a*d)*g^3*(a+b*x)^2)],
[(c*i+d*i*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/(a*g+b*g*x)^4,x,7,1/4*B^2*d*i*n^2*(c+d*x)^2/((b*c-a*d)^2*g^4*(a+b*x)^2)-2/27*b*B^2*i*n^2*(c+d*x)^3/((b*c-a*d)^2*g^4*(a+b*x)^3)+1/2*B*d*i*n*(c+d*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)^2*g^4*(a+b*x)^2)-2/9*b*B*i*n*(c+d*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)^2*g^4*(a+b*x)^3)+1/2*d*i*(c+d*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/((b*c-a*d)^2*g^4*(a+b*x)^2)-1/3*b*i*(c+d*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/((b*c-a*d)^2*g^4*(a+b*x)^3)],
[(c*i+d*i*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/(a*g+b*g*x)^5,x,9,-1/4*B^2*d^2*i*n^2*(c+d*x)^2/((b*c-a*d)^3*g^5*(a+b*x)^2)+4/27*b*B^2*d*i*n^2*(c+d*x)^3/((b*c-a*d)^3*g^5*(a+b*x)^3)-1/32*b^2*B^2*i*n^2*(c+d*x)^4/((b*c-a*d)^3*g^5*(a+b*x)^4)-1/2*B*d^2*i*n*(c+d*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)^3*g^5*(a+b*x)^2)+4/9*b*B*d*i*n*(c+d*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)^3*g^5*(a+b*x)^3)-1/8*b^2*B*i*n*(c+d*x)^4*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)^3*g^5*(a+b*x)^4)-1/2*d^2*i*(c+d*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/((b*c-a*d)^3*g^5*(a+b*x)^2)+2/3*b*d*i*(c+d*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/((b*c-a*d)^3*g^5*(a+b*x)^3)-1/4*b^2*i*(c+d*x)^4*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/((b*c-a*d)^3*g^5*(a+b*x)^4)],
[(a*g+b*g*x)^3*(c*i+d*i*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2,x,17,3/20*B^2*(b*c-a*d)^5*g^3*i^2*n^2*x/(b^2*d^3)+1/60*B^2*(b*c-a*d)^2*g^3*i^2*n^2*(a+b*x)^4/b^3-3/40*B^2*(b*c-a*d)^4*g^3*i^2*n^2*(c+d*x)^2/(b*d^4)+1/60*B^2*(b*c-a*d)^3*g^3*i^2*n^2*(c+d*x)^3/d^4-1/90*B*(b*c-a*d)^3*g^3*i^2*n*(a+b*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(b^3*d)-1/20*B*(b*c-a*d)^2*g^3*i^2*n*(a+b*x)^4*(A+B*log(e*((a+b*x)/(c+d*x))^n))/b^3-1/15*B*(b*c-a*d)*g^3*i^2*n*(a+b*x)^4*(c+d*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/b^2+1/60*(b*c-a*d)^2*g^3*i^2*(a+b*x)^4*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/b^3+1/15*(b*c-a*d)*g^3*i^2*(a+b*x)^4*(c+d*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/b^2+1/6*g^3*i^2*(a+b*x)^4*(c+d*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/b+1/180*B*(b*c-a*d)^4*g^3*i^2*n*(a+b*x)^2*(3*A+B*n+3*B*log(e*((a+b*x)/(c+d*x))^n))/(b^3*d^2)-1/180*B*(b*c-a*d)^5*g^3*i^2*n*(a+b*x)*(6*A+5*B*n+6*B*log(e*((a+b*x)/(c+d*x))^n))/(b^3*d^3)-1/180*B*(b*c-a*d)^6*g^3*i^2*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^3*d^4)-1/20*B^2*(b*c-a*d)^6*g^3*i^2*n^2*log(c+d*x)/(b^3*d^4)-1/30*B^2*(b*c-a*d)^6*g^3*i^2*n^2*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(b^3*d^4)],
[(a*g+b*g*x)^2*(c*i+d*i*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2,x,15,-1/10*B^2*(b*c-a*d)^4*g^2*i^2*n^2*x/(b^2*d^2)-1/20*B^2*(b*c-a*d)^3*g^2*i^2*n^2*(c+d*x)^2/(b*d^3)+1/30*B^2*(b*c-a*d)^2*g^2*i^2*n^2*(c+d*x)^3/d^3-1/30*B*(b*c-a*d)^3*g^2*i^2*n*(a+b*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(b^3*d)-1/15*B*(b*c-a*d)^2*g^2*i^2*n*(a+b*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))/b^3-1/5*B*(b*c-a*d)^3*g^2*i^2*n*(c+d*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(b*d^3)+4/15*B*(b*c-a*d)^2*g^2*i^2*n*(c+d*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))/d^3-1/10*b*B*(b*c-a*d)*g^2*i^2*n*(c+d*x)^4*(A+B*log(e*((a+b*x)/(c+d*x))^n))/d^3+1/30*(b*c-a*d)^2*g^2*i^2*(a+b*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/b^3+1/10*(b*c-a*d)*g^2*i^2*(a+b*x)^3*(c+d*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/b^2+1/5*g^2*i^2*(a+b*x)^3*(c+d*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/b+1/30*B*(b*c-a*d)^4*g^2*i^2*n*(a+b*x)*(2*A+B*n+2*B*log(e*((a+b*x)/(c+d*x))^n))/(b^3*d^2)+1/30*B*(b*c-a*d)^5*g^2*i^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^3*d^3)+1/30*B^2*(b*c-a*d)^5*g^2*i^2*n^2*log((a+b*x)/(c+d*x))/(b^3*d^3)+1/10*B^2*(b*c-a*d)^5*g^2*i^2*n^2*log(c+d*x)/(b^3*d^3)+1/15*B^2*(b*c-a*d)^5*g^2*i^2*n^2*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(b^3*d^3)],
[(a*g+b*g*x)*(c*i+d*i*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2,x,14,1/12*B^2*(b*c-a*d)^3*g*i^2*n^2*x/(b^2*d)+1/12*B^2*(b*c-a*d)^2*g*i^2*n^2*(c+d*x)^2/(b*d^2)-1/6*B*(b*c-a*d)^3*g*i^2*n*(a+b*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(b^3*d)-1/6*B*(b*c-a*d)^2*g*i^2*n*(a+b*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))/b^3+1/4*B*(b*c-a*d)^2*g*i^2*n*(c+d*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(b*d^2)-1/6*B*(b*c-a*d)*g*i^2*n*(c+d*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))/d^2+1/12*(b*c-a*d)^2*g*i^2*(a+b*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/b^3+1/6*(b*c-a*d)*g*i^2*(a+b*x)^2*(c+d*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/b^2+1/4*g*i^2*(a+b*x)^2*(c+d*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/b-1/6*B*(b*c-a*d)^4*g*i^2*n*(A+B*n+B*log(e*((a+b*x)/(c+d*x))^n))*log((b*c-a*d)/(b*(c+d*x)))/(b^3*d^2)-1/12*B^2*(b*c-a*d)^4*g*i^2*n^2*log((a+b*x)/(c+d*x))/(b^3*d^2)-1/4*B^2*(b*c-a*d)^4*g*i^2*n^2*log(c+d*x)/(b^3*d^2)-1/6*B^2*(b*c-a*d)^4*g*i^2*n^2*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(b^3*d^2)],
[(c*i+d*i*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*i^2*n^2*x/b^2-2/3*B*(b*c-a*d)^2*i^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)*i^2*n*(c+d*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(b*d)+1/3*i^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*i^2*n^2*log((a+b*x)/(c+d*x))/(b^3*d)+B^2*(b*c-a*d)^3*i^2*n^2*log(c+d*x)/(b^3*d)+2/3*B*(b*c-a*d)^3*i^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*i^2*n^2*polylog(2,b*(c+d*x)/(d*(a+b*x)))/(b^3*d)],
[(c*i+d*i*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/(a*g+b*g*x),x,15,-B*d*(b*c-a*d)*i^2*n*(a+b*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(b^3*g)+d*(b*c-a*d)*i^2*(a+b*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/(b^3*g)+1/2*i^2*(c+d*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/(b*g)+2*B*(b*c-a*d)^2*i^2*n*(A+B*log(e*((a+b*x)/(c+d*x))^n))*log((b*c-a*d)/(b*(c+d*x)))/(b^3*g)+B^2*(b*c-a*d)^2*i^2*n^2*log(c+d*x)/(b^3*g)+B*(b*c-a*d)^2*i^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*g)-(b*c-a*d)^2*i^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2*log(1-b*(c+d*x)/(d*(a+b*x)))/(b^3*g)+2*B^2*(b*c-a*d)^2*i^2*n^2*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(b^3*g)-B^2*(b*c-a*d)^2*i^2*n^2*polylog(2,b*(c+d*x)/(d*(a+b*x)))/(b^3*g)+2*B*(b*c-a*d)^2*i^2*n*(A+B*log(e*((a+b*x)/(c+d*x))^n))*polylog(2,b*(c+d*x)/(d*(a+b*x)))/(b^3*g)+2*B^2*(b*c-a*d)^2*i^2*n^2*polylog(3,b*(c+d*x)/(d*(a+b*x)))/(b^3*g)],
[(c*i+d*i*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/(a*g+b*g*x)^2,x,11,-2*B^2*(b*c-a*d)*i^2*n^2*(c+d*x)/(b^2*g^2*(a+b*x))-2*B*(b*c-a*d)*i^2*n*(c+d*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(b^2*g^2*(a+b*x))+d^2*i^2*(a+b*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/(b^3*g^2)-(b*c-a*d)*i^2*(c+d*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/(b^2*g^2*(a+b*x))+2*B*d*(b*c-a*d)*i^2*n*(A+B*log(e*((a+b*x)/(c+d*x))^n))*log((b*c-a*d)/(b*(c+d*x)))/(b^3*g^2)-2*d*(b*c-a*d)*i^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2*log(1-b*(c+d*x)/(d*(a+b*x)))/(b^3*g^2)+2*B^2*d*(b*c-a*d)*i^2*n^2*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(b^3*g^2)+4*B*d*(b*c-a*d)*i^2*n*(A+B*log(e*((a+b*x)/(c+d*x))^n))*polylog(2,b*(c+d*x)/(d*(a+b*x)))/(b^3*g^2)+4*B^2*d*(b*c-a*d)*i^2*n^2*polylog(3,b*(c+d*x)/(d*(a+b*x)))/(b^3*g^2)],
[(c*i+d*i*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/(a*g+b*g*x)^3,x,10,-2*B^2*d*i^2*n^2*(c+d*x)/(b^2*g^3*(a+b*x))-1/4*B^2*i^2*n^2*(c+d*x)^2/(b*g^3*(a+b*x)^2)-2*B*d*i^2*n*(c+d*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(b^2*g^3*(a+b*x))-1/2*B*i^2*n*(c+d*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(b*g^3*(a+b*x)^2)-d*i^2*(c+d*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/(b^2*g^3*(a+b*x))-1/2*i^2*(c+d*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/(b*g^3*(a+b*x)^2)-d^2*i^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2*log(1-b*(c+d*x)/(d*(a+b*x)))/(b^3*g^3)+2*B*d^2*i^2*n*(A+B*log(e*((a+b*x)/(c+d*x))^n))*polylog(2,b*(c+d*x)/(d*(a+b*x)))/(b^3*g^3)+2*B^2*d^2*i^2*n^2*polylog(3,b*(c+d*x)/(d*(a+b*x)))/(b^3*g^3)],
[(c*i+d*i*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/(a*g+b*g*x)^4,x,3,-2/27*B^2*i^2*n^2*(c+d*x)^3/((b*c-a*d)*g^4*(a+b*x)^3)-2/9*B*i^2*n*(c+d*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)*g^4*(a+b*x)^3)-1/3*i^2*(c+d*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/((b*c-a*d)*g^4*(a+b*x)^3)],
[(c*i+d*i*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/(a*g+b*g*x)^5,x,7,2/27*B^2*d*i^2*n^2*(c+d*x)^3/((b*c-a*d)^2*g^5*(a+b*x)^3)-1/32*b*B^2*i^2*n^2*(c+d*x)^4/((b*c-a*d)^2*g^5*(a+b*x)^4)+2/9*B*d*i^2*n*(c+d*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)^2*g^5*(a+b*x)^3)-1/8*b*B*i^2*n*(c+d*x)^4*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)^2*g^5*(a+b*x)^4)+1/3*d*i^2*(c+d*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/((b*c-a*d)^2*g^5*(a+b*x)^3)-1/4*b*i^2*(c+d*x)^4*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/((b*c-a*d)^2*g^5*(a+b*x)^4)],
[(c*i+d*i*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/(a*g+b*g*x)^6,x,9,-2/27*B^2*d^2*i^2*n^2*(c+d*x)^3/((b*c-a*d)^3*g^6*(a+b*x)^3)+1/16*b*B^2*d*i^2*n^2*(c+d*x)^4/((b*c-a*d)^3*g^6*(a+b*x)^4)-2/125*b^2*B^2*i^2*n^2*(c+d*x)^5/((b*c-a*d)^3*g^6*(a+b*x)^5)-2/9*B*d^2*i^2*n*(c+d*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)^3*g^6*(a+b*x)^3)+1/4*b*B*d*i^2*n*(c+d*x)^4*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)^3*g^6*(a+b*x)^4)-2/25*b^2*B*i^2*n*(c+d*x)^5*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)^3*g^6*(a+b*x)^5)-1/3*d^2*i^2*(c+d*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/((b*c-a*d)^3*g^6*(a+b*x)^3)+1/2*b*d*i^2*(c+d*x)^4*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/((b*c-a*d)^3*g^6*(a+b*x)^4)-1/5*b^2*i^2*(c+d*x)^5*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/((b*c-a*d)^3*g^6*(a+b*x)^5)],
[(a*g+b*g*x)^3*(c*i+d*i*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2,x,22,5/84*B^2*(b*c-a*d)^6*g^3*i^3*n^2*x/(b^3*d^3)+1/140*B^2*(b*c-a*d)^3*g^3*i^3*n^2*(a+b*x)^4/b^4-29/840*B^2*(b*c-a*d)^5*g^3*i^3*n^2*(c+d*x)^2/(b^2*d^4)+47/1260*B^2*(b*c-a*d)^4*g^3*i^3*n^2*(c+d*x)^3/(b*d^4)-13/420*B^2*(b*c-a*d)^3*g^3*i^3*n^2*(c+d*x)^4/d^4+1/105*b*B^2*(b*c-a*d)^2*g^3*i^3*n^2*(c+d*x)^5/d^4-1/210*B*(b*c-a*d)^4*g^3*i^3*n*(a+b*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(b^4*d)-3/140*B*(b*c-a*d)^3*g^3*i^3*n*(a+b*x)^4*(A+B*log(e*((a+b*x)/(c+d*x))^n))/b^4-1/35*B*(b*c-a*d)^2*g^3*i^3*n*(a+b*x)^4*(c+d*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/b^3+2/21*B*(b*c-a*d)^4*g^3*i^3*n*(c+d*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(b*d^4)-3/14*B*(b*c-a*d)^3*g^3*i^3*n*(c+d*x)^4*(A+B*log(e*((a+b*x)/(c+d*x))^n))/d^4+6/35*b*B*(b*c-a*d)^2*g^3*i^3*n*(c+d*x)^5*(A+B*log(e*((a+b*x)/(c+d*x))^n))/d^4-1/21*b^2*B*(b*c-a*d)*g^3*i^3*n*(c+d*x)^6*(A+B*log(e*((a+b*x)/(c+d*x))^n))/d^4+1/140*(b*c-a*d)^3*g^3*i^3*(a+b*x)^4*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/b^4+1/35*(b*c-a*d)^2*g^3*i^3*(a+b*x)^4*(c+d*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/b^3+1/14*(b*c-a*d)*g^3*i^3*(a+b*x)^4*(c+d*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/b^2+1/7*g^3*i^3*(a+b*x)^4*(c+d*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/b+1/420*B*(b*c-a*d)^5*g^3*i^3*n*(a+b*x)^2*(3*A+B*n+3*B*log(e*((a+b*x)/(c+d*x))^n))/(b^4*d^2)-1/420*B*(b*c-a*d)^6*g^3*i^3*n*(a+b*x)*(6*A+5*B*n+6*B*log(e*((a+b*x)/(c+d*x))^n))/(b^4*d^3)-1/420*B*(b*c-a*d)^7*g^3*i^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^4*d^4)-1/210*B^2*(b*c-a*d)^7*g^3*i^3*n^2*log((a+b*x)/(c+d*x))/(b^4*d^4)-11/420*B^2*(b*c-a*d)^7*g^3*i^3*n^2*log(c+d*x)/(b^4*d^4)-1/70*B^2*(b*c-a*d)^7*g^3*i^3*n^2*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(b^4*d^4)],
[(a*g+b*g*x)^2*(c*i+d*i*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2,x,20,-7/180*B^2*(b*c-a*d)^5*g^2*i^3*n^2*x/(b^3*d^2)-7/360*B^2*(b*c-a*d)^4*g^2*i^3*n^2*(c+d*x)^2/(b^2*d^3)-1/60*B^2*(b*c-a*d)^3*g^2*i^3*n^2*(c+d*x)^3/(b*d^3)+1/60*B^2*(b*c-a*d)^2*g^2*i^3*n^2*(c+d*x)^4/d^3-1/60*B*(b*c-a*d)^4*g^2*i^3*n*(a+b*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(b^4*d)-1/30*B*(b*c-a*d)^3*g^2*i^3*n*(a+b*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))/b^4-1/10*B*(b*c-a*d)^4*g^2*i^3*n*(c+d*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(b^2*d^3)+1/45*B*(b*c-a*d)^3*g^2*i^3*n*(c+d*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(b*d^3)+7/60*B*(b*c-a*d)^2*g^2*i^3*n*(c+d*x)^4*(A+B*log(e*((a+b*x)/(c+d*x))^n))/d^3-1/15*b*B*(b*c-a*d)*g^2*i^3*n*(c+d*x)^5*(A+B*log(e*((a+b*x)/(c+d*x))^n))/d^3+1/60*(b*c-a*d)^3*g^2*i^3*(a+b*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/b^4+1/20*(b*c-a*d)^2*g^2*i^3*(a+b*x)^3*(c+d*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/b^3+1/10*(b*c-a*d)*g^2*i^3*(a+b*x)^3*(c+d*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/b^2+1/6*g^2*i^3*(a+b*x)^3*(c+d*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/b+1/60*B*(b*c-a*d)^5*g^2*i^3*n*(a+b*x)*(2*A+B*n+2*B*log(e*((a+b*x)/(c+d*x))^n))/(b^4*d^2)+1/60*B*(b*c-a*d)^6*g^2*i^3*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^4*d^3)+1/36*B^2*(b*c-a*d)^6*g^2*i^3*n^2*log((a+b*x)/(c+d*x))/(b^4*d^3)+11/180*B^2*(b*c-a*d)^6*g^2*i^3*n^2*log(c+d*x)/(b^4*d^3)+1/30*B^2*(b*c-a*d)^6*g^2*i^3*n^2*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(b^4*d^3)],
[(a*g+b*g*x)*(c*i+d*i*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2,x,19,1/60*B^2*(b*c-a*d)^4*g*i^3*n^2*x/(b^3*d)+1/30*B^2*(b*c-a*d)^3*g*i^3*n^2*(c+d*x)^2/(b^2*d^2)+1/30*B^2*(b*c-a*d)^2*g*i^3*n^2*(c+d*x)^3/(b*d^2)-1/10*B*(b*c-a*d)^4*g*i^3*n*(a+b*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(b^4*d)-1/10*B*(b*c-a*d)^3*g*i^3*n*(a+b*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))/b^4+3/20*B*(b*c-a*d)^3*g*i^3*n*(c+d*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(b^2*d^2)+1/30*B*(b*c-a*d)^2*g*i^3*n*(c+d*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(b*d^2)-1/10*B*(b*c-a*d)*g*i^3*n*(c+d*x)^4*(A+B*log(e*((a+b*x)/(c+d*x))^n))/d^2+1/20*(b*c-a*d)^3*g*i^3*(a+b*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/b^4+1/10*(b*c-a*d)^2*g*i^3*(a+b*x)^2*(c+d*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/b^3+3/20*(b*c-a*d)*g*i^3*(a+b*x)^2*(c+d*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/b^2+1/5*g*i^3*(a+b*x)^2*(c+d*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/b-1/10*B*(b*c-a*d)^5*g*i^3*n*(A+B*n+B*log(e*((a+b*x)/(c+d*x))^n))*log((b*c-a*d)/(b*(c+d*x)))/(b^4*d^2)-1/12*B^2*(b*c-a*d)^5*g*i^3*n^2*log((a+b*x)/(c+d*x))/(b^4*d^2)-11/60*B^2*(b*c-a*d)^5*g*i^3*n^2*log(c+d*x)/(b^4*d^2)-1/10*B^2*(b*c-a*d)^5*g*i^3*n^2*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(b^4*d^2)],
[(c*i+d*i*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*i^3*n^2*x/b^3+1/12*B^2*(b*c-a*d)^2*i^3*n^2*(c+d*x)^2/(b^2*d)-1/2*B*(b*c-a*d)^3*i^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*i^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)*i^3*n*(c+d*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(b*d)+1/4*i^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*i^3*n^2*log((a+b*x)/(c+d*x))/(b^4*d)+11/12*B^2*(b*c-a*d)^4*i^3*n^2*log(c+d*x)/(b^4*d)+1/2*B*(b*c-a*d)^4*i^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*i^3*n^2*polylog(2,b*(c+d*x)/(d*(a+b*x)))/(b^4*d)],
[(c*i+d*i*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/(a*g+b*g*x),x,26,1/3*B^2*d*(b*c-a*d)^2*i^3*n^2*x/(b^3*g)-5/3*B*d*(b*c-a*d)^2*i^3*n*(a+b*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(b^4*g)-1/3*B*(b*c-a*d)*i^3*n*(c+d*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(b^2*g)+d*(b*c-a*d)^2*i^3*(a+b*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/(b^4*g)+1/2*(b*c-a*d)*i^3*(c+d*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/(b^2*g)+1/3*i^3*(c+d*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/(b*g)+2*B*(b*c-a*d)^3*i^3*n*(A+B*log(e*((a+b*x)/(c+d*x))^n))*log((b*c-a*d)/(b*(c+d*x)))/(b^4*g)+1/3*B^2*(b*c-a*d)^3*i^3*n^2*log((a+b*x)/(c+d*x))/(b^4*g)+2*B^2*(b*c-a*d)^3*i^3*n^2*log(c+d*x)/(b^4*g)+5/3*B*(b*c-a*d)^3*i^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*g)-(b*c-a*d)^3*i^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2*log(1-b*(c+d*x)/(d*(a+b*x)))/(b^4*g)+2*B^2*(b*c-a*d)^3*i^3*n^2*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(b^4*g)-5/3*B^2*(b*c-a*d)^3*i^3*n^2*polylog(2,b*(c+d*x)/(d*(a+b*x)))/(b^4*g)+2*B*(b*c-a*d)^3*i^3*n*(A+B*log(e*((a+b*x)/(c+d*x))^n))*polylog(2,b*(c+d*x)/(d*(a+b*x)))/(b^4*g)+2*B^2*(b*c-a*d)^3*i^3*n^2*polylog(3,b*(c+d*x)/(d*(a+b*x)))/(b^4*g)],
[(c*i+d*i*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/(a*g+b*g*x)^2,x,17,-2*B^2*(b*c-a*d)^2*i^3*n^2*(c+d*x)/(b^3*g^2*(a+b*x))-B*d^2*(b*c-a*d)*i^3*n*(a+b*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(b^4*g^2)-2*B*(b*c-a*d)^2*i^3*n*(c+d*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(b^3*g^2*(a+b*x))+2*d^2*(b*c-a*d)*i^3*(a+b*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/(b^4*g^2)-(b*c-a*d)^2*i^3*(c+d*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/(b^3*g^2*(a+b*x))+1/2*d*i^3*(c+d*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/(b^2*g^2)+4*B*d*(b*c-a*d)^2*i^3*n*(A+B*log(e*((a+b*x)/(c+d*x))^n))*log((b*c-a*d)/(b*(c+d*x)))/(b^4*g^2)+B^2*d*(b*c-a*d)^2*i^3*n^2*log(c+d*x)/(b^4*g^2)+B*d*(b*c-a*d)^2*i^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*g^2)-3*d*(b*c-a*d)^2*i^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2*log(1-b*(c+d*x)/(d*(a+b*x)))/(b^4*g^2)+4*B^2*d*(b*c-a*d)^2*i^3*n^2*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(b^4*g^2)-B^2*d*(b*c-a*d)^2*i^3*n^2*polylog(2,b*(c+d*x)/(d*(a+b*x)))/(b^4*g^2)+6*B*d*(b*c-a*d)^2*i^3*n*(A+B*log(e*((a+b*x)/(c+d*x))^n))*polylog(2,b*(c+d*x)/(d*(a+b*x)))/(b^4*g^2)+6*B^2*d*(b*c-a*d)^2*i^3*n^2*polylog(3,b*(c+d*x)/(d*(a+b*x)))/(b^4*g^2)],
[(c*i+d*i*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/(a*g+b*g*x)^3,x,13,-4*B^2*d*(b*c-a*d)*i^3*n^2*(c+d*x)/(b^3*g^3*(a+b*x))-1/4*B^2*(b*c-a*d)*i^3*n^2*(c+d*x)^2/(b^2*g^3*(a+b*x)^2)-4*B*d*(b*c-a*d)*i^3*n*(c+d*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(b^3*g^3*(a+b*x))-1/2*B*(b*c-a*d)*i^3*n*(c+d*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(b^2*g^3*(a+b*x)^2)+d^3*i^3*(a+b*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/(b^4*g^3)-2*d*(b*c-a*d)*i^3*(c+d*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/(b^3*g^3*(a+b*x))-1/2*(b*c-a*d)*i^3*(c+d*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/(b^2*g^3*(a+b*x)^2)+2*B*d^2*(b*c-a*d)*i^3*n*(A+B*log(e*((a+b*x)/(c+d*x))^n))*log((b*c-a*d)/(b*(c+d*x)))/(b^4*g^3)-3*d^2*(b*c-a*d)*i^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2*log(1-b*(c+d*x)/(d*(a+b*x)))/(b^4*g^3)+2*B^2*d^2*(b*c-a*d)*i^3*n^2*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(b^4*g^3)+6*B*d^2*(b*c-a*d)*i^3*n*(A+B*log(e*((a+b*x)/(c+d*x))^n))*polylog(2,b*(c+d*x)/(d*(a+b*x)))/(b^4*g^3)+6*B^2*d^2*(b*c-a*d)*i^3*n^2*polylog(3,b*(c+d*x)/(d*(a+b*x)))/(b^4*g^3)],
[(c*i+d*i*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/(a*g+b*g*x)^4,x,13,-2*B^2*d^2*i^3*n^2*(c+d*x)/(b^3*g^4*(a+b*x))-1/4*B^2*d*i^3*n^2*(c+d*x)^2/(b^2*g^4*(a+b*x)^2)-2/27*B^2*i^3*n^2*(c+d*x)^3/(b*g^4*(a+b*x)^3)-2*B*d^2*i^3*n*(c+d*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(b^3*g^4*(a+b*x))-1/2*B*d*i^3*n*(c+d*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(b^2*g^4*(a+b*x)^2)-2/9*B*i^3*n*(c+d*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(b*g^4*(a+b*x)^3)-d^2*i^3*(c+d*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/(b^3*g^4*(a+b*x))-1/2*d*i^3*(c+d*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/(b^2*g^4*(a+b*x)^2)-1/3*i^3*(c+d*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/(b*g^4*(a+b*x)^3)-d^3*i^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2*log(1-b*(c+d*x)/(d*(a+b*x)))/(b^4*g^4)+2*B*d^3*i^3*n*(A+B*log(e*((a+b*x)/(c+d*x))^n))*polylog(2,b*(c+d*x)/(d*(a+b*x)))/(b^4*g^4)+2*B^2*d^3*i^3*n^2*polylog(3,b*(c+d*x)/(d*(a+b*x)))/(b^4*g^4)],

# q<0
[(a*g+b*g*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/(c*i+d*i*x),x,25,1/3*b*B^2*(b*c-a*d)^2*g^3*n^2*x/(d^3*i)+7/3*B*(b*c-a*d)^2*g^3*n*(a+b*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(d^3*i)-1/3*b^2*B*(b*c-a*d)*g^3*n*(c+d*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(d^4*i)+3*(b*c-a*d)^2*g^3*(a+b*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/(d^3*i)-3/2*b^2*(b*c-a*d)*g^3*(c+d*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/(d^4*i)+1/3*b^3*g^3*(c+d*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/(d^4*i)+6*B*(b*c-a*d)^3*g^3*n*(A+B*log(e*((a+b*x)/(c+d*x))^n))*log((b*c-a*d)/(b*(c+d*x)))/(d^4*i)+(b*c-a*d)^3*g^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2*log((b*c-a*d)/(b*(c+d*x)))/(d^4*i)+1/3*B^2*(b*c-a*d)^3*g^3*n^2*log((a+b*x)/(c+d*x))/(d^4*i)-2*B^2*(b*c-a*d)^3*g^3*n^2*log(c+d*x)/(d^4*i)-7/3*B*(b*c-a*d)^3*g^3*n*(A+B*log(e*((a+b*x)/(c+d*x))^n))*log(1-b*(c+d*x)/(d*(a+b*x)))/(d^4*i)+6*B^2*(b*c-a*d)^3*g^3*n^2*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(d^4*i)+2*B*(b*c-a*d)^3*g^3*n*(A+B*log(e*((a+b*x)/(c+d*x))^n))*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(d^4*i)+7/3*B^2*(b*c-a*d)^3*g^3*n^2*polylog(2,b*(c+d*x)/(d*(a+b*x)))/(d^4*i)-2*B^2*(b*c-a*d)^3*g^3*n^2*polylog(3,d*(a+b*x)/(b*(c+d*x)))/(d^4*i)],
[(a*g+b*g*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/(c*i+d*i*x),x,15,-B*(b*c-a*d)*g^2*n*(a+b*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(d^2*i)-2*(b*c-a*d)*g^2*(a+b*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/(d^2*i)+1/2*b^2*g^2*(c+d*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/(d^3*i)-4*B*(b*c-a*d)^2*g^2*n*(A+B*log(e*((a+b*x)/(c+d*x))^n))*log((b*c-a*d)/(b*(c+d*x)))/(d^3*i)-(b*c-a*d)^2*g^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2*log((b*c-a*d)/(b*(c+d*x)))/(d^3*i)+B^2*(b*c-a*d)^2*g^2*n^2*log(c+d*x)/(d^3*i)+B*(b*c-a*d)^2*g^2*n*(A+B*log(e*((a+b*x)/(c+d*x))^n))*log(1-b*(c+d*x)/(d*(a+b*x)))/(d^3*i)-4*B^2*(b*c-a*d)^2*g^2*n^2*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(d^3*i)-2*B*(b*c-a*d)^2*g^2*n*(A+B*log(e*((a+b*x)/(c+d*x))^n))*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(d^3*i)-B^2*(b*c-a*d)^2*g^2*n^2*polylog(2,b*(c+d*x)/(d*(a+b*x)))/(d^3*i)+2*B^2*(b*c-a*d)^2*g^2*n^2*polylog(3,d*(a+b*x)/(b*(c+d*x)))/(d^3*i)],
[(a*g+b*g*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/(c*i+d*i*x),x,9,g*(a+b*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/(d*i)+2*B*(b*c-a*d)*g*n*(A+B*log(e*((a+b*x)/(c+d*x))^n))*log((b*c-a*d)/(b*(c+d*x)))/(d^2*i)+(b*c-a*d)*g*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2*log((b*c-a*d)/(b*(c+d*x)))/(d^2*i)+2*B^2*(b*c-a*d)*g*n^2*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(d^2*i)+2*B*(b*c-a*d)*g*n*(A+B*log(e*((a+b*x)/(c+d*x))^n))*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(d^2*i)-2*B^2*(b*c-a*d)*g*n^2*polylog(3,d*(a+b*x)/(b*(c+d*x)))/(d^2*i)],
[(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/(c*i+d*i*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*i)-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*i)+2*B^2*n^2*polylog(3,d*(a+b*x)/(b*(c+d*x)))/(d*i)],
[(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/((a*g+b*g*x)*(c*i+d*i*x)),x,3,1/3*(A+B*log(e*((a+b*x)/(c+d*x))^n))^3/(B*(b*c-a*d)*g*i*n)],
[(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/((a*g+b*g*x)^2*(c*i+d*i*x)),x,7,-2*b*B^2*n^2*(c+d*x)/((b*c-a*d)^2*g^2*i*(a+b*x))-2*b*B*n*(c+d*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)^2*g^2*i*(a+b*x))-b*(c+d*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/((b*c-a*d)^2*g^2*i*(a+b*x))-1/3*d*(A+B*log(e*((a+b*x)/(c+d*x))^n))^3/(B*(b*c-a*d)^2*g^2*i*n)],
[(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/((a*g+b*g*x)^3*(c*i+d*i*x)),x,9,4*b*B^2*d*n^2*(c+d*x)/((b*c-a*d)^3*g^3*i*(a+b*x))-1/4*b^2*B^2*n^2*(c+d*x)^2/((b*c-a*d)^3*g^3*i*(a+b*x)^2)+4*b*B*d*n*(c+d*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)^3*g^3*i*(a+b*x))-1/2*b^2*B*n*(c+d*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)^3*g^3*i*(a+b*x)^2)+2*b*d*(c+d*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/((b*c-a*d)^3*g^3*i*(a+b*x))-1/2*b^2*(c+d*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/((b*c-a*d)^3*g^3*i*(a+b*x)^2)+1/3*d^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))^3/(B*(b*c-a*d)^3*g^3*i*n)],
[(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/((a*g+b*g*x)^4*(c*i+d*i*x)),x,11,-6*b*B^2*d^2*n^2*(c+d*x)/((b*c-a*d)^4*g^4*i*(a+b*x))+3/4*b^2*B^2*d*n^2*(c+d*x)^2/((b*c-a*d)^4*g^4*i*(a+b*x)^2)-2/27*b^3*B^2*n^2*(c+d*x)^3/((b*c-a*d)^4*g^4*i*(a+b*x)^3)-6*b*B*d^2*n*(c+d*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)^4*g^4*i*(a+b*x))+3/2*b^2*B*d*n*(c+d*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)^4*g^4*i*(a+b*x)^2)-2/9*b^3*B*n*(c+d*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)^4*g^4*i*(a+b*x)^3)-3*b*d^2*(c+d*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/((b*c-a*d)^4*g^4*i*(a+b*x))+3/2*b^2*d*(c+d*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/((b*c-a*d)^4*g^4*i*(a+b*x)^2)-1/3*b^3*(c+d*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/((b*c-a*d)^4*g^4*i*(a+b*x)^3)-1/3*d^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))^3/(B*(b*c-a*d)^4*g^4*i*n)],
[(a*g+b*g*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/(c*i+d*i*x)^2,x,18,2*A*B*(b*c-a*d)^2*g^3*n*(a+b*x)/(d^3*i^2*(c+d*x))-2*B^2*(b*c-a*d)^2*g^3*n^2*(a+b*x)/(d^3*i^2*(c+d*x))+2*B^2*(b*c-a*d)^2*g^3*n*(a+b*x)*log(e*((a+b*x)/(c+d*x))^n)/(d^3*i^2*(c+d*x))-b*B*(b*c-a*d)*g^3*n*(a+b*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(d^3*i^2)-3*b*(b*c-a*d)*g^3*(a+b*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/(d^3*i^2)-(b*c-a*d)^2*g^3*(a+b*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/(d^3*i^2*(c+d*x))+1/2*b^3*g^3*(c+d*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/(d^4*i^2)-6*b*B*(b*c-a*d)^2*g^3*n*(A+B*log(e*((a+b*x)/(c+d*x))^n))*log((b*c-a*d)/(b*(c+d*x)))/(d^4*i^2)-3*b*(b*c-a*d)^2*g^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2*log((b*c-a*d)/(b*(c+d*x)))/(d^4*i^2)+b*B^2*(b*c-a*d)^2*g^3*n^2*log(c+d*x)/(d^4*i^2)+b*B*(b*c-a*d)^2*g^3*n*(A+B*log(e*((a+b*x)/(c+d*x))^n))*log(1-b*(c+d*x)/(d*(a+b*x)))/(d^4*i^2)-6*b*B^2*(b*c-a*d)^2*g^3*n^2*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(d^4*i^2)-6*b*B*(b*c-a*d)^2*g^3*n*(A+B*log(e*((a+b*x)/(c+d*x))^n))*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(d^4*i^2)-b*B^2*(b*c-a*d)^2*g^3*n^2*polylog(2,b*(c+d*x)/(d*(a+b*x)))/(d^4*i^2)+6*b*B^2*(b*c-a*d)^2*g^3*n^2*polylog(3,d*(a+b*x)/(b*(c+d*x)))/(d^4*i^2)],
[(a*g+b*g*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/(c*i+d*i*x)^2,x,12,-2*A*B*(b*c-a*d)*g^2*n*(a+b*x)/(d^2*i^2*(c+d*x))+2*B^2*(b*c-a*d)*g^2*n^2*(a+b*x)/(d^2*i^2*(c+d*x))-2*B^2*(b*c-a*d)*g^2*n*(a+b*x)*log(e*((a+b*x)/(c+d*x))^n)/(d^2*i^2*(c+d*x))+b*g^2*(a+b*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/(d^2*i^2)+(b*c-a*d)*g^2*(a+b*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/(d^2*i^2*(c+d*x))+2*b*B*(b*c-a*d)*g^2*n*(A+B*log(e*((a+b*x)/(c+d*x))^n))*log((b*c-a*d)/(b*(c+d*x)))/(d^3*i^2)+2*b*(b*c-a*d)*g^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2*log((b*c-a*d)/(b*(c+d*x)))/(d^3*i^2)+2*b*B^2*(b*c-a*d)*g^2*n^2*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(d^3*i^2)+4*b*B*(b*c-a*d)*g^2*n*(A+B*log(e*((a+b*x)/(c+d*x))^n))*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(d^3*i^2)-4*b*B^2*(b*c-a*d)*g^2*n^2*polylog(3,d*(a+b*x)/(b*(c+d*x)))/(d^3*i^2)],
[(a*g+b*g*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/(c*i+d*i*x)^2,x,9,2*A*B*g*n*(a+b*x)/(d*i^2*(c+d*x))-2*B^2*g*n^2*(a+b*x)/(d*i^2*(c+d*x))+2*B^2*g*n*(a+b*x)*log(e*((a+b*x)/(c+d*x))^n)/(d*i^2*(c+d*x))-g*(a+b*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/(d*i^2*(c+d*x))-b*g*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2*log((b*c-a*d)/(b*(c+d*x)))/(d^2*i^2)-2*b*B*g*n*(A+B*log(e*((a+b*x)/(c+d*x))^n))*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(d^2*i^2)+2*b*B^2*g*n^2*polylog(3,d*(a+b*x)/(b*(c+d*x)))/(d^2*i^2)],
[(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/(c*i+d*i*x)^2,x,4,-2*A*B*n*(a+b*x)/((b*c-a*d)*i^2*(c+d*x))+2*B^2*n^2*(a+b*x)/((b*c-a*d)*i^2*(c+d*x))-2*B^2*n*(a+b*x)*log(e*((a+b*x)/(c+d*x))^n)/((b*c-a*d)*i^2*(c+d*x))+(a+b*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/((b*c-a*d)*i^2*(c+d*x))],
[(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/((a*g+b*g*x)*(c*i+d*i*x)^2),x,7,2*A*B*d*n*(a+b*x)/((b*c-a*d)^2*g*i^2*(c+d*x))-2*B^2*d*n^2*(a+b*x)/((b*c-a*d)^2*g*i^2*(c+d*x))+2*B^2*d*n*(a+b*x)*log(e*((a+b*x)/(c+d*x))^n)/((b*c-a*d)^2*g*i^2*(c+d*x))-d*(a+b*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/((b*c-a*d)^2*g*i^2*(c+d*x))+1/3*b*(A+B*log(e*((a+b*x)/(c+d*x))^n))^3/(B*(b*c-a*d)^2*g*i^2*n)],
[(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/((a*g+b*g*x)^2*(c*i+d*i*x)^2),x,10,-2*A*B*d^2*n*(a+b*x)/((b*c-a*d)^3*g^2*i^2*(c+d*x))+2*B^2*d^2*n^2*(a+b*x)/((b*c-a*d)^3*g^2*i^2*(c+d*x))-2*b^2*B^2*n^2*(c+d*x)/((b*c-a*d)^3*g^2*i^2*(a+b*x))-2*B^2*d^2*n*(a+b*x)*log(e*((a+b*x)/(c+d*x))^n)/((b*c-a*d)^3*g^2*i^2*(c+d*x))-2*b^2*B*n*(c+d*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)^3*g^2*i^2*(a+b*x))+d^2*(a+b*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/((b*c-a*d)^3*g^2*i^2*(c+d*x))-b^2*(c+d*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/((b*c-a*d)^3*g^2*i^2*(a+b*x))-2/3*b*d*(A+B*log(e*((a+b*x)/(c+d*x))^n))^3/(B*(b*c-a*d)^3*g^2*i^2*n)],
[(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/((a*g+b*g*x)^3*(c*i+d*i*x)^2),x,12,2*A*B*d^3*n*(a+b*x)/((b*c-a*d)^4*g^3*i^2*(c+d*x))-2*B^2*d^3*n^2*(a+b*x)/((b*c-a*d)^4*g^3*i^2*(c+d*x))+6*b^2*B^2*d*n^2*(c+d*x)/((b*c-a*d)^4*g^3*i^2*(a+b*x))-1/4*b^3*B^2*n^2*(c+d*x)^2/((b*c-a*d)^4*g^3*i^2*(a+b*x)^2)+2*B^2*d^3*n*(a+b*x)*log(e*((a+b*x)/(c+d*x))^n)/((b*c-a*d)^4*g^3*i^2*(c+d*x))+6*b^2*B*d*n*(c+d*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)^4*g^3*i^2*(a+b*x))-1/2*b^3*B*n*(c+d*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)^4*g^3*i^2*(a+b*x)^2)-d^3*(a+b*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/((b*c-a*d)^4*g^3*i^2*(c+d*x))+3*b^2*d*(c+d*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/((b*c-a*d)^4*g^3*i^2*(a+b*x))-1/2*b^3*(c+d*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/((b*c-a*d)^4*g^3*i^2*(a+b*x)^2)+b*d^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))^3/(B*(b*c-a*d)^4*g^3*i^2*n)],
[(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/((a*g+b*g*x)^4*(c*i+d*i*x)^2),x,14,-2*A*B*d^4*n*(a+b*x)/((b*c-a*d)^5*g^4*i^2*(c+d*x))+2*B^2*d^4*n^2*(a+b*x)/((b*c-a*d)^5*g^4*i^2*(c+d*x))-12*b^2*B^2*d^2*n^2*(c+d*x)/((b*c-a*d)^5*g^4*i^2*(a+b*x))+b^3*B^2*d*n^2*(c+d*x)^2/((b*c-a*d)^5*g^4*i^2*(a+b*x)^2)-2/27*b^4*B^2*n^2*(c+d*x)^3/((b*c-a*d)^5*g^4*i^2*(a+b*x)^3)-2*B^2*d^4*n*(a+b*x)*log(e*((a+b*x)/(c+d*x))^n)/((b*c-a*d)^5*g^4*i^2*(c+d*x))-12*b^2*B*d^2*n*(c+d*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)^5*g^4*i^2*(a+b*x))+2*b^3*B*d*n*(c+d*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)^5*g^4*i^2*(a+b*x)^2)-2/9*b^4*B*n*(c+d*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)^5*g^4*i^2*(a+b*x)^3)+d^4*(a+b*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/((b*c-a*d)^5*g^4*i^2*(c+d*x))-6*b^2*d^2*(c+d*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/((b*c-a*d)^5*g^4*i^2*(a+b*x))+2*b^3*d*(c+d*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/((b*c-a*d)^5*g^4*i^2*(a+b*x)^2)-1/3*b^4*(c+d*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/((b*c-a*d)^5*g^4*i^2*(a+b*x)^3)-4/3*b*d^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))^3/(B*(b*c-a*d)^5*g^4*i^2*n)],
[(a*g+b*g*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/(c*i+d*i*x)^3,x,14,1/4*B^2*(b*c-a*d)*g^3*n^2*(a+b*x)^2/(d^2*i^3*(c+d*x)^2)-4*A*b*B*(b*c-a*d)*g^3*n*(a+b*x)/(d^3*i^3*(c+d*x))+4*b*B^2*(b*c-a*d)*g^3*n^2*(a+b*x)/(d^3*i^3*(c+d*x))-4*b*B^2*(b*c-a*d)*g^3*n*(a+b*x)*log(e*((a+b*x)/(c+d*x))^n)/(d^3*i^3*(c+d*x))-1/2*B*(b*c-a*d)*g^3*n*(a+b*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(d^2*i^3*(c+d*x)^2)+b^2*g^3*(a+b*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/(d^3*i^3)+1/2*(b*c-a*d)*g^3*(a+b*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/(d^2*i^3*(c+d*x)^2)+2*b*(b*c-a*d)*g^3*(a+b*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/(d^3*i^3*(c+d*x))+2*b^2*B*(b*c-a*d)*g^3*n*(A+B*log(e*((a+b*x)/(c+d*x))^n))*log((b*c-a*d)/(b*(c+d*x)))/(d^4*i^3)+3*b^2*(b*c-a*d)*g^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2*log((b*c-a*d)/(b*(c+d*x)))/(d^4*i^3)+2*b^2*B^2*(b*c-a*d)*g^3*n^2*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(d^4*i^3)+6*b^2*B*(b*c-a*d)*g^3*n*(A+B*log(e*((a+b*x)/(c+d*x))^n))*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(d^4*i^3)-6*b^2*B^2*(b*c-a*d)*g^3*n^2*polylog(3,d*(a+b*x)/(b*(c+d*x)))/(d^4*i^3)],
[(a*g+b*g*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/(c*i+d*i*x)^3,x,11,-1/4*B^2*g^2*n^2*(a+b*x)^2/(d*i^3*(c+d*x)^2)+2*A*b*B*g^2*n*(a+b*x)/(d^2*i^3*(c+d*x))-2*b*B^2*g^2*n^2*(a+b*x)/(d^2*i^3*(c+d*x))+2*b*B^2*g^2*n*(a+b*x)*log(e*((a+b*x)/(c+d*x))^n)/(d^2*i^3*(c+d*x))+1/2*B*g^2*n*(a+b*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(d*i^3*(c+d*x)^2)-1/2*g^2*(a+b*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/(d*i^3*(c+d*x)^2)-b*g^2*(a+b*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/(d^2*i^3*(c+d*x))-b^2*g^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2*log((b*c-a*d)/(b*(c+d*x)))/(d^3*i^3)-2*b^2*B*g^2*n*(A+B*log(e*((a+b*x)/(c+d*x))^n))*polylog(2,d*(a+b*x)/(b*(c+d*x)))/(d^3*i^3)+2*b^2*B^2*g^2*n^2*polylog(3,d*(a+b*x)/(b*(c+d*x)))/(d^3*i^3)],
[(a*g+b*g*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/(c*i+d*i*x)^3,x,3,1/4*B^2*g*n^2*(a+b*x)^2/((b*c-a*d)*i^3*(c+d*x)^2)-1/2*B*g*n*(a+b*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)*i^3*(c+d*x)^2)+1/2*g*(a+b*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/((b*c-a*d)*i^3*(c+d*x)^2)],
[(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/(c*i+d*i*x)^3,x,8,-1/4*B^2*d*n^2*(a+b*x)^2/((b*c-a*d)^2*i^3*(c+d*x)^2)-2*A*b*B*n*(a+b*x)/((b*c-a*d)^2*i^3*(c+d*x))+2*b*B^2*n^2*(a+b*x)/((b*c-a*d)^2*i^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*i^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*i^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*i^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*i^3*(c+d*x))],
[(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/((a*g+b*g*x)*(c*i+d*i*x)^3),x,15,1/4*B^2*d^2*n^2*(a+b*x)^2/((b*c-a*d)^3*g*i^3*(c+d*x)^2)+4*A*b*B*d*n*(a+b*x)/((b*c-a*d)^3*g*i^3*(c+d*x))-4*b*B^2*d*n^2*(a+b*x)/((b*c-a*d)^3*g*i^3*(c+d*x))+4*b*B^2*d*n*(a+b*x)*log(e*((a+b*x)/(c+d*x))^n)/((b*c-a*d)^3*g*i^3*(c+d*x))-1/2*B*d^2*n*(a+b*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)^3*g*i^3*(c+d*x)^2)+1/2*d^2*(a+b*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/((b*c-a*d)^3*g*i^3*(c+d*x)^2)-2*b*d*(a+b*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/((b*c-a*d)^3*g*i^3*(c+d*x))+1/3*b^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))^3/(B*(b*c-a*d)^3*g*i^3*n)],
[(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/((a*g+b*g*x)^2*(c*i+d*i*x)^3),x,12,-1/4*B^2*d^3*n^2*(a+b*x)^2/((b*c-a*d)^4*g^2*i^3*(c+d*x)^2)-6*A*b*B*d^2*n*(a+b*x)/((b*c-a*d)^4*g^2*i^3*(c+d*x))+6*b*B^2*d^2*n^2*(a+b*x)/((b*c-a*d)^4*g^2*i^3*(c+d*x))-2*b^3*B^2*n^2*(c+d*x)/((b*c-a*d)^4*g^2*i^3*(a+b*x))-6*b*B^2*d^2*n*(a+b*x)*log(e*((a+b*x)/(c+d*x))^n)/((b*c-a*d)^4*g^2*i^3*(c+d*x))+1/2*B*d^3*n*(a+b*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)^4*g^2*i^3*(c+d*x)^2)-2*b^3*B*n*(c+d*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)^4*g^2*i^3*(a+b*x))-1/2*d^3*(a+b*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/((b*c-a*d)^4*g^2*i^3*(c+d*x)^2)+3*b*d^2*(a+b*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/((b*c-a*d)^4*g^2*i^3*(c+d*x))-b^3*(c+d*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/((b*c-a*d)^4*g^2*i^3*(a+b*x))-b^2*d*(A+B*log(e*((a+b*x)/(c+d*x))^n))^3/(B*(b*c-a*d)^4*g^2*i^3*n)],
[(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/((a*g+b*g*x)^3*(c*i+d*i*x)^3),x,14,1/4*B^2*d^4*n^2*(a+b*x)^2/((b*c-a*d)^5*g^3*i^3*(c+d*x)^2)+8*A*b*B*d^3*n*(a+b*x)/((b*c-a*d)^5*g^3*i^3*(c+d*x))-8*b*B^2*d^3*n^2*(a+b*x)/((b*c-a*d)^5*g^3*i^3*(c+d*x))+8*b^3*B^2*d*n^2*(c+d*x)/((b*c-a*d)^5*g^3*i^3*(a+b*x))-1/4*b^4*B^2*n^2*(c+d*x)^2/((b*c-a*d)^5*g^3*i^3*(a+b*x)^2)+8*b*B^2*d^3*n*(a+b*x)*log(e*((a+b*x)/(c+d*x))^n)/((b*c-a*d)^5*g^3*i^3*(c+d*x))-1/2*B*d^4*n*(a+b*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)^5*g^3*i^3*(c+d*x)^2)+8*b^3*B*d*n*(c+d*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)^5*g^3*i^3*(a+b*x))-1/2*b^4*B*n*(c+d*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)^5*g^3*i^3*(a+b*x)^2)+1/2*d^4*(a+b*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/((b*c-a*d)^5*g^3*i^3*(c+d*x)^2)-4*b*d^3*(a+b*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/((b*c-a*d)^5*g^3*i^3*(c+d*x))+4*b^3*d*(c+d*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/((b*c-a*d)^5*g^3*i^3*(a+b*x))-1/2*b^4*(c+d*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/((b*c-a*d)^5*g^3*i^3*(a+b*x)^2)+2*b^2*d^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))^3/(B*(b*c-a*d)^5*g^3*i^3*n)],
[(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/((a*g+b*g*x)^4*(c*i+d*i*x)^3),x,16,-1/4*B^2*d^5*n^2*(a+b*x)^2/((b*c-a*d)^6*g^4*i^3*(c+d*x)^2)-10*A*b*B*d^4*n*(a+b*x)/((b*c-a*d)^6*g^4*i^3*(c+d*x))+10*b*B^2*d^4*n^2*(a+b*x)/((b*c-a*d)^6*g^4*i^3*(c+d*x))-20*b^3*B^2*d^2*n^2*(c+d*x)/((b*c-a*d)^6*g^4*i^3*(a+b*x))+5/4*b^4*B^2*d*n^2*(c+d*x)^2/((b*c-a*d)^6*g^4*i^3*(a+b*x)^2)-2/27*b^5*B^2*n^2*(c+d*x)^3/((b*c-a*d)^6*g^4*i^3*(a+b*x)^3)-10*b*B^2*d^4*n*(a+b*x)*log(e*((a+b*x)/(c+d*x))^n)/((b*c-a*d)^6*g^4*i^3*(c+d*x))+1/2*B*d^5*n*(a+b*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)^6*g^4*i^3*(c+d*x)^2)-20*b^3*B*d^2*n*(c+d*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)^6*g^4*i^3*(a+b*x))+5/2*b^4*B*d*n*(c+d*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)^6*g^4*i^3*(a+b*x)^2)-2/9*b^5*B*n*(c+d*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)^6*g^4*i^3*(a+b*x)^3)-1/2*d^5*(a+b*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/((b*c-a*d)^6*g^4*i^3*(c+d*x)^2)+5*b*d^4*(a+b*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/((b*c-a*d)^6*g^4*i^3*(c+d*x))-10*b^3*d^2*(c+d*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/((b*c-a*d)^6*g^4*i^3*(a+b*x))+5/2*b^4*d*(c+d*x)^2*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/((b*c-a*d)^6*g^4*i^3*(a+b*x)^2)-1/3*b^5*(c+d*x)^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/((b*c-a*d)^6*g^4*i^3*(a+b*x)^3)-10/3*b^2*d^3*(A+B*log(e*((a+b*x)/(c+d*x))^n))^3/(B*(b*c-a*d)^6*g^4*i^3*n)],

# Integrands of the form (f+g x)^m (h+i x)^q (A+B Log[e ((a+b x) / (c+d x))^n])^p when b f-a g=0 and d h-c i=0 and m+q+2=0
[(a*g+b*g*x)^m*(c*i+d*i*x)^(-2-m)*(A+B*log(e*((a+b*x)/(c+d*x))^n))^p,x,3,(a+b*x)*(g*(a+b*x))^m*GAMMA(1+p,-(1+m)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(B*n))*(A+B*log(e*((a+b*x)/(c+d*x))^n))^p/((b*c-a*d)*exp(A*(1+m)/(B*n))*i^2*(1+m)*(e*((a+b*x)/(c+d*x))^n)^((1+m)/n)*(c+d*x)*(i*(c+d*x))^m*(-(1+m)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(B*n))^p)],
[(a*g+b*g*x)^(-2-m)*(c*i+d*i*x)^m*(A+B*log(e*((a+b*x)/(c+d*x))^n))^p,x,3,-exp(A*(1+m)/(B*n))*(a+b*x)*(g*(a+b*x))^(-2-m)*(e*((a+b*x)/(c+d*x))^n)^((1+m)/n)*(i*(c+d*x))^(2+m)*GAMMA(1+p,(1+m)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(B*n))*(A+B*log(e*((a+b*x)/(c+d*x))^n))^p/((b*c-a*d)*i^2*(1+m)*(c+d*x)*((1+m)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(B*n))^p)],
[(a*g+b*g*x)^m*(c*i+d*i*x)^(-2-m)*(A+B*log(e*((a+b*x)/(c+d*x))^n))^3,x,4,-6*B^3*n^3*(a+b*x)*(g*(a+b*x))^m/((b*c-a*d)*i^2*(1+m)^4*(c+d*x)*(i*(c+d*x))^m)+6*B^2*n^2*(a+b*x)*(g*(a+b*x))^m*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)*i^2*(1+m)^3*(c+d*x)*(i*(c+d*x))^m)-3*B*n*(a+b*x)*(g*(a+b*x))^m*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/((b*c-a*d)*i^2*(1+m)^2*(c+d*x)*(i*(c+d*x))^m)+(a+b*x)*(g*(a+b*x))^m*(A+B*log(e*((a+b*x)/(c+d*x))^n))^3/((b*c-a*d)*i^2*(1+m)*(c+d*x)*(i*(c+d*x))^m)],
[(a*g+b*g*x)^m*(c*i+d*i*x)^(-2-m)*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2,x,3,2*B^2*n^2*(a+b*x)*(g*(a+b*x))^m/((b*c-a*d)*i^2*(1+m)^3*(c+d*x)*(i*(c+d*x))^m)-2*B*n*(a+b*x)*(g*(a+b*x))^m*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)*i^2*(1+m)^2*(c+d*x)*(i*(c+d*x))^m)+(a+b*x)*(g*(a+b*x))^m*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/((b*c-a*d)*i^2*(1+m)*(c+d*x)*(i*(c+d*x))^m)],
[(a*g+b*g*x)^m*(c*i+d*i*x)^(-2-m)*(A+B*log(e*((a+b*x)/(c+d*x))^n)),x,2,-B*n*(a+b*x)*(g*(a+b*x))^m/((b*c-a*d)*i^2*(1+m)^2*(c+d*x)*(i*(c+d*x))^m)+(a+b*x)*(g*(a+b*x))^m*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)*i^2*(1+m)*(c+d*x)*(i*(c+d*x))^m)],
[(a*g+b*g*x)^m*(c*i+d*i*x)^(-2-m)/(A+B*log(e*((a+b*x)/(c+d*x))^n)),x,3,(a+b*x)*(g*(a+b*x))^m*Ei((1+m)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(B*n))/(B*(b*c-a*d)*exp(A*(1+m)/(B*n))*i^2*n*(e*((a+b*x)/(c+d*x))^n)^((1+m)/n)*(c+d*x)*(i*(c+d*x))^m)],
[(a*g+b*g*x)^m*(c*i+d*i*x)^(-2-m)/(A+B*log(e*((a+b*x)/(c+d*x))^n))^2,x,4,(1+m)*(a+b*x)*(g*(a+b*x))^m*Ei((1+m)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(B*n))/(B^2*(b*c-a*d)*exp(A*(1+m)/(B*n))*i^2*n^2*(e*((a+b*x)/(c+d*x))^n)^((1+m)/n)*(c+d*x)*(i*(c+d*x))^m)-(a+b*x)*(g*(a+b*x))^m/(B*(b*c-a*d)*i^2*n*(c+d*x)*(i*(c+d*x))^m*(A+B*log(e*((a+b*x)/(c+d*x))^n)))],
[(a*g+b*g*x)^m*(c*i+d*i*x)^(-2-m)/(A+B*log(e*((a+b*x)/(c+d*x))^n))^3,x,5,1/2*(1+m)^2*(a+b*x)*(g*(a+b*x))^m*Ei((1+m)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(B*n))/(B^3*(b*c-a*d)*exp(A*(1+m)/(B*n))*i^2*n^3*(e*((a+b*x)/(c+d*x))^n)^((1+m)/n)*(c+d*x)*(i*(c+d*x))^m)-1/2*(a+b*x)*(g*(a+b*x))^m/(B*(b*c-a*d)*i^2*n*(c+d*x)*(i*(c+d*x))^m*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2)-1/2*(1+m)*(a+b*x)*(g*(a+b*x))^m/(B^2*(b*c-a*d)*i^2*n^2*(c+d*x)*(i*(c+d*x))^m*(A+B*log(e*((a+b*x)/(c+d*x))^n)))],
[(a*g+b*g*x)^(-2-m)*(c*i+d*i*x)^m*(A+B*log(e*((a+b*x)/(c+d*x))^n))^3,x,4,-6*B^3*n^3*(a+b*x)*(g*(a+b*x))^(-2-m)*(i*(c+d*x))^(2+m)/((b*c-a*d)*i^2*(1+m)^4*(c+d*x))-6*B^2*n^2*(a+b*x)*(g*(a+b*x))^(-2-m)*(i*(c+d*x))^(2+m)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)*i^2*(1+m)^3*(c+d*x))-3*B*n*(a+b*x)*(g*(a+b*x))^(-2-m)*(i*(c+d*x))^(2+m)*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/((b*c-a*d)*i^2*(1+m)^2*(c+d*x))-(a+b*x)*(g*(a+b*x))^(-2-m)*(i*(c+d*x))^(2+m)*(A+B*log(e*((a+b*x)/(c+d*x))^n))^3/((b*c-a*d)*i^2*(1+m)*(c+d*x))],
[(a*g+b*g*x)^(-2-m)*(c*i+d*i*x)^m*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2,x,3,-2*B^2*n^2*(a+b*x)*(g*(a+b*x))^(-2-m)*(i*(c+d*x))^(2+m)/((b*c-a*d)*i^2*(1+m)^3*(c+d*x))-2*B*n*(a+b*x)*(g*(a+b*x))^(-2-m)*(i*(c+d*x))^(2+m)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)*i^2*(1+m)^2*(c+d*x))-(a+b*x)*(g*(a+b*x))^(-2-m)*(i*(c+d*x))^(2+m)*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2/((b*c-a*d)*i^2*(1+m)*(c+d*x))],
[(a*g+b*g*x)^(-2-m)*(c*i+d*i*x)^m*(A+B*log(e*((a+b*x)/(c+d*x))^n)),x,2,-B*n*(a+b*x)*(g*(a+b*x))^(-2-m)*(i*(c+d*x))^(2+m)/((b*c-a*d)*i^2*(1+m)^2*(c+d*x))-(a+b*x)*(g*(a+b*x))^(-2-m)*(i*(c+d*x))^(2+m)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)*i^2*(1+m)*(c+d*x))],
[(a*g+b*g*x)^(-2-m)*(c*i+d*i*x)^m/(A+B*log(e*((a+b*x)/(c+d*x))^n)),x,3,exp(A*(1+m)/(B*n))*(a+b*x)*(g*(a+b*x))^(-2-m)*(e*((a+b*x)/(c+d*x))^n)^((1+m)/n)*(i*(c+d*x))^(2+m)*Ei(-(1+m)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(B*n))/(B*(b*c-a*d)*i^2*n*(c+d*x))],
[(a*g+b*g*x)^(-2-m)*(c*i+d*i*x)^m/(A+B*log(e*((a+b*x)/(c+d*x))^n))^2,x,4,-exp(A*(1+m)/(B*n))*(1+m)*(a+b*x)*(g*(a+b*x))^(-2-m)*(e*((a+b*x)/(c+d*x))^n)^((1+m)/n)*(i*(c+d*x))^(2+m)*Ei(-(1+m)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(B*n))/(B^2*(b*c-a*d)*i^2*n^2*(c+d*x))-(a+b*x)*(g*(a+b*x))^(-2-m)*(i*(c+d*x))^(2+m)/(B*(b*c-a*d)*i^2*n*(c+d*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n)))],
[(a*g+b*g*x)^(-2-m)*(c*i+d*i*x)^m/(A+B*log(e*((a+b*x)/(c+d*x))^n))^3,x,5,1/2*exp(A*(1+m)/(B*n))*(1+m)^2*(a+b*x)*(g*(a+b*x))^(-2-m)*(e*((a+b*x)/(c+d*x))^n)^((1+m)/n)*(i*(c+d*x))^(2+m)*Ei(-(1+m)*(A+B*log(e*((a+b*x)/(c+d*x))^n))/(B*n))/(B^3*(b*c-a*d)*i^2*n^3*(c+d*x))-1/2*(a+b*x)*(g*(a+b*x))^(-2-m)*(i*(c+d*x))^(2+m)/(B*(b*c-a*d)*i^2*n*(c+d*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2)+1/2*(1+m)*(a+b*x)*(g*(a+b*x))^(-2-m)*(i*(c+d*x))^(2+m)/(B^2*(b*c-a*d)*i^2*n^2*(c+d*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n)))],

# Integrands of the form (f+g x)^m (h+i x)^q (A+B Log[e ((a+b x) / (c+d x))^n])^p when b f-a g=0 and d h-c i=0 and p symbolic
[log(e*((a+b*x)/(c+d*x))^n)^p/((a+b*x)*(c+d*x)),x,3,log(e*((a+b*x)/(c+d*x))^n)^(1+p)/((b*c-a*d)*n*(1+p))],
[log(e*((a+b*x)/(c+d*x))^n)^p/(a*c+(b*c+a*d)*x+b*d*x^2),x,4,log(e*((a+b*x)/(c+d*x))^n)^(1+p)/((b*c-a*d)*n*(1+p))],

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

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

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

# Integrands of the form (f+g x)^m (h+i x)^q (A+B Log[e (a+b x)^n/(c+d x)^n]) when b f-a g=0 and d h-c i=0
[(a*g+b*g*x)^m*(c*i+d*i*x)^(-2-m)*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^p,x,4,(a+b*x)*(g*(a+b*x))^m*GAMMA(1+p,-(1+m)*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))/(B*n))*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^p/((b*c-a*d)*exp(A*(1+m)/(B*n))*i^2*(1+m)*(c+d*x)*(i*(c+d*x))^m*(e*(a+b*x)^n/(c+d*x)^n)^((1+m)/n)*(-(1+m)*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))/(B*n))^p)],
[(a*g+b*g*x)^(-2-m)*(c*i+d*i*x)^m*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^p,x,4,-exp(A*(1+m)/(B*n))*(a+b*x)*(g*(a+b*x))^(-2-m)*(i*(c+d*x))^(2+m)*(e*(a+b*x)^n/(c+d*x)^n)^((1+m)/n)*GAMMA(1+p,(1+m)*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))/(B*n))*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^p/((b*c-a*d)*i^2*(1+m)*(c+d*x)*((1+m)*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))/(B*n))^p)],
[(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^3/((a+b*x)*(c+d*x)),x,4,1/4*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^4/(B*(b*c-a*d)*n)],
[(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^2/((a+b*x)*(c+d*x)),x,4,1/3*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^3/(B*(b*c-a*d)*n)],
[(A+B*log(e*(a+b*x)^n/(c+d*x)^n))/((a+b*x)*(c+d*x)),x,3,1/2*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^2/(B*(b*c-a*d)*n)],
[1/((a+b*x)*(c+d*x)*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))),x,4,log(A+B*log(e*(a+b*x)^n/(c+d*x)^n))/(B*(b*c-a*d)*n)],
[1/((a+b*x)*(c+d*x)*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^2),x,4,(-1)/(B*(b*c-a*d)*n*(A+B*log(e*(a+b*x)^n/(c+d*x)^n)))],
[1/((a+b*x)*(c+d*x)*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^3),x,4,(-1/2)/(B*(b*c-a*d)*n*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^2)],
[(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^p/((a+b*x)*(c+d*x)),x,4,(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^(1+p)/(B*(b*c-a*d)*n*(1+p))],
[(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^p/((a*f+b*f*x)*(c*g+d*g*x)),x,4,(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^(1+p)/(B*(b*c-a*d)*f*g*n*(1+p))],
[(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^p/(a*c*f+(b*c+a*d)*f*x+b*d*f*x^2),x,5,(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^(1+p)/(B*(b*c-a*d)*f*n*(1+p))],
[1/((a+b*x)*(c+d*x)*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))),x,4,log(A+B*log(e*(a+b*x)^n/(c+d*x)^n))/(B*(b*c-a*d)*n)],
[1/((a*f+b*f*x)*(c*g+d*g*x)*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))),x,4,log(A+B*log(e*(a+b*x)^n/(c+d*x)^n))/(B*(b*c-a*d)*f*g*n)],
[1/((a*c*f+(b*c+a*d)*f*x+b*d*f*x^2)*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))),x,5,log(A+B*log(e*(a+b*x)^n/(c+d*x)^n))/(B*(b*c-a*d)*f*n)],

# Integrands of the form (f+g x)^m (h+i x)^q / (A+B Log[e (a+b x)^n/(c+d x)^n]) when b f-a g=0 and d h-c i=0 and m+n+2=0
[(a+b*x)^m*(c+d*x)^(-2-m)/log(e*(a+b*x)^n/(c+d*x)^n),x,4,(a+b*x)^(1+m)*(c+d*x)^(-1-m)*Ei((1+m)*log(e*(a+b*x)^n/(c+d*x)^n)/n)/((b*c-a*d)*n*(e*(a+b*x)^n/(c+d*x)^n)^((1+m)/n))],
[(a+b*x)^3/((c+d*x)^5*log(e*((a+b*x)/(c+d*x))^n)),x,3,(a+b*x)^4*Ei(4*log(e*((a+b*x)/(c+d*x))^n)/n)/((b*c-a*d)*n*(e*((a+b*x)/(c+d*x))^n)^(4/n)*(c+d*x)^4)],
[(a+b*x)^2/((c+d*x)^4*log(e*((a+b*x)/(c+d*x))^n)),x,3,(a+b*x)^3*Ei(3*log(e*((a+b*x)/(c+d*x))^n)/n)/((b*c-a*d)*n*(e*((a+b*x)/(c+d*x))^n)^(3/n)*(c+d*x)^3)],
[(a+b*x)/((c+d*x)^3*log(e*((a+b*x)/(c+d*x))^n)),x,3,(a+b*x)^2*Ei(2*log(e*((a+b*x)/(c+d*x))^n)/n)/((b*c-a*d)*n*(e*((a+b*x)/(c+d*x))^n)^(2/n)*(c+d*x)^2)],
[1/((c+d*x)^2*log(e*((a+b*x)/(c+d*x))^n)),x,3,(a+b*x)*Ei(log(e*((a+b*x)/(c+d*x))^n)/n)/((b*c-a*d)*n*(e*((a+b*x)/(c+d*x))^n)^(1/n)*(c+d*x))],
[1/((a+b*x)*(c+d*x)*log(e*((a+b*x)/(c+d*x))^n)),x,3,log(log(e*((a+b*x)/(c+d*x))^n))/((b*c-a*d)*n)],
[1/((a+b*x)^2*log(e*((a+b*x)/(c+d*x))^n)),x,3,(e*((a+b*x)/(c+d*x))^n)^(1/n)*(c+d*x)*Ei(-log(e*((a+b*x)/(c+d*x))^n)/n)/((b*c-a*d)*n*(a+b*x))],
[(c+d*x)/((a+b*x)^3*log(e*((a+b*x)/(c+d*x))^n)),x,3,(e*((a+b*x)/(c+d*x))^n)^(2/n)*(c+d*x)^2*Ei(-2*log(e*((a+b*x)/(c+d*x))^n)/n)/((b*c-a*d)*n*(a+b*x)^2)],
[(c+d*x)^2/((a+b*x)^4*log(e*((a+b*x)/(c+d*x))^n)),x,3,(e*((a+b*x)/(c+d*x))^n)^(3/n)*(c+d*x)^3*Ei(-3*log(e*((a+b*x)/(c+d*x))^n)/n)/((b*c-a*d)*n*(a+b*x)^3)],

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

# Integrands of the form (A+B Log[e (a+b x)^n/(c+d x)^n])^p / ((f+g x) (h+i x)) when b f-a g=0
[(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^4/((f+g*x)*(a*h+b*h*x)),x,8,-(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^4*log(1-(b*f-a*g)*(c+d*x)/((d*f-c*g)*(a+b*x)))/((b*f-a*g)*h)+4*B*n*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^3*polylog(2,(b*f-a*g)*(c+d*x)/((d*f-c*g)*(a+b*x)))/((b*f-a*g)*h)+12*B^2*n^2*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^2*polylog(3,(b*f-a*g)*(c+d*x)/((d*f-c*g)*(a+b*x)))/((b*f-a*g)*h)+24*B^3*n^3*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))*polylog(4,(b*f-a*g)*(c+d*x)/((d*f-c*g)*(a+b*x)))/((b*f-a*g)*h)+24*B^4*n^4*polylog(5,(b*f-a*g)*(c+d*x)/((d*f-c*g)*(a+b*x)))/((b*f-a*g)*h)],
[(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^3/((f+g*x)*(a*h+b*h*x)),x,7,-(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^3*log(1-(b*f-a*g)*(c+d*x)/((d*f-c*g)*(a+b*x)))/((b*f-a*g)*h)+3*B*n*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^2*polylog(2,(b*f-a*g)*(c+d*x)/((d*f-c*g)*(a+b*x)))/((b*f-a*g)*h)+6*B^2*n^2*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))*polylog(3,(b*f-a*g)*(c+d*x)/((d*f-c*g)*(a+b*x)))/((b*f-a*g)*h)+6*B^3*n^3*polylog(4,(b*f-a*g)*(c+d*x)/((d*f-c*g)*(a+b*x)))/((b*f-a*g)*h)],
[(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^2/((f+g*x)*(a*h+b*h*x)),x,6,-(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^2*log(1-(b*f-a*g)*(c+d*x)/((d*f-c*g)*(a+b*x)))/((b*f-a*g)*h)+2*B*n*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))*polylog(2,(b*f-a*g)*(c+d*x)/((d*f-c*g)*(a+b*x)))/((b*f-a*g)*h)+2*B^2*n^2*polylog(3,(b*f-a*g)*(c+d*x)/((d*f-c*g)*(a+b*x)))/((b*f-a*g)*h)],
[(A+B*log(e*(a+b*x)^n/(c+d*x)^n))/((f+g*x)*(a*h+b*h*x)),x,5,-(A+B*log(e*(a+b*x)^n/(c+d*x)^n))*log(1-(b*f-a*g)*(c+d*x)/((d*f-c*g)*(a+b*x)))/((b*f-a*g)*h)+B*n*polylog(2,(b*f-a*g)*(c+d*x)/((d*f-c*g)*(a+b*x)))/((b*f-a*g)*h)],
[1/((f+g*x)*(a*h+b*h*x)*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))),x,1,_eval(Unintegrable(1/((f+g*x)*(a*h+b*h*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))),x),e*((a+b*x)/(c+d*x))^n=e*(a+b*x)^n/(c+d*x)^n)],
[1/((f+g*x)*(a*h+b*h*x)*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^2),x,1,_eval(Unintegrable(1/((f+g*x)*(a*h+b*h*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2),x),e*((a+b*x)/(c+d*x))^n=e*(a+b*x)^n/(c+d*x)^n)],
[log((c+d*x)/(a+b*x))/((a+b*x)*((a-c)*h+(b-d)*h*x)),x,2,-polylog(2,1+(-c-d*x)/(a+b*x))/((b*c-a*d)*h)],
[log((a-c*g+(b-d*g)*x)/(a+b*x))/((a+b*x)*(c+d*x)),x,2,polylog(2,g*(c+d*x)/(a+b*x))/(b*c-a*d)],
[log(1-g*(c+d*x)/(a+b*x))/((a+b*x)*(c+d*x)),x,3,polylog(2,g*(c+d*x)/(a+b*x))/(b*c-a*d)],
[log((a-c*g+b*x-d*g*x)/(a+b*x))/((a+b*x)*(c+d*x)),x,3,polylog(2,g*(c+d*x)/(a+b*x))/(b*c-a*d)],

# Integrands of the form (A+B Log[e (a+b x)^n/(c+d x)^n])^p / (g+h x+i x^2)
[(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^3/(a*f*h+b*g*h*x^2+h*(b*f*x+a*g*x)),x,8,-(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^3*log(1-(b*f-a*g)*(c+d*x)/((d*f-c*g)*(a+b*x)))/((b*f-a*g)*h)+3*B*n*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^2*polylog(2,(b*f-a*g)*(c+d*x)/((d*f-c*g)*(a+b*x)))/((b*f-a*g)*h)+6*B^2*n^2*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))*polylog(3,(b*f-a*g)*(c+d*x)/((d*f-c*g)*(a+b*x)))/((b*f-a*g)*h)+6*B^3*n^3*polylog(4,(b*f-a*g)*(c+d*x)/((d*f-c*g)*(a+b*x)))/((b*f-a*g)*h)],
[(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^2/(a*f*h+b*g*h*x^2+h*(b*f*x+a*g*x)),x,7,-(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^2*log(1-(b*f-a*g)*(c+d*x)/((d*f-c*g)*(a+b*x)))/((b*f-a*g)*h)+2*B*n*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))*polylog(2,(b*f-a*g)*(c+d*x)/((d*f-c*g)*(a+b*x)))/((b*f-a*g)*h)+2*B^2*n^2*polylog(3,(b*f-a*g)*(c+d*x)/((d*f-c*g)*(a+b*x)))/((b*f-a*g)*h)],
[(A+B*log(e*(a+b*x)^n/(c+d*x)^n))/(a*f*h+b*g*h*x^2+h*(b*f*x+a*g*x)),x,6,-(A+B*log(e*(a+b*x)^n/(c+d*x)^n))*log(1-(b*f-a*g)*(c+d*x)/((d*f-c*g)*(a+b*x)))/((b*f-a*g)*h)+B*n*polylog(2,(b*f-a*g)*(c+d*x)/((d*f-c*g)*(a+b*x)))/((b*f-a*g)*h)],
[1/((a*f*h+b*g*h*x^2+h*(b*f*x+a*g*x))*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))),x,3,_eval(Unintegrable(1/((a+b*x)*(f+g*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))),x),e*((a+b*x)/(c+d*x))^n=e*(a+b*x)^n/(c+d*x)^n)/h],
[1/((a*f*h+b*g*h*x^2+h*(b*f*x+a*g*x))*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^2),x,3,_eval(Unintegrable(1/((a+b*x)*(f+g*x)*(A+B*log(e*((a+b*x)/(c+d*x))^n))^2),x),e*((a+b*x)/(c+d*x))^n=e*(a+b*x)^n/(c+d*x)^n)/h]]:
