# Maple integration test file: "3 Logarithms\3.1.4 (f x)^m (d+e x^r)^q (a+b log(c x^n))^p.txt"

lst:=[

# Integrands of the form (f x)^m (d+e x^r)^q (a+b Log[c x^n])^p

# Integrands of the form (f x)^m (d+e x^1)^q (a+b Log[c x^n])^p

# Integrands of the form x^m (d+e x)^q (a+b Log[c x^n])

# q>0
[x^3*(d+e*x)*(a+b*log(c*x^n)),x,4,-1/16*b*d*n*x^4-1/25*b*e*n*x^5+1/20*(5*d*x^4+4*e*x^5)*(a+b*log(c*x^n))],
[x^2*(d+e*x)*(a+b*log(c*x^n)),x,4,-1/9*b*d*n*x^3-1/16*b*e*n*x^4+1/12*(4*d*x^3+3*e*x^4)*(a+b*log(c*x^n))],
[x*(d+e*x)*(a+b*log(c*x^n)),x,4,-1/4*b*d*n*x^2-1/9*b*e*n*x^3+1/6*(3*d*x^2+2*e*x^3)*(a+b*log(c*x^n))],
[(d+e*x)*(a+b*log(c*x^n)),x,2,-b*d*n*x-1/4*b*e*n*x^2+d*x*(a+b*log(c*x^n))+1/2*e*x^2*(a+b*log(c*x^n))],
[(d+e*x)*(a+b*log(c*x^n))/x,x,4,a*e*x-b*e*n*x+b*e*x*log(c*x^n)+1/2*d*(a+b*log(c*x^n))^2/(b*n)],
[(d+e*x)*(a+b*log(c*x^n))/x^2,x,4,-b*d*n/x-d*(a+b*log(c*x^n))/x+1/2*e*(a+b*log(c*x^n))^2/(b*n),-b*d*n/x-1/2*b*e*n*log(x)^2-d*(a+b*log(c*x^n))/x+e*log(x)*(a+b*log(c*x^n))],
[(d+e*x)*(a+b*log(c*x^n))/x^3,x,4,-1/4*b*d*n/x^2-b*e*n/x+1/2*b*e^2*n*log(x)/d-1/2*(d+e*x)^2*(a+b*log(c*x^n))/(d*x^2)],
[(d+e*x)*(a+b*log(c*x^n))/x^4,x,4,-1/9*b*d*n/x^3-1/4*b*e*n/x^2-1/3*d*(a+b*log(c*x^n))/x^3-1/2*e*(a+b*log(c*x^n))/x^2],
[x^3*(d+e*x)^2*(a+b*log(c*x^n)),x,4,-1/16*b*d^2*n*x^4-2/25*b*d*e*n*x^5-1/36*b*e^2*n*x^6+1/60*(15*d^2*x^4+24*d*e*x^5+10*e^2*x^6)*(a+b*log(c*x^n))],
[x^2*(d+e*x)^2*(a+b*log(c*x^n)),x,4,-1/9*b*d^2*n*x^3-1/8*b*d*e*n*x^4-1/25*b*e^2*n*x^5+1/30*(10*d^2*x^3+15*d*e*x^4+6*e^2*x^5)*(a+b*log(c*x^n))],
[x*(d+e*x)^2*(a+b*log(c*x^n)),x,4,-1/4*b*d^2*n*x^2-2/9*b*d*e*n*x^3-1/16*b*e^2*n*x^4+1/12*(6*d^2*x^2+8*d*e*x^3+3*e^2*x^4)*(a+b*log(c*x^n))],
[(d+e*x)^2*(a+b*log(c*x^n)),x,4,-b*d^2*n*x-1/2*b*d*e*n*x^2-1/9*b*e^2*n*x^3-1/3*b*d^3*n*log(x)/e+1/3*(d+e*x)^3*(a+b*log(c*x^n))/e],
[(d+e*x)^2*(a+b*log(c*x^n))/x,x,3,-1/4*b*n*(4*d+e*x)^2-1/2*b*d^2*n*log(x)^2+2*d*e*x*(a+b*log(c*x^n))+1/2*e^2*x^2*(a+b*log(c*x^n))+d^2*log(x)*(a+b*log(c*x^n))],
[(d+e*x)^2*(a+b*log(c*x^n))/x^2,x,3,-b*d^2*n/x-b*e^2*n*x-b*d*e*n*log(x)^2-d^2*(a+b*log(c*x^n))/x+e^2*x*(a+b*log(c*x^n))+2*d*e*log(x)*(a+b*log(c*x^n))],
[(d+e*x)^2*(a+b*log(c*x^n))/x^3,x,6,-1/4*b*n*(d+4*e*x)^2/x^2-1/2*b*e^2*n*log(x)^2-1/2*d^2*(a+b*log(c*x^n))/x^2-2*d*e*(a+b*log(c*x^n))/x+e^2*log(x)*(a+b*log(c*x^n))],
[(d+e*x)^2*(a+b*log(c*x^n))/x^4,x,4,-1/9*b*d^2*n/x^3-1/2*b*d*e*n/x^2-b*e^2*n/x+1/3*b*e^3*n*log(x)/d-1/3*(d+e*x)^3*(a+b*log(c*x^n))/(d*x^3)],
[(d+e*x)^2*(a+b*log(c*x^n))/x^5,x,4,-1/16*b*d^2*n/x^4-2/9*b*d*e*n/x^3-1/4*b*e^2*n/x^2-1/4*d^2*(a+b*log(c*x^n))/x^4-2/3*d*e*(a+b*log(c*x^n))/x^3-1/2*e^2*(a+b*log(c*x^n))/x^2],
[(d+e*x)^2*(a+b*log(c*x^n))/x^6,x,4,-1/25*b*d^2*n/x^5-1/8*b*d*e*n/x^4-1/9*b*e^2*n/x^3-1/5*d^2*(a+b*log(c*x^n))/x^5-1/2*d*e*(a+b*log(c*x^n))/x^4-1/3*e^2*(a+b*log(c*x^n))/x^3],
[x^3*(d+e*x)^3*(a+b*log(c*x^n)),x,4,-1/16*b*d^3*n*x^4-3/25*b*d^2*e*n*x^5-1/12*b*d*e^2*n*x^6-1/49*b*e^3*n*x^7+1/140*(35*d^3*x^4+84*d^2*e*x^5+70*d*e^2*x^6+20*e^3*x^7)*(a+b*log(c*x^n))],
[x^2*(d+e*x)^3*(a+b*log(c*x^n)),x,4,-1/9*b*d^3*n*x^3-3/16*b*d^2*e*n*x^4-3/25*b*d*e^2*n*x^5-1/36*b*e^3*n*x^6+1/60*(20*d^3*x^3+45*d^2*e*x^4+36*d*e^2*x^5+10*e^3*x^6)*(a+b*log(c*x^n))],
[x*(d+e*x)^3*(a+b*log(c*x^n)),x,5,1/5*b*d^4*n*x/e+3/20*b*d^3*n*x^2+1/15*b*d^2*e*n*x^3+1/80*b*d*e^2*n*x^4-1/25*b*n*(d+e*x)^5/e^2+1/20*b*d^5*n*log(x)/e^2-1/20*(5*d*(d+e*x)^4/e^2-4*(d+e*x)^5/e^2)*(a+b*log(c*x^n))],
[(d+e*x)^3*(a+b*log(c*x^n)),x,4,-b*d^3*n*x-3/4*b*d^2*e*n*x^2-1/3*b*d*e^2*n*x^3-1/16*b*e^3*n*x^4-1/4*b*d^4*n*log(x)/e+1/4*(d+e*x)^4*(a+b*log(c*x^n))/e],
[(d+e*x)^3*(a+b*log(c*x^n))/x,x,4,-3*b*d^2*e*n*x-3/4*b*d*e^2*n*x^2-1/9*b*e^3*n*x^3-1/2*b*d^3*n*log(x)^2+3*d^2*e*x*(a+b*log(c*x^n))+3/2*d*e^2*x^2*(a+b*log(c*x^n))+1/3*e^3*x^3*(a+b*log(c*x^n))+d^3*log(x)*(a+b*log(c*x^n))],
[(d+e*x)^3*(a+b*log(c*x^n))/x^2,x,3,-b*d^3*n/x-3*b*d*e^2*n*x-1/4*b*e^3*n*x^2-3/2*b*d^2*e*n*log(x)^2-d^3*(a+b*log(c*x^n))/x+3*d*e^2*x*(a+b*log(c*x^n))+1/2*e^3*x^2*(a+b*log(c*x^n))+3*d^2*e*log(x)*(a+b*log(c*x^n))],
[(d+e*x)^3*(a+b*log(c*x^n))/x^3,x,3,-1/4*b*d^3*n/x^2-3*b*d^2*e*n/x-b*e^3*n*x-3/2*b*d*e^2*n*log(x)^2-1/2*d^3*(a+b*log(c*x^n))/x^2-3*d^2*e*(a+b*log(c*x^n))/x+e^3*x*(a+b*log(c*x^n))+3*d*e^2*log(x)*(a+b*log(c*x^n))],
[(d+e*x)^3*(a+b*log(c*x^n))/x^4,x,7,-1/9*b*d^3*n/x^3-3/4*b*d^2*e*n/x^2-3*b*d*e^2*n/x-1/2*b*e^3*n*log(x)^2-1/3*d^3*(a+b*log(c*x^n))/x^3-3/2*d^2*e*(a+b*log(c*x^n))/x^2-3*d*e^2*(a+b*log(c*x^n))/x+e^3*log(x)*(a+b*log(c*x^n))],
[(d+e*x)^3*(a+b*log(c*x^n))/x^5,x,4,-1/16*b*d^3*n/x^4-1/3*b*d^2*e*n/x^3-3/4*b*d*e^2*n/x^2-b*e^3*n/x+1/4*b*e^4*n*log(x)/d-1/4*(d+e*x)^4*(a+b*log(c*x^n))/(d*x^4)],
[(d+e*x)^3*(a+b*log(c*x^n))/x^6,x,5,1/80*b*d^2*e*n/x^4+1/15*b*d*e^2*n/x^3+3/20*b*e^3*n/x^2+1/5*b*e^4*n/(d*x)-1/25*b*n*(d+e*x)^5/(d^2*x^5)-1/20*b*e^5*n*log(x)/d^2-1/5*(d+e*x)^4*(a+b*log(c*x^n))/(d*x^5)+1/20*e*(d+e*x)^4*(a+b*log(c*x^n))/(d^2*x^4)],
[(d+e*x)^3*(a+b*log(c*x^n))/x^7,x,4,-1/36*b*d^3*n/x^6-3/25*b*d^2*e*n/x^5-3/16*b*d*e^2*n/x^4-1/9*b*e^3*n/x^3-1/6*d^3*(a+b*log(c*x^n))/x^6-3/5*d^2*e*(a+b*log(c*x^n))/x^5-3/4*d*e^2*(a+b*log(c*x^n))/x^4-1/3*e^3*(a+b*log(c*x^n))/x^3],
[(d+e*x)^3*(a+b*log(c*x^n))/x^8,x,4,-1/49*b*d^3*n/x^7-1/12*b*d^2*e*n/x^6-3/25*b*d*e^2*n/x^5-1/16*b*e^3*n/x^4-1/7*d^3*(a+b*log(c*x^n))/x^7-1/2*d^2*e*(a+b*log(c*x^n))/x^6-3/5*d*e^2*(a+b*log(c*x^n))/x^5-1/4*e^3*(a+b*log(c*x^n))/x^4],

# q<0
[x^3*(a+b*log(c*x^n))/(d+e*x),x,8,a*d^2*x/e^3-b*d^2*n*x/e^3+1/4*b*d*n*x^2/e^2-1/9*b*n*x^3/e+b*d^2*x*log(c*x^n)/e^3-1/2*d*x^2*(a+b*log(c*x^n))/e^2+1/3*x^3*(a+b*log(c*x^n))/e-d^3*(a+b*log(c*x^n))*log(1+e*x/d)/e^4-b*d^3*n*polylog(2,-e*x/d)/e^4],
[x^2*(a+b*log(c*x^n))/(d+e*x),x,7,-a*d*x/e^2+b*d*n*x/e^2-1/4*b*n*x^2/e-b*d*x*log(c*x^n)/e^2+1/2*x^2*(a+b*log(c*x^n))/e+d^2*(a+b*log(c*x^n))*log(1+e*x/d)/e^3+b*d^2*n*polylog(2,-e*x/d)/e^3],
[x*(a+b*log(c*x^n))/(d+e*x),x,6,a*x/e-b*n*x/e+b*x*log(c*x^n)/e-d*(a+b*log(c*x^n))*log(1+e*x/d)/e^2-b*d*n*polylog(2,-e*x/d)/e^2],
[(a+b*log(c*x^n))/(d+e*x),x,2,(a+b*log(c*x^n))*log(1+e*x/d)/e+b*n*polylog(2,-e*x/d)/e],
[(a+b*log(c*x^n))/(x*(d+e*x)),x,2,-log(1+d/(e*x))*(a+b*log(c*x^n))/d+b*n*polylog(2,-d/(e*x))/d],
[(a+b*log(c*x^n))/(x^2*(d+e*x)),x,4,-b*n/(d*x)+(-a-b*log(c*x^n))/(d*x)+e*log(1+d/(e*x))*(a+b*log(c*x^n))/d^2-b*e*n*polylog(2,-d/(e*x))/d^2],
[(a+b*log(c*x^n))/(x^3*(d+e*x)),x,6,-1/4*b*n/(d*x^2)+b*e*n/(d^2*x)+1/2*(-a-b*log(c*x^n))/(d*x^2)+e*(a+b*log(c*x^n))/(d^2*x)-e^2*log(1+d/(e*x))*(a+b*log(c*x^n))/d^3+b*e^2*n*polylog(2,-d/(e*x))/d^3],
[(a+b*log(c*x^n))/(x^4*(d+e*x)),x,8,-1/9*b*n/(d*x^3)+1/4*b*e*n/(d^2*x^2)-b*e^2*n/(d^3*x)+1/3*(-a-b*log(c*x^n))/(d*x^3)+1/2*e*(a+b*log(c*x^n))/(d^2*x^2)-e^2*(a+b*log(c*x^n))/(d^3*x)+e^3*log(1+d/(e*x))*(a+b*log(c*x^n))/d^4-b*e^3*n*polylog(2,-d/(e*x))/d^4],
[x^3*(a+b*log(c*x^n))/(d+e*x)^2,x,8,3*b*d*n*x/e^3-d*(3*a+b*n)*x/e^3-3/4*b*n*x^2/e^2-3*b*d*x*log(c*x^n)/e^3-x^3*(a+b*log(c*x^n))/(e*(d+e*x))+1/2*x^2*(3*a+b*n+3*b*log(c*x^n))/e^2+d^2*(3*a+b*n+3*b*log(c*x^n))*log(1+e*x/d)/e^4+3*b*d^2*n*polylog(2,-e*x/d)/e^4],
[x^2*(a+b*log(c*x^n))/(d+e*x)^2,x,7,-b*n*x/e^2+2*x*(a+b*log(c*x^n))/e^2-x^2*(a+b*log(c*x^n))/(e*(d+e*x))-d*(2*a+b*n+2*b*log(c*x^n))*log(1+e*x/d)/e^3-2*b*d*n*polylog(2,-e*x/d)/e^3,-2*b*n*x/e^2+(2*a+b*n)*x/e^2+2*b*x*log(c*x^n)/e^2-x^2*(a+b*log(c*x^n))/(e*(d+e*x))-d*(2*a+b*n+2*b*log(c*x^n))*log(1+e*x/d)/e^3-2*b*d*n*polylog(2,-e*x/d)/e^3],
[x*(a+b*log(c*x^n))/(d+e*x)^2,x,3,-x*(a+b*log(c*x^n))/(e*(d+e*x))+(a+b*n+b*log(c*x^n))*log(1+e*x/d)/e^2+b*n*polylog(2,-e*x/d)/e^2],
[(a+b*log(c*x^n))/(d+e*x)^2,x,2,x*(a+b*log(c*x^n))/(d*(d+e*x))-b*n*log(d+e*x)/(d*e)],
[(a+b*log(c*x^n))/(x*(d+e*x)^2),x,5,-e*x*(a+b*log(c*x^n))/(d^2*(d+e*x))-log(1+d/(e*x))*(a+b*log(c*x^n))/d^2+b*n*log(d+e*x)/d^2+b*n*polylog(2,-d/(e*x))/d^2],
[(a+b*log(c*x^n))/(x^2*(d+e*x)^2),x,7,-b*n/(d^2*x)+(-a-b*log(c*x^n))/(d^2*x)+e^2*x*(a+b*log(c*x^n))/(d^3*(d+e*x))+2*e*log(1+d/(e*x))*(a+b*log(c*x^n))/d^3-b*e*n*log(d+e*x)/d^3-2*b*e*n*polylog(2,-d/(e*x))/d^3],
[(a+b*log(c*x^n))/(x^3*(d+e*x)^2),x,8,-1/4*b*n/(d^2*x^2)+2*b*e*n/(d^3*x)+1/2*(-a-b*log(c*x^n))/(d^2*x^2)+2*e*(a+b*log(c*x^n))/(d^3*x)-e^3*x*(a+b*log(c*x^n))/(d^4*(d+e*x))-3*e^2*log(1+d/(e*x))*(a+b*log(c*x^n))/d^4+b*e^2*n*log(d+e*x)/d^4+3*b*e^2*n*polylog(2,-d/(e*x))/d^4],
[x^3*(a+b*log(c*x^n))/(d+e*x)^3,x,8,-3*b*n*x/e^3+1/2*(6*a+5*b*n)*x/e^3+3*b*x*log(c*x^n)/e^3-1/2*x^3*(a+b*log(c*x^n))/(e*(d+e*x)^2)-1/2*x^2*(3*a+b*n+3*b*log(c*x^n))/(e^2*(d+e*x))-1/2*d*(6*a+5*b*n+6*b*log(c*x^n))*log(1+e*x/d)/e^4-3*b*d*n*polylog(2,-e*x/d)/e^4],
[x^2*(a+b*log(c*x^n))/(d+e*x)^3,x,4,-1/2*x^2*(a+b*log(c*x^n))/(e*(d+e*x)^2)-1/2*x*(2*a+b*n+2*b*log(c*x^n))/(e^2*(d+e*x))+1/2*(2*a+3*b*n+2*b*log(c*x^n))*log(1+e*x/d)/e^3+b*n*polylog(2,-e*x/d)/e^3],
[x*(a+b*log(c*x^n))/(d+e*x)^3,x,3,-1/2*b*n/(e^2*(d+e*x))+1/2*x^2*(a+b*log(c*x^n))/(d*(d+e*x)^2)-1/2*b*n*log(d+e*x)/(d*e^2)],
[(a+b*log(c*x^n))/(d+e*x)^3,x,3,1/2*b*n/(d*e*(d+e*x))+1/2*b*n*log(x)/(d^2*e)+1/2*(-a-b*log(c*x^n))/(e*(d+e*x)^2)-1/2*b*n*log(d+e*x)/(d^2*e)],
[(a+b*log(c*x^n))/(x*(d+e*x)^3),x,9,-1/2*b*n/(d^2*(d+e*x))-1/2*b*n*log(x)/d^3+1/2*(a+b*log(c*x^n))/(d*(d+e*x)^2)-e*x*(a+b*log(c*x^n))/(d^3*(d+e*x))-log(1+d/(e*x))*(a+b*log(c*x^n))/d^3+3/2*b*n*log(d+e*x)/d^3+b*n*polylog(2,-d/(e*x))/d^3],
[(a+b*log(c*x^n))/(x^2*(d+e*x)^3),x,10,-b*n/(d^3*x)+1/2*b*e*n/(d^3*(d+e*x))+1/2*b*e*n*log(x)/d^4+(-a-b*log(c*x^n))/(d^3*x)-1/2*e*(a+b*log(c*x^n))/(d^2*(d+e*x)^2)+2*e^2*x*(a+b*log(c*x^n))/(d^4*(d+e*x))+3*e*log(1+d/(e*x))*(a+b*log(c*x^n))/d^4-5/2*b*e*n*log(d+e*x)/d^4-3*b*e*n*polylog(2,-d/(e*x))/d^4],
[(a+b*log(c*x^n))/(x^3*(d+e*x)^3),x,11,-1/4*b*n/(d^3*x^2)+3*b*e*n/(d^4*x)-1/2*b*e^2*n/(d^4*(d+e*x))-1/2*b*e^2*n*log(x)/d^5+1/2*(-a-b*log(c*x^n))/(d^3*x^2)+3*e*(a+b*log(c*x^n))/(d^4*x)+1/2*e^2*(a+b*log(c*x^n))/(d^3*(d+e*x)^2)-3*e^3*x*(a+b*log(c*x^n))/(d^5*(d+e*x))-6*e^2*log(1+d/(e*x))*(a+b*log(c*x^n))/d^5+7/2*b*e^2*n*log(d+e*x)/d^5+6*b*e^2*n*polylog(2,-d/(e*x))/d^5],
[x^5*(a+b*log(c*x^n))/(d+e*x)^4,x,10,10*b*d*n*x/e^5-1/6*d*(60*a+47*b*n)*x/e^5-5/2*b*n*x^2/e^4-10*b*d*x*log(c*x^n)/e^5-1/3*x^5*(a+b*log(c*x^n))/(e*(d+e*x)^3)-1/6*x^4*(5*a+b*n+5*b*log(c*x^n))/(e^2*(d+e*x)^2)-1/6*x^3*(20*a+9*b*n+20*b*log(c*x^n))/(e^3*(d+e*x))+1/12*x^2*(60*a+47*b*n+60*b*log(c*x^n))/e^4+1/6*d^2*(60*a+47*b*n+60*b*log(c*x^n))*log(1+e*x/d)/e^6+10*b*d^2*n*polylog(2,-e*x/d)/e^6],
[x^4*(a+b*log(c*x^n))/(d+e*x)^4,x,9,-4*b*n*x/e^4+1/3*(12*a+13*b*n)*x/e^4+4*b*x*log(c*x^n)/e^4-1/3*x^4*(a+b*log(c*x^n))/(e*(d+e*x)^3)-1/6*x^3*(4*a+b*n+4*b*log(c*x^n))/(e^2*(d+e*x)^2)-1/6*x^2*(12*a+7*b*n+12*b*log(c*x^n))/(e^3*(d+e*x))-1/3*d*(12*a+13*b*n+12*b*log(c*x^n))*log(1+e*x/d)/e^5-4*b*d*n*polylog(2,-e*x/d)/e^5],
[x^3*(a+b*log(c*x^n))/(d+e*x)^4,x,5,-1/3*x^3*(a+b*log(c*x^n))/(e*(d+e*x)^3)-1/6*x^2*(3*a+b*n+3*b*log(c*x^n))/(e^2*(d+e*x)^2)-1/6*x*(6*a+5*b*n+6*b*log(c*x^n))/(e^3*(d+e*x))+1/6*(6*a+11*b*n+6*b*log(c*x^n))*log(1+e*x/d)/e^4+b*n*polylog(2,-e*x/d)/e^4],
[x^2*(a+b*log(c*x^n))/(d+e*x)^4,x,3,1/6*b*d*n/(e^3*(d+e*x)^2)-2/3*b*n/(e^3*(d+e*x))+1/3*x^3*(a+b*log(c*x^n))/(d*(d+e*x)^3)-1/3*b*n*log(d+e*x)/(d*e^3)],
[x*(a+b*log(c*x^n))/(d+e*x)^4,x,4,-1/6*b*n/(e^2*(d+e*x)^2)+1/6*b*n/(d*e^2*(d+e*x))+1/6*b*n*log(x)/(d^2*e^2)+1/3*d*(a+b*log(c*x^n))/(e^2*(d+e*x)^3)+1/2*(-a-b*log(c*x^n))/(e^2*(d+e*x)^2)-1/6*b*n*log(d+e*x)/(d^2*e^2)],
[(a+b*log(c*x^n))/(d+e*x)^4,x,3,1/6*b*n/(d*e*(d+e*x)^2)+1/3*b*n/(d^2*e*(d+e*x))+1/3*b*n*log(x)/(d^3*e)+1/3*(-a-b*log(c*x^n))/(e*(d+e*x)^3)-1/3*b*n*log(d+e*x)/(d^3*e)],
[(a+b*log(c*x^n))/(x*(d+e*x)^4),x,13,-1/6*b*n/(d^2*(d+e*x)^2)-5/6*b*n/(d^3*(d+e*x))-5/6*b*n*log(x)/d^4+1/3*(a+b*log(c*x^n))/(d*(d+e*x)^3)+1/2*(a+b*log(c*x^n))/(d^2*(d+e*x)^2)-e*x*(a+b*log(c*x^n))/(d^4*(d+e*x))-log(1+d/(e*x))*(a+b*log(c*x^n))/d^4+11/6*b*n*log(d+e*x)/d^4+b*n*polylog(2,-d/(e*x))/d^4],
[(a+b*log(c*x^n))/(x^2*(d+e*x)^4),x,13,-b*n/(d^4*x)+1/6*b*e*n/(d^3*(d+e*x)^2)+4/3*b*e*n/(d^4*(d+e*x))+4/3*b*e*n*log(x)/d^5+(-a-b*log(c*x^n))/(d^4*x)-1/3*e*(a+b*log(c*x^n))/(d^2*(d+e*x)^3)-e*(a+b*log(c*x^n))/(d^3*(d+e*x)^2)+3*e^2*x*(a+b*log(c*x^n))/(d^5*(d+e*x))+4*e*log(1+d/(e*x))*(a+b*log(c*x^n))/d^5-13/3*b*e*n*log(d+e*x)/d^5-4*b*e*n*polylog(2,-d/(e*x))/d^5],
[(a+b*log(c*x^n))/(x^3*(d+e*x)^4),x,14,-1/4*b*n/(d^4*x^2)+4*b*e*n/(d^5*x)-1/6*b*e^2*n/(d^4*(d+e*x)^2)-11/6*b*e^2*n/(d^5*(d+e*x))-11/6*b*e^2*n*log(x)/d^6+1/2*(-a-b*log(c*x^n))/(d^4*x^2)+4*e*(a+b*log(c*x^n))/(d^5*x)+1/3*e^2*(a+b*log(c*x^n))/(d^3*(d+e*x)^3)+3/2*e^2*(a+b*log(c*x^n))/(d^4*(d+e*x)^2)-6*e^3*x*(a+b*log(c*x^n))/(d^6*(d+e*x))-10*e^2*log(1+d/(e*x))*(a+b*log(c*x^n))/d^6+47/6*b*e^2*n*log(d+e*x)/d^6+10*b*e^2*n*polylog(2,-d/(e*x))/d^6],
[x^8*(a+b*log(c*x^n))/(d+e*x)^7,x,13,28*b*d*n*x/e^8-1/10*d*(280*a+341*b*n)*x/e^8-7*b*n*x^2/e^7-28*b*d*x*log(c*x^n)/e^8-1/6*x^8*(a+b*log(c*x^n))/(e*(d+e*x)^6)-1/30*x^7*(8*a+b*n+8*b*log(c*x^n))/(e^2*(d+e*x)^5)-1/120*x^6*(56*a+15*b*n+56*b*log(c*x^n))/(e^3*(d+e*x)^4)-1/180*x^5*(168*a+73*b*n+168*b*log(c*x^n))/(e^4*(d+e*x)^3)+1/20*x^2*(280*a+341*b*n+280*b*log(c*x^n))/e^7-1/360*x^4*(840*a+533*b*n+840*b*log(c*x^n))/(e^5*(d+e*x)^2)-1/90*x^3*(840*a+743*b*n+840*b*log(c*x^n))/(e^6*(d+e*x))+1/10*d^2*(280*a+341*b*n+280*b*log(c*x^n))*log(1+e*x/d)/e^9+28*b*d^2*n*polylog(2,-e*x/d)/e^9],
[x^7*(a+b*log(c*x^n))/(d+e*x)^7,x,12,-7*b*n*x/e^7+1/20*(140*a+223*b*n)*x/e^7+7*b*x*log(c*x^n)/e^7-1/6*x^7*(a+b*log(c*x^n))/(e*(d+e*x)^6)-1/30*x^6*(7*a+b*n+7*b*log(c*x^n))/(e^2*(d+e*x)^5)-1/120*x^5*(42*a+13*b*n+42*b*log(c*x^n))/(e^3*(d+e*x)^4)-1/40*x^2*(140*a+153*b*n+140*b*log(c*x^n))/(e^6*(d+e*x))-1/360*x^4*(210*a+107*b*n+210*b*log(c*x^n))/(e^4*(d+e*x)^3)-1/360*x^3*(420*a+319*b*n+420*b*log(c*x^n))/(e^5*(d+e*x)^2)-1/20*d*(140*a+223*b*n+140*b*log(c*x^n))*log(1+e*x/d)/e^8-7*b*d*n*polylog(2,-e*x/d)/e^8],
[x^6*(a+b*log(c*x^n))/(d+e*x)^7,x,8,-1/6*x^6*(a+b*log(c*x^n))/(e*(d+e*x)^6)-1/30*x^5*(6*a+b*n+6*b*log(c*x^n))/(e^2*(d+e*x)^5)-1/40*x^2*(20*a+19*b*n+20*b*log(c*x^n))/(e^5*(d+e*x)^2)-1/20*x*(20*a+29*b*n+20*b*log(c*x^n))/(e^6*(d+e*x))-1/120*x^4*(30*a+11*b*n+30*b*log(c*x^n))/(e^3*(d+e*x)^4)-1/180*x^3*(60*a+37*b*n+60*b*log(c*x^n))/(e^4*(d+e*x)^3)+1/20*(20*a+49*b*n+20*b*log(c*x^n))*log(1+e*x/d)/e^7+b*n*polylog(2,-e*x/d)/e^7],
[x^5*(a+b*log(c*x^n))/(d+e*x)^7,x,3,-1/30*b*d^4*n/(e^6*(d+e*x)^5)+5/24*b*d^3*n/(e^6*(d+e*x)^4)-5/9*b*d^2*n/(e^6*(d+e*x)^3)+5/6*b*d*n/(e^6*(d+e*x)^2)-5/6*b*n/(e^6*(d+e*x))+1/6*x^6*(a+b*log(c*x^n))/(d*(d+e*x)^6)-1/6*b*n*log(d+e*x)/(d*e^6)],
[x^4*(a+b*log(c*x^n))/(d+e*x)^7,x,5,-1/30*b*n*x^5/(d^2*(d+e*x)^5)+1/120*b*d^2*n/(e^5*(d+e*x)^4)-2/45*b*d*n/(e^5*(d+e*x)^3)+1/10*b*n/(e^5*(d+e*x)^2)-2/15*b*n/(d*e^5*(d+e*x))+1/6*x^5*(a+b*log(c*x^n))/(d*(d+e*x)^6)+1/30*x^5*(a+b*log(c*x^n))/(d^2*(d+e*x)^5)-1/30*b*n*log(d+e*x)/(d^2*e^5)],
[x^3*(a+b*log(c*x^n))/(d+e*x)^7,x,4,-1/30*b*d^2*n/(e^4*(d+e*x)^5)+13/120*b*d*n/(e^4*(d+e*x)^4)-19/180*b*n/(e^4*(d+e*x)^3)+1/120*b*n/(d*e^4*(d+e*x)^2)+1/60*b*n/(d^2*e^4*(d+e*x))+1/60*b*n*log(x)/(d^3*e^4)+1/6*d^3*(a+b*log(c*x^n))/(e^4*(d+e*x)^6)-3/5*d^2*(a+b*log(c*x^n))/(e^4*(d+e*x)^5)+3/4*d*(a+b*log(c*x^n))/(e^4*(d+e*x)^4)+1/3*(-a-b*log(c*x^n))/(e^4*(d+e*x)^3)-1/60*b*n*log(d+e*x)/(d^3*e^4)],
[x^2*(a+b*log(c*x^n))/(d+e*x)^7,x,4,1/30*b*d*n/(e^3*(d+e*x)^5)-7/120*b*n/(e^3*(d+e*x)^4)+1/180*b*n/(d*e^3*(d+e*x)^3)+1/120*b*n/(d^2*e^3*(d+e*x)^2)+1/60*b*n/(d^3*e^3*(d+e*x))+1/60*b*n*log(x)/(d^4*e^3)-1/6*d^2*(a+b*log(c*x^n))/(e^3*(d+e*x)^6)+2/5*d*(a+b*log(c*x^n))/(e^3*(d+e*x)^5)+1/4*(-a-b*log(c*x^n))/(e^3*(d+e*x)^4)-1/60*b*n*log(d+e*x)/(d^4*e^3)],
[x*(a+b*log(c*x^n))/(d+e*x)^7,x,4,-1/30*b*n/(e^2*(d+e*x)^5)+1/120*b*n/(d*e^2*(d+e*x)^4)+1/90*b*n/(d^2*e^2*(d+e*x)^3)+1/60*b*n/(d^3*e^2*(d+e*x)^2)+1/30*b*n/(d^4*e^2*(d+e*x))+1/30*b*n*log(x)/(d^5*e^2)+1/6*d*(a+b*log(c*x^n))/(e^2*(d+e*x)^6)+1/5*(-a-b*log(c*x^n))/(e^2*(d+e*x)^5)-1/30*b*n*log(d+e*x)/(d^5*e^2)],
[(a+b*log(c*x^n))/(d+e*x)^7,x,3,1/30*b*n/(d*e*(d+e*x)^5)+1/24*b*n/(d^2*e*(d+e*x)^4)+1/18*b*n/(d^3*e*(d+e*x)^3)+1/12*b*n/(d^4*e*(d+e*x)^2)+1/6*b*n/(d^5*e*(d+e*x))+1/6*b*n*log(x)/(d^6*e)+1/6*(-a-b*log(c*x^n))/(e*(d+e*x)^6)-1/6*b*n*log(d+e*x)/(d^6*e)],
[(a+b*log(c*x^n))/(x*(d+e*x)^7),x,25,-1/30*b*n/(d^2*(d+e*x)^5)-11/120*b*n/(d^3*(d+e*x)^4)-37/180*b*n/(d^4*(d+e*x)^3)-19/40*b*n/(d^5*(d+e*x)^2)-29/20*b*n/(d^6*(d+e*x))-29/20*b*n*log(x)/d^7+1/6*(a+b*log(c*x^n))/(d*(d+e*x)^6)+1/5*(a+b*log(c*x^n))/(d^2*(d+e*x)^5)+1/4*(a+b*log(c*x^n))/(d^3*(d+e*x)^4)+1/3*(a+b*log(c*x^n))/(d^4*(d+e*x)^3)+1/2*(a+b*log(c*x^n))/(d^5*(d+e*x)^2)-e*x*(a+b*log(c*x^n))/(d^7*(d+e*x))-log(1+d/(e*x))*(a+b*log(c*x^n))/d^7+49/20*b*n*log(d+e*x)/d^7+b*n*polylog(2,-d/(e*x))/d^7],
[(a+b*log(c*x^n))/(x^2*(d+e*x)^7),x,22,-b*n/(d^7*x)+1/30*b*e*n/(d^3*(d+e*x)^5)+17/120*b*e*n/(d^4*(d+e*x)^4)+79/180*b*e*n/(d^5*(d+e*x)^3)+53/40*b*e*n/(d^6*(d+e*x)^2)+103/20*b*e*n/(d^7*(d+e*x))+103/20*b*e*n*log(x)/d^8+(-a-b*log(c*x^n))/(d^7*x)-1/6*e*(a+b*log(c*x^n))/(d^2*(d+e*x)^6)-2/5*e*(a+b*log(c*x^n))/(d^3*(d+e*x)^5)-3/4*e*(a+b*log(c*x^n))/(d^4*(d+e*x)^4)-4/3*e*(a+b*log(c*x^n))/(d^5*(d+e*x)^3)-5/2*e*(a+b*log(c*x^n))/(d^6*(d+e*x)^2)+6*e^2*x*(a+b*log(c*x^n))/(d^8*(d+e*x))+7*e*log(1+d/(e*x))*(a+b*log(c*x^n))/d^8-223/20*b*e*n*log(d+e*x)/d^8-7*b*e*n*polylog(2,-d/(e*x))/d^8],
[(a+b*log(c*x^n))/(x^3*(d+e*x)^7),x,23,-1/4*b*n/(d^7*x^2)+7*b*e*n/(d^8*x)-1/30*b*e^2*n/(d^4*(d+e*x)^5)-23/120*b*e^2*n/(d^5*(d+e*x)^4)-34/45*b*e^2*n/(d^6*(d+e*x)^3)-14/5*b*e^2*n/(d^7*(d+e*x)^2)-131/10*b*e^2*n/(d^8*(d+e*x))-131/10*b*e^2*n*log(x)/d^9+1/2*(-a-b*log(c*x^n))/(d^7*x^2)+7*e*(a+b*log(c*x^n))/(d^8*x)+1/6*e^2*(a+b*log(c*x^n))/(d^3*(d+e*x)^6)+3/5*e^2*(a+b*log(c*x^n))/(d^4*(d+e*x)^5)+3/2*e^2*(a+b*log(c*x^n))/(d^5*(d+e*x)^4)+10/3*e^2*(a+b*log(c*x^n))/(d^6*(d+e*x)^3)+15/2*e^2*(a+b*log(c*x^n))/(d^7*(d+e*x)^2)-21*e^3*x*(a+b*log(c*x^n))/(d^9*(d+e*x))-28*e^2*log(1+d/(e*x))*(a+b*log(c*x^n))/d^9+341/10*b*e^2*n*log(d+e*x)/d^9+28*b*e^2*n*polylog(2,-d/(e*x))/d^9],
[log(c*x)/(1-c*x),x,1,polylog(2,1-c*x)/c],
[log(x/c)/(c-x),x,1,polylog(2,1-x/c)],

# Integrands of the form x^m (d+e x)^q (a+b Log[c x^n])^2

# q>0
[x^2*(d+e*x)*(a+b*log(c*x^n))^2,x,6,2/27*b^2*d*n^2*x^3+1/32*b^2*e*n^2*x^4-2/9*b*d*n*x^3*(a+b*log(c*x^n))-1/8*b*e*n*x^4*(a+b*log(c*x^n))+1/3*d*x^3*(a+b*log(c*x^n))^2+1/4*e*x^4*(a+b*log(c*x^n))^2],
[x*(d+e*x)*(a+b*log(c*x^n))^2,x,6,1/4*b^2*d*n^2*x^2+2/27*b^2*e*n^2*x^3-1/2*b*d*n*x^2*(a+b*log(c*x^n))-2/9*b*e*n*x^3*(a+b*log(c*x^n))+1/2*d*x^2*(a+b*log(c*x^n))^2+1/3*e*x^3*(a+b*log(c*x^n))^2],
[(d+e*x)*(a+b*log(c*x^n))^2,x,7,-2*a*b*d*n*x+2*b^2*d*n^2*x+1/4*b^2*e*n^2*x^2-2*b^2*d*n*x*log(c*x^n)-1/2*b*e*n*x^2*(a+b*log(c*x^n))+d*x*(a+b*log(c*x^n))^2+1/2*e*x^2*(a+b*log(c*x^n))^2],
[(d+e*x)*(a+b*log(c*x^n))^2/x,x,6,-2*a*b*e*n*x+2*b^2*e*n^2*x-2*b^2*e*n*x*log(c*x^n)+e*x*(a+b*log(c*x^n))^2+1/3*d*(a+b*log(c*x^n))^3/(b*n)],
[(d+e*x)*(a+b*log(c*x^n))^2/x^2,x,6,-2*b^2*d*n^2/x-2*b*d*n*(a+b*log(c*x^n))/x-d*(a+b*log(c*x^n))^2/x+1/3*e*(a+b*log(c*x^n))^3/(b*n)],
[(d+e*x)*(a+b*log(c*x^n))^2/x^3,x,6,-1/4*b^2*d*n^2/x^2-2*b^2*e*n^2/x-1/2*b*d*n*(a+b*log(c*x^n))/x^2-2*b*e*n*(a+b*log(c*x^n))/x-1/2*d*(a+b*log(c*x^n))^2/x^2-e*(a+b*log(c*x^n))^2/x],
[(d+e*x)*(a+b*log(c*x^n))^2/x^4,x,6,-2/27*b^2*d*n^2/x^3-1/4*b^2*e*n^2/x^2-2/9*b*d*n*(a+b*log(c*x^n))/x^3-1/2*b*e*n*(a+b*log(c*x^n))/x^2-1/3*d*(a+b*log(c*x^n))^2/x^3-1/2*e*(a+b*log(c*x^n))^2/x^2],
[(d+e*x)*(a+b*log(c*x^n))^2/x^5,x,6,-1/32*b^2*d*n^2/x^4-2/27*b^2*e*n^2/x^3-1/8*b*d*n*(a+b*log(c*x^n))/x^4-2/9*b*e*n*(a+b*log(c*x^n))/x^3-1/4*d*(a+b*log(c*x^n))^2/x^4-1/3*e*(a+b*log(c*x^n))^2/x^3],
[x^2*(d+e*x)^2*(a+b*log(c*x^n))^2,x,8,2/27*b^2*d^2*n^2*x^3+1/16*b^2*d*e*n^2*x^4+2/125*b^2*e^2*n^2*x^5-2/9*b*d^2*n*x^3*(a+b*log(c*x^n))-1/4*b*d*e*n*x^4*(a+b*log(c*x^n))-2/25*b*e^2*n*x^5*(a+b*log(c*x^n))+1/3*d^2*x^3*(a+b*log(c*x^n))^2+1/2*d*e*x^4*(a+b*log(c*x^n))^2+1/5*e^2*x^5*(a+b*log(c*x^n))^2],
[x*(d+e*x)^2*(a+b*log(c*x^n))^2,x,8,1/4*b^2*d^2*n^2*x^2+4/27*b^2*d*e*n^2*x^3+1/32*b^2*e^2*n^2*x^4-1/2*b*d^2*n*x^2*(a+b*log(c*x^n))-4/9*b*d*e*n*x^3*(a+b*log(c*x^n))-1/8*b*e^2*n*x^4*(a+b*log(c*x^n))+1/2*d^2*x^2*(a+b*log(c*x^n))^2+2/3*d*e*x^3*(a+b*log(c*x^n))^2+1/4*e^2*x^4*(a+b*log(c*x^n))^2],
[(d+e*x)^2*(a+b*log(c*x^n))^2,x,5,2*b^2*d^2*n^2*x+1/2*b^2*d*e*n^2*x^2+2/27*b^2*e^2*n^2*x^3+1/3*b^2*d^3*n^2*log(x)^2/e-2*b*d^2*n*x*(a+b*log(c*x^n))-b*d*e*n*x^2*(a+b*log(c*x^n))-2/9*b*e^2*n*x^3*(a+b*log(c*x^n))-2/3*b*d^3*n*log(x)*(a+b*log(c*x^n))/e+1/3*(d+e*x)^3*(a+b*log(c*x^n))^2/e],
[(d+e*x)^2*(a+b*log(c*x^n))^2/x,x,14,-4*a*b*d*e*n*x+4*b^2*d*e*n^2*x+1/4*b^2*e^2*n^2*x^2-4*b^2*d*e*n*x*log(c*x^n)-1/2*b*e^2*n*x^2*(a+b*log(c*x^n))+2*d*e*x*(a+b*log(c*x^n))^2+1/2*e^2*x^2*(a+b*log(c*x^n))^2+1/3*d^2*(a+b*log(c*x^n))^3/(b*n)],
[(d+e*x)^2*(a+b*log(c*x^n))^2/x^2,x,9,-2*b^2*d^2*n^2/x-2*a*b*e^2*n*x+2*b^2*e^2*n^2*x-2*b^2*e^2*n*x*log(c*x^n)-2*b*d^2*n*(a+b*log(c*x^n))/x-d^2*(a+b*log(c*x^n))^2/x+e^2*x*(a+b*log(c*x^n))^2+2/3*d*e*(a+b*log(c*x^n))^3/(b*n)],
[(d+e*x)^2*(a+b*log(c*x^n))^2/x^3,x,8,-1/4*b^2*d^2*n^2/x^2-4*b^2*d*e*n^2/x-1/2*b*d^2*n*(a+b*log(c*x^n))/x^2-4*b*d*e*n*(a+b*log(c*x^n))/x-1/2*d^2*(a+b*log(c*x^n))^2/x^2-2*d*e*(a+b*log(c*x^n))^2/x+1/3*e^2*(a+b*log(c*x^n))^3/(b*n)],
[(d+e*x)^2*(a+b*log(c*x^n))^2/x^4,x,8,-2/27*b^2*d^2*n^2/x^3-1/2*b^2*d*e*n^2/x^2-2*b^2*e^2*n^2/x-2/9*b*d^2*n*(a+b*log(c*x^n))/x^3-b*d*e*n*(a+b*log(c*x^n))/x^2-2*b*e^2*n*(a+b*log(c*x^n))/x-1/3*d^2*(a+b*log(c*x^n))^2/x^3-d*e*(a+b*log(c*x^n))^2/x^2-e^2*(a+b*log(c*x^n))^2/x],
[(d+e*x)^2*(a+b*log(c*x^n))^2/x^5,x,8,-1/32*b^2*d^2*n^2/x^4-4/27*b^2*d*e*n^2/x^3-1/4*b^2*e^2*n^2/x^2-1/8*b*d^2*n*(a+b*log(c*x^n))/x^4-4/9*b*d*e*n*(a+b*log(c*x^n))/x^3-1/2*b*e^2*n*(a+b*log(c*x^n))/x^2-1/4*d^2*(a+b*log(c*x^n))^2/x^4-2/3*d*e*(a+b*log(c*x^n))^2/x^3-1/2*e^2*(a+b*log(c*x^n))^2/x^2],

# q<0
[x^3*(a+b*log(c*x^n))^2/(d+e*x),x,12,-2*a*b*d^2*n*x/e^3+2*b^2*d^2*n^2*x/e^3-1/4*b^2*d*n^2*x^2/e^2+2/27*b^2*n^2*x^3/e-2*b^2*d^2*n*x*log(c*x^n)/e^3+1/2*b*d*n*x^2*(a+b*log(c*x^n))/e^2-2/9*b*n*x^3*(a+b*log(c*x^n))/e+d^2*x*(a+b*log(c*x^n))^2/e^3-1/2*d*x^2*(a+b*log(c*x^n))^2/e^2+1/3*x^3*(a+b*log(c*x^n))^2/e-d^3*(a+b*log(c*x^n))^2*log(1+e*x/d)/e^4-2*b*d^3*n*(a+b*log(c*x^n))*polylog(2,-e*x/d)/e^4+2*b^2*d^3*n^2*polylog(3,-e*x/d)/e^4],
[x^2*(a+b*log(c*x^n))^2/(d+e*x),x,10,2*a*b*d*n*x/e^2-2*b^2*d*n^2*x/e^2+1/4*b^2*n^2*x^2/e+2*b^2*d*n*x*log(c*x^n)/e^2-1/2*b*n*x^2*(a+b*log(c*x^n))/e-d*x*(a+b*log(c*x^n))^2/e^2+1/2*x^2*(a+b*log(c*x^n))^2/e+d^2*(a+b*log(c*x^n))^2*log(1+e*x/d)/e^3+2*b*d^2*n*(a+b*log(c*x^n))*polylog(2,-e*x/d)/e^3-2*b^2*d^2*n^2*polylog(3,-e*x/d)/e^3],
[x*(a+b*log(c*x^n))^2/(d+e*x),x,8,-2*a*b*n*x/e+2*b^2*n^2*x/e-2*b^2*n*x*log(c*x^n)/e+x*(a+b*log(c*x^n))^2/e-d*(a+b*log(c*x^n))^2*log(1+e*x/d)/e^2-2*b*d*n*(a+b*log(c*x^n))*polylog(2,-e*x/d)/e^2+2*b^2*d*n^2*polylog(3,-e*x/d)/e^2],
[(a+b*log(c*x^n))^2/(d+e*x),x,3,(a+b*log(c*x^n))^2*log(1+e*x/d)/e+2*b*n*(a+b*log(c*x^n))*polylog(2,-e*x/d)/e-2*b^2*n^2*polylog(3,-e*x/d)/e],
[(a+b*log(c*x^n))^2/(x*(d+e*x)),x,3,-log(1+d/(e*x))*(a+b*log(c*x^n))^2/d+2*b*n*(a+b*log(c*x^n))*polylog(2,-d/(e*x))/d+2*b^2*n^2*polylog(3,-d/(e*x))/d],
[(a+b*log(c*x^n))^2/(x^2*(d+e*x)),x,6,-2*b^2*n^2/(d*x)-2*b*n*(a+b*log(c*x^n))/(d*x)-(a+b*log(c*x^n))^2/(d*x)+e*log(1+d/(e*x))*(a+b*log(c*x^n))^2/d^2-2*b*e*n*(a+b*log(c*x^n))*polylog(2,-d/(e*x))/d^2-2*b^2*e*n^2*polylog(3,-d/(e*x))/d^2],
[(a+b*log(c*x^n))^2/(x^3*(d+e*x)),x,9,-1/4*b^2*n^2/(d*x^2)+2*b^2*e*n^2/(d^2*x)-1/2*b*n*(a+b*log(c*x^n))/(d*x^2)+2*b*e*n*(a+b*log(c*x^n))/(d^2*x)-1/2*(a+b*log(c*x^n))^2/(d*x^2)+e*(a+b*log(c*x^n))^2/(d^2*x)-e^2*log(1+d/(e*x))*(a+b*log(c*x^n))^2/d^3+2*b*e^2*n*(a+b*log(c*x^n))*polylog(2,-d/(e*x))/d^3+2*b^2*e^2*n^2*polylog(3,-d/(e*x))/d^3],
[(a+b*log(c*x^n))^2/(x^4*(d+e*x)),x,12,-2/27*b^2*n^2/(d*x^3)+1/4*b^2*e*n^2/(d^2*x^2)-2*b^2*e^2*n^2/(d^3*x)-2/9*b*n*(a+b*log(c*x^n))/(d*x^3)+1/2*b*e*n*(a+b*log(c*x^n))/(d^2*x^2)-2*b*e^2*n*(a+b*log(c*x^n))/(d^3*x)-1/3*(a+b*log(c*x^n))^2/(d*x^3)+1/2*e*(a+b*log(c*x^n))^2/(d^2*x^2)-e^2*(a+b*log(c*x^n))^2/(d^3*x)+e^3*log(1+d/(e*x))*(a+b*log(c*x^n))^2/d^4-2*b*e^3*n*(a+b*log(c*x^n))*polylog(2,-d/(e*x))/d^4-2*b^2*e^3*n^2*polylog(3,-d/(e*x))/d^4],
[x^3*(a+b*log(c*x^n))^2/(d+e*x)^2,x,13,4*a*b*d*n*x/e^3-4*b^2*d*n^2*x/e^3+1/4*b^2*n^2*x^2/e^2+4*b^2*d*n*x*log(c*x^n)/e^3-1/2*b*n*x^2*(a+b*log(c*x^n))/e^2-2*d*x*(a+b*log(c*x^n))^2/e^3+1/2*x^2*(a+b*log(c*x^n))^2/e^2-d^2*x*(a+b*log(c*x^n))^2/(e^3*(d+e*x))+2*b*d^2*n*(a+b*log(c*x^n))*log(1+e*x/d)/e^4+3*d^2*(a+b*log(c*x^n))^2*log(1+e*x/d)/e^4+2*b^2*d^2*n^2*polylog(2,-e*x/d)/e^4+6*b*d^2*n*(a+b*log(c*x^n))*polylog(2,-e*x/d)/e^4-6*b^2*d^2*n^2*polylog(3,-e*x/d)/e^4],
[x^2*(a+b*log(c*x^n))^2/(d+e*x)^2,x,11,-2*a*b*n*x/e^2+2*b^2*n^2*x/e^2-2*b^2*n*x*log(c*x^n)/e^2+x*(a+b*log(c*x^n))^2/e^2+d*x*(a+b*log(c*x^n))^2/(e^2*(d+e*x))-2*b*d*n*(a+b*log(c*x^n))*log(1+e*x/d)/e^3-2*d*(a+b*log(c*x^n))^2*log(1+e*x/d)/e^3-2*b^2*d*n^2*polylog(2,-e*x/d)/e^3-4*b*d*n*(a+b*log(c*x^n))*polylog(2,-e*x/d)/e^3+4*b^2*d*n^2*polylog(3,-e*x/d)/e^3],
[x*(a+b*log(c*x^n))^2/(d+e*x)^2,x,8,-x*(a+b*log(c*x^n))^2/(e*(d+e*x))+2*b*n*(a+b*log(c*x^n))*log(1+e*x/d)/e^2+(a+b*log(c*x^n))^2*log(1+e*x/d)/e^2+2*b^2*n^2*polylog(2,-e*x/d)/e^2+2*b*n*(a+b*log(c*x^n))*polylog(2,-e*x/d)/e^2-2*b^2*n^2*polylog(3,-e*x/d)/e^2],
[(a+b*log(c*x^n))^2/(d+e*x)^2,x,3,x*(a+b*log(c*x^n))^2/(d*(d+e*x))-2*b*n*(a+b*log(c*x^n))*log(1+e*x/d)/(d*e)-2*b^2*n^2*polylog(2,-e*x/d)/(d*e)],
[(a+b*log(c*x^n))^2/(x*(d+e*x)^2),x,7,-e*x*(a+b*log(c*x^n))^2/(d^2*(d+e*x))-log(1+d/(e*x))*(a+b*log(c*x^n))^2/d^2+2*b*n*(a+b*log(c*x^n))*log(1+e*x/d)/d^2+2*b*n*(a+b*log(c*x^n))*polylog(2,-d/(e*x))/d^2+2*b^2*n^2*polylog(2,-e*x/d)/d^2+2*b^2*n^2*polylog(3,-d/(e*x))/d^2],
[(a+b*log(c*x^n))^2/(x^2*(d+e*x)^2),x,10,-2*b^2*n^2/(d^2*x)-2*b*n*(a+b*log(c*x^n))/(d^2*x)-(a+b*log(c*x^n))^2/(d^2*x)+e^2*x*(a+b*log(c*x^n))^2/(d^3*(d+e*x))+2*e*log(1+d/(e*x))*(a+b*log(c*x^n))^2/d^3-2*b*e*n*(a+b*log(c*x^n))*log(1+e*x/d)/d^3-4*b*e*n*(a+b*log(c*x^n))*polylog(2,-d/(e*x))/d^3-2*b^2*e*n^2*polylog(2,-e*x/d)/d^3-4*b^2*e*n^2*polylog(3,-d/(e*x))/d^3],
[(a+b*log(c*x^n))^2/(x^3*(d+e*x)^2),x,12,-1/4*b^2*n^2/(d^2*x^2)+4*b^2*e*n^2/(d^3*x)-1/2*b*n*(a+b*log(c*x^n))/(d^2*x^2)+4*b*e*n*(a+b*log(c*x^n))/(d^3*x)-1/2*(a+b*log(c*x^n))^2/(d^2*x^2)+2*e*(a+b*log(c*x^n))^2/(d^3*x)-e^3*x*(a+b*log(c*x^n))^2/(d^4*(d+e*x))-3*e^2*log(1+d/(e*x))*(a+b*log(c*x^n))^2/d^4+2*b*e^2*n*(a+b*log(c*x^n))*log(1+e*x/d)/d^4+6*b*e^2*n*(a+b*log(c*x^n))*polylog(2,-d/(e*x))/d^4+2*b^2*e^2*n^2*polylog(2,-e*x/d)/d^4+6*b^2*e^2*n^2*polylog(3,-d/(e*x))/d^4],
[x^3*(a+b*log(c*x^n))^2/(d+e*x)^3,x,17,-2*a*b*n*x/e^3+2*b^2*n^2*x/e^3-2*b^2*n*x*log(c*x^n)/e^3+b*d*n*x*(a+b*log(c*x^n))/(e^3*(d+e*x))-1/2*d*(a+b*log(c*x^n))^2/e^4+x*(a+b*log(c*x^n))^2/e^3+1/2*d^3*(a+b*log(c*x^n))^2/(e^4*(d+e*x)^2)+3*d*x*(a+b*log(c*x^n))^2/(e^3*(d+e*x))-b^2*d*n^2*log(d+e*x)/e^4-5*b*d*n*(a+b*log(c*x^n))*log(1+e*x/d)/e^4-3*d*(a+b*log(c*x^n))^2*log(1+e*x/d)/e^4-5*b^2*d*n^2*polylog(2,-e*x/d)/e^4-6*b*d*n*(a+b*log(c*x^n))*polylog(2,-e*x/d)/e^4+6*b^2*d*n^2*polylog(3,-e*x/d)/e^4,-2*a*b*n*x/e^3+2*b^2*n^2*x/e^3-2*b^2*n*x*log(c*x^n)/e^3+b*d*n*x*(a+b*log(c*x^n))/(e^3*(d+e*x))+b*d*n*log(1+d/(e*x))*(a+b*log(c*x^n))/e^4+x*(a+b*log(c*x^n))^2/e^3+1/2*d^3*(a+b*log(c*x^n))^2/(e^4*(d+e*x)^2)+3*d*x*(a+b*log(c*x^n))^2/(e^3*(d+e*x))-b^2*d*n^2*log(d+e*x)/e^4-6*b*d*n*(a+b*log(c*x^n))*log(1+e*x/d)/e^4-3*d*(a+b*log(c*x^n))^2*log(1+e*x/d)/e^4-b^2*d*n^2*polylog(2,-d/(e*x))/e^4-6*b^2*d*n^2*polylog(2,-e*x/d)/e^4-6*b*d*n*(a+b*log(c*x^n))*polylog(2,-e*x/d)/e^4+6*b^2*d*n^2*polylog(3,-e*x/d)/e^4],
[x^2*(a+b*log(c*x^n))^2/(d+e*x)^3,x,14,-b*n*x*(a+b*log(c*x^n))/(e^2*(d+e*x))+1/2*(a+b*log(c*x^n))^2/e^3-1/2*d^2*(a+b*log(c*x^n))^2/(e^3*(d+e*x)^2)-2*x*(a+b*log(c*x^n))^2/(e^2*(d+e*x))+b^2*n^2*log(d+e*x)/e^3+3*b*n*(a+b*log(c*x^n))*log(1+e*x/d)/e^3+(a+b*log(c*x^n))^2*log(1+e*x/d)/e^3+3*b^2*n^2*polylog(2,-e*x/d)/e^3+2*b*n*(a+b*log(c*x^n))*polylog(2,-e*x/d)/e^3-2*b^2*n^2*polylog(3,-e*x/d)/e^3,-b*n*x*(a+b*log(c*x^n))/(e^2*(d+e*x))-b*n*log(1+d/(e*x))*(a+b*log(c*x^n))/e^3-1/2*d^2*(a+b*log(c*x^n))^2/(e^3*(d+e*x)^2)-2*x*(a+b*log(c*x^n))^2/(e^2*(d+e*x))+b^2*n^2*log(d+e*x)/e^3+4*b*n*(a+b*log(c*x^n))*log(1+e*x/d)/e^3+(a+b*log(c*x^n))^2*log(1+e*x/d)/e^3+b^2*n^2*polylog(2,-d/(e*x))/e^3+4*b^2*n^2*polylog(2,-e*x/d)/e^3+2*b*n*(a+b*log(c*x^n))*polylog(2,-e*x/d)/e^3-2*b^2*n^2*polylog(3,-e*x/d)/e^3],
[x*(a+b*log(c*x^n))^2/(d+e*x)^3,x,4,b*n*x*(a+b*log(c*x^n))/(d*e*(d+e*x))+1/2*x^2*(a+b*log(c*x^n))^2/(d*(d+e*x)^2)-b*n*(a+b*n+b*log(c*x^n))*log(1+e*x/d)/(d*e^2)-b^2*n^2*polylog(2,-e*x/d)/(d*e^2)],
[(a+b*log(c*x^n))^2/(d+e*x)^3,x,6,-b*n*x*(a+b*log(c*x^n))/(d^2*(d+e*x))-b*n*log(1+d/(e*x))*(a+b*log(c*x^n))/(d^2*e)-1/2*(a+b*log(c*x^n))^2/(e*(d+e*x)^2)+b^2*n^2*log(d+e*x)/(d^2*e)+b^2*n^2*polylog(2,-d/(e*x))/(d^2*e)],
[(a+b*log(c*x^n))^2/(x*(d+e*x)^3),x,14,b*e*n*x*(a+b*log(c*x^n))/(d^3*(d+e*x))-1/2*(a+b*log(c*x^n))^2/d^3+1/2*(a+b*log(c*x^n))^2/(d*(d+e*x)^2)-e*x*(a+b*log(c*x^n))^2/(d^3*(d+e*x))+1/3*(a+b*log(c*x^n))^3/(b*d^3*n)-b^2*n^2*log(d+e*x)/d^3+3*b*n*(a+b*log(c*x^n))*log(1+e*x/d)/d^3-(a+b*log(c*x^n))^2*log(1+e*x/d)/d^3+3*b^2*n^2*polylog(2,-e*x/d)/d^3-2*b*n*(a+b*log(c*x^n))*polylog(2,-e*x/d)/d^3+2*b^2*n^2*polylog(3,-e*x/d)/d^3,b*e*n*x*(a+b*log(c*x^n))/(d^3*(d+e*x))+b*n*log(1+d/(e*x))*(a+b*log(c*x^n))/d^3+1/2*(a+b*log(c*x^n))^2/(d*(d+e*x)^2)-e*x*(a+b*log(c*x^n))^2/(d^3*(d+e*x))-log(1+d/(e*x))*(a+b*log(c*x^n))^2/d^3-b^2*n^2*log(d+e*x)/d^3+2*b*n*(a+b*log(c*x^n))*log(1+e*x/d)/d^3-b^2*n^2*polylog(2,-d/(e*x))/d^3+2*b*n*(a+b*log(c*x^n))*polylog(2,-d/(e*x))/d^3+2*b^2*n^2*polylog(2,-e*x/d)/d^3+2*b^2*n^2*polylog(3,-d/(e*x))/d^3],
[(a+b*log(c*x^n))^2/(x^2*(d+e*x)^3),x,16,-2*b^2*n^2/(d^3*x)-2*b*n*(a+b*log(c*x^n))/(d^3*x)-b*e^2*n*x*(a+b*log(c*x^n))/(d^4*(d+e*x))+1/2*e*(a+b*log(c*x^n))^2/d^4-(a+b*log(c*x^n))^2/(d^3*x)-1/2*e*(a+b*log(c*x^n))^2/(d^2*(d+e*x)^2)+2*e^2*x*(a+b*log(c*x^n))^2/(d^4*(d+e*x))-e*(a+b*log(c*x^n))^3/(b*d^4*n)+b^2*e*n^2*log(d+e*x)/d^4-5*b*e*n*(a+b*log(c*x^n))*log(1+e*x/d)/d^4+3*e*(a+b*log(c*x^n))^2*log(1+e*x/d)/d^4-5*b^2*e*n^2*polylog(2,-e*x/d)/d^4+6*b*e*n*(a+b*log(c*x^n))*polylog(2,-e*x/d)/d^4-6*b^2*e*n^2*polylog(3,-e*x/d)/d^4,-2*b^2*n^2/(d^3*x)-2*b*n*(a+b*log(c*x^n))/(d^3*x)-b*e^2*n*x*(a+b*log(c*x^n))/(d^4*(d+e*x))-b*e*n*log(1+d/(e*x))*(a+b*log(c*x^n))/d^4-(a+b*log(c*x^n))^2/(d^3*x)-1/2*e*(a+b*log(c*x^n))^2/(d^2*(d+e*x)^2)+2*e^2*x*(a+b*log(c*x^n))^2/(d^4*(d+e*x))+3*e*log(1+d/(e*x))*(a+b*log(c*x^n))^2/d^4+b^2*e*n^2*log(d+e*x)/d^4-4*b*e*n*(a+b*log(c*x^n))*log(1+e*x/d)/d^4+b^2*e*n^2*polylog(2,-d/(e*x))/d^4-6*b*e*n*(a+b*log(c*x^n))*polylog(2,-d/(e*x))/d^4-4*b^2*e*n^2*polylog(2,-e*x/d)/d^4-6*b^2*e*n^2*polylog(3,-d/(e*x))/d^4],
[x^4*(a+b*log(c*x^n))^2/(d+e*x)^4,x,27,-2*a*b*n*x/e^4+2*b^2*n^2*x/e^4-1/3*b^2*d^2*n^2/(e^5*(d+e*x))-1/3*b^2*d*n^2*log(x)/e^5-2*b^2*n*x*log(c*x^n)/e^4+1/3*b*d^3*n*(a+b*log(c*x^n))/(e^5*(d+e*x)^2)+10/3*b*d*n*x*(a+b*log(c*x^n))/(e^4*(d+e*x))-5/3*d*(a+b*log(c*x^n))^2/e^5+x*(a+b*log(c*x^n))^2/e^4-1/3*d^4*(a+b*log(c*x^n))^2/(e^5*(d+e*x)^3)+2*d^3*(a+b*log(c*x^n))^2/(e^5*(d+e*x)^2)+6*d*x*(a+b*log(c*x^n))^2/(e^4*(d+e*x))-3*b^2*d*n^2*log(d+e*x)/e^5-26/3*b*d*n*(a+b*log(c*x^n))*log(1+e*x/d)/e^5-4*d*(a+b*log(c*x^n))^2*log(1+e*x/d)/e^5-26/3*b^2*d*n^2*polylog(2,-e*x/d)/e^5-8*b*d*n*(a+b*log(c*x^n))*polylog(2,-e*x/d)/e^5+8*b^2*d*n^2*polylog(3,-e*x/d)/e^5,-2*a*b*n*x/e^4+2*b^2*n^2*x/e^4-1/3*b^2*d^2*n^2/(e^5*(d+e*x))-1/3*b^2*d*n^2*log(x)/e^5-2*b^2*n*x*log(c*x^n)/e^4+1/3*b*d^3*n*(a+b*log(c*x^n))/(e^5*(d+e*x)^2)+10/3*b*d*n*x*(a+b*log(c*x^n))/(e^4*(d+e*x))+10/3*b*d*n*log(1+d/(e*x))*(a+b*log(c*x^n))/e^5+x*(a+b*log(c*x^n))^2/e^4-1/3*d^4*(a+b*log(c*x^n))^2/(e^5*(d+e*x)^3)+2*d^3*(a+b*log(c*x^n))^2/(e^5*(d+e*x)^2)+6*d*x*(a+b*log(c*x^n))^2/(e^4*(d+e*x))-3*b^2*d*n^2*log(d+e*x)/e^5-12*b*d*n*(a+b*log(c*x^n))*log(1+e*x/d)/e^5-4*d*(a+b*log(c*x^n))^2*log(1+e*x/d)/e^5-10/3*b^2*d*n^2*polylog(2,-d/(e*x))/e^5-12*b^2*d*n^2*polylog(2,-e*x/d)/e^5-8*b*d*n*(a+b*log(c*x^n))*polylog(2,-e*x/d)/e^5+8*b^2*d*n^2*polylog(3,-e*x/d)/e^5],
[x^3*(a+b*log(c*x^n))^2/(d+e*x)^4,x,24,1/3*b^2*d*n^2/(e^4*(d+e*x))+1/3*b^2*n^2*log(x)/e^4-1/3*b*d^2*n*(a+b*log(c*x^n))/(e^4*(d+e*x)^2)-7/3*b*n*x*(a+b*log(c*x^n))/(e^3*(d+e*x))+7/6*(a+b*log(c*x^n))^2/e^4+1/3*d^3*(a+b*log(c*x^n))^2/(e^4*(d+e*x)^3)-3/2*d^2*(a+b*log(c*x^n))^2/(e^4*(d+e*x)^2)-3*x*(a+b*log(c*x^n))^2/(e^3*(d+e*x))+2*b^2*n^2*log(d+e*x)/e^4+11/3*b*n*(a+b*log(c*x^n))*log(1+e*x/d)/e^4+(a+b*log(c*x^n))^2*log(1+e*x/d)/e^4+11/3*b^2*n^2*polylog(2,-e*x/d)/e^4+2*b*n*(a+b*log(c*x^n))*polylog(2,-e*x/d)/e^4-2*b^2*n^2*polylog(3,-e*x/d)/e^4,1/3*b^2*d*n^2/(e^4*(d+e*x))+1/3*b^2*n^2*log(x)/e^4-1/3*b*d^2*n*(a+b*log(c*x^n))/(e^4*(d+e*x)^2)-7/3*b*n*x*(a+b*log(c*x^n))/(e^3*(d+e*x))-7/3*b*n*log(1+d/(e*x))*(a+b*log(c*x^n))/e^4+1/3*d^3*(a+b*log(c*x^n))^2/(e^4*(d+e*x)^3)-3/2*d^2*(a+b*log(c*x^n))^2/(e^4*(d+e*x)^2)-3*x*(a+b*log(c*x^n))^2/(e^3*(d+e*x))+2*b^2*n^2*log(d+e*x)/e^4+6*b*n*(a+b*log(c*x^n))*log(1+e*x/d)/e^4+(a+b*log(c*x^n))^2*log(1+e*x/d)/e^4+7/3*b^2*n^2*polylog(2,-d/(e*x))/e^4+6*b^2*n^2*polylog(2,-e*x/d)/e^4+2*b*n*(a+b*log(c*x^n))*polylog(2,-e*x/d)/e^4-2*b^2*n^2*polylog(3,-e*x/d)/e^4],
[x^2*(a+b*log(c*x^n))^2/(d+e*x)^4,x,5,1/3*b*n*x^2*(a+b*log(c*x^n))/(d*e*(d+e*x)^2)+1/3*x^3*(a+b*log(c*x^n))^2/(d*(d+e*x)^3)+1/3*b*n*x*(2*a+b*n+2*b*log(c*x^n))/(d*e^2*(d+e*x))-1/3*b*n*(2*a+3*b*n+2*b*log(c*x^n))*log(1+e*x/d)/(d*e^3)-2/3*b^2*n^2*polylog(2,-e*x/d)/(d*e^3)],
[x*(a+b*log(c*x^n))^2/(d+e*x)^4,x,8,1/3*b^2*n^2/(d*e^2*(d+e*x))-1/3*b*n*(a+b*log(c*x^n))/(e^2*(d+e*x)^2)+1/3*b*n*(a+b*log(c*x^n))/(d*e^2*(d+e*x))+1/6*(a+b*log(c*x^n))^2/(d^2*e^2)+1/3*d*(a+b*log(c*x^n))^2/(e^2*(d+e*x)^3)-1/2*(a+b*log(c*x^n))^2/(e^2*(d+e*x)^2)-1/3*b*n*(a+b*log(c*x^n))*log(1+e*x/d)/(d^2*e^2)-1/3*b^2*n^2*polylog(2,-e*x/d)/(d^2*e^2),1/3*b^2*n^2/(d*e^2*(d+e*x))-1/3*b*n*x^2*(a+b*log(c*x^n))/(d^2*(d+e*x)^2)+1/3*b*n*x*(a+b*log(c*x^n))/(d^2*e*(d+e*x))+1/3*x^2*(a+b*log(c*x^n))^2/(d*(d+e*x)^3)+1/6*x^2*(a+b*log(c*x^n))^2/(d^2*(d+e*x)^2)+1/3*b^2*n^2*log(d+e*x)/(d^2*e^2)-1/3*b*n*(a+b*n+b*log(c*x^n))*log(1+e*x/d)/(d^2*e^2)-1/3*b^2*n^2*polylog(2,-e*x/d)/(d^2*e^2)],
[(a+b*log(c*x^n))^2/(d+e*x)^4,x,10,-1/3*b^2*n^2/(d^2*e*(d+e*x))-1/3*b^2*n^2*log(x)/(d^3*e)+1/3*b*n*(a+b*log(c*x^n))/(d*e*(d+e*x)^2)-2/3*b*n*x*(a+b*log(c*x^n))/(d^3*(d+e*x))-2/3*b*n*log(1+d/(e*x))*(a+b*log(c*x^n))/(d^3*e)-1/3*(a+b*log(c*x^n))^2/(e*(d+e*x)^3)+b^2*n^2*log(d+e*x)/(d^3*e)+2/3*b^2*n^2*polylog(2,-d/(e*x))/(d^3*e)],
[(a+b*log(c*x^n))^2/(x*(d+e*x)^4),x,25,1/3*b^2*n^2/(d^3*(d+e*x))+1/3*b^2*n^2*log(x)/d^4-1/3*b*n*(a+b*log(c*x^n))/(d^2*(d+e*x)^2)+5/3*b*e*n*x*(a+b*log(c*x^n))/(d^4*(d+e*x))-5/6*(a+b*log(c*x^n))^2/d^4+1/3*(a+b*log(c*x^n))^2/(d*(d+e*x)^3)+1/2*(a+b*log(c*x^n))^2/(d^2*(d+e*x)^2)-e*x*(a+b*log(c*x^n))^2/(d^4*(d+e*x))+1/3*(a+b*log(c*x^n))^3/(b*d^4*n)-2*b^2*n^2*log(d+e*x)/d^4+11/3*b*n*(a+b*log(c*x^n))*log(1+e*x/d)/d^4-(a+b*log(c*x^n))^2*log(1+e*x/d)/d^4+11/3*b^2*n^2*polylog(2,-e*x/d)/d^4-2*b*n*(a+b*log(c*x^n))*polylog(2,-e*x/d)/d^4+2*b^2*n^2*polylog(3,-e*x/d)/d^4,1/3*b^2*n^2/(d^3*(d+e*x))+1/3*b^2*n^2*log(x)/d^4-1/3*b*n*(a+b*log(c*x^n))/(d^2*(d+e*x)^2)+5/3*b*e*n*x*(a+b*log(c*x^n))/(d^4*(d+e*x))+5/3*b*n*log(1+d/(e*x))*(a+b*log(c*x^n))/d^4+1/3*(a+b*log(c*x^n))^2/(d*(d+e*x)^3)+1/2*(a+b*log(c*x^n))^2/(d^2*(d+e*x)^2)-e*x*(a+b*log(c*x^n))^2/(d^4*(d+e*x))-log(1+d/(e*x))*(a+b*log(c*x^n))^2/d^4-2*b^2*n^2*log(d+e*x)/d^4+2*b*n*(a+b*log(c*x^n))*log(1+e*x/d)/d^4-5/3*b^2*n^2*polylog(2,-d/(e*x))/d^4+2*b*n*(a+b*log(c*x^n))*polylog(2,-d/(e*x))/d^4+2*b^2*n^2*polylog(2,-e*x/d)/d^4+2*b^2*n^2*polylog(3,-d/(e*x))/d^4],
[(a+b*log(c*x^n))^2/(x^2*(d+e*x)^4),x,26,-2*b^2*n^2/(d^4*x)-1/3*b^2*e*n^2/(d^4*(d+e*x))-1/3*b^2*e*n^2*log(x)/d^5-2*b*n*(a+b*log(c*x^n))/(d^4*x)+1/3*b*e*n*(a+b*log(c*x^n))/(d^3*(d+e*x)^2)-8/3*b*e^2*n*x*(a+b*log(c*x^n))/(d^5*(d+e*x))+4/3*e*(a+b*log(c*x^n))^2/d^5-(a+b*log(c*x^n))^2/(d^4*x)-1/3*e*(a+b*log(c*x^n))^2/(d^2*(d+e*x)^3)-e*(a+b*log(c*x^n))^2/(d^3*(d+e*x)^2)+3*e^2*x*(a+b*log(c*x^n))^2/(d^5*(d+e*x))-4/3*e*(a+b*log(c*x^n))^3/(b*d^5*n)+3*b^2*e*n^2*log(d+e*x)/d^5-26/3*b*e*n*(a+b*log(c*x^n))*log(1+e*x/d)/d^5+4*e*(a+b*log(c*x^n))^2*log(1+e*x/d)/d^5-26/3*b^2*e*n^2*polylog(2,-e*x/d)/d^5+8*b*e*n*(a+b*log(c*x^n))*polylog(2,-e*x/d)/d^5-8*b^2*e*n^2*polylog(3,-e*x/d)/d^5,-2*b^2*n^2/(d^4*x)-1/3*b^2*e*n^2/(d^4*(d+e*x))-1/3*b^2*e*n^2*log(x)/d^5-2*b*n*(a+b*log(c*x^n))/(d^4*x)+1/3*b*e*n*(a+b*log(c*x^n))/(d^3*(d+e*x)^2)-8/3*b*e^2*n*x*(a+b*log(c*x^n))/(d^5*(d+e*x))-8/3*b*e*n*log(1+d/(e*x))*(a+b*log(c*x^n))/d^5-(a+b*log(c*x^n))^2/(d^4*x)-1/3*e*(a+b*log(c*x^n))^2/(d^2*(d+e*x)^3)-e*(a+b*log(c*x^n))^2/(d^3*(d+e*x)^2)+3*e^2*x*(a+b*log(c*x^n))^2/(d^5*(d+e*x))+4*e*log(1+d/(e*x))*(a+b*log(c*x^n))^2/d^5+3*b^2*e*n^2*log(d+e*x)/d^5-6*b*e*n*(a+b*log(c*x^n))*log(1+e*x/d)/d^5+8/3*b^2*e*n^2*polylog(2,-d/(e*x))/d^5-8*b*e*n*(a+b*log(c*x^n))*polylog(2,-d/(e*x))/d^5-6*b^2*e*n^2*polylog(2,-e*x/d)/d^5-8*b^2*e*n^2*polylog(3,-d/(e*x))/d^5],
[x*log(x)^2/(d+e*x)^4,x,8,-1/3*x/(d^2*e*(d+e*x))+1/3*x*log(x)/(d*e*(d+e*x)^2)+1/6*x^2*(3*d+e*x)*log(x)^2/(d^2*(d+e*x)^3)-1/3*log(x)*log(1+e*x/d)/(d^2*e^2)-1/3*polylog(2,-e*x/d)/(d^2*e^2),1/3/(d*e^2*(d+e*x))-1/3*x^2*log(x)/(d^2*(d+e*x)^2)+1/3*x*log(x)/(d^2*e*(d+e*x))+1/3*x^2*log(x)^2/(d*(d+e*x)^3)+1/6*x^2*log(x)^2/(d^2*(d+e*x)^2)+1/3*log(d+e*x)/(d^2*e^2)-1/3*(1+log(x))*log(1+e*x/d)/(d^2*e^2)-1/3*polylog(2,-e*x/d)/(d^2*e^2)],

# Integrands of the form x^m (d+e x)^q (a+b Log[c x^n])^3

# q>0

# q<0
[(a+b*log(c*x^n))^3/(x*(d+e*x)),x,4,-log(1+d/(e*x))*(a+b*log(c*x^n))^3/d+3*b*n*(a+b*log(c*x^n))^2*polylog(2,-d/(e*x))/d+6*b^2*n^2*(a+b*log(c*x^n))*polylog(3,-d/(e*x))/d+6*b^3*n^3*polylog(4,-d/(e*x))/d],
[(a+b*log(c*x^n))^3/(x*(d+e*x)^2),x,9,-e*x*(a+b*log(c*x^n))^3/(d^2*(d+e*x))-log(1+d/(e*x))*(a+b*log(c*x^n))^3/d^2+3*b*n*(a+b*log(c*x^n))^2*log(1+e*x/d)/d^2+3*b*n*(a+b*log(c*x^n))^2*polylog(2,-d/(e*x))/d^2+6*b^2*n^2*(a+b*log(c*x^n))*polylog(2,-e*x/d)/d^2+6*b^2*n^2*(a+b*log(c*x^n))*polylog(3,-d/(e*x))/d^2-6*b^3*n^3*polylog(3,-e*x/d)/d^2+6*b^3*n^3*polylog(4,-d/(e*x))/d^2],
[(a+b*log(c*x^n))^3/(x*(d+e*x)^3),x,18,3/2*b*e*n*x*(a+b*log(c*x^n))^2/(d^3*(d+e*x))-1/2*(a+b*log(c*x^n))^3/d^3+1/2*(a+b*log(c*x^n))^3/(d*(d+e*x)^2)-e*x*(a+b*log(c*x^n))^3/(d^3*(d+e*x))+1/4*(a+b*log(c*x^n))^4/(b*d^3*n)-3*b^2*n^2*(a+b*log(c*x^n))*log(1+e*x/d)/d^3+9/2*b*n*(a+b*log(c*x^n))^2*log(1+e*x/d)/d^3-(a+b*log(c*x^n))^3*log(1+e*x/d)/d^3-3*b^3*n^3*polylog(2,-e*x/d)/d^3+9*b^2*n^2*(a+b*log(c*x^n))*polylog(2,-e*x/d)/d^3-3*b*n*(a+b*log(c*x^n))^2*polylog(2,-e*x/d)/d^3-9*b^3*n^3*polylog(3,-e*x/d)/d^3+6*b^2*n^2*(a+b*log(c*x^n))*polylog(3,-e*x/d)/d^3-6*b^3*n^3*polylog(4,-e*x/d)/d^3,3/2*b*e*n*x*(a+b*log(c*x^n))^2/(d^3*(d+e*x))+3/2*b*n*log(1+d/(e*x))*(a+b*log(c*x^n))^2/d^3+1/2*(a+b*log(c*x^n))^3/(d*(d+e*x)^2)-e*x*(a+b*log(c*x^n))^3/(d^3*(d+e*x))-log(1+d/(e*x))*(a+b*log(c*x^n))^3/d^3-3*b^2*n^2*(a+b*log(c*x^n))*log(1+e*x/d)/d^3+3*b*n*(a+b*log(c*x^n))^2*log(1+e*x/d)/d^3-3*b^2*n^2*(a+b*log(c*x^n))*polylog(2,-d/(e*x))/d^3+3*b*n*(a+b*log(c*x^n))^2*polylog(2,-d/(e*x))/d^3-3*b^3*n^3*polylog(2,-e*x/d)/d^3+6*b^2*n^2*(a+b*log(c*x^n))*polylog(2,-e*x/d)/d^3-3*b^3*n^3*polylog(3,-d/(e*x))/d^3+6*b^2*n^2*(a+b*log(c*x^n))*polylog(3,-d/(e*x))/d^3-6*b^3*n^3*polylog(3,-e*x/d)/d^3+6*b^3*n^3*polylog(4,-d/(e*x))/d^3],

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

# q>0
[(d+e*x)*(a+b*log(c*x^n))^(1/2),x,10,-1/4*e*x^2*erfi(sqrt(2)*sqrt(a+b*log(c*x^n))/(sqrt(b)*sqrt(n)))*sqrt(b)*sqrt(n)*sqrt(1/2*Pi)/(exp(2*a/(b*n))*(c*x^n)^(2/n))-1/2*d*x*erfi(sqrt(a+b*log(c*x^n))/(sqrt(b)*sqrt(n)))*sqrt(b)*sqrt(n)*sqrt(Pi)/(exp(a/(b*n))*(c*x^n)^(1/n))+d*x*sqrt(a+b*log(c*x^n))+1/2*e*x^2*sqrt(a+b*log(c*x^n))],
[(d+e*x)^2*(a+b*log(c*x^n))^(1/2),x,14,-1/6*e^2*x^3*erfi(sqrt(3)*sqrt(a+b*log(c*x^n))/(sqrt(b)*sqrt(n)))*sqrt(b)*sqrt(n)*sqrt(1/3*Pi)/(exp(3*a/(b*n))*(c*x^n)^(3/n))-1/2*d*e*x^2*erfi(sqrt(2)*sqrt(a+b*log(c*x^n))/(sqrt(b)*sqrt(n)))*sqrt(b)*sqrt(n)*sqrt(1/2*Pi)/(exp(2*a/(b*n))*(c*x^n)^(2/n))-1/2*d^2*x*erfi(sqrt(a+b*log(c*x^n))/(sqrt(b)*sqrt(n)))*sqrt(b)*sqrt(n)*sqrt(Pi)/(exp(a/(b*n))*(c*x^n)^(1/n))+d^2*x*sqrt(a+b*log(c*x^n))+d*e*x^2*sqrt(a+b*log(c*x^n))+1/3*e^2*x^3*sqrt(a+b*log(c*x^n))],
[(d+e*x)^3*(a+b*log(c*x^n))^(1/2),x,18,-1/2*d*e^2*x^3*erfi(sqrt(3)*sqrt(a+b*log(c*x^n))/(sqrt(b)*sqrt(n)))*sqrt(b)*sqrt(n)*sqrt(1/3*Pi)/(exp(3*a/(b*n))*(c*x^n)^(3/n))-3/4*d^2*e*x^2*erfi(sqrt(2)*sqrt(a+b*log(c*x^n))/(sqrt(b)*sqrt(n)))*sqrt(b)*sqrt(n)*sqrt(1/2*Pi)/(exp(2*a/(b*n))*(c*x^n)^(2/n))-1/2*d^3*x*erfi(sqrt(a+b*log(c*x^n))/(sqrt(b)*sqrt(n)))*sqrt(b)*sqrt(n)*sqrt(Pi)/(exp(a/(b*n))*(c*x^n)^(1/n))-1/16*e^3*x^4*erfi(2*sqrt(a+b*log(c*x^n))/(sqrt(b)*sqrt(n)))*sqrt(b)*sqrt(n)*sqrt(Pi)/(exp(4*a/(b*n))*(c*x^n)^(4/n))+d^3*x*sqrt(a+b*log(c*x^n))+3/2*d^2*e*x^2*sqrt(a+b*log(c*x^n))+d*e^2*x^3*sqrt(a+b*log(c*x^n))+1/4*e^3*x^4*sqrt(a+b*log(c*x^n))],

# q<0
[(a+b*log(c*x^n))^(1/2)/(d+e*x),x,0,Unintegrable(sqrt(a+b*log(c*x^n))/(d+e*x),x)],
[(a+b*log(c*x^n))^(1/2)/(d+e*x)^2,x,1,x*sqrt(a+b*log(c*x^n))/(d*(d+e*x))-1/2*b*n*Unintegrable(1/((d+e*x)*sqrt(a+b*log(c*x^n))),x)/d],
[(a+b*log(c*x^n))^(1/2)/(d+e*x)^3,x,1,-1/2*sqrt(a+b*log(c*x^n))/(e*(d+e*x)^2)+1/4*b*n*Unintegrable(1/(x*(d+e*x)^2*sqrt(a+b*log(c*x^n))),x)/e],

# Integrands of the form x^m (d+e x)^(q/2) (a+b Log[c x^n])

# q>0
[x^3*(a+b*log(c*x^n))*sqrt(d+e*x),x,9,64/945*b*d^3*n*(d+e*x)^(3/2)/e^4-356/1575*b*d^2*n*(d+e*x)^(5/2)/e^4+80/441*b*d*n*(d+e*x)^(7/2)/e^4-4/81*b*n*(d+e*x)^(9/2)/e^4-64/315*b*d^(9/2)*n*arctanh(sqrt(d+e*x)/sqrt(d))/e^4-2/3*d^3*(d+e*x)^(3/2)*(a+b*log(c*x^n))/e^4+6/5*d^2*(d+e*x)^(5/2)*(a+b*log(c*x^n))/e^4-6/7*d*(d+e*x)^(7/2)*(a+b*log(c*x^n))/e^4+2/9*(d+e*x)^(9/2)*(a+b*log(c*x^n))/e^4+64/315*b*d^4*n*sqrt(d+e*x)/e^4],
[x^2*(a+b*log(c*x^n))*sqrt(d+e*x),x,7,-32/315*b*d^2*n*(d+e*x)^(3/2)/e^3+36/175*b*d*n*(d+e*x)^(5/2)/e^3-4/49*b*n*(d+e*x)^(7/2)/e^3+32/105*b*d^(7/2)*n*arctanh(sqrt(d+e*x)/sqrt(d))/e^3+2/3*d^2*(d+e*x)^(3/2)*(a+b*log(c*x^n))/e^3-4/5*d*(d+e*x)^(5/2)*(a+b*log(c*x^n))/e^3+2/7*(d+e*x)^(7/2)*(a+b*log(c*x^n))/e^3-32/105*b*d^3*n*sqrt(d+e*x)/e^3],
[x*(a+b*log(c*x^n))*sqrt(d+e*x),x,8,8/45*b*d*n*(d+e*x)^(3/2)/e^2-4/25*b*n*(d+e*x)^(5/2)/e^2-8/15*b*d^(5/2)*n*arctanh(sqrt(d+e*x)/sqrt(d))/e^2-2/3*d*(d+e*x)^(3/2)*(a+b*log(c*x^n))/e^2+2/5*(d+e*x)^(5/2)*(a+b*log(c*x^n))/e^2+8/15*b*d^2*n*sqrt(d+e*x)/e^2],
[(a+b*log(c*x^n))*sqrt(d+e*x),x,5,-4/9*b*n*(d+e*x)^(3/2)/e+4/3*b*d^(3/2)*n*arctanh(sqrt(d+e*x)/sqrt(d))/e+2/3*(d+e*x)^(3/2)*(a+b*log(c*x^n))/e-4/3*b*d*n*sqrt(d+e*x)/e],
[(a+b*log(c*x^n))*sqrt(d+e*x)/x,x,12,4*b*n*arctanh(sqrt(d+e*x)/sqrt(d))*sqrt(d)+2*b*n*arctanh(sqrt(d+e*x)/sqrt(d))^2*sqrt(d)-2*arctanh(sqrt(d+e*x)/sqrt(d))*(a+b*log(c*x^n))*sqrt(d)-4*b*n*arctanh(sqrt(d+e*x)/sqrt(d))*log(2*sqrt(d)/(sqrt(d)-sqrt(d+e*x)))*sqrt(d)-2*b*n*polylog(2,1-2*sqrt(d)/(sqrt(d)-sqrt(d+e*x)))*sqrt(d)-4*b*n*sqrt(d+e*x)+2*(a+b*log(c*x^n))*sqrt(d+e*x)],
[(a+b*log(c*x^n))*sqrt(d+e*x)/x^2,x,11,-b*e*n*arctanh(sqrt(d+e*x)/sqrt(d))/sqrt(d)+b*e*n*arctanh(sqrt(d+e*x)/sqrt(d))^2/sqrt(d)-e*arctanh(sqrt(d+e*x)/sqrt(d))*(a+b*log(c*x^n))/sqrt(d)-2*b*e*n*arctanh(sqrt(d+e*x)/sqrt(d))*log(2*sqrt(d)/(sqrt(d)-sqrt(d+e*x)))/sqrt(d)-b*e*n*polylog(2,1-2*sqrt(d)/(sqrt(d)-sqrt(d+e*x)))/sqrt(d)-b*n*sqrt(d+e*x)/x-(a+b*log(c*x^n))*sqrt(d+e*x)/x],
[(a+b*log(c*x^n))*sqrt(d+e*x)/x^3,x,16,-1/8*b*e^2*n*arctanh(sqrt(d+e*x)/sqrt(d))/d^(3/2)-1/4*b*e^2*n*arctanh(sqrt(d+e*x)/sqrt(d))^2/d^(3/2)+1/4*e^2*arctanh(sqrt(d+e*x)/sqrt(d))*(a+b*log(c*x^n))/d^(3/2)+1/2*b*e^2*n*arctanh(sqrt(d+e*x)/sqrt(d))*log(2*sqrt(d)/(sqrt(d)-sqrt(d+e*x)))/d^(3/2)+1/4*b*e^2*n*polylog(2,1-2*sqrt(d)/(sqrt(d)-sqrt(d+e*x)))/d^(3/2)-1/4*b*n*sqrt(d+e*x)/x^2-3/8*b*e*n*sqrt(d+e*x)/(d*x)-1/2*(a+b*log(c*x^n))*sqrt(d+e*x)/x^2-1/4*e*(a+b*log(c*x^n))*sqrt(d+e*x)/(d*x)],
[x^3*(d+e*x)^(3/2)*(a+b*log(c*x^n)),x,9,64/3465*b*d^4*n*(d+e*x)^(3/2)/e^4+64/5775*b*d^3*n*(d+e*x)^(5/2)/e^4-172/1617*b*d^2*n*(d+e*x)^(7/2)/e^4+32/297*b*d*n*(d+e*x)^(9/2)/e^4-4/121*b*n*(d+e*x)^(11/2)/e^4-64/1155*b*d^(11/2)*n*arctanh(sqrt(d+e*x)/sqrt(d))/e^4-2/5*d^3*(d+e*x)^(5/2)*(a+b*log(c*x^n))/e^4+6/7*d^2*(d+e*x)^(7/2)*(a+b*log(c*x^n))/e^4-2/3*d*(d+e*x)^(9/2)*(a+b*log(c*x^n))/e^4+2/11*(d+e*x)^(11/2)*(a+b*log(c*x^n))/e^4+64/1155*b*d^5*n*sqrt(d+e*x)/e^4],
[x^2*(d+e*x)^(3/2)*(a+b*log(c*x^n)),x,6,-32/945*b*d^3*n*(d+e*x)^(3/2)/e^3-32/1575*b*d^2*n*(d+e*x)^(5/2)/e^3+44/441*b*d*n*(d+e*x)^(7/2)/e^3-4/81*b*n*(d+e*x)^(9/2)/e^3+32/315*b*d^(9/2)*n*arctanh(sqrt(d+e*x)/sqrt(d))/e^3+2/5*d^2*(d+e*x)^(5/2)*(a+b*log(c*x^n))/e^3-4/7*d*(d+e*x)^(7/2)*(a+b*log(c*x^n))/e^3+2/9*(d+e*x)^(9/2)*(a+b*log(c*x^n))/e^3-32/315*b*d^4*n*sqrt(d+e*x)/e^3],
[x*(d+e*x)^(3/2)*(a+b*log(c*x^n)),x,8,8/105*b*d^2*n*(d+e*x)^(3/2)/e^2+8/175*b*d*n*(d+e*x)^(5/2)/e^2-4/49*b*n*(d+e*x)^(7/2)/e^2-8/35*b*d^(7/2)*n*arctanh(sqrt(d+e*x)/sqrt(d))/e^2-2/5*d*(d+e*x)^(5/2)*(a+b*log(c*x^n))/e^2+2/7*(d+e*x)^(7/2)*(a+b*log(c*x^n))/e^2+8/35*b*d^3*n*sqrt(d+e*x)/e^2],
[(d+e*x)^(3/2)*(a+b*log(c*x^n)),x,6,-4/15*b*d*n*(d+e*x)^(3/2)/e-4/25*b*n*(d+e*x)^(5/2)/e+4/5*b*d^(5/2)*n*arctanh(sqrt(d+e*x)/sqrt(d))/e+2/5*(d+e*x)^(5/2)*(a+b*log(c*x^n))/e-4/5*b*d^2*n*sqrt(d+e*x)/e],
[(d+e*x)^(3/2)*(a+b*log(c*x^n))/x,x,18,-4/9*b*n*(d+e*x)^(3/2)+16/3*b*d^(3/2)*n*arctanh(sqrt(d+e*x)/sqrt(d))+2*b*d^(3/2)*n*arctanh(sqrt(d+e*x)/sqrt(d))^2+2/3*(d+e*x)^(3/2)*(a+b*log(c*x^n))-2*d^(3/2)*arctanh(sqrt(d+e*x)/sqrt(d))*(a+b*log(c*x^n))-4*b*d^(3/2)*n*arctanh(sqrt(d+e*x)/sqrt(d))*log(2*sqrt(d)/(sqrt(d)-sqrt(d+e*x)))-2*b*d^(3/2)*n*polylog(2,1-2*sqrt(d)/(sqrt(d)-sqrt(d+e*x)))-16/3*b*d*n*sqrt(d+e*x)+2*d*(a+b*log(c*x^n))*sqrt(d+e*x)],
[(d+e*x)^(3/2)*(a+b*log(c*x^n))/x^2,x,14,-(d+e*x)^(3/2)*(a+b*log(c*x^n))/x+3*b*e*n*arctanh(sqrt(d+e*x)/sqrt(d))*sqrt(d)+3*b*e*n*arctanh(sqrt(d+e*x)/sqrt(d))^2*sqrt(d)-3*e*arctanh(sqrt(d+e*x)/sqrt(d))*(a+b*log(c*x^n))*sqrt(d)-6*b*e*n*arctanh(sqrt(d+e*x)/sqrt(d))*log(2*sqrt(d)/(sqrt(d)-sqrt(d+e*x)))*sqrt(d)-3*b*e*n*polylog(2,1-2*sqrt(d)/(sqrt(d)-sqrt(d+e*x)))*sqrt(d)-4*b*e*n*sqrt(d+e*x)-b*d*n*sqrt(d+e*x)/x+3*e*(a+b*log(c*x^n))*sqrt(d+e*x)],
[(d+e*x)^(3/2)*(a+b*log(c*x^n))/x^3,x,16,-1/2*(d+e*x)^(3/2)*(a+b*log(c*x^n))/x^2-9/8*b*e^2*n*arctanh(sqrt(d+e*x)/sqrt(d))/sqrt(d)+3/4*b*e^2*n*arctanh(sqrt(d+e*x)/sqrt(d))^2/sqrt(d)-3/4*e^2*arctanh(sqrt(d+e*x)/sqrt(d))*(a+b*log(c*x^n))/sqrt(d)-3/2*b*e^2*n*arctanh(sqrt(d+e*x)/sqrt(d))*log(2*sqrt(d)/(sqrt(d)-sqrt(d+e*x)))/sqrt(d)-3/4*b*e^2*n*polylog(2,1-2*sqrt(d)/(sqrt(d)-sqrt(d+e*x)))/sqrt(d)-1/4*b*d*n*sqrt(d+e*x)/x^2-11/8*b*e*n*sqrt(d+e*x)/x-3/4*e*(a+b*log(c*x^n))*sqrt(d+e*x)/x],

# q<0
[x^3*(a+b*log(c*x^n))/sqrt(d+e*x),x,7,-76/105*b*d^2*n*(d+e*x)^(3/2)/e^4+64/175*b*d*n*(d+e*x)^(5/2)/e^4-4/49*b*n*(d+e*x)^(7/2)/e^4-64/35*b*d^(7/2)*n*arctanh(sqrt(d+e*x)/sqrt(d))/e^4+2*d^2*(d+e*x)^(3/2)*(a+b*log(c*x^n))/e^4-6/5*d*(d+e*x)^(5/2)*(a+b*log(c*x^n))/e^4+2/7*(d+e*x)^(7/2)*(a+b*log(c*x^n))/e^4+64/35*b*d^3*n*sqrt(d+e*x)/e^4-2*d^3*(a+b*log(c*x^n))*sqrt(d+e*x)/e^4],
[x^2*(a+b*log(c*x^n))/sqrt(d+e*x),x,6,28/45*b*d*n*(d+e*x)^(3/2)/e^3-4/25*b*n*(d+e*x)^(5/2)/e^3+32/15*b*d^(5/2)*n*arctanh(sqrt(d+e*x)/sqrt(d))/e^3-4/3*d*(d+e*x)^(3/2)*(a+b*log(c*x^n))/e^3+2/5*(d+e*x)^(5/2)*(a+b*log(c*x^n))/e^3-32/15*b*d^2*n*sqrt(d+e*x)/e^3+2*d^2*(a+b*log(c*x^n))*sqrt(d+e*x)/e^3],
[x*(a+b*log(c*x^n))/sqrt(d+e*x),x,6,-4/9*b*n*(d+e*x)^(3/2)/e^2-8/3*b*d^(3/2)*n*arctanh(sqrt(d+e*x)/sqrt(d))/e^2+2/3*(d+e*x)^(3/2)*(a+b*log(c*x^n))/e^2+8/3*b*d*n*sqrt(d+e*x)/e^2-2*d*(a+b*log(c*x^n))*sqrt(d+e*x)/e^2],
[(a+b*log(c*x^n))/sqrt(d+e*x),x,4,4*b*n*arctanh(sqrt(d+e*x)/sqrt(d))*sqrt(d)/e-4*b*n*sqrt(d+e*x)/e+2*(a+b*log(c*x^n))*sqrt(d+e*x)/e],
[(a+b*log(c*x^n))/(x*sqrt(d+e*x)),x,7,2*b*n*arctanh(sqrt(d+e*x)/sqrt(d))^2/sqrt(d)-2*arctanh(sqrt(d+e*x)/sqrt(d))*(a+b*log(c*x^n))/sqrt(d)-4*b*n*arctanh(sqrt(d+e*x)/sqrt(d))*log(2*sqrt(d)/(sqrt(d)-sqrt(d+e*x)))/sqrt(d)-2*b*n*polylog(2,1-2*sqrt(d)/(sqrt(d)-sqrt(d+e*x)))/sqrt(d)],
[(a+b*log(c*x^n))/(x^2*sqrt(d+e*x)),x,11,-b*e*n*arctanh(sqrt(d+e*x)/sqrt(d))/d^(3/2)-b*e*n*arctanh(sqrt(d+e*x)/sqrt(d))^2/d^(3/2)+e*arctanh(sqrt(d+e*x)/sqrt(d))*(a+b*log(c*x^n))/d^(3/2)+2*b*e*n*arctanh(sqrt(d+e*x)/sqrt(d))*log(2*sqrt(d)/(sqrt(d)-sqrt(d+e*x)))/d^(3/2)+b*e*n*polylog(2,1-2*sqrt(d)/(sqrt(d)-sqrt(d+e*x)))/d^(3/2)-b*n*sqrt(d+e*x)/(d*x)-(a+b*log(c*x^n))*sqrt(d+e*x)/(d*x)],
[(a+b*log(c*x^n))/(x^3*sqrt(d+e*x)),x,16,7/8*b*e^2*n*arctanh(sqrt(d+e*x)/sqrt(d))/d^(5/2)+3/4*b*e^2*n*arctanh(sqrt(d+e*x)/sqrt(d))^2/d^(5/2)-3/4*e^2*arctanh(sqrt(d+e*x)/sqrt(d))*(a+b*log(c*x^n))/d^(5/2)-3/2*b*e^2*n*arctanh(sqrt(d+e*x)/sqrt(d))*log(2*sqrt(d)/(sqrt(d)-sqrt(d+e*x)))/d^(5/2)-3/4*b*e^2*n*polylog(2,1-2*sqrt(d)/(sqrt(d)-sqrt(d+e*x)))/d^(5/2)-1/4*b*n*sqrt(d+e*x)/(d*x^2)+5/8*b*e*n*sqrt(d+e*x)/(d^2*x)-1/2*(a+b*log(c*x^n))*sqrt(d+e*x)/(d*x^2)+3/4*e*(a+b*log(c*x^n))*sqrt(d+e*x)/(d^2*x)],
[x^3*(a+b*log(c*x^n))/(d+e*x)^(3/2),x,6,16/15*b*d*n*(d+e*x)^(3/2)/e^4-4/25*b*n*(d+e*x)^(5/2)/e^4+64/5*b*d^(5/2)*n*arctanh(sqrt(d+e*x)/sqrt(d))/e^4-2*d*(d+e*x)^(3/2)*(a+b*log(c*x^n))/e^4+2/5*(d+e*x)^(5/2)*(a+b*log(c*x^n))/e^4+2*d^3*(a+b*log(c*x^n))/(e^4*sqrt(d+e*x))-44/5*b*d^2*n*sqrt(d+e*x)/e^4+6*d^2*(a+b*log(c*x^n))*sqrt(d+e*x)/e^4],
[x^2*(a+b*log(c*x^n))/(d+e*x)^(3/2),x,6,-4/9*b*n*(d+e*x)^(3/2)/e^3-32/3*b*d^(3/2)*n*arctanh(sqrt(d+e*x)/sqrt(d))/e^3+2/3*(d+e*x)^(3/2)*(a+b*log(c*x^n))/e^3-2*d^2*(a+b*log(c*x^n))/(e^3*sqrt(d+e*x))+20/3*b*d*n*sqrt(d+e*x)/e^3-4*d*(a+b*log(c*x^n))*sqrt(d+e*x)/e^3],
[x*(a+b*log(c*x^n))/(d+e*x)^(3/2),x,5,8*b*n*arctanh(sqrt(d+e*x)/sqrt(d))*sqrt(d)/e^2+2*d*(a+b*log(c*x^n))/(e^2*sqrt(d+e*x))-4*b*n*sqrt(d+e*x)/e^2+2*(a+b*log(c*x^n))*sqrt(d+e*x)/e^2],
[(a+b*log(c*x^n))/(d+e*x)^(3/2),x,3,-4*b*n*arctanh(sqrt(d+e*x)/sqrt(d))/(e*sqrt(d))-2*(a+b*log(c*x^n))/(e*sqrt(d+e*x))],
[(a+b*log(c*x^n))/(x*(d+e*x)^(3/2)),x,11,4*b*n*arctanh(sqrt(d+e*x)/sqrt(d))/d^(3/2)+2*b*n*arctanh(sqrt(d+e*x)/sqrt(d))^2/d^(3/2)-2*arctanh(sqrt(d+e*x)/sqrt(d))*(a+b*log(c*x^n))/d^(3/2)-4*b*n*arctanh(sqrt(d+e*x)/sqrt(d))*log(2*sqrt(d)/(sqrt(d)-sqrt(d+e*x)))/d^(3/2)-2*b*n*polylog(2,1-2*sqrt(d)/(sqrt(d)-sqrt(d+e*x)))/d^(3/2)+2*(a+b*log(c*x^n))/(d*sqrt(d+e*x))],
[(a+b*log(c*x^n))/(x^2*(d+e*x)^(3/2)),x,11,-5*b*e*n*arctanh(sqrt(d+e*x)/sqrt(d))/d^(5/2)-3*b*e*n*arctanh(sqrt(d+e*x)/sqrt(d))^2/d^(5/2)+3*e*arctanh(sqrt(d+e*x)/sqrt(d))*(a+b*log(c*x^n))/d^(5/2)+6*b*e*n*arctanh(sqrt(d+e*x)/sqrt(d))*log(2*sqrt(d)/(sqrt(d)-sqrt(d+e*x)))/d^(5/2)+3*b*e*n*polylog(2,1-2*sqrt(d)/(sqrt(d)-sqrt(d+e*x)))/d^(5/2)-3*e*(a+b*log(c*x^n))/(d^2*sqrt(d+e*x))+(-a-b*log(c*x^n))/(d*x*sqrt(d+e*x))-b*n*sqrt(d+e*x)/(d^2*x)],

# Integrands of the form x^m (d+e x)^q / (a+b Log[c x^n])

# q>0

# q<0
[x^2/((d+e*x)*(a+b*log(c*x^n))),x,0,Unintegrable(x^2/((d+e*x)*(a+b*log(c*x^n))),x)],
[x/((d+e*x)*(a+b*log(c*x^n))),x,0,Unintegrable(x/((d+e*x)*(a+b*log(c*x^n))),x)],
[1/((d+e*x)*(a+b*log(c*x^n))),x,0,Unintegrable(1/((d+e*x)*(a+b*log(c*x^n))),x)],
[1/(x*(d+e*x)*(a+b*log(c*x^n))),x,0,Unintegrable(1/(x*(d+e*x)*(a+b*log(c*x^n))),x)],
[1/(x^2*(d+e*x)*(a+b*log(c*x^n))),x,0,Unintegrable(1/(x^2*(d+e*x)*(a+b*log(c*x^n))),x)],

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

# Integrands of the form (f x)^m (d+e x)^q (a+b Log[c x^n])^p when q symbolic
[x*(a+b*x)^m*log(c*x^n),x,0,Unintegrable(x*(a+b*x)^m*log(c*x^n),x)],
[(a+b*x)^m*log(c*x^n),x,2,n*(a+b*x)^(2+m)*hypergeom([1,2+m],[3+m],1+b*x/a)/(a*b*(2+3*m+m^2))+(a+b*x)^(1+m)*log(c*x^n)/(b*(1+m))],
[(a+b*x)^m*log(c*x^n)/x,x,0,Unintegrable((a+b*x)^m*log(c*x^n)/x,x)],

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

# Integrands of the form x^m (d+e x^2)^q (a+b Log[c x^n])

# q>0
[x^5*(d+e*x^2)*(a+b*log(c*x^n)),x,2,-1/36*b*d*n*x^6-1/64*b*e*n*x^8+1/24*(4*d*x^6+3*e*x^8)*(a+b*log(c*x^n))],
[x^3*(d+e*x^2)*(a+b*log(c*x^n)),x,2,-1/16*b*d*n*x^4-1/36*b*e*n*x^6+1/12*(3*d*x^4+2*e*x^6)*(a+b*log(c*x^n))],
[x*(d+e*x^2)*(a+b*log(c*x^n)),x,4,-1/4*b*d*n*x^2-1/16*b*e*n*x^4+1/4*(2*d*x^2+e*x^4)*(a+b*log(c*x^n))],
[(d+e*x^2)*(a+b*log(c*x^n))/x,x,4,-1/4*b*e*n*x^2+1/2*e*x^2*(a+b*log(c*x^n))+1/2*d*(a+b*log(c*x^n))^2/(b*n)],
[(d+e*x^2)*(a+b*log(c*x^n))/x^3,x,3,-1/4*b*d*n/x^2-1/2*d*(a+b*log(c*x^n))/x^2+1/2*e*(a+b*log(c*x^n))^2/(b*n),-1/4*b*d*n/x^2-1/2*b*e*n*log(x)^2-1/2*d*(a+b*log(c*x^n))/x^2+e*log(x)*(a+b*log(c*x^n))],
[(d+e*x^2)*(a+b*log(c*x^n))/x^5,x,4,-1/16*b*d*n/x^4-1/4*b*e*n/x^2-1/4*d*(a+b*log(c*x^n))/x^4-1/2*e*(a+b*log(c*x^n))/x^2],
[x^4*(d+e*x^2)*(a+b*log(c*x^n)),x,2,-1/25*b*d*n*x^5-1/49*b*e*n*x^7+1/35*(7*d*x^5+5*e*x^7)*(a+b*log(c*x^n))],
[x^2*(d+e*x^2)*(a+b*log(c*x^n)),x,2,-1/9*b*d*n*x^3-1/25*b*e*n*x^5+1/15*(5*d*x^3+3*e*x^5)*(a+b*log(c*x^n))],
[(d+e*x^2)*(a+b*log(c*x^n)),x,2,-b*d*n*x-1/9*b*e*n*x^3+d*x*(a+b*log(c*x^n))+1/3*e*x^3*(a+b*log(c*x^n))],
[(d+e*x^2)*(a+b*log(c*x^n))/x^2,x,2,-b*d*n/x-b*e*n*x-d*(a+b*log(c*x^n))/x+e*x*(a+b*log(c*x^n))],
[(d+e*x^2)*(a+b*log(c*x^n))/x^4,x,4,-1/9*b*d*n/x^3-b*e*n/x-1/3*d*(a+b*log(c*x^n))/x^3-e*(a+b*log(c*x^n))/x],
[(d+e*x^2)*(a+b*log(c*x^n))/x^6,x,4,-1/25*b*d*n/x^5-1/9*b*e*n/x^3-1/5*d*(a+b*log(c*x^n))/x^5-1/3*e*(a+b*log(c*x^n))/x^3],
[x^5*(d+e*x^2)^2*(a+b*log(c*x^n)),x,4,-1/36*b*d^2*n*x^6-1/32*b*d*e*n*x^8-1/100*b*e^2*n*x^10+1/60*(10*d^2*x^6+15*d*e*x^8+6*e^2*x^10)*(a+b*log(c*x^n))],
[x^3*(d+e*x^2)^2*(a+b*log(c*x^n)),x,4,-1/16*b*d^2*n*x^4-1/18*b*d*e*n*x^6-1/64*b*e^2*n*x^8+1/24*(6*d^2*x^4+8*d*e*x^6+3*e^2*x^8)*(a+b*log(c*x^n))],
[x*(d+e*x^2)^2*(a+b*log(c*x^n)),x,5,-1/4*b*d^2*n*x^2-1/8*b*d*e*n*x^4-1/36*b*e^2*n*x^6-1/6*b*d^3*n*log(x)/e+1/6*(d+e*x^2)^3*(a+b*log(c*x^n))/e],
[(d+e*x^2)^2*(a+b*log(c*x^n))/x,x,3,-1/2*b*d*e*n*x^2-1/16*b*e^2*n*x^4-1/2*b*d^2*n*log(x)^2+d*e*x^2*(a+b*log(c*x^n))+1/4*e^2*x^4*(a+b*log(c*x^n))+d^2*log(x)*(a+b*log(c*x^n))],
[(d+e*x^2)^2*(a+b*log(c*x^n))/x^3,x,7,-1/4*b*d^2*n/x^2-1/4*b*e^2*n*x^2-b*d*e*n*log(x)^2-1/2*d^2*(a+b*log(c*x^n))/x^2+1/2*e^2*x^2*(a+b*log(c*x^n))+2*d*e*log(x)*(a+b*log(c*x^n))],
[(d+e*x^2)^2*(a+b*log(c*x^n))/x^5,x,7,-1/16*b*d^2*n/x^4-1/2*b*d*e*n/x^2-1/2*b*e^2*n*log(x)^2-1/4*d^2*(a+b*log(c*x^n))/x^4-d*e*(a+b*log(c*x^n))/x^2+e^2*log(x)*(a+b*log(c*x^n))],
[x^4*(d+e*x^2)^2*(a+b*log(c*x^n)),x,2,-1/25*b*d^2*n*x^5-2/49*b*d*e*n*x^7-1/81*b*e^2*n*x^9+1/315*(63*d^2*x^5+90*d*e*x^7+35*e^2*x^9)*(a+b*log(c*x^n))],
[x^2*(d+e*x^2)^2*(a+b*log(c*x^n)),x,2,-1/9*b*d^2*n*x^3-2/25*b*d*e*n*x^5-1/49*b*e^2*n*x^7+1/105*(35*d^2*x^3+42*d*e*x^5+15*e^2*x^7)*(a+b*log(c*x^n))],
[(d+e*x^2)^2*(a+b*log(c*x^n)),x,2,-b*d^2*n*x-2/9*b*d*e*n*x^3-1/25*b*e^2*n*x^5+d^2*x*(a+b*log(c*x^n))+2/3*d*e*x^3*(a+b*log(c*x^n))+1/5*e^2*x^5*(a+b*log(c*x^n))],
[(d+e*x^2)^2*(a+b*log(c*x^n))/x^2,x,2,-b*d^2*n/x-2*b*d*e*n*x-1/9*b*e^2*n*x^3-d^2*(a+b*log(c*x^n))/x+2*d*e*x*(a+b*log(c*x^n))+1/3*e^2*x^3*(a+b*log(c*x^n))],
[(d+e*x^2)^2*(a+b*log(c*x^n))/x^4,x,2,-1/9*b*d^2*n/x^3-2*b*d*e*n/x-b*e^2*n*x-1/3*d^2*(a+b*log(c*x^n))/x^3-2*d*e*(a+b*log(c*x^n))/x+e^2*x*(a+b*log(c*x^n))],
[(d+e*x^2)^2*(a+b*log(c*x^n))/x^6,x,4,-1/25*b*d^2*n/x^5-2/9*b*d*e*n/x^3-b*e^2*n/x-1/5*d^2*(a+b*log(c*x^n))/x^5-2/3*d*e*(a+b*log(c*x^n))/x^3-e^2*(a+b*log(c*x^n))/x],
[(d+e*x^2)^2*(a+b*log(c*x^n))/x^8,x,4,-1/49*b*d^2*n/x^7-2/25*b*d*e*n/x^5-1/9*b*e^2*n/x^3-1/7*d^2*(a+b*log(c*x^n))/x^7-2/5*d*e*(a+b*log(c*x^n))/x^5-1/3*e^2*(a+b*log(c*x^n))/x^3],
[x^5*(d+e*x^2)^3*(a+b*log(c*x^n)),x,4,-1/36*b*d^3*n*x^6-3/64*b*d^2*e*n*x^8-3/100*b*d*e^2*n*x^10-1/144*b*e^3*n*x^12+1/120*(20*d^3*x^6+45*d^2*e*x^8+36*d*e^2*x^10+10*e^3*x^12)*(a+b*log(c*x^n))],
[x^3*(d+e*x^2)^3*(a+b*log(c*x^n)),x,6,1/20*b*d^4*n*x^2/e+3/80*b*d^3*n*x^4+1/60*b*d^2*e*n*x^6+1/320*b*d*e^2*n*x^8-1/100*b*n*(d+e*x^2)^5/e^2+1/40*b*d^5*n*log(x)/e^2-1/40*(5*d*(d+e*x^2)^4/e^2-4*(d+e*x^2)^5/e^2)*(a+b*log(c*x^n))],
[x*(d+e*x^2)^3*(a+b*log(c*x^n)),x,5,-1/4*b*d^3*n*x^2-3/16*b*d^2*e*n*x^4-1/12*b*d*e^2*n*x^6-1/64*b*e^3*n*x^8-1/8*b*d^4*n*log(x)/e+1/8*(d+e*x^2)^4*(a+b*log(c*x^n))/e],
[(d+e*x^2)^3*(a+b*log(c*x^n))/x,x,5,-3/4*b*d^2*e*n*x^2-3/16*b*d*e^2*n*x^4-1/36*b*e^3*n*x^6-1/2*b*d^3*n*log(x)^2+3/2*d^2*e*x^2*(a+b*log(c*x^n))+3/4*d*e^2*x^4*(a+b*log(c*x^n))+1/6*e^3*x^6*(a+b*log(c*x^n))+d^3*log(x)*(a+b*log(c*x^n))],
[(d+e*x^2)^3*(a+b*log(c*x^n))/x^3,x,7,-1/4*b*d^3*n/x^2-3/4*b*d*e^2*n*x^2-1/16*b*e^3*n*x^4-3/2*b*d^2*e*n*log(x)^2-1/2*d^3*(a+b*log(c*x^n))/x^2+3/2*d*e^2*x^2*(a+b*log(c*x^n))+1/4*e^3*x^4*(a+b*log(c*x^n))+3*d^2*e*log(x)*(a+b*log(c*x^n))],
[(d+e*x^2)^3*(a+b*log(c*x^n))/x^5,x,7,-1/16*b*d^3*n/x^4-3/4*b*d^2*e*n/x^2-1/4*b*e^3*n*x^2-3/2*b*d*e^2*n*log(x)^2-1/4*d^3*(a+b*log(c*x^n))/x^4-3/2*d^2*e*(a+b*log(c*x^n))/x^2+1/2*e^3*x^2*(a+b*log(c*x^n))+3*d*e^2*log(x)*(a+b*log(c*x^n))],
[x^4*(d+e*x^2)^3*(a+b*log(c*x^n)),x,2,-1/25*b*d^3*n*x^5-3/49*b*d^2*e*n*x^7-1/27*b*d*e^2*n*x^9-1/121*b*e^3*n*x^11+1/1155*(231*d^3*x^5+495*d^2*e*x^7+385*d*e^2*x^9+105*e^3*x^11)*(a+b*log(c*x^n))],
[x^2*(d+e*x^2)^3*(a+b*log(c*x^n)),x,2,-1/9*b*d^3*n*x^3-3/25*b*d^2*e*n*x^5-3/49*b*d*e^2*n*x^7-1/81*b*e^3*n*x^9+1/315*(105*d^3*x^3+189*d^2*e*x^5+135*d*e^2*x^7+35*e^3*x^9)*(a+b*log(c*x^n))],
[(d+e*x^2)^3*(a+b*log(c*x^n)),x,2,-b*d^3*n*x-1/3*b*d^2*e*n*x^3-3/25*b*d*e^2*n*x^5-1/49*b*e^3*n*x^7+d^3*x*(a+b*log(c*x^n))+d^2*e*x^3*(a+b*log(c*x^n))+3/5*d*e^2*x^5*(a+b*log(c*x^n))+1/7*e^3*x^7*(a+b*log(c*x^n))],
[(d+e*x^2)^3*(a+b*log(c*x^n))/x^2,x,2,-b*d^3*n/x-3*b*d^2*e*n*x-1/3*b*d*e^2*n*x^3-1/25*b*e^3*n*x^5-d^3*(a+b*log(c*x^n))/x+3*d^2*e*x*(a+b*log(c*x^n))+d*e^2*x^3*(a+b*log(c*x^n))+1/5*e^3*x^5*(a+b*log(c*x^n))],
[(d+e*x^2)^3*(a+b*log(c*x^n))/x^4,x,3,-1/9*b*d^3*n/x^3-3*b*d^2*e*n/x-3*b*d*e^2*n*x-1/9*b*e^3*n*x^3-1/3*d^3*(a+b*log(c*x^n))/x^3-3*d^2*e*(a+b*log(c*x^n))/x+3*d*e^2*x*(a+b*log(c*x^n))+1/3*e^3*x^3*(a+b*log(c*x^n))],
[(d+e*x^2)^3*(a+b*log(c*x^n))/x^6,x,2,-1/25*b*d^3*n/x^5-1/3*b*d^2*e*n/x^3-3*b*d*e^2*n/x-b*e^3*n*x-1/5*d^3*(a+b*log(c*x^n))/x^5-d^2*e*(a+b*log(c*x^n))/x^3-3*d*e^2*(a+b*log(c*x^n))/x+e^3*x*(a+b*log(c*x^n))],
[(d+e*x^2)^3*(a+b*log(c*x^n))/x^8,x,4,-1/49*b*d^3*n/x^7-3/25*b*d^2*e*n/x^5-1/3*b*d*e^2*n/x^3-b*e^3*n/x-1/7*d^3*(a+b*log(c*x^n))/x^7-3/5*d^2*e*(a+b*log(c*x^n))/x^5-d*e^2*(a+b*log(c*x^n))/x^3-e^3*(a+b*log(c*x^n))/x],
[(d+e*x^2)^3*(a+b*log(c*x^n))/x^10,x,4,-1/81*b*d^3*n/x^9-3/49*b*d^2*e*n/x^7-3/25*b*d*e^2*n/x^5-1/9*b*e^3*n/x^3-1/9*d^3*(a+b*log(c*x^n))/x^9-3/7*d^2*e*(a+b*log(c*x^n))/x^7-3/5*d*e^2*(a+b*log(c*x^n))/x^5-1/3*e^3*(a+b*log(c*x^n))/x^3],

# q<0
[x^5*(a+b*log(c*x^n))/(d+e*x^2),x,6,1/4*b*d*n*x^2/e^2-1/16*b*n*x^4/e-1/2*d*x^2*(a+b*log(c*x^n))/e^2+1/4*x^4*(a+b*log(c*x^n))/e+1/2*d^2*(a+b*log(c*x^n))*log(1+e*x^2/d)/e^3+1/4*b*d^2*n*polylog(2,-e*x^2/d)/e^3],
[x^3*(a+b*log(c*x^n))/(d+e*x^2),x,5,-1/4*b*n*x^2/e+1/2*x^2*(a+b*log(c*x^n))/e-1/2*d*(a+b*log(c*x^n))*log(1+e*x^2/d)/e^2-1/4*b*d*n*polylog(2,-e*x^2/d)/e^2],
[x*(a+b*log(c*x^n))/(d+e*x^2),x,2,1/2*(a+b*log(c*x^n))*log(1+e*x^2/d)/e+1/4*b*n*polylog(2,-e*x^2/d)/e],
[(a+b*log(c*x^n))/(x*(d+e*x^2)),x,2,-1/2*log(1+d/(e*x^2))*(a+b*log(c*x^n))/d+1/4*b*n*polylog(2,-d/(e*x^2))/d],
[(a+b*log(c*x^n))/(x^3*(d+e*x^2)),x,4,-1/4*b*n/(d*x^2)+1/2*(-a-b*log(c*x^n))/(d*x^2)+1/2*e*log(1+d/(e*x^2))*(a+b*log(c*x^n))/d^2-1/4*b*e*n*polylog(2,-d/(e*x^2))/d^2],
[(a+b*log(c*x^n))/(x^5*(d+e*x^2)),x,6,-1/16*b*n/(d*x^4)+1/4*b*e*n/(d^2*x^2)+1/4*(-a-b*log(c*x^n))/(d*x^4)+1/2*e*(a+b*log(c*x^n))/(d^2*x^2)-1/2*e^2*log(1+d/(e*x^2))*(a+b*log(c*x^n))/d^3+1/4*b*e^2*n*polylog(2,-d/(e*x^2))/d^3],
[x^4*(a+b*log(c*x^n))/(d+e*x^2),x,10,-a*d*x/e^2+b*d*n*x/e^2-1/9*b*n*x^3/e-b*d*x*log(c*x^n)/e^2+1/3*x^3*(a+b*log(c*x^n))/e+d^(3/2)*arctan(x*sqrt(e)/sqrt(d))*(a+b*log(c*x^n))/e^(5/2)-1/2*I*b*d^(3/2)*n*polylog(2,-I*x*sqrt(e)/sqrt(d))/e^(5/2)+1/2*I*b*d^(3/2)*n*polylog(2,I*x*sqrt(e)/sqrt(d))/e^(5/2)],
[x^2*(a+b*log(c*x^n))/(d+e*x^2),x,9,a*x/e-b*n*x/e+b*x*log(c*x^n)/e-arctan(x*sqrt(e)/sqrt(d))*(a+b*log(c*x^n))*sqrt(d)/e^(3/2)+1/2*I*b*n*polylog(2,-I*x*sqrt(e)/sqrt(d))*sqrt(d)/e^(3/2)-1/2*I*b*n*polylog(2,I*x*sqrt(e)/sqrt(d))*sqrt(d)/e^(3/2)],
[(a+b*log(c*x^n))/(d+e*x^2),x,5,arctan(x*sqrt(e)/sqrt(d))*(a+b*log(c*x^n))/(sqrt(d)*sqrt(e))-1/2*I*b*n*polylog(2,-I*x*sqrt(e)/sqrt(d))/(sqrt(d)*sqrt(e))+1/2*I*b*n*polylog(2,I*x*sqrt(e)/sqrt(d))/(sqrt(d)*sqrt(e))],
[(a+b*log(c*x^n))/(x^2*(d+e*x^2)),x,7,-b*n/(d*x)+(-a-b*log(c*x^n))/(d*x)-arctan(x*sqrt(e)/sqrt(d))*(a+b*log(c*x^n))*sqrt(e)/d^(3/2)+1/2*I*b*n*polylog(2,-I*x*sqrt(e)/sqrt(d))*sqrt(e)/d^(3/2)-1/2*I*b*n*polylog(2,I*x*sqrt(e)/sqrt(d))*sqrt(e)/d^(3/2)],
[(a+b*log(c*x^n))/(x^4*(d+e*x^2)),x,9,-1/9*b*n/(d*x^3)+b*e*n/(d^2*x)+1/3*(-a-b*log(c*x^n))/(d*x^3)+e*(a+b*log(c*x^n))/(d^2*x)+e^(3/2)*arctan(x*sqrt(e)/sqrt(d))*(a+b*log(c*x^n))/d^(5/2)-1/2*I*b*e^(3/2)*n*polylog(2,-I*x*sqrt(e)/sqrt(d))/d^(5/2)+1/2*I*b*e^(3/2)*n*polylog(2,I*x*sqrt(e)/sqrt(d))/d^(5/2)],
[x^5*(a+b*log(c*x^n))/(d+e*x^2)^2,x,7,-1/4*b*n*x^2/e^2+1/2*x^2*(a+b*log(c*x^n))/e^2+1/2*d*x^2*(a+b*log(c*x^n))/(e^2*(d+e*x^2))-1/4*b*d*n*log(d+e*x^2)/e^3-d*(a+b*log(c*x^n))*log(1+e*x^2/d)/e^3-1/2*b*d*n*polylog(2,-e*x^2/d)/e^3],
[x^3*(a+b*log(c*x^n))/(d+e*x^2)^2,x,6,-1/2*x^2*(a+b*log(c*x^n))/(e*(d+e*x^2))+1/4*b*n*log(d+e*x^2)/e^2+1/2*(a+b*log(c*x^n))*log(1+e*x^2/d)/e^2+1/4*b*n*polylog(2,-e*x^2/d)/e^2],
[x*(a+b*log(c*x^n))/(d+e*x^2)^2,x,2,1/2*x^2*(a+b*log(c*x^n))/(d*(d+e*x^2))-1/4*b*n*log(d+e*x^2)/(d*e)],
[(a+b*log(c*x^n))/(x*(d+e*x^2)^2),x,3,1/2*(a+b*log(c*x^n))/(d*(d+e*x^2))-1/4*log(1+d/(e*x^2))*(2*a-b*n+2*b*log(c*x^n))/d^2+1/4*b*n*polylog(2,-d/(e*x^2))/d^2],
[(a+b*log(c*x^n))/(x^3*(d+e*x^2)^2),x,5,-1/2*b*n/(d^2*x^2)+1/2*(a+b*log(c*x^n))/(d*x^2*(d+e*x^2))+1/4*(-4*a+b*n-4*b*log(c*x^n))/(d^2*x^2)+1/4*e*log(1+d/(e*x^2))*(4*a-b*n+4*b*log(c*x^n))/d^3-1/2*b*e*n*polylog(2,-d/(e*x^2))/d^3],
[x^4*(a+b*log(c*x^n))/(d+e*x^2)^2,x,16,a*x/e^2-b*n*x/e^2+b*x*log(c*x^n)/e^2+1/2*d*x*(a+b*log(c*x^n))/(e^2*(d+e*x^2))-1/2*b*n*arctan(x*sqrt(e)/sqrt(d))*sqrt(d)/e^(5/2)-3/2*arctan(x*sqrt(e)/sqrt(d))*(a+b*log(c*x^n))*sqrt(d)/e^(5/2)+3/4*I*b*n*polylog(2,-I*x*sqrt(e)/sqrt(d))*sqrt(d)/e^(5/2)-3/4*I*b*n*polylog(2,I*x*sqrt(e)/sqrt(d))*sqrt(d)/e^(5/2)],
[x^2*(a+b*log(c*x^n))/(d+e*x^2)^2,x,14,-1/2*x*(a+b*log(c*x^n))/(e*(d+e*x^2))+1/2*b*n*arctan(x*sqrt(e)/sqrt(d))/(e^(3/2)*sqrt(d))+1/2*arctan(x*sqrt(e)/sqrt(d))*(a+b*log(c*x^n))/(e^(3/2)*sqrt(d))-1/4*I*b*n*polylog(2,-I*x*sqrt(e)/sqrt(d))/(e^(3/2)*sqrt(d))+1/4*I*b*n*polylog(2,I*x*sqrt(e)/sqrt(d))/(e^(3/2)*sqrt(d))],
[(a+b*log(c*x^n))/(d+e*x^2)^2,x,7,1/2*x*(a+b*log(c*x^n))/(d*(d+e*x^2))-1/2*b*n*arctan(x*sqrt(e)/sqrt(d))/(d^(3/2)*sqrt(e))+1/2*arctan(x*sqrt(e)/sqrt(d))*(a+b*log(c*x^n))/(d^(3/2)*sqrt(e))-1/4*I*b*n*polylog(2,-I*x*sqrt(e)/sqrt(d))/(d^(3/2)*sqrt(e))+1/4*I*b*n*polylog(2,I*x*sqrt(e)/sqrt(d))/(d^(3/2)*sqrt(e))],
[(a+b*log(c*x^n))/(x^2*(d+e*x^2)^2),x,8,-3/2*b*n/(d^2*x)+1/2*(a+b*log(c*x^n))/(d*x*(d+e*x^2))+1/2*(-3*a+b*n-3*b*log(c*x^n))/(d^2*x)-1/2*arctan(x*sqrt(e)/sqrt(d))*(3*a-b*n+3*b*log(c*x^n))*sqrt(e)/d^(5/2)+3/4*I*b*n*polylog(2,-I*x*sqrt(e)/sqrt(d))*sqrt(e)/d^(5/2)-3/4*I*b*n*polylog(2,I*x*sqrt(e)/sqrt(d))*sqrt(e)/d^(5/2)],
[(a+b*log(c*x^n))/(x^4*(d+e*x^2)^2),x,10,-5/18*b*n/(d^2*x^3)+5/2*b*e*n/(d^3*x)+1/2*(a+b*log(c*x^n))/(d*x^3*(d+e*x^2))+1/6*(-5*a+b*n-5*b*log(c*x^n))/(d^2*x^3)+1/2*e*(5*a-b*n+5*b*log(c*x^n))/(d^3*x)+1/2*e^(3/2)*arctan(x*sqrt(e)/sqrt(d))*(5*a-b*n+5*b*log(c*x^n))/d^(7/2)-5/4*I*b*e^(3/2)*n*polylog(2,-I*x*sqrt(e)/sqrt(d))/d^(7/2)+5/4*I*b*e^(3/2)*n*polylog(2,I*x*sqrt(e)/sqrt(d))/d^(7/2)],
[x^5*(a+b*log(c*x^n))/(d+e*x^2)^3,x,10,1/8*b*d*n/(e^3*(d+e*x^2))+1/4*b*n*log(x)/e^3-1/4*d^2*(a+b*log(c*x^n))/(e^3*(d+e*x^2)^2)-x^2*(a+b*log(c*x^n))/(e^2*(d+e*x^2))+3/8*b*n*log(d+e*x^2)/e^3+1/2*(a+b*log(c*x^n))*log(1+e*x^2/d)/e^3+1/4*b*n*polylog(2,-e*x^2/d)/e^3],
[x^3*(a+b*log(c*x^n))/(d+e*x^2)^3,x,4,-1/8*b*n/(e^2*(d+e*x^2))+1/4*x^4*(a+b*log(c*x^n))/(d*(d+e*x^2)^2)-1/8*b*n*log(d+e*x^2)/(d*e^2)],
[x*(a+b*log(c*x^n))/(d+e*x^2)^3,x,4,1/8*b*n/(d*e*(d+e*x^2))+1/4*b*n*log(x)/(d^2*e)+1/4*(-a-b*log(c*x^n))/(e*(d+e*x^2)^2)-1/8*b*n*log(d+e*x^2)/(d^2*e)],
[(a+b*log(c*x^n))/(x*(d+e*x^2)^3),x,4,1/4*(a+b*log(c*x^n))/(d*(d+e*x^2)^2)-1/8*log(1+d/(e*x^2))*(4*a-3*b*n+4*b*log(c*x^n))/d^3+1/8*(4*a-b*n+4*b*log(c*x^n))/(d^2*(d+e*x^2))+1/4*b*n*polylog(2,-d/(e*x^2))/d^3],
[(a+b*log(c*x^n))/(x^3*(d+e*x^2)^3),x,6,-3/4*b*n/(d^3*x^2)+1/4*(a+b*log(c*x^n))/(d*x^2*(d+e*x^2)^2)+1/8*(6*a-b*n+6*b*log(c*x^n))/(d^2*x^2*(d+e*x^2))+1/8*(-12*a+5*b*n-12*b*log(c*x^n))/(d^3*x^2)+1/8*e*log(1+d/(e*x^2))*(12*a-5*b*n+12*b*log(c*x^n))/d^4-3/4*b*e*n*polylog(2,-d/(e*x^2))/d^4],
[x^4*(a+b*log(c*x^n))/(d+e*x^2)^3,x,24,-1/8*b*n*x/(e^2*(d+e*x^2))+1/4*d*x*(a+b*log(c*x^n))/(e^2*(d+e*x^2)^2)-5/8*x*(a+b*log(c*x^n))/(e^2*(d+e*x^2))+1/2*b*n*arctan(x*sqrt(e)/sqrt(d))/(e^(5/2)*sqrt(d))+3/8*arctan(x*sqrt(e)/sqrt(d))*(a+b*log(c*x^n))/(e^(5/2)*sqrt(d))-3/16*I*b*n*polylog(2,-I*x*sqrt(e)/sqrt(d))/(e^(5/2)*sqrt(d))+3/16*I*b*n*polylog(2,I*x*sqrt(e)/sqrt(d))/(e^(5/2)*sqrt(d))],
[x^2*(a+b*log(c*x^n))/(d+e*x^2)^3,x,19,1/8*b*n*x/(d*e*(d+e*x^2))-1/4*x*(a+b*log(c*x^n))/(e*(d+e*x^2)^2)+1/8*x*(a+b*log(c*x^n))/(d*e*(d+e*x^2))+1/8*arctan(x*sqrt(e)/sqrt(d))*(a+b*log(c*x^n))/(d^(3/2)*e^(3/2))-1/16*I*b*n*polylog(2,-I*x*sqrt(e)/sqrt(d))/(d^(3/2)*e^(3/2))+1/16*I*b*n*polylog(2,I*x*sqrt(e)/sqrt(d))/(d^(3/2)*e^(3/2))],
[(a+b*log(c*x^n))/(d+e*x^2)^3,x,10,-1/8*b*n*x/(d^2*(d+e*x^2))+1/4*x*(a+b*log(c*x^n))/(d*(d+e*x^2)^2)+3/8*x*(a+b*log(c*x^n))/(d^2*(d+e*x^2))-1/2*b*n*arctan(x*sqrt(e)/sqrt(d))/(d^(5/2)*sqrt(e))+3/8*arctan(x*sqrt(e)/sqrt(d))*(a+b*log(c*x^n))/(d^(5/2)*sqrt(e))-3/16*I*b*n*polylog(2,-I*x*sqrt(e)/sqrt(d))/(d^(5/2)*sqrt(e))+3/16*I*b*n*polylog(2,I*x*sqrt(e)/sqrt(d))/(d^(5/2)*sqrt(e))],
[(a+b*log(c*x^n))/(x^2*(d+e*x^2)^3),x,9,-15/8*b*n/(d^3*x)+1/4*(a+b*log(c*x^n))/(d*x*(d+e*x^2)^2)+1/8*(5*a-b*n+5*b*log(c*x^n))/(d^2*x*(d+e*x^2))+1/8*(-15*a+8*b*n-15*b*log(c*x^n))/(d^3*x)-1/8*arctan(x*sqrt(e)/sqrt(d))*(15*a-8*b*n+15*b*log(c*x^n))*sqrt(e)/d^(7/2)+15/16*I*b*n*polylog(2,-I*x*sqrt(e)/sqrt(d))*sqrt(e)/d^(7/2)-15/16*I*b*n*polylog(2,I*x*sqrt(e)/sqrt(d))*sqrt(e)/d^(7/2)],
[(a+b*log(c*x^n))/(x^4*(d+e*x^2)^3),x,11,-35/72*b*n/(d^3*x^3)+35/8*b*e*n/(d^4*x)+1/4*(a+b*log(c*x^n))/(d*x^3*(d+e*x^2)^2)+1/8*(7*a-b*n+7*b*log(c*x^n))/(d^2*x^3*(d+e*x^2))+1/24*(-35*a+12*b*n-35*b*log(c*x^n))/(d^3*x^3)+1/8*e*(35*a-12*b*n+35*b*log(c*x^n))/(d^4*x)+1/8*e^(3/2)*arctan(x*sqrt(e)/sqrt(d))*(35*a-12*b*n+35*b*log(c*x^n))/d^(9/2)-35/16*I*b*e^(3/2)*n*polylog(2,-I*x*sqrt(e)/sqrt(d))/d^(9/2)+35/16*I*b*e^(3/2)*n*polylog(2,I*x*sqrt(e)/sqrt(d))/d^(9/2)],
[x*log(c*x^2)/(1-c*x^2),x,2,1/2*polylog(2,1-c*x^2)/c],
[x*log(x^2/c)/(c-x^2),x,2,1/2*polylog(2,1-x^2/c)],
[log(x)/(1-x^2),x,2,arctanh(x)*log(x)+1/2*polylog(2,-x)-1/2*polylog(2,x)],
[log(x)/(1+x^2),x,4,arctan(x)*log(x)-1/2*I*polylog(2,-I*x)+1/2*I*polylog(2,I*x)],
[(a+b*log(c*x))/(1-e*x^2),x,3,arctanh(x*sqrt(e))*(a+b*log(c*x))/sqrt(e)+1/2*b*polylog(2,-x*sqrt(e))/sqrt(e)-1/2*b*polylog(2,x*sqrt(e))/sqrt(e)],
[(a+b*log(c*x^n))/(1-e*x^2),x,3,arctanh(x*sqrt(e))*(a+b*log(c*x^n))/sqrt(e)+1/2*b*n*polylog(2,-x*sqrt(e))/sqrt(e)-1/2*b*n*polylog(2,x*sqrt(e))/sqrt(e)],

# Integrands of the form x^m (d+e x^2)^q (a+b Log[c x^n])^2

# q>0

# q<0
[(a+b*log(c*x^n))^2/(d+e*x^2)^2,x,16,1/2*b*n*(a+b*log(c*x^n))*log(1-x*sqrt(e)/sqrt(-d))/((-d)^(3/2)*sqrt(e))-1/4*(a+b*log(c*x^n))^2*log(1-x*sqrt(e)/sqrt(-d))/((-d)^(3/2)*sqrt(e))-1/2*b*n*(a+b*log(c*x^n))*log(1+x*sqrt(e)/sqrt(-d))/((-d)^(3/2)*sqrt(e))+1/4*(a+b*log(c*x^n))^2*log(1+x*sqrt(e)/sqrt(-d))/((-d)^(3/2)*sqrt(e))-1/2*b^2*n^2*polylog(2,-x*sqrt(e)/sqrt(-d))/((-d)^(3/2)*sqrt(e))+1/2*b*n*(a+b*log(c*x^n))*polylog(2,-x*sqrt(e)/sqrt(-d))/((-d)^(3/2)*sqrt(e))+1/2*b^2*n^2*polylog(2,x*sqrt(e)/sqrt(-d))/((-d)^(3/2)*sqrt(e))-1/2*b*n*(a+b*log(c*x^n))*polylog(2,x*sqrt(e)/sqrt(-d))/((-d)^(3/2)*sqrt(e))-1/2*b^2*n^2*polylog(3,-x*sqrt(e)/sqrt(-d))/((-d)^(3/2)*sqrt(e))+1/2*b^2*n^2*polylog(3,x*sqrt(e)/sqrt(-d))/((-d)^(3/2)*sqrt(e))+1/4*x*(a+b*log(c*x^n))^2/((-d)^(3/2)*(sqrt(-d)-x*sqrt(e)))+1/4*x*(a+b*log(c*x^n))^2/((-d)^(3/2)*(sqrt(-d)+x*sqrt(e)))],

# Integrands of the form x^m (d+e x^2)^q (a+b Log[c x^n])^3

# q>0

# q<0
[(a+b*log(c*x^n))^3/(d+e*x^2)^2,x,20,3/4*b*n*(a+b*log(c*x^n))^2*log(1-x*sqrt(e)/sqrt(-d))/((-d)^(3/2)*sqrt(e))-1/4*(a+b*log(c*x^n))^3*log(1-x*sqrt(e)/sqrt(-d))/((-d)^(3/2)*sqrt(e))-3/4*b*n*(a+b*log(c*x^n))^2*log(1+x*sqrt(e)/sqrt(-d))/((-d)^(3/2)*sqrt(e))+1/4*(a+b*log(c*x^n))^3*log(1+x*sqrt(e)/sqrt(-d))/((-d)^(3/2)*sqrt(e))-3/2*b^2*n^2*(a+b*log(c*x^n))*polylog(2,-x*sqrt(e)/sqrt(-d))/((-d)^(3/2)*sqrt(e))+3/4*b*n*(a+b*log(c*x^n))^2*polylog(2,-x*sqrt(e)/sqrt(-d))/((-d)^(3/2)*sqrt(e))+3/2*b^2*n^2*(a+b*log(c*x^n))*polylog(2,x*sqrt(e)/sqrt(-d))/((-d)^(3/2)*sqrt(e))-3/4*b*n*(a+b*log(c*x^n))^2*polylog(2,x*sqrt(e)/sqrt(-d))/((-d)^(3/2)*sqrt(e))+3/2*b^3*n^3*polylog(3,-x*sqrt(e)/sqrt(-d))/((-d)^(3/2)*sqrt(e))-3/2*b^2*n^2*(a+b*log(c*x^n))*polylog(3,-x*sqrt(e)/sqrt(-d))/((-d)^(3/2)*sqrt(e))-3/2*b^3*n^3*polylog(3,x*sqrt(e)/sqrt(-d))/((-d)^(3/2)*sqrt(e))+3/2*b^2*n^2*(a+b*log(c*x^n))*polylog(3,x*sqrt(e)/sqrt(-d))/((-d)^(3/2)*sqrt(e))+3/2*b^3*n^3*polylog(4,-x*sqrt(e)/sqrt(-d))/((-d)^(3/2)*sqrt(e))-3/2*b^3*n^3*polylog(4,x*sqrt(e)/sqrt(-d))/((-d)^(3/2)*sqrt(e))+1/4*x*(a+b*log(c*x^n))^3/((-d)^(3/2)*(sqrt(-d)-x*sqrt(e)))+1/4*x*(a+b*log(c*x^n))^3/((-d)^(3/2)*(sqrt(-d)+x*sqrt(e)))],

# Integrands of the form x^m (d+e x^2)^q (a+b Log[c x^n])^p

# q>0

# q<0
[1/((d+e*x^2)^2*(a+b*log(c*x^n))),x,0,Unintegrable(1/((d+e*x^2)^2*(a+b*log(c*x^n))),x)],
[1/((d+e*x^2)^2*(a+b*log(c*x^n))^2),x,0,Unintegrable(1/((d+e*x^2)^2*(a+b*log(c*x^n))^2),x)],

# Integrands of the form x^m (d+e x^2)^(q/2) (a+b Log[c x^n])

# q>0
[x^5*(a+b*log(c*x^n))*sqrt(d+e*x^2),x,8,-8/315*b*d^2*n*(d+e*x^2)^(3/2)/e^3+9/175*b*d*n*(d+e*x^2)^(5/2)/e^3-1/49*b*n*(d+e*x^2)^(7/2)/e^3+8/105*b*d^(7/2)*n*arctanh(sqrt(d+e*x^2)/sqrt(d))/e^3+1/3*d^2*(d+e*x^2)^(3/2)*(a+b*log(c*x^n))/e^3-2/5*d*(d+e*x^2)^(5/2)*(a+b*log(c*x^n))/e^3+1/7*(d+e*x^2)^(7/2)*(a+b*log(c*x^n))/e^3-8/105*b*d^3*n*sqrt(d+e*x^2)/e^3],
[x^3*(a+b*log(c*x^n))*sqrt(d+e*x^2),x,9,2/45*b*d*n*(d+e*x^2)^(3/2)/e^2-1/25*b*n*(d+e*x^2)^(5/2)/e^2-2/15*b*d^(5/2)*n*arctanh(sqrt(d+e*x^2)/sqrt(d))/e^2-1/3*d*(d+e*x^2)^(3/2)*(a+b*log(c*x^n))/e^2+1/5*(d+e*x^2)^(5/2)*(a+b*log(c*x^n))/e^2+2/15*b*d^2*n*sqrt(d+e*x^2)/e^2],
[x*(a+b*log(c*x^n))*sqrt(d+e*x^2),x,6,-1/9*b*n*(d+e*x^2)^(3/2)/e+1/3*b*d^(3/2)*n*arctanh(sqrt(d+e*x^2)/sqrt(d))/e+1/3*(d+e*x^2)^(3/2)*(a+b*log(c*x^n))/e-1/3*b*d*n*sqrt(d+e*x^2)/e],
[(a+b*log(c*x^n))*sqrt(d+e*x^2)/x,x,12,b*n*arctanh(sqrt(d+e*x^2)/sqrt(d))*sqrt(d)+1/2*b*n*arctanh(sqrt(d+e*x^2)/sqrt(d))^2*sqrt(d)-b*n*arctanh(sqrt(d+e*x^2)/sqrt(d))*log(2*sqrt(d)/(sqrt(d)-sqrt(d+e*x^2)))*sqrt(d)-1/2*b*n*polylog(2,1-2*sqrt(d)/(sqrt(d)-sqrt(d+e*x^2)))*sqrt(d)-b*n*sqrt(d+e*x^2)+(a+b*log(c*x^n))*(-arctanh(sqrt(d+e*x^2)/sqrt(d))*sqrt(d)+sqrt(d+e*x^2))],
[(a+b*log(c*x^n))*sqrt(d+e*x^2)/x^3,x,14,-1/4*b*e*n*arctanh(sqrt(d+e*x^2)/sqrt(d))/sqrt(d)+1/4*b*e*n*arctanh(sqrt(d+e*x^2)/sqrt(d))^2/sqrt(d)-1/2*e*arctanh(sqrt(d+e*x^2)/sqrt(d))*(a+b*log(c*x^n))/sqrt(d)-1/2*b*e*n*arctanh(sqrt(d+e*x^2)/sqrt(d))*log(2*sqrt(d)/(sqrt(d)-sqrt(d+e*x^2)))/sqrt(d)-1/4*b*e*n*polylog(2,1-2*sqrt(d)/(sqrt(d)-sqrt(d+e*x^2)))/sqrt(d)-1/4*b*n*sqrt(d+e*x^2)/x^2-1/2*(a+b*log(c*x^n))*sqrt(d+e*x^2)/x^2],
[x^4*(a+b*log(c*x^n))*sqrt(d+e*x^2),x,19,7/192*b*d^2*n*x*sqrt(d+e*x^2)/e^2-5/288*b*d*n*x^3*sqrt(d+e*x^2)/e-1/36*b*n*x^5*sqrt(d+e*x^2)-1/16*d^2*x*(a+b*log(c*x^n))*sqrt(d+e*x^2)/e^2+1/24*d*x^3*(a+b*log(c*x^n))*sqrt(d+e*x^2)/e+1/6*x^5*(a+b*log(c*x^n))*sqrt(d+e*x^2)+5/192*b*d^(5/2)*n*arcsinh(x*sqrt(e)/sqrt(d))*sqrt(d+e*x^2)/(e^(5/2)*sqrt(1+e*x^2/d))+1/32*b*d^(5/2)*n*arcsinh(x*sqrt(e)/sqrt(d))^2*sqrt(d+e*x^2)/(e^(5/2)*sqrt(1+e*x^2/d))-1/16*b*d^(5/2)*n*arcsinh(x*sqrt(e)/sqrt(d))*log(1-exp(2*arcsinh(x*sqrt(e)/sqrt(d))))*sqrt(d+e*x^2)/(e^(5/2)*sqrt(1+e*x^2/d))+1/16*d^(5/2)*arcsinh(x*sqrt(e)/sqrt(d))*(a+b*log(c*x^n))*sqrt(d+e*x^2)/(e^(5/2)*sqrt(1+e*x^2/d))-1/32*b*d^(5/2)*n*polylog(2,exp(2*arcsinh(x*sqrt(e)/sqrt(d))))*sqrt(d+e*x^2)/(e^(5/2)*sqrt(1+e*x^2/d))],
[x^2*(a+b*log(c*x^n))*sqrt(d+e*x^2),x,15,-3/32*b*d*n*x*sqrt(d+e*x^2)/e-1/16*b*n*x^3*sqrt(d+e*x^2)+1/8*d*x*(a+b*log(c*x^n))*sqrt(d+e*x^2)/e+1/4*x^3*(a+b*log(c*x^n))*sqrt(d+e*x^2)-1/32*b*d^(3/2)*n*arcsinh(x*sqrt(e)/sqrt(d))*sqrt(d+e*x^2)/(e^(3/2)*sqrt(1+e*x^2/d))-1/16*b*d^(3/2)*n*arcsinh(x*sqrt(e)/sqrt(d))^2*sqrt(d+e*x^2)/(e^(3/2)*sqrt(1+e*x^2/d))+1/8*b*d^(3/2)*n*arcsinh(x*sqrt(e)/sqrt(d))*log(1-exp(2*arcsinh(x*sqrt(e)/sqrt(d))))*sqrt(d+e*x^2)/(e^(3/2)*sqrt(1+e*x^2/d))-1/8*d^(3/2)*arcsinh(x*sqrt(e)/sqrt(d))*(a+b*log(c*x^n))*sqrt(d+e*x^2)/(e^(3/2)*sqrt(1+e*x^2/d))+1/16*b*d^(3/2)*n*polylog(2,exp(2*arcsinh(x*sqrt(e)/sqrt(d))))*sqrt(d+e*x^2)/(e^(3/2)*sqrt(1+e*x^2/d))],
[(a+b*log(c*x^n))*sqrt(d+e*x^2),x,11,-1/4*b*d*n*arctanh(x*sqrt(e)/sqrt(d+e*x^2))/sqrt(e)-1/4*b*n*x*sqrt(d+e*x^2)+1/2*x*(a+b*log(c*x^n))*sqrt(d+e*x^2)+1/4*b*d^(3/2)*n*arcsinh(x*sqrt(e)/sqrt(d))^2*sqrt(1+e*x^2/d)/(sqrt(e)*sqrt(d+e*x^2))-1/2*b*d^(3/2)*n*arcsinh(x*sqrt(e)/sqrt(d))*log(1-exp(2*arcsinh(x*sqrt(e)/sqrt(d))))*sqrt(1+e*x^2/d)/(sqrt(e)*sqrt(d+e*x^2))+1/2*d^(3/2)*arcsinh(x*sqrt(e)/sqrt(d))*(a+b*log(c*x^n))*sqrt(1+e*x^2/d)/(sqrt(e)*sqrt(d+e*x^2))-1/4*b*d^(3/2)*n*polylog(2,exp(2*arcsinh(x*sqrt(e)/sqrt(d))))*sqrt(1+e*x^2/d)/(sqrt(e)*sqrt(d+e*x^2))],
[(a+b*log(c*x^n))*sqrt(d+e*x^2)/x^2,x,11,-b*n*sqrt(d+e*x^2)/x-(a+b*log(c*x^n))*sqrt(d+e*x^2)/x+b*n*arcsinh(x*sqrt(e)/sqrt(d))*sqrt(e)*sqrt(d+e*x^2)/(sqrt(d)*sqrt(1+e*x^2/d))+1/2*b*n*arcsinh(x*sqrt(e)/sqrt(d))^2*sqrt(e)*sqrt(d+e*x^2)/(sqrt(d)*sqrt(1+e*x^2/d))-b*n*arcsinh(x*sqrt(e)/sqrt(d))*log(1-exp(2*arcsinh(x*sqrt(e)/sqrt(d))))*sqrt(e)*sqrt(d+e*x^2)/(sqrt(d)*sqrt(1+e*x^2/d))+arcsinh(x*sqrt(e)/sqrt(d))*(a+b*log(c*x^n))*sqrt(e)*sqrt(d+e*x^2)/(sqrt(d)*sqrt(1+e*x^2/d))-1/2*b*n*polylog(2,exp(2*arcsinh(x*sqrt(e)/sqrt(d))))*sqrt(e)*sqrt(d+e*x^2)/(sqrt(d)*sqrt(1+e*x^2/d))],
[(a+b*log(c*x^n))*sqrt(d+e*x^2)/x^4,x,5,-1/9*b*n*(d+e*x^2)^(3/2)/(d*x^3)+1/3*b*e^(3/2)*n*arctanh(x*sqrt(e)/sqrt(d+e*x^2))/d-1/3*(d+e*x^2)^(3/2)*(a+b*log(c*x^n))/(d*x^3)-1/3*b*e*n*sqrt(d+e*x^2)/(d*x)],
[(a+b*log(c*x^n))*sqrt(d+e*x^2)/x^6,x,8,2/45*b*e*n*(d+e*x^2)^(3/2)/(d^2*x^3)-1/25*b*n*(d+e*x^2)^(5/2)/(d^2*x^5)-2/15*b*e^(5/2)*n*arctanh(x*sqrt(e)/sqrt(d+e*x^2))/d^2-1/5*(d+e*x^2)^(3/2)*(a+b*log(c*x^n))/(d*x^5)+2/15*e*(d+e*x^2)^(3/2)*(a+b*log(c*x^n))/(d^2*x^3)+2/15*b*e^2*n*sqrt(d+e*x^2)/(d^2*x)],
[(a+b*log(c*x^n))*sqrt(d+e*x^2)/x^8,x,9,-1/49*b*n*(d+e*x^2)^(3/2)/(d*x^7)+13/1225*b*e*n*(d+e*x^2)^(3/2)/(d^2*x^5)+62/11025*b*e^2*n*(d+e*x^2)^(3/2)/(d^3*x^3)+8/105*b*e^(7/2)*n*arctanh(x*sqrt(e)/sqrt(d+e*x^2))/d^3-1/7*(d+e*x^2)^(3/2)*(a+b*log(c*x^n))/(d*x^7)+4/35*e*(d+e*x^2)^(3/2)*(a+b*log(c*x^n))/(d^2*x^5)-8/105*e^2*(d+e*x^2)^(3/2)*(a+b*log(c*x^n))/(d^3*x^3)-8/105*b*e^3*n*sqrt(d+e*x^2)/(d^3*x)],
[x^5*(d+e*x^2)^(3/2)*(a+b*log(c*x^n)),x,7,-8/945*b*d^3*n*(d+e*x^2)^(3/2)/e^3-8/1575*b*d^2*n*(d+e*x^2)^(5/2)/e^3+11/441*b*d*n*(d+e*x^2)^(7/2)/e^3-1/81*b*n*(d+e*x^2)^(9/2)/e^3+8/315*b*d^(9/2)*n*arctanh(sqrt(d+e*x^2)/sqrt(d))/e^3+1/5*d^2*(d+e*x^2)^(5/2)*(a+b*log(c*x^n))/e^3-2/7*d*(d+e*x^2)^(7/2)*(a+b*log(c*x^n))/e^3+1/9*(d+e*x^2)^(9/2)*(a+b*log(c*x^n))/e^3-8/315*b*d^4*n*sqrt(d+e*x^2)/e^3],
[x^3*(d+e*x^2)^(3/2)*(a+b*log(c*x^n)),x,9,2/105*b*d^2*n*(d+e*x^2)^(3/2)/e^2+2/175*b*d*n*(d+e*x^2)^(5/2)/e^2-1/49*b*n*(d+e*x^2)^(7/2)/e^2-2/35*b*d^(7/2)*n*arctanh(sqrt(d+e*x^2)/sqrt(d))/e^2-1/5*d*(d+e*x^2)^(5/2)*(a+b*log(c*x^n))/e^2+1/7*(d+e*x^2)^(7/2)*(a+b*log(c*x^n))/e^2+2/35*b*d^3*n*sqrt(d+e*x^2)/e^2],
[x*(d+e*x^2)^(3/2)*(a+b*log(c*x^n)),x,7,-1/15*b*d*n*(d+e*x^2)^(3/2)/e-1/25*b*n*(d+e*x^2)^(5/2)/e+1/5*b*d^(5/2)*n*arctanh(sqrt(d+e*x^2)/sqrt(d))/e+1/5*(d+e*x^2)^(5/2)*(a+b*log(c*x^n))/e-1/5*b*d^2*n*sqrt(d+e*x^2)/e],
[(d+e*x^2)^(3/2)*(a+b*log(c*x^n))/x,x,17,-1/9*b*n*(d+e*x^2)^(3/2)+4/3*b*d^(3/2)*n*arctanh(sqrt(d+e*x^2)/sqrt(d))+1/2*b*d^(3/2)*n*arctanh(sqrt(d+e*x^2)/sqrt(d))^2-b*d^(3/2)*n*arctanh(sqrt(d+e*x^2)/sqrt(d))*log(2*sqrt(d)/(sqrt(d)-sqrt(d+e*x^2)))-1/2*b*d^(3/2)*n*polylog(2,1-2*sqrt(d)/(sqrt(d)-sqrt(d+e*x^2)))-4/3*b*d*n*sqrt(d+e*x^2)+1/3*(a+b*log(c*x^n))*((d+e*x^2)^(3/2)-3*d^(3/2)*arctanh(sqrt(d+e*x^2)/sqrt(d))+3*d*sqrt(d+e*x^2))],
[(d+e*x^2)^(3/2)*(a+b*log(c*x^n))/x^3,x,18,-1/2*(d+e*x^2)^(3/2)*(a+b*log(c*x^n))/x^2+3/4*b*e*n*arctanh(sqrt(d+e*x^2)/sqrt(d))*sqrt(d)+3/4*b*e*n*arctanh(sqrt(d+e*x^2)/sqrt(d))^2*sqrt(d)-3/2*e*arctanh(sqrt(d+e*x^2)/sqrt(d))*(a+b*log(c*x^n))*sqrt(d)-3/2*b*e*n*arctanh(sqrt(d+e*x^2)/sqrt(d))*log(2*sqrt(d)/(sqrt(d)-sqrt(d+e*x^2)))*sqrt(d)-3/4*b*e*n*polylog(2,1-2*sqrt(d)/(sqrt(d)-sqrt(d+e*x^2)))*sqrt(d)-b*e*n*sqrt(d+e*x^2)-1/4*b*d*n*sqrt(d+e*x^2)/x^2+3/2*e*(a+b*log(c*x^n))*sqrt(d+e*x^2)],
[x^2*(d+e*x^2)^(3/2)*(a+b*log(c*x^n)),x,19,1/6*x^3*(d+e*x^2)^(3/2)*(a+b*log(c*x^n))-11/192*b*d^2*n*x*sqrt(d+e*x^2)/e-23/288*b*d*n*x^3*sqrt(d+e*x^2)-1/36*b*e*n*x^5*sqrt(d+e*x^2)+1/16*d^2*x*(a+b*log(c*x^n))*sqrt(d+e*x^2)/e+1/8*d*x^3*(a+b*log(c*x^n))*sqrt(d+e*x^2)-1/192*b*d^(5/2)*n*arcsinh(x*sqrt(e)/sqrt(d))*sqrt(d+e*x^2)/(e^(3/2)*sqrt(1+e*x^2/d))-1/32*b*d^(5/2)*n*arcsinh(x*sqrt(e)/sqrt(d))^2*sqrt(d+e*x^2)/(e^(3/2)*sqrt(1+e*x^2/d))+1/16*b*d^(5/2)*n*arcsinh(x*sqrt(e)/sqrt(d))*log(1-exp(2*arcsinh(x*sqrt(e)/sqrt(d))))*sqrt(d+e*x^2)/(e^(3/2)*sqrt(1+e*x^2/d))-1/16*d^(5/2)*arcsinh(x*sqrt(e)/sqrt(d))*(a+b*log(c*x^n))*sqrt(d+e*x^2)/(e^(3/2)*sqrt(1+e*x^2/d))+1/32*b*d^(5/2)*n*polylog(2,exp(2*arcsinh(x*sqrt(e)/sqrt(d))))*sqrt(d+e*x^2)/(e^(3/2)*sqrt(1+e*x^2/d))],
[(d+e*x^2)^(3/2)*(a+b*log(c*x^n)),x,16,-1/16*b*n*x*(d+e*x^2)^(3/2)+1/4*x*(d+e*x^2)^(3/2)*(a+b*log(c*x^n))-9/32*b*d^2*n*arctanh(x*sqrt(e)/sqrt(d+e*x^2))/sqrt(e)-9/32*b*d*n*x*sqrt(d+e*x^2)+3/8*d*x*(a+b*log(c*x^n))*sqrt(d+e*x^2)+3/16*b*d^(5/2)*n*arcsinh(x*sqrt(e)/sqrt(d))^2*sqrt(1+e*x^2/d)/(sqrt(e)*sqrt(d+e*x^2))-3/8*b*d^(5/2)*n*arcsinh(x*sqrt(e)/sqrt(d))*log(1-exp(2*arcsinh(x*sqrt(e)/sqrt(d))))*sqrt(1+e*x^2/d)/(sqrt(e)*sqrt(d+e*x^2))+3/8*d^(5/2)*arcsinh(x*sqrt(e)/sqrt(d))*(a+b*log(c*x^n))*sqrt(1+e*x^2/d)/(sqrt(e)*sqrt(d+e*x^2))-3/16*b*d^(5/2)*n*polylog(2,exp(2*arcsinh(x*sqrt(e)/sqrt(d))))*sqrt(1+e*x^2/d)/(sqrt(e)*sqrt(d+e*x^2))],
[(d+e*x^2)^(3/2)*(a+b*log(c*x^n))/x^2,x,14,-(d+e*x^2)^(3/2)*(a+b*log(c*x^n))/x-b*d*n*sqrt(d+e*x^2)/x-1/4*b*e*n*x*sqrt(d+e*x^2)+3/2*e*x*(a+b*log(c*x^n))*sqrt(d+e*x^2)+3/4*b*n*arcsinh(x*sqrt(e)/sqrt(d))*sqrt(d)*sqrt(e)*sqrt(d+e*x^2)/sqrt(1+e*x^2/d)+3/4*b*n*arcsinh(x*sqrt(e)/sqrt(d))^2*sqrt(d)*sqrt(e)*sqrt(d+e*x^2)/sqrt(1+e*x^2/d)-3/2*b*n*arcsinh(x*sqrt(e)/sqrt(d))*log(1-exp(2*arcsinh(x*sqrt(e)/sqrt(d))))*sqrt(d)*sqrt(e)*sqrt(d+e*x^2)/sqrt(1+e*x^2/d)+3/2*arcsinh(x*sqrt(e)/sqrt(d))*(a+b*log(c*x^n))*sqrt(d)*sqrt(e)*sqrt(d+e*x^2)/sqrt(1+e*x^2/d)-3/4*b*n*polylog(2,exp(2*arcsinh(x*sqrt(e)/sqrt(d))))*sqrt(d)*sqrt(e)*sqrt(d+e*x^2)/sqrt(1+e*x^2/d)],
[(d+e*x^2)^(3/2)*(a+b*log(c*x^n))/x^4,x,13,-1/9*b*n*(d+e*x^2)^(3/2)/x^3-1/3*(d+e*x^2)^(3/2)*(a+b*log(c*x^n))/x^3-4/3*b*e*n*sqrt(d+e*x^2)/x-e*(a+b*log(c*x^n))*sqrt(d+e*x^2)/x+4/3*b*e^(3/2)*n*arcsinh(x*sqrt(e)/sqrt(d))*sqrt(d+e*x^2)/(sqrt(d)*sqrt(1+e*x^2/d))+1/2*b*e^(3/2)*n*arcsinh(x*sqrt(e)/sqrt(d))^2*sqrt(d+e*x^2)/(sqrt(d)*sqrt(1+e*x^2/d))-b*e^(3/2)*n*arcsinh(x*sqrt(e)/sqrt(d))*log(1-exp(2*arcsinh(x*sqrt(e)/sqrt(d))))*sqrt(d+e*x^2)/(sqrt(d)*sqrt(1+e*x^2/d))+e^(3/2)*arcsinh(x*sqrt(e)/sqrt(d))*(a+b*log(c*x^n))*sqrt(d+e*x^2)/(sqrt(d)*sqrt(1+e*x^2/d))-1/2*b*e^(3/2)*n*polylog(2,exp(2*arcsinh(x*sqrt(e)/sqrt(d))))*sqrt(d+e*x^2)/(sqrt(d)*sqrt(1+e*x^2/d))],
[(d+e*x^2)^(3/2)*(a+b*log(c*x^n))/x^6,x,6,-1/15*b*e*n*(d+e*x^2)^(3/2)/(d*x^3)-1/25*b*n*(d+e*x^2)^(5/2)/(d*x^5)+1/5*b*e^(5/2)*n*arctanh(x*sqrt(e)/sqrt(d+e*x^2))/d-1/5*(d+e*x^2)^(5/2)*(a+b*log(c*x^n))/(d*x^5)-1/5*b*e^2*n*sqrt(d+e*x^2)/(d*x)],
[(d+e*x^2)^(3/2)*(a+b*log(c*x^n))/x^8,x,8,2/105*b*e^2*n*(d+e*x^2)^(3/2)/(d^2*x^3)+2/175*b*e*n*(d+e*x^2)^(5/2)/(d^2*x^5)-1/49*b*n*(d+e*x^2)^(7/2)/(d^2*x^7)-2/35*b*e^(7/2)*n*arctanh(x*sqrt(e)/sqrt(d+e*x^2))/d^2-1/7*(d+e*x^2)^(5/2)*(a+b*log(c*x^n))/(d*x^7)+2/35*e*(d+e*x^2)^(5/2)*(a+b*log(c*x^n))/(d^2*x^5)+2/35*b*e^3*n*sqrt(d+e*x^2)/(d^2*x)],
[(d+e*x^2)^(3/2)*(a+b*log(c*x^n))/x^10,x,9,-8/945*b*e^3*n*(d+e*x^2)^(3/2)/(d^3*x^3)-8/1575*b*e^2*n*(d+e*x^2)^(5/2)/(d^3*x^5)-1/81*b*n*(d+e*x^2)^(7/2)/(d^2*x^9)+50/3969*b*e*n*(d+e*x^2)^(7/2)/(d^3*x^7)+8/315*b*e^(9/2)*n*arctanh(x*sqrt(e)/sqrt(d+e*x^2))/d^3-1/9*(d+e*x^2)^(5/2)*(a+b*log(c*x^n))/(d*x^9)+4/63*e*(d+e*x^2)^(5/2)*(a+b*log(c*x^n))/(d^2*x^7)-8/315*e^2*(d+e*x^2)^(5/2)*(a+b*log(c*x^n))/(d^3*x^5)-8/315*b*e^4*n*sqrt(d+e*x^2)/(d^3*x)],
[x*log(x)*sqrt(4+x^2),x,6,-1/9*(4+x^2)^(3/2)+8/3*arctanh(1/2*sqrt(4+x^2))+1/3*(4+x^2)^(3/2)*log(x)-4/3*sqrt(4+x^2)],

# q<0
[x^5*(a+b*log(c*x^n))/sqrt(d+e*x^2),x,7,7/45*b*d*n*(d+e*x^2)^(3/2)/e^3-1/25*b*n*(d+e*x^2)^(5/2)/e^3+8/15*b*d^(5/2)*n*arctanh(sqrt(d+e*x^2)/sqrt(d))/e^3-2/3*d*(d+e*x^2)^(3/2)*(a+b*log(c*x^n))/e^3+1/5*(d+e*x^2)^(5/2)*(a+b*log(c*x^n))/e^3-8/15*b*d^2*n*sqrt(d+e*x^2)/e^3+d^2*(a+b*log(c*x^n))*sqrt(d+e*x^2)/e^3],
[x^3*(a+b*log(c*x^n))/sqrt(d+e*x^2),x,7,-1/9*b*n*(d+e*x^2)^(3/2)/e^2-2/3*b*d^(3/2)*n*arctanh(sqrt(d+e*x^2)/sqrt(d))/e^2+1/3*(d+e*x^2)^(3/2)*(a+b*log(c*x^n))/e^2+2/3*b*d*n*sqrt(d+e*x^2)/e^2-d*(a+b*log(c*x^n))*sqrt(d+e*x^2)/e^2],
[x*(a+b*log(c*x^n))/sqrt(d+e*x^2),x,5,b*n*arctanh(sqrt(d+e*x^2)/sqrt(d))*sqrt(d)/e-b*n*sqrt(d+e*x^2)/e+(a+b*log(c*x^n))*sqrt(d+e*x^2)/e],
[(a+b*log(c*x^n))/(x*sqrt(d+e*x^2)),x,8,1/2*b*n*arctanh(sqrt(d+e*x^2)/sqrt(d))^2/sqrt(d)-arctanh(sqrt(d+e*x^2)/sqrt(d))*(a+b*log(c*x^n))/sqrt(d)-b*n*arctanh(sqrt(d+e*x^2)/sqrt(d))*log(2*sqrt(d)/(sqrt(d)-sqrt(d+e*x^2)))/sqrt(d)-1/2*b*n*polylog(2,1-2*sqrt(d)/(sqrt(d)-sqrt(d+e*x^2)))/sqrt(d)],
[(a+b*log(c*x^n))/(x^3*sqrt(d+e*x^2)),x,14,-1/4*b*e*n*arctanh(sqrt(d+e*x^2)/sqrt(d))/d^(3/2)-1/4*b*e*n*arctanh(sqrt(d+e*x^2)/sqrt(d))^2/d^(3/2)+1/2*e*arctanh(sqrt(d+e*x^2)/sqrt(d))*(a+b*log(c*x^n))/d^(3/2)+1/2*b*e*n*arctanh(sqrt(d+e*x^2)/sqrt(d))*log(2*sqrt(d)/(sqrt(d)-sqrt(d+e*x^2)))/d^(3/2)+1/4*b*e*n*polylog(2,1-2*sqrt(d)/(sqrt(d)-sqrt(d+e*x^2)))/d^(3/2)-1/4*b*n*sqrt(d+e*x^2)/(d*x^2)-1/2*(a+b*log(c*x^n))*sqrt(d+e*x^2)/(d*x^2)],
[x^2*(a+b*log(c*x^n))/sqrt(d+e*x^2),x,12,-1/4*b*n*x*sqrt(d+e*x^2)/e+1/2*x*(a+b*log(c*x^n))*sqrt(d+e*x^2)/e-1/4*b*d^(3/2)*n*arcsinh(x*sqrt(e)/sqrt(d))*sqrt(1+e*x^2/d)/(e^(3/2)*sqrt(d+e*x^2))-1/4*b*d^(3/2)*n*arcsinh(x*sqrt(e)/sqrt(d))^2*sqrt(1+e*x^2/d)/(e^(3/2)*sqrt(d+e*x^2))+1/2*b*d^(3/2)*n*arcsinh(x*sqrt(e)/sqrt(d))*log(1-exp(2*arcsinh(x*sqrt(e)/sqrt(d))))*sqrt(1+e*x^2/d)/(e^(3/2)*sqrt(d+e*x^2))-1/2*d^(3/2)*arcsinh(x*sqrt(e)/sqrt(d))*(a+b*log(c*x^n))*sqrt(1+e*x^2/d)/(e^(3/2)*sqrt(d+e*x^2))+1/4*b*d^(3/2)*n*polylog(2,exp(2*arcsinh(x*sqrt(e)/sqrt(d))))*sqrt(1+e*x^2/d)/(e^(3/2)*sqrt(d+e*x^2))],
[(a+b*log(c*x^n))/sqrt(d+e*x^2),x,7,1/2*b*n*arcsinh(x*sqrt(e)/sqrt(d))^2*sqrt(d)*sqrt(1+e*x^2/d)/(sqrt(e)*sqrt(d+e*x^2))-b*n*arcsinh(x*sqrt(e)/sqrt(d))*log(1-exp(2*arcsinh(x*sqrt(e)/sqrt(d))))*sqrt(d)*sqrt(1+e*x^2/d)/(sqrt(e)*sqrt(d+e*x^2))+arcsinh(x*sqrt(e)/sqrt(d))*(a+b*log(c*x^n))*sqrt(d)*sqrt(1+e*x^2/d)/(sqrt(e)*sqrt(d+e*x^2))-1/2*b*n*polylog(2,exp(2*arcsinh(x*sqrt(e)/sqrt(d))))*sqrt(d)*sqrt(1+e*x^2/d)/(sqrt(e)*sqrt(d+e*x^2))],
[(a+b*log(c*x^n))/(x^2*sqrt(d+e*x^2)),x,4,b*n*arctanh(x*sqrt(e)/sqrt(d+e*x^2))*sqrt(e)/d-b*n*sqrt(d+e*x^2)/(d*x)-(a+b*log(c*x^n))*sqrt(d+e*x^2)/(d*x)],
[(a+b*log(c*x^n))/(x^4*sqrt(d+e*x^2)),x,6,-1/9*b*n*(d+e*x^2)^(3/2)/(d^2*x^3)-2/3*b*e^(3/2)*n*arctanh(x*sqrt(e)/sqrt(d+e*x^2))/d^2+2/3*b*e*n*sqrt(d+e*x^2)/(d^2*x)-1/3*(a+b*log(c*x^n))*sqrt(d+e*x^2)/(d*x^3)+2/3*e*(a+b*log(c*x^n))*sqrt(d+e*x^2)/(d^2*x)],
[(a+b*log(c*x^n))/(x^6*sqrt(d+e*x^2)),x,7,-1/25*b*n*(d+e*x^2)^(3/2)/(d^2*x^5)+26/225*b*e*n*(d+e*x^2)^(3/2)/(d^3*x^3)+8/15*b*e^(5/2)*n*arctanh(x*sqrt(e)/sqrt(d+e*x^2))/d^3-8/15*b*e^2*n*sqrt(d+e*x^2)/(d^3*x)-1/5*(a+b*log(c*x^n))*sqrt(d+e*x^2)/(d*x^5)+4/15*e*(a+b*log(c*x^n))*sqrt(d+e*x^2)/(d^2*x^3)-8/15*e^2*(a+b*log(c*x^n))*sqrt(d+e*x^2)/(d^3*x)],
[x^7*(a+b*log(c*x^n))/(d+e*x^2)^(3/2),x,7,4/15*b*d*n*(d+e*x^2)^(3/2)/e^4-1/25*b*n*(d+e*x^2)^(5/2)/e^4+16/5*b*d^(5/2)*n*arctanh(sqrt(d+e*x^2)/sqrt(d))/e^4-d*(d+e*x^2)^(3/2)*(a+b*log(c*x^n))/e^4+1/5*(d+e*x^2)^(5/2)*(a+b*log(c*x^n))/e^4+d^3*(a+b*log(c*x^n))/(e^4*sqrt(d+e*x^2))-11/5*b*d^2*n*sqrt(d+e*x^2)/e^4+3*d^2*(a+b*log(c*x^n))*sqrt(d+e*x^2)/e^4],
[x^5*(a+b*log(c*x^n))/(d+e*x^2)^(3/2),x,7,-1/9*b*n*(d+e*x^2)^(3/2)/e^3-8/3*b*d^(3/2)*n*arctanh(sqrt(d+e*x^2)/sqrt(d))/e^3+1/3*(d+e*x^2)^(3/2)*(a+b*log(c*x^n))/e^3-d^2*(a+b*log(c*x^n))/(e^3*sqrt(d+e*x^2))+5/3*b*d*n*sqrt(d+e*x^2)/e^3-2*d*(a+b*log(c*x^n))*sqrt(d+e*x^2)/e^3],
[x^3*(a+b*log(c*x^n))/(d+e*x^2)^(3/2),x,6,2*b*n*arctanh(sqrt(d+e*x^2)/sqrt(d))*sqrt(d)/e^2+d*(a+b*log(c*x^n))/(e^2*sqrt(d+e*x^2))-b*n*sqrt(d+e*x^2)/e^2+(a+b*log(c*x^n))*sqrt(d+e*x^2)/e^2],
[x*(a+b*log(c*x^n))/(d+e*x^2)^(3/2),x,4,-b*n*arctanh(sqrt(d+e*x^2)/sqrt(d))/(e*sqrt(d))+(-a-b*log(c*x^n))/(e*sqrt(d+e*x^2))],
[(a+b*log(c*x^n))/(x*(d+e*x^2)^(3/2)),x,11,b*n*arctanh(sqrt(d+e*x^2)/sqrt(d))/d^(3/2)+1/2*b*n*arctanh(sqrt(d+e*x^2)/sqrt(d))^2/d^(3/2)-b*n*arctanh(sqrt(d+e*x^2)/sqrt(d))*log(2*sqrt(d)/(sqrt(d)-sqrt(d+e*x^2)))/d^(3/2)-1/2*b*n*polylog(2,1-2*sqrt(d)/(sqrt(d)-sqrt(d+e*x^2)))/d^(3/2)+(a+b*log(c*x^n))*(-arctanh(sqrt(d+e*x^2)/sqrt(d))/d^(3/2)+1/(d*sqrt(d+e*x^2)))],
[(a+b*log(c*x^n))/(x^3*(d+e*x^2)^(3/2)),x,12,-5/4*b*e*n*arctanh(sqrt(d+e*x^2)/sqrt(d))/d^(5/2)-3/4*b*e*n*arctanh(sqrt(d+e*x^2)/sqrt(d))^2/d^(5/2)+3/2*e*arctanh(sqrt(d+e*x^2)/sqrt(d))*(a+b*log(c*x^n))/d^(5/2)+3/2*b*e*n*arctanh(sqrt(d+e*x^2)/sqrt(d))*log(2*sqrt(d)/(sqrt(d)-sqrt(d+e*x^2)))/d^(5/2)+3/4*b*e*n*polylog(2,1-2*sqrt(d)/(sqrt(d)-sqrt(d+e*x^2)))/d^(5/2)-3/2*e*(a+b*log(c*x^n))/(d^2*sqrt(d+e*x^2))+1/2*(-a-b*log(c*x^n))/(d*x^2*sqrt(d+e*x^2))-1/4*b*n*sqrt(d+e*x^2)/(d^2*x^2)],
[x^2*(a+b*log(c*x^n))/(d+e*x^2)^(3/2),x,11,-x*(a+b*log(c*x^n))/(e*sqrt(d+e*x^2))+b*n*arcsinh(x*sqrt(e)/sqrt(d))*sqrt(d)*sqrt(1+e*x^2/d)/(e^(3/2)*sqrt(d+e*x^2))+1/2*b*n*arcsinh(x*sqrt(e)/sqrt(d))^2*sqrt(d)*sqrt(1+e*x^2/d)/(e^(3/2)*sqrt(d+e*x^2))-b*n*arcsinh(x*sqrt(e)/sqrt(d))*log(1-exp(2*arcsinh(x*sqrt(e)/sqrt(d))))*sqrt(d)*sqrt(1+e*x^2/d)/(e^(3/2)*sqrt(d+e*x^2))+arcsinh(x*sqrt(e)/sqrt(d))*(a+b*log(c*x^n))*sqrt(d)*sqrt(1+e*x^2/d)/(e^(3/2)*sqrt(d+e*x^2))-1/2*b*n*polylog(2,exp(2*arcsinh(x*sqrt(e)/sqrt(d))))*sqrt(d)*sqrt(1+e*x^2/d)/(e^(3/2)*sqrt(d+e*x^2))],
[(a+b*log(c*x^n))/(d+e*x^2)^(3/2),x,3,-b*n*arctanh(x*sqrt(e)/sqrt(d+e*x^2))/(d*sqrt(e))+x*(a+b*log(c*x^n))/(d*sqrt(d+e*x^2))],
[(a+b*log(c*x^n))/(x^2*(d+e*x^2)^(3/2)),x,5,2*b*n*arctanh(x*sqrt(e)/sqrt(d+e*x^2))*sqrt(e)/d^2+(-a-b*log(c*x^n))/(d*x*sqrt(d+e*x^2))-2*e*x*(a+b*log(c*x^n))/(d^2*sqrt(d+e*x^2))-b*n*sqrt(d+e*x^2)/(d^2*x)],
[(a+b*log(c*x^n))/(x^4*(d+e*x^2)^(3/2)),x,6,-8/3*b*e^(3/2)*n*arctanh(x*sqrt(e)/sqrt(d+e*x^2))/d^3+1/3*(-a-b*log(c*x^n))/(d*x^3*sqrt(d+e*x^2))+4/3*e*(a+b*log(c*x^n))/(d^2*x*sqrt(d+e*x^2))+8/3*e^2*x*(a+b*log(c*x^n))/(d^3*sqrt(d+e*x^2))-1/9*b*n*sqrt(d+e*x^2)/(d^2*x^3)+14/9*b*e*n*sqrt(d+e*x^2)/(d^3*x)],
[(a+b*log(c*x^n))/(x^6*(d+e*x^2)^(3/2)),x,8,16/5*b*e^(5/2)*n*arctanh(x*sqrt(e)/sqrt(d+e*x^2))/d^4+1/5*(-a-b*log(c*x^n))/(d*x^5*sqrt(d+e*x^2))+2/5*e*(a+b*log(c*x^n))/(d^2*x^3*sqrt(d+e*x^2))-8/5*e^2*(a+b*log(c*x^n))/(d^3*x*sqrt(d+e*x^2))-16/5*e^3*x*(a+b*log(c*x^n))/(d^4*sqrt(d+e*x^2))-1/25*b*n*sqrt(d+e*x^2)/(d^2*x^5)+14/75*b*e*n*sqrt(d+e*x^2)/(d^3*x^3)-148/75*b*e^2*n*sqrt(d+e*x^2)/(d^4*x)],
[x^7*(a+b*log(c*x^n))/(d+e*x^2)^(5/2),x,9,-1/9*b*n*(d+e*x^2)^(3/2)/e^4-16/3*b*d^(3/2)*n*arctanh(sqrt(d+e*x^2)/sqrt(d))/e^4+1/3*d^3*(a+b*log(c*x^n))/(e^4*(d+e*x^2)^(3/2))+1/3*(d+e*x^2)^(3/2)*(a+b*log(c*x^n))/e^4-1/3*b*d^2*n/(e^4*sqrt(d+e*x^2))-3*d^2*(a+b*log(c*x^n))/(e^4*sqrt(d+e*x^2))+8/3*b*d*n*sqrt(d+e*x^2)/e^4-3*d*(a+b*log(c*x^n))*sqrt(d+e*x^2)/e^4],
[x^5*(a+b*log(c*x^n))/(d+e*x^2)^(5/2),x,7,-1/3*d^2*(a+b*log(c*x^n))/(e^3*(d+e*x^2)^(3/2))+8/3*b*n*arctanh(sqrt(d+e*x^2)/sqrt(d))*sqrt(d)/e^3+1/3*b*d*n/(e^3*sqrt(d+e*x^2))+2*d*(a+b*log(c*x^n))/(e^3*sqrt(d+e*x^2))-b*n*sqrt(d+e*x^2)/e^3+(a+b*log(c*x^n))*sqrt(d+e*x^2)/e^3],
[x^3*(a+b*log(c*x^n))/(d+e*x^2)^(5/2),x,6,1/3*d*(a+b*log(c*x^n))/(e^2*(d+e*x^2)^(3/2))-2/3*b*n*arctanh(sqrt(d+e*x^2)/sqrt(d))/(e^2*sqrt(d))-1/3*b*n/(e^2*sqrt(d+e*x^2))+(-a-b*log(c*x^n))/(e^2*sqrt(d+e*x^2))],
[x*(a+b*log(c*x^n))/(d+e*x^2)^(5/2),x,5,-1/3*b*n*arctanh(sqrt(d+e*x^2)/sqrt(d))/(d^(3/2)*e)+1/3*(-a-b*log(c*x^n))/(e*(d+e*x^2)^(3/2))+1/3*b*n/(d*e*sqrt(d+e*x^2))],
[(a+b*log(c*x^n))/(x*(d+e*x^2)^(5/2)),x,15,4/3*b*n*arctanh(sqrt(d+e*x^2)/sqrt(d))/d^(5/2)+1/2*b*n*arctanh(sqrt(d+e*x^2)/sqrt(d))^2/d^(5/2)-b*n*arctanh(sqrt(d+e*x^2)/sqrt(d))*log(2*sqrt(d)/(sqrt(d)-sqrt(d+e*x^2)))/d^(5/2)-1/2*b*n*polylog(2,1-2*sqrt(d)/(sqrt(d)-sqrt(d+e*x^2)))/d^(5/2)+1/3*(a+b*log(c*x^n))*(1/(d*(d+e*x^2)^(3/2))-3*arctanh(sqrt(d+e*x^2)/sqrt(d))/d^(5/2)+3/(d^2*sqrt(d+e*x^2)))-1/3*b*n/(d^2*sqrt(d+e*x^2))],
[(a+b*log(c*x^n))/(x^3*(d+e*x^2)^(5/2)),x,14,-31/12*b*e*n*arctanh(sqrt(d+e*x^2)/sqrt(d))/d^(7/2)-5/4*b*e*n*arctanh(sqrt(d+e*x^2)/sqrt(d))^2/d^(7/2)-5/6*e*(a+b*log(c*x^n))/(d^2*(d+e*x^2)^(3/2))+1/2*(-a-b*log(c*x^n))/(d*x^2*(d+e*x^2)^(3/2))+5/2*e*arctanh(sqrt(d+e*x^2)/sqrt(d))*(a+b*log(c*x^n))/d^(7/2)+5/2*b*e*n*arctanh(sqrt(d+e*x^2)/sqrt(d))*log(2*sqrt(d)/(sqrt(d)-sqrt(d+e*x^2)))/d^(7/2)+5/4*b*e*n*polylog(2,1-2*sqrt(d)/(sqrt(d)-sqrt(d+e*x^2)))/d^(7/2)+1/3*b*e*n/(d^3*sqrt(d+e*x^2))-5/2*e*(a+b*log(c*x^n))/(d^3*sqrt(d+e*x^2))-1/4*b*n*sqrt(d+e*x^2)/(d^3*x^2)],
[x^6*(a+b*log(c*x^n))/(d+e*x^2)^(5/2),x,24,-1/3*x^5*(a+b*log(c*x^n))/(e*(d+e*x^2)^(3/2))+5/6*b*d*n*x/(e^3*sqrt(d+e*x^2))+1/2*b*n*x^3/(e^2*sqrt(d+e*x^2))-5/3*x^3*(a+b*log(c*x^n))/(e^2*sqrt(d+e*x^2))-3/4*b*n*x*sqrt(d+e*x^2)/e^3+5/2*x*(a+b*log(c*x^n))*sqrt(d+e*x^2)/e^3-31/12*b*d^(3/2)*n*arcsinh(x*sqrt(e)/sqrt(d))*sqrt(1+e*x^2/d)/(e^(7/2)*sqrt(d+e*x^2))-5/4*b*d^(3/2)*n*arcsinh(x*sqrt(e)/sqrt(d))^2*sqrt(1+e*x^2/d)/(e^(7/2)*sqrt(d+e*x^2))-5*b*d^(3/2)*n*arcsinh(x*sqrt(e)/sqrt(d))*arctanh(exp(2*arcsinh(x*sqrt(e)/sqrt(d))))*sqrt(1+e*x^2/d)/(e^(7/2)*sqrt(d+e*x^2))+5/2*b*d^(3/2)*n*arcsinh(x*sqrt(e)/sqrt(d))*log(1+exp(2*arcsinh(x*sqrt(e)/sqrt(d))))*sqrt(1+e*x^2/d)/(e^(7/2)*sqrt(d+e*x^2))-5/2*d^(3/2)*arcsinh(x*sqrt(e)/sqrt(d))*(a+b*log(c*x^n))*sqrt(1+e*x^2/d)/(e^(7/2)*sqrt(d+e*x^2))+5/4*b*d^(3/2)*n*polylog(2,exp(2*arcsinh(x*sqrt(e)/sqrt(d))))*sqrt(1+e*x^2/d)/(e^(7/2)*sqrt(d+e*x^2))],
[x^4*(a+b*log(c*x^n))/(d+e*x^2)^(5/2),x,13,-1/3*x^3*(a+b*log(c*x^n))/(e*(d+e*x^2)^(3/2))-1/3*b*n*x/(e^2*sqrt(d+e*x^2))-x*(a+b*log(c*x^n))/(e^2*sqrt(d+e*x^2))+4/3*b*n*arcsinh(x*sqrt(e)/sqrt(d))*sqrt(d)*sqrt(1+e*x^2/d)/(e^(5/2)*sqrt(d+e*x^2))+1/2*b*n*arcsinh(x*sqrt(e)/sqrt(d))^2*sqrt(d)*sqrt(1+e*x^2/d)/(e^(5/2)*sqrt(d+e*x^2))-b*n*arcsinh(x*sqrt(e)/sqrt(d))*log(1-exp(2*arcsinh(x*sqrt(e)/sqrt(d))))*sqrt(d)*sqrt(1+e*x^2/d)/(e^(5/2)*sqrt(d+e*x^2))+arcsinh(x*sqrt(e)/sqrt(d))*(a+b*log(c*x^n))*sqrt(d)*sqrt(1+e*x^2/d)/(e^(5/2)*sqrt(d+e*x^2))-1/2*b*n*polylog(2,exp(2*arcsinh(x*sqrt(e)/sqrt(d))))*sqrt(d)*sqrt(1+e*x^2/d)/(e^(5/2)*sqrt(d+e*x^2))],
[x^2*(a+b*log(c*x^n))/(d+e*x^2)^(5/2),x,4,-1/3*b*n*arctanh(x*sqrt(e)/sqrt(d+e*x^2))/(d*e^(3/2))+1/3*x^3*(a+b*log(c*x^n))/(d*(d+e*x^2)^(3/2))+1/3*b*n*x/(d*e*sqrt(d+e*x^2))],
[(a+b*log(c*x^n))/(d+e*x^2)^(5/2),x,5,1/3*x*(a+b*log(c*x^n))/(d*(d+e*x^2)^(3/2))-2/3*b*n*arctanh(x*sqrt(e)/sqrt(d+e*x^2))/(d^2*sqrt(e))-1/3*b*n*x/(d^2*sqrt(d+e*x^2))+2/3*x*(a+b*log(c*x^n))/(d^2*sqrt(d+e*x^2))],
[(a+b*log(c*x^n))/(x^2*(d+e*x^2)^(5/2)),x,6,(-a-b*log(c*x^n))/(d*x*(d+e*x^2)^(3/2))-4/3*e*x*(a+b*log(c*x^n))/(d^2*(d+e*x^2)^(3/2))+8/3*b*n*arctanh(x*sqrt(e)/sqrt(d+e*x^2))*sqrt(e)/d^3-b*n/(d^2*x*sqrt(d+e*x^2))-2/3*b*e*n*x/(d^3*sqrt(d+e*x^2))-8/3*e*x*(a+b*log(c*x^n))/(d^3*sqrt(d+e*x^2))],
[(a+b*log(c*x^n))/(x^4*(d+e*x^2)^(5/2)),x,7,-16/3*b*e^(3/2)*n*arctanh(x*sqrt(e)/sqrt(d+e*x^2))/d^4+1/3*(-a-b*log(c*x^n))/(d*x^3*(d+e*x^2)^(3/2))+2*e*(a+b*log(c*x^n))/(d^2*x*(d+e*x^2)^(3/2))+8/3*e^2*x*(a+b*log(c*x^n))/(d^3*(d+e*x^2)^(3/2))-1/3*b*e^2*n*x/(d^4*sqrt(d+e*x^2))+16/3*e^2*x*(a+b*log(c*x^n))/(d^4*sqrt(d+e*x^2))-1/9*b*n*sqrt(d+e*x^2)/(d^3*x^3)+23/9*b*e*n*sqrt(d+e*x^2)/(d^4*x)],
[x^3*(a+b*log(c*x^n))/(sqrt(d-e*x)*sqrt(d+e*x)),x,8,2/3*b*d^2*n*(d^2-e^2*x^2)/(e^4*sqrt(d-e*x)*sqrt(d+e*x))-1/9*b*n*(d^2-e^2*x^2)^2/(e^4*sqrt(d-e*x)*sqrt(d+e*x))-d^2*(d^2-e^2*x^2)*(a+b*log(c*x^n))/(e^4*sqrt(d-e*x)*sqrt(d+e*x))+1/3*(d^2-e^2*x^2)^2*(a+b*log(c*x^n))/(e^4*sqrt(d-e*x)*sqrt(d+e*x))-2/3*b*d^4*n*arctanh(sqrt(1-e^2*x^2/d^2))*sqrt(1-e^2*x^2/d^2)/(e^4*sqrt(d-e*x)*sqrt(d+e*x))],
[x*(a+b*log(c*x^n))/(sqrt(d-e*x)*sqrt(d+e*x)),x,6,b*n*(d^2-e^2*x^2)/(e^2*sqrt(d-e*x)*sqrt(d+e*x))-(d^2-e^2*x^2)*(a+b*log(c*x^n))/(e^2*sqrt(d-e*x)*sqrt(d+e*x))-b*d^2*n*arctanh(sqrt(1-e^2*x^2/d^2))*sqrt(1-e^2*x^2/d^2)/(e^2*sqrt(d-e*x)*sqrt(d+e*x))],
[(a+b*log(c*x^n))/(x*sqrt(d-e*x)*sqrt(d+e*x)),x,8,1/2*b*n*arctanh(sqrt(1-e^2*x^2/d^2))^2*sqrt(1-e^2*x^2/d^2)/(sqrt(d-e*x)*sqrt(d+e*x))-arctanh(sqrt(1-e^2*x^2/d^2))*(a+b*log(c*x^n))*sqrt(1-e^2*x^2/d^2)/(sqrt(d-e*x)*sqrt(d+e*x))-b*n*arctanh(sqrt(1-e^2*x^2/d^2))*log(2/(1-sqrt(1-e^2*x^2/d^2)))*sqrt(1-e^2*x^2/d^2)/(sqrt(d-e*x)*sqrt(d+e*x))-1/2*b*n*polylog(2,(-1-sqrt(1-e^2*x^2/d^2))/(1-sqrt(1-e^2*x^2/d^2)))*sqrt(1-e^2*x^2/d^2)/(sqrt(d-e*x)*sqrt(d+e*x))],
[(a+b*log(c*x^n))/(x^3*sqrt(d-e*x)*sqrt(d+e*x)),x,13,-1/4*b*n*(d^2-e^2*x^2)/(d^2*x^2*sqrt(d-e*x)*sqrt(d+e*x))-1/2*(d^2-e^2*x^2)*(a+b*log(c*x^n))/(d^2*x^2*sqrt(d-e*x)*sqrt(d+e*x))+1/4*b*e^2*n*arctanh(sqrt(1-e^2*x^2/d^2))*sqrt(1-e^2*x^2/d^2)/(d^2*sqrt(d-e*x)*sqrt(d+e*x))+1/4*b*e^2*n*arctanh(sqrt(1-e^2*x^2/d^2))^2*sqrt(1-e^2*x^2/d^2)/(d^2*sqrt(d-e*x)*sqrt(d+e*x))-1/2*e^2*arctanh(sqrt(1-e^2*x^2/d^2))*(a+b*log(c*x^n))*sqrt(1-e^2*x^2/d^2)/(d^2*sqrt(d-e*x)*sqrt(d+e*x))-1/2*b*e^2*n*arctanh(sqrt(1-e^2*x^2/d^2))*log(2/(1-sqrt(1-e^2*x^2/d^2)))*sqrt(1-e^2*x^2/d^2)/(d^2*sqrt(d-e*x)*sqrt(d+e*x))-1/4*b*e^2*n*polylog(2,(-1-sqrt(1-e^2*x^2/d^2))/(1-sqrt(1-e^2*x^2/d^2)))*sqrt(1-e^2*x^2/d^2)/(d^2*sqrt(d-e*x)*sqrt(d+e*x))],
[x^2*(a+b*log(c*x^n))/(sqrt(d-e*x)*sqrt(d+e*x)),x,12,1/4*b*n*x*(d^2-e^2*x^2)/(e^2*sqrt(d-e*x)*sqrt(d+e*x))-1/2*x*(d^2-e^2*x^2)*(a+b*log(c*x^n))/(e^2*sqrt(d-e*x)*sqrt(d+e*x))+1/4*b*d^3*n*arcsin(e*x/d)*sqrt(1-e^2*x^2/d^2)/(e^3*sqrt(d-e*x)*sqrt(d+e*x))+1/4*I*b*d^3*n*arcsin(e*x/d)^2*sqrt(1-e^2*x^2/d^2)/(e^3*sqrt(d-e*x)*sqrt(d+e*x))-1/2*b*d^3*n*arcsin(e*x/d)*log(1-exp(2*I*arcsin(e*x/d)))*sqrt(1-e^2*x^2/d^2)/(e^3*sqrt(d-e*x)*sqrt(d+e*x))+1/2*d^3*arcsin(e*x/d)*(a+b*log(c*x^n))*sqrt(1-e^2*x^2/d^2)/(e^3*sqrt(d-e*x)*sqrt(d+e*x))+1/4*I*b*d^3*n*polylog(2,exp(2*I*arcsin(e*x/d)))*sqrt(1-e^2*x^2/d^2)/(e^3*sqrt(d-e*x)*sqrt(d+e*x))],
[(a+b*log(c*x^n))/(sqrt(d-e*x)*sqrt(d+e*x)),x,7,1/2*I*b*d*n*arcsin(e*x/d)^2*sqrt(1-e^2*x^2/d^2)/(e*sqrt(d-e*x)*sqrt(d+e*x))-b*d*n*arcsin(e*x/d)*log(1-exp(2*I*arcsin(e*x/d)))*sqrt(1-e^2*x^2/d^2)/(e*sqrt(d-e*x)*sqrt(d+e*x))+d*arcsin(e*x/d)*(a+b*log(c*x^n))*sqrt(1-e^2*x^2/d^2)/(e*sqrt(d-e*x)*sqrt(d+e*x))+1/2*I*b*d*n*polylog(2,exp(2*I*arcsin(e*x/d)))*sqrt(1-e^2*x^2/d^2)/(e*sqrt(d-e*x)*sqrt(d+e*x))],
[(a+b*log(c*x^n))/(x^2*sqrt(d-e*x)*sqrt(d+e*x)),x,4,-b*n*(d^2-e^2*x^2)/(d^2*x*sqrt(d-e*x)*sqrt(d+e*x))-(d^2-e^2*x^2)*(a+b*log(c*x^n))/(d^2*x*sqrt(d-e*x)*sqrt(d+e*x))-b*e*n*arcsin(e*x/d)*sqrt(1-e^2*x^2/d^2)/(d*sqrt(d-e*x)*sqrt(d+e*x))],
[(a+b*log(c*x^n))/(x^4*sqrt(d-e*x)*sqrt(d+e*x)),x,6,-2/3*b*e^2*n*(d^2-e^2*x^2)/(d^4*x*sqrt(d-e*x)*sqrt(d+e*x))-1/9*b*n*(d^2-e^2*x^2)^2/(d^4*x^3*sqrt(d-e*x)*sqrt(d+e*x))-1/3*(d^2-e^2*x^2)*(a+b*log(c*x^n))/(d^2*x^3*sqrt(d-e*x)*sqrt(d+e*x))-2/3*e^2*(d^2-e^2*x^2)*(a+b*log(c*x^n))/(d^4*x*sqrt(d-e*x)*sqrt(d+e*x))-2/3*b*e^3*n*arcsin(e*x/d)*sqrt(1-e^2*x^2/d^2)/(d^3*sqrt(d-e*x)*sqrt(d+e*x))],
[x*log(x)/sqrt(-1+x^2),x,5,arctan(sqrt(-1+x^2))-sqrt(-1+x^2)+log(x)*sqrt(-1+x^2)],

# Integrands of the form (f x)^m (d+e x^2)^q (a+b Log[c x^n]) when m symbolic
[(f*x)^m*(d+e*x^2)^3*(a+b*log(c*x^n)),x,3,-b*d^3*n*(f*x)^(1+m)/(f*(1+m)^2)-3*b*d^2*e*n*(f*x)^(3+m)/(f^3*(3+m)^2)-3*b*d*e^2*n*(f*x)^(5+m)/(f^5*(5+m)^2)-b*e^3*n*(f*x)^(7+m)/(f^7*(7+m)^2)+d^3*(f*x)^(1+m)*(a+b*log(c*x^n))/(f*(1+m))+3*d^2*e*(f*x)^(3+m)*(a+b*log(c*x^n))/(f^3*(3+m))+3*d*e^2*(f*x)^(5+m)*(a+b*log(c*x^n))/(f^5*(5+m))+e^3*(f*x)^(7+m)*(a+b*log(c*x^n))/(f^7*(7+m))],
[(f*x)^m*(d+e*x^2)^2*(a+b*log(c*x^n)),x,4,-b*d^2*n*(f*x)^(1+m)/(f*(1+m)^2)-2*b*d*e*n*(f*x)^(3+m)/(f^3*(3+m)^2)-b*e^2*n*(f*x)^(5+m)/(f^5*(5+m)^2)+d^2*(f*x)^(1+m)*(a+b*log(c*x^n))/(f*(1+m))+2*d*e*(f*x)^(3+m)*(a+b*log(c*x^n))/(f^3*(3+m))+e^2*(f*x)^(5+m)*(a+b*log(c*x^n))/(f^5*(5+m))],
[(f*x)^m*(d+e*x^2)*(a+b*log(c*x^n)),x,4,-b*d*n*(f*x)^(1+m)/(f*(1+m)^2)-b*e*n*(f*x)^(3+m)/(f^3*(3+m)^2)+d*(f*x)^(1+m)*(a+b*log(c*x^n))/(f*(1+m))+e*(f*x)^(3+m)*(a+b*log(c*x^n))/(f^3*(3+m))],
[(f*x)^m*(a+b*log(c*x^n)),x,1,-b*n*(f*x)^(1+m)/(f*(1+m)^2)+(f*x)^(1+m)*(a+b*log(c*x^n))/(f*(1+m))],
[(f*x)^m*(a+b*log(c*x^n))/(d+e*x^2),x,0,Unintegrable((f*x)^m*(a+b*log(c*x^n))/(d+e*x^2),x)],
[(f*x)^m*(a+b*log(c*x^n))/(d+e*x^2)^2,x,0,Unintegrable((f*x)^m*(a+b*log(c*x^n))/(d+e*x^2)^2,x)],

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

# Integrands of the form (d+e x^3)^q (a+b Log[c x^n])^p
[(a+b*log(c*x^n))^3/(d+e*x^3)^2,x,26,1/9*x*(a+b*log(c*x^n))^3/(d^(5/3)*(d^(1/3)+e^(1/3)*x))-(-1)^(1/3)*x*(a+b*log(c*x^n))^3/((1+(-1)^(1/3))^4*d^(5/3)*((-1)^(2/3)*d^(1/3)+e^(1/3)*x))+1/9*x*(a+b*log(c*x^n))^3/(d^(5/3)*(d^(1/3)+(-1)^(2/3)*e^(1/3)*x))-1/3*b*n*(a+b*log(c*x^n))^2*log(1+e^(1/3)*x/d^(1/3))/(d^(5/3)*e^(1/3))+2/9*(a+b*log(c*x^n))^3*log(1+e^(1/3)*x/d^(1/3))/(d^(5/3)*e^(1/3))+3*(-1)^(1/3)*b*n*(a+b*log(c*x^n))^2*log(1-(-1)^(1/3)*e^(1/3)*x/d^(1/3))/((1+(-1)^(1/3))^4*d^(5/3)*e^(1/3))+1/3*(-1)^(1/3)*b*n*(a+b*log(c*x^n))^2*log(1+(-1)^(2/3)*e^(1/3)*x/d^(1/3))/(d^(5/3)*e^(1/3))-2/3*b^2*n^2*(a+b*log(c*x^n))*polylog(2,-e^(1/3)*x/d^(1/3))/(d^(5/3)*e^(1/3))+2/3*b*n*(a+b*log(c*x^n))^2*polylog(2,-e^(1/3)*x/d^(1/3))/(d^(5/3)*e^(1/3))+6*(-1)^(1/3)*b^2*n^2*(a+b*log(c*x^n))*polylog(2,(-1)^(1/3)*e^(1/3)*x/d^(1/3))/((1+(-1)^(1/3))^4*d^(5/3)*e^(1/3))+2/3*(-1)^(1/3)*b^2*n^2*(a+b*log(c*x^n))*polylog(2,-(-1)^(2/3)*e^(1/3)*x/d^(1/3))/(d^(5/3)*e^(1/3))+2/3*b^3*n^3*polylog(3,-e^(1/3)*x/d^(1/3))/(d^(5/3)*e^(1/3))-4/3*b^2*n^2*(a+b*log(c*x^n))*polylog(3,-e^(1/3)*x/d^(1/3))/(d^(5/3)*e^(1/3))-6*(-1)^(1/3)*b^3*n^3*polylog(3,(-1)^(1/3)*e^(1/3)*x/d^(1/3))/((1+(-1)^(1/3))^4*d^(5/3)*e^(1/3))-2/3*(-1)^(1/3)*b^3*n^3*polylog(3,-(-1)^(2/3)*e^(1/3)*x/d^(1/3))/(d^(5/3)*e^(1/3))+4/3*b^3*n^3*polylog(4,-e^(1/3)*x/d^(1/3))/(d^(5/3)*e^(1/3))-4/9*(a+b*log(c*x^n))^3*log(1-1/2*e^(1/3)*x*(1-I*sqrt(3))/d^(1/3))/(d^(5/3)*e^(1/3)*(1-I*sqrt(3)))-4/3*b*n*(a+b*log(c*x^n))^2*polylog(2,1/2*e^(1/3)*x*(1-I*sqrt(3))/d^(1/3))/(d^(5/3)*e^(1/3)*(1-I*sqrt(3)))+8/3*b^2*n^2*(a+b*log(c*x^n))*polylog(3,1/2*e^(1/3)*x*(1-I*sqrt(3))/d^(1/3))/(d^(5/3)*e^(1/3)*(1-I*sqrt(3)))-8/3*b^3*n^3*polylog(4,1/2*e^(1/3)*x*(1-I*sqrt(3))/d^(1/3))/(d^(5/3)*e^(1/3)*(1-I*sqrt(3)))-4/9*(a+b*log(c*x^n))^3*log(1-1/2*e^(1/3)*x*(1+I*sqrt(3))/d^(1/3))/(d^(5/3)*e^(1/3)*(1+I*sqrt(3)))-4/3*b*n*(a+b*log(c*x^n))^2*polylog(2,1/2*e^(1/3)*x*(1+I*sqrt(3))/d^(1/3))/(d^(5/3)*e^(1/3)*(1+I*sqrt(3)))+8/3*b^2*n^2*(a+b*log(c*x^n))*polylog(3,1/2*e^(1/3)*x*(1+I*sqrt(3))/d^(1/3))/(d^(5/3)*e^(1/3)*(1+I*sqrt(3)))-8/3*b^3*n^3*polylog(4,1/2*e^(1/3)*x*(1+I*sqrt(3))/d^(1/3))/(d^(5/3)*e^(1/3)*(1+I*sqrt(3)))],
[(a+b*log(c*x^n))^2/(d+e*x^3)^2,x,20,1/9*x*(a+b*log(c*x^n))^2/(d^(5/3)*(d^(1/3)+e^(1/3)*x))-(-1)^(1/3)*x*(a+b*log(c*x^n))^2/((1+(-1)^(1/3))^4*d^(5/3)*((-1)^(2/3)*d^(1/3)+e^(1/3)*x))+1/9*x*(a+b*log(c*x^n))^2/(d^(5/3)*(d^(1/3)+(-1)^(2/3)*e^(1/3)*x))-2/9*b*n*(a+b*log(c*x^n))*log(1+e^(1/3)*x/d^(1/3))/(d^(5/3)*e^(1/3))+2/9*(a+b*log(c*x^n))^2*log(1+e^(1/3)*x/d^(1/3))/(d^(5/3)*e^(1/3))+2*(-1)^(1/3)*b*n*(a+b*log(c*x^n))*log(1-(-1)^(1/3)*e^(1/3)*x/d^(1/3))/((1+(-1)^(1/3))^4*d^(5/3)*e^(1/3))+2/9*(-1)^(1/3)*b*n*(a+b*log(c*x^n))*log(1+(-1)^(2/3)*e^(1/3)*x/d^(1/3))/(d^(5/3)*e^(1/3))-2/9*b^2*n^2*polylog(2,-e^(1/3)*x/d^(1/3))/(d^(5/3)*e^(1/3))+4/9*b*n*(a+b*log(c*x^n))*polylog(2,-e^(1/3)*x/d^(1/3))/(d^(5/3)*e^(1/3))+2*(-1)^(1/3)*b^2*n^2*polylog(2,(-1)^(1/3)*e^(1/3)*x/d^(1/3))/((1+(-1)^(1/3))^4*d^(5/3)*e^(1/3))+2/9*(-1)^(1/3)*b^2*n^2*polylog(2,-(-1)^(2/3)*e^(1/3)*x/d^(1/3))/(d^(5/3)*e^(1/3))-4/9*b^2*n^2*polylog(3,-e^(1/3)*x/d^(1/3))/(d^(5/3)*e^(1/3))-4/9*(a+b*log(c*x^n))^2*log(1-1/2*e^(1/3)*x*(1-I*sqrt(3))/d^(1/3))/(d^(5/3)*e^(1/3)*(1-I*sqrt(3)))-8/9*b*n*(a+b*log(c*x^n))*polylog(2,1/2*e^(1/3)*x*(1-I*sqrt(3))/d^(1/3))/(d^(5/3)*e^(1/3)*(1-I*sqrt(3)))+8/9*b^2*n^2*polylog(3,1/2*e^(1/3)*x*(1-I*sqrt(3))/d^(1/3))/(d^(5/3)*e^(1/3)*(1-I*sqrt(3)))-4/9*(a+b*log(c*x^n))^2*log(1-1/2*e^(1/3)*x*(1+I*sqrt(3))/d^(1/3))/(d^(5/3)*e^(1/3)*(1+I*sqrt(3)))-8/9*b*n*(a+b*log(c*x^n))*polylog(2,1/2*e^(1/3)*x*(1+I*sqrt(3))/d^(1/3))/(d^(5/3)*e^(1/3)*(1+I*sqrt(3)))+8/9*b^2*n^2*polylog(3,1/2*e^(1/3)*x*(1+I*sqrt(3))/d^(1/3))/(d^(5/3)*e^(1/3)*(1+I*sqrt(3)))],
[(a+b*log(c*x^n))/(d+e*x^3)^2,x,14,1/9*x*(a+b*log(c*x^n))/(d^(5/3)*(d^(1/3)+e^(1/3)*x))-(-1)^(1/3)*x*(a+b*log(c*x^n))/((1+(-1)^(1/3))^4*d^(5/3)*((-1)^(2/3)*d^(1/3)+e^(1/3)*x))+1/9*x*(a+b*log(c*x^n))/(d^(5/3)*(d^(1/3)+(-1)^(2/3)*e^(1/3)*x))+(-1)^(1/3)*b*n*log(-(-1)^(2/3)*d^(1/3)-e^(1/3)*x)/((1+(-1)^(1/3))^4*d^(5/3)*e^(1/3))-1/9*b*n*log(d^(1/3)+e^(1/3)*x)/(d^(5/3)*e^(1/3))+1/9*(-1)^(1/3)*b*n*log(d^(1/3)+(-1)^(2/3)*e^(1/3)*x)/(d^(5/3)*e^(1/3))+2/9*(a+b*log(c*x^n))*log(1+e^(1/3)*x/d^(1/3))/(d^(5/3)*e^(1/3))+2/9*b*n*polylog(2,-e^(1/3)*x/d^(1/3))/(d^(5/3)*e^(1/3))-4/9*(a+b*log(c*x^n))*log(1-1/2*e^(1/3)*x*(1-I*sqrt(3))/d^(1/3))/(d^(5/3)*e^(1/3)*(1-I*sqrt(3)))-4/9*b*n*polylog(2,1/2*e^(1/3)*x*(1-I*sqrt(3))/d^(1/3))/(d^(5/3)*e^(1/3)*(1-I*sqrt(3)))-4/9*(a+b*log(c*x^n))*log(1-1/2*e^(1/3)*x*(1+I*sqrt(3))/d^(1/3))/(d^(5/3)*e^(1/3)*(1+I*sqrt(3)))-4/9*b*n*polylog(2,1/2*e^(1/3)*x*(1+I*sqrt(3))/d^(1/3))/(d^(5/3)*e^(1/3)*(1+I*sqrt(3)))],
[1/((d+e*x^3)^2*(a+b*log(c*x^n))),x,0,Unintegrable(1/((d+e*x^3)^2*(a+b*log(c*x^n))),x)],
[1/((d+e*x^3)^2*(a+b*log(c*x^n))^2),x,0,Unintegrable(1/((d+e*x^3)^2*(a+b*log(c*x^n))^2),x)],

# Integrands of the form (f x)^m (d+e x^r)^q (a+b Log[c x^n])^p

# Integrands of the form x^m (d+e / x)^q (a+b Log[c x^n])

# q>0

# q<0
[x^3*(a+b*log(c*x^n))/(d+e/x),x,9,-a*e^3*x/d^4+b*e^3*n*x/d^4-1/4*b*e^2*n*x^2/d^3+1/9*b*e*n*x^3/d^2-1/16*b*n*x^4/d-b*e^3*x*log(c*x^n)/d^4+1/2*e^2*x^2*(a+b*log(c*x^n))/d^3-1/3*e*x^3*(a+b*log(c*x^n))/d^2+1/4*x^4*(a+b*log(c*x^n))/d+e^4*(a+b*log(c*x^n))*log(1+d*x/e)/d^5+b*e^4*n*polylog(2,-d*x/e)/d^5],
[x^2*(a+b*log(c*x^n))/(d+e/x),x,8,a*e^2*x/d^3-b*e^2*n*x/d^3+1/4*b*e*n*x^2/d^2-1/9*b*n*x^3/d+b*e^2*x*log(c*x^n)/d^3-1/2*e*x^2*(a+b*log(c*x^n))/d^2+1/3*x^3*(a+b*log(c*x^n))/d-e^3*(a+b*log(c*x^n))*log(1+d*x/e)/d^4-b*e^3*n*polylog(2,-d*x/e)/d^4],
[x*(a+b*log(c*x^n))/(d+e/x),x,7,-a*e*x/d^2+b*e*n*x/d^2-1/4*b*n*x^2/d-b*e*x*log(c*x^n)/d^2+1/2*x^2*(a+b*log(c*x^n))/d+e^2*(a+b*log(c*x^n))*log(1+d*x/e)/d^3+b*e^2*n*polylog(2,-d*x/e)/d^3],
[(a+b*log(c*x^n))/(d+e/x),x,6,a*x/d-b*n*x/d+b*x*log(c*x^n)/d-e*(a+b*log(c*x^n))*log(1+d*x/e)/d^2-b*e*n*polylog(2,-d*x/e)/d^2],
[(a+b*log(c*x^n))/((d+e/x)*x),x,3,(a+b*log(c*x^n))*log(1+d*x/e)/d+b*n*polylog(2,-d*x/e)/d],
[(a+b*log(c*x^n))/((d+e/x)*x^2),x,2,-log(1+e/(d*x))*(a+b*log(c*x^n))/e+b*n*polylog(2,-e/(d*x))/e],
[(a+b*log(c*x^n))/((d+e/x)*x^3),x,6,-b*n/(e*x)+(-a-b*log(c*x^n))/(e*x)-1/2*d*(a+b*log(c*x^n))^2/(b*e^2*n)+d*(a+b*log(c*x^n))*log(1+d*x/e)/e^2+b*d*n*polylog(2,-d*x/e)/e^2],
[(a+b*log(c*x^n))/((d+e/x)*x^4),x,7,-1/4*b*n/(e*x^2)+b*d*n/(e^2*x)+1/2*(-a-b*log(c*x^n))/(e*x^2)+d*(a+b*log(c*x^n))/(e^2*x)+1/2*d^2*(a+b*log(c*x^n))^2/(b*e^3*n)-d^2*(a+b*log(c*x^n))*log(1+d*x/e)/e^3-b*d^2*n*polylog(2,-d*x/e)/e^3],
[x^3*(a+b*log(c*x))/(d+e/x),x,9,-a*e^3*x/d^4+b*e^3*x/d^4-1/4*b*e^2*x^2/d^3+1/9*b*e*x^3/d^2-1/16*b*x^4/d-b*e^3*x*log(c*x)/d^4+1/2*e^2*x^2*(a+b*log(c*x))/d^3-1/3*e*x^3*(a+b*log(c*x))/d^2+1/4*x^4*(a+b*log(c*x))/d+e^4*(a+b*log(c*x))*log(1+d*x/e)/d^5+b*e^4*polylog(2,-d*x/e)/d^5],
[x^2*(a+b*log(c*x))/(d+e/x),x,8,a*e^2*x/d^3-b*e^2*x/d^3+1/4*b*e*x^2/d^2-1/9*b*x^3/d+b*e^2*x*log(c*x)/d^3-1/2*e*x^2*(a+b*log(c*x))/d^2+1/3*x^3*(a+b*log(c*x))/d-e^3*(a+b*log(c*x))*log(1+d*x/e)/d^4-b*e^3*polylog(2,-d*x/e)/d^4],
[x*(a+b*log(c*x))/(d+e/x),x,7,-a*e*x/d^2+b*e*x/d^2-1/4*b*x^2/d-b*e*x*log(c*x)/d^2+1/2*x^2*(a+b*log(c*x))/d+e^2*(a+b*log(c*x))*log(1+d*x/e)/d^3+b*e^2*polylog(2,-d*x/e)/d^3],
[(a+b*log(c*x))/(d+e/x),x,6,a*x/d-b*x/d+b*x*log(c*x)/d-e*(a+b*log(c*x))*log(1+d*x/e)/d^2-b*e*polylog(2,-d*x/e)/d^2],
[(a+b*log(c*x))/((d+e/x)*x),x,3,(a+b*log(c*x))*log(1+d*x/e)/d+b*polylog(2,-d*x/e)/d],
[(a+b*log(c*x))/((d+e/x)*x^2),x,2,-log(1+e/(d*x))*(a+b*log(c*x))/e+b*polylog(2,-e/(d*x))/e],
[(a+b*log(c*x))/((d+e/x)*x^3),x,6,-b/(e*x)+(-a-b*log(c*x))/(e*x)-1/2*d*(a+b*log(c*x))^2/(b*e^2)+d*(a+b*log(c*x))*log(1+d*x/e)/e^2+b*d*polylog(2,-d*x/e)/e^2],
[(a+b*log(c*x))/((d+e/x)*x^4),x,7,-1/4*b/(e*x^2)+b*d/(e^2*x)+1/2*(-a-b*log(c*x))/(e*x^2)+d*(a+b*log(c*x))/(e^2*x)+1/2*d^2*(a+b*log(c*x))^2/(b*e^3)-d^2*(a+b*log(c*x))*log(1+d*x/e)/e^3-b*d^2*polylog(2,-d*x/e)/e^3],

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

# Integrands of the form (f x)^m (d+e x^r)^q (a+b Log[c x^n])^p when m=r-1

# p>0
[(f*x)^(-1+m)*(d+e*x^m)^3*(a+b*log(c*x^n)),x,5,-b*d^3*n*x*(f*x)^(-1+m)/m^2-3/4*b*d^2*e*n*x^(1+m)*(f*x)^(-1+m)/m^2-1/3*b*d*e^2*n*x^(1+2*m)*(f*x)^(-1+m)/m^2-1/16*b*e^3*n*x^(1+3*m)*(f*x)^(-1+m)/m^2-1/4*b*d^4*n*x^(1-m)*(f*x)^(-1+m)*log(x)/(e*m)+1/4*x^(1-m)*(f*x)^(-1+m)*(d+e*x^m)^4*(a+b*log(c*x^n))/(e*m)],
[(f*x)^(-1+m)*(d+e*x^m)^2*(a+b*log(c*x^n)),x,5,-b*d^2*n*x*(f*x)^(-1+m)/m^2-1/2*b*d*e*n*x^(1+m)*(f*x)^(-1+m)/m^2-1/9*b*e^2*n*x^(1+2*m)*(f*x)^(-1+m)/m^2-1/3*b*d^3*n*x^(1-m)*(f*x)^(-1+m)*log(x)/(e*m)+1/3*x^(1-m)*(f*x)^(-1+m)*(d+e*x^m)^3*(a+b*log(c*x^n))/(e*m)],
[(f*x)^(-1+m)*(d+e*x^m)*(a+b*log(c*x^n)),x,5,-b*d*n*(f*x)^m/(f*m^2)-1/4*b*e*n*x^m*(f*x)^m/(f*m^2)+d*(f*x)^m*(a+b*log(c*x^n))/(f*m)+1/2*e*x^m*(f*x)^m*(a+b*log(c*x^n))/(f*m),-b*d*n*x*(f*x)^(-1+m)/m^2-1/4*b*e*n*x^(1+m)*(f*x)^(-1+m)/m^2-1/2*b*d^2*n*x^(1-m)*(f*x)^(-1+m)*log(x)/(e*m)+1/2*x^(1-m)*(f*x)^(-1+m)*(d+e*x^m)^2*(a+b*log(c*x^n))/(e*m)],
[(f*x)^(-1+m)*(a+b*log(c*x^n)),x,1,-b*n*(f*x)^m/(f*m^2)+(f*x)^m*(a+b*log(c*x^n))/(f*m)],
[(f*x)^(-1+m)*(a+b*log(c*x^n))/(d+e*x^m),x,3,x^(1-m)*(f*x)^(-1+m)*(a+b*log(c*x^n))*log(1+e*x^m/d)/(e*m)+b*n*x^(1-m)*(f*x)^(-1+m)*polylog(2,-e*x^m/d)/(e*m^2)],
[(f*x)^(-1+m)*(a+b*log(c*x^n))/(d+e*x^m)^2,x,3,(f*x)^m*(a+b*log(c*x^n))/(d*f*m*(d+e*x^m))-b*n*(f*x)^m*log(d+e*x^m)/(d*e*f*m^2*x^m)],
[(f*x)^(-1+m)*(a+b*log(c*x^n))/(d+e*x^m)^3,x,5,1/2*b*n*x^(1-m)*(f*x)^(-1+m)/(d*e*m^2*(d+e*x^m))+1/2*b*n*x^(1-m)*(f*x)^(-1+m)*log(x)/(d^2*e*m)-1/2*x^(1-m)*(f*x)^(-1+m)*(a+b*log(c*x^n))/(e*m*(d+e*x^m)^2)-1/2*b*n*x^(1-m)*(f*x)^(-1+m)*log(d+e*x^m)/(d^2*e*m^2)],
[(f*x)^(-1+m)*(a+b*log(c*x^n))/(d+e*x^m)^4,x,5,1/6*b*n*x^(1-m)*(f*x)^(-1+m)/(d*e*m^2*(d+e*x^m)^2)+1/3*b*n*x^(1-m)*(f*x)^(-1+m)/(d^2*e*m^2*(d+e*x^m))+1/3*b*n*x^(1-m)*(f*x)^(-1+m)*log(x)/(d^3*e*m)-1/3*x^(1-m)*(f*x)^(-1+m)*(a+b*log(c*x^n))/(e*m*(d+e*x^m)^3)-1/3*b*n*x^(1-m)*(f*x)^(-1+m)*log(d+e*x^m)/(d^3*e*m^2)],
[(f*x)^(-1+m)*(d+e*x^m)^3*(a+b*log(c*x^n))^2,x,7,2*b^2*d^3*n^2*x*(f*x)^(-1+m)/m^3+3/4*b^2*d^2*e*n^2*x^(1+m)*(f*x)^(-1+m)/m^3+2/9*b^2*d*e^2*n^2*x^(1+2*m)*(f*x)^(-1+m)/m^3+1/32*b^2*e^3*n^2*x^(1+3*m)*(f*x)^(-1+m)/m^3+1/4*b^2*d^4*n^2*x^(1-m)*(f*x)^(-1+m)*log(x)^2/(e*m)-2*b*d^3*n*x*(f*x)^(-1+m)*(a+b*log(c*x^n))/m^2-3/2*b*d^2*e*n*x^(1+m)*(f*x)^(-1+m)*(a+b*log(c*x^n))/m^2-2/3*b*d*e^2*n*x^(1+2*m)*(f*x)^(-1+m)*(a+b*log(c*x^n))/m^2-1/8*b*e^3*n*x^(1+3*m)*(f*x)^(-1+m)*(a+b*log(c*x^n))/m^2-1/2*b*d^4*n*x^(1-m)*(f*x)^(-1+m)*log(x)*(a+b*log(c*x^n))/(e*m)+1/4*x^(1-m)*(f*x)^(-1+m)*(d+e*x^m)^4*(a+b*log(c*x^n))^2/(e*m)],
[(f*x)^(-1+m)*(d+e*x^m)^2*(a+b*log(c*x^n))^2,x,7,2*b^2*d^2*n^2*x*(f*x)^(-1+m)/m^3+1/2*b^2*d*e*n^2*x^(1+m)*(f*x)^(-1+m)/m^3+2/27*b^2*e^2*n^2*x^(1+2*m)*(f*x)^(-1+m)/m^3+1/3*b^2*d^3*n^2*x^(1-m)*(f*x)^(-1+m)*log(x)^2/(e*m)-2*b*d^2*n*x*(f*x)^(-1+m)*(a+b*log(c*x^n))/m^2-b*d*e*n*x^(1+m)*(f*x)^(-1+m)*(a+b*log(c*x^n))/m^2-2/9*b*e^2*n*x^(1+2*m)*(f*x)^(-1+m)*(a+b*log(c*x^n))/m^2-2/3*b*d^3*n*x^(1-m)*(f*x)^(-1+m)*log(x)*(a+b*log(c*x^n))/(e*m)+1/3*x^(1-m)*(f*x)^(-1+m)*(d+e*x^m)^3*(a+b*log(c*x^n))^2/(e*m)],
[(f*x)^(-1+m)*(d+e*x^m)*(a+b*log(c*x^n))^2,x,7,2*b^2*d*n^2*x*(f*x)^(-1+m)/m^3+1/4*b^2*e*n^2*x^(1+m)*(f*x)^(-1+m)/m^3+1/2*b^2*d^2*n^2*x^(1-m)*(f*x)^(-1+m)*log(x)^2/(e*m)-2*b*d*n*x*(f*x)^(-1+m)*(a+b*log(c*x^n))/m^2-1/2*b*e*n*x^(1+m)*(f*x)^(-1+m)*(a+b*log(c*x^n))/m^2-b*d^2*n*x^(1-m)*(f*x)^(-1+m)*log(x)*(a+b*log(c*x^n))/(e*m)+1/2*x^(1-m)*(f*x)^(-1+m)*(d+e*x^m)^2*(a+b*log(c*x^n))^2/(e*m)],
[(f*x)^(-1+m)*(a+b*log(c*x^n))^2,x,2,2*b^2*n^2*(f*x)^m/(f*m^3)-2*b*n*(f*x)^m*(a+b*log(c*x^n))/(f*m^2)+(f*x)^m*(a+b*log(c*x^n))^2/(f*m)],
[(f*x)^(-1+m)*(a+b*log(c*x^n))^2/(d+e*x^m),x,4,x^(1-m)*(f*x)^(-1+m)*(a+b*log(c*x^n))^2*log(1+e*x^m/d)/(e*m)+2*b*n*x^(1-m)*(f*x)^(-1+m)*(a+b*log(c*x^n))*polylog(2,-e*x^m/d)/(e*m^2)-2*b^2*n^2*x^(1-m)*(f*x)^(-1+m)*polylog(3,-e*x^m/d)/(e*m^3)],
[(f*x)^(-1+m)*(a+b*log(c*x^n))^2/(d+e*x^m)^2,x,4,-x^(1-m)*(f*x)^(-1+m)*(a+b*log(c*x^n))^2/(e*m*(d+e*x^m))-2*b*n*x^(1-m)*(f*x)^(-1+m)*(a+b*log(c*x^n))*log(1+d/(e*x^m))/(d*e*m^2)+2*b^2*n^2*x^(1-m)*(f*x)^(-1+m)*polylog(2,-d/(e*x^m))/(d*e*m^3)],
[(f*x)^(-1+m)*(a+b*log(c*x^n))^2/(d+e*x^m)^3,x,7,-b*n*x*(f*x)^(-1+m)*(a+b*log(c*x^n))/(d^2*m^2*(d+e*x^m))-1/2*x^(1-m)*(f*x)^(-1+m)*(a+b*log(c*x^n))^2/(e*m*(d+e*x^m)^2)-b*n*x^(1-m)*(f*x)^(-1+m)*(a+b*log(c*x^n))*log(1+d/(e*x^m))/(d^2*e*m^2)+b^2*n^2*x^(1-m)*(f*x)^(-1+m)*log(d+e*x^m)/(d^2*e*m^3)+b^2*n^2*x^(1-m)*(f*x)^(-1+m)*polylog(2,-d/(e*x^m))/(d^2*e*m^3)],
[(f*x)^(-1+m)*(a+b*log(c*x^n))^2/(d+e*x^m)^4,x,12,-1/3*b^2*n^2*x^(1-m)*(f*x)^(-1+m)/(d^2*e*m^3*(d+e*x^m))-1/3*b^2*n^2*x^(1-m)*(f*x)^(-1+m)*log(x)/(d^3*e*m^2)+1/3*b*n*x^(1-m)*(f*x)^(-1+m)*(a+b*log(c*x^n))/(d*e*m^2*(d+e*x^m)^2)-2/3*b*n*x*(f*x)^(-1+m)*(a+b*log(c*x^n))/(d^3*m^2*(d+e*x^m))-1/3*x^(1-m)*(f*x)^(-1+m)*(a+b*log(c*x^n))^2/(e*m*(d+e*x^m)^3)-2/3*b*n*x^(1-m)*(f*x)^(-1+m)*(a+b*log(c*x^n))*log(1+d/(e*x^m))/(d^3*e*m^2)+b^2*n^2*x^(1-m)*(f*x)^(-1+m)*log(d+e*x^m)/(d^3*e*m^3)+2/3*b^2*n^2*x^(1-m)*(f*x)^(-1+m)*polylog(2,-d/(e*x^m))/(d^3*e*m^3)],

# p<0

# Integrands of the form x^m (d+e x^r)^q (a+b Log[c x^n])

# q>0
[x^5*(d+e*x^r)*(a+b*log(c*x^n)),x,4,-1/36*b*d*n*x^6-b*e*n*x^(6+r)/(6+r)^2+1/6*(d*x^6+6*e*x^(6+r)/(6+r))*(a+b*log(c*x^n))],
[x^3*(d+e*x^r)*(a+b*log(c*x^n)),x,4,-1/16*b*d*n*x^4-b*e*n*x^(4+r)/(4+r)^2+1/4*(d*x^4+4*e*x^(4+r)/(4+r))*(a+b*log(c*x^n))],
[x*(d+e*x^r)*(a+b*log(c*x^n)),x,4,-1/4*b*d*n*x^2-b*e*n*x^(2+r)/(2+r)^2+1/2*(d*x^2+2*e*x^(2+r)/(2+r))*(a+b*log(c*x^n))],
[(d+e*x^r)*(a+b*log(c*x^n))/x,x,4,-b*e*n*x^r/r^2+e*x^r*(a+b*log(c*x^n))/r+1/2*d*(a+b*log(c*x^n))^2/(b*n)],
[(d+e*x^r)*(a+b*log(c*x^n))/x^3,x,4,-1/4*b*d*n/x^2-b*e*n*x^(-2+r)/(2-r)^2-1/2*d*(a+b*log(c*x^n))/x^2-e*x^(-2+r)*(a+b*log(c*x^n))/(2-r)],
[(d+e*x^r)*(a+b*log(c*x^n))/x^5,x,4,-1/16*b*d*n/x^4-b*e*n*x^(-4+r)/(4-r)^2-1/4*d*(a+b*log(c*x^n))/x^4-e*x^(-4+r)*(a+b*log(c*x^n))/(4-r)],
[x^4*(d+e*x^r)*(a+b*log(c*x^n)),x,4,-1/25*b*d*n*x^5-b*e*n*x^(5+r)/(5+r)^2+1/5*(d*x^5+5*e*x^(5+r)/(5+r))*(a+b*log(c*x^n))],
[x^2*(d+e*x^r)*(a+b*log(c*x^n)),x,4,-1/9*b*d*n*x^3-b*e*n*x^(3+r)/(3+r)^2+1/3*(d*x^3+3*e*x^(3+r)/(3+r))*(a+b*log(c*x^n))],
[(d+e*x^r)*(a+b*log(c*x^n)),x,3,-b*d*n*x-b*e*n*x^(1+r)/(1+r)^2+d*x*(a+b*log(c*x^n))+e*x^(1+r)*(a+b*log(c*x^n))/(1+r)],
[(d+e*x^r)*(a+b*log(c*x^n))/x^2,x,4,-b*d*n/x-b*e*n*x^(-1+r)/(1-r)^2-d*(a+b*log(c*x^n))/x-e*x^(-1+r)*(a+b*log(c*x^n))/(1-r)],
[(d+e*x^r)*(a+b*log(c*x^n))/x^4,x,4,-1/9*b*d*n/x^3-b*e*n*x^(-3+r)/(3-r)^2-1/3*d*(a+b*log(c*x^n))/x^3-e*x^(-3+r)*(a+b*log(c*x^n))/(3-r)],
[(d+e*x^r)*(a+b*log(c*x^n))/x^6,x,4,-1/25*b*d*n/x^5-b*e*n*x^(-5+r)/(5-r)^2-1/5*d*(a+b*log(c*x^n))/x^5-e*x^(-5+r)*(a+b*log(c*x^n))/(5-r)],
[x^5*(d+e*x^r)^2*(a+b*log(c*x^n)),x,4,-1/36*b*d^2*n*x^6-1/4*b*e^2*n*x^(2*(3+r))/(3+r)^2-2*b*d*e*n*x^(6+r)/(6+r)^2+1/6*(d^2*x^6+3*e^2*x^(2*(3+r))/(3+r)+12*d*e*x^(6+r)/(6+r))*(a+b*log(c*x^n))],
[x^3*(d+e*x^r)^2*(a+b*log(c*x^n)),x,4,-1/16*b*d^2*n*x^4-1/4*b*e^2*n*x^(2*(2+r))/(2+r)^2-2*b*d*e*n*x^(4+r)/(4+r)^2+1/4*(d^2*x^4+2*e^2*x^(2*(2+r))/(2+r)+8*d*e*x^(4+r)/(4+r))*(a+b*log(c*x^n))],
[x*(d+e*x^r)^2*(a+b*log(c*x^n)),x,4,-1/4*b*d^2*n*x^2-1/4*b*e^2*n*x^(2*(1+r))/(1+r)^2-2*b*d*e*n*x^(2+r)/(2+r)^2+1/2*(d^2*x^2+e^2*x^(2*(1+r))/(1+r)+4*d*e*x^(2+r)/(2+r))*(a+b*log(c*x^n))],
[(d+e*x^r)^2*(a+b*log(c*x^n))/x,x,5,-2*b*d*e*n*x^r/r^2-1/4*b*e^2*n*x^(2*r)/r^2-1/2*b*d^2*n*log(x)^2+2*d*e*x^r*(a+b*log(c*x^n))/r+1/2*e^2*x^(2*r)*(a+b*log(c*x^n))/r+d^2*log(x)*(a+b*log(c*x^n))],
[(d+e*x^r)^2*(a+b*log(c*x^n))/x^3,x,4,-1/4*b*d^2*n/x^2-1/4*b*e^2*n/((1-r)^2*x^(2*(1-r)))-2*b*d*e*n*x^(-2+r)/(2-r)^2-1/2*d^2*(a+b*log(c*x^n))/x^2-1/2*e^2*(a+b*log(c*x^n))/((1-r)*x^(2*(1-r)))-2*d*e*x^(-2+r)*(a+b*log(c*x^n))/(2-r)],
[(d+e*x^r)^2*(a+b*log(c*x^n))/x^5,x,4,-1/16*b*d^2*n/x^4-1/4*b*e^2*n/((2-r)^2*x^(2*(2-r)))-2*b*d*e*n*x^(-4+r)/(4-r)^2-1/4*d^2*(a+b*log(c*x^n))/x^4-1/2*e^2*(a+b*log(c*x^n))/((2-r)*x^(2*(2-r)))-2*d*e*x^(-4+r)*(a+b*log(c*x^n))/(4-r)],
[x^4*(d+e*x^r)^2*(a+b*log(c*x^n)),x,4,-1/25*b*d^2*n*x^5-2*b*d*e*n*x^(5+r)/(5+r)^2-b*e^2*n*x^(5+2*r)/(5+2*r)^2+1/5*(d^2*x^5+10*d*e*x^(5+r)/(5+r)+5*e^2*x^(5+2*r)/(5+2*r))*(a+b*log(c*x^n))],
[x^2*(d+e*x^r)^2*(a+b*log(c*x^n)),x,4,-1/9*b*d^2*n*x^3-2*b*d*e*n*x^(3+r)/(3+r)^2-b*e^2*n*x^(3+2*r)/(3+2*r)^2+1/3*(d^2*x^3+6*d*e*x^(3+r)/(3+r)+3*e^2*x^(3+2*r)/(3+2*r))*(a+b*log(c*x^n))],
[(d+e*x^r)^2*(a+b*log(c*x^n)),x,2,-b*d^2*n*x-2*b*d*e*n*x^(1+r)/(1+r)^2-b*e^2*n*x^(1+2*r)/(1+2*r)^2+d^2*x*(a+b*log(c*x^n))+2*d*e*x^(1+r)*(a+b*log(c*x^n))/(1+r)+e^2*x^(1+2*r)*(a+b*log(c*x^n))/(1+2*r)],
[(d+e*x^r)^2*(a+b*log(c*x^n))/x^2,x,3,-b*d^2*n/x-2*b*d*e*n*x^(-1+r)/(1-r)^2-b*e^2*n*x^(-1+2*r)/(1-2*r)^2-d^2*(a+b*log(c*x^n))/x-2*d*e*x^(-1+r)*(a+b*log(c*x^n))/(1-r)-e^2*x^(-1+2*r)*(a+b*log(c*x^n))/(1-2*r)],
[(d+e*x^r)^2*(a+b*log(c*x^n))/x^4,x,4,-1/9*b*d^2*n/x^3-2*b*d*e*n*x^(-3+r)/(3-r)^2-b*e^2*n*x^(-3+2*r)/(3-2*r)^2-1/3*d^2*(a+b*log(c*x^n))/x^3-2*d*e*x^(-3+r)*(a+b*log(c*x^n))/(3-r)-e^2*x^(-3+2*r)*(a+b*log(c*x^n))/(3-2*r)],
[(d+e*x^r)^2*(a+b*log(c*x^n))/x^6,x,4,-1/25*b*d^2*n/x^5-2*b*d*e*n*x^(-5+r)/(5-r)^2-b*e^2*n*x^(-5+2*r)/(5-2*r)^2-1/5*d^2*(a+b*log(c*x^n))/x^5-2*d*e*x^(-5+r)*(a+b*log(c*x^n))/(5-r)-e^2*x^(-5+2*r)*(a+b*log(c*x^n))/(5-2*r)],
[(d+e*x^r)^2*(a+b*log(c*x^n))/x^8,x,4,-1/49*b*d^2*n/x^7-2*b*d*e*n*x^(-7+r)/(7-r)^2-b*e^2*n*x^(-7+2*r)/(7-2*r)^2-1/7*d^2*(a+b*log(c*x^n))/x^7-2*d*e*x^(-7+r)*(a+b*log(c*x^n))/(7-r)-e^2*x^(-7+2*r)*(a+b*log(c*x^n))/(7-2*r)],
[x^5*(d+e*x^r)^3*(a+b*log(c*x^n)),x,4,-1/36*b*d^3*n*x^6-1/9*b*e^3*n*x^(3*(2+r))/(2+r)^2-3/4*b*d*e^2*n*x^(2*(3+r))/(3+r)^2-3*b*d^2*e*n*x^(6+r)/(6+r)^2+1/6*(d^3*x^6+2*e^3*x^(3*(2+r))/(2+r)+9*d*e^2*x^(2*(3+r))/(3+r)+18*d^2*e*x^(6+r)/(6+r))*(a+b*log(c*x^n))],
[x^3*(d+e*x^r)^3*(a+b*log(c*x^n)),x,4,-1/16*b*d^3*n*x^4-3/4*b*d*e^2*n*x^(2*(2+r))/(2+r)^2-3*b*d^2*e*n*x^(4+r)/(4+r)^2-b*e^3*n*x^(4+3*r)/(4+3*r)^2+1/4*(d^3*x^4+6*d*e^2*x^(2*(2+r))/(2+r)+12*d^2*e*x^(4+r)/(4+r)+4*e^3*x^(4+3*r)/(4+3*r))*(a+b*log(c*x^n))],
[x*(d+e*x^r)^3*(a+b*log(c*x^n)),x,4,-1/4*b*d^3*n*x^2-3/4*b*d*e^2*n*x^(2*(1+r))/(1+r)^2-3*b*d^2*e*n*x^(2+r)/(2+r)^2-b*e^3*n*x^(2+3*r)/(2+3*r)^2+1/2*(d^3*x^2+3*d*e^2*x^(2*(1+r))/(1+r)+6*d^2*e*x^(2+r)/(2+r)+2*e^3*x^(2+3*r)/(2+3*r))*(a+b*log(c*x^n))],
[(d+e*x^r)^3*(a+b*log(c*x^n))/x,x,5,-3*b*d^2*e*n*x^r/r^2-3/4*b*d*e^2*n*x^(2*r)/r^2-1/9*b*e^3*n*x^(3*r)/r^2-1/2*b*d^3*n*log(x)^2+3*d^2*e*x^r*(a+b*log(c*x^n))/r+3/2*d*e^2*x^(2*r)*(a+b*log(c*x^n))/r+1/3*e^3*x^(3*r)*(a+b*log(c*x^n))/r+d^3*log(x)*(a+b*log(c*x^n))],
[(d+e*x^r)^3*(a+b*log(c*x^n))/x^3,x,4,-1/4*b*d^3*n/x^2-3/4*b*d*e^2*n/((1-r)^2*x^(2*(1-r)))-3*b*d^2*e*n*x^(-2+r)/(2-r)^2-b*e^3*n*x^(-2+3*r)/(2-3*r)^2-1/2*d^3*(a+b*log(c*x^n))/x^2-3/2*d*e^2*(a+b*log(c*x^n))/((1-r)*x^(2*(1-r)))-3*d^2*e*x^(-2+r)*(a+b*log(c*x^n))/(2-r)-e^3*x^(-2+3*r)*(a+b*log(c*x^n))/(2-3*r)],
[(d+e*x^r)^3*(a+b*log(c*x^n))/x^5,x,4,-1/16*b*d^3*n/x^4-3/4*b*d*e^2*n/((2-r)^2*x^(2*(2-r)))-3*b*d^2*e*n*x^(-4+r)/(4-r)^2-b*e^3*n*x^(-4+3*r)/(4-3*r)^2-1/4*d^3*(a+b*log(c*x^n))/x^4-3/2*d*e^2*(a+b*log(c*x^n))/((2-r)*x^(2*(2-r)))-3*d^2*e*x^(-4+r)*(a+b*log(c*x^n))/(4-r)-e^3*x^(-4+3*r)*(a+b*log(c*x^n))/(4-3*r)],
[x^4*(d+e*x^r)^3*(a+b*log(c*x^n)),x,4,-1/25*b*d^3*n*x^5-3*b*d^2*e*n*x^(5+r)/(5+r)^2-3*b*d*e^2*n*x^(5+2*r)/(5+2*r)^2-b*e^3*n*x^(5+3*r)/(5+3*r)^2+1/5*(d^3*x^5+15*d^2*e*x^(5+r)/(5+r)+15*d*e^2*x^(5+2*r)/(5+2*r)+5*e^3*x^(5+3*r)/(5+3*r))*(a+b*log(c*x^n))],
[x^2*(d+e*x^r)^3*(a+b*log(c*x^n)),x,4,-1/9*b*d^3*n*x^3-1/9*b*e^3*n*x^(3*(1+r))/(1+r)^2-3*b*d^2*e*n*x^(3+r)/(3+r)^2-3*b*d*e^2*n*x^(3+2*r)/(3+2*r)^2+1/3*(d^3*x^3+e^3*x^(3*(1+r))/(1+r)+9*d^2*e*x^(3+r)/(3+r)+9*d*e^2*x^(3+2*r)/(3+2*r))*(a+b*log(c*x^n))],
[(d+e*x^r)^3*(a+b*log(c*x^n)),x,2,-b*d^3*n*x-3*b*d^2*e*n*x^(1+r)/(1+r)^2-3*b*d*e^2*n*x^(1+2*r)/(1+2*r)^2-b*e^3*n*x^(1+3*r)/(1+3*r)^2+d^3*x*(a+b*log(c*x^n))+3*d^2*e*x^(1+r)*(a+b*log(c*x^n))/(1+r)+3*d*e^2*x^(1+2*r)*(a+b*log(c*x^n))/(1+2*r)+e^3*x^(1+3*r)*(a+b*log(c*x^n))/(1+3*r)],
[(d+e*x^r)^3*(a+b*log(c*x^n))/x^2,x,3,-b*d^3*n/x-3*b*d^2*e*n*x^(-1+r)/(1-r)^2-3*b*d*e^2*n*x^(-1+2*r)/(1-2*r)^2-b*e^3*n*x^(-1+3*r)/(1-3*r)^2-d^3*(a+b*log(c*x^n))/x-3*d^2*e*x^(-1+r)*(a+b*log(c*x^n))/(1-r)-3*d*e^2*x^(-1+2*r)*(a+b*log(c*x^n))/(1-2*r)-e^3*x^(-1+3*r)*(a+b*log(c*x^n))/(1-3*r)],
[(d+e*x^r)^3*(a+b*log(c*x^n))/x^4,x,4,-1/9*b*d^3*n/x^3-1/9*b*e^3*n/((1-r)^2*x^(3*(1-r)))-3*b*d^2*e*n*x^(-3+r)/(3-r)^2-3*b*d*e^2*n*x^(-3+2*r)/(3-2*r)^2-1/3*d^3*(a+b*log(c*x^n))/x^3-1/3*e^3*(a+b*log(c*x^n))/((1-r)*x^(3*(1-r)))-3*d^2*e*x^(-3+r)*(a+b*log(c*x^n))/(3-r)-3*d*e^2*x^(-3+2*r)*(a+b*log(c*x^n))/(3-2*r)],
[(d+e*x^r)^3*(a+b*log(c*x^n))/x^6,x,4,-1/25*b*d^3*n/x^5-3*b*d^2*e*n*x^(-5+r)/(5-r)^2-3*b*d*e^2*n*x^(-5+2*r)/(5-2*r)^2-b*e^3*n*x^(-5+3*r)/(5-3*r)^2-1/5*d^3*(a+b*log(c*x^n))/x^5-3*d^2*e*x^(-5+r)*(a+b*log(c*x^n))/(5-r)-3*d*e^2*x^(-5+2*r)*(a+b*log(c*x^n))/(5-2*r)-e^3*x^(-5+3*r)*(a+b*log(c*x^n))/(5-3*r)],
[(d+e*x^r)^3*(a+b*log(c*x^n))/x^8,x,4,-1/49*b*d^3*n/x^7-3*b*d^2*e*n*x^(-7+r)/(7-r)^2-3*b*d*e^2*n*x^(-7+2*r)/(7-2*r)^2-b*e^3*n*x^(-7+3*r)/(7-3*r)^2-1/7*d^3*(a+b*log(c*x^n))/x^7-3*d^2*e*x^(-7+r)*(a+b*log(c*x^n))/(7-r)-3*d*e^2*x^(-7+2*r)*(a+b*log(c*x^n))/(7-2*r)-e^3*x^(-7+3*r)*(a+b*log(c*x^n))/(7-3*r)],
[(d+e*x^r)^3*(a+b*log(c*x^n))/x^10,x,4,-1/81*b*d^3*n/x^9-1/9*b*e^3*n/((3-r)^2*x^(3*(3-r)))-3*b*d^2*e*n*x^(-9+r)/(9-r)^2-3*b*d*e^2*n*x^(-9+2*r)/(9-2*r)^2-1/9*d^3*(a+b*log(c*x^n))/x^9-1/3*e^3*(a+b*log(c*x^n))/((3-r)*x^(3*(3-r)))-3*d^2*e*x^(-9+r)*(a+b*log(c*x^n))/(9-r)-3*d*e^2*x^(-9+2*r)*(a+b*log(c*x^n))/(9-2*r)],

# q<0
[x^3*(a+b*log(c*x^n))/(d+e*x^r),x,0,Unintegrable(x^3*(a+b*log(c*x^n))/(d+e*x^r),x)],
[x*(a+b*log(c*x^n))/(d+e*x^r),x,0,Unintegrable(x*(a+b*log(c*x^n))/(d+e*x^r),x)],
[(a+b*log(c*x^n))/(x*(d+e*x^r)),x,2,-(a+b*log(c*x^n))*log(1+d/(e*x^r))/(d*r)+b*n*polylog(2,-d/(e*x^r))/(d*r^2)],
[(a+b*log(c*x^n))/(x^3*(d+e*x^r)),x,0,Unintegrable((a+b*log(c*x^n))/(x^3*(d+e*x^r)),x)],
[x^2*(a+b*log(c*x^n))/(d+e*x^r),x,0,Unintegrable(x^2*(a+b*log(c*x^n))/(d+e*x^r),x)],
[(a+b*log(c*x^n))/(d+e*x^r),x,0,Unintegrable((a+b*log(c*x^n))/(d+e*x^r),x)],
[(a+b*log(c*x^n))/(x^2*(d+e*x^r)),x,0,Unintegrable((a+b*log(c*x^n))/(x^2*(d+e*x^r)),x)],
[x^3*(a+b*log(c*x^n))/(d+e*x^r)^2,x,0,Unintegrable(x^3*(a+b*log(c*x^n))/(d+e*x^r)^2,x)],
[x*(a+b*log(c*x^n))/(d+e*x^r)^2,x,0,Unintegrable(x*(a+b*log(c*x^n))/(d+e*x^r)^2,x)],
[(a+b*log(c*x^n))/(x*(d+e*x^r)^2),x,5,-e*x^r*(a+b*log(c*x^n))/(d^2*r*(d+e*x^r))-(a+b*log(c*x^n))*log(1+d/(e*x^r))/(d^2*r)+b*n*log(d+e*x^r)/(d^2*r^2)+b*n*polylog(2,-d/(e*x^r))/(d^2*r^2)],
[(a+b*log(c*x^n))/(x^3*(d+e*x^r)^2),x,0,Unintegrable((a+b*log(c*x^n))/(x^3*(d+e*x^r)^2),x)],
[x^2*(a+b*log(c*x^n))/(d+e*x^r)^2,x,0,Unintegrable(x^2*(a+b*log(c*x^n))/(d+e*x^r)^2,x)],
[(a+b*log(c*x^n))/(d+e*x^r)^2,x,0,Unintegrable((a+b*log(c*x^n))/(d+e*x^r)^2,x)],
[(a+b*log(c*x^n))/(x^2*(d+e*x^r)^2),x,0,Unintegrable((a+b*log(c*x^n))/(x^2*(d+e*x^r)^2),x)],
[(a+b*log(c*x^n))/(x*(c+(-1)/x^n)),x,4,a*log(1-c*x^n)/(c*n)-b*polylog(2,1-c*x^n)/(c*n)],

# Integrands of the form (d+e x^r)^q (a+b Log[c x^n])^p/x

# p>0
[(d+e*x^r)^3*(a+b*log(c*x^n))/x,x,5,-3*b*d^2*e*n*x^r/r^2-3/4*b*d*e^2*n*x^(2*r)/r^2-1/9*b*e^3*n*x^(3*r)/r^2-1/2*b*d^3*n*log(x)^2+3*d^2*e*x^r*(a+b*log(c*x^n))/r+3/2*d*e^2*x^(2*r)*(a+b*log(c*x^n))/r+1/3*e^3*x^(3*r)*(a+b*log(c*x^n))/r+d^3*log(x)*(a+b*log(c*x^n))],
[(d+e*x^r)^2*(a+b*log(c*x^n))/x,x,5,-2*b*d*e*n*x^r/r^2-1/4*b*e^2*n*x^(2*r)/r^2-1/2*b*d^2*n*log(x)^2+2*d*e*x^r*(a+b*log(c*x^n))/r+1/2*e^2*x^(2*r)*(a+b*log(c*x^n))/r+d^2*log(x)*(a+b*log(c*x^n))],
[(d+e*x^r)*(a+b*log(c*x^n))/x,x,4,-b*e*n*x^r/r^2+e*x^r*(a+b*log(c*x^n))/r+1/2*d*(a+b*log(c*x^n))^2/(b*n)],
[(a+b*log(c*x^n))/(x*(d+e*x^r)),x,2,-(a+b*log(c*x^n))*log(1+d/(e*x^r))/(d*r)+b*n*polylog(2,-d/(e*x^r))/(d*r^2)],
[(a+b*log(c*x^n))/(x*(d+e*x^r)^2),x,5,-e*x^r*(a+b*log(c*x^n))/(d^2*r*(d+e*x^r))-(a+b*log(c*x^n))*log(1+d/(e*x^r))/(d^2*r)+b*n*log(d+e*x^r)/(d^2*r^2)+b*n*polylog(2,-d/(e*x^r))/(d^2*r^2)],
[(a+b*log(c*x^n))/(x*(d+e*x^r)^3),x,10,-1/2*b*n/(d^2*r^2*(d+e*x^r))-1/2*b*n*log(x)/(d^3*r)+1/2*(a+b*log(c*x^n))/(d*r*(d+e*x^r)^2)-e*x^r*(a+b*log(c*x^n))/(d^3*r*(d+e*x^r))-(a+b*log(c*x^n))*log(1+d/(e*x^r))/(d^3*r)+3/2*b*n*log(d+e*x^r)/(d^3*r^2)+b*n*polylog(2,-d/(e*x^r))/(d^3*r^2)],
[(d+e*x^r)^3*(a+b*log(c*x^n))^2/x,x,10,6*b^2*d^2*e*n^2*x^r/r^3+3/4*b^2*d*e^2*n^2*x^(2*r)/r^3+2/27*b^2*e^3*n^2*x^(3*r)/r^3-6*b*d^2*e*n*x^r*(a+b*log(c*x^n))/r^2-3/2*b*d*e^2*n*x^(2*r)*(a+b*log(c*x^n))/r^2-2/9*b*e^3*n*x^(3*r)*(a+b*log(c*x^n))/r^2+3*d^2*e*x^r*(a+b*log(c*x^n))^2/r+3/2*d*e^2*x^(2*r)*(a+b*log(c*x^n))^2/r+1/3*e^3*x^(3*r)*(a+b*log(c*x^n))^2/r+1/3*d^3*(a+b*log(c*x^n))^3/(b*n)],
[(d+e*x^r)^2*(a+b*log(c*x^n))^2/x,x,8,4*b^2*d*e*n^2*x^r/r^3+1/4*b^2*e^2*n^2*x^(2*r)/r^3-4*b*d*e*n*x^r*(a+b*log(c*x^n))/r^2-1/2*b*e^2*n*x^(2*r)*(a+b*log(c*x^n))/r^2+2*d*e*x^r*(a+b*log(c*x^n))^2/r+1/2*e^2*x^(2*r)*(a+b*log(c*x^n))^2/r+1/3*d^2*(a+b*log(c*x^n))^3/(b*n)],
[(d+e*x^r)*(a+b*log(c*x^n))^2/x,x,6,2*b^2*e*n^2*x^r/r^3-2*b*e*n*x^r*(a+b*log(c*x^n))/r^2+e*x^r*(a+b*log(c*x^n))^2/r+1/3*d*(a+b*log(c*x^n))^3/(b*n)],
[(a+b*log(c*x^n))^2/(x*(d+e*x^r)),x,3,-(a+b*log(c*x^n))^2*log(1+d/(e*x^r))/(d*r)+2*b*n*(a+b*log(c*x^n))*polylog(2,-d/(e*x^r))/(d*r^2)+2*b^2*n^2*polylog(3,-d/(e*x^r))/(d*r^3)],
[(a+b*log(c*x^n))^2/(x*(d+e*x^r)^2),x,7,(a+b*log(c*x^n))^2/(d*r*(d+e*x^r))+2*b*n*(a+b*log(c*x^n))*log(1+d/(e*x^r))/(d^2*r^2)-(a+b*log(c*x^n))^2*log(1+d/(e*x^r))/(d^2*r)-2*b^2*n^2*polylog(2,-d/(e*x^r))/(d^2*r^3)+2*b*n*(a+b*log(c*x^n))*polylog(2,-d/(e*x^r))/(d^2*r^2)+2*b^2*n^2*polylog(3,-d/(e*x^r))/(d^2*r^3)],
[(a+b*log(c*x^n))^2/(x*(d+e*x^r)^3),x,14,b*e*n*x^r*(a+b*log(c*x^n))/(d^3*r^2*(d+e*x^r))+1/2*(a+b*log(c*x^n))^2/(d*r*(d+e*x^r)^2)+(a+b*log(c*x^n))^2/(d^2*r*(d+e*x^r))+3*b*n*(a+b*log(c*x^n))*log(1+d/(e*x^r))/(d^3*r^2)-(a+b*log(c*x^n))^2*log(1+d/(e*x^r))/(d^3*r)-b^2*n^2*log(d+e*x^r)/(d^3*r^3)-3*b^2*n^2*polylog(2,-d/(e*x^r))/(d^3*r^3)+2*b*n*(a+b*log(c*x^n))*polylog(2,-d/(e*x^r))/(d^3*r^2)+2*b^2*n^2*polylog(3,-d/(e*x^r))/(d^3*r^3)],

# p<0

# Integrands of the form x^m (d+e x^r)^(q/2) (a+b Log[c x^n])
[(d+e*x^r)^(5/2)*(a+b*log(c*x^n))/x,x,23,-32/45*b*d*n*(d+e*x^r)^(3/2)/r^2-4/25*b*n*(d+e*x^r)^(5/2)/r^2+92/15*b*d^(5/2)*n*arctanh(sqrt(d+e*x^r)/sqrt(d))/r^2+2*b*d^(5/2)*n*arctanh(sqrt(d+e*x^r)/sqrt(d))^2/r^2-4*b*d^(5/2)*n*arctanh(sqrt(d+e*x^r)/sqrt(d))*log(2*sqrt(d)/(sqrt(d)-sqrt(d+e*x^r)))/r^2-2*b*d^(5/2)*n*polylog(2,1-2*sqrt(d)/(sqrt(d)-sqrt(d+e*x^r)))/r^2-92/15*b*d^2*n*sqrt(d+e*x^r)/r^2+2/15*(a+b*log(c*x^n))*(5*d*(d+e*x^r)^(3/2)/r+3*(d+e*x^r)^(5/2)/r-15*d^(5/2)*arctanh(sqrt(d+e*x^r)/sqrt(d))/r+15*d^2*sqrt(d+e*x^r)/r)],
[(d+e*x^r)^(3/2)*(a+b*log(c*x^n))/x,x,17,-4/9*b*n*(d+e*x^r)^(3/2)/r^2+16/3*b*d^(3/2)*n*arctanh(sqrt(d+e*x^r)/sqrt(d))/r^2+2*b*d^(3/2)*n*arctanh(sqrt(d+e*x^r)/sqrt(d))^2/r^2-4*b*d^(3/2)*n*arctanh(sqrt(d+e*x^r)/sqrt(d))*log(2*sqrt(d)/(sqrt(d)-sqrt(d+e*x^r)))/r^2-2*b*d^(3/2)*n*polylog(2,1-2*sqrt(d)/(sqrt(d)-sqrt(d+e*x^r)))/r^2-16/3*b*d*n*sqrt(d+e*x^r)/r^2+2/3*(a+b*log(c*x^n))*((d+e*x^r)^(3/2)/r-3*d^(3/2)*arctanh(sqrt(d+e*x^r)/sqrt(d))/r+3*d*sqrt(d+e*x^r)/r)],
[(d+e*x^r)^(1/2)*(a+b*log(c*x^n))/x,x,12,4*b*n*arctanh(sqrt(d+e*x^r)/sqrt(d))*sqrt(d)/r^2+2*b*n*arctanh(sqrt(d+e*x^r)/sqrt(d))^2*sqrt(d)/r^2-4*b*n*arctanh(sqrt(d+e*x^r)/sqrt(d))*log(2*sqrt(d)/(sqrt(d)-sqrt(d+e*x^r)))*sqrt(d)/r^2-2*b*n*polylog(2,1-2*sqrt(d)/(sqrt(d)-sqrt(d+e*x^r)))*sqrt(d)/r^2-4*b*n*sqrt(d+e*x^r)/r^2+2*(a+b*log(c*x^n))*(-arctanh(sqrt(d+e*x^r)/sqrt(d))*sqrt(d)/r+sqrt(d+e*x^r)/r)],
[(a+b*log(c*x^n))/(x*(d+e*x^r)^(1/2)),x,8,2*b*n*arctanh(sqrt(d+e*x^r)/sqrt(d))^2/(r^2*sqrt(d))-2*arctanh(sqrt(d+e*x^r)/sqrt(d))*(a+b*log(c*x^n))/(r*sqrt(d))-4*b*n*arctanh(sqrt(d+e*x^r)/sqrt(d))*log(2*sqrt(d)/(sqrt(d)-sqrt(d+e*x^r)))/(r^2*sqrt(d))-2*b*n*polylog(2,1-2*sqrt(d)/(sqrt(d)-sqrt(d+e*x^r)))/(r^2*sqrt(d))],
[(a+b*log(c*x^n))/(x*(d+e*x^r)^(3/2)),x,11,4*b*n*arctanh(sqrt(d+e*x^r)/sqrt(d))/(d^(3/2)*r^2)+2*b*n*arctanh(sqrt(d+e*x^r)/sqrt(d))^2/(d^(3/2)*r^2)-4*b*n*arctanh(sqrt(d+e*x^r)/sqrt(d))*log(2*sqrt(d)/(sqrt(d)-sqrt(d+e*x^r)))/(d^(3/2)*r^2)-2*b*n*polylog(2,1-2*sqrt(d)/(sqrt(d)-sqrt(d+e*x^r)))/(d^(3/2)*r^2)+2*(a+b*log(c*x^n))*(-arctanh(sqrt(d+e*x^r)/sqrt(d))/(d^(3/2)*r)+1/(d*r*sqrt(d+e*x^r)))],
[(a+b*log(c*x^n))/(x*(d+e*x^r)^(5/2)),x,15,16/3*b*n*arctanh(sqrt(d+e*x^r)/sqrt(d))/(d^(5/2)*r^2)+2*b*n*arctanh(sqrt(d+e*x^r)/sqrt(d))^2/(d^(5/2)*r^2)-4*b*n*arctanh(sqrt(d+e*x^r)/sqrt(d))*log(2*sqrt(d)/(sqrt(d)-sqrt(d+e*x^r)))/(d^(5/2)*r^2)-2*b*n*polylog(2,1-2*sqrt(d)/(sqrt(d)-sqrt(d+e*x^r)))/(d^(5/2)*r^2)+2/3*(a+b*log(c*x^n))*(1/(d*r*(d+e*x^r)^(3/2))-3*arctanh(sqrt(d+e*x^r)/sqrt(d))/(d^(5/2)*r)+3/(d^2*r*sqrt(d+e*x^r)))-4/3*b*n/(d^2*r^2*sqrt(d+e*x^r))],
[(a+b*log(c*x^n))/(x*(d+e*x^r)^(7/2)),x,20,-4/15*b*n/(d^2*r^2*(d+e*x^r)^(3/2))+92/15*b*n*arctanh(sqrt(d+e*x^r)/sqrt(d))/(d^(7/2)*r^2)+2*b*n*arctanh(sqrt(d+e*x^r)/sqrt(d))^2/(d^(7/2)*r^2)-4*b*n*arctanh(sqrt(d+e*x^r)/sqrt(d))*log(2*sqrt(d)/(sqrt(d)-sqrt(d+e*x^r)))/(d^(7/2)*r^2)-2*b*n*polylog(2,1-2*sqrt(d)/(sqrt(d)-sqrt(d+e*x^r)))/(d^(7/2)*r^2)+2/15*(a+b*log(c*x^n))*(3/(d*r*(d+e*x^r)^(5/2))+5/(d^2*r*(d+e*x^r)^(3/2))-15*arctanh(sqrt(d+e*x^r)/sqrt(d))/(d^(7/2)*r)+15/(d^3*r*sqrt(d+e*x^r)))-32/15*b*n/(d^3*r^2*sqrt(d+e*x^r))],

# Integrands of the form (f x)^m (d+e x^r)^q (a+b Log[c x^n]) when m and r symbolic
[(f*x)^m*(d+e*x^r)^3*(a+b*log(c*x^n)),x,9,-3*b*d^2*e*n*x^(1+r)*(f*x)^m/(1+m+r)^2-3*b*d*e^2*n*x^(1+2*r)*(f*x)^m/(1+m+2*r)^2-b*e^3*n*x^(1+3*r)*(f*x)^m/(1+m+3*r)^2-b*d^3*n*(f*x)^(1+m)/(f*(1+m)^2)+3*d^2*e*x^(1+r)*(f*x)^m*(a+b*log(c*x^n))/(1+m+r)+3*d*e^2*x^(1+2*r)*(f*x)^m*(a+b*log(c*x^n))/(1+m+2*r)+e^3*x^(1+3*r)*(f*x)^m*(a+b*log(c*x^n))/(1+m+3*r)+d^3*(f*x)^(1+m)*(a+b*log(c*x^n))/(f*(1+m))],
[(f*x)^m*(d+e*x^r)^2*(a+b*log(c*x^n)),x,7,-2*b*d*e*n*x^(1+r)*(f*x)^m/(1+m+r)^2-b*e^2*n*x^(1+2*r)*(f*x)^m/(1+m+2*r)^2-b*d^2*n*(f*x)^(1+m)/(f*(1+m)^2)+2*d*e*x^(1+r)*(f*x)^m*(a+b*log(c*x^n))/(1+m+r)+e^2*x^(1+2*r)*(f*x)^m*(a+b*log(c*x^n))/(1+m+2*r)+d^2*(f*x)^(1+m)*(a+b*log(c*x^n))/(f*(1+m))],
[(f*x)^m*(d+e*x^r)*(a+b*log(c*x^n)),x,6,-b*e*n*x^(1+r)*(f*x)^m/(1+m+r)^2-b*d*n*(f*x)^(1+m)/(f*(1+m)^2)+e*x^(1+r)*(f*x)^m*(a+b*log(c*x^n))/(1+m+r)+d*(f*x)^(1+m)*(a+b*log(c*x^n))/(f*(1+m))],
[(f*x)^m*(a+b*log(c*x^n)),x,1,-b*n*(f*x)^(1+m)/(f*(1+m)^2)+(f*x)^(1+m)*(a+b*log(c*x^n))/(f*(1+m))],
[(f*x)^m*(a+b*log(c*x^n))/(d+e*x^r),x,0,Unintegrable((f*x)^m*(a+b*log(c*x^n))/(d+e*x^r),x)],
[(f*x)^m*(a+b*log(c*x^n))/(d+e*x^r)^2,x,0,Unintegrable((f*x)^m*(a+b*log(c*x^n))/(d+e*x^r)^2,x)],

# Integrands of the form (f x)^m (d+e x^r)^q (a+b Log[c x^n])^p when m, p and r symbolic
[(d+e/x^(1/(1+q)))^q*(a+b*log(c*x^n)),x,3,-b*n*x*(d+e/x^(1/(1+q)))^q*hypergeom([-1-q,-1-q],[-q],-e/(d*x^(1/(1+q))))/(1+e/(d*x^(1/(1+q))))^q+x*(d+e/x^(1/(1+q)))^(1+q)*(a+b*log(c*x^n))/d],
[(f*x)^(-1-(1+q)*r)*(d+e*x^r)^q*(a+b*log(c*x^n)),x,3,-b*n*(d+e*x^r)^q*hypergeom([-1-q,-1-q],[-q],-e*x^r/d)/(f*(1+q)^2*r^2*(f*x)^((1+q)*r)*(1+e*x^r/d)^q)-(d+e*x^r)^(1+q)*(a+b*log(c*x^n))/(d*f*(1+q)*r*(f*x)^((1+q)*r))],
[(f*x)^m*(d+e*x^r)^3*(a+b*log(c*x^n))^p,x,13,d^3*(f*x)^(1+m)*GAMMA(1+p,-(1+m)*(a+b*log(c*x^n))/(b*n))*(a+b*log(c*x^n))^p/(exp(a*(1+m)/(b*n))*f*(1+m)*(c*x^n)^((1+m)/n)*(-(1+m)*(a+b*log(c*x^n))/(b*n))^p)+3*d^2*e*x^(1+r)*(f*x)^m*GAMMA(1+p,-(1+m+r)*(a+b*log(c*x^n))/(b*n))*(a+b*log(c*x^n))^p/(exp(a*(1+m+r)/(b*n))*(1+m+r)*(c*x^n)^((1+m+r)/n)*(-(1+m+r)*(a+b*log(c*x^n))/(b*n))^p)+3*d*e^2*x^(1+2*r)*(f*x)^m*GAMMA(1+p,-(1+m+2*r)*(a+b*log(c*x^n))/(b*n))*(a+b*log(c*x^n))^p/(exp(a*(1+m+2*r)/(b*n))*(1+m+2*r)*(c*x^n)^((1+m+2*r)/n)*(-(1+m+2*r)*(a+b*log(c*x^n))/(b*n))^p)+e^3*x^(1+3*r)*(f*x)^m*GAMMA(1+p,-(1+m+3*r)*(a+b*log(c*x^n))/(b*n))*(a+b*log(c*x^n))^p/(exp(a*(1+m+3*r)/(b*n))*(1+m+3*r)*(c*x^n)^((1+m+3*r)/n)*(-(1+m+3*r)*(a+b*log(c*x^n))/(b*n))^p)],
[(f*x)^m*(d+e*x^r)^2*(a+b*log(c*x^n))^p,x,10,d^2*(f*x)^(1+m)*GAMMA(1+p,-(1+m)*(a+b*log(c*x^n))/(b*n))*(a+b*log(c*x^n))^p/(exp(a*(1+m)/(b*n))*f*(1+m)*(c*x^n)^((1+m)/n)*(-(1+m)*(a+b*log(c*x^n))/(b*n))^p)+2*d*e*x^(1+r)*(f*x)^m*GAMMA(1+p,-(1+m+r)*(a+b*log(c*x^n))/(b*n))*(a+b*log(c*x^n))^p/(exp(a*(1+m+r)/(b*n))*(1+m+r)*(c*x^n)^((1+m+r)/n)*(-(1+m+r)*(a+b*log(c*x^n))/(b*n))^p)+e^2*x^(1+2*r)*(f*x)^m*GAMMA(1+p,-(1+m+2*r)*(a+b*log(c*x^n))/(b*n))*(a+b*log(c*x^n))^p/(exp(a*(1+m+2*r)/(b*n))*(1+m+2*r)*(c*x^n)^((1+m+2*r)/n)*(-(1+m+2*r)*(a+b*log(c*x^n))/(b*n))^p)],
[(f*x)^m*(d+e*x^r)*(a+b*log(c*x^n))^p,x,7,d*(f*x)^(1+m)*GAMMA(1+p,-(1+m)*(a+b*log(c*x^n))/(b*n))*(a+b*log(c*x^n))^p/(exp(a*(1+m)/(b*n))*f*(1+m)*(c*x^n)^((1+m)/n)*(-(1+m)*(a+b*log(c*x^n))/(b*n))^p)+e*x^(1+r)*(f*x)^m*GAMMA(1+p,-(1+m+r)*(a+b*log(c*x^n))/(b*n))*(a+b*log(c*x^n))^p/(exp(a*(1+m+r)/(b*n))*(1+m+r)*(c*x^n)^((1+m+r)/n)*(-(1+m+r)*(a+b*log(c*x^n))/(b*n))^p)],
[(f*x)^m*(a+b*log(c*x^n))^p,x,2,(f*x)^(1+m)*GAMMA(1+p,-(1+m)*(a+b*log(c*x^n))/(b*n))*(a+b*log(c*x^n))^p/(exp(a*(1+m)/(b*n))*f*(1+m)*(c*x^n)^((1+m)/n)*(-(1+m)*(a+b*log(c*x^n))/(b*n))^p)],
[(f*x)^m*(a+b*log(c*x^n))^p/(d+e*x^r),x,0,Unintegrable((f*x)^m*(a+b*log(c*x^n))^p/(d+e*x^r),x)],
[(f*x)^m*(a+b*log(c*x^n))^p/(d+e*x^r)^2,x,0,Unintegrable((f*x)^m*(a+b*log(c*x^n))^p/(d+e*x^r)^2,x)],

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

# Integrands of the form (f+g x)^m (d+e x)^q (a+b Log[c x^n])^p
[(f+g*x)*(a+b*log(c*x^n))/(d+e*x)^3,x,3,1/2*b*(e*f-d*g)*n/(d*e^2*(d+e*x))+1/2*b*f^2*n*log(x)/(d^2*(e*f-d*g))-1/2*(f+g*x)^2*(a+b*log(c*x^n))/((e*f-d*g)*(d+e*x)^2)-1/2*b*(e*f+d*g)*n*log(d+e*x)/(d^2*e^2)],
[(f+g*x)*(a+b*log(c*x^n))^2/(d+e*x)^3,x,8,-b*(e*f-d*g)*n*x*(a+b*log(c*x^n))/(d^2*e*(d+e*x))+1/2*f^2*(a+b*log(c*x^n))^2/(d^2*(e*f-d*g))-1/2*(f+g*x)^2*(a+b*log(c*x^n))^2/((e*f-d*g)*(d+e*x)^2)+b^2*(e*f-d*g)*n^2*log(d+e*x)/(d^2*e^2)-b*(e*f+d*g)*n*(a+b*log(c*x^n))*log(1+e*x/d)/(d^2*e^2)-b^2*(e*f+d*g)*n^2*polylog(2,-e*x/d)/(d^2*e^2)],
[(f+g*x)*(a+b*log(c*x^n))^3/(d+e*x)^3,x,11,-3/2*b*(e*f-d*g)*n*x*(a+b*log(c*x^n))^2/(d^2*e*(d+e*x))+1/2*f^2*(a+b*log(c*x^n))^3/(d^2*(e*f-d*g))-1/2*(f+g*x)^2*(a+b*log(c*x^n))^3/((e*f-d*g)*(d+e*x)^2)+3*b^2*(e*f-d*g)*n^2*(a+b*log(c*x^n))*log(1+e*x/d)/(d^2*e^2)-3/2*b*(e*f+d*g)*n*(a+b*log(c*x^n))^2*log(1+e*x/d)/(d^2*e^2)+3*b^3*(e*f-d*g)*n^3*polylog(2,-e*x/d)/(d^2*e^2)-3*b^2*(e*f+d*g)*n^2*(a+b*log(c*x^n))*polylog(2,-e*x/d)/(d^2*e^2)+3*b^3*(e*f+d*g)*n^3*polylog(3,-e*x/d)/(d^2*e^2)]]:
