# Maple integration test file: "3 Logarithms\3.1.5 u (a+b log(c x^n))^p.txt"

lst:=[

# Integrands of the form AF[x] (a+b Log[c x^n])^p

# Integrands of the form (g x)^m (d+e x+f x^2)^q RFx (a+b Log[c x^n])^p
[(a+b*log(c*x^n))/(d+e*x+f*x^2),x,6,(a+b*log(c*x^n))*log(1+2*f*x/(e-sqrt(e^2-4*d*f)))/sqrt(e^2-4*d*f)-(a+b*log(c*x^n))*log(1+2*f*x/(e+sqrt(e^2-4*d*f)))/sqrt(e^2-4*d*f)+b*n*polylog(2,-2*f*x/(e-sqrt(e^2-4*d*f)))/sqrt(e^2-4*d*f)-b*n*polylog(2,-2*f*x/(e+sqrt(e^2-4*d*f)))/sqrt(e^2-4*d*f)],

# Integrands of the form EF[x] (a+b Log[c x^n])^p

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

# Integrands of the form x^q Log[d (e+f x^1)] (a+b Log[c x^n])^p when d e=1
[x^3*(a+b*log(c*x^n))*log(1+e*x),x,6,-5/16*b*n*x/e^3+3/32*b*n*x^2/e^2-7/144*b*n*x^3/e+1/32*b*n*x^4+1/4*x*(a+b*log(c*x^n))/e^3-1/8*x^2*(a+b*log(c*x^n))/e^2+1/12*x^3*(a+b*log(c*x^n))/e-1/16*x^4*(a+b*log(c*x^n))+1/16*b*n*log(1+e*x)/e^4-1/16*b*n*x^4*log(1+e*x)-1/4*(a+b*log(c*x^n))*log(1+e*x)/e^4+1/4*x^4*(a+b*log(c*x^n))*log(1+e*x)-1/4*b*n*polylog(2,-e*x)/e^4],
[x^2*(a+b*log(c*x^n))*log(1+e*x),x,6,4/9*b*n*x/e^2-5/36*b*n*x^2/e+2/27*b*n*x^3-1/3*x*(a+b*log(c*x^n))/e^2+1/6*x^2*(a+b*log(c*x^n))/e-1/9*x^3*(a+b*log(c*x^n))-1/9*b*n*log(1+e*x)/e^3-1/9*b*n*x^3*log(1+e*x)+1/3*(a+b*log(c*x^n))*log(1+e*x)/e^3+1/3*x^3*(a+b*log(c*x^n))*log(1+e*x)+1/3*b*n*polylog(2,-e*x)/e^3],
[x*(a+b*log(c*x^n))*log(1+e*x),x,6,-3/4*b*n*x/e+1/4*b*n*x^2+1/2*x*(a+b*log(c*x^n))/e-1/4*x^2*(a+b*log(c*x^n))+1/4*b*n*log(1+e*x)/e^2-1/4*b*n*x^2*log(1+e*x)-1/2*(a+b*log(c*x^n))*log(1+e*x)/e^2+1/2*x^2*(a+b*log(c*x^n))*log(1+e*x)-1/2*b*n*polylog(2,-e*x)/e^2],
[(a+b*log(c*x^n))*log(1+e*x),x,7,2*b*n*x-x*(a+b*log(c*x^n))-b*n*(1+e*x)*log(1+e*x)/e+(1+e*x)*(a+b*log(c*x^n))*log(1+e*x)/e+b*n*polylog(2,-e*x)/e],
[(a+b*log(c*x^n))*log(1+e*x)/x,x,2,-(a+b*log(c*x^n))*polylog(2,-e*x)+b*n*polylog(3,-e*x)],
[(a+b*log(c*x^n))*log(1+e*x)/x^2,x,8,b*e*n*log(x)-1/2*b*e*n*log(x)^2+e*log(x)*(a+b*log(c*x^n))-b*e*n*log(1+e*x)-b*n*log(1+e*x)/x-e*(a+b*log(c*x^n))*log(1+e*x)-(a+b*log(c*x^n))*log(1+e*x)/x-b*e*n*polylog(2,-e*x)],
[(a+b*log(c*x^n))*log(1+e*x)/x^3,x,7,-3/4*b*e*n/x-1/4*b*e^2*n*log(x)+1/4*b*e^2*n*log(x)^2-1/2*e*(a+b*log(c*x^n))/x-1/2*e^2*log(x)*(a+b*log(c*x^n))+1/4*b*e^2*n*log(1+e*x)-1/4*b*n*log(1+e*x)/x^2+1/2*e^2*(a+b*log(c*x^n))*log(1+e*x)-1/2*(a+b*log(c*x^n))*log(1+e*x)/x^2+1/2*b*e^2*n*polylog(2,-e*x)],
[(a+b*log(c*x^n))*log(1+e*x)/x^4,x,7,-5/36*b*e*n/x^2+4/9*b*e^2*n/x+1/9*b*e^3*n*log(x)-1/6*b*e^3*n*log(x)^2-1/6*e*(a+b*log(c*x^n))/x^2+1/3*e^2*(a+b*log(c*x^n))/x+1/3*e^3*log(x)*(a+b*log(c*x^n))-1/9*b*e^3*n*log(1+e*x)-1/9*b*n*log(1+e*x)/x^3-1/3*e^3*(a+b*log(c*x^n))*log(1+e*x)-1/3*(a+b*log(c*x^n))*log(1+e*x)/x^3-1/3*b*e^3*n*polylog(2,-e*x)],
[x^3*(a+b*log(c*x^n))^2*log(1+e*x),x,15,-1/2*a*b*n*x/e^3+21/32*b^2*n^2*x/e^3-7/64*b^2*n^2*x^2/e^2+37/864*b^2*n^2*x^3/e-3/128*b^2*n^2*x^4-1/2*b^2*n*x*log(c*x^n)/e^3-1/8*b*n*x*(a+b*log(c*x^n))/e^3+3/16*b*n*x^2*(a+b*log(c*x^n))/e^2-7/72*b*n*x^3*(a+b*log(c*x^n))/e+1/16*b*n*x^4*(a+b*log(c*x^n))+1/4*x*(a+b*log(c*x^n))^2/e^3-1/8*x^2*(a+b*log(c*x^n))^2/e^2+1/12*x^3*(a+b*log(c*x^n))^2/e-1/16*x^4*(a+b*log(c*x^n))^2-1/32*b^2*n^2*log(1+e*x)/e^4+1/32*b^2*n^2*x^4*log(1+e*x)+1/8*b*n*(a+b*log(c*x^n))*log(1+e*x)/e^4-1/8*b*n*x^4*(a+b*log(c*x^n))*log(1+e*x)-1/4*(a+b*log(c*x^n))^2*log(1+e*x)/e^4+1/4*x^4*(a+b*log(c*x^n))^2*log(1+e*x)+1/8*b^2*n^2*polylog(2,-e*x)/e^4-1/2*b*n*(a+b*log(c*x^n))*polylog(2,-e*x)/e^4+1/2*b^2*n^2*polylog(3,-e*x)/e^4],
[x^2*(a+b*log(c*x^n))^2*log(1+e*x),x,14,2/3*a*b*n*x/e^2-26/27*b^2*n^2*x/e^2+19/108*b^2*n^2*x^2/e-2/27*b^2*n^2*x^3+2/3*b^2*n*x*log(c*x^n)/e^2+2/9*b*n*x*(a+b*log(c*x^n))/e^2-5/18*b*n*x^2*(a+b*log(c*x^n))/e+4/27*b*n*x^3*(a+b*log(c*x^n))-1/3*x*(a+b*log(c*x^n))^2/e^2+1/6*x^2*(a+b*log(c*x^n))^2/e-1/9*x^3*(a+b*log(c*x^n))^2+2/27*b^2*n^2*log(1+e*x)/e^3+2/27*b^2*n^2*x^3*log(1+e*x)-2/9*b*n*(a+b*log(c*x^n))*log(1+e*x)/e^3-2/9*b*n*x^3*(a+b*log(c*x^n))*log(1+e*x)+1/3*(a+b*log(c*x^n))^2*log(1+e*x)/e^3+1/3*x^3*(a+b*log(c*x^n))^2*log(1+e*x)-2/9*b^2*n^2*polylog(2,-e*x)/e^3+2/3*b*n*(a+b*log(c*x^n))*polylog(2,-e*x)/e^3-2/3*b^2*n^2*polylog(3,-e*x)/e^3],
[x*(a+b*log(c*x^n))^2*log(1+e*x),x,13,-a*b*n*x/e+7/4*b^2*n^2*x/e-3/8*b^2*n^2*x^2-b^2*n*x*log(c*x^n)/e-1/2*b*n*x*(a+b*log(c*x^n))/e+1/2*b*n*x^2*(a+b*log(c*x^n))+1/2*x*(a+b*log(c*x^n))^2/e-1/4*x^2*(a+b*log(c*x^n))^2-1/4*b^2*n^2*log(1+e*x)/e^2+1/4*b^2*n^2*x^2*log(1+e*x)+1/2*b*n*(a+b*log(c*x^n))*log(1+e*x)/e^2-1/2*b*n*x^2*(a+b*log(c*x^n))*log(1+e*x)-1/2*(a+b*log(c*x^n))^2*log(1+e*x)/e^2+1/2*x^2*(a+b*log(c*x^n))^2*log(1+e*x)+1/2*b^2*n^2*polylog(2,-e*x)/e^2-b*n*(a+b*log(c*x^n))*polylog(2,-e*x)/e^2+b^2*n^2*polylog(3,-e*x)/e^2],
[(a+b*log(c*x^n))^2*log(1+e*x),x,14,2*a*b*n*x-6*b^2*n^2*x+2*b^2*n*x*log(c*x^n)+2*b*n*x*(a+b*log(c*x^n))-x*(a+b*log(c*x^n))^2+2*b^2*n^2*(1+e*x)*log(1+e*x)/e-2*b*n*(1+e*x)*(a+b*log(c*x^n))*log(1+e*x)/e+(1+e*x)*(a+b*log(c*x^n))^2*log(1+e*x)/e-2*b^2*n^2*polylog(2,-e*x)/e+2*b*n*(a+b*log(c*x^n))*polylog(2,-e*x)/e-2*b^2*n^2*polylog(3,-e*x)/e],
[(a+b*log(c*x^n))^2*log(1+e*x)/x,x,3,-(a+b*log(c*x^n))^2*polylog(2,-e*x)+2*b*n*(a+b*log(c*x^n))*polylog(3,-e*x)-2*b^2*n^2*polylog(4,-e*x)],
[(a+b*log(c*x^n))^2*log(1+e*x)/x^2,x,10,2*b^2*e*n^2*log(x)-2*b*e*n*log(1+1/(e*x))*(a+b*log(c*x^n))-e*log(1+1/(e*x))*(a+b*log(c*x^n))^2-2*b^2*e*n^2*log(1+e*x)-2*b^2*n^2*log(1+e*x)/x-2*b*n*(a+b*log(c*x^n))*log(1+e*x)/x-(a+b*log(c*x^n))^2*log(1+e*x)/x+2*b^2*e*n^2*polylog(2,(-1)/(e*x))+2*b*e*n*(a+b*log(c*x^n))*polylog(2,(-1)/(e*x))+2*b^2*e*n^2*polylog(3,(-1)/(e*x))],
[(a+b*log(c*x^n))^2*log(1+e*x)/x^3,x,14,-7/4*b^2*e*n^2/x-1/4*b^2*e^2*n^2*log(x)-3/2*b*e*n*(a+b*log(c*x^n))/x+1/2*b*e^2*n*log(1+1/(e*x))*(a+b*log(c*x^n))-1/2*e*(a+b*log(c*x^n))^2/x+1/2*e^2*log(1+1/(e*x))*(a+b*log(c*x^n))^2+1/4*b^2*e^2*n^2*log(1+e*x)-1/4*b^2*n^2*log(1+e*x)/x^2-1/2*b*n*(a+b*log(c*x^n))*log(1+e*x)/x^2-1/2*(a+b*log(c*x^n))^2*log(1+e*x)/x^2-1/2*b^2*e^2*n^2*polylog(2,(-1)/(e*x))-b*e^2*n*(a+b*log(c*x^n))*polylog(2,(-1)/(e*x))-b^2*e^2*n^2*polylog(3,(-1)/(e*x))],
[x^3*(a+b*log(c*x^n))^3*log(1+e*x),x,29,15/8*a*b^2*n^2*x/e^3-255/128*b^3*n^3*x/e^3+45/256*b^3*n^3*x^2/e^2-175/3456*b^3*n^3*x^3/e+3/128*b^3*n^3*x^4+15/8*b^3*n^2*x*log(c*x^n)/e^3+3/32*b^2*n^2*x*(a+b*log(c*x^n))/e^3-21/64*b^2*n^2*x^2*(a+b*log(c*x^n))/e^2+37/288*b^2*n^2*x^3*(a+b*log(c*x^n))/e-9/128*b^2*n^2*x^4*(a+b*log(c*x^n))-15/16*b*n*x*(a+b*log(c*x^n))^2/e^3+9/32*b*n*x^2*(a+b*log(c*x^n))^2/e^2-7/48*b*n*x^3*(a+b*log(c*x^n))^2/e+3/32*b*n*x^4*(a+b*log(c*x^n))^2+1/4*x*(a+b*log(c*x^n))^3/e^3-1/8*x^2*(a+b*log(c*x^n))^3/e^2+1/12*x^3*(a+b*log(c*x^n))^3/e-1/16*x^4*(a+b*log(c*x^n))^3+3/128*b^3*n^3*log(1+e*x)/e^4-3/128*b^3*n^3*x^4*log(1+e*x)-3/32*b^2*n^2*(a+b*log(c*x^n))*log(1+e*x)/e^4+3/32*b^2*n^2*x^4*(a+b*log(c*x^n))*log(1+e*x)+3/16*b*n*(a+b*log(c*x^n))^2*log(1+e*x)/e^4-3/16*b*n*x^4*(a+b*log(c*x^n))^2*log(1+e*x)-1/4*(a+b*log(c*x^n))^3*log(1+e*x)/e^4+1/4*x^4*(a+b*log(c*x^n))^3*log(1+e*x)-3/32*b^3*n^3*polylog(2,-e*x)/e^4+3/8*b^2*n^2*(a+b*log(c*x^n))*polylog(2,-e*x)/e^4-3/4*b*n*(a+b*log(c*x^n))^2*polylog(2,-e*x)/e^4-3/8*b^3*n^3*polylog(3,-e*x)/e^4+3/2*b^2*n^2*(a+b*log(c*x^n))*polylog(3,-e*x)/e^4-3/2*b^3*n^3*polylog(4,-e*x)/e^4],
[x^2*(a+b*log(c*x^n))^3*log(1+e*x),x,26,-8/3*a*b^2*n^2*x/e^2+80/27*b^3*n^3*x/e^2-65/216*b^3*n^3*x^2/e+8/81*b^3*n^3*x^3-8/3*b^3*n^2*x*log(c*x^n)/e^2-2/9*b^2*n^2*x*(a+b*log(c*x^n))/e^2+19/36*b^2*n^2*x^2*(a+b*log(c*x^n))/e-2/9*b^2*n^2*x^3*(a+b*log(c*x^n))+4/3*b*n*x*(a+b*log(c*x^n))^2/e^2-5/12*b*n*x^2*(a+b*log(c*x^n))^2/e+2/9*b*n*x^3*(a+b*log(c*x^n))^2-1/3*x*(a+b*log(c*x^n))^3/e^2+1/6*x^2*(a+b*log(c*x^n))^3/e-1/9*x^3*(a+b*log(c*x^n))^3-2/27*b^3*n^3*log(1+e*x)/e^3-2/27*b^3*n^3*x^3*log(1+e*x)+2/9*b^2*n^2*(a+b*log(c*x^n))*log(1+e*x)/e^3+2/9*b^2*n^2*x^3*(a+b*log(c*x^n))*log(1+e*x)-1/3*b*n*(a+b*log(c*x^n))^2*log(1+e*x)/e^3-1/3*b*n*x^3*(a+b*log(c*x^n))^2*log(1+e*x)+1/3*(a+b*log(c*x^n))^3*log(1+e*x)/e^3+1/3*x^3*(a+b*log(c*x^n))^3*log(1+e*x)+2/9*b^3*n^3*polylog(2,-e*x)/e^3-2/3*b^2*n^2*(a+b*log(c*x^n))*polylog(2,-e*x)/e^3+b*n*(a+b*log(c*x^n))^2*polylog(2,-e*x)/e^3+2/3*b^3*n^3*polylog(3,-e*x)/e^3-2*b^2*n^2*(a+b*log(c*x^n))*polylog(3,-e*x)/e^3+2*b^3*n^3*polylog(4,-e*x)/e^3],
[x*(a+b*log(c*x^n))^3*log(1+e*x),x,23,9/2*a*b^2*n^2*x/e-45/8*b^3*n^3*x/e+3/4*b^3*n^3*x^2+9/2*b^3*n^2*x*log(c*x^n)/e+3/4*b^2*n^2*x*(a+b*log(c*x^n))/e-9/8*b^2*n^2*x^2*(a+b*log(c*x^n))-9/4*b*n*x*(a+b*log(c*x^n))^2/e+3/4*b*n*x^2*(a+b*log(c*x^n))^2+1/2*x*(a+b*log(c*x^n))^3/e-1/4*x^2*(a+b*log(c*x^n))^3+3/8*b^3*n^3*log(1+e*x)/e^2-3/8*b^3*n^3*x^2*log(1+e*x)-3/4*b^2*n^2*(a+b*log(c*x^n))*log(1+e*x)/e^2+3/4*b^2*n^2*x^2*(a+b*log(c*x^n))*log(1+e*x)+3/4*b*n*(a+b*log(c*x^n))^2*log(1+e*x)/e^2-3/4*b*n*x^2*(a+b*log(c*x^n))^2*log(1+e*x)-1/2*(a+b*log(c*x^n))^3*log(1+e*x)/e^2+1/2*x^2*(a+b*log(c*x^n))^3*log(1+e*x)-3/4*b^3*n^3*polylog(2,-e*x)/e^2+3/2*b^2*n^2*(a+b*log(c*x^n))*polylog(2,-e*x)/e^2-3/2*b*n*(a+b*log(c*x^n))^2*polylog(2,-e*x)/e^2-3/2*b^3*n^3*polylog(3,-e*x)/e^2+3*b^2*n^2*(a+b*log(c*x^n))*polylog(3,-e*x)/e^2-3*b^3*n^3*polylog(4,-e*x)/e^2],
[(a+b*log(c*x^n))^3*log(1+e*x),x,24,-12*a*b^2*n^2*x+24*b^3*n^3*x-12*b^3*n^2*x*log(c*x^n)-6*b^2*n^2*x*(a+b*log(c*x^n))+6*b*n*x*(a+b*log(c*x^n))^2-x*(a+b*log(c*x^n))^3-6*b^3*n^3*(1+e*x)*log(1+e*x)/e+6*b^2*n^2*(1+e*x)*(a+b*log(c*x^n))*log(1+e*x)/e-3*b*n*(1+e*x)*(a+b*log(c*x^n))^2*log(1+e*x)/e+(1+e*x)*(a+b*log(c*x^n))^3*log(1+e*x)/e+6*b^3*n^3*polylog(2,-e*x)/e-6*b^2*n^2*(a+b*log(c*x^n))*polylog(2,-e*x)/e+3*b*n*(a+b*log(c*x^n))^2*polylog(2,-e*x)/e+6*b^3*n^3*polylog(3,-e*x)/e-6*b^2*n^2*(a+b*log(c*x^n))*polylog(3,-e*x)/e+6*b^3*n^3*polylog(4,-e*x)/e],
[(a+b*log(c*x^n))^3*log(1+e*x)/x,x,4,-(a+b*log(c*x^n))^3*polylog(2,-e*x)+3*b*n*(a+b*log(c*x^n))^2*polylog(3,-e*x)-6*b^2*n^2*(a+b*log(c*x^n))*polylog(4,-e*x)+6*b^3*n^3*polylog(5,-e*x)],
[(a+b*log(c*x^n))^3*log(1+e*x)/x^2,x,14,6*b^3*e*n^3*log(x)-6*b^2*e*n^2*log(1+1/(e*x))*(a+b*log(c*x^n))-3*b*e*n*log(1+1/(e*x))*(a+b*log(c*x^n))^2-e*log(1+1/(e*x))*(a+b*log(c*x^n))^3-6*b^3*e*n^3*log(1+e*x)-6*b^3*n^3*log(1+e*x)/x-6*b^2*n^2*(a+b*log(c*x^n))*log(1+e*x)/x-3*b*n*(a+b*log(c*x^n))^2*log(1+e*x)/x-(a+b*log(c*x^n))^3*log(1+e*x)/x+6*b^3*e*n^3*polylog(2,(-1)/(e*x))+6*b^2*e*n^2*(a+b*log(c*x^n))*polylog(2,(-1)/(e*x))+3*b*e*n*(a+b*log(c*x^n))^2*polylog(2,(-1)/(e*x))+6*b^3*e*n^3*polylog(3,(-1)/(e*x))+6*b^2*e*n^2*(a+b*log(c*x^n))*polylog(3,(-1)/(e*x))+6*b^3*e*n^3*polylog(4,(-1)/(e*x))],
[(a+b*log(c*x^n))^3*log(1+e*x)/x^3,x,22,-45/8*b^3*e*n^3/x-3/8*b^3*e^2*n^3*log(x)-21/4*b^2*e*n^2*(a+b*log(c*x^n))/x+3/4*b^2*e^2*n^2*log(1+1/(e*x))*(a+b*log(c*x^n))-9/4*b*e*n*(a+b*log(c*x^n))^2/x+3/4*b*e^2*n*log(1+1/(e*x))*(a+b*log(c*x^n))^2-1/2*e*(a+b*log(c*x^n))^3/x+1/2*e^2*log(1+1/(e*x))*(a+b*log(c*x^n))^3+3/8*b^3*e^2*n^3*log(1+e*x)-3/8*b^3*n^3*log(1+e*x)/x^2-3/4*b^2*n^2*(a+b*log(c*x^n))*log(1+e*x)/x^2-3/4*b*n*(a+b*log(c*x^n))^2*log(1+e*x)/x^2-1/2*(a+b*log(c*x^n))^3*log(1+e*x)/x^2-3/4*b^3*e^2*n^3*polylog(2,(-1)/(e*x))-3/2*b^2*e^2*n^2*(a+b*log(c*x^n))*polylog(2,(-1)/(e*x))-3/2*b*e^2*n*(a+b*log(c*x^n))^2*polylog(2,(-1)/(e*x))-3/2*b^3*e^2*n^3*polylog(3,(-1)/(e*x))-3*b^2*e^2*n^2*(a+b*log(c*x^n))*polylog(3,(-1)/(e*x))-3*b^3*e^2*n^3*polylog(4,(-1)/(e*x))],

# Integrands of the form x^q Log[d (e+f x^2)] (a+b Log[c x^n])^p when d e=1
[x^3*(a+b*log(c*x^n))*log(d*(1/d+f*x^2)),x,7,-3/16*b*n*x^2/(d*f)+1/16*b*n*x^4+1/4*x^2*(a+b*log(c*x^n))/(d*f)-1/8*x^4*(a+b*log(c*x^n))+1/16*b*n*log(1+d*f*x^2)/(d^2*f^2)-1/16*b*n*x^4*log(1+d*f*x^2)-1/4*(a+b*log(c*x^n))*log(1+d*f*x^2)/(d^2*f^2)+1/4*x^4*(a+b*log(c*x^n))*log(1+d*f*x^2)-1/8*b*n*polylog(2,-d*f*x^2)/(d^2*f^2)],
[x*(a+b*log(c*x^n))*log(d*(1/d+f*x^2)),x,8,1/2*b*n*x^2-1/2*x^2*(a+b*log(c*x^n))-1/4*b*n*(1+d*f*x^2)*log(1+d*f*x^2)/(d*f)+1/2*(1+d*f*x^2)*(a+b*log(c*x^n))*log(1+d*f*x^2)/(d*f)+1/4*b*n*polylog(2,-d*f*x^2)/(d*f)],
[(a+b*log(c*x^n))*log(d*(1/d+f*x^2))/x,x,2,-1/2*(a+b*log(c*x^n))*polylog(2,-d*f*x^2)+1/4*b*n*polylog(3,-d*f*x^2)],
[(a+b*log(c*x^n))*log(d*(1/d+f*x^2))/x^3,x,9,1/2*b*d*f*n*log(x)-1/2*b*d*f*n*log(x)^2+d*f*log(x)*(a+b*log(c*x^n))-1/4*b*d*f*n*log(1+d*f*x^2)-1/4*b*n*log(1+d*f*x^2)/x^2-1/2*d*f*(a+b*log(c*x^n))*log(1+d*f*x^2)-1/2*(a+b*log(c*x^n))*log(1+d*f*x^2)/x^2-1/4*b*d*f*n*polylog(2,-d*f*x^2)],
[x^2*(a+b*log(c*x^n))*log(d*(1/d+f*x^2)),x,9,-8/9*b*n*x/(d*f)+4/27*b*n*x^3+2/9*b*n*arctan(x*sqrt(d)*sqrt(f))/(d^(3/2)*f^(3/2))+2/3*x*(a+b*log(c*x^n))/(d*f)-2/9*x^3*(a+b*log(c*x^n))-2/3*arctan(x*sqrt(d)*sqrt(f))*(a+b*log(c*x^n))/(d^(3/2)*f^(3/2))-1/9*b*n*x^3*log(1+d*f*x^2)+1/3*x^3*(a+b*log(c*x^n))*log(1+d*f*x^2)+1/3*I*b*n*polylog(2,-I*x*sqrt(d)*sqrt(f))/(d^(3/2)*f^(3/2))-1/3*I*b*n*polylog(2,I*x*sqrt(d)*sqrt(f))/(d^(3/2)*f^(3/2))],
[(a+b*log(c*x^n))*log(d*(1/d+f*x^2)),x,8,4*b*n*x-2*x*(a+b*log(c*x^n))-b*n*x*log(1+d*f*x^2)+x*(a+b*log(c*x^n))*log(1+d*f*x^2)-2*b*n*arctan(x*sqrt(d)*sqrt(f))/(sqrt(d)*sqrt(f))+2*arctan(x*sqrt(d)*sqrt(f))*(a+b*log(c*x^n))/(sqrt(d)*sqrt(f))-I*b*n*polylog(2,-I*x*sqrt(d)*sqrt(f))/(sqrt(d)*sqrt(f))+I*b*n*polylog(2,I*x*sqrt(d)*sqrt(f))/(sqrt(d)*sqrt(f))],
[(a+b*log(c*x^n))*log(d*(1/d+f*x^2))/x^2,x,7,-b*n*log(1+d*f*x^2)/x-(a+b*log(c*x^n))*log(1+d*f*x^2)/x+2*b*n*arctan(x*sqrt(d)*sqrt(f))*sqrt(d)*sqrt(f)+2*arctan(x*sqrt(d)*sqrt(f))*(a+b*log(c*x^n))*sqrt(d)*sqrt(f)-I*b*n*polylog(2,-I*x*sqrt(d)*sqrt(f))*sqrt(d)*sqrt(f)+I*b*n*polylog(2,I*x*sqrt(d)*sqrt(f))*sqrt(d)*sqrt(f)],
[(a+b*log(c*x^n))*log(d*(1/d+f*x^2))/x^4,x,8,-8/9*b*d*f*n/x-2/9*b*d^(3/2)*f^(3/2)*n*arctan(x*sqrt(d)*sqrt(f))-2/3*d*f*(a+b*log(c*x^n))/x-2/3*d^(3/2)*f^(3/2)*arctan(x*sqrt(d)*sqrt(f))*(a+b*log(c*x^n))-1/9*b*n*log(1+d*f*x^2)/x^3-1/3*(a+b*log(c*x^n))*log(1+d*f*x^2)/x^3+1/3*I*b*d^(3/2)*f^(3/2)*n*polylog(2,-I*x*sqrt(d)*sqrt(f))-1/3*I*b*d^(3/2)*f^(3/2)*n*polylog(2,I*x*sqrt(d)*sqrt(f))],
[x^3*(a+b*log(c*x^n))^2*log(d*(1/d+f*x^2)),x,13,7/32*b^2*n^2*x^2/(d*f)-3/64*b^2*n^2*x^4-3/8*b*n*x^2*(a+b*log(c*x^n))/(d*f)+1/8*b*n*x^4*(a+b*log(c*x^n))+1/4*x^2*(a+b*log(c*x^n))^2/(d*f)-1/8*x^4*(a+b*log(c*x^n))^2-1/32*b^2*n^2*log(1+d*f*x^2)/(d^2*f^2)+1/32*b^2*n^2*x^4*log(1+d*f*x^2)+1/8*b*n*(a+b*log(c*x^n))*log(1+d*f*x^2)/(d^2*f^2)-1/8*b*n*x^4*(a+b*log(c*x^n))*log(1+d*f*x^2)-1/4*(a+b*log(c*x^n))^2*log(1+d*f*x^2)/(d^2*f^2)+1/4*x^4*(a+b*log(c*x^n))^2*log(1+d*f*x^2)+1/16*b^2*n^2*polylog(2,-d*f*x^2)/(d^2*f^2)-1/4*b*n*(a+b*log(c*x^n))*polylog(2,-d*f*x^2)/(d^2*f^2)+1/8*b^2*n^2*polylog(3,-d*f*x^2)/(d^2*f^2)],
[x*(a+b*log(c*x^n))^2*log(d*(1/d+f*x^2)),x,15,-3/4*b^2*n^2*x^2+b*n*x^2*(a+b*log(c*x^n))-1/2*x^2*(a+b*log(c*x^n))^2+1/4*b^2*n^2*(1+d*f*x^2)*log(1+d*f*x^2)/(d*f)-1/2*b*n*(1+d*f*x^2)*(a+b*log(c*x^n))*log(1+d*f*x^2)/(d*f)+1/2*(1+d*f*x^2)*(a+b*log(c*x^n))^2*log(1+d*f*x^2)/(d*f)-1/4*b^2*n^2*polylog(2,-d*f*x^2)/(d*f)+1/2*b*n*(a+b*log(c*x^n))*polylog(2,-d*f*x^2)/(d*f)-1/4*b^2*n^2*polylog(3,-d*f*x^2)/(d*f)],
[(a+b*log(c*x^n))^2*log(d*(1/d+f*x^2))/x,x,3,-1/2*(a+b*log(c*x^n))^2*polylog(2,-d*f*x^2)+1/2*b*n*(a+b*log(c*x^n))*polylog(3,-d*f*x^2)-1/4*b^2*n^2*polylog(4,-d*f*x^2)],
[(a+b*log(c*x^n))^2*log(d*(1/d+f*x^2))/x^3,x,11,1/2*b^2*d*f*n^2*log(x)-1/2*b*d*f*n*log(1+1/(d*f*x^2))*(a+b*log(c*x^n))-1/2*d*f*log(1+1/(d*f*x^2))*(a+b*log(c*x^n))^2-1/4*b^2*d*f*n^2*log(1+d*f*x^2)-1/4*b^2*n^2*log(1+d*f*x^2)/x^2-1/2*b*n*(a+b*log(c*x^n))*log(1+d*f*x^2)/x^2-1/2*(a+b*log(c*x^n))^2*log(1+d*f*x^2)/x^2+1/4*b^2*d*f*n^2*polylog(2,(-1)/(d*f*x^2))+1/2*b*d*f*n*(a+b*log(c*x^n))*polylog(2,(-1)/(d*f*x^2))+1/4*b^2*d*f*n^2*polylog(3,(-1)/(d*f*x^2))],
[x^2*(a+b*log(c*x^n))^2*log(d*(1/d+f*x^2)),x,30,-16/9*a*b*n*x/(d*f)+52/27*b^2*n^2*x/(d*f)-4/27*b^2*n^2*x^3-4/27*b^2*n^2*arctan(x*sqrt(d)*sqrt(f))/(d^(3/2)*f^(3/2))-16/9*b^2*n*x*log(c*x^n)/(d*f)+8/27*b*n*x^3*(a+b*log(c*x^n))+4/9*b*n*arctan(x*sqrt(d)*sqrt(f))*(a+b*log(c*x^n))/(d^(3/2)*f^(3/2))+2/3*x*(a+b*log(c*x^n))^2/(d*f)-2/9*x^3*(a+b*log(c*x^n))^2+2/27*b^2*n^2*x^3*log(1+d*f*x^2)-2/9*b*n*x^3*(a+b*log(c*x^n))*log(1+d*f*x^2)+1/3*x^3*(a+b*log(c*x^n))^2*log(1+d*f*x^2)-1/3*(a+b*log(c*x^n))^2*log(1-x*sqrt(-d)*sqrt(f))/((-d)^(3/2)*f^(3/2))+1/3*(a+b*log(c*x^n))^2*log(1+x*sqrt(-d)*sqrt(f))/((-d)^(3/2)*f^(3/2))+2/3*b*n*(a+b*log(c*x^n))*polylog(2,-x*sqrt(-d)*sqrt(f))/((-d)^(3/2)*f^(3/2))-2/3*b*n*(a+b*log(c*x^n))*polylog(2,x*sqrt(-d)*sqrt(f))/((-d)^(3/2)*f^(3/2))-2/9*I*b^2*n^2*polylog(2,-I*x*sqrt(d)*sqrt(f))/(d^(3/2)*f^(3/2))+2/9*I*b^2*n^2*polylog(2,I*x*sqrt(d)*sqrt(f))/(d^(3/2)*f^(3/2))-2/3*b^2*n^2*polylog(3,-x*sqrt(-d)*sqrt(f))/((-d)^(3/2)*f^(3/2))+2/3*b^2*n^2*polylog(3,x*sqrt(-d)*sqrt(f))/((-d)^(3/2)*f^(3/2))],
[(a+b*log(c*x^n))^2*log(d*(1/d+f*x^2)),x,26,4*a*b*n*x-8*b^2*n^2*x+4*b*n*(a-b*n)*x+8*b^2*n*x*log(c*x^n)-2*x*(a+b*log(c*x^n))^2-2*a*b*n*x*log(1+d*f*x^2)+2*b^2*n^2*x*log(1+d*f*x^2)-2*b^2*n*x*log(c*x^n)*log(1+d*f*x^2)+x*(a+b*log(c*x^n))^2*log(1+d*f*x^2)-(a+b*log(c*x^n))^2*log(1-x*sqrt(-d)*sqrt(f))/(sqrt(-d)*sqrt(f))+(a+b*log(c*x^n))^2*log(1+x*sqrt(-d)*sqrt(f))/(sqrt(-d)*sqrt(f))+2*b*n*(a+b*log(c*x^n))*polylog(2,-x*sqrt(-d)*sqrt(f))/(sqrt(-d)*sqrt(f))-2*b*n*(a+b*log(c*x^n))*polylog(2,x*sqrt(-d)*sqrt(f))/(sqrt(-d)*sqrt(f))-2*b^2*n^2*polylog(3,-x*sqrt(-d)*sqrt(f))/(sqrt(-d)*sqrt(f))+2*b^2*n^2*polylog(3,x*sqrt(-d)*sqrt(f))/(sqrt(-d)*sqrt(f))-4*b*n*(a-b*n)*arctan(x*sqrt(d)*sqrt(f))/(sqrt(d)*sqrt(f))-4*b^2*n*arctan(x*sqrt(d)*sqrt(f))*log(c*x^n)/(sqrt(d)*sqrt(f))+2*I*b^2*n^2*polylog(2,-I*x*sqrt(d)*sqrt(f))/(sqrt(d)*sqrt(f))-2*I*b^2*n^2*polylog(2,I*x*sqrt(d)*sqrt(f))/(sqrt(d)*sqrt(f))],
[(a+b*log(c*x^n))^2*log(d*(1/d+f*x^2))/x^2,x,16,-2*b^2*n^2*log(1+d*f*x^2)/x-2*b*n*(a+b*log(c*x^n))*log(1+d*f*x^2)/x-(a+b*log(c*x^n))^2*log(1+d*f*x^2)/x+(a+b*log(c*x^n))^2*log(1-x*sqrt(-d)*sqrt(f))*sqrt(-d)*sqrt(f)-(a+b*log(c*x^n))^2*log(1+x*sqrt(-d)*sqrt(f))*sqrt(-d)*sqrt(f)-2*b*n*(a+b*log(c*x^n))*polylog(2,-x*sqrt(-d)*sqrt(f))*sqrt(-d)*sqrt(f)+2*b*n*(a+b*log(c*x^n))*polylog(2,x*sqrt(-d)*sqrt(f))*sqrt(-d)*sqrt(f)+2*b^2*n^2*polylog(3,-x*sqrt(-d)*sqrt(f))*sqrt(-d)*sqrt(f)-2*b^2*n^2*polylog(3,x*sqrt(-d)*sqrt(f))*sqrt(-d)*sqrt(f)+4*b^2*n^2*arctan(x*sqrt(d)*sqrt(f))*sqrt(d)*sqrt(f)+4*b*n*arctan(x*sqrt(d)*sqrt(f))*(a+b*log(c*x^n))*sqrt(d)*sqrt(f)-2*I*b^2*n^2*polylog(2,-I*x*sqrt(d)*sqrt(f))*sqrt(d)*sqrt(f)+2*I*b^2*n^2*polylog(2,I*x*sqrt(d)*sqrt(f))*sqrt(d)*sqrt(f)],
[(a+b*log(c*x^n))^2*log(d*(1/d+f*x^2))/x^4,x,22,-52/27*b^2*d*f*n^2/x-4/27*b^2*d^(3/2)*f^(3/2)*n^2*arctan(x*sqrt(d)*sqrt(f))-16/9*b*d*f*n*(a+b*log(c*x^n))/x-4/9*b*d^(3/2)*f^(3/2)*n*arctan(x*sqrt(d)*sqrt(f))*(a+b*log(c*x^n))-2/3*d*f*(a+b*log(c*x^n))^2/x-2/27*b^2*n^2*log(1+d*f*x^2)/x^3-2/9*b*n*(a+b*log(c*x^n))*log(1+d*f*x^2)/x^3-1/3*(a+b*log(c*x^n))^2*log(1+d*f*x^2)/x^3+1/3*(-d)^(3/2)*f^(3/2)*(a+b*log(c*x^n))^2*log(1-x*sqrt(-d)*sqrt(f))-1/3*(-d)^(3/2)*f^(3/2)*(a+b*log(c*x^n))^2*log(1+x*sqrt(-d)*sqrt(f))-2/3*b*(-d)^(3/2)*f^(3/2)*n*(a+b*log(c*x^n))*polylog(2,-x*sqrt(-d)*sqrt(f))+2/3*b*(-d)^(3/2)*f^(3/2)*n*(a+b*log(c*x^n))*polylog(2,x*sqrt(-d)*sqrt(f))+2/9*I*b^2*d^(3/2)*f^(3/2)*n^2*polylog(2,-I*x*sqrt(d)*sqrt(f))-2/9*I*b^2*d^(3/2)*f^(3/2)*n^2*polylog(2,I*x*sqrt(d)*sqrt(f))+2/3*b^2*(-d)^(3/2)*f^(3/2)*n^2*polylog(3,-x*sqrt(-d)*sqrt(f))-2/3*b^2*(-d)^(3/2)*f^(3/2)*n^2*polylog(3,x*sqrt(-d)*sqrt(f))],
[x^3*(a+b*log(c*x^n))^3*log(d*(1/d+f*x^2)),x,22,-45/128*b^3*n^3*x^2/(d*f)+3/64*b^3*n^3*x^4+21/32*b^2*n^2*x^2*(a+b*log(c*x^n))/(d*f)-9/64*b^2*n^2*x^4*(a+b*log(c*x^n))-9/16*b*n*x^2*(a+b*log(c*x^n))^2/(d*f)+3/16*b*n*x^4*(a+b*log(c*x^n))^2+1/4*x^2*(a+b*log(c*x^n))^3/(d*f)-1/8*x^4*(a+b*log(c*x^n))^3+3/128*b^3*n^3*log(1+d*f*x^2)/(d^2*f^2)-3/128*b^3*n^3*x^4*log(1+d*f*x^2)-3/32*b^2*n^2*(a+b*log(c*x^n))*log(1+d*f*x^2)/(d^2*f^2)+3/32*b^2*n^2*x^4*(a+b*log(c*x^n))*log(1+d*f*x^2)+3/16*b*n*(a+b*log(c*x^n))^2*log(1+d*f*x^2)/(d^2*f^2)-3/16*b*n*x^4*(a+b*log(c*x^n))^2*log(1+d*f*x^2)-1/4*(a+b*log(c*x^n))^3*log(1+d*f*x^2)/(d^2*f^2)+1/4*x^4*(a+b*log(c*x^n))^3*log(1+d*f*x^2)-3/64*b^3*n^3*polylog(2,-d*f*x^2)/(d^2*f^2)+3/16*b^2*n^2*(a+b*log(c*x^n))*polylog(2,-d*f*x^2)/(d^2*f^2)-3/8*b*n*(a+b*log(c*x^n))^2*polylog(2,-d*f*x^2)/(d^2*f^2)-3/32*b^3*n^3*polylog(3,-d*f*x^2)/(d^2*f^2)+3/8*b^2*n^2*(a+b*log(c*x^n))*polylog(3,-d*f*x^2)/(d^2*f^2)-3/16*b^3*n^3*polylog(4,-d*f*x^2)/(d^2*f^2)],
[x*(a+b*log(c*x^n))^3*log(d*(1/d+f*x^2)),x,24,3/2*b^3*n^3*x^2-9/4*b^2*n^2*x^2*(a+b*log(c*x^n))+3/2*b*n*x^2*(a+b*log(c*x^n))^2-1/2*x^2*(a+b*log(c*x^n))^3-3/8*b^3*n^3*(1+d*f*x^2)*log(1+d*f*x^2)/(d*f)+3/4*b^2*n^2*(1+d*f*x^2)*(a+b*log(c*x^n))*log(1+d*f*x^2)/(d*f)-3/4*b*n*(1+d*f*x^2)*(a+b*log(c*x^n))^2*log(1+d*f*x^2)/(d*f)+1/2*(1+d*f*x^2)*(a+b*log(c*x^n))^3*log(1+d*f*x^2)/(d*f)+3/8*b^3*n^3*polylog(2,-d*f*x^2)/(d*f)-3/4*b^2*n^2*(a+b*log(c*x^n))*polylog(2,-d*f*x^2)/(d*f)+3/4*b*n*(a+b*log(c*x^n))^2*polylog(2,-d*f*x^2)/(d*f)+3/8*b^3*n^3*polylog(3,-d*f*x^2)/(d*f)-3/4*b^2*n^2*(a+b*log(c*x^n))*polylog(3,-d*f*x^2)/(d*f)+3/8*b^3*n^3*polylog(4,-d*f*x^2)/(d*f)],
[(a+b*log(c*x^n))^3*log(d*(1/d+f*x^2))/x,x,4,-1/2*(a+b*log(c*x^n))^3*polylog(2,-d*f*x^2)+3/4*b*n*(a+b*log(c*x^n))^2*polylog(3,-d*f*x^2)-3/4*b^2*n^2*(a+b*log(c*x^n))*polylog(4,-d*f*x^2)+3/8*b^3*n^3*polylog(5,-d*f*x^2)],
[(a+b*log(c*x^n))^3*log(d*(1/d+f*x^2))/x^3,x,15,3/4*b^3*d*f*n^3*log(x)-3/4*b^2*d*f*n^2*log(1+1/(d*f*x^2))*(a+b*log(c*x^n))-3/4*b*d*f*n*log(1+1/(d*f*x^2))*(a+b*log(c*x^n))^2-1/2*d*f*log(1+1/(d*f*x^2))*(a+b*log(c*x^n))^3-3/8*b^3*d*f*n^3*log(1+d*f*x^2)-3/8*b^3*n^3*log(1+d*f*x^2)/x^2-3/4*b^2*n^2*(a+b*log(c*x^n))*log(1+d*f*x^2)/x^2-3/4*b*n*(a+b*log(c*x^n))^2*log(1+d*f*x^2)/x^2-1/2*(a+b*log(c*x^n))^3*log(1+d*f*x^2)/x^2+3/8*b^3*d*f*n^3*polylog(2,(-1)/(d*f*x^2))+3/4*b^2*d*f*n^2*(a+b*log(c*x^n))*polylog(2,(-1)/(d*f*x^2))+3/4*b*d*f*n*(a+b*log(c*x^n))^2*polylog(2,(-1)/(d*f*x^2))+3/8*b^3*d*f*n^3*polylog(3,(-1)/(d*f*x^2))+3/4*b^2*d*f*n^2*(a+b*log(c*x^n))*polylog(3,(-1)/(d*f*x^2))+3/8*b^3*d*f*n^3*polylog(4,(-1)/(d*f*x^2))],
[(a+b*log(c*x^n))^3*log(d*(1/d+f*x^2)),x,42,-24*a*b^2*n^2*x+36*b^3*n^3*x-12*b^2*n^2*(a-b*n)*x-36*b^3*n^2*x*log(c*x^n)+12*b*n*x*(a+b*log(c*x^n))^2-2*x*(a+b*log(c*x^n))^3+6*a*b^2*n^2*x*log(1+d*f*x^2)-6*b^3*n^3*x*log(1+d*f*x^2)+6*b^3*n^2*x*log(c*x^n)*log(1+d*f*x^2)-3*b*n*x*(a+b*log(c*x^n))^2*log(1+d*f*x^2)+x*(a+b*log(c*x^n))^3*log(1+d*f*x^2)+3*b*n*(a+b*log(c*x^n))^2*log(1-x*sqrt(-d)*sqrt(f))/(sqrt(-d)*sqrt(f))-(a+b*log(c*x^n))^3*log(1-x*sqrt(-d)*sqrt(f))/(sqrt(-d)*sqrt(f))-3*b*n*(a+b*log(c*x^n))^2*log(1+x*sqrt(-d)*sqrt(f))/(sqrt(-d)*sqrt(f))+(a+b*log(c*x^n))^3*log(1+x*sqrt(-d)*sqrt(f))/(sqrt(-d)*sqrt(f))-6*b^2*n^2*(a+b*log(c*x^n))*polylog(2,-x*sqrt(-d)*sqrt(f))/(sqrt(-d)*sqrt(f))+3*b*n*(a+b*log(c*x^n))^2*polylog(2,-x*sqrt(-d)*sqrt(f))/(sqrt(-d)*sqrt(f))+6*b^2*n^2*(a+b*log(c*x^n))*polylog(2,x*sqrt(-d)*sqrt(f))/(sqrt(-d)*sqrt(f))-3*b*n*(a+b*log(c*x^n))^2*polylog(2,x*sqrt(-d)*sqrt(f))/(sqrt(-d)*sqrt(f))+6*b^3*n^3*polylog(3,-x*sqrt(-d)*sqrt(f))/(sqrt(-d)*sqrt(f))-6*b^2*n^2*(a+b*log(c*x^n))*polylog(3,-x*sqrt(-d)*sqrt(f))/(sqrt(-d)*sqrt(f))-6*b^3*n^3*polylog(3,x*sqrt(-d)*sqrt(f))/(sqrt(-d)*sqrt(f))+6*b^2*n^2*(a+b*log(c*x^n))*polylog(3,x*sqrt(-d)*sqrt(f))/(sqrt(-d)*sqrt(f))+6*b^3*n^3*polylog(4,-x*sqrt(-d)*sqrt(f))/(sqrt(-d)*sqrt(f))-6*b^3*n^3*polylog(4,x*sqrt(-d)*sqrt(f))/(sqrt(-d)*sqrt(f))+12*b^2*n^2*(a-b*n)*arctan(x*sqrt(d)*sqrt(f))/(sqrt(d)*sqrt(f))+12*b^3*n^2*arctan(x*sqrt(d)*sqrt(f))*log(c*x^n)/(sqrt(d)*sqrt(f))-6*I*b^3*n^3*polylog(2,-I*x*sqrt(d)*sqrt(f))/(sqrt(d)*sqrt(f))+6*I*b^3*n^3*polylog(2,I*x*sqrt(d)*sqrt(f))/(sqrt(d)*sqrt(f))],
[(a+b*log(c*x^n))^3*log(d*(1/d+f*x^2))/x^2,x,26,-6*b^3*n^3*log(1+d*f*x^2)/x-6*b^2*n^2*(a+b*log(c*x^n))*log(1+d*f*x^2)/x-3*b*n*(a+b*log(c*x^n))^2*log(1+d*f*x^2)/x-(a+b*log(c*x^n))^3*log(1+d*f*x^2)/x+3*b*n*(a+b*log(c*x^n))^2*log(1-x*sqrt(-d)*sqrt(f))*sqrt(-d)*sqrt(f)+(a+b*log(c*x^n))^3*log(1-x*sqrt(-d)*sqrt(f))*sqrt(-d)*sqrt(f)-3*b*n*(a+b*log(c*x^n))^2*log(1+x*sqrt(-d)*sqrt(f))*sqrt(-d)*sqrt(f)-(a+b*log(c*x^n))^3*log(1+x*sqrt(-d)*sqrt(f))*sqrt(-d)*sqrt(f)-6*b^2*n^2*(a+b*log(c*x^n))*polylog(2,-x*sqrt(-d)*sqrt(f))*sqrt(-d)*sqrt(f)-3*b*n*(a+b*log(c*x^n))^2*polylog(2,-x*sqrt(-d)*sqrt(f))*sqrt(-d)*sqrt(f)+6*b^2*n^2*(a+b*log(c*x^n))*polylog(2,x*sqrt(-d)*sqrt(f))*sqrt(-d)*sqrt(f)+3*b*n*(a+b*log(c*x^n))^2*polylog(2,x*sqrt(-d)*sqrt(f))*sqrt(-d)*sqrt(f)+6*b^3*n^3*polylog(3,-x*sqrt(-d)*sqrt(f))*sqrt(-d)*sqrt(f)+6*b^2*n^2*(a+b*log(c*x^n))*polylog(3,-x*sqrt(-d)*sqrt(f))*sqrt(-d)*sqrt(f)-6*b^3*n^3*polylog(3,x*sqrt(-d)*sqrt(f))*sqrt(-d)*sqrt(f)-6*b^2*n^2*(a+b*log(c*x^n))*polylog(3,x*sqrt(-d)*sqrt(f))*sqrt(-d)*sqrt(f)-6*b^3*n^3*polylog(4,-x*sqrt(-d)*sqrt(f))*sqrt(-d)*sqrt(f)+6*b^3*n^3*polylog(4,x*sqrt(-d)*sqrt(f))*sqrt(-d)*sqrt(f)+12*b^3*n^3*arctan(x*sqrt(d)*sqrt(f))*sqrt(d)*sqrt(f)+12*b^2*n^2*arctan(x*sqrt(d)*sqrt(f))*(a+b*log(c*x^n))*sqrt(d)*sqrt(f)-6*I*b^3*n^3*polylog(2,-I*x*sqrt(d)*sqrt(f))*sqrt(d)*sqrt(f)+6*I*b^3*n^3*polylog(2,I*x*sqrt(d)*sqrt(f))*sqrt(d)*sqrt(f)],

# Integrands of the form x^q Log[d (e+f x^(1/2))] (a+b Log[c x^n])^p when d e=1
[x^2*(a+b*log(c*x^n))*log(d*(1/d+f*sqrt(x))),x,7,2/9*b*n*x/(d^4*f^4)-1/9*b*n*x^(3/2)/(d^3*f^3)+5/72*b*n*x^2/(d^2*f^2)-11/225*b*n*x^(5/2)/(d*f)+1/27*b*n*x^3-1/6*x*(a+b*log(c*x^n))/(d^4*f^4)+1/9*x^(3/2)*(a+b*log(c*x^n))/(d^3*f^3)-1/12*x^2*(a+b*log(c*x^n))/(d^2*f^2)+1/15*x^(5/2)*(a+b*log(c*x^n))/(d*f)-1/18*x^3*(a+b*log(c*x^n))+1/9*b*n*log(1+d*f*sqrt(x))/(d^6*f^6)-1/9*b*n*x^3*log(1+d*f*sqrt(x))-1/3*(a+b*log(c*x^n))*log(1+d*f*sqrt(x))/(d^6*f^6)+1/3*x^3*(a+b*log(c*x^n))*log(1+d*f*sqrt(x))-2/3*b*n*polylog(2,-d*f*sqrt(x))/(d^6*f^6)-7/9*b*n*sqrt(x)/(d^5*f^5)+1/3*(a+b*log(c*x^n))*sqrt(x)/(d^5*f^5)],
[x*(a+b*log(c*x^n))*log(d*(1/d+f*sqrt(x))),x,7,3/8*b*n*x/(d^2*f^2)-7/36*b*n*x^(3/2)/(d*f)+1/8*b*n*x^2-1/4*x*(a+b*log(c*x^n))/(d^2*f^2)+1/6*x^(3/2)*(a+b*log(c*x^n))/(d*f)-1/8*x^2*(a+b*log(c*x^n))+1/4*b*n*log(1+d*f*sqrt(x))/(d^4*f^4)-1/4*b*n*x^2*log(1+d*f*sqrt(x))-1/2*(a+b*log(c*x^n))*log(1+d*f*sqrt(x))/(d^4*f^4)+1/2*x^2*(a+b*log(c*x^n))*log(1+d*f*sqrt(x))-b*n*polylog(2,-d*f*sqrt(x))/(d^4*f^4)-5/4*b*n*sqrt(x)/(d^3*f^3)+1/2*(a+b*log(c*x^n))*sqrt(x)/(d^3*f^3)],
[(a+b*log(c*x^n))*log(d*(1/d+f*sqrt(x))),x,7,b*n*x-1/2*x*(a+b*log(c*x^n))-b*n*x*log(d*(1/d+f*sqrt(x)))+x*(a+b*log(c*x^n))*log(d*(1/d+f*sqrt(x)))+b*n*log(1+d*f*sqrt(x))/(d^2*f^2)-(a+b*log(c*x^n))*log(1+d*f*sqrt(x))/(d^2*f^2)-2*b*n*polylog(2,-d*f*sqrt(x))/(d^2*f^2)-3*b*n*sqrt(x)/(d*f)+(a+b*log(c*x^n))*sqrt(x)/(d*f)],
[(a+b*log(c*x^n))*log(d*(1/d+f*sqrt(x)))/x,x,2,-2*(a+b*log(c*x^n))*polylog(2,-d*f*sqrt(x))+4*b*n*polylog(3,-d*f*sqrt(x))],
[(a+b*log(c*x^n))*log(d*(1/d+f*sqrt(x)))/x^2,x,8,-1/2*b*d^2*f^2*n*log(x)+1/4*b*d^2*f^2*n*log(x)^2-1/2*d^2*f^2*log(x)*(a+b*log(c*x^n))+b*d^2*f^2*n*log(1+d*f*sqrt(x))-b*n*log(1+d*f*sqrt(x))/x+d^2*f^2*(a+b*log(c*x^n))*log(1+d*f*sqrt(x))-(a+b*log(c*x^n))*log(1+d*f*sqrt(x))/x+2*b*d^2*f^2*n*polylog(2,-d*f*sqrt(x))-3*b*d*f*n/sqrt(x)-d*f*(a+b*log(c*x^n))/sqrt(x)],
[(a+b*log(c*x^n))*log(d*(1/d+f*sqrt(x)))/x^3,x,8,-7/36*b*d*f*n/x^(3/2)+3/8*b*d^2*f^2*n/x-1/8*b*d^4*f^4*n*log(x)+1/8*b*d^4*f^4*n*log(x)^2-1/6*d*f*(a+b*log(c*x^n))/x^(3/2)+1/4*d^2*f^2*(a+b*log(c*x^n))/x-1/4*d^4*f^4*log(x)*(a+b*log(c*x^n))+1/4*b*d^4*f^4*n*log(1+d*f*sqrt(x))-1/4*b*n*log(1+d*f*sqrt(x))/x^2+1/2*d^4*f^4*(a+b*log(c*x^n))*log(1+d*f*sqrt(x))-1/2*(a+b*log(c*x^n))*log(1+d*f*sqrt(x))/x^2+b*d^4*f^4*n*polylog(2,-d*f*sqrt(x))-5/4*b*d^3*f^3*n/sqrt(x)-1/2*d^3*f^3*(a+b*log(c*x^n))/sqrt(x)],
[(a+b*log(c*x^n))*log(d*(1/d+f*sqrt(x)))/x^4,x,8,-11/225*b*d*f*n/x^(5/2)+5/72*b*d^2*f^2*n/x^2-1/9*b*d^3*f^3*n/x^(3/2)+2/9*b*d^4*f^4*n/x-1/18*b*d^6*f^6*n*log(x)+1/12*b*d^6*f^6*n*log(x)^2-1/15*d*f*(a+b*log(c*x^n))/x^(5/2)+1/12*d^2*f^2*(a+b*log(c*x^n))/x^2-1/9*d^3*f^3*(a+b*log(c*x^n))/x^(3/2)+1/6*d^4*f^4*(a+b*log(c*x^n))/x-1/6*d^6*f^6*log(x)*(a+b*log(c*x^n))+1/9*b*d^6*f^6*n*log(1+d*f*sqrt(x))-1/9*b*n*log(1+d*f*sqrt(x))/x^3+1/3*d^6*f^6*(a+b*log(c*x^n))*log(1+d*f*sqrt(x))-1/3*(a+b*log(c*x^n))*log(1+d*f*sqrt(x))/x^3+2/3*b*d^6*f^6*n*polylog(2,-d*f*sqrt(x))-7/9*b*d^5*f^5*n/sqrt(x)-1/3*d^5*f^5*(a+b*log(c*x^n))/sqrt(x)],
[x^2*(a+b*log(c*x^n))^2*log(d*(1/d+f*sqrt(x))),x,18,1/3*a*b*n*x/(d^4*f^4)-13/27*b^2*n^2*x/(d^4*f^4)+14/81*b^2*n^2*x^(3/2)/(d^3*f^3)-19/216*b^2*n^2*x^2/(d^2*f^2)+182/3375*b^2*n^2*x^(5/2)/(d*f)-1/27*b^2*n^2*x^3+1/3*b^2*n*x*log(c*x^n)/(d^4*f^4)+1/9*b*n*x*(a+b*log(c*x^n))/(d^4*f^4)-2/9*b*n*x^(3/2)*(a+b*log(c*x^n))/(d^3*f^3)+5/36*b*n*x^2*(a+b*log(c*x^n))/(d^2*f^2)-22/225*b*n*x^(5/2)*(a+b*log(c*x^n))/(d*f)+2/27*b*n*x^3*(a+b*log(c*x^n))-1/6*x*(a+b*log(c*x^n))^2/(d^4*f^4)+1/9*x^(3/2)*(a+b*log(c*x^n))^2/(d^3*f^3)-1/12*x^2*(a+b*log(c*x^n))^2/(d^2*f^2)+1/15*x^(5/2)*(a+b*log(c*x^n))^2/(d*f)-1/18*x^3*(a+b*log(c*x^n))^2-2/27*b^2*n^2*log(1+d*f*sqrt(x))/(d^6*f^6)+2/27*b^2*n^2*x^3*log(1+d*f*sqrt(x))+2/9*b*n*(a+b*log(c*x^n))*log(1+d*f*sqrt(x))/(d^6*f^6)-2/9*b*n*x^3*(a+b*log(c*x^n))*log(1+d*f*sqrt(x))-1/3*(a+b*log(c*x^n))^2*log(1+d*f*sqrt(x))/(d^6*f^6)+1/3*x^3*(a+b*log(c*x^n))^2*log(1+d*f*sqrt(x))+4/9*b^2*n^2*polylog(2,-d*f*sqrt(x))/(d^6*f^6)-4/3*b*n*(a+b*log(c*x^n))*polylog(2,-d*f*sqrt(x))/(d^6*f^6)+8/3*b^2*n^2*polylog(3,-d*f*sqrt(x))/(d^6*f^6)+86/27*b^2*n^2*sqrt(x)/(d^5*f^5)-14/9*b*n*(a+b*log(c*x^n))*sqrt(x)/(d^5*f^5)+1/3*(a+b*log(c*x^n))^2*sqrt(x)/(d^5*f^5)],
[x*(a+b*log(c*x^n))^2*log(d*(1/d+f*sqrt(x))),x,16,1/2*a*b*n*x/(d^2*f^2)-7/8*b^2*n^2*x/(d^2*f^2)+37/108*b^2*n^2*x^(3/2)/(d*f)-3/16*b^2*n^2*x^2+1/2*b^2*n*x*log(c*x^n)/(d^2*f^2)+1/4*b*n*x*(a+b*log(c*x^n))/(d^2*f^2)-7/18*b*n*x^(3/2)*(a+b*log(c*x^n))/(d*f)+1/4*b*n*x^2*(a+b*log(c*x^n))-1/4*x*(a+b*log(c*x^n))^2/(d^2*f^2)+1/6*x^(3/2)*(a+b*log(c*x^n))^2/(d*f)-1/8*x^2*(a+b*log(c*x^n))^2-1/4*b^2*n^2*log(1+d*f*sqrt(x))/(d^4*f^4)+1/4*b^2*n^2*x^2*log(1+d*f*sqrt(x))+1/2*b*n*(a+b*log(c*x^n))*log(1+d*f*sqrt(x))/(d^4*f^4)-1/2*b*n*x^2*(a+b*log(c*x^n))*log(1+d*f*sqrt(x))-1/2*(a+b*log(c*x^n))^2*log(1+d*f*sqrt(x))/(d^4*f^4)+1/2*x^2*(a+b*log(c*x^n))^2*log(1+d*f*sqrt(x))+b^2*n^2*polylog(2,-d*f*sqrt(x))/(d^4*f^4)-2*b*n*(a+b*log(c*x^n))*polylog(2,-d*f*sqrt(x))/(d^4*f^4)+4*b^2*n^2*polylog(3,-d*f*sqrt(x))/(d^4*f^4)+21/4*b^2*n^2*sqrt(x)/(d^3*f^3)-5/2*b*n*(a+b*log(c*x^n))*sqrt(x)/(d^3*f^3)+1/2*(a+b*log(c*x^n))^2*sqrt(x)/(d^3*f^3)],
[(a+b*log(c*x^n))^2*log(d*(1/d+f*sqrt(x))),x,14,a*b*n*x-3*b^2*n^2*x+b^2*n*x*log(c*x^n)+b*n*x*(a+b*log(c*x^n))-1/2*x*(a+b*log(c*x^n))^2+2*b^2*n^2*x*log(d*(1/d+f*sqrt(x)))-2*b*n*x*(a+b*log(c*x^n))*log(d*(1/d+f*sqrt(x)))+x*(a+b*log(c*x^n))^2*log(d*(1/d+f*sqrt(x)))-2*b^2*n^2*log(1+d*f*sqrt(x))/(d^2*f^2)+2*b*n*(a+b*log(c*x^n))*log(1+d*f*sqrt(x))/(d^2*f^2)-(a+b*log(c*x^n))^2*log(1+d*f*sqrt(x))/(d^2*f^2)+4*b^2*n^2*polylog(2,-d*f*sqrt(x))/(d^2*f^2)-4*b*n*(a+b*log(c*x^n))*polylog(2,-d*f*sqrt(x))/(d^2*f^2)+8*b^2*n^2*polylog(3,-d*f*sqrt(x))/(d^2*f^2)+14*b^2*n^2*sqrt(x)/(d*f)-6*b*n*(a+b*log(c*x^n))*sqrt(x)/(d*f)+(a+b*log(c*x^n))^2*sqrt(x)/(d*f)],
[(a+b*log(c*x^n))^2*log(d*(1/d+f*sqrt(x)))/x,x,3,-2*(a+b*log(c*x^n))^2*polylog(2,-d*f*sqrt(x))+8*b*n*(a+b*log(c*x^n))*polylog(3,-d*f*sqrt(x))-16*b^2*n^2*polylog(4,-d*f*sqrt(x))],
[(a+b*log(c*x^n))^2*log(d*(1/d+f*sqrt(x)))/x^2,x,17,-b^2*d^2*f^2*n^2*log(x)+1/2*b^2*d^2*f^2*n^2*log(x)^2-b*d^2*f^2*n*log(x)*(a+b*log(c*x^n))-1/6*d^2*f^2*(a+b*log(c*x^n))^3/(b*n)+2*b^2*d^2*f^2*n^2*log(1+d*f*sqrt(x))-2*b^2*n^2*log(1+d*f*sqrt(x))/x+2*b*d^2*f^2*n*(a+b*log(c*x^n))*log(1+d*f*sqrt(x))-2*b*n*(a+b*log(c*x^n))*log(1+d*f*sqrt(x))/x+d^2*f^2*(a+b*log(c*x^n))^2*log(1+d*f*sqrt(x))-(a+b*log(c*x^n))^2*log(1+d*f*sqrt(x))/x+4*b^2*d^2*f^2*n^2*polylog(2,-d*f*sqrt(x))+4*b*d^2*f^2*n*(a+b*log(c*x^n))*polylog(2,-d*f*sqrt(x))-8*b^2*d^2*f^2*n^2*polylog(3,-d*f*sqrt(x))-14*b^2*d*f*n^2/sqrt(x)-6*b*d*f*n*(a+b*log(c*x^n))/sqrt(x)-d*f*(a+b*log(c*x^n))^2/sqrt(x)],
[(a+b*log(c*x^n))^2*log(d*(1/d+f*sqrt(x)))/x^3,x,19,-37/108*b^2*d*f*n^2/x^(3/2)+7/8*b^2*d^2*f^2*n^2/x-1/8*b^2*d^4*f^4*n^2*log(x)+1/8*b^2*d^4*f^4*n^2*log(x)^2-7/18*b*d*f*n*(a+b*log(c*x^n))/x^(3/2)+3/4*b*d^2*f^2*n*(a+b*log(c*x^n))/x-1/4*b*d^4*f^4*n*log(x)*(a+b*log(c*x^n))-1/6*d*f*(a+b*log(c*x^n))^2/x^(3/2)+1/4*d^2*f^2*(a+b*log(c*x^n))^2/x-1/12*d^4*f^4*(a+b*log(c*x^n))^3/(b*n)+1/4*b^2*d^4*f^4*n^2*log(1+d*f*sqrt(x))-1/4*b^2*n^2*log(1+d*f*sqrt(x))/x^2+1/2*b*d^4*f^4*n*(a+b*log(c*x^n))*log(1+d*f*sqrt(x))-1/2*b*n*(a+b*log(c*x^n))*log(1+d*f*sqrt(x))/x^2+1/2*d^4*f^4*(a+b*log(c*x^n))^2*log(1+d*f*sqrt(x))-1/2*(a+b*log(c*x^n))^2*log(1+d*f*sqrt(x))/x^2+b^2*d^4*f^4*n^2*polylog(2,-d*f*sqrt(x))+2*b*d^4*f^4*n*(a+b*log(c*x^n))*polylog(2,-d*f*sqrt(x))-4*b^2*d^4*f^4*n^2*polylog(3,-d*f*sqrt(x))-21/4*b^2*d^3*f^3*n^2/sqrt(x)-5/2*b*d^3*f^3*n*(a+b*log(c*x^n))/sqrt(x)-1/2*d^3*f^3*(a+b*log(c*x^n))^2/sqrt(x)],
[x*(a+b*log(c*x^n))^3*log(d*(1/d+f*sqrt(x))),x,30,-9/4*a*b^2*n^2*x/(d^2*f^2)+45/16*b^3*n^3*x/(d^2*f^2)-175/216*b^3*n^3*x^(3/2)/(d*f)+3/8*b^3*n^3*x^2-9/4*b^3*n^2*x*log(c*x^n)/(d^2*f^2)-3/8*b^2*n^2*x*(a+b*log(c*x^n))/(d^2*f^2)+37/36*b^2*n^2*x^(3/2)*(a+b*log(c*x^n))/(d*f)-9/16*b^2*n^2*x^2*(a+b*log(c*x^n))+9/8*b*n*x*(a+b*log(c*x^n))^2/(d^2*f^2)-7/12*b*n*x^(3/2)*(a+b*log(c*x^n))^2/(d*f)+3/8*b*n*x^2*(a+b*log(c*x^n))^2-1/4*x*(a+b*log(c*x^n))^3/(d^2*f^2)+1/6*x^(3/2)*(a+b*log(c*x^n))^3/(d*f)-1/8*x^2*(a+b*log(c*x^n))^3+3/8*b^3*n^3*log(1+d*f*sqrt(x))/(d^4*f^4)-3/8*b^3*n^3*x^2*log(1+d*f*sqrt(x))-3/4*b^2*n^2*(a+b*log(c*x^n))*log(1+d*f*sqrt(x))/(d^4*f^4)+3/4*b^2*n^2*x^2*(a+b*log(c*x^n))*log(1+d*f*sqrt(x))+3/4*b*n*(a+b*log(c*x^n))^2*log(1+d*f*sqrt(x))/(d^4*f^4)-3/4*b*n*x^2*(a+b*log(c*x^n))^2*log(1+d*f*sqrt(x))-1/2*(a+b*log(c*x^n))^3*log(1+d*f*sqrt(x))/(d^4*f^4)+1/2*x^2*(a+b*log(c*x^n))^3*log(1+d*f*sqrt(x))-3/2*b^3*n^3*polylog(2,-d*f*sqrt(x))/(d^4*f^4)+3*b^2*n^2*(a+b*log(c*x^n))*polylog(2,-d*f*sqrt(x))/(d^4*f^4)-3*b*n*(a+b*log(c*x^n))^2*polylog(2,-d*f*sqrt(x))/(d^4*f^4)-6*b^3*n^3*polylog(3,-d*f*sqrt(x))/(d^4*f^4)+12*b^2*n^2*(a+b*log(c*x^n))*polylog(3,-d*f*sqrt(x))/(d^4*f^4)-24*b^3*n^3*polylog(4,-d*f*sqrt(x))/(d^4*f^4)-255/8*b^3*n^3*sqrt(x)/(d^3*f^3)+63/4*b^2*n^2*(a+b*log(c*x^n))*sqrt(x)/(d^3*f^3)-15/4*b*n*(a+b*log(c*x^n))^2*sqrt(x)/(d^3*f^3)+1/2*(a+b*log(c*x^n))^3*sqrt(x)/(d^3*f^3)],
[(a+b*log(c*x^n))^3*log(d*(1/d+f*sqrt(x))),x,24,-6*a*b^2*n^2*x+12*b^3*n^3*x-6*b^3*n^2*x*log(c*x^n)-3*b^2*n^2*x*(a+b*log(c*x^n))+3*b*n*x*(a+b*log(c*x^n))^2-1/2*x*(a+b*log(c*x^n))^3-6*b^3*n^3*x*log(d*(1/d+f*sqrt(x)))+6*b^2*n^2*x*(a+b*log(c*x^n))*log(d*(1/d+f*sqrt(x)))-3*b*n*x*(a+b*log(c*x^n))^2*log(d*(1/d+f*sqrt(x)))+x*(a+b*log(c*x^n))^3*log(d*(1/d+f*sqrt(x)))+6*b^3*n^3*log(1+d*f*sqrt(x))/(d^2*f^2)-6*b^2*n^2*(a+b*log(c*x^n))*log(1+d*f*sqrt(x))/(d^2*f^2)+3*b*n*(a+b*log(c*x^n))^2*log(1+d*f*sqrt(x))/(d^2*f^2)-(a+b*log(c*x^n))^3*log(1+d*f*sqrt(x))/(d^2*f^2)-12*b^3*n^3*polylog(2,-d*f*sqrt(x))/(d^2*f^2)+12*b^2*n^2*(a+b*log(c*x^n))*polylog(2,-d*f*sqrt(x))/(d^2*f^2)-6*b*n*(a+b*log(c*x^n))^2*polylog(2,-d*f*sqrt(x))/(d^2*f^2)-24*b^3*n^3*polylog(3,-d*f*sqrt(x))/(d^2*f^2)+24*b^2*n^2*(a+b*log(c*x^n))*polylog(3,-d*f*sqrt(x))/(d^2*f^2)-48*b^3*n^3*polylog(4,-d*f*sqrt(x))/(d^2*f^2)-90*b^3*n^3*sqrt(x)/(d*f)+42*b^2*n^2*(a+b*log(c*x^n))*sqrt(x)/(d*f)-9*b*n*(a+b*log(c*x^n))^2*sqrt(x)/(d*f)+(a+b*log(c*x^n))^3*sqrt(x)/(d*f)],
[(a+b*log(c*x^n))^3*log(d*(1/d+f*sqrt(x)))/x,x,4,-2*(a+b*log(c*x^n))^3*polylog(2,-d*f*sqrt(x))+12*b*n*(a+b*log(c*x^n))^2*polylog(3,-d*f*sqrt(x))-48*b^2*n^2*(a+b*log(c*x^n))*polylog(4,-d*f*sqrt(x))+96*b^3*n^3*polylog(5,-d*f*sqrt(x))],
[(a+b*log(c*x^n))^3*log(d*(1/d+f*sqrt(x)))/x^2,x,28,-3*b^3*d^2*f^2*n^3*log(x)+3/2*b^3*d^2*f^2*n^3*log(x)^2-3*b^2*d^2*f^2*n^2*log(x)*(a+b*log(c*x^n))-1/2*d^2*f^2*(a+b*log(c*x^n))^3-1/8*d^2*f^2*(a+b*log(c*x^n))^4/(b*n)+6*b^3*d^2*f^2*n^3*log(1+d*f*sqrt(x))-6*b^3*n^3*log(1+d*f*sqrt(x))/x+6*b^2*d^2*f^2*n^2*(a+b*log(c*x^n))*log(1+d*f*sqrt(x))-6*b^2*n^2*(a+b*log(c*x^n))*log(1+d*f*sqrt(x))/x+3*b*d^2*f^2*n*(a+b*log(c*x^n))^2*log(1+d*f*sqrt(x))-3*b*n*(a+b*log(c*x^n))^2*log(1+d*f*sqrt(x))/x+d^2*f^2*(a+b*log(c*x^n))^3*log(1+d*f*sqrt(x))-(a+b*log(c*x^n))^3*log(1+d*f*sqrt(x))/x+12*b^3*d^2*f^2*n^3*polylog(2,-d*f*sqrt(x))+12*b^2*d^2*f^2*n^2*(a+b*log(c*x^n))*polylog(2,-d*f*sqrt(x))+6*b*d^2*f^2*n*(a+b*log(c*x^n))^2*polylog(2,-d*f*sqrt(x))-24*b^3*d^2*f^2*n^3*polylog(3,-d*f*sqrt(x))-24*b^2*d^2*f^2*n^2*(a+b*log(c*x^n))*polylog(3,-d*f*sqrt(x))+48*b^3*d^2*f^2*n^3*polylog(4,-d*f*sqrt(x))-90*b^3*d*f*n^3/sqrt(x)-42*b^2*d*f*n^2*(a+b*log(c*x^n))/sqrt(x)-9*b*d*f*n*(a+b*log(c*x^n))^2/sqrt(x)-d*f*(a+b*log(c*x^n))^3/sqrt(x)],
[(a+b*log(c*x^n))^3*log(d*(1/d+f*sqrt(x)))/x^3,x,34,-175/216*b^3*d*f*n^3/x^(3/2)+45/16*b^3*d^2*f^2*n^3/x-3/16*b^3*d^4*f^4*n^3*log(x)+3/16*b^3*d^4*f^4*n^3*log(x)^2-37/36*b^2*d*f*n^2*(a+b*log(c*x^n))/x^(3/2)+21/8*b^2*d^2*f^2*n^2*(a+b*log(c*x^n))/x-3/8*b^2*d^4*f^4*n^2*log(x)*(a+b*log(c*x^n))-7/12*b*d*f*n*(a+b*log(c*x^n))^2/x^(3/2)+9/8*b*d^2*f^2*n*(a+b*log(c*x^n))^2/x-1/8*d^4*f^4*(a+b*log(c*x^n))^3-1/6*d*f*(a+b*log(c*x^n))^3/x^(3/2)+1/4*d^2*f^2*(a+b*log(c*x^n))^3/x-1/16*d^4*f^4*(a+b*log(c*x^n))^4/(b*n)+3/8*b^3*d^4*f^4*n^3*log(1+d*f*sqrt(x))-3/8*b^3*n^3*log(1+d*f*sqrt(x))/x^2+3/4*b^2*d^4*f^4*n^2*(a+b*log(c*x^n))*log(1+d*f*sqrt(x))-3/4*b^2*n^2*(a+b*log(c*x^n))*log(1+d*f*sqrt(x))/x^2+3/4*b*d^4*f^4*n*(a+b*log(c*x^n))^2*log(1+d*f*sqrt(x))-3/4*b*n*(a+b*log(c*x^n))^2*log(1+d*f*sqrt(x))/x^2+1/2*d^4*f^4*(a+b*log(c*x^n))^3*log(1+d*f*sqrt(x))-1/2*(a+b*log(c*x^n))^3*log(1+d*f*sqrt(x))/x^2+3/2*b^3*d^4*f^4*n^3*polylog(2,-d*f*sqrt(x))+3*b^2*d^4*f^4*n^2*(a+b*log(c*x^n))*polylog(2,-d*f*sqrt(x))+3*b*d^4*f^4*n*(a+b*log(c*x^n))^2*polylog(2,-d*f*sqrt(x))-6*b^3*d^4*f^4*n^3*polylog(3,-d*f*sqrt(x))-12*b^2*d^4*f^4*n^2*(a+b*log(c*x^n))*polylog(3,-d*f*sqrt(x))+24*b^3*d^4*f^4*n^3*polylog(4,-d*f*sqrt(x))-255/8*b^3*d^3*f^3*n^3/sqrt(x)-63/4*b^2*d^3*f^3*n^2*(a+b*log(c*x^n))/sqrt(x)-15/4*b*d^3*f^3*n*(a+b*log(c*x^n))^2/sqrt(x)-1/2*d^3*f^3*(a+b*log(c*x^n))^3/sqrt(x)],

# Integrands of the form x^q Log[d (e+f x^m)] (a+b Log[c x^n])^p when d e=1
[(a+b*log(c*x^n))^4*log(d*(1/d+f*x^m))/x,x,5,-(a+b*log(c*x^n))^4*polylog(2,-d*f*x^m)/m+4*b*n*(a+b*log(c*x^n))^3*polylog(3,-d*f*x^m)/m^2-12*b^2*n^2*(a+b*log(c*x^n))^2*polylog(4,-d*f*x^m)/m^3+24*b^3*n^3*(a+b*log(c*x^n))*polylog(5,-d*f*x^m)/m^4-24*b^4*n^4*polylog(6,-d*f*x^m)/m^5],
[(a+b*log(c*x^n))^3*log(d*(1/d+f*x^m))/x,x,4,-(a+b*log(c*x^n))^3*polylog(2,-d*f*x^m)/m+3*b*n*(a+b*log(c*x^n))^2*polylog(3,-d*f*x^m)/m^2-6*b^2*n^2*(a+b*log(c*x^n))*polylog(4,-d*f*x^m)/m^3+6*b^3*n^3*polylog(5,-d*f*x^m)/m^4],
[(a+b*log(c*x^n))^2*log(d*(1/d+f*x^m))/x,x,3,-(a+b*log(c*x^n))^2*polylog(2,-d*f*x^m)/m+2*b*n*(a+b*log(c*x^n))*polylog(3,-d*f*x^m)/m^2-2*b^2*n^2*polylog(4,-d*f*x^m)/m^3],
[(a+b*log(c*x^n))*log(d*(1/d+f*x^m))/x,x,2,-(a+b*log(c*x^n))*polylog(2,-d*f*x^m)/m+b*n*polylog(3,-d*f*x^m)/m^2],
[log(d*(1/d+f*x^m))/(x*(a+b*log(c*x^n))),x,0,Unintegrable(log(d*(1/d+f*x^m))/(x*(a+b*log(c*x^n))),x)],
[log(d*(1/d+f*x^m))/(x*(a+b*log(c*x^n))^2),x,0,Unintegrable(log(d*(1/d+f*x^m))/(x*(a+b*log(c*x^n))^2),x)],

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

# Integrands of the form x^q Log[d (e+f x^1)^k] (a+b Log[c x^n])^p
[x^3*(a+b*log(c*x^n))*log(d*(e+f*x)^m),x,7,-5/16*b*e^3*m*n*x/f^3+3/32*b*e^2*m*n*x^2/f^2-7/144*b*e*m*n*x^3/f+1/32*b*m*n*x^4+1/4*e^3*m*x*(a+b*log(c*x^n))/f^3-1/8*e^2*m*x^2*(a+b*log(c*x^n))/f^2+1/12*e*m*x^3*(a+b*log(c*x^n))/f-1/16*m*x^4*(a+b*log(c*x^n))+1/16*b*e^4*m*n*log(e+f*x)/f^4+1/4*b*e^4*m*n*log(-f*x/e)*log(e+f*x)/f^4-1/4*e^4*m*(a+b*log(c*x^n))*log(e+f*x)/f^4-1/16*b*n*x^4*log(d*(e+f*x)^m)+1/4*x^4*(a+b*log(c*x^n))*log(d*(e+f*x)^m)+1/4*b*e^4*m*n*polylog(2,1+f*x/e)/f^4],
[x^2*(a+b*log(c*x^n))*log(d*(e+f*x)^m),x,7,4/9*b*e^2*m*n*x/f^2-5/36*b*e*m*n*x^2/f+2/27*b*m*n*x^3-1/3*e^2*m*x*(a+b*log(c*x^n))/f^2+1/6*e*m*x^2*(a+b*log(c*x^n))/f-1/9*m*x^3*(a+b*log(c*x^n))-1/9*b*e^3*m*n*log(e+f*x)/f^3-1/3*b*e^3*m*n*log(-f*x/e)*log(e+f*x)/f^3+1/3*e^3*m*(a+b*log(c*x^n))*log(e+f*x)/f^3-1/9*b*n*x^3*log(d*(e+f*x)^m)+1/3*x^3*(a+b*log(c*x^n))*log(d*(e+f*x)^m)-1/3*b*e^3*m*n*polylog(2,1+f*x/e)/f^3],
[x*(a+b*log(c*x^n))*log(d*(e+f*x)^m),x,7,-3/4*b*e*m*n*x/f+1/4*b*m*n*x^2+1/2*e*m*x*(a+b*log(c*x^n))/f-1/4*m*x^2*(a+b*log(c*x^n))+1/4*b*e^2*m*n*log(e+f*x)/f^2+1/2*b*e^2*m*n*log(-f*x/e)*log(e+f*x)/f^2-1/2*e^2*m*(a+b*log(c*x^n))*log(e+f*x)/f^2-1/4*b*n*x^2*log(d*(e+f*x)^m)+1/2*x^2*(a+b*log(c*x^n))*log(d*(e+f*x)^m)+1/2*b*e^2*m*n*polylog(2,1+f*x/e)/f^2],
[(a+b*log(c*x^n))*log(d*(e+f*x)^m),x,8,2*b*m*n*x-m*x*(a+b*log(c*x^n))-b*n*(e+f*x)*log(d*(e+f*x)^m)/f-b*e*n*log(-f*x/e)*log(d*(e+f*x)^m)/f+(e+f*x)*(a+b*log(c*x^n))*log(d*(e+f*x)^m)/f-b*e*m*n*polylog(2,1+f*x/e)/f],
[(a+b*log(c*x^n))*log(d*(e+f*x)^m)/x,x,4,1/2*(a+b*log(c*x^n))^2*log(d*(e+f*x)^m)/(b*n)-1/2*m*(a+b*log(c*x^n))^2*log(1+f*x/e)/(b*n)-m*(a+b*log(c*x^n))*polylog(2,-f*x/e)+b*m*n*polylog(3,-f*x/e)],
[(a+b*log(c*x^n))*log(d*(e+f*x)^m)/x^2,x,9,b*f*m*n*log(x)/e-1/2*b*f*m*n*log(x)^2/e+f*m*log(x)*(a+b*log(c*x^n))/e-b*f*m*n*log(e+f*x)/e+b*f*m*n*log(-f*x/e)*log(e+f*x)/e-f*m*(a+b*log(c*x^n))*log(e+f*x)/e-b*n*log(d*(e+f*x)^m)/x-(a+b*log(c*x^n))*log(d*(e+f*x)^m)/x+b*f*m*n*polylog(2,1+f*x/e)/e],
[(a+b*log(c*x^n))*log(d*(e+f*x)^m)/x^3,x,8,-3/4*b*f*m*n/(e*x)-1/4*b*f^2*m*n*log(x)/e^2+1/4*b*f^2*m*n*log(x)^2/e^2-1/2*f*m*(a+b*log(c*x^n))/(e*x)-1/2*f^2*m*log(x)*(a+b*log(c*x^n))/e^2+1/4*b*f^2*m*n*log(e+f*x)/e^2-1/2*b*f^2*m*n*log(-f*x/e)*log(e+f*x)/e^2+1/2*f^2*m*(a+b*log(c*x^n))*log(e+f*x)/e^2-1/4*b*n*log(d*(e+f*x)^m)/x^2-1/2*(a+b*log(c*x^n))*log(d*(e+f*x)^m)/x^2-1/2*b*f^2*m*n*polylog(2,1+f*x/e)/e^2],
[(a+b*log(c*x^n))*log(d*(e+f*x)^m)/x^4,x,8,-5/36*b*f*m*n/(e*x^2)+4/9*b*f^2*m*n/(e^2*x)+1/9*b*f^3*m*n*log(x)/e^3-1/6*b*f^3*m*n*log(x)^2/e^3-1/6*f*m*(a+b*log(c*x^n))/(e*x^2)+1/3*f^2*m*(a+b*log(c*x^n))/(e^2*x)+1/3*f^3*m*log(x)*(a+b*log(c*x^n))/e^3-1/9*b*f^3*m*n*log(e+f*x)/e^3+1/3*b*f^3*m*n*log(-f*x/e)*log(e+f*x)/e^3-1/3*f^3*m*(a+b*log(c*x^n))*log(e+f*x)/e^3-1/9*b*n*log(d*(e+f*x)^m)/x^3-1/3*(a+b*log(c*x^n))*log(d*(e+f*x)^m)/x^3+1/3*b*f^3*m*n*polylog(2,1+f*x/e)/e^3],
[x^2*(a+b*log(c*x^n))^2*log(d*(e+f*x)^m),x,24,8/9*a*b*e^2*m*n*x/f^2-26/27*b^2*e^2*m*n^2*x/f^2+19/108*b^2*e*m*n^2*x^2/f-2/27*b^2*m*n^2*x^3+8/9*b^2*e^2*m*n*x*log(c*x^n)/f^2-5/18*b*e*m*n*x^2*(a+b*log(c*x^n))/f+4/27*b*m*n*x^3*(a+b*log(c*x^n))-1/3*e^2*m*x*(a+b*log(c*x^n))^2/f^2+1/6*e*m*x^2*(a+b*log(c*x^n))^2/f-1/9*m*x^3*(a+b*log(c*x^n))^2+2/27*b^2*e^3*m*n^2*log(e+f*x)/f^3+2/27*b^2*n^2*x^3*log(d*(e+f*x)^m)-2/9*b*n*x^3*(a+b*log(c*x^n))*log(d*(e+f*x)^m)+1/3*x^3*(a+b*log(c*x^n))^2*log(d*(e+f*x)^m)-2/9*b*e^3*m*n*(a+b*log(c*x^n))*log(1+f*x/e)/f^3+1/3*e^3*m*(a+b*log(c*x^n))^2*log(1+f*x/e)/f^3-2/9*b^2*e^3*m*n^2*polylog(2,-f*x/e)/f^3+2/3*b*e^3*m*n*(a+b*log(c*x^n))*polylog(2,-f*x/e)/f^3-2/3*b^2*e^3*m*n^2*polylog(3,-f*x/e)/f^3],
[x*(a+b*log(c*x^n))^2*log(d*(e+f*x)^m),x,21,-3/2*a*b*e*m*n*x/f+7/4*b^2*e*m*n^2*x/f-3/8*b^2*m*n^2*x^2-3/2*b^2*e*m*n*x*log(c*x^n)/f+1/2*b*m*n*x^2*(a+b*log(c*x^n))+1/2*e*m*x*(a+b*log(c*x^n))^2/f-1/4*m*x^2*(a+b*log(c*x^n))^2-1/4*b^2*e^2*m*n^2*log(e+f*x)/f^2+1/4*b^2*n^2*x^2*log(d*(e+f*x)^m)-1/2*b*n*x^2*(a+b*log(c*x^n))*log(d*(e+f*x)^m)+1/2*x^2*(a+b*log(c*x^n))^2*log(d*(e+f*x)^m)+1/2*b*e^2*m*n*(a+b*log(c*x^n))*log(1+f*x/e)/f^2-1/2*e^2*m*(a+b*log(c*x^n))^2*log(1+f*x/e)/f^2+1/2*b^2*e^2*m*n^2*polylog(2,-f*x/e)/f^2-b*e^2*m*n*(a+b*log(c*x^n))*polylog(2,-f*x/e)/f^2+b^2*e^2*m*n^2*polylog(3,-f*x/e)/f^2],
[(a+b*log(c*x^n))^2*log(d*(e+f*x)^m),x,18,2*a*b*m*n*x-4*b^2*m*n^2*x+2*b*m*n*(a-b*n)*x+4*b^2*m*n*x*log(c*x^n)-m*x*(a+b*log(c*x^n))^2-2*b*e*m*n*(a-b*n)*log(e+f*x)/f-2*a*b*n*x*log(d*(e+f*x)^m)+2*b^2*n^2*x*log(d*(e+f*x)^m)-2*b^2*n*x*log(c*x^n)*log(d*(e+f*x)^m)+x*(a+b*log(c*x^n))^2*log(d*(e+f*x)^m)-2*b^2*e*m*n*log(c*x^n)*log(1+f*x/e)/f+e*m*(a+b*log(c*x^n))^2*log(1+f*x/e)/f-2*b^2*e*m*n^2*polylog(2,-f*x/e)/f+2*b*e*m*n*(a+b*log(c*x^n))*polylog(2,-f*x/e)/f-2*b^2*e*m*n^2*polylog(3,-f*x/e)/f],
[(a+b*log(c*x^n))^2*log(d*(e+f*x)^m)/x,x,5,1/3*(a+b*log(c*x^n))^3*log(d*(e+f*x)^m)/(b*n)-1/3*m*(a+b*log(c*x^n))^3*log(1+f*x/e)/(b*n)-m*(a+b*log(c*x^n))^2*polylog(2,-f*x/e)+2*b*m*n*(a+b*log(c*x^n))*polylog(3,-f*x/e)-2*b^2*m*n^2*polylog(4,-f*x/e)],
[(a+b*log(c*x^n))^2*log(d*(e+f*x)^m)/x^2,x,10,2*b^2*f*m*n^2*log(x)/e-2*b*f*m*n*log(1+e/(f*x))*(a+b*log(c*x^n))/e-f*m*log(1+e/(f*x))*(a+b*log(c*x^n))^2/e-2*b^2*f*m*n^2*log(e+f*x)/e-2*b^2*n^2*log(d*(e+f*x)^m)/x-2*b*n*(a+b*log(c*x^n))*log(d*(e+f*x)^m)/x-(a+b*log(c*x^n))^2*log(d*(e+f*x)^m)/x+2*b^2*f*m*n^2*polylog(2,-e/(f*x))/e+2*b*f*m*n*(a+b*log(c*x^n))*polylog(2,-e/(f*x))/e+2*b^2*f*m*n^2*polylog(3,-e/(f*x))/e],
[(a+b*log(c*x^n))^2*log(d*(e+f*x)^m)/x^3,x,14,-7/4*b^2*f*m*n^2/(e*x)-1/4*b^2*f^2*m*n^2*log(x)/e^2-3/2*b*f*m*n*(a+b*log(c*x^n))/(e*x)+1/2*b*f^2*m*n*log(1+e/(f*x))*(a+b*log(c*x^n))/e^2-1/2*f*m*(a+b*log(c*x^n))^2/(e*x)+1/2*f^2*m*log(1+e/(f*x))*(a+b*log(c*x^n))^2/e^2+1/4*b^2*f^2*m*n^2*log(e+f*x)/e^2-1/4*b^2*n^2*log(d*(e+f*x)^m)/x^2-1/2*b*n*(a+b*log(c*x^n))*log(d*(e+f*x)^m)/x^2-1/2*(a+b*log(c*x^n))^2*log(d*(e+f*x)^m)/x^2-1/2*b^2*f^2*m*n^2*polylog(2,-e/(f*x))/e^2-b*f^2*m*n*(a+b*log(c*x^n))*polylog(2,-e/(f*x))/e^2-b^2*f^2*m*n^2*polylog(3,-e/(f*x))/e^2],
[(a+b*log(c*x^n))^2*log(d*(e+f*x)^m)/x^4,x,19,-19/108*b^2*f*m*n^2/(e*x^2)+26/27*b^2*f^2*m*n^2/(e^2*x)+2/27*b^2*f^3*m*n^2*log(x)/e^3-5/18*b*f*m*n*(a+b*log(c*x^n))/(e*x^2)+8/9*b*f^2*m*n*(a+b*log(c*x^n))/(e^2*x)-2/9*b*f^3*m*n*log(1+e/(f*x))*(a+b*log(c*x^n))/e^3-1/6*f*m*(a+b*log(c*x^n))^2/(e*x^2)+1/3*f^2*m*(a+b*log(c*x^n))^2/(e^2*x)-1/3*f^3*m*log(1+e/(f*x))*(a+b*log(c*x^n))^2/e^3-2/27*b^2*f^3*m*n^2*log(e+f*x)/e^3-2/27*b^2*n^2*log(d*(e+f*x)^m)/x^3-2/9*b*n*(a+b*log(c*x^n))*log(d*(e+f*x)^m)/x^3-1/3*(a+b*log(c*x^n))^2*log(d*(e+f*x)^m)/x^3+2/9*b^2*f^3*m*n^2*polylog(2,-e/(f*x))/e^3+2/3*b*f^3*m*n*(a+b*log(c*x^n))*polylog(2,-e/(f*x))/e^3+2/3*b^2*f^3*m*n^2*polylog(3,-e/(f*x))/e^3],
[x*(a+b*log(c*x^n))^3*log(d*(e+f*x)^m),x,34,21/4*a*b^2*e*m*n^2*x/f-45/8*b^3*e*m*n^3*x/f+3/4*b^3*m*n^3*x^2+21/4*b^3*e*m*n^2*x*log(c*x^n)/f-9/8*b^2*m*n^2*x^2*(a+b*log(c*x^n))-9/4*b*e*m*n*x*(a+b*log(c*x^n))^2/f+3/4*b*m*n*x^2*(a+b*log(c*x^n))^2+1/2*e*m*x*(a+b*log(c*x^n))^3/f-1/4*m*x^2*(a+b*log(c*x^n))^3+3/8*b^3*e^2*m*n^3*log(e+f*x)/f^2-3/8*b^3*n^3*x^2*log(d*(e+f*x)^m)+3/4*b^2*n^2*x^2*(a+b*log(c*x^n))*log(d*(e+f*x)^m)-3/4*b*n*x^2*(a+b*log(c*x^n))^2*log(d*(e+f*x)^m)+1/2*x^2*(a+b*log(c*x^n))^3*log(d*(e+f*x)^m)-3/4*b^2*e^2*m*n^2*(a+b*log(c*x^n))*log(1+f*x/e)/f^2+3/4*b*e^2*m*n*(a+b*log(c*x^n))^2*log(1+f*x/e)/f^2-1/2*e^2*m*(a+b*log(c*x^n))^3*log(1+f*x/e)/f^2-3/4*b^3*e^2*m*n^3*polylog(2,-f*x/e)/f^2+3/2*b^2*e^2*m*n^2*(a+b*log(c*x^n))*polylog(2,-f*x/e)/f^2-3/2*b*e^2*m*n*(a+b*log(c*x^n))^2*polylog(2,-f*x/e)/f^2-3/2*b^3*e^2*m*n^3*polylog(3,-f*x/e)/f^2+3*b^2*e^2*m*n^2*(a+b*log(c*x^n))*polylog(3,-f*x/e)/f^2-3*b^3*e^2*m*n^3*polylog(4,-f*x/e)/f^2],
[(a+b*log(c*x^n))^3*log(d*(e+f*x)^m),x,28,-12*a*b^2*m*n^2*x+18*b^3*m*n^3*x-6*b^2*m*n^2*(a-b*n)*x-18*b^3*m*n^2*x*log(c*x^n)+6*b*m*n*x*(a+b*log(c*x^n))^2-m*x*(a+b*log(c*x^n))^3+6*b^2*e*m*n^2*(a-b*n)*log(e+f*x)/f+6*a*b^2*n^2*x*log(d*(e+f*x)^m)-6*b^3*n^3*x*log(d*(e+f*x)^m)+6*b^3*n^2*x*log(c*x^n)*log(d*(e+f*x)^m)-3*b*n*x*(a+b*log(c*x^n))^2*log(d*(e+f*x)^m)+x*(a+b*log(c*x^n))^3*log(d*(e+f*x)^m)+6*b^3*e*m*n^2*log(c*x^n)*log(1+f*x/e)/f-3*b*e*m*n*(a+b*log(c*x^n))^2*log(1+f*x/e)/f+e*m*(a+b*log(c*x^n))^3*log(1+f*x/e)/f+6*b^3*e*m*n^3*polylog(2,-f*x/e)/f-6*b^2*e*m*n^2*(a+b*log(c*x^n))*polylog(2,-f*x/e)/f+3*b*e*m*n*(a+b*log(c*x^n))^2*polylog(2,-f*x/e)/f+6*b^3*e*m*n^3*polylog(3,-f*x/e)/f-6*b^2*e*m*n^2*(a+b*log(c*x^n))*polylog(3,-f*x/e)/f+6*b^3*e*m*n^3*polylog(4,-f*x/e)/f],
[(a+b*log(c*x^n))^3*log(d*(e+f*x)^m)/x,x,6,1/4*(a+b*log(c*x^n))^4*log(d*(e+f*x)^m)/(b*n)-1/4*m*(a+b*log(c*x^n))^4*log(1+f*x/e)/(b*n)-m*(a+b*log(c*x^n))^3*polylog(2,-f*x/e)+3*b*m*n*(a+b*log(c*x^n))^2*polylog(3,-f*x/e)-6*b^2*m*n^2*(a+b*log(c*x^n))*polylog(4,-f*x/e)+6*b^3*m*n^3*polylog(5,-f*x/e)],
[(a+b*log(c*x^n))^3*log(d*(e+f*x)^m)/x^2,x,14,6*b^3*f*m*n^3*log(x)/e-6*b^2*f*m*n^2*log(1+e/(f*x))*(a+b*log(c*x^n))/e-3*b*f*m*n*log(1+e/(f*x))*(a+b*log(c*x^n))^2/e-f*m*log(1+e/(f*x))*(a+b*log(c*x^n))^3/e-6*b^3*f*m*n^3*log(e+f*x)/e-6*b^3*n^3*log(d*(e+f*x)^m)/x-6*b^2*n^2*(a+b*log(c*x^n))*log(d*(e+f*x)^m)/x-3*b*n*(a+b*log(c*x^n))^2*log(d*(e+f*x)^m)/x-(a+b*log(c*x^n))^3*log(d*(e+f*x)^m)/x+6*b^3*f*m*n^3*polylog(2,-e/(f*x))/e+6*b^2*f*m*n^2*(a+b*log(c*x^n))*polylog(2,-e/(f*x))/e+3*b*f*m*n*(a+b*log(c*x^n))^2*polylog(2,-e/(f*x))/e+6*b^3*f*m*n^3*polylog(3,-e/(f*x))/e+6*b^2*f*m*n^2*(a+b*log(c*x^n))*polylog(3,-e/(f*x))/e+6*b^3*f*m*n^3*polylog(4,-e/(f*x))/e],
[(a+b*log(c*x^n))^3*log(d*(e+f*x)^m)/x^3,x,22,-45/8*b^3*f*m*n^3/(e*x)-3/8*b^3*f^2*m*n^3*log(x)/e^2-21/4*b^2*f*m*n^2*(a+b*log(c*x^n))/(e*x)+3/4*b^2*f^2*m*n^2*log(1+e/(f*x))*(a+b*log(c*x^n))/e^2-9/4*b*f*m*n*(a+b*log(c*x^n))^2/(e*x)+3/4*b*f^2*m*n*log(1+e/(f*x))*(a+b*log(c*x^n))^2/e^2-1/2*f*m*(a+b*log(c*x^n))^3/(e*x)+1/2*f^2*m*log(1+e/(f*x))*(a+b*log(c*x^n))^3/e^2+3/8*b^3*f^2*m*n^3*log(e+f*x)/e^2-3/8*b^3*n^3*log(d*(e+f*x)^m)/x^2-3/4*b^2*n^2*(a+b*log(c*x^n))*log(d*(e+f*x)^m)/x^2-3/4*b*n*(a+b*log(c*x^n))^2*log(d*(e+f*x)^m)/x^2-1/2*(a+b*log(c*x^n))^3*log(d*(e+f*x)^m)/x^2-3/4*b^3*f^2*m*n^3*polylog(2,-e/(f*x))/e^2-3/2*b^2*f^2*m*n^2*(a+b*log(c*x^n))*polylog(2,-e/(f*x))/e^2-3/2*b*f^2*m*n*(a+b*log(c*x^n))^2*polylog(2,-e/(f*x))/e^2-3/2*b^3*f^2*m*n^3*polylog(3,-e/(f*x))/e^2-3*b^2*f^2*m*n^2*(a+b*log(c*x^n))*polylog(3,-e/(f*x))/e^2-3*b^3*f^2*m*n^3*polylog(4,-e/(f*x))/e^2],

# Integrands of the form x^q Log[d (e+f x^2)^k] (a+b Log[c x^n])^p
[x^3*(a+b*log(c*x^n))*log(d*(e+f*x^2)^m),x,9,-3/16*b*e*m*n*x^2/f+1/16*b*m*n*x^4+1/4*e*m*x^2*(a+b*log(c*x^n))/f-1/8*m*x^4*(a+b*log(c*x^n))+1/16*b*e^2*m*n*log(e+f*x^2)/f^2+1/8*b*e^2*m*n*log(-f*x^2/e)*log(e+f*x^2)/f^2-1/4*e^2*m*(a+b*log(c*x^n))*log(e+f*x^2)/f^2-1/16*b*n*x^4*log(d*(e+f*x^2)^m)+1/4*x^4*(a+b*log(c*x^n))*log(d*(e+f*x^2)^m)+1/8*b*e^2*m*n*polylog(2,1+f*x^2/e)/f^2],
[x*(a+b*log(c*x^n))*log(d*(e+f*x^2)^m),x,9,1/2*b*m*n*x^2-1/2*m*x^2*(a+b*log(c*x^n))-1/4*b*n*(e+f*x^2)*log(d*(e+f*x^2)^m)/f-1/4*b*e*n*log(-f*x^2/e)*log(d*(e+f*x^2)^m)/f+1/2*(e+f*x^2)*(a+b*log(c*x^n))*log(d*(e+f*x^2)^m)/f-1/4*b*e*m*n*polylog(2,1+f*x^2/e)/f],
[(a+b*log(c*x^n))*log(d*(e+f*x^2)^m)/x,x,4,1/2*(a+b*log(c*x^n))^2*log(d*(e+f*x^2)^m)/(b*n)-1/2*m*(a+b*log(c*x^n))^2*log(1+f*x^2/e)/(b*n)-1/2*m*(a+b*log(c*x^n))*polylog(2,-f*x^2/e)+1/4*b*m*n*polylog(3,-f*x^2/e)],
[(a+b*log(c*x^n))*log(d*(e+f*x^2)^m)/x^3,x,11,1/2*b*f*m*n*log(x)/e-1/2*b*f*m*n*log(x)^2/e+f*m*log(x)*(a+b*log(c*x^n))/e-1/4*b*f*m*n*log(e+f*x^2)/e+1/4*b*f*m*n*log(-f*x^2/e)*log(e+f*x^2)/e-1/2*f*m*(a+b*log(c*x^n))*log(e+f*x^2)/e-1/4*b*n*log(d*(e+f*x^2)^m)/x^2-1/2*(a+b*log(c*x^n))*log(d*(e+f*x^2)^m)/x^2+1/4*b*f*m*n*polylog(2,1+f*x^2/e)/e],
[(a+b*log(c*x^n))*log(d*(e+f*x^2)^m)/x^5,x,10,-3/16*b*f*m*n/(e*x^2)-1/8*b*f^2*m*n*log(x)/e^2+1/4*b*f^2*m*n*log(x)^2/e^2-1/4*f*m*(a+b*log(c*x^n))/(e*x^2)-1/2*f^2*m*log(x)*(a+b*log(c*x^n))/e^2+1/16*b*f^2*m*n*log(e+f*x^2)/e^2-1/8*b*f^2*m*n*log(-f*x^2/e)*log(e+f*x^2)/e^2+1/4*f^2*m*(a+b*log(c*x^n))*log(e+f*x^2)/e^2-1/16*b*n*log(d*(e+f*x^2)^m)/x^4-1/4*(a+b*log(c*x^n))*log(d*(e+f*x^2)^m)/x^4-1/8*b*f^2*m*n*polylog(2,1+f*x^2/e)/e^2],
[x^2*(a+b*log(c*x^n))*log(d*(e+f*x^2)^m),x,9,-8/9*b*e*m*n*x/f+4/27*b*m*n*x^3+2/9*b*e^(3/2)*m*n*arctan(x*sqrt(f)/sqrt(e))/f^(3/2)+2/3*e*m*x*(a+b*log(c*x^n))/f-2/9*m*x^3*(a+b*log(c*x^n))-2/3*e^(3/2)*m*arctan(x*sqrt(f)/sqrt(e))*(a+b*log(c*x^n))/f^(3/2)-1/9*b*n*x^3*log(d*(e+f*x^2)^m)+1/3*x^3*(a+b*log(c*x^n))*log(d*(e+f*x^2)^m)+1/3*I*b*e^(3/2)*m*n*polylog(2,-I*x*sqrt(f)/sqrt(e))/f^(3/2)-1/3*I*b*e^(3/2)*m*n*polylog(2,I*x*sqrt(f)/sqrt(e))/f^(3/2)],
[(a+b*log(c*x^n))*log(d*(e+f*x^2)^m),x,8,4*b*m*n*x-2*m*x*(a+b*log(c*x^n))-b*n*x*log(d*(e+f*x^2)^m)+x*(a+b*log(c*x^n))*log(d*(e+f*x^2)^m)-2*b*m*n*arctan(x*sqrt(f)/sqrt(e))*sqrt(e)/sqrt(f)+2*m*arctan(x*sqrt(f)/sqrt(e))*(a+b*log(c*x^n))*sqrt(e)/sqrt(f)-I*b*m*n*polylog(2,-I*x*sqrt(f)/sqrt(e))*sqrt(e)/sqrt(f)+I*b*m*n*polylog(2,I*x*sqrt(f)/sqrt(e))*sqrt(e)/sqrt(f)],
[(a+b*log(c*x^n))*log(d*(e+f*x^2)^m)/x^2,x,7,-b*n*log(d*(e+f*x^2)^m)/x-(a+b*log(c*x^n))*log(d*(e+f*x^2)^m)/x+2*b*m*n*arctan(x*sqrt(f)/sqrt(e))*sqrt(f)/sqrt(e)+2*m*arctan(x*sqrt(f)/sqrt(e))*(a+b*log(c*x^n))*sqrt(f)/sqrt(e)-I*b*m*n*polylog(2,-I*x*sqrt(f)/sqrt(e))*sqrt(f)/sqrt(e)+I*b*m*n*polylog(2,I*x*sqrt(f)/sqrt(e))*sqrt(f)/sqrt(e)],
[(a+b*log(c*x^n))*log(d*(e+f*x^2)^m)/x^4,x,8,-8/9*b*f*m*n/(e*x)-2/9*b*f^(3/2)*m*n*arctan(x*sqrt(f)/sqrt(e))/e^(3/2)-2/3*f*m*(a+b*log(c*x^n))/(e*x)-2/3*f^(3/2)*m*arctan(x*sqrt(f)/sqrt(e))*(a+b*log(c*x^n))/e^(3/2)-1/9*b*n*log(d*(e+f*x^2)^m)/x^3-1/3*(a+b*log(c*x^n))*log(d*(e+f*x^2)^m)/x^3+1/3*I*b*f^(3/2)*m*n*polylog(2,-I*x*sqrt(f)/sqrt(e))/e^(3/2)-1/3*I*b*f^(3/2)*m*n*polylog(2,I*x*sqrt(f)/sqrt(e))/e^(3/2)],
[(a+b*log(c*x^n))*log(d*(e+f*x^2)^m)/x^6,x,9,-16/225*b*f*m*n/(e*x^3)+12/25*b*f^2*m*n/(e^2*x)+2/25*b*f^(5/2)*m*n*arctan(x*sqrt(f)/sqrt(e))/e^(5/2)-2/15*f*m*(a+b*log(c*x^n))/(e*x^3)+2/5*f^2*m*(a+b*log(c*x^n))/(e^2*x)+2/5*f^(5/2)*m*arctan(x*sqrt(f)/sqrt(e))*(a+b*log(c*x^n))/e^(5/2)-1/25*b*n*log(d*(e+f*x^2)^m)/x^5-1/5*(a+b*log(c*x^n))*log(d*(e+f*x^2)^m)/x^5-1/5*I*b*f^(5/2)*m*n*polylog(2,-I*x*sqrt(f)/sqrt(e))/e^(5/2)+1/5*I*b*f^(5/2)*m*n*polylog(2,I*x*sqrt(f)/sqrt(e))/e^(5/2)],
[x*(a+b*log(c*x^n))^2*log(d*(e+f*x^2)^m),x,17,-3/4*b^2*m*n^2*x^2+b*m*n*x^2*(a+b*log(c*x^n))-1/2*m*x^2*(a+b*log(c*x^n))^2+1/4*b^2*e*m*n^2*log(e+f*x^2)/f+1/4*b^2*n^2*x^2*log(d*(e+f*x^2)^m)-1/2*b*n*x^2*(a+b*log(c*x^n))*log(d*(e+f*x^2)^m)+1/2*x^2*(a+b*log(c*x^n))^2*log(d*(e+f*x^2)^m)-1/2*b*e*m*n*(a+b*log(c*x^n))*log(1+f*x^2/e)/f+1/2*e*m*(a+b*log(c*x^n))^2*log(1+f*x^2/e)/f-1/4*b^2*e*m*n^2*polylog(2,-f*x^2/e)/f+1/2*b*e*m*n*(a+b*log(c*x^n))*polylog(2,-f*x^2/e)/f-1/4*b^2*e*m*n^2*polylog(3,-f*x^2/e)/f],
[(a+b*log(c*x^n))^2*log(d*(e+f*x^2)^m)/x,x,5,1/3*(a+b*log(c*x^n))^3*log(d*(e+f*x^2)^m)/(b*n)-1/3*m*(a+b*log(c*x^n))^3*log(1+f*x^2/e)/(b*n)-1/2*m*(a+b*log(c*x^n))^2*polylog(2,-f*x^2/e)+1/2*b*m*n*(a+b*log(c*x^n))*polylog(3,-f*x^2/e)-1/4*b^2*m*n^2*polylog(4,-f*x^2/e)],
[(a+b*log(c*x^n))^2*log(d*(e+f*x^2)^m)/x^3,x,11,1/2*b^2*f*m*n^2*log(x)/e-1/2*b*f*m*n*log(1+e/(f*x^2))*(a+b*log(c*x^n))/e-1/2*f*m*log(1+e/(f*x^2))*(a+b*log(c*x^n))^2/e-1/4*b^2*f*m*n^2*log(e+f*x^2)/e-1/4*b^2*n^2*log(d*(e+f*x^2)^m)/x^2-1/2*b*n*(a+b*log(c*x^n))*log(d*(e+f*x^2)^m)/x^2-1/2*(a+b*log(c*x^n))^2*log(d*(e+f*x^2)^m)/x^2+1/4*b^2*f*m*n^2*polylog(2,-e/(f*x^2))/e+1/2*b*f*m*n*(a+b*log(c*x^n))*polylog(2,-e/(f*x^2))/e+1/4*b^2*f*m*n^2*polylog(3,-e/(f*x^2))/e],
[(a+b*log(c*x^n))^2*log(d*(e+f*x^2)^m)/x^5,x,15,-7/32*b^2*f*m*n^2/(e*x^2)-1/16*b^2*f^2*m*n^2*log(x)/e^2-3/8*b*f*m*n*(a+b*log(c*x^n))/(e*x^2)+1/8*b*f^2*m*n*log(1+e/(f*x^2))*(a+b*log(c*x^n))/e^2-1/4*f*m*(a+b*log(c*x^n))^2/(e*x^2)+1/4*f^2*m*log(1+e/(f*x^2))*(a+b*log(c*x^n))^2/e^2+1/32*b^2*f^2*m*n^2*log(e+f*x^2)/e^2-1/32*b^2*n^2*log(d*(e+f*x^2)^m)/x^4-1/8*b*n*(a+b*log(c*x^n))*log(d*(e+f*x^2)^m)/x^4-1/4*(a+b*log(c*x^n))^2*log(d*(e+f*x^2)^m)/x^4-1/16*b^2*f^2*m*n^2*polylog(2,-e/(f*x^2))/e^2-1/4*b*f^2*m*n*(a+b*log(c*x^n))*polylog(2,-e/(f*x^2))/e^2-1/8*b^2*f^2*m*n^2*polylog(3,-e/(f*x^2))/e^2],
[x^2*(a+b*log(c*x^n))^2*log(d*(e+f*x^2)^m),x,30,-16/9*a*b*e*m*n*x/f+52/27*b^2*e*m*n^2*x/f-4/27*b^2*m*n^2*x^3-4/27*b^2*e^(3/2)*m*n^2*arctan(x*sqrt(f)/sqrt(e))/f^(3/2)-16/9*b^2*e*m*n*x*log(c*x^n)/f+8/27*b*m*n*x^3*(a+b*log(c*x^n))+4/9*b*e^(3/2)*m*n*arctan(x*sqrt(f)/sqrt(e))*(a+b*log(c*x^n))/f^(3/2)+2/3*e*m*x*(a+b*log(c*x^n))^2/f-2/9*m*x^3*(a+b*log(c*x^n))^2+2/27*b^2*n^2*x^3*log(d*(e+f*x^2)^m)-2/9*b*n*x^3*(a+b*log(c*x^n))*log(d*(e+f*x^2)^m)+1/3*x^3*(a+b*log(c*x^n))^2*log(d*(e+f*x^2)^m)-1/3*(-e)^(3/2)*m*(a+b*log(c*x^n))^2*log(1-x*sqrt(f)/sqrt(-e))/f^(3/2)+1/3*(-e)^(3/2)*m*(a+b*log(c*x^n))^2*log(1+x*sqrt(f)/sqrt(-e))/f^(3/2)+2/3*b*(-e)^(3/2)*m*n*(a+b*log(c*x^n))*polylog(2,-x*sqrt(f)/sqrt(-e))/f^(3/2)-2/3*b*(-e)^(3/2)*m*n*(a+b*log(c*x^n))*polylog(2,x*sqrt(f)/sqrt(-e))/f^(3/2)-2/9*I*b^2*e^(3/2)*m*n^2*polylog(2,-I*x*sqrt(f)/sqrt(e))/f^(3/2)+2/9*I*b^2*e^(3/2)*m*n^2*polylog(2,I*x*sqrt(f)/sqrt(e))/f^(3/2)-2/3*b^2*(-e)^(3/2)*m*n^2*polylog(3,-x*sqrt(f)/sqrt(-e))/f^(3/2)+2/3*b^2*(-e)^(3/2)*m*n^2*polylog(3,x*sqrt(f)/sqrt(-e))/f^(3/2)],
[(a+b*log(c*x^n))^2*log(d*(e+f*x^2)^m),x,26,4*a*b*m*n*x-8*b^2*m*n^2*x+4*b*m*n*(a-b*n)*x+8*b^2*m*n*x*log(c*x^n)-2*m*x*(a+b*log(c*x^n))^2-2*a*b*n*x*log(d*(e+f*x^2)^m)+2*b^2*n^2*x*log(d*(e+f*x^2)^m)-2*b^2*n*x*log(c*x^n)*log(d*(e+f*x^2)^m)+x*(a+b*log(c*x^n))^2*log(d*(e+f*x^2)^m)-m*(a+b*log(c*x^n))^2*log(1-x*sqrt(f)/sqrt(-e))*sqrt(-e)/sqrt(f)+m*(a+b*log(c*x^n))^2*log(1+x*sqrt(f)/sqrt(-e))*sqrt(-e)/sqrt(f)+2*b*m*n*(a+b*log(c*x^n))*polylog(2,-x*sqrt(f)/sqrt(-e))*sqrt(-e)/sqrt(f)-2*b*m*n*(a+b*log(c*x^n))*polylog(2,x*sqrt(f)/sqrt(-e))*sqrt(-e)/sqrt(f)-2*b^2*m*n^2*polylog(3,-x*sqrt(f)/sqrt(-e))*sqrt(-e)/sqrt(f)+2*b^2*m*n^2*polylog(3,x*sqrt(f)/sqrt(-e))*sqrt(-e)/sqrt(f)-4*b*m*n*(a-b*n)*arctan(x*sqrt(f)/sqrt(e))*sqrt(e)/sqrt(f)-4*b^2*m*n*arctan(x*sqrt(f)/sqrt(e))*log(c*x^n)*sqrt(e)/sqrt(f)+2*I*b^2*m*n^2*polylog(2,-I*x*sqrt(f)/sqrt(e))*sqrt(e)/sqrt(f)-2*I*b^2*m*n^2*polylog(2,I*x*sqrt(f)/sqrt(e))*sqrt(e)/sqrt(f)],
[(a+b*log(c*x^n))^2*log(d*(e+f*x^2)^m)/x^2,x,16,-2*b^2*n^2*log(d*(e+f*x^2)^m)/x-2*b*n*(a+b*log(c*x^n))*log(d*(e+f*x^2)^m)/x-(a+b*log(c*x^n))^2*log(d*(e+f*x^2)^m)/x+m*(a+b*log(c*x^n))^2*log(1-x*sqrt(f)/sqrt(-e))*sqrt(f)/sqrt(-e)-m*(a+b*log(c*x^n))^2*log(1+x*sqrt(f)/sqrt(-e))*sqrt(f)/sqrt(-e)-2*b*m*n*(a+b*log(c*x^n))*polylog(2,-x*sqrt(f)/sqrt(-e))*sqrt(f)/sqrt(-e)+2*b*m*n*(a+b*log(c*x^n))*polylog(2,x*sqrt(f)/sqrt(-e))*sqrt(f)/sqrt(-e)+2*b^2*m*n^2*polylog(3,-x*sqrt(f)/sqrt(-e))*sqrt(f)/sqrt(-e)-2*b^2*m*n^2*polylog(3,x*sqrt(f)/sqrt(-e))*sqrt(f)/sqrt(-e)+4*b^2*m*n^2*arctan(x*sqrt(f)/sqrt(e))*sqrt(f)/sqrt(e)+4*b*m*n*arctan(x*sqrt(f)/sqrt(e))*(a+b*log(c*x^n))*sqrt(f)/sqrt(e)-2*I*b^2*m*n^2*polylog(2,-I*x*sqrt(f)/sqrt(e))*sqrt(f)/sqrt(e)+2*I*b^2*m*n^2*polylog(2,I*x*sqrt(f)/sqrt(e))*sqrt(f)/sqrt(e)],
[(a+b*log(c*x^n))^2*log(d*(e+f*x^2)^m)/x^4,x,22,-52/27*b^2*f*m*n^2/(e*x)-4/27*b^2*f^(3/2)*m*n^2*arctan(x*sqrt(f)/sqrt(e))/e^(3/2)-16/9*b*f*m*n*(a+b*log(c*x^n))/(e*x)-4/9*b*f^(3/2)*m*n*arctan(x*sqrt(f)/sqrt(e))*(a+b*log(c*x^n))/e^(3/2)-2/3*f*m*(a+b*log(c*x^n))^2/(e*x)-2/27*b^2*n^2*log(d*(e+f*x^2)^m)/x^3-2/9*b*n*(a+b*log(c*x^n))*log(d*(e+f*x^2)^m)/x^3-1/3*(a+b*log(c*x^n))^2*log(d*(e+f*x^2)^m)/x^3+1/3*f^(3/2)*m*(a+b*log(c*x^n))^2*log(1-x*sqrt(f)/sqrt(-e))/(-e)^(3/2)-1/3*f^(3/2)*m*(a+b*log(c*x^n))^2*log(1+x*sqrt(f)/sqrt(-e))/(-e)^(3/2)-2/3*b*f^(3/2)*m*n*(a+b*log(c*x^n))*polylog(2,-x*sqrt(f)/sqrt(-e))/(-e)^(3/2)+2/3*b*f^(3/2)*m*n*(a+b*log(c*x^n))*polylog(2,x*sqrt(f)/sqrt(-e))/(-e)^(3/2)+2/9*I*b^2*f^(3/2)*m*n^2*polylog(2,-I*x*sqrt(f)/sqrt(e))/e^(3/2)-2/9*I*b^2*f^(3/2)*m*n^2*polylog(2,I*x*sqrt(f)/sqrt(e))/e^(3/2)+2/3*b^2*f^(3/2)*m*n^2*polylog(3,-x*sqrt(f)/sqrt(-e))/(-e)^(3/2)-2/3*b^2*f^(3/2)*m*n^2*polylog(3,x*sqrt(f)/sqrt(-e))/(-e)^(3/2)],
[x*(a+b*log(c*x^n))^3*log(d*(e+f*x^2)^m),x,26,3/2*b^3*m*n^3*x^2-9/4*b^2*m*n^2*x^2*(a+b*log(c*x^n))+3/2*b*m*n*x^2*(a+b*log(c*x^n))^2-1/2*m*x^2*(a+b*log(c*x^n))^3-3/8*b^3*e*m*n^3*log(e+f*x^2)/f-3/8*b^3*n^3*x^2*log(d*(e+f*x^2)^m)+3/4*b^2*n^2*x^2*(a+b*log(c*x^n))*log(d*(e+f*x^2)^m)-3/4*b*n*x^2*(a+b*log(c*x^n))^2*log(d*(e+f*x^2)^m)+1/2*x^2*(a+b*log(c*x^n))^3*log(d*(e+f*x^2)^m)+3/4*b^2*e*m*n^2*(a+b*log(c*x^n))*log(1+f*x^2/e)/f-3/4*b*e*m*n*(a+b*log(c*x^n))^2*log(1+f*x^2/e)/f+1/2*e*m*(a+b*log(c*x^n))^3*log(1+f*x^2/e)/f+3/8*b^3*e*m*n^3*polylog(2,-f*x^2/e)/f-3/4*b^2*e*m*n^2*(a+b*log(c*x^n))*polylog(2,-f*x^2/e)/f+3/4*b*e*m*n*(a+b*log(c*x^n))^2*polylog(2,-f*x^2/e)/f+3/8*b^3*e*m*n^3*polylog(3,-f*x^2/e)/f-3/4*b^2*e*m*n^2*(a+b*log(c*x^n))*polylog(3,-f*x^2/e)/f+3/8*b^3*e*m*n^3*polylog(4,-f*x^2/e)/f],
[(a+b*log(c*x^n))^3*log(d*(e+f*x^2)^m)/x,x,6,1/4*(a+b*log(c*x^n))^4*log(d*(e+f*x^2)^m)/(b*n)-1/4*m*(a+b*log(c*x^n))^4*log(1+f*x^2/e)/(b*n)-1/2*m*(a+b*log(c*x^n))^3*polylog(2,-f*x^2/e)+3/4*b*m*n*(a+b*log(c*x^n))^2*polylog(3,-f*x^2/e)-3/4*b^2*m*n^2*(a+b*log(c*x^n))*polylog(4,-f*x^2/e)+3/8*b^3*m*n^3*polylog(5,-f*x^2/e)],
[(a+b*log(c*x^n))^3*log(d*(e+f*x^2)^m)/x^3,x,15,3/4*b^3*f*m*n^3*log(x)/e-3/4*b^2*f*m*n^2*log(1+e/(f*x^2))*(a+b*log(c*x^n))/e-3/4*b*f*m*n*log(1+e/(f*x^2))*(a+b*log(c*x^n))^2/e-1/2*f*m*log(1+e/(f*x^2))*(a+b*log(c*x^n))^3/e-3/8*b^3*f*m*n^3*log(e+f*x^2)/e-3/8*b^3*n^3*log(d*(e+f*x^2)^m)/x^2-3/4*b^2*n^2*(a+b*log(c*x^n))*log(d*(e+f*x^2)^m)/x^2-3/4*b*n*(a+b*log(c*x^n))^2*log(d*(e+f*x^2)^m)/x^2-1/2*(a+b*log(c*x^n))^3*log(d*(e+f*x^2)^m)/x^2+3/8*b^3*f*m*n^3*polylog(2,-e/(f*x^2))/e+3/4*b^2*f*m*n^2*(a+b*log(c*x^n))*polylog(2,-e/(f*x^2))/e+3/4*b*f*m*n*(a+b*log(c*x^n))^2*polylog(2,-e/(f*x^2))/e+3/8*b^3*f*m*n^3*polylog(3,-e/(f*x^2))/e+3/4*b^2*f*m*n^2*(a+b*log(c*x^n))*polylog(3,-e/(f*x^2))/e+3/8*b^3*f*m*n^3*polylog(4,-e/(f*x^2))/e],
[x^2*(a+b*log(c*x^n))^3*log(d*(e+f*x^2)^m),x,49,52/9*a*b^2*e*m*n^2*x/f-160/27*b^3*e*m*n^3*x/f+16/81*b^3*m*n^3*x^3+4/27*b^3*e^(3/2)*m*n^3*arctan(x*sqrt(f)/sqrt(e))/f^(3/2)+52/9*b^3*e*m*n^2*x*log(c*x^n)/f-4/9*b^2*m*n^2*x^3*(a+b*log(c*x^n))-4/9*b^2*e^(3/2)*m*n^2*arctan(x*sqrt(f)/sqrt(e))*(a+b*log(c*x^n))/f^(3/2)-8/3*b*e*m*n*x*(a+b*log(c*x^n))^2/f+4/9*b*m*n*x^3*(a+b*log(c*x^n))^2+2/3*e*m*x*(a+b*log(c*x^n))^3/f-2/9*m*x^3*(a+b*log(c*x^n))^3-2/27*b^3*n^3*x^3*log(d*(e+f*x^2)^m)+2/9*b^2*n^2*x^3*(a+b*log(c*x^n))*log(d*(e+f*x^2)^m)-1/3*b*n*x^3*(a+b*log(c*x^n))^2*log(d*(e+f*x^2)^m)+1/3*x^3*(a+b*log(c*x^n))^3*log(d*(e+f*x^2)^m)+1/3*b*(-e)^(3/2)*m*n*(a+b*log(c*x^n))^2*log(1-x*sqrt(f)/sqrt(-e))/f^(3/2)-1/3*(-e)^(3/2)*m*(a+b*log(c*x^n))^3*log(1-x*sqrt(f)/sqrt(-e))/f^(3/2)-1/3*b*(-e)^(3/2)*m*n*(a+b*log(c*x^n))^2*log(1+x*sqrt(f)/sqrt(-e))/f^(3/2)+1/3*(-e)^(3/2)*m*(a+b*log(c*x^n))^3*log(1+x*sqrt(f)/sqrt(-e))/f^(3/2)-2/3*b^2*(-e)^(3/2)*m*n^2*(a+b*log(c*x^n))*polylog(2,-x*sqrt(f)/sqrt(-e))/f^(3/2)+b*(-e)^(3/2)*m*n*(a+b*log(c*x^n))^2*polylog(2,-x*sqrt(f)/sqrt(-e))/f^(3/2)+2/3*b^2*(-e)^(3/2)*m*n^2*(a+b*log(c*x^n))*polylog(2,x*sqrt(f)/sqrt(-e))/f^(3/2)-b*(-e)^(3/2)*m*n*(a+b*log(c*x^n))^2*polylog(2,x*sqrt(f)/sqrt(-e))/f^(3/2)+2/9*I*b^3*e^(3/2)*m*n^3*polylog(2,-I*x*sqrt(f)/sqrt(e))/f^(3/2)-2/9*I*b^3*e^(3/2)*m*n^3*polylog(2,I*x*sqrt(f)/sqrt(e))/f^(3/2)+2/3*b^3*(-e)^(3/2)*m*n^3*polylog(3,-x*sqrt(f)/sqrt(-e))/f^(3/2)-2*b^2*(-e)^(3/2)*m*n^2*(a+b*log(c*x^n))*polylog(3,-x*sqrt(f)/sqrt(-e))/f^(3/2)-2/3*b^3*(-e)^(3/2)*m*n^3*polylog(3,x*sqrt(f)/sqrt(-e))/f^(3/2)+2*b^2*(-e)^(3/2)*m*n^2*(a+b*log(c*x^n))*polylog(3,x*sqrt(f)/sqrt(-e))/f^(3/2)+2*b^3*(-e)^(3/2)*m*n^3*polylog(4,-x*sqrt(f)/sqrt(-e))/f^(3/2)-2*b^3*(-e)^(3/2)*m*n^3*polylog(4,x*sqrt(f)/sqrt(-e))/f^(3/2)],
[(a+b*log(c*x^n))^3*log(d*(e+f*x^2)^m),x,42,-24*a*b^2*m*n^2*x+36*b^3*m*n^3*x-12*b^2*m*n^2*(a-b*n)*x-36*b^3*m*n^2*x*log(c*x^n)+12*b*m*n*x*(a+b*log(c*x^n))^2-2*m*x*(a+b*log(c*x^n))^3+6*a*b^2*n^2*x*log(d*(e+f*x^2)^m)-6*b^3*n^3*x*log(d*(e+f*x^2)^m)+6*b^3*n^2*x*log(c*x^n)*log(d*(e+f*x^2)^m)-3*b*n*x*(a+b*log(c*x^n))^2*log(d*(e+f*x^2)^m)+x*(a+b*log(c*x^n))^3*log(d*(e+f*x^2)^m)+3*b*m*n*(a+b*log(c*x^n))^2*log(1-x*sqrt(f)/sqrt(-e))*sqrt(-e)/sqrt(f)-m*(a+b*log(c*x^n))^3*log(1-x*sqrt(f)/sqrt(-e))*sqrt(-e)/sqrt(f)-3*b*m*n*(a+b*log(c*x^n))^2*log(1+x*sqrt(f)/sqrt(-e))*sqrt(-e)/sqrt(f)+m*(a+b*log(c*x^n))^3*log(1+x*sqrt(f)/sqrt(-e))*sqrt(-e)/sqrt(f)-6*b^2*m*n^2*(a+b*log(c*x^n))*polylog(2,-x*sqrt(f)/sqrt(-e))*sqrt(-e)/sqrt(f)+3*b*m*n*(a+b*log(c*x^n))^2*polylog(2,-x*sqrt(f)/sqrt(-e))*sqrt(-e)/sqrt(f)+6*b^2*m*n^2*(a+b*log(c*x^n))*polylog(2,x*sqrt(f)/sqrt(-e))*sqrt(-e)/sqrt(f)-3*b*m*n*(a+b*log(c*x^n))^2*polylog(2,x*sqrt(f)/sqrt(-e))*sqrt(-e)/sqrt(f)+6*b^3*m*n^3*polylog(3,-x*sqrt(f)/sqrt(-e))*sqrt(-e)/sqrt(f)-6*b^2*m*n^2*(a+b*log(c*x^n))*polylog(3,-x*sqrt(f)/sqrt(-e))*sqrt(-e)/sqrt(f)-6*b^3*m*n^3*polylog(3,x*sqrt(f)/sqrt(-e))*sqrt(-e)/sqrt(f)+6*b^2*m*n^2*(a+b*log(c*x^n))*polylog(3,x*sqrt(f)/sqrt(-e))*sqrt(-e)/sqrt(f)+6*b^3*m*n^3*polylog(4,-x*sqrt(f)/sqrt(-e))*sqrt(-e)/sqrt(f)-6*b^3*m*n^3*polylog(4,x*sqrt(f)/sqrt(-e))*sqrt(-e)/sqrt(f)+12*b^2*m*n^2*(a-b*n)*arctan(x*sqrt(f)/sqrt(e))*sqrt(e)/sqrt(f)+12*b^3*m*n^2*arctan(x*sqrt(f)/sqrt(e))*log(c*x^n)*sqrt(e)/sqrt(f)-6*I*b^3*m*n^3*polylog(2,-I*x*sqrt(f)/sqrt(e))*sqrt(e)/sqrt(f)+6*I*b^3*m*n^3*polylog(2,I*x*sqrt(f)/sqrt(e))*sqrt(e)/sqrt(f)],
[(a+b*log(c*x^n))^3*log(d*(e+f*x^2)^m)/x^2,x,26,-6*b^3*n^3*log(d*(e+f*x^2)^m)/x-6*b^2*n^2*(a+b*log(c*x^n))*log(d*(e+f*x^2)^m)/x-3*b*n*(a+b*log(c*x^n))^2*log(d*(e+f*x^2)^m)/x-(a+b*log(c*x^n))^3*log(d*(e+f*x^2)^m)/x+3*b*m*n*(a+b*log(c*x^n))^2*log(1-x*sqrt(f)/sqrt(-e))*sqrt(f)/sqrt(-e)+m*(a+b*log(c*x^n))^3*log(1-x*sqrt(f)/sqrt(-e))*sqrt(f)/sqrt(-e)-3*b*m*n*(a+b*log(c*x^n))^2*log(1+x*sqrt(f)/sqrt(-e))*sqrt(f)/sqrt(-e)-m*(a+b*log(c*x^n))^3*log(1+x*sqrt(f)/sqrt(-e))*sqrt(f)/sqrt(-e)-6*b^2*m*n^2*(a+b*log(c*x^n))*polylog(2,-x*sqrt(f)/sqrt(-e))*sqrt(f)/sqrt(-e)-3*b*m*n*(a+b*log(c*x^n))^2*polylog(2,-x*sqrt(f)/sqrt(-e))*sqrt(f)/sqrt(-e)+6*b^2*m*n^2*(a+b*log(c*x^n))*polylog(2,x*sqrt(f)/sqrt(-e))*sqrt(f)/sqrt(-e)+3*b*m*n*(a+b*log(c*x^n))^2*polylog(2,x*sqrt(f)/sqrt(-e))*sqrt(f)/sqrt(-e)+6*b^3*m*n^3*polylog(3,-x*sqrt(f)/sqrt(-e))*sqrt(f)/sqrt(-e)+6*b^2*m*n^2*(a+b*log(c*x^n))*polylog(3,-x*sqrt(f)/sqrt(-e))*sqrt(f)/sqrt(-e)-6*b^3*m*n^3*polylog(3,x*sqrt(f)/sqrt(-e))*sqrt(f)/sqrt(-e)-6*b^2*m*n^2*(a+b*log(c*x^n))*polylog(3,x*sqrt(f)/sqrt(-e))*sqrt(f)/sqrt(-e)-6*b^3*m*n^3*polylog(4,-x*sqrt(f)/sqrt(-e))*sqrt(f)/sqrt(-e)+6*b^3*m*n^3*polylog(4,x*sqrt(f)/sqrt(-e))*sqrt(f)/sqrt(-e)+12*b^3*m*n^3*arctan(x*sqrt(f)/sqrt(e))*sqrt(f)/sqrt(e)+12*b^2*m*n^2*arctan(x*sqrt(f)/sqrt(e))*(a+b*log(c*x^n))*sqrt(f)/sqrt(e)-6*I*b^3*m*n^3*polylog(2,-I*x*sqrt(f)/sqrt(e))*sqrt(f)/sqrt(e)+6*I*b^3*m*n^3*polylog(2,I*x*sqrt(f)/sqrt(e))*sqrt(f)/sqrt(e)],
[(a+b*log(c*x^n))^3*log(d*(e+f*x^2)^m)/x^4,x,36,-160/27*b^3*f*m*n^3/(e*x)-4/27*b^3*f^(3/2)*m*n^3*arctan(x*sqrt(f)/sqrt(e))/e^(3/2)-52/9*b^2*f*m*n^2*(a+b*log(c*x^n))/(e*x)-4/9*b^2*f^(3/2)*m*n^2*arctan(x*sqrt(f)/sqrt(e))*(a+b*log(c*x^n))/e^(3/2)-8/3*b*f*m*n*(a+b*log(c*x^n))^2/(e*x)-2/3*f*m*(a+b*log(c*x^n))^3/(e*x)-2/27*b^3*n^3*log(d*(e+f*x^2)^m)/x^3-2/9*b^2*n^2*(a+b*log(c*x^n))*log(d*(e+f*x^2)^m)/x^3-1/3*b*n*(a+b*log(c*x^n))^2*log(d*(e+f*x^2)^m)/x^3-1/3*(a+b*log(c*x^n))^3*log(d*(e+f*x^2)^m)/x^3+1/3*b*f^(3/2)*m*n*(a+b*log(c*x^n))^2*log(1-x*sqrt(f)/sqrt(-e))/(-e)^(3/2)+1/3*f^(3/2)*m*(a+b*log(c*x^n))^3*log(1-x*sqrt(f)/sqrt(-e))/(-e)^(3/2)-1/3*b*f^(3/2)*m*n*(a+b*log(c*x^n))^2*log(1+x*sqrt(f)/sqrt(-e))/(-e)^(3/2)-1/3*f^(3/2)*m*(a+b*log(c*x^n))^3*log(1+x*sqrt(f)/sqrt(-e))/(-e)^(3/2)-2/3*b^2*f^(3/2)*m*n^2*(a+b*log(c*x^n))*polylog(2,-x*sqrt(f)/sqrt(-e))/(-e)^(3/2)-b*f^(3/2)*m*n*(a+b*log(c*x^n))^2*polylog(2,-x*sqrt(f)/sqrt(-e))/(-e)^(3/2)+2/3*b^2*f^(3/2)*m*n^2*(a+b*log(c*x^n))*polylog(2,x*sqrt(f)/sqrt(-e))/(-e)^(3/2)+b*f^(3/2)*m*n*(a+b*log(c*x^n))^2*polylog(2,x*sqrt(f)/sqrt(-e))/(-e)^(3/2)+2/9*I*b^3*f^(3/2)*m*n^3*polylog(2,-I*x*sqrt(f)/sqrt(e))/e^(3/2)-2/9*I*b^3*f^(3/2)*m*n^3*polylog(2,I*x*sqrt(f)/sqrt(e))/e^(3/2)+2/3*b^3*f^(3/2)*m*n^3*polylog(3,-x*sqrt(f)/sqrt(-e))/(-e)^(3/2)+2*b^2*f^(3/2)*m*n^2*(a+b*log(c*x^n))*polylog(3,-x*sqrt(f)/sqrt(-e))/(-e)^(3/2)-2/3*b^3*f^(3/2)*m*n^3*polylog(3,x*sqrt(f)/sqrt(-e))/(-e)^(3/2)-2*b^2*f^(3/2)*m*n^2*(a+b*log(c*x^n))*polylog(3,x*sqrt(f)/sqrt(-e))/(-e)^(3/2)-2*b^3*f^(3/2)*m*n^3*polylog(4,-x*sqrt(f)/sqrt(-e))/(-e)^(3/2)+2*b^3*f^(3/2)*m*n^3*polylog(4,x*sqrt(f)/sqrt(-e))/(-e)^(3/2)],

# Integrands of the form x^q Log[d (e+f x^(1/2))^k] (a+b Log[c x^n])^p
[x^2*(a+b*log(c*x^n))*log(d*(e+f*sqrt(x))^k),x,9,2/9*b*e^4*k*n*x/f^4-1/9*b*e^3*k*n*x^(3/2)/f^3+5/72*b*e^2*k*n*x^2/f^2-11/225*b*e*k*n*x^(5/2)/f+1/27*b*k*n*x^3-1/6*e^4*k*x*(a+b*log(c*x^n))/f^4+1/9*e^3*k*x^(3/2)*(a+b*log(c*x^n))/f^3-1/12*e^2*k*x^2*(a+b*log(c*x^n))/f^2+1/15*e*k*x^(5/2)*(a+b*log(c*x^n))/f-1/18*k*x^3*(a+b*log(c*x^n))+1/9*b*e^6*k*n*log(e+f*sqrt(x))/f^6-1/3*e^6*k*(a+b*log(c*x^n))*log(e+f*sqrt(x))/f^6+2/3*b*e^6*k*n*log(-f*sqrt(x)/e)*log(e+f*sqrt(x))/f^6-1/9*b*n*x^3*log(d*(e+f*sqrt(x))^k)+1/3*x^3*(a+b*log(c*x^n))*log(d*(e+f*sqrt(x))^k)+2/3*b*e^6*k*n*polylog(2,1+f*sqrt(x)/e)/f^6-7/9*b*e^5*k*n*sqrt(x)/f^5+1/3*e^5*k*(a+b*log(c*x^n))*sqrt(x)/f^5],
[x*(a+b*log(c*x^n))*log(d*(e+f*sqrt(x))^k),x,9,3/8*b*e^2*k*n*x/f^2-7/36*b*e*k*n*x^(3/2)/f+1/8*b*k*n*x^2-1/4*e^2*k*x*(a+b*log(c*x^n))/f^2+1/6*e*k*x^(3/2)*(a+b*log(c*x^n))/f-1/8*k*x^2*(a+b*log(c*x^n))+1/4*b*e^4*k*n*log(e+f*sqrt(x))/f^4-1/2*e^4*k*(a+b*log(c*x^n))*log(e+f*sqrt(x))/f^4+b*e^4*k*n*log(-f*sqrt(x)/e)*log(e+f*sqrt(x))/f^4-1/4*b*n*x^2*log(d*(e+f*sqrt(x))^k)+1/2*x^2*(a+b*log(c*x^n))*log(d*(e+f*sqrt(x))^k)+b*e^4*k*n*polylog(2,1+f*sqrt(x)/e)/f^4-5/4*b*e^3*k*n*sqrt(x)/f^3+1/2*e^3*k*(a+b*log(c*x^n))*sqrt(x)/f^3],
[(a+b*log(c*x^n))*log(d*(e+f*sqrt(x))^k),x,9,b*k*n*x-1/2*k*x*(a+b*log(c*x^n))+b*e^2*k*n*log(e+f*sqrt(x))/f^2-e^2*k*(a+b*log(c*x^n))*log(e+f*sqrt(x))/f^2+2*b*e^2*k*n*log(-f*sqrt(x)/e)*log(e+f*sqrt(x))/f^2-b*n*x*log(d*(e+f*sqrt(x))^k)+x*(a+b*log(c*x^n))*log(d*(e+f*sqrt(x))^k)+2*b*e^2*k*n*polylog(2,1+f*sqrt(x)/e)/f^2-3*b*e*k*n*sqrt(x)/f+e*k*(a+b*log(c*x^n))*sqrt(x)/f],
[(a+b*log(c*x^n))*log(d*(e+f*sqrt(x))^k)/x,x,4,1/2*(a+b*log(c*x^n))^2*log(d*(e+f*sqrt(x))^k)/(b*n)-1/2*k*(a+b*log(c*x^n))^2*log(1+f*sqrt(x)/e)/(b*n)-2*k*(a+b*log(c*x^n))*polylog(2,-f*sqrt(x)/e)+4*b*k*n*polylog(3,-f*sqrt(x)/e)],
[(a+b*log(c*x^n))*log(d*(e+f*sqrt(x))^k)/x^2,x,10,-1/2*b*f^2*k*n*log(x)/e^2+1/4*b*f^2*k*n*log(x)^2/e^2-1/2*f^2*k*log(x)*(a+b*log(c*x^n))/e^2+b*f^2*k*n*log(e+f*sqrt(x))/e^2+f^2*k*(a+b*log(c*x^n))*log(e+f*sqrt(x))/e^2-2*b*f^2*k*n*log(-f*sqrt(x)/e)*log(e+f*sqrt(x))/e^2-b*n*log(d*(e+f*sqrt(x))^k)/x-(a+b*log(c*x^n))*log(d*(e+f*sqrt(x))^k)/x-2*b*f^2*k*n*polylog(2,1+f*sqrt(x)/e)/e^2-3*b*f*k*n/(e*sqrt(x))-f*k*(a+b*log(c*x^n))/(e*sqrt(x))],
[(a+b*log(c*x^n))*log(d*(e+f*sqrt(x))^k)/x^3,x,10,-7/36*b*f*k*n/(e*x^(3/2))+3/8*b*f^2*k*n/(e^2*x)-1/8*b*f^4*k*n*log(x)/e^4+1/8*b*f^4*k*n*log(x)^2/e^4-1/6*f*k*(a+b*log(c*x^n))/(e*x^(3/2))+1/4*f^2*k*(a+b*log(c*x^n))/(e^2*x)-1/4*f^4*k*log(x)*(a+b*log(c*x^n))/e^4+1/4*b*f^4*k*n*log(e+f*sqrt(x))/e^4+1/2*f^4*k*(a+b*log(c*x^n))*log(e+f*sqrt(x))/e^4-b*f^4*k*n*log(-f*sqrt(x)/e)*log(e+f*sqrt(x))/e^4-1/4*b*n*log(d*(e+f*sqrt(x))^k)/x^2-1/2*(a+b*log(c*x^n))*log(d*(e+f*sqrt(x))^k)/x^2-b*f^4*k*n*polylog(2,1+f*sqrt(x)/e)/e^4-5/4*b*f^3*k*n/(e^3*sqrt(x))-1/2*f^3*k*(a+b*log(c*x^n))/(e^3*sqrt(x))],
[(a+b*log(c*x^n))*log(d*(e+f*sqrt(x))^k)/x^4,x,10,-11/225*b*f*k*n/(e*x^(5/2))+5/72*b*f^2*k*n/(e^2*x^2)-1/9*b*f^3*k*n/(e^3*x^(3/2))+2/9*b*f^4*k*n/(e^4*x)-1/18*b*f^6*k*n*log(x)/e^6+1/12*b*f^6*k*n*log(x)^2/e^6-1/15*f*k*(a+b*log(c*x^n))/(e*x^(5/2))+1/12*f^2*k*(a+b*log(c*x^n))/(e^2*x^2)-1/9*f^3*k*(a+b*log(c*x^n))/(e^3*x^(3/2))+1/6*f^4*k*(a+b*log(c*x^n))/(e^4*x)-1/6*f^6*k*log(x)*(a+b*log(c*x^n))/e^6+1/9*b*f^6*k*n*log(e+f*sqrt(x))/e^6+1/3*f^6*k*(a+b*log(c*x^n))*log(e+f*sqrt(x))/e^6-2/3*b*f^6*k*n*log(-f*sqrt(x)/e)*log(e+f*sqrt(x))/e^6-1/9*b*n*log(d*(e+f*sqrt(x))^k)/x^3-1/3*(a+b*log(c*x^n))*log(d*(e+f*sqrt(x))^k)/x^3-2/3*b*f^6*k*n*polylog(2,1+f*sqrt(x)/e)/e^6-7/9*b*f^5*k*n/(e^5*sqrt(x))-1/3*f^5*k*(a+b*log(c*x^n))/(e^5*sqrt(x))],
[x^2*(a+b*log(c*x^n))^2*log(d*(e+f*sqrt(x))),x,22,1/3*a*b*e^4*n*x/f^4-13/27*b^2*e^4*n^2*x/f^4+14/81*b^2*e^3*n^2*x^(3/2)/f^3-19/216*b^2*e^2*n^2*x^2/f^2+182/3375*b^2*e*n^2*x^(5/2)/f-1/27*b^2*n^2*x^3+1/3*b^2*e^4*n*x*log(c*x^n)/f^4+1/9*b*e^4*n*x*(a+b*log(c*x^n))/f^4-2/9*b*e^3*n*x^(3/2)*(a+b*log(c*x^n))/f^3+5/36*b*e^2*n*x^2*(a+b*log(c*x^n))/f^2-22/225*b*e*n*x^(5/2)*(a+b*log(c*x^n))/f+2/27*b*n*x^3*(a+b*log(c*x^n))-1/6*e^4*x*(a+b*log(c*x^n))^2/f^4+1/9*e^3*x^(3/2)*(a+b*log(c*x^n))^2/f^3-1/12*e^2*x^2*(a+b*log(c*x^n))^2/f^2+1/15*e*x^(5/2)*(a+b*log(c*x^n))^2/f-1/18*x^3*(a+b*log(c*x^n))^2-2/27*b^2*e^6*n^2*log(e+f*sqrt(x))/f^6+2/9*b*e^6*n*(a+b*log(c*x^n))*log(e+f*sqrt(x))/f^6-4/9*b^2*e^6*n^2*log(-f*sqrt(x)/e)*log(e+f*sqrt(x))/f^6+2/27*b^2*n^2*x^3*log(d*(e+f*sqrt(x)))-2/9*b*n*x^3*(a+b*log(c*x^n))*log(d*(e+f*sqrt(x)))+1/3*x^3*(a+b*log(c*x^n))^2*log(d*(e+f*sqrt(x)))-1/3*e^6*(a+b*log(c*x^n))^2*log(1+f*sqrt(x)/e)/f^6-4/3*b*e^6*n*(a+b*log(c*x^n))*polylog(2,-f*sqrt(x)/e)/f^6-4/9*b^2*e^6*n^2*polylog(2,1+f*sqrt(x)/e)/f^6+8/3*b^2*e^6*n^2*polylog(3,-f*sqrt(x)/e)/f^6+86/27*b^2*e^5*n^2*sqrt(x)/f^5-14/9*b*e^5*n*(a+b*log(c*x^n))*sqrt(x)/f^5+1/3*e^5*(a+b*log(c*x^n))^2*sqrt(x)/f^5],
[x*(a+b*log(c*x^n))^2*log(d*(e+f*sqrt(x))),x,20,1/2*a*b*e^2*n*x/f^2-7/8*b^2*e^2*n^2*x/f^2+37/108*b^2*e*n^2*x^(3/2)/f-3/16*b^2*n^2*x^2+1/2*b^2*e^2*n*x*log(c*x^n)/f^2+1/4*b*e^2*n*x*(a+b*log(c*x^n))/f^2-7/18*b*e*n*x^(3/2)*(a+b*log(c*x^n))/f+1/4*b*n*x^2*(a+b*log(c*x^n))-1/4*e^2*x*(a+b*log(c*x^n))^2/f^2+1/6*e*x^(3/2)*(a+b*log(c*x^n))^2/f-1/8*x^2*(a+b*log(c*x^n))^2-1/4*b^2*e^4*n^2*log(e+f*sqrt(x))/f^4+1/2*b*e^4*n*(a+b*log(c*x^n))*log(e+f*sqrt(x))/f^4-b^2*e^4*n^2*log(-f*sqrt(x)/e)*log(e+f*sqrt(x))/f^4+1/4*b^2*n^2*x^2*log(d*(e+f*sqrt(x)))-1/2*b*n*x^2*(a+b*log(c*x^n))*log(d*(e+f*sqrt(x)))+1/2*x^2*(a+b*log(c*x^n))^2*log(d*(e+f*sqrt(x)))-1/2*e^4*(a+b*log(c*x^n))^2*log(1+f*sqrt(x)/e)/f^4-2*b*e^4*n*(a+b*log(c*x^n))*polylog(2,-f*sqrt(x)/e)/f^4-b^2*e^4*n^2*polylog(2,1+f*sqrt(x)/e)/f^4+4*b^2*e^4*n^2*polylog(3,-f*sqrt(x)/e)/f^4+21/4*b^2*e^3*n^2*sqrt(x)/f^3-5/2*b*e^3*n*(a+b*log(c*x^n))*sqrt(x)/f^3+1/2*e^3*(a+b*log(c*x^n))^2*sqrt(x)/f^3],
[(a+b*log(c*x^n))^2*log(d*(e+f*sqrt(x))),x,18,a*b*n*x-3*b^2*n^2*x+b^2*n*x*log(c*x^n)+b*n*x*(a+b*log(c*x^n))-1/2*x*(a+b*log(c*x^n))^2-2*b^2*e^2*n^2*log(e+f*sqrt(x))/f^2+2*b*e^2*n*(a+b*log(c*x^n))*log(e+f*sqrt(x))/f^2-4*b^2*e^2*n^2*log(-f*sqrt(x)/e)*log(e+f*sqrt(x))/f^2+2*b^2*n^2*x*log(d*(e+f*sqrt(x)))-2*b*n*x*(a+b*log(c*x^n))*log(d*(e+f*sqrt(x)))+x*(a+b*log(c*x^n))^2*log(d*(e+f*sqrt(x)))-e^2*(a+b*log(c*x^n))^2*log(1+f*sqrt(x)/e)/f^2-4*b*e^2*n*(a+b*log(c*x^n))*polylog(2,-f*sqrt(x)/e)/f^2-4*b^2*e^2*n^2*polylog(2,1+f*sqrt(x)/e)/f^2+8*b^2*e^2*n^2*polylog(3,-f*sqrt(x)/e)/f^2+14*b^2*e*n^2*sqrt(x)/f-6*b*e*n*(a+b*log(c*x^n))*sqrt(x)/f+e*(a+b*log(c*x^n))^2*sqrt(x)/f],
[(a+b*log(c*x^n))^2*log(d*(e+f*sqrt(x)))/x,x,5,1/3*(a+b*log(c*x^n))^3*log(d*(e+f*sqrt(x)))/(b*n)-1/3*(a+b*log(c*x^n))^3*log(1+f*sqrt(x)/e)/(b*n)-2*(a+b*log(c*x^n))^2*polylog(2,-f*sqrt(x)/e)+8*b*n*(a+b*log(c*x^n))*polylog(3,-f*sqrt(x)/e)-16*b^2*n^2*polylog(4,-f*sqrt(x)/e)],
[(a+b*log(c*x^n))^2*log(d*(e+f*sqrt(x)))/x^2,x,21,-b^2*f^2*n^2*log(x)/e^2+1/2*b^2*f^2*n^2*log(x)^2/e^2-b*f^2*n*log(x)*(a+b*log(c*x^n))/e^2-1/6*f^2*(a+b*log(c*x^n))^3/(b*e^2*n)+2*b^2*f^2*n^2*log(e+f*sqrt(x))/e^2+2*b*f^2*n*(a+b*log(c*x^n))*log(e+f*sqrt(x))/e^2-4*b^2*f^2*n^2*log(-f*sqrt(x)/e)*log(e+f*sqrt(x))/e^2-2*b^2*n^2*log(d*(e+f*sqrt(x)))/x-2*b*n*(a+b*log(c*x^n))*log(d*(e+f*sqrt(x)))/x-(a+b*log(c*x^n))^2*log(d*(e+f*sqrt(x)))/x+f^2*(a+b*log(c*x^n))^2*log(1+f*sqrt(x)/e)/e^2+4*b*f^2*n*(a+b*log(c*x^n))*polylog(2,-f*sqrt(x)/e)/e^2-4*b^2*f^2*n^2*polylog(2,1+f*sqrt(x)/e)/e^2-8*b^2*f^2*n^2*polylog(3,-f*sqrt(x)/e)/e^2-14*b^2*f*n^2/(e*sqrt(x))-6*b*f*n*(a+b*log(c*x^n))/(e*sqrt(x))-f*(a+b*log(c*x^n))^2/(e*sqrt(x))],
[(a+b*log(c*x^n))^2*log(d*(e+f*sqrt(x)))/x^3,x,23,-37/108*b^2*f*n^2/(e*x^(3/2))+7/8*b^2*f^2*n^2/(e^2*x)-1/8*b^2*f^4*n^2*log(x)/e^4+1/8*b^2*f^4*n^2*log(x)^2/e^4-7/18*b*f*n*(a+b*log(c*x^n))/(e*x^(3/2))+3/4*b*f^2*n*(a+b*log(c*x^n))/(e^2*x)-1/4*b*f^4*n*log(x)*(a+b*log(c*x^n))/e^4-1/6*f*(a+b*log(c*x^n))^2/(e*x^(3/2))+1/4*f^2*(a+b*log(c*x^n))^2/(e^2*x)-1/12*f^4*(a+b*log(c*x^n))^3/(b*e^4*n)+1/4*b^2*f^4*n^2*log(e+f*sqrt(x))/e^4+1/2*b*f^4*n*(a+b*log(c*x^n))*log(e+f*sqrt(x))/e^4-b^2*f^4*n^2*log(-f*sqrt(x)/e)*log(e+f*sqrt(x))/e^4-1/4*b^2*n^2*log(d*(e+f*sqrt(x)))/x^2-1/2*b*n*(a+b*log(c*x^n))*log(d*(e+f*sqrt(x)))/x^2-1/2*(a+b*log(c*x^n))^2*log(d*(e+f*sqrt(x)))/x^2+1/2*f^4*(a+b*log(c*x^n))^2*log(1+f*sqrt(x)/e)/e^4+2*b*f^4*n*(a+b*log(c*x^n))*polylog(2,-f*sqrt(x)/e)/e^4-b^2*f^4*n^2*polylog(2,1+f*sqrt(x)/e)/e^4-4*b^2*f^4*n^2*polylog(3,-f*sqrt(x)/e)/e^4-21/4*b^2*f^3*n^2/(e^3*sqrt(x))-5/2*b*f^3*n*(a+b*log(c*x^n))/(e^3*sqrt(x))-1/2*f^3*(a+b*log(c*x^n))^2/(e^3*sqrt(x))],
[x*(a+b*log(c*x^n))^3*log(d*(e+f*sqrt(x))),x,36,-9/4*a*b^2*e^2*n^2*x/f^2+45/16*b^3*e^2*n^3*x/f^2-175/216*b^3*e*n^3*x^(3/2)/f+3/8*b^3*n^3*x^2-9/4*b^3*e^2*n^2*x*log(c*x^n)/f^2-3/8*b^2*e^2*n^2*x*(a+b*log(c*x^n))/f^2+37/36*b^2*e*n^2*x^(3/2)*(a+b*log(c*x^n))/f-9/16*b^2*n^2*x^2*(a+b*log(c*x^n))+9/8*b*e^2*n*x*(a+b*log(c*x^n))^2/f^2-7/12*b*e*n*x^(3/2)*(a+b*log(c*x^n))^2/f+3/8*b*n*x^2*(a+b*log(c*x^n))^2-1/4*e^2*x*(a+b*log(c*x^n))^3/f^2+1/6*e*x^(3/2)*(a+b*log(c*x^n))^3/f-1/8*x^2*(a+b*log(c*x^n))^3+3/8*b^3*e^4*n^3*log(e+f*sqrt(x))/f^4-3/4*b^2*e^4*n^2*(a+b*log(c*x^n))*log(e+f*sqrt(x))/f^4+3/2*b^3*e^4*n^3*log(-f*sqrt(x)/e)*log(e+f*sqrt(x))/f^4-3/8*b^3*n^3*x^2*log(d*(e+f*sqrt(x)))+3/4*b^2*n^2*x^2*(a+b*log(c*x^n))*log(d*(e+f*sqrt(x)))-3/4*b*n*x^2*(a+b*log(c*x^n))^2*log(d*(e+f*sqrt(x)))+1/2*x^2*(a+b*log(c*x^n))^3*log(d*(e+f*sqrt(x)))+3/4*b*e^4*n*(a+b*log(c*x^n))^2*log(1+f*sqrt(x)/e)/f^4-1/2*e^4*(a+b*log(c*x^n))^3*log(1+f*sqrt(x)/e)/f^4+3*b^2*e^4*n^2*(a+b*log(c*x^n))*polylog(2,-f*sqrt(x)/e)/f^4-3*b*e^4*n*(a+b*log(c*x^n))^2*polylog(2,-f*sqrt(x)/e)/f^4+3/2*b^3*e^4*n^3*polylog(2,1+f*sqrt(x)/e)/f^4-6*b^3*e^4*n^3*polylog(3,-f*sqrt(x)/e)/f^4+12*b^2*e^4*n^2*(a+b*log(c*x^n))*polylog(3,-f*sqrt(x)/e)/f^4-24*b^3*e^4*n^3*polylog(4,-f*sqrt(x)/e)/f^4-255/8*b^3*e^3*n^3*sqrt(x)/f^3+63/4*b^2*e^3*n^2*(a+b*log(c*x^n))*sqrt(x)/f^3-15/4*b*e^3*n*(a+b*log(c*x^n))^2*sqrt(x)/f^3+1/2*e^3*(a+b*log(c*x^n))^3*sqrt(x)/f^3],
[(a+b*log(c*x^n))^3*log(d*(e+f*sqrt(x))),x,30,-6*a*b^2*n^2*x+12*b^3*n^3*x-6*b^3*n^2*x*log(c*x^n)-3*b^2*n^2*x*(a+b*log(c*x^n))+3*b*n*x*(a+b*log(c*x^n))^2-1/2*x*(a+b*log(c*x^n))^3+6*b^3*e^2*n^3*log(e+f*sqrt(x))/f^2-6*b^2*e^2*n^2*(a+b*log(c*x^n))*log(e+f*sqrt(x))/f^2+12*b^3*e^2*n^3*log(-f*sqrt(x)/e)*log(e+f*sqrt(x))/f^2-6*b^3*n^3*x*log(d*(e+f*sqrt(x)))+6*b^2*n^2*x*(a+b*log(c*x^n))*log(d*(e+f*sqrt(x)))-3*b*n*x*(a+b*log(c*x^n))^2*log(d*(e+f*sqrt(x)))+x*(a+b*log(c*x^n))^3*log(d*(e+f*sqrt(x)))+3*b*e^2*n*(a+b*log(c*x^n))^2*log(1+f*sqrt(x)/e)/f^2-e^2*(a+b*log(c*x^n))^3*log(1+f*sqrt(x)/e)/f^2+12*b^2*e^2*n^2*(a+b*log(c*x^n))*polylog(2,-f*sqrt(x)/e)/f^2-6*b*e^2*n*(a+b*log(c*x^n))^2*polylog(2,-f*sqrt(x)/e)/f^2+12*b^3*e^2*n^3*polylog(2,1+f*sqrt(x)/e)/f^2-24*b^3*e^2*n^3*polylog(3,-f*sqrt(x)/e)/f^2+24*b^2*e^2*n^2*(a+b*log(c*x^n))*polylog(3,-f*sqrt(x)/e)/f^2-48*b^3*e^2*n^3*polylog(4,-f*sqrt(x)/e)/f^2-90*b^3*e*n^3*sqrt(x)/f+42*b^2*e*n^2*(a+b*log(c*x^n))*sqrt(x)/f-9*b*e*n*(a+b*log(c*x^n))^2*sqrt(x)/f+e*(a+b*log(c*x^n))^3*sqrt(x)/f],
[(a+b*log(c*x^n))^3*log(d*(e+f*sqrt(x)))/x,x,6,1/4*(a+b*log(c*x^n))^4*log(d*(e+f*sqrt(x)))/(b*n)-1/4*(a+b*log(c*x^n))^4*log(1+f*sqrt(x)/e)/(b*n)-2*(a+b*log(c*x^n))^3*polylog(2,-f*sqrt(x)/e)+12*b*n*(a+b*log(c*x^n))^2*polylog(3,-f*sqrt(x)/e)-48*b^2*n^2*(a+b*log(c*x^n))*polylog(4,-f*sqrt(x)/e)+96*b^3*n^3*polylog(5,-f*sqrt(x)/e)],
[(a+b*log(c*x^n))^3*log(d*(e+f*sqrt(x)))/x^2,x,34,-3*b^3*f^2*n^3*log(x)/e^2+3/2*b^3*f^2*n^3*log(x)^2/e^2-3*b^2*f^2*n^2*log(x)*(a+b*log(c*x^n))/e^2-1/2*f^2*(a+b*log(c*x^n))^3/e^2-1/8*f^2*(a+b*log(c*x^n))^4/(b*e^2*n)+6*b^3*f^2*n^3*log(e+f*sqrt(x))/e^2+6*b^2*f^2*n^2*(a+b*log(c*x^n))*log(e+f*sqrt(x))/e^2-12*b^3*f^2*n^3*log(-f*sqrt(x)/e)*log(e+f*sqrt(x))/e^2-6*b^3*n^3*log(d*(e+f*sqrt(x)))/x-6*b^2*n^2*(a+b*log(c*x^n))*log(d*(e+f*sqrt(x)))/x-3*b*n*(a+b*log(c*x^n))^2*log(d*(e+f*sqrt(x)))/x-(a+b*log(c*x^n))^3*log(d*(e+f*sqrt(x)))/x+3*b*f^2*n*(a+b*log(c*x^n))^2*log(1+f*sqrt(x)/e)/e^2+f^2*(a+b*log(c*x^n))^3*log(1+f*sqrt(x)/e)/e^2+12*b^2*f^2*n^2*(a+b*log(c*x^n))*polylog(2,-f*sqrt(x)/e)/e^2+6*b*f^2*n*(a+b*log(c*x^n))^2*polylog(2,-f*sqrt(x)/e)/e^2-12*b^3*f^2*n^3*polylog(2,1+f*sqrt(x)/e)/e^2-24*b^3*f^2*n^3*polylog(3,-f*sqrt(x)/e)/e^2-24*b^2*f^2*n^2*(a+b*log(c*x^n))*polylog(3,-f*sqrt(x)/e)/e^2+48*b^3*f^2*n^3*polylog(4,-f*sqrt(x)/e)/e^2-90*b^3*f*n^3/(e*sqrt(x))-42*b^2*f*n^2*(a+b*log(c*x^n))/(e*sqrt(x))-9*b*f*n*(a+b*log(c*x^n))^2/(e*sqrt(x))-f*(a+b*log(c*x^n))^3/(e*sqrt(x))],
[(a+b*log(c*x^n))^3*log(d*(e+f*sqrt(x)))/x^3,x,40,-175/216*b^3*f*n^3/(e*x^(3/2))+45/16*b^3*f^2*n^3/(e^2*x)-3/16*b^3*f^4*n^3*log(x)/e^4+3/16*b^3*f^4*n^3*log(x)^2/e^4-37/36*b^2*f*n^2*(a+b*log(c*x^n))/(e*x^(3/2))+21/8*b^2*f^2*n^2*(a+b*log(c*x^n))/(e^2*x)-3/8*b^2*f^4*n^2*log(x)*(a+b*log(c*x^n))/e^4-7/12*b*f*n*(a+b*log(c*x^n))^2/(e*x^(3/2))+9/8*b*f^2*n*(a+b*log(c*x^n))^2/(e^2*x)-1/8*f^4*(a+b*log(c*x^n))^3/e^4-1/6*f*(a+b*log(c*x^n))^3/(e*x^(3/2))+1/4*f^2*(a+b*log(c*x^n))^3/(e^2*x)-1/16*f^4*(a+b*log(c*x^n))^4/(b*e^4*n)+3/8*b^3*f^4*n^3*log(e+f*sqrt(x))/e^4+3/4*b^2*f^4*n^2*(a+b*log(c*x^n))*log(e+f*sqrt(x))/e^4-3/2*b^3*f^4*n^3*log(-f*sqrt(x)/e)*log(e+f*sqrt(x))/e^4-3/8*b^3*n^3*log(d*(e+f*sqrt(x)))/x^2-3/4*b^2*n^2*(a+b*log(c*x^n))*log(d*(e+f*sqrt(x)))/x^2-3/4*b*n*(a+b*log(c*x^n))^2*log(d*(e+f*sqrt(x)))/x^2-1/2*(a+b*log(c*x^n))^3*log(d*(e+f*sqrt(x)))/x^2+3/4*b*f^4*n*(a+b*log(c*x^n))^2*log(1+f*sqrt(x)/e)/e^4+1/2*f^4*(a+b*log(c*x^n))^3*log(1+f*sqrt(x)/e)/e^4+3*b^2*f^4*n^2*(a+b*log(c*x^n))*polylog(2,-f*sqrt(x)/e)/e^4+3*b*f^4*n*(a+b*log(c*x^n))^2*polylog(2,-f*sqrt(x)/e)/e^4-3/2*b^3*f^4*n^3*polylog(2,1+f*sqrt(x)/e)/e^4-6*b^3*f^4*n^3*polylog(3,-f*sqrt(x)/e)/e^4-12*b^2*f^4*n^2*(a+b*log(c*x^n))*polylog(3,-f*sqrt(x)/e)/e^4+24*b^3*f^4*n^3*polylog(4,-f*sqrt(x)/e)/e^4-255/8*b^3*f^3*n^3/(e^3*sqrt(x))-63/4*b^2*f^3*n^2*(a+b*log(c*x^n))/(e^3*sqrt(x))-15/4*b*f^3*n*(a+b*log(c*x^n))^2/(e^3*sqrt(x))-1/2*f^3*(a+b*log(c*x^n))^3/(e^3*sqrt(x))],

# Integrands of the form x^(q/2) Log[d (e+f x^m)^k] (a+b Log[c x^n])
[x^(3/2)*(a+b*log(c*x^n))*log(d*(e+f*sqrt(x))^k),x,9,-7/25*b*e^3*k*n*x/f^3+32/225*b*e^2*k*n*x^(3/2)/f^2-9/100*b*e*k*n*x^2/f+8/125*b*k*n*x^(5/2)+1/5*e^3*k*x*(a+b*log(c*x^n))/f^3-2/15*e^2*k*x^(3/2)*(a+b*log(c*x^n))/f^2+1/10*e*k*x^2*(a+b*log(c*x^n))/f-2/25*k*x^(5/2)*(a+b*log(c*x^n))-4/25*b*e^5*k*n*log(e+f*sqrt(x))/f^5+2/5*e^5*k*(a+b*log(c*x^n))*log(e+f*sqrt(x))/f^5-4/5*b*e^5*k*n*log(-f*sqrt(x)/e)*log(e+f*sqrt(x))/f^5-4/25*b*n*x^(5/2)*log(d*(e+f*sqrt(x))^k)+2/5*x^(5/2)*(a+b*log(c*x^n))*log(d*(e+f*sqrt(x))^k)-4/5*b*e^5*k*n*polylog(2,1+f*sqrt(x)/e)/f^5+24/25*b*e^4*k*n*sqrt(x)/f^4-2/5*e^4*k*(a+b*log(c*x^n))*sqrt(x)/f^4],
[x^(1/2)*(a+b*log(c*x^n))*log(d*(e+f*sqrt(x))^k),x,9,-5/9*b*e*k*n*x/f+8/27*b*k*n*x^(3/2)+1/3*e*k*x*(a+b*log(c*x^n))/f-2/9*k*x^(3/2)*(a+b*log(c*x^n))-4/9*b*e^3*k*n*log(e+f*sqrt(x))/f^3+2/3*e^3*k*(a+b*log(c*x^n))*log(e+f*sqrt(x))/f^3-4/3*b*e^3*k*n*log(-f*sqrt(x)/e)*log(e+f*sqrt(x))/f^3-4/9*b*n*x^(3/2)*log(d*(e+f*sqrt(x))^k)+2/3*x^(3/2)*(a+b*log(c*x^n))*log(d*(e+f*sqrt(x))^k)-4/3*b*e^3*k*n*polylog(2,1+f*sqrt(x)/e)/f^3+16/9*b*e^2*k*n*sqrt(x)/f^2-2/3*e^2*k*(a+b*log(c*x^n))*sqrt(x)/f^2],
[(a+b*log(c*x^n))*log(d*(e+f*sqrt(x))^k)/x^(3/2),x,11,2*b*f*k*n*log(x)/e-1/2*b*f*k*n*log(x)^2/e+f*k*log(x)*(a+b*log(c*x^n))/e-4*b*f*k*n*log(e+f*sqrt(x))/e-2*f*k*(a+b*log(c*x^n))*log(e+f*sqrt(x))/e+4*b*f*k*n*log(-f*sqrt(x)/e)*log(e+f*sqrt(x))/e+4*b*f*k*n*polylog(2,1+f*sqrt(x)/e)/e-4*b*n*log(d*(e+f*sqrt(x))^k)/sqrt(x)-2*(a+b*log(c*x^n))*log(d*(e+f*sqrt(x))^k)/sqrt(x)],
[(a+b*log(c*x^n))*log(d*(e+f*sqrt(x))^k)/x^(5/2),x,10,-5/9*b*f*k*n/(e*x)+2/9*b*f^3*k*n*log(x)/e^3-1/6*b*f^3*k*n*log(x)^2/e^3-1/3*f*k*(a+b*log(c*x^n))/(e*x)+1/3*f^3*k*log(x)*(a+b*log(c*x^n))/e^3-4/9*b*f^3*k*n*log(e+f*sqrt(x))/e^3-2/3*f^3*k*(a+b*log(c*x^n))*log(e+f*sqrt(x))/e^3+4/3*b*f^3*k*n*log(-f*sqrt(x)/e)*log(e+f*sqrt(x))/e^3-4/9*b*n*log(d*(e+f*sqrt(x))^k)/x^(3/2)-2/3*(a+b*log(c*x^n))*log(d*(e+f*sqrt(x))^k)/x^(3/2)+4/3*b*f^3*k*n*polylog(2,1+f*sqrt(x)/e)/e^3+16/9*b*f^2*k*n/(e^2*sqrt(x))+2/3*f^2*k*(a+b*log(c*x^n))/(e^2*sqrt(x))],
[(a+b*log(c*x^n))*log(d*(e+f*sqrt(x))^k)/x^(7/2),x,10,-9/100*b*f*k*n/(e*x^2)+32/225*b*f^2*k*n/(e^2*x^(3/2))-7/25*b*f^3*k*n/(e^3*x)+2/25*b*f^5*k*n*log(x)/e^5-1/10*b*f^5*k*n*log(x)^2/e^5-1/10*f*k*(a+b*log(c*x^n))/(e*x^2)+2/15*f^2*k*(a+b*log(c*x^n))/(e^2*x^(3/2))-1/5*f^3*k*(a+b*log(c*x^n))/(e^3*x)+1/5*f^5*k*log(x)*(a+b*log(c*x^n))/e^5-4/25*b*f^5*k*n*log(e+f*sqrt(x))/e^5-2/5*f^5*k*(a+b*log(c*x^n))*log(e+f*sqrt(x))/e^5+4/5*b*f^5*k*n*log(-f*sqrt(x)/e)*log(e+f*sqrt(x))/e^5-4/25*b*n*log(d*(e+f*sqrt(x))^k)/x^(5/2)-2/5*(a+b*log(c*x^n))*log(d*(e+f*sqrt(x))^k)/x^(5/2)+4/5*b*f^5*k*n*polylog(2,1+f*sqrt(x)/e)/e^5+24/25*b*f^4*k*n/(e^4*sqrt(x))+2/5*f^4*k*(a+b*log(c*x^n))/(e^4*sqrt(x))],

# Integrands of the form x^q Log[d (e+f x^m)^k] (a+b Log[c x^n]) with m symbolic
[(g*x)^q*(a+b*log(c*x^n))*log(d*(e+f*x^m)^k),x,0,Unintegrable((g*x)^q*(a+b*log(c*x^n))*log(d*(e+f*x^m)^k),x)],
[(a+b*log(c*x^n))^3*log(d*(e+f*x^m)^r)/x,x,6,1/4*(a+b*log(c*x^n))^4*log(d*(e+f*x^m)^r)/(b*n)-1/4*r*(a+b*log(c*x^n))^4*log(1+f*x^m/e)/(b*n)-r*(a+b*log(c*x^n))^3*polylog(2,-f*x^m/e)/m+3*b*n*r*(a+b*log(c*x^n))^2*polylog(3,-f*x^m/e)/m^2-6*b^2*n^2*r*(a+b*log(c*x^n))*polylog(4,-f*x^m/e)/m^3+6*b^3*n^3*r*polylog(5,-f*x^m/e)/m^4],
[(a+b*log(c*x^n))^2*log(d*(e+f*x^m)^r)/x,x,5,1/3*(a+b*log(c*x^n))^3*log(d*(e+f*x^m)^r)/(b*n)-1/3*r*(a+b*log(c*x^n))^3*log(1+f*x^m/e)/(b*n)-r*(a+b*log(c*x^n))^2*polylog(2,-f*x^m/e)/m+2*b*n*r*(a+b*log(c*x^n))*polylog(3,-f*x^m/e)/m^2-2*b^2*n^2*r*polylog(4,-f*x^m/e)/m^3],
[(a+b*log(c*x^n))*log(d*(e+f*x^m)^r)/x,x,4,1/2*(a+b*log(c*x^n))^2*log(d*(e+f*x^m)^r)/(b*n)-1/2*r*(a+b*log(c*x^n))^2*log(1+f*x^m/e)/(b*n)-r*(a+b*log(c*x^n))*polylog(2,-f*x^m/e)/m+b*n*r*polylog(3,-f*x^m/e)/m^2],
[log(d*(e+f*x^m)^r)/(x*(a+b*log(c*x^n))),x,0,Unintegrable(log(d*(e+f*x^m)^r)/(x*(a+b*log(c*x^n))),x)],
[log(d*(e+f*x^m)^r)/(x*(a+b*log(c*x^n))^2),x,0,Unintegrable(log(d*(e+f*x^m)^r)/(x*(a+b*log(c*x^n))^2),x)],
[x^2*(a+b*log(c*x^n))*log(d*(e+f*x^m)^k),x,0,Unintegrable(x^2*(a+b*log(c*x^n))*log(d*(e+f*x^m)^k),x)],
[x*(a+b*log(c*x^n))*log(d*(e+f*x^m)^k),x,0,Unintegrable(x*(a+b*log(c*x^n))*log(d*(e+f*x^m)^k),x)],
[(a+b*log(c*x^n))*log(d*(e+f*x^m)^k),x,0,Unintegrable((a+b*log(c*x^n))*log(d*(e+f*x^m)^k),x)],
[(a+b*log(c*x^n))*log(d*(e+f*x^m)^k)/x,x,4,1/2*(a+b*log(c*x^n))^2*log(d*(e+f*x^m)^k)/(b*n)-1/2*k*(a+b*log(c*x^n))^2*log(1+f*x^m/e)/(b*n)-k*(a+b*log(c*x^n))*polylog(2,-f*x^m/e)/m+b*k*n*polylog(3,-f*x^m/e)/m^2],
[(a+b*log(c*x^n))*log(d*(e+f*x^m)^k)/x^2,x,0,Unintegrable((a+b*log(c*x^n))*log(d*(e+f*x^m)^k)/x^2,x)],
[(a+b*log(c*x^n))*log(d*(e+f*x^m)^k)/x^3,x,0,Unintegrable((a+b*log(c*x^n))*log(d*(e+f*x^m)^k)/x^3,x)],
[(g*x)^(-1+3*m)*(a+b*log(c*x^n))*log(d*(e+f*x^m)^k),x,18,2/27*b*k*n*(g*x)^(3*m)/(g*m^2)+4/9*b*e^2*k*n*(g*x)^(3*m)/(f^2*g*m^2*x^(2*m))-5/36*b*e*k*n*(g*x)^(3*m)/(f*g*m^2*x^m)-1/9*k*(g*x)^(3*m)*(a+b*log(c*x^n))/(g*m)-1/3*e^2*k*(g*x)^(3*m)*(a+b*log(c*x^n))/(f^2*g*m*x^(2*m))+1/6*e*k*(g*x)^(3*m)*(a+b*log(c*x^n))/(f*g*m*x^m)-1/9*b*e^3*k*n*(g*x)^(3*m)*log(e+f*x^m)/(f^3*g*m^2*x^(3*m))-1/3*b*e^3*k*n*(g*x)^(3*m)*log(-f*x^m/e)*log(e+f*x^m)/(f^3*g*m^2*x^(3*m))+1/3*e^3*k*(g*x)^(3*m)*(a+b*log(c*x^n))*log(e+f*x^m)/(f^3*g*m*x^(3*m))-1/9*b*n*(g*x)^(3*m)*log(d*(e+f*x^m)^k)/(g*m^2)+1/3*(g*x)^(3*m)*(a+b*log(c*x^n))*log(d*(e+f*x^m)^k)/(g*m)-1/3*b*e^3*k*n*(g*x)^(3*m)*polylog(2,1+f*x^m/e)/(f^3*g*m^2*x^(3*m))],
[(g*x)^(-1+2*m)*(a+b*log(c*x^n))*log(d*(e+f*x^m)^k),x,16,1/4*b*k*n*(g*x)^(2*m)/(g*m^2)-3/4*b*e*k*n*(g*x)^(2*m)/(f*g*m^2*x^m)-1/4*k*(g*x)^(2*m)*(a+b*log(c*x^n))/(g*m)+1/2*e*k*(g*x)^(2*m)*(a+b*log(c*x^n))/(f*g*m*x^m)+1/4*b*e^2*k*n*(g*x)^(2*m)*log(e+f*x^m)/(f^2*g*m^2*x^(2*m))+1/2*b*e^2*k*n*(g*x)^(2*m)*log(-f*x^m/e)*log(e+f*x^m)/(f^2*g*m^2*x^(2*m))-1/2*e^2*k*(g*x)^(2*m)*(a+b*log(c*x^n))*log(e+f*x^m)/(f^2*g*m*x^(2*m))-1/4*b*n*(g*x)^(2*m)*log(d*(e+f*x^m)^k)/(g*m^2)+1/2*(g*x)^(2*m)*(a+b*log(c*x^n))*log(d*(e+f*x^m)^k)/(g*m)+1/2*b*e^2*k*n*(g*x)^(2*m)*polylog(2,1+f*x^m/e)/(f^2*g*m^2*x^(2*m))],
[(g*x)^(-1+m)*(a+b*log(c*x^n))*log(d*(e+f*x^m)^k),x,14,2*b*k*n*(g*x)^m/(g*m^2)-k*(g*x)^m*(a+b*log(c*x^n))/(g*m)-b*e*k*n*(g*x)^m*log(e+f*x^m)/(f*g*m^2*x^m)-b*e*k*n*(g*x)^m*log(-f*x^m/e)*log(e+f*x^m)/(f*g*m^2*x^m)+e*k*(g*x)^m*(a+b*log(c*x^n))*log(e+f*x^m)/(f*g*m*x^m)-b*n*(g*x)^m*log(d*(e+f*x^m)^k)/(g*m^2)+(g*x)^m*(a+b*log(c*x^n))*log(d*(e+f*x^m)^k)/(g*m)-b*e*k*n*(g*x)^m*polylog(2,1+f*x^m/e)/(f*g*m^2*x^m)],
[(g*x)^(-1-m)*(a+b*log(c*x^n))*log(d*(e+f*x^m)^k),x,15,b*f*k*n*x^m*log(x)/(e*g*m*(g*x)^m)-1/2*b*f*k*n*x^m*log(x)^2/(e*g*(g*x)^m)+f*k*x^m*log(x)*(a+b*log(c*x^n))/(e*g*(g*x)^m)-b*f*k*n*x^m*log(e+f*x^m)/(e*g*m^2*(g*x)^m)+b*f*k*n*x^m*log(-f*x^m/e)*log(e+f*x^m)/(e*g*m^2*(g*x)^m)-f*k*x^m*(a+b*log(c*x^n))*log(e+f*x^m)/(e*g*m*(g*x)^m)-b*n*log(d*(e+f*x^m)^k)/(g*m^2*(g*x)^m)-(a+b*log(c*x^n))*log(d*(e+f*x^m)^k)/(g*m*(g*x)^m)+b*f*k*n*x^m*polylog(2,1+f*x^m/e)/(e*g*m^2*(g*x)^m)],
[(g*x)^(-1-2*m)*(a+b*log(c*x^n))*log(d*(e+f*x^m)^k),x,16,-3/4*b*f*k*n*x^m/(e*g*m^2*(g*x)^(2*m))-1/4*b*f^2*k*n*x^(2*m)*log(x)/(e^2*g*m*(g*x)^(2*m))+1/4*b*f^2*k*n*x^(2*m)*log(x)^2/(e^2*g*(g*x)^(2*m))-1/2*f*k*x^m*(a+b*log(c*x^n))/(e*g*m*(g*x)^(2*m))-1/2*f^2*k*x^(2*m)*log(x)*(a+b*log(c*x^n))/(e^2*g*(g*x)^(2*m))+1/4*b*f^2*k*n*x^(2*m)*log(e+f*x^m)/(e^2*g*m^2*(g*x)^(2*m))-1/2*b*f^2*k*n*x^(2*m)*log(-f*x^m/e)*log(e+f*x^m)/(e^2*g*m^2*(g*x)^(2*m))+1/2*f^2*k*x^(2*m)*(a+b*log(c*x^n))*log(e+f*x^m)/(e^2*g*m*(g*x)^(2*m))-1/4*b*n*log(d*(e+f*x^m)^k)/(g*m^2*(g*x)^(2*m))-1/2*(a+b*log(c*x^n))*log(d*(e+f*x^m)^k)/(g*m*(g*x)^(2*m))-1/2*b*f^2*k*n*x^(2*m)*polylog(2,1+f*x^m/e)/(e^2*g*m^2*(g*x)^(2*m))],
[(g*x)^(-1-3*m)*(a+b*log(c*x^n))*log(d*(e+f*x^m)^k),x,18,-5/36*b*f*k*n*x^m/(e*g*m^2*(g*x)^(3*m))+4/9*b*f^2*k*n*x^(2*m)/(e^2*g*m^2*(g*x)^(3*m))+1/9*b*f^3*k*n*x^(3*m)*log(x)/(e^3*g*m*(g*x)^(3*m))-1/6*b*f^3*k*n*x^(3*m)*log(x)^2/(e^3*g*(g*x)^(3*m))-1/6*f*k*x^m*(a+b*log(c*x^n))/(e*g*m*(g*x)^(3*m))+1/3*f^2*k*x^(2*m)*(a+b*log(c*x^n))/(e^2*g*m*(g*x)^(3*m))+1/3*f^3*k*x^(3*m)*log(x)*(a+b*log(c*x^n))/(e^3*g*(g*x)^(3*m))-1/9*b*f^3*k*n*x^(3*m)*log(e+f*x^m)/(e^3*g*m^2*(g*x)^(3*m))+1/3*b*f^3*k*n*x^(3*m)*log(-f*x^m/e)*log(e+f*x^m)/(e^3*g*m^2*(g*x)^(3*m))-1/3*f^3*k*x^(3*m)*(a+b*log(c*x^n))*log(e+f*x^m)/(e^3*g*m*(g*x)^(3*m))-1/9*b*n*log(d*(e+f*x^m)^k)/(g*m^2*(g*x)^(3*m))-1/3*(a+b*log(c*x^n))*log(d*(e+f*x^m)^k)/(g*m*(g*x)^(3*m))+1/3*b*f^3*k*n*x^(3*m)*polylog(2,1+f*x^m/e)/(e^3*g*m^2*(g*x)^(3*m))],

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

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

# p>0
[x^2*(a+b*log(c*x^n))*(d+e*log(f*x^r)),x,3,1/27*b*e*n*r*x^3-1/27*e*r*x^3*(3*a-b*n+3*b*log(c*x^n))-1/9*b*n*x^3*(d+e*log(f*x^r))+1/3*x^3*(a+b*log(c*x^n))*(d+e*log(f*x^r))],
[x*(a+b*log(c*x^n))*(d+e*log(f*x^r)),x,3,1/8*b*e*n*r*x^2-1/8*e*r*x^2*(2*a-b*n+2*b*log(c*x^n))-1/4*b*n*x^2*(d+e*log(f*x^r))+1/2*x^2*(a+b*log(c*x^n))*(d+e*log(f*x^r))],
[(a+b*log(c*x^n))*(d+e*log(f*x^r)),x,3,b*e*n*r*x-e*(a-b*n)*r*x-b*e*r*x*log(c*x^n)+a*x*(d+e*log(f*x^r))-b*n*x*(d+e*log(f*x^r))+b*x*log(c*x^n)*(d+e*log(f*x^r))],
[(a+b*log(c*x^n))*(d+e*log(f*x^r))/x,x,4,-1/6*e*r*(a+b*log(c*x^n))^3/(b^2*n^2)+1/2*(a+b*log(c*x^n))^2*(d+e*log(f*x^r))/(b*n)],
[(a+b*log(c*x^n))*(d+e*log(f*x^r))/x^2,x,2,-b*e*n*r/x-e*r*(a+b*n+b*log(c*x^n))/x-b*n*(d+e*log(f*x^r))/x-(a+b*log(c*x^n))*(d+e*log(f*x^r))/x],
[(a+b*log(c*x^n))*(d+e*log(f*x^r))/x^3,x,3,-1/8*b*e*n*r/x^2-1/8*e*r*(2*a+b*n+2*b*log(c*x^n))/x^2-1/4*b*n*(d+e*log(f*x^r))/x^2-1/2*(a+b*log(c*x^n))*(d+e*log(f*x^r))/x^2],
[(a+b*log(c*x^n))*(d+e*log(f*x^r))/x^4,x,3,-1/27*b*e*n*r/x^3-1/27*e*r*(3*a+b*n+3*b*log(c*x^n))/x^3-1/9*b*n*(d+e*log(f*x^r))/x^3-1/3*(a+b*log(c*x^n))*(d+e*log(f*x^r))/x^3],
[x^2*(a+b*log(c*x^n))^2*(d+e*log(f*x^r)),x,7,-2/81*b^2*e*n^2*r*x^3+2/81*b*e*n*(3*a-b*n)*r*x^3-1/81*e*(9*a^2-6*a*b*n+2*b^2*n^2)*r*x^3+2/27*b^2*e*n*r*x^3*log(c*x^n)-2/27*b*e*(3*a-b*n)*r*x^3*log(c*x^n)-1/9*b^2*e*r*x^3*log(c*x^n)^2+2/27*b^2*n^2*x^3*(d+e*log(f*x^r))-2/9*b*n*x^3*(a+b*log(c*x^n))*(d+e*log(f*x^r))+1/3*x^3*(a+b*log(c*x^n))^2*(d+e*log(f*x^r))],
[x*(a+b*log(c*x^n))^2*(d+e*log(f*x^r)),x,7,-1/8*b^2*e*n^2*r*x^2+1/8*b*e*n*(2*a-b*n)*r*x^2-1/8*e*(2*a^2-2*a*b*n+b^2*n^2)*r*x^2+1/4*b^2*e*n*r*x^2*log(c*x^n)-1/4*b*e*(2*a-b*n)*r*x^2*log(c*x^n)-1/4*b^2*e*r*x^2*log(c*x^n)^2+1/4*b^2*n^2*x^2*(d+e*log(f*x^r))-1/2*b*n*x^2*(a+b*log(c*x^n))*(d+e*log(f*x^r))+1/2*x^2*(a+b*log(c*x^n))^2*(d+e*log(f*x^r))],
[(a+b*log(c*x^n))^2*(d+e*log(f*x^r)),x,6,2*a*b*e*n*r*x-4*b^2*e*n^2*r*x+2*b*e*n*(a-b*n)*r*x+4*b^2*e*n*r*x*log(c*x^n)-e*r*x*(a+b*log(c*x^n))^2-2*a*b*n*x*(d+e*log(f*x^r))+2*b^2*n^2*x*(d+e*log(f*x^r))-2*b^2*n*x*log(c*x^n)*(d+e*log(f*x^r))+x*(a+b*log(c*x^n))^2*(d+e*log(f*x^r))],
[(a+b*log(c*x^n))^2*(d+e*log(f*x^r))/x,x,4,-1/12*e*r*(a+b*log(c*x^n))^4/(b^2*n^2)+1/3*(a+b*log(c*x^n))^3*(d+e*log(f*x^r))/(b*n)],
[(a+b*log(c*x^n))^2*(d+e*log(f*x^r))/x^2,x,6,-2*b^2*e*n^2*r/x-2*b*e*n*(a+b*n)*r/x-e*(a^2+2*a*b*n+2*b^2*n^2)*r/x-2*b^2*e*n*r*log(c*x^n)/x-2*b*e*(a+b*n)*r*log(c*x^n)/x-b^2*e*r*log(c*x^n)^2/x-2*b^2*n^2*(d+e*log(f*x^r))/x-2*b*n*(a+b*log(c*x^n))*(d+e*log(f*x^r))/x-(a+b*log(c*x^n))^2*(d+e*log(f*x^r))/x],
[(a+b*log(c*x^n))^2*(d+e*log(f*x^r))/x^3,x,7,-1/8*b^2*e*n^2*r/x^2-1/8*b*e*n*(2*a+b*n)*r/x^2-1/8*e*(2*a^2+2*a*b*n+b^2*n^2)*r/x^2-1/4*b^2*e*n*r*log(c*x^n)/x^2-1/4*b*e*(2*a+b*n)*r*log(c*x^n)/x^2-1/4*b^2*e*r*log(c*x^n)^2/x^2-1/4*b^2*n^2*(d+e*log(f*x^r))/x^2-1/2*b*n*(a+b*log(c*x^n))*(d+e*log(f*x^r))/x^2-1/2*(a+b*log(c*x^n))^2*(d+e*log(f*x^r))/x^2],
[(a+b*log(c*x^n))^2*(d+e*log(f*x^r))/x^4,x,7,-2/81*b^2*e*n^2*r/x^3-2/81*b*e*n*(3*a+b*n)*r/x^3-1/81*e*(9*a^2+6*a*b*n+2*b^2*n^2)*r/x^3-2/27*b^2*e*n*r*log(c*x^n)/x^3-2/27*b*e*(3*a+b*n)*r*log(c*x^n)/x^3-1/9*b^2*e*r*log(c*x^n)^2/x^3-2/27*b^2*n^2*(d+e*log(f*x^r))/x^3-2/9*b*n*(a+b*log(c*x^n))*(d+e*log(f*x^r))/x^3-1/3*(a+b*log(c*x^n))^2*(d+e*log(f*x^r))/x^3],

# p<0
[x^2*(a+b*log(c*x^n))/(d+e*log(f*x^m)),x,6,1/3*b*n*x^3/(e*m)-b*n*x^3*Ei(3*(d+e*log(f*x^m))/(e*m))*(d+e*log(f*x^m))/(e^2*exp(3*d/(e*m))*m^2*(f*x^m)^(3/m))+x^3*Ei(3*(d+e*log(f*x^m))/(e*m))*(a+b*log(c*x^n))/(e*exp(3*d/(e*m))*m*(f*x^m)^(3/m))],
[x*(a+b*log(c*x^n))/(d+e*log(f*x^m)),x,6,1/2*b*n*x^2/(e*m)-b*n*x^2*Ei(2*(d+e*log(f*x^m))/(e*m))*(d+e*log(f*x^m))/(e^2*exp(2*d/(e*m))*m^2*(f*x^m)^(2/m))+x^2*Ei(2*(d+e*log(f*x^m))/(e*m))*(a+b*log(c*x^n))/(e*exp(2*d/(e*m))*m*(f*x^m)^(2/m))],
[(a+b*log(c*x^n))/(d+e*log(f*x^m)),x,6,b*n*x/(e*m)-b*n*x*Ei((d+e*log(f*x^m))/(e*m))*(d+e*log(f*x^m))/(e^2*exp(d/(e*m))*m^2*(f*x^m)^(1/m))+x*Ei((d+e*log(f*x^m))/(e*m))*(a+b*log(c*x^n))/(e*exp(d/(e*m))*m*(f*x^m)^(1/m))],
[(a+b*log(c*x^n))/(x*(d+e*log(f*x^m))),x,5,b*n*log(x)/(e*m)-b*n*(d+e*log(f*x^m))*log(d+e*log(f*x^m))/(e^2*m^2)+(a+b*log(c*x^n))*log(d+e*log(f*x^m))/(e*m)],
[(a+b*log(c*x^n))/(x^2*(d+e*log(f*x^m))),x,6,-b*n/(e*m*x)-b*exp(d/(e*m))*n*(f*x^m)^(1/m)*Ei((-d-e*log(f*x^m))/(e*m))*(d+e*log(f*x^m))/(e^2*m^2*x)+exp(d/(e*m))*(f*x^m)^(1/m)*Ei((-d-e*log(f*x^m))/(e*m))*(a+b*log(c*x^n))/(e*m*x)],
[(a+b*log(c*x^n))/(x^3*(d+e*log(f*x^m))),x,6,-1/2*b*n/(e*m*x^2)-b*exp(2*d/(e*m))*n*(f*x^m)^(2/m)*Ei(-2*(d+e*log(f*x^m))/(e*m))*(d+e*log(f*x^m))/(e^2*m^2*x^2)+exp(2*d/(e*m))*(f*x^m)^(2/m)*Ei(-2*(d+e*log(f*x^m))/(e*m))*(a+b*log(c*x^n))/(e*m*x^2)],
[(a+b*log(c*x^n))/(d+e*log(c*x^n))^2,x,7,(-b*d+a*e+b*e*n)*x*Ei((d+e*log(c*x^n))/(e*n))/(e^3*exp(d/(e*n))*n^2*(c*x^n)^(1/n))+(b*d-a*e)*x/(e^2*n*(d+e*log(c*x^n))),-(b*d-a*e)*x*Ei((d+e*log(c*x^n))/(e*n))/(e^3*exp(d/(e*n))*n^2*(c*x^n)^(1/n))+b*x*Ei((d+e*log(c*x^n))/(e*n))/(e^2*exp(d/(e*n))*n*(c*x^n)^(1/n))+(b*d-a*e)*x/(e^2*n*(d+e*log(c*x^n)))],
[(a+b*log(c*x^n))/(x*log(x)),x,2,b*n*log(x)-b*n*log(x)*log(log(x))+(a+b*log(c*x^n))*log(log(x))],

# Integrands of the form (g x)^m (a+b Log[c x^n])^p (d+e Log[f x^r]) with p symbolic
[(g*x)^m*(a+b*log(c*x^n))^p*(d+e*log(f*x^r)),x,8,-e*r*x*(g*x)^m*GAMMA(2+p,-a*(1+m)/(b*n)-(1+m)*log(c*x^n)/n)*(a+b*log(c*x^n))^p/(exp(a*(1+m)/(b*n))*(1+m)^2*(c*x^n)^((1+m)/n)*(-(1+m)*(a+b*log(c*x^n))/(b*n))^p)-e*r*x*(g*x)^m*GAMMA(1+p,-a*(1+m)/(b*n)-(1+m)*log(c*x^n)/n)*(a+b*log(c*x^n))^(1+p)/(b*exp(a*(1+m)/(b*n))*(1+m)*n*(c*x^n)^((1+m)/n)*(-(1+m)*(a+b*log(c*x^n))/(b*n))^p)+(g*x)^(1+m)*GAMMA(1+p,-(1+m)*(a+b*log(c*x^n))/(b*n))*(a+b*log(c*x^n))^p*(d+e*log(f*x^r))/(exp(a*(1+m)/(b*n))*g*(1+m)*(c*x^n)^((1+m)/n)*(-(1+m)*(a+b*log(c*x^n))/(b*n))^p)],
[x^2*(a+b*log(c*x^n))^p*(d+e*log(f*x^r)),x,7,-3^(-2-p)*e*r*x^3*GAMMA(2+p,-3*a/(b*n)-3*log(c*x^n)/n)*(a+b*log(c*x^n))^p/(exp(3*a/(b*n))*(c*x^n)^(3/n)*((-a-b*log(c*x^n))/(b*n))^p)-3^(-1-p)*e*r*x^3*GAMMA(1+p,-3*a/(b*n)-3*log(c*x^n)/n)*(a+b*log(c*x^n))^(1+p)/(b*exp(3*a/(b*n))*n*(c*x^n)^(3/n)*((-a-b*log(c*x^n))/(b*n))^p)+3^(-1-p)*x^3*GAMMA(1+p,-3*(a+b*log(c*x^n))/(b*n))*(a+b*log(c*x^n))^p*(d+e*log(f*x^r))/(exp(3*a/(b*n))*(c*x^n)^(3/n)*((-a-b*log(c*x^n))/(b*n))^p)],
[x*(a+b*log(c*x^n))^p*(d+e*log(f*x^r)),x,7,-2^(-2-p)*e*r*x^2*GAMMA(2+p,-2*a/(b*n)-2*log(c*x^n)/n)*(a+b*log(c*x^n))^p/(exp(2*a/(b*n))*(c*x^n)^(2/n)*((-a-b*log(c*x^n))/(b*n))^p)-2^(-1-p)*e*r*x^2*GAMMA(1+p,-2*a/(b*n)-2*log(c*x^n)/n)*(a+b*log(c*x^n))^(1+p)/(b*exp(2*a/(b*n))*n*(c*x^n)^(2/n)*((-a-b*log(c*x^n))/(b*n))^p)+2^(-1-p)*x^2*GAMMA(1+p,-2*(a+b*log(c*x^n))/(b*n))*(a+b*log(c*x^n))^p*(d+e*log(f*x^r))/(exp(2*a/(b*n))*(c*x^n)^(2/n)*((-a-b*log(c*x^n))/(b*n))^p)],
[(a+b*log(c*x^n))^p*(d+e*log(f*x^r)),x,7,-e*r*x*GAMMA(2+p,-a/(b*n)-log(c*x^n)/n)*(a+b*log(c*x^n))^p/(exp(a/(b*n))*(c*x^n)^(1/n)*((-a-b*log(c*x^n))/(b*n))^p)-e*r*x*GAMMA(1+p,-a/(b*n)-log(c*x^n)/n)*(a+b*log(c*x^n))^(1+p)/(b*exp(a/(b*n))*n*(c*x^n)^(1/n)*((-a-b*log(c*x^n))/(b*n))^p)+x*GAMMA(1+p,(-a-b*log(c*x^n))/(b*n))*(a+b*log(c*x^n))^p*(d+e*log(f*x^r))/(exp(a/(b*n))*(c*x^n)^(1/n)*((-a-b*log(c*x^n))/(b*n))^p)],
[(a+b*log(c*x^n))^p*(d+e*log(f*x^r))/x,x,4,-e*r*(a+b*log(c*x^n))^(2+p)/(b^2*n^2*(1+p)*(2+p))+(a+b*log(c*x^n))^(1+p)*(d+e*log(f*x^r))/(b*n*(1+p))],
[(a+b*log(c*x^n))^p*(d+e*log(f*x^r))/x^2,x,7,-e*exp(a/(b*n))*r*(c*x^n)^(1/n)*GAMMA(2+p,a/(b*n)+log(c*x^n)/n)*(a+b*log(c*x^n))^p/(x*((a+b*log(c*x^n))/(b*n))^p)+e*exp(a/(b*n))*r*(c*x^n)^(1/n)*GAMMA(1+p,a/(b*n)+log(c*x^n)/n)*(a+b*log(c*x^n))^(1+p)/(b*n*x*((a+b*log(c*x^n))/(b*n))^p)-exp(a/(b*n))*(c*x^n)^(1/n)*GAMMA(1+p,(a+b*log(c*x^n))/(b*n))*(a+b*log(c*x^n))^p*(d+e*log(f*x^r))/(x*((a+b*log(c*x^n))/(b*n))^p)],
[(a+b*log(c*x^n))^p*(d+e*log(f*x^r))/x^3,x,7,-2^(-2-p)*e*exp(2*a/(b*n))*r*(c*x^n)^(2/n)*GAMMA(2+p,2*a/(b*n)+2*log(c*x^n)/n)*(a+b*log(c*x^n))^p/(x^2*((a+b*log(c*x^n))/(b*n))^p)+2^(-1-p)*e*exp(2*a/(b*n))*r*(c*x^n)^(2/n)*GAMMA(1+p,2*a/(b*n)+2*log(c*x^n)/n)*(a+b*log(c*x^n))^(1+p)/(b*n*x^2*((a+b*log(c*x^n))/(b*n))^p)-2^(-1-p)*exp(2*a/(b*n))*(c*x^n)^(2/n)*GAMMA(1+p,2*(a+b*log(c*x^n))/(b*n))*(a+b*log(c*x^n))^p*(d+e*log(f*x^r))/(x^2*((a+b*log(c*x^n))/(b*n))^p)],
[(a+b*log(c*x^n))^p*(d+e*log(f*x^r))/x^4,x,7,-3^(-2-p)*e*exp(3*a/(b*n))*r*(c*x^n)^(3/n)*GAMMA(2+p,3*a/(b*n)+3*log(c*x^n)/n)*(a+b*log(c*x^n))^p/(x^3*((a+b*log(c*x^n))/(b*n))^p)+3^(-1-p)*e*exp(3*a/(b*n))*r*(c*x^n)^(3/n)*GAMMA(1+p,3*a/(b*n)+3*log(c*x^n)/n)*(a+b*log(c*x^n))^(1+p)/(b*n*x^3*((a+b*log(c*x^n))/(b*n))^p)-3^(-1-p)*exp(3*a/(b*n))*(c*x^n)^(3/n)*GAMMA(1+p,3*(a+b*log(c*x^n))/(b*n))*(a+b*log(c*x^n))^p*(d+e*log(f*x^r))/(x^3*((a+b*log(c*x^n))/(b*n))^p)],

# Integrands of the form Pq[x] ArcTrig[d (e +x)]^m (a+b Log[c x^n])
[(d+e*x^2)*arcsin(a*x)*log(c*x^n),x,17,2/27*e*n*(1-a^2*x^2)^(3/2)/a^3-d*n*x*arcsin(a*x)-1/9*e*n*x^3*arcsin(a*x)-1/9*e*n*arctanh(sqrt(1-a^2*x^2))/a^3+1/3*(3*a^2*d+e)*n*arctanh(sqrt(1-a^2*x^2))/a^3-1/9*e*(1-a^2*x^2)^(3/2)*log(c*x^n)/a^3+d*x*arcsin(a*x)*log(c*x^n)+1/3*e*x^3*arcsin(a*x)*log(c*x^n)-d*n*sqrt(1-a^2*x^2)/a-1/3*(3*a^2*d+e)*n*sqrt(1-a^2*x^2)/a^3+1/3*(3*a^2*d+e)*log(c*x^n)*sqrt(1-a^2*x^2)/a^3],
[(d+e*x^2)*arccos(a*x)*log(c*x^n),x,17,-2/27*e*n*(1-a^2*x^2)^(3/2)/a^3-d*n*x*arccos(a*x)-1/9*e*n*x^3*arccos(a*x)+1/9*e*n*arctanh(sqrt(1-a^2*x^2))/a^3-1/3*(3*a^2*d+e)*n*arctanh(sqrt(1-a^2*x^2))/a^3+1/9*e*(1-a^2*x^2)^(3/2)*log(c*x^n)/a^3+d*x*arccos(a*x)*log(c*x^n)+1/3*e*x^3*arccos(a*x)*log(c*x^n)+d*n*sqrt(1-a^2*x^2)/a+1/3*(3*a^2*d+e)*n*sqrt(1-a^2*x^2)/a^3-1/3*(3*a^2*d+e)*log(c*x^n)*sqrt(1-a^2*x^2)/a^3],
[(d+e*x^2)*arctan(a*x)*log(c*x^n),x,9,5/36*e*n*x^2/a-d*n*x*arctan(a*x)-1/9*e*n*x^3*arctan(a*x)-1/6*e*x^2*log(c*x^n)/a+d*x*arctan(a*x)*log(c*x^n)+1/3*e*x^3*arctan(a*x)*log(c*x^n)+1/2*d*n*log(1+a^2*x^2)/a-1/18*e*n*log(1+a^2*x^2)/a^3-1/6*(3*a^2*d-e)*log(c*x^n)*log(1+a^2*x^2)/a^3-1/12*(3*a^2*d-e)*n*polylog(2,-a^2*x^2)/a^3],
[(d+e*x^2)*arccot(a*x)*log(c*x^n),x,9,-5/36*e*n*x^2/a-d*n*x*arccot(a*x)-1/9*e*n*x^3*arccot(a*x)+1/6*e*x^2*log(c*x^n)/a+d*x*arccot(a*x)*log(c*x^n)+1/3*e*x^3*arccot(a*x)*log(c*x^n)-1/2*d*n*log(1+a^2*x^2)/a+1/18*e*n*log(1+a^2*x^2)/a^3+1/6*(3*a^2*d-e)*log(c*x^n)*log(1+a^2*x^2)/a^3+1/12*(3*a^2*d-e)*n*polylog(2,-a^2*x^2)/a^3],
[(d+e*x^2)*arcsinh(a*x)*log(c*x^n),x,17,2/27*e*n*(1+a^2*x^2)^(3/2)/a^3-d*n*x*arcsinh(a*x)-1/9*e*n*x^3*arcsinh(a*x)-1/3*(3*a^2*d-e)*n*arctanh(sqrt(1+a^2*x^2))/a^3-1/9*e*n*arctanh(sqrt(1+a^2*x^2))/a^3-1/9*e*(1+a^2*x^2)^(3/2)*log(c*x^n)/a^3+d*x*arcsinh(a*x)*log(c*x^n)+1/3*e*x^3*arcsinh(a*x)*log(c*x^n)+d*n*sqrt(1+a^2*x^2)/a+1/3*(3*a^2*d-e)*n*sqrt(1+a^2*x^2)/a^3-1/3*(3*a^2*d-e)*log(c*x^n)*sqrt(1+a^2*x^2)/a^3],
[(d+e*x^2)*arccosh(a*x)*log(c*x^n),x,12,1/27*e*n*(-1+a*x)^(3/2)*(1+a*x)^(3/2)/a^3-d*n*x*arccosh(a*x)-1/9*e*n*x^3*arccosh(a*x)-1/9*(9*a^2*d+2*e)*n*arctan(sqrt(-1+a*x)*sqrt(1+a*x))/a^3+d*x*arccosh(a*x)*log(c*x^n)+1/3*e*x^3*arccosh(a*x)*log(c*x^n)+d*n*sqrt(-1+a*x)*sqrt(1+a*x)/a+2/27*e*n*sqrt(-1+a*x)*sqrt(1+a*x)/a^3+1/9*(9*a^2*d+2*e)*n*sqrt(-1+a*x)*sqrt(1+a*x)/a^3+1/27*e*n*x^2*sqrt(-1+a*x)*sqrt(1+a*x)/a-1/9*(9*a^2*d+2*e)*log(c*x^n)*sqrt(-1+a*x)*sqrt(1+a*x)/a^3-1/9*e*x^2*log(c*x^n)*sqrt(-1+a*x)*sqrt(1+a*x)/a],
[(d+e*x^2)*arctanh(a*x)*log(c*x^n),x,9,-5/36*e*n*x^2/a-d*n*x*arctanh(a*x)-1/9*e*n*x^3*arctanh(a*x)+1/6*e*x^2*log(c*x^n)/a+d*x*arctanh(a*x)*log(c*x^n)+1/3*e*x^3*arctanh(a*x)*log(c*x^n)-1/2*d*n*log(1-a^2*x^2)/a-1/18*e*n*log(1-a^2*x^2)/a^3+1/6*(3*a^2*d+e)*log(c*x^n)*log(1-a^2*x^2)/a^3+1/12*(3*a^2*d+e)*n*polylog(2,a^2*x^2)/a^3],
[(d+e*x^2)*arccoth(a*x)*log(c*x^n),x,9,-5/36*e*n*x^2/a-d*n*x*arccoth(a*x)-1/9*e*n*x^3*arccoth(a*x)+1/6*e*x^2*log(c*x^n)/a+d*x*arccoth(a*x)*log(c*x^n)+1/3*e*x^3*arccoth(a*x)*log(c*x^n)-1/2*d*n*log(1-a^2*x^2)/a-1/18*e*n*log(1-a^2*x^2)/a^3+1/6*(3*a^2*d+e)*log(c*x^n)*log(1-a^2*x^2)/a^3+1/12*(3*a^2*d+e)*n*polylog(2,a^2*x^2)/a^3],
[(d+e*x^2)*arcsin(a*x)^2*log(c*x^n),x,21,2*d*n*x+2/27*e*n*x/a^2+4/9*(9*d+2*e/a^2)*n*x+2/27*e*n*x^3+2/27*e*n*(1-a^2*x^2)^(3/2)*arcsin(a*x)/a^3-d*n*x*arcsin(a*x)^2-1/9*e*n*x^3*arcsin(a*x)^2+4/9*(9*a^2*d+2*e)*n*arcsin(a*x)*arctanh(exp(I*arcsin(a*x)))/a^3-2*d*x*log(c*x^n)-4/9*e*x*log(c*x^n)/a^2-2/27*e*x^3*log(c*x^n)+d*x*arcsin(a*x)^2*log(c*x^n)+1/3*e*x^3*arcsin(a*x)^2*log(c*x^n)-2/9*I*(9*a^2*d+2*e)*n*polylog(2,-exp(I*arcsin(a*x)))/a^3+2/9*I*(9*a^2*d+2*e)*n*polylog(2,exp(I*arcsin(a*x)))/a^3-2*d*n*arcsin(a*x)*sqrt(1-a^2*x^2)/a-4/27*e*n*arcsin(a*x)*sqrt(1-a^2*x^2)/a^3-2/9*(9*a^2*d+2*e)*n*arcsin(a*x)*sqrt(1-a^2*x^2)/a^3-2/27*e*n*x^2*arcsin(a*x)*sqrt(1-a^2*x^2)/a+2*d*arcsin(a*x)*log(c*x^n)*sqrt(1-a^2*x^2)/a+4/9*e*arcsin(a*x)*log(c*x^n)*sqrt(1-a^2*x^2)/a^3+2/9*e*x^2*arcsin(a*x)*log(c*x^n)*sqrt(1-a^2*x^2)/a],
[(d+e*x^2)*arccos(a*x)^2*log(c*x^n),x,21,2*d*n*x+2/27*e*n*x/a^2+4/9*(9*d+2*e/a^2)*n*x+2/27*e*n*x^3-2/27*e*n*(1-a^2*x^2)^(3/2)*arccos(a*x)/a^3-d*n*x*arccos(a*x)^2-1/9*e*n*x^3*arccos(a*x)^2+4/9*I*(9*a^2*d+2*e)*n*arccos(a*x)*arctan(exp(I*arccos(a*x)))/a^3-2*d*x*log(c*x^n)-4/9*e*x*log(c*x^n)/a^2-2/27*e*x^3*log(c*x^n)+d*x*arccos(a*x)^2*log(c*x^n)+1/3*e*x^3*arccos(a*x)^2*log(c*x^n)-2/9*I*(9*a^2*d+2*e)*n*polylog(2,-I*exp(I*arccos(a*x)))/a^3+2/9*I*(9*a^2*d+2*e)*n*polylog(2,I*exp(I*arccos(a*x)))/a^3+2*d*n*arccos(a*x)*sqrt(1-a^2*x^2)/a+4/27*e*n*arccos(a*x)*sqrt(1-a^2*x^2)/a^3+2/9*(9*a^2*d+2*e)*n*arccos(a*x)*sqrt(1-a^2*x^2)/a^3+2/27*e*n*x^2*arccos(a*x)*sqrt(1-a^2*x^2)/a-2*d*arccos(a*x)*log(c*x^n)*sqrt(1-a^2*x^2)/a-4/9*e*arccos(a*x)*log(c*x^n)*sqrt(1-a^2*x^2)/a^3-2/9*e*x^2*arccos(a*x)*log(c*x^n)*sqrt(1-a^2*x^2)/a],
[(d+e*x^2)*arcsinh(a*x)^2*log(c*x^n),x,21,-2*d*n*x+2/27*e*n*x/a^2-4/9*(9*d-2*e/a^2)*n*x-2/27*e*n*x^3+2/27*e*n*(1+a^2*x^2)^(3/2)*arcsinh(a*x)/a^3-d*n*x*arcsinh(a*x)^2-1/9*e*n*x^3*arcsinh(a*x)^2-4/9*(9*a^2*d-2*e)*n*arcsinh(a*x)*arctanh(exp(arcsinh(a*x)))/a^3+2*d*x*log(c*x^n)-4/9*e*x*log(c*x^n)/a^2+2/27*e*x^3*log(c*x^n)+d*x*arcsinh(a*x)^2*log(c*x^n)+1/3*e*x^3*arcsinh(a*x)^2*log(c*x^n)-2/9*(9*a^2*d-2*e)*n*polylog(2,-exp(arcsinh(a*x)))/a^3+2/9*(9*a^2*d-2*e)*n*polylog(2,exp(arcsinh(a*x)))/a^3+2*d*n*arcsinh(a*x)*sqrt(1+a^2*x^2)/a+2/9*(9*a^2*d-2*e)*n*arcsinh(a*x)*sqrt(1+a^2*x^2)/a^3-4/27*e*n*arcsinh(a*x)*sqrt(1+a^2*x^2)/a^3+2/27*e*n*x^2*arcsinh(a*x)*sqrt(1+a^2*x^2)/a-2*d*arcsinh(a*x)*log(c*x^n)*sqrt(1+a^2*x^2)/a+4/9*e*arcsinh(a*x)*log(c*x^n)*sqrt(1+a^2*x^2)/a^3-2/9*e*x^2*arcsinh(a*x)*log(c*x^n)*sqrt(1+a^2*x^2)/a],
[(d+e*x^2)*arccosh(a*x)^2*log(c*x^n),x,22,-2*d*n*x-2/27*e*n*x/a^2-4/9*(9*d+2*e/a^2)*n*x-2/27*e*n*x^3+2/27*e*n*(-1+a*x)^(3/2)*(1+a*x)^(3/2)*arccosh(a*x)/a^3-d*n*x*arccosh(a*x)^2-1/9*e*n*x^3*arccosh(a*x)^2-4/9*(9*a^2*d+2*e)*n*arccosh(a*x)*arctan(exp(arccosh(a*x)))/a^3+2*d*x*log(c*x^n)+4/9*e*x*log(c*x^n)/a^2+2/27*e*x^3*log(c*x^n)+d*x*arccosh(a*x)^2*log(c*x^n)+1/3*e*x^3*arccosh(a*x)^2*log(c*x^n)+2/9*I*(9*a^2*d+2*e)*n*polylog(2,-I*exp(arccosh(a*x)))/a^3-2/9*I*(9*a^2*d+2*e)*n*polylog(2,I*exp(arccosh(a*x)))/a^3+2*d*n*arccosh(a*x)*sqrt(-1+a*x)*sqrt(1+a*x)/a+4/27*e*n*arccosh(a*x)*sqrt(-1+a*x)*sqrt(1+a*x)/a^3+2/9*(9*a^2*d+2*e)*n*arccosh(a*x)*sqrt(-1+a*x)*sqrt(1+a*x)/a^3+2/27*e*n*x^2*arccosh(a*x)*sqrt(-1+a*x)*sqrt(1+a*x)/a-2*d*arccosh(a*x)*log(c*x^n)*sqrt(-1+a*x)*sqrt(1+a*x)/a-4/9*e*arccosh(a*x)*log(c*x^n)*sqrt(-1+a*x)*sqrt(1+a*x)/a^3-2/9*e*x^2*arccosh(a*x)*log(c*x^n)*sqrt(-1+a*x)*sqrt(1+a*x)/a],

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

# Integrands of the form PolyLog[k, e x^q] (a+b Log[c x^n])^p / x
[(a+b*log(c*x^n))^p*polylog(k,e*x^q)/x,x,0,Unintegrable((a+b*log(c*x^n))^p*polylog(k,e*x^q)/x,x)],
[(a+b*log(c*x^n))^3*polylog(k,e*x^q)/x,x,4,(a+b*log(c*x^n))^3*polylog(1+k,e*x^q)/q-3*b*n*(a+b*log(c*x^n))^2*polylog(2+k,e*x^q)/q^2+6*b^2*n^2*(a+b*log(c*x^n))*polylog(3+k,e*x^q)/q^3-6*b^3*n^3*polylog(4+k,e*x^q)/q^4],
[(a+b*log(c*x^n))^2*polylog(k,e*x^q)/x,x,3,(a+b*log(c*x^n))^2*polylog(1+k,e*x^q)/q-2*b*n*(a+b*log(c*x^n))*polylog(2+k,e*x^q)/q^2+2*b^2*n^2*polylog(3+k,e*x^q)/q^3],
[(a+b*log(c*x^n))*polylog(k,e*x^q)/x,x,2,(a+b*log(c*x^n))*polylog(1+k,e*x^q)/q-b*n*polylog(2+k,e*x^q)/q^2],
[polylog(k,e*x^q)/(x*(a+b*log(c*x^n))),x,0,Unintegrable(polylog(k,e*x^q)/(x*(a+b*log(c*x^n))),x)],
[polylog(k,e*x^q)/(x*(a+b*log(c*x^n))^2),x,1,-polylog(k,e*x^q)/(b*n*(a+b*log(c*x^n)))+q*Unintegrable(polylog(-1+k,e*x^q)/(x*(a+b*log(c*x^n))),x)/(b*n)],
[polylog(k,e*x^q)/(x*(a+b*log(c*x^n))^3),x,2,-1/2*q*polylog(-1+k,e*x^q)/(b^2*n^2*(a+b*log(c*x^n)))-1/2*polylog(k,e*x^q)/(b*n*(a+b*log(c*x^n))^2)+1/2*q^2*Unintegrable(polylog(-2+k,e*x^q)/(x*(a+b*log(c*x^n))),x)/(b^2*n^2)],
[log(x)*polylog(n,a*x)/x,x,2,log(x)*polylog(1+n,a*x)-polylog(2+n,a*x)],
[log(x)^2*polylog(n,a*x)/x,x,3,log(x)^2*polylog(1+n,a*x)-2*log(x)*polylog(2+n,a*x)+2*polylog(3+n,a*x)],
[q*polylog(-1+k,e*x^q)/(b*n*x*(a+b*log(c*x^n)))-polylog(k,e*x^q)/(x*(a+b*log(c*x^n))^2),x,2,polylog(k,e*x^q)/(b*n*(a+b*log(c*x^n)))],

# Integrands of the form (d x)^m PolyLog[k, e x^q] (a+b Log[c x^n])
[x^2*(a+b*log(c*x^n))*polylog(2,e*x),x,10,5/27*b*n*x/e^2+7/108*b*n*x^2/e+1/27*b*n*x^3-1/9*x*(a+b*log(c*x^n))/e^2-1/18*x^2*(a+b*log(c*x^n))/e-1/27*x^3*(a+b*log(c*x^n))+2/27*b*n*log(1-e*x)/e^3-2/27*b*n*x^3*log(1-e*x)-1/9*(a+b*log(c*x^n))*log(1-e*x)/e^3+1/9*x^3*(a+b*log(c*x^n))*log(1-e*x)-1/9*b*n*polylog(2,e*x)/e^3-1/9*b*n*x^3*polylog(2,e*x)+1/3*x^3*(a+b*log(c*x^n))*polylog(2,e*x)],
[x*(a+b*log(c*x^n))*polylog(2,e*x),x,10,1/2*b*n*x/e+3/16*b*n*x^2-1/4*x*(a+b*log(c*x^n))/e-1/8*x^2*(a+b*log(c*x^n))+1/4*b*n*log(1-e*x)/e^2-1/4*b*n*x^2*log(1-e*x)-1/4*(a+b*log(c*x^n))*log(1-e*x)/e^2+1/4*x^2*(a+b*log(c*x^n))*log(1-e*x)-1/4*b*n*polylog(2,e*x)/e^2-1/4*b*n*x^2*polylog(2,e*x)+1/2*x^2*(a+b*log(c*x^n))*polylog(2,e*x)],
[(a+b*log(c*x^n))*polylog(2,e*x),x,10,3*b*n*x-x*(a+b*log(c*x^n))+2*b*n*(1-e*x)*log(1-e*x)/e-(1-e*x)*(a+b*log(c*x^n))*log(1-e*x)/e-b*n*polylog(2,e*x)/e-b*n*x*polylog(2,e*x)+x*(a+b*log(c*x^n))*polylog(2,e*x)],
[(a+b*log(c*x^n))*polylog(2,e*x)/x,x,2,(a+b*log(c*x^n))*polylog(3,e*x)-b*n*polylog(4,e*x)],
[(a+b*log(c*x^n))*polylog(2,e*x)/x^2,x,13,2*b*e*n*log(x)-1/2*b*e*n*log(x)^2+e*log(x)*(a+b*log(c*x^n))-2*b*e*n*log(1-e*x)+2*b*n*log(1-e*x)/x-e*(a+b*log(c*x^n))*log(1-e*x)+(a+b*log(c*x^n))*log(1-e*x)/x-b*e*n*polylog(2,e*x)-b*n*polylog(2,e*x)/x-(a+b*log(c*x^n))*polylog(2,e*x)/x],
[(a+b*log(c*x^n))*polylog(2,e*x)/x^3,x,11,-1/2*b*e*n/x+1/4*b*e^2*n*log(x)-1/8*b*e^2*n*log(x)^2-1/4*e*(a+b*log(c*x^n))/x+1/4*e^2*log(x)*(a+b*log(c*x^n))-1/4*b*e^2*n*log(1-e*x)+1/4*b*n*log(1-e*x)/x^2-1/4*e^2*(a+b*log(c*x^n))*log(1-e*x)+1/4*(a+b*log(c*x^n))*log(1-e*x)/x^2-1/4*b*e^2*n*polylog(2,e*x)-1/4*b*n*polylog(2,e*x)/x^2-1/2*(a+b*log(c*x^n))*polylog(2,e*x)/x^2],
[x^2*(a+b*log(c*x^n))*polylog(3,e*x),x,15,-2/27*b*n*x/e^2-1/36*b*n*x^2/e-4/243*b*n*x^3+1/27*x*(a+b*log(c*x^n))/e^2+1/54*x^2*(a+b*log(c*x^n))/e+1/81*x^3*(a+b*log(c*x^n))-1/27*b*n*log(1-e*x)/e^3+1/27*b*n*x^3*log(1-e*x)+1/27*(a+b*log(c*x^n))*log(1-e*x)/e^3-1/27*x^3*(a+b*log(c*x^n))*log(1-e*x)+1/27*b*n*polylog(2,e*x)/e^3+2/27*b*n*x^3*polylog(2,e*x)-1/9*x^3*(a+b*log(c*x^n))*polylog(2,e*x)-1/9*b*n*x^3*polylog(3,e*x)+1/3*x^3*(a+b*log(c*x^n))*polylog(3,e*x)],
[x*(a+b*log(c*x^n))*polylog(3,e*x),x,15,-5/16*b*n*x/e-1/8*b*n*x^2+1/8*x*(a+b*log(c*x^n))/e+1/16*x^2*(a+b*log(c*x^n))-3/16*b*n*log(1-e*x)/e^2+3/16*b*n*x^2*log(1-e*x)+1/8*(a+b*log(c*x^n))*log(1-e*x)/e^2-1/8*x^2*(a+b*log(c*x^n))*log(1-e*x)+1/8*b*n*polylog(2,e*x)/e^2+1/4*b*n*x^2*polylog(2,e*x)-1/4*x^2*(a+b*log(c*x^n))*polylog(2,e*x)-1/4*b*n*x^2*polylog(3,e*x)+1/2*x^2*(a+b*log(c*x^n))*polylog(3,e*x)],
[(a+b*log(c*x^n))*polylog(3,e*x),x,14,-4*b*n*x+x*(a+b*log(c*x^n))-3*b*n*(1-e*x)*log(1-e*x)/e+(1-e*x)*(a+b*log(c*x^n))*log(1-e*x)/e+b*n*polylog(2,e*x)/e+2*b*n*x*polylog(2,e*x)-x*(a+b*log(c*x^n))*polylog(2,e*x)-b*n*x*polylog(3,e*x)+x*(a+b*log(c*x^n))*polylog(3,e*x)],
[(a+b*log(c*x^n))*polylog(3,e*x)/x,x,2,(a+b*log(c*x^n))*polylog(4,e*x)-b*n*polylog(5,e*x)],
[(a+b*log(c*x^n))*polylog(3,e*x)/x^2,x,19,3*b*e*n*log(x)-1/2*b*e*n*log(x)^2+e*log(x)*(a+b*log(c*x^n))-3*b*e*n*log(1-e*x)+3*b*n*log(1-e*x)/x-e*(a+b*log(c*x^n))*log(1-e*x)+(a+b*log(c*x^n))*log(1-e*x)/x-b*e*n*polylog(2,e*x)-2*b*n*polylog(2,e*x)/x-(a+b*log(c*x^n))*polylog(2,e*x)/x-b*n*polylog(3,e*x)/x-(a+b*log(c*x^n))*polylog(3,e*x)/x],
[(a+b*log(c*x^n))*polylog(3,e*x)/x^3,x,16,-5/16*b*e*n/x+3/16*b*e^2*n*log(x)-1/16*b*e^2*n*log(x)^2-1/8*e*(a+b*log(c*x^n))/x+1/8*e^2*log(x)*(a+b*log(c*x^n))-3/16*b*e^2*n*log(1-e*x)+3/16*b*n*log(1-e*x)/x^2-1/8*e^2*(a+b*log(c*x^n))*log(1-e*x)+1/8*(a+b*log(c*x^n))*log(1-e*x)/x^2-1/8*b*e^2*n*polylog(2,e*x)-1/4*b*n*polylog(2,e*x)/x^2-1/4*(a+b*log(c*x^n))*polylog(2,e*x)/x^2-1/4*b*n*polylog(3,e*x)/x^2-1/2*(a+b*log(c*x^n))*polylog(3,e*x)/x^2],
[(d*x)^m*(a+b*log(c*x^n))*polylog(1,e*x^q),x,0,-Unintegrable((d*x)^m*(a+b*log(c*x^n))*log(1-e*x^q),x)],
[(d*x)^m*(a+b*log(c*x^n))*polylog(2,e*x^q),x,4,-b*e*n*q^2*x^(1+q)*(d*x)^m*hypergeom([1,(1+m+q)/q],[(1+m+2*q)/q],e*x^q)/((1+m)^3*(1+m+q))-b*n*q*(d*x)^(1+m)*log(1-e*x^q)/(d*(1+m)^3)-b*n*(d*x)^(1+m)*polylog(2,e*x^q)/(d*(1+m)^2)+(d*x)^(1+m)*(a+b*log(c*x^n))*polylog(2,e*x^q)/(d*(1+m))+q*Unintegrable((d*x)^m*(a+b*log(c*x^n))*log(1-e*x^q),x)/(1+m)],
[(d*x)^m*(a+b*log(c*x^n))*polylog(3,e*x^q),x,9,2*b*e*n*q^3*x^(1+q)*(d*x)^m*hypergeom([1,(1+m+q)/q],[(1+m+2*q)/q],e*x^q)/((1+m)^4*(1+m+q))+2*b*n*q^2*(d*x)^(1+m)*log(1-e*x^q)/(d*(1+m)^4)+2*b*n*q*(d*x)^(1+m)*polylog(2,e*x^q)/(d*(1+m)^3)-q*(d*x)^(1+m)*(a+b*log(c*x^n))*polylog(2,e*x^q)/(d*(1+m)^2)-b*n*(d*x)^(1+m)*polylog(3,e*x^q)/(d*(1+m)^2)+(d*x)^(1+m)*(a+b*log(c*x^n))*polylog(3,e*x^q)/(d*(1+m))-q^2*Unintegrable((d*x)^m*(a+b*log(c*x^n))*log(1-e*x^q),x)/(1+m)^2],

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

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

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

# p>0
[x^2*log(c*(b*x^n)^p),x,2,-1/9*n*p*x^3+1/3*x^3*log(c*(b*x^n)^p)],
[x*log(c*(b*x^n)^p),x,2,-1/4*n*p*x^2+1/2*x^2*log(c*(b*x^n)^p)],
[log(c*(b*x^n)^p),x,2,-n*p*x+x*log(c*(b*x^n)^p)],
[log(c*(b*x^n)^p)/x,x,2,1/2*log(c*(b*x^n)^p)^2/(n*p)],
[log(c*(b*x^n)^p)/x^2,x,2,-n*p/x-log(c*(b*x^n)^p)/x],
[log(c*(b*x^n)^p)/x^3,x,2,-1/4*n*p/x^2-1/2*log(c*(b*x^n)^p)/x^2],
[log(c*(b*x^n)^p)/x^4,x,2,-1/9*n*p/x^3-1/3*log(c*(b*x^n)^p)/x^3],
[x^2*log(c*(b*x^n)^p)^2,x,3,2/27*n^2*p^2*x^3-2/9*n*p*x^3*log(c*(b*x^n)^p)+1/3*x^3*log(c*(b*x^n)^p)^2],
[x*log(c*(b*x^n)^p)^2,x,3,1/4*n^2*p^2*x^2-1/2*n*p*x^2*log(c*(b*x^n)^p)+1/2*x^2*log(c*(b*x^n)^p)^2],
[log(c*(b*x^n)^p)^2,x,3,2*n^2*p^2*x-2*n*p*x*log(c*(b*x^n)^p)+x*log(c*(b*x^n)^p)^2],
[log(c*(b*x^n)^p)^2/x,x,3,1/3*log(c*(b*x^n)^p)^3/(n*p)],
[log(c*(b*x^n)^p)^2/x^2,x,3,-2*n^2*p^2/x-2*n*p*log(c*(b*x^n)^p)/x-log(c*(b*x^n)^p)^2/x],
[log(c*(b*x^n)^p)^2/x^3,x,3,-1/4*n^2*p^2/x^2-1/2*n*p*log(c*(b*x^n)^p)/x^2-1/2*log(c*(b*x^n)^p)^2/x^2],
[log(c*(b*x^n)^p)^2/x^4,x,3,-2/27*n^2*p^2/x^3-2/9*n*p*log(c*(b*x^n)^p)/x^3-1/3*log(c*(b*x^n)^p)^2/x^3],

# p<0

# Integrands of the form (e x)^q (a+b Log[c (d x^m)^n])^p with q symbolic
[(e*x)^q*(a+b*log(c*(d*x^m)^n))^3,x,4,-6*b^3*m^3*n^3*(e*x)^(1+q)/(e*(1+q)^4)+6*b^2*m^2*n^2*(e*x)^(1+q)*(a+b*log(c*(d*x^m)^n))/(e*(1+q)^3)-3*b*m*n*(e*x)^(1+q)*(a+b*log(c*(d*x^m)^n))^2/(e*(1+q)^2)+(e*x)^(1+q)*(a+b*log(c*(d*x^m)^n))^3/(e*(1+q))],
[(e*x)^q*(a+b*log(c*(d*x^m)^n))^2,x,3,2*b^2*m^2*n^2*(e*x)^(1+q)/(e*(1+q)^3)-2*b*m*n*(e*x)^(1+q)*(a+b*log(c*(d*x^m)^n))/(e*(1+q)^2)+(e*x)^(1+q)*(a+b*log(c*(d*x^m)^n))^2/(e*(1+q))],
[(e*x)^q*(a+b*log(c*(d*x^m)^n)),x,2,-b*m*n*(e*x)^(1+q)/(e*(1+q)^2)+(e*x)^(1+q)*(a+b*log(c*(d*x^m)^n))/(e*(1+q))],
[(e*x)^q/(a+b*log(c*(d*x^m)^n)),x,3,(e*x)^(1+q)*Ei((1+q)*(a+b*log(c*(d*x^m)^n))/(b*m*n))/(b*e*exp(a*(1+q)/(b*m*n))*m*n*(c*(d*x^m)^n)^((1+q)/(m*n)))],
[(e*x)^q/(a+b*log(c*(d*x^m)^n))^2,x,4,(1+q)*(e*x)^(1+q)*Ei((1+q)*(a+b*log(c*(d*x^m)^n))/(b*m*n))/(b^2*e*exp(a*(1+q)/(b*m*n))*m^2*n^2*(c*(d*x^m)^n)^((1+q)/(m*n)))-(e*x)^(1+q)/(b*e*m*n*(a+b*log(c*(d*x^m)^n)))],

# Integrands of the form (e x)^q (a+b Log[c (d x^m)^n])^p with p symbolic
[(e*x)^q*(a+b*log(c*(d*x^m)^n))^p,x,3,(e*x)^(1+q)*GAMMA(1+p,-(1+q)*(a+b*log(c*(d*x^m)^n))/(b*m*n))*(a+b*log(c*(d*x^m)^n))^p/(e*exp(a*(1+q)/(b*m*n))*(1+q)*(c*(d*x^m)^n)^((1+q)/(m*n))*(-(1+q)*(a+b*log(c*(d*x^m)^n))/(b*m*n))^p)],
[x^2*(a+b*log(c*(d*x^m)^n))^p,x,3,3^(-1-p)*x^3*GAMMA(1+p,-3*(a+b*log(c*(d*x^m)^n))/(b*m*n))*(a+b*log(c*(d*x^m)^n))^p/(exp(3*a/(b*m*n))*(c*(d*x^m)^n)^(3/(m*n))*((-a-b*log(c*(d*x^m)^n))/(b*m*n))^p)],
[x*(a+b*log(c*(d*x^m)^n))^p,x,3,2^(-1-p)*x^2*GAMMA(1+p,-2*(a+b*log(c*(d*x^m)^n))/(b*m*n))*(a+b*log(c*(d*x^m)^n))^p/(exp(2*a/(b*m*n))*(c*(d*x^m)^n)^(2/(m*n))*((-a-b*log(c*(d*x^m)^n))/(b*m*n))^p)],
[(a+b*log(c*(d*x^m)^n))^p,x,3,x*GAMMA(1+p,(-a-b*log(c*(d*x^m)^n))/(b*m*n))*(a+b*log(c*(d*x^m)^n))^p/(exp(a/(b*m*n))*(c*(d*x^m)^n)^(1/(m*n))*((-a-b*log(c*(d*x^m)^n))/(b*m*n))^p)],
[(a+b*log(c*(d*x^m)^n))^p/x,x,3,(a+b*log(c*(d*x^m)^n))^(1+p)/(b*m*n*(1+p))],
[(a+b*log(c*(d*x^m)^n))^p/x^2,x,3,-exp(a/(b*m*n))*(c*(d*x^m)^n)^(1/(m*n))*GAMMA(1+p,(a+b*log(c*(d*x^m)^n))/(b*m*n))*(a+b*log(c*(d*x^m)^n))^p/(x*((a+b*log(c*(d*x^m)^n))/(b*m*n))^p)],
[(a+b*log(c*(d*x^m)^n))^p/x^3,x,3,-2^(-1-p)*exp(2*a/(b*m*n))*(c*(d*x^m)^n)^(2/(m*n))*GAMMA(1+p,2*(a+b*log(c*(d*x^m)^n))/(b*m*n))*(a+b*log(c*(d*x^m)^n))^p/(x^2*((a+b*log(c*(d*x^m)^n))/(b*m*n))^p)],

# Integrands of the form (e+f x^r)^q (a+b Log[c (d x^m)^n])^p
[(a+b*log(c*(d*x^m)^n))/(e+f*x^2),x,6,arctan(x*sqrt(f)/sqrt(e))*(a+b*log(c*(d*x^m)^n))/(sqrt(e)*sqrt(f))-1/2*I*b*m*n*polylog(2,-I*x*sqrt(f)/sqrt(e))/(sqrt(e)*sqrt(f))+1/2*I*b*m*n*polylog(2,I*x*sqrt(f)/sqrt(e))/(sqrt(e)*sqrt(f))]]:
