# Maple integration test file: "3 Logarithms\3.3 u (a+b log(c (d+e x)^n))^p.txt"

lst:=[

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

# Integrands of the form Log[c (d+e x)]^p

# Integrands of the form Log[c (d+e x)]^p
[log(c*(d+e*x))^4,x,5,24*x-24*(d+e*x)*log(c*(d+e*x))/e+12*(d+e*x)*log(c*(d+e*x))^2/e-4*(d+e*x)*log(c*(d+e*x))^3/e+(d+e*x)*log(c*(d+e*x))^4/e],
[log(c*(d+e*x))^3,x,4,-6*x+6*(d+e*x)*log(c*(d+e*x))/e-3*(d+e*x)*log(c*(d+e*x))^2/e+(d+e*x)*log(c*(d+e*x))^3/e],
[log(c*(d+e*x))^2,x,3,2*x-2*(d+e*x)*log(c*(d+e*x))/e+(d+e*x)*log(c*(d+e*x))^2/e],
[log(c*(d+e*x)),x,2,-x+(d+e*x)*log(c*(d+e*x))/e],
[1/log(c*(d+e*x)),x,2,Li(c*(d+e*x))/(c*e)],
[1/log(c*(d+e*x))^2,x,3,Li(c*(d+e*x))/(c*e)+(-d-e*x)/(e*log(c*(d+e*x)))],
[1/log(c*(d+e*x))^3,x,4,1/2*Li(c*(d+e*x))/(c*e)+1/2*(-d-e*x)/(e*log(c*(d+e*x))^2)+1/2*(-d-e*x)/(e*log(c*(d+e*x)))],
[1/log(c*(d+e*x))^4,x,5,1/6*Li(c*(d+e*x))/(c*e)+1/3*(-d-e*x)/(e*log(c*(d+e*x))^3)+1/6*(-d-e*x)/(e*log(c*(d+e*x))^2)+1/6*(-d-e*x)/(e*log(c*(d+e*x)))],

# Integrands of the form Log[c (d+e x)]^(p/2)
[log(c*(d+e*x))^(5/2),x,7,-5/2*(d+e*x)*log(c*(d+e*x))^(3/2)/e+(d+e*x)*log(c*(d+e*x))^(5/2)/e-15/8*erfi(sqrt(log(c*(d+e*x))))*sqrt(Pi)/(c*e)+15/4*(d+e*x)*sqrt(log(c*(d+e*x)))/e],
[log(c*(d+e*x))^(3/2),x,6,(d+e*x)*log(c*(d+e*x))^(3/2)/e+3/4*erfi(sqrt(log(c*(d+e*x))))*sqrt(Pi)/(c*e)-3/2*(d+e*x)*sqrt(log(c*(d+e*x)))/e],
[log(c*(d+e*x))^(1/2),x,5,-1/2*erfi(sqrt(log(c*(d+e*x))))*sqrt(Pi)/(c*e)+(d+e*x)*sqrt(log(c*(d+e*x)))/e],
[1/log(c*(d+e*x))^(1/2),x,4,erfi(sqrt(log(c*(d+e*x))))*sqrt(Pi)/(c*e)],
[1/log(c*(d+e*x))^(3/2),x,5,2*erfi(sqrt(log(c*(d+e*x))))*sqrt(Pi)/(c*e)-2*(d+e*x)/(e*sqrt(log(c*(d+e*x))))],
[1/log(c*(d+e*x))^(5/2),x,6,-2/3*(d+e*x)/(e*log(c*(d+e*x))^(3/2))+4/3*erfi(sqrt(log(c*(d+e*x))))*sqrt(Pi)/(c*e)-4/3*(d+e*x)/(e*sqrt(log(c*(d+e*x))))],
[1/log(c*(d+e*x))^(7/2),x,7,-2/5*(d+e*x)/(e*log(c*(d+e*x))^(5/2))-4/15*(d+e*x)/(e*log(c*(d+e*x))^(3/2))+8/15*erfi(sqrt(log(c*(d+e*x))))*sqrt(Pi)/(c*e)-8/15*(d+e*x)/(e*sqrt(log(c*(d+e*x))))],

# Integrands of the form Log[c (d+e x)]^p with p symbolic
[log(c*(d+e*x))^p,x,3,GAMMA(1+p,-log(c*(d+e*x)))*log(c*(d+e*x))^p/(c*e*(-log(c*(d+e*x)))^p)],

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

# Integrands of the form (a+b Log[c (d+e x)^n])^p
[(a+b*log(c*(d+e*x)^n))^4,x,6,-24*a*b^3*n^3*x+24*b^4*n^4*x-24*b^4*n^3*(d+e*x)*log(c*(d+e*x)^n)/e+12*b^2*n^2*(d+e*x)*(a+b*log(c*(d+e*x)^n))^2/e-4*b*n*(d+e*x)*(a+b*log(c*(d+e*x)^n))^3/e+(d+e*x)*(a+b*log(c*(d+e*x)^n))^4/e],
[(a+b*log(c*(d+e*x)^n))^3,x,5,6*a*b^2*n^2*x-6*b^3*n^3*x+6*b^3*n^2*(d+e*x)*log(c*(d+e*x)^n)/e-3*b*n*(d+e*x)*(a+b*log(c*(d+e*x)^n))^2/e+(d+e*x)*(a+b*log(c*(d+e*x)^n))^3/e],
[(a+b*log(c*(d+e*x)^n))^2,x,4,-2*a*b*n*x+2*b^2*n^2*x-2*b^2*n*(d+e*x)*log(c*(d+e*x)^n)/e+(d+e*x)*(a+b*log(c*(d+e*x)^n))^2/e],
[a+b*log(c*(d+e*x)^n),x,3,a*x-b*n*x+b*(d+e*x)*log(c*(d+e*x)^n)/e],
[1/(a+b*log(c*(d+e*x)^n)),x,3,(d+e*x)*Ei((a+b*log(c*(d+e*x)^n))/(b*n))/(b*e*exp(a/(b*n))*n*(c*(d+e*x)^n)^(1/n))],
[1/(a+b*log(c*(d+e*x)^n))^2,x,4,(d+e*x)*Ei((a+b*log(c*(d+e*x)^n))/(b*n))/(b^2*e*exp(a/(b*n))*n^2*(c*(d+e*x)^n)^(1/n))+(-d-e*x)/(b*e*n*(a+b*log(c*(d+e*x)^n)))],
[1/(a+b*log(c*(d+e*x)^n))^3,x,5,1/2*(d+e*x)*Ei((a+b*log(c*(d+e*x)^n))/(b*n))/(b^3*e*exp(a/(b*n))*n^3*(c*(d+e*x)^n)^(1/n))+1/2*(-d-e*x)/(b*e*n*(a+b*log(c*(d+e*x)^n))^2)+1/2*(-d-e*x)/(b^2*e*n^2*(a+b*log(c*(d+e*x)^n)))],

# Integrands of the form (a+b Log[c (d+e x)^n])^(p/2)
[(a+b*log(c*(d+e*x)^n))^(5/2),x,7,-5/2*b*n*(d+e*x)*(a+b*log(c*(d+e*x)^n))^(3/2)/e+(d+e*x)*(a+b*log(c*(d+e*x)^n))^(5/2)/e-15/8*b^(5/2)*n^(5/2)*(d+e*x)*erfi(sqrt(a+b*log(c*(d+e*x)^n))/(sqrt(b)*sqrt(n)))*sqrt(Pi)/(e*exp(a/(b*n))*(c*(d+e*x)^n)^(1/n))+15/4*b^2*n^2*(d+e*x)*sqrt(a+b*log(c*(d+e*x)^n))/e],
[(a+b*log(c*(d+e*x)^n))^(3/2),x,6,(d+e*x)*(a+b*log(c*(d+e*x)^n))^(3/2)/e+3/4*b^(3/2)*n^(3/2)*(d+e*x)*erfi(sqrt(a+b*log(c*(d+e*x)^n))/(sqrt(b)*sqrt(n)))*sqrt(Pi)/(e*exp(a/(b*n))*(c*(d+e*x)^n)^(1/n))-3/2*b*n*(d+e*x)*sqrt(a+b*log(c*(d+e*x)^n))/e],
[(a+b*log(c*(d+e*x)^n))^(1/2),x,5,-1/2*(d+e*x)*erfi(sqrt(a+b*log(c*(d+e*x)^n))/(sqrt(b)*sqrt(n)))*sqrt(b)*sqrt(n)*sqrt(Pi)/(e*exp(a/(b*n))*(c*(d+e*x)^n)^(1/n))+(d+e*x)*sqrt(a+b*log(c*(d+e*x)^n))/e],
[1/(a+b*log(c*(d+e*x)^n))^(1/2),x,4,(d+e*x)*erfi(sqrt(a+b*log(c*(d+e*x)^n))/(sqrt(b)*sqrt(n)))*sqrt(Pi)/(e*exp(a/(b*n))*(c*(d+e*x)^n)^(1/n)*sqrt(b)*sqrt(n))],
[1/(a+b*log(c*(d+e*x)^n))^(3/2),x,5,2*(d+e*x)*erfi(sqrt(a+b*log(c*(d+e*x)^n))/(sqrt(b)*sqrt(n)))*sqrt(Pi)/(b^(3/2)*e*exp(a/(b*n))*n^(3/2)*(c*(d+e*x)^n)^(1/n))-2*(d+e*x)/(b*e*n*sqrt(a+b*log(c*(d+e*x)^n)))],
[1/(a+b*log(c*(d+e*x)^n))^(5/2),x,6,-2/3*(d+e*x)/(b*e*n*(a+b*log(c*(d+e*x)^n))^(3/2))+4/3*(d+e*x)*erfi(sqrt(a+b*log(c*(d+e*x)^n))/(sqrt(b)*sqrt(n)))*sqrt(Pi)/(b^(5/2)*e*exp(a/(b*n))*n^(5/2)*(c*(d+e*x)^n)^(1/n))-4/3*(d+e*x)/(b^2*e*n^2*sqrt(a+b*log(c*(d+e*x)^n)))],
[1/(a+b*log(c*(d+e*x)^n))^(7/2),x,7,-2/5*(d+e*x)/(b*e*n*(a+b*log(c*(d+e*x)^n))^(5/2))-4/15*(d+e*x)/(b^2*e*n^2*(a+b*log(c*(d+e*x)^n))^(3/2))+8/15*(d+e*x)*erfi(sqrt(a+b*log(c*(d+e*x)^n))/(sqrt(b)*sqrt(n)))*sqrt(Pi)/(b^(7/2)*e*exp(a/(b*n))*n^(7/2)*(c*(d+e*x)^n)^(1/n))-8/15*(d+e*x)/(b^3*e*n^3*sqrt(a+b*log(c*(d+e*x)^n)))],

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

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

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

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

# p>0
[(f+g*x)^4*(a+b*log(c*(d+e*x)^n)),x,3,-1/5*b*(e*f-d*g)^4*n*x/e^4-1/10*b*(e*f-d*g)^3*n*(f+g*x)^2/(e^3*g)-1/15*b*(e*f-d*g)^2*n*(f+g*x)^3/(e^2*g)-1/20*b*(e*f-d*g)*n*(f+g*x)^4/(e*g)-1/25*b*n*(f+g*x)^5/g-1/5*b*(e*f-d*g)^5*n*log(d+e*x)/(e^5*g)+1/5*(f+g*x)^5*(a+b*log(c*(d+e*x)^n))/g],
[(f+g*x)^3*(a+b*log(c*(d+e*x)^n)),x,3,-1/4*b*(e*f-d*g)^3*n*x/e^3-1/8*b*(e*f-d*g)^2*n*(f+g*x)^2/(e^2*g)-1/12*b*(e*f-d*g)*n*(f+g*x)^3/(e*g)-1/16*b*n*(f+g*x)^4/g-1/4*b*(e*f-d*g)^4*n*log(d+e*x)/(e^4*g)+1/4*(f+g*x)^4*(a+b*log(c*(d+e*x)^n))/g],
[(f+g*x)^2*(a+b*log(c*(d+e*x)^n)),x,3,-1/3*b*(e*f-d*g)^2*n*x/e^2-1/6*b*(e*f-d*g)*n*(f+g*x)^2/(e*g)-1/9*b*n*(f+g*x)^3/g-1/3*b*(e*f-d*g)^3*n*log(d+e*x)/(e^3*g)+1/3*(f+g*x)^3*(a+b*log(c*(d+e*x)^n))/g],
[(f+g*x)*(a+b*log(c*(d+e*x)^n)),x,3,-1/2*b*(e*f-d*g)*n*x/e-1/4*b*n*(f+g*x)^2/g-1/2*b*(e*f-d*g)^2*n*log(d+e*x)/(e^2*g)+1/2*(f+g*x)^2*(a+b*log(c*(d+e*x)^n))/g],
[a+b*log(c*(d+e*x)^n),x,3,a*x-b*n*x+b*(d+e*x)*log(c*(d+e*x)^n)/e],
[(a+b*log(c*(d+e*x)^n))/(f+g*x),x,3,(a+b*log(c*(d+e*x)^n))*log(e*(f+g*x)/(e*f-d*g))/g+b*n*polylog(2,-g*(d+e*x)/(e*f-d*g))/g],
[(a+b*log(c*(d+e*x)^n))/(f+g*x)^2,x,4,b*e*n*log(d+e*x)/(g*(e*f-d*g))+(-a-b*log(c*(d+e*x)^n))/(g*(f+g*x))-b*e*n*log(f+g*x)/(g*(e*f-d*g))],
[(a+b*log(c*(d+e*x)^n))/(f+g*x)^3,x,3,1/2*b*e*n/(g*(e*f-d*g)*(f+g*x))+1/2*b*e^2*n*log(d+e*x)/(g*(e*f-d*g)^2)+1/2*(-a-b*log(c*(d+e*x)^n))/(g*(f+g*x)^2)-1/2*b*e^2*n*log(f+g*x)/(g*(e*f-d*g)^2)],
[(a+b*log(c*(d+e*x)^n))/(f+g*x)^4,x,3,1/6*b*e*n/(g*(e*f-d*g)*(f+g*x)^2)+1/3*b*e^2*n/(g*(e*f-d*g)^2*(f+g*x))+1/3*b*e^3*n*log(d+e*x)/(g*(e*f-d*g)^3)+1/3*(-a-b*log(c*(d+e*x)^n))/(g*(f+g*x)^3)-1/3*b*e^3*n*log(f+g*x)/(g*(e*f-d*g)^3)],
[(f+g*x)^3*(a+b*log(c*(d+e*x)^n))^2,x,8,2*b^2*(e*f-d*g)^3*n^2*x/e^3+3/4*b^2*g*(e*f-d*g)^2*n^2*(d+e*x)^2/e^4+2/9*b^2*g^2*(e*f-d*g)*n^2*(d+e*x)^3/e^4+1/32*b^2*g^3*n^2*(d+e*x)^4/e^4+1/4*b^2*(e*f-d*g)^4*n^2*log(d+e*x)^2/(e^4*g)-2*b*(e*f-d*g)^3*n*(d+e*x)*(a+b*log(c*(d+e*x)^n))/e^4-3/2*b*g*(e*f-d*g)^2*n*(d+e*x)^2*(a+b*log(c*(d+e*x)^n))/e^4-2/3*b*g^2*(e*f-d*g)*n*(d+e*x)^3*(a+b*log(c*(d+e*x)^n))/e^4-1/8*b*g^3*n*(d+e*x)^4*(a+b*log(c*(d+e*x)^n))/e^4-1/2*b*(e*f-d*g)^4*n*log(d+e*x)*(a+b*log(c*(d+e*x)^n))/(e^4*g)+1/4*(f+g*x)^4*(a+b*log(c*(d+e*x)^n))^2/g],
[(f+g*x)^2*(a+b*log(c*(d+e*x)^n))^2,x,8,2*b^2*(e*f-d*g)^2*n^2*x/e^2+1/2*b^2*g*(e*f-d*g)*n^2*(d+e*x)^2/e^3+2/27*b^2*g^2*n^2*(d+e*x)^3/e^3+1/3*b^2*(e*f-d*g)^3*n^2*log(d+e*x)^2/(e^3*g)-2*b*(e*f-d*g)^2*n*(d+e*x)*(a+b*log(c*(d+e*x)^n))/e^3-b*g*(e*f-d*g)*n*(d+e*x)^2*(a+b*log(c*(d+e*x)^n))/e^3-2/9*b*g^2*n*(d+e*x)^3*(a+b*log(c*(d+e*x)^n))/e^3-2/3*b*(e*f-d*g)^3*n*log(d+e*x)*(a+b*log(c*(d+e*x)^n))/(e^3*g)+1/3*(f+g*x)^3*(a+b*log(c*(d+e*x)^n))^2/g],
[(f+g*x)*(a+b*log(c*(d+e*x)^n))^2,x,9,-2*a*b*(e*f-d*g)*n*x/e+2*b^2*(e*f-d*g)*n^2*x/e+1/4*b^2*g*n^2*(d+e*x)^2/e^2-2*b^2*(e*f-d*g)*n*(d+e*x)*log(c*(d+e*x)^n)/e^2-1/2*b*g*n*(d+e*x)^2*(a+b*log(c*(d+e*x)^n))/e^2+(e*f-d*g)*(d+e*x)*(a+b*log(c*(d+e*x)^n))^2/e^2+1/2*g*(d+e*x)^2*(a+b*log(c*(d+e*x)^n))^2/e^2],
[(a+b*log(c*(d+e*x)^n))^2,x,4,-2*a*b*n*x+2*b^2*n^2*x-2*b^2*n*(d+e*x)*log(c*(d+e*x)^n)/e+(d+e*x)*(a+b*log(c*(d+e*x)^n))^2/e],
[(a+b*log(c*(d+e*x)^n))^2/(f+g*x),x,4,(a+b*log(c*(d+e*x)^n))^2*log(e*(f+g*x)/(e*f-d*g))/g+2*b*n*(a+b*log(c*(d+e*x)^n))*polylog(2,-g*(d+e*x)/(e*f-d*g))/g-2*b^2*n^2*polylog(3,-g*(d+e*x)/(e*f-d*g))/g],
[(a+b*log(c*(d+e*x)^n))^2/(f+g*x)^2,x,4,(d+e*x)*(a+b*log(c*(d+e*x)^n))^2/((e*f-d*g)*(f+g*x))-2*b*e*n*(a+b*log(c*(d+e*x)^n))*log(e*(f+g*x)/(e*f-d*g))/(g*(e*f-d*g))-2*b^2*e*n^2*polylog(2,-g*(d+e*x)/(e*f-d*g))/(g*(e*f-d*g))],
[(a+b*log(c*(d+e*x)^n))^2/(f+g*x)^3,x,7,-b*e*n*(d+e*x)*(a+b*log(c*(d+e*x)^n))/((e*f-d*g)^2*(f+g*x))-1/2*(a+b*log(c*(d+e*x)^n))^2/(g*(f+g*x)^2)+b^2*e^2*n^2*log(f+g*x)/(g*(e*f-d*g)^2)-b*e^2*n*(a+b*log(c*(d+e*x)^n))*log(1+(e*f-d*g)/(g*(d+e*x)))/(g*(e*f-d*g)^2)+b^2*e^2*n^2*polylog(2,(-e*f+d*g)/(g*(d+e*x)))/(g*(e*f-d*g)^2)],
[(a+b*log(c*(d+e*x)^n))^2/(f+g*x)^4,x,11,-1/3*b^2*e^2*n^2/(g*(e*f-d*g)^2*(f+g*x))-1/3*b^2*e^3*n^2*log(d+e*x)/(g*(e*f-d*g)^3)+1/3*b*e*n*(a+b*log(c*(d+e*x)^n))/(g*(e*f-d*g)*(f+g*x)^2)-2/3*b*e^2*n*(d+e*x)*(a+b*log(c*(d+e*x)^n))/((e*f-d*g)^3*(f+g*x))-1/3*(a+b*log(c*(d+e*x)^n))^2/(g*(f+g*x)^3)+b^2*e^3*n^2*log(f+g*x)/(g*(e*f-d*g)^3)-2/3*b*e^3*n*(a+b*log(c*(d+e*x)^n))*log(1+(e*f-d*g)/(g*(d+e*x)))/(g*(e*f-d*g)^3)+2/3*b^2*e^3*n^2*polylog(2,(-e*f+d*g)/(g*(d+e*x)))/(g*(e*f-d*g)^3)],
[(f+g*x)^3*(a+b*log(c*(d+e*x)^n))^3,x,19,6*a*b^2*(e*f-d*g)^3*n^2*x/e^3-6*b^3*(e*f-d*g)^3*n^3*x/e^3-9/8*b^3*g*(e*f-d*g)^2*n^3*(d+e*x)^2/e^4-2/9*b^3*g^2*(e*f-d*g)*n^3*(d+e*x)^3/e^4-3/128*b^3*g^3*n^3*(d+e*x)^4/e^4+6*b^3*(e*f-d*g)^3*n^2*(d+e*x)*log(c*(d+e*x)^n)/e^4+9/4*b^2*g*(e*f-d*g)^2*n^2*(d+e*x)^2*(a+b*log(c*(d+e*x)^n))/e^4+2/3*b^2*g^2*(e*f-d*g)*n^2*(d+e*x)^3*(a+b*log(c*(d+e*x)^n))/e^4+3/32*b^2*g^3*n^2*(d+e*x)^4*(a+b*log(c*(d+e*x)^n))/e^4-3*b*(e*f-d*g)^3*n*(d+e*x)*(a+b*log(c*(d+e*x)^n))^2/e^4-9/4*b*g*(e*f-d*g)^2*n*(d+e*x)^2*(a+b*log(c*(d+e*x)^n))^2/e^4-b*g^2*(e*f-d*g)*n*(d+e*x)^3*(a+b*log(c*(d+e*x)^n))^2/e^4-3/16*b*g^3*n*(d+e*x)^4*(a+b*log(c*(d+e*x)^n))^2/e^4+(e*f-d*g)^3*(d+e*x)*(a+b*log(c*(d+e*x)^n))^3/e^4+3/2*g*(e*f-d*g)^2*(d+e*x)^2*(a+b*log(c*(d+e*x)^n))^3/e^4+g^2*(e*f-d*g)*(d+e*x)^3*(a+b*log(c*(d+e*x)^n))^3/e^4+1/4*g^3*(d+e*x)^4*(a+b*log(c*(d+e*x)^n))^3/e^4],
[(f+g*x)^2*(a+b*log(c*(d+e*x)^n))^3,x,15,6*a*b^2*(e*f-d*g)^2*n^2*x/e^2-6*b^3*(e*f-d*g)^2*n^3*x/e^2-3/4*b^3*g*(e*f-d*g)*n^3*(d+e*x)^2/e^3-2/27*b^3*g^2*n^3*(d+e*x)^3/e^3+6*b^3*(e*f-d*g)^2*n^2*(d+e*x)*log(c*(d+e*x)^n)/e^3+3/2*b^2*g*(e*f-d*g)*n^2*(d+e*x)^2*(a+b*log(c*(d+e*x)^n))/e^3+2/9*b^2*g^2*n^2*(d+e*x)^3*(a+b*log(c*(d+e*x)^n))/e^3-3*b*(e*f-d*g)^2*n*(d+e*x)*(a+b*log(c*(d+e*x)^n))^2/e^3-3/2*b*g*(e*f-d*g)*n*(d+e*x)^2*(a+b*log(c*(d+e*x)^n))^2/e^3-1/3*b*g^2*n*(d+e*x)^3*(a+b*log(c*(d+e*x)^n))^2/e^3+(e*f-d*g)^2*(d+e*x)*(a+b*log(c*(d+e*x)^n))^3/e^3+g*(e*f-d*g)*(d+e*x)^2*(a+b*log(c*(d+e*x)^n))^3/e^3+1/3*g^2*(d+e*x)^3*(a+b*log(c*(d+e*x)^n))^3/e^3],
[(f+g*x)*(a+b*log(c*(d+e*x)^n))^3,x,11,6*a*b^2*(e*f-d*g)*n^2*x/e-6*b^3*(e*f-d*g)*n^3*x/e-3/8*b^3*g*n^3*(d+e*x)^2/e^2+6*b^3*(e*f-d*g)*n^2*(d+e*x)*log(c*(d+e*x)^n)/e^2+3/4*b^2*g*n^2*(d+e*x)^2*(a+b*log(c*(d+e*x)^n))/e^2-3*b*(e*f-d*g)*n*(d+e*x)*(a+b*log(c*(d+e*x)^n))^2/e^2-3/4*b*g*n*(d+e*x)^2*(a+b*log(c*(d+e*x)^n))^2/e^2+(e*f-d*g)*(d+e*x)*(a+b*log(c*(d+e*x)^n))^3/e^2+1/2*g*(d+e*x)^2*(a+b*log(c*(d+e*x)^n))^3/e^2],
[(a+b*log(c*(d+e*x)^n))^3,x,5,6*a*b^2*n^2*x-6*b^3*n^3*x+6*b^3*n^2*(d+e*x)*log(c*(d+e*x)^n)/e-3*b*n*(d+e*x)*(a+b*log(c*(d+e*x)^n))^2/e+(d+e*x)*(a+b*log(c*(d+e*x)^n))^3/e],
[(a+b*log(c*(d+e*x)^n))^3/(f+g*x),x,5,(a+b*log(c*(d+e*x)^n))^3*log(e*(f+g*x)/(e*f-d*g))/g+3*b*n*(a+b*log(c*(d+e*x)^n))^2*polylog(2,-g*(d+e*x)/(e*f-d*g))/g-6*b^2*n^2*(a+b*log(c*(d+e*x)^n))*polylog(3,-g*(d+e*x)/(e*f-d*g))/g+6*b^3*n^3*polylog(4,-g*(d+e*x)/(e*f-d*g))/g],
[(a+b*log(c*(d+e*x)^n))^3/(f+g*x)^2,x,5,(d+e*x)*(a+b*log(c*(d+e*x)^n))^3/((e*f-d*g)*(f+g*x))-3*b*e*n*(a+b*log(c*(d+e*x)^n))^2*log(e*(f+g*x)/(e*f-d*g))/(g*(e*f-d*g))-6*b^2*e*n^2*(a+b*log(c*(d+e*x)^n))*polylog(2,-g*(d+e*x)/(e*f-d*g))/(g*(e*f-d*g))+6*b^3*e*n^3*polylog(3,-g*(d+e*x)/(e*f-d*g))/(g*(e*f-d*g))],
[(a+b*log(c*(d+e*x)^n))^3/(f+g*x)^3,x,9,-3/2*b*e*n*(d+e*x)*(a+b*log(c*(d+e*x)^n))^2/((e*f-d*g)^2*(f+g*x))-1/2*(a+b*log(c*(d+e*x)^n))^3/(g*(f+g*x)^2)+3*b^2*e^2*n^2*(a+b*log(c*(d+e*x)^n))*log(e*(f+g*x)/(e*f-d*g))/(g*(e*f-d*g)^2)-3/2*b*e^2*n*(a+b*log(c*(d+e*x)^n))^2*log(1+(e*f-d*g)/(g*(d+e*x)))/(g*(e*f-d*g)^2)+3*b^2*e^2*n^2*(a+b*log(c*(d+e*x)^n))*polylog(2,(-e*f+d*g)/(g*(d+e*x)))/(g*(e*f-d*g)^2)+3*b^3*e^2*n^3*polylog(2,-g*(d+e*x)/(e*f-d*g))/(g*(e*f-d*g)^2)+3*b^3*e^2*n^3*polylog(3,(-e*f+d*g)/(g*(d+e*x)))/(g*(e*f-d*g)^2)],
[(a+b*log(c*(d+e*x)^n))^3/(f+g*x)^4,x,16,b^2*e^2*n^2*(d+e*x)*(a+b*log(c*(d+e*x)^n))/((e*f-d*g)^3*(f+g*x))+1/2*b*e*n*(a+b*log(c*(d+e*x)^n))^2/(g*(e*f-d*g)*(f+g*x)^2)-b*e^2*n*(d+e*x)*(a+b*log(c*(d+e*x)^n))^2/((e*f-d*g)^3*(f+g*x))-1/3*(a+b*log(c*(d+e*x)^n))^3/(g*(f+g*x)^3)-b^3*e^3*n^3*log(f+g*x)/(g*(e*f-d*g)^3)+2*b^2*e^3*n^2*(a+b*log(c*(d+e*x)^n))*log(e*(f+g*x)/(e*f-d*g))/(g*(e*f-d*g)^3)+b^2*e^3*n^2*(a+b*log(c*(d+e*x)^n))*log(1+(e*f-d*g)/(g*(d+e*x)))/(g*(e*f-d*g)^3)-b*e^3*n*(a+b*log(c*(d+e*x)^n))^2*log(1+(e*f-d*g)/(g*(d+e*x)))/(g*(e*f-d*g)^3)-b^3*e^3*n^3*polylog(2,(-e*f+d*g)/(g*(d+e*x)))/(g*(e*f-d*g)^3)+2*b^2*e^3*n^2*(a+b*log(c*(d+e*x)^n))*polylog(2,(-e*f+d*g)/(g*(d+e*x)))/(g*(e*f-d*g)^3)+2*b^3*e^3*n^3*polylog(2,-g*(d+e*x)/(e*f-d*g))/(g*(e*f-d*g)^3)+2*b^3*e^3*n^3*polylog(3,(-e*f+d*g)/(g*(d+e*x)))/(g*(e*f-d*g)^3)],
[(f+g*x)*(a+b*log(c*(d+e*x)^n))^4,x,13,-24*a*b^3*(e*f-d*g)*n^3*x/e+24*b^4*(e*f-d*g)*n^4*x/e+3/4*b^4*g*n^4*(d+e*x)^2/e^2-24*b^4*(e*f-d*g)*n^3*(d+e*x)*log(c*(d+e*x)^n)/e^2-3/2*b^3*g*n^3*(d+e*x)^2*(a+b*log(c*(d+e*x)^n))/e^2+12*b^2*(e*f-d*g)*n^2*(d+e*x)*(a+b*log(c*(d+e*x)^n))^2/e^2+3/2*b^2*g*n^2*(d+e*x)^2*(a+b*log(c*(d+e*x)^n))^2/e^2-4*b*(e*f-d*g)*n*(d+e*x)*(a+b*log(c*(d+e*x)^n))^3/e^2-b*g*n*(d+e*x)^2*(a+b*log(c*(d+e*x)^n))^3/e^2+(e*f-d*g)*(d+e*x)*(a+b*log(c*(d+e*x)^n))^4/e^2+1/2*g*(d+e*x)^2*(a+b*log(c*(d+e*x)^n))^4/e^2],
[(a+b*log(c*(d+e*x)^n))^4,x,6,-24*a*b^3*n^3*x+24*b^4*n^4*x-24*b^4*n^3*(d+e*x)*log(c*(d+e*x)^n)/e+12*b^2*n^2*(d+e*x)*(a+b*log(c*(d+e*x)^n))^2/e-4*b*n*(d+e*x)*(a+b*log(c*(d+e*x)^n))^3/e+(d+e*x)*(a+b*log(c*(d+e*x)^n))^4/e],
[(a+b*log(c*(d+e*x)^n))^4/(f+g*x),x,6,(a+b*log(c*(d+e*x)^n))^4*log(e*(f+g*x)/(e*f-d*g))/g+4*b*n*(a+b*log(c*(d+e*x)^n))^3*polylog(2,-g*(d+e*x)/(e*f-d*g))/g-12*b^2*n^2*(a+b*log(c*(d+e*x)^n))^2*polylog(3,-g*(d+e*x)/(e*f-d*g))/g+24*b^3*n^3*(a+b*log(c*(d+e*x)^n))*polylog(4,-g*(d+e*x)/(e*f-d*g))/g-24*b^4*n^4*polylog(5,-g*(d+e*x)/(e*f-d*g))/g],
[(a+b*log(c*(d+e*x)^n))^4/(f+g*x)^2,x,6,(d+e*x)*(a+b*log(c*(d+e*x)^n))^4/((e*f-d*g)*(f+g*x))-4*b*e*n*(a+b*log(c*(d+e*x)^n))^3*log(e*(f+g*x)/(e*f-d*g))/(g*(e*f-d*g))-12*b^2*e*n^2*(a+b*log(c*(d+e*x)^n))^2*polylog(2,-g*(d+e*x)/(e*f-d*g))/(g*(e*f-d*g))+24*b^3*e*n^3*(a+b*log(c*(d+e*x)^n))*polylog(3,-g*(d+e*x)/(e*f-d*g))/(g*(e*f-d*g))-24*b^4*e*n^4*polylog(4,-g*(d+e*x)/(e*f-d*g))/(g*(e*f-d*g))],
[log(a+b*x),x,2,-x+(a+b*x)*log(a+b*x)/b],
[log(a+b*x)^2,x,3,2*x-2*(a+b*x)*log(a+b*x)/b+(a+b*x)*log(a+b*x)^2/b],
[log(a+b*x)^3,x,4,-6*x+6*(a+b*x)*log(a+b*x)/b-3*(a+b*x)*log(a+b*x)^2/b+(a+b*x)*log(a+b*x)^3/b],
[log(a+b*x+c*x),x,3,-x+(a+(b+c)*x)*log(a+(b+c)*x)/(b+c)],
[log(a+b*x+c*x)^2,x,4,2*x-2*(a+(b+c)*x)*log(a+(b+c)*x)/(b+c)+(a+(b+c)*x)*log(a+(b+c)*x)^2/(b+c)],
[log(a+b*x+c*x)^3,x,5,-6*x+6*(a+(b+c)*x)*log(a+(b+c)*x)/(b+c)-3*(a+(b+c)*x)*log(a+(b+c)*x)^2/(b+c)+(a+(b+c)*x)*log(a+(b+c)*x)^3/(b+c)],
[log(c*(d+e*x)^n),x,2,-n*x+(d+e*x)*log(c*(d+e*x)^n)/e],
[log(-g*(d+e*x)/(e*f-d*g))/(f+g*x),x,2,-polylog(2,e*(f+g*x)/(e*f-d*g))/g],
[(a+b*log(c*(1/c+e*x)))/x,x,2,a*log(x)-b*polylog(2,-c*e*x)],
[log(3+e*x)/x,x,2,log(3)*log(x)-polylog(2,-1/3*e*x)],
[log(2+e*x)/x,x,2,log(2)*log(x)-polylog(2,-1/2*e*x)],
[log(1+e*x)/x,x,1,-polylog(2,-e*x)],
[log(e*x)/x,x,1,1/2*log(e*x)^2],
[log(-1+e*x)/x,x,2,log(e*x)*log(-1+e*x)+polylog(2,1-e*x)],
[log(-2+e*x)/x,x,2,log(1/2*e*x)*log(-2+e*x)+polylog(2,1-1/2*e*x)],
[(a+b*log(3+e*x))/x,x,2,(a+b*log(3))*log(x)-b*polylog(2,-1/3*e*x)],
[(a+b*log(2+e*x))/x,x,2,(a+b*log(2))*log(x)-b*polylog(2,-1/2*e*x)],
[(a+b*log(1+e*x))/x,x,2,a*log(x)-b*polylog(2,-e*x)],
[(a+b*log(e*x))/x,x,1,1/2*(a+b*log(e*x))^2/b],
[(a+b*log(-1+e*x))/x,x,2,log(e*x)*(a+b*log(-1+e*x))+b*polylog(2,1-e*x)],
[(a+b*log(-2+e*x))/x,x,2,log(1/2*e*x)*(a+b*log(-2+e*x))+b*polylog(2,1-1/2*e*x)],
[x^2*log(c*(a+b*x)^n)^2,x,7,2*a^2*n^2*x/b^2-1/2*a*n^2*(a+b*x)^2/b^3+2/27*n^2*(a+b*x)^3/b^3-1/3*a^3*n^2*log(a+b*x)^2/b^3-2*a^2*n*(a+b*x)*log(c*(a+b*x)^n)/b^3+a*n*(a+b*x)^2*log(c*(a+b*x)^n)/b^3-2/9*n*(a+b*x)^3*log(c*(a+b*x)^n)/b^3+2/3*a^3*n*log(a+b*x)*log(c*(a+b*x)^n)/b^3+1/3*x^3*log(c*(a+b*x)^n)^2],
[log(c*(a+b*x)^n)^2/x^4,x,11,-1/3*b^2*n^2/(a^2*x)-b^3*n^2*log(x)/a^3+1/3*b^3*n^2*log(a+b*x)/a^3-1/3*b*n*log(c*(a+b*x)^n)/(a*x^2)+2/3*b^2*n*(a+b*x)*log(c*(a+b*x)^n)/(a^3*x)-1/3*log(c*(a+b*x)^n)^2/x^3+2/3*b^3*n*log(c*(a+b*x)^n)*log(1-a/(a+b*x))/a^3-2/3*b^3*n^2*polylog(2,a/(a+b*x))/a^3],
[x^2*log(c*(a+b*x)^n)^3,x,14,-6*a^2*n^3*x/b^2+3/4*a*n^3*(a+b*x)^2/b^3-2/27*n^3*(a+b*x)^3/b^3+6*a^2*n^2*(a+b*x)*log(c*(a+b*x)^n)/b^3-3/2*a*n^2*(a+b*x)^2*log(c*(a+b*x)^n)/b^3+2/9*n^2*(a+b*x)^3*log(c*(a+b*x)^n)/b^3-3*a^2*n*(a+b*x)*log(c*(a+b*x)^n)^2/b^3+3/2*a*n*(a+b*x)^2*log(c*(a+b*x)^n)^2/b^3-1/3*n*(a+b*x)^3*log(c*(a+b*x)^n)^2/b^3+a^2*(a+b*x)*log(c*(a+b*x)^n)^3/b^3-a*(a+b*x)^2*log(c*(a+b*x)^n)^3/b^3+1/3*(a+b*x)^3*log(c*(a+b*x)^n)^3/b^3],

# p<0
[(f+g*x)^3/(a+b*log(c*(d+e*x)^n)),x,14,(e*f-d*g)^3*(d+e*x)*Ei((a+b*log(c*(d+e*x)^n))/(b*n))/(b*e^4*exp(a/(b*n))*n*(c*(d+e*x)^n)^(1/n))+3*g*(e*f-d*g)^2*(d+e*x)^2*Ei(2*(a+b*log(c*(d+e*x)^n))/(b*n))/(b*e^4*exp(2*a/(b*n))*n*(c*(d+e*x)^n)^(2/n))+3*g^2*(e*f-d*g)*(d+e*x)^3*Ei(3*(a+b*log(c*(d+e*x)^n))/(b*n))/(b*e^4*exp(3*a/(b*n))*n*(c*(d+e*x)^n)^(3/n))+g^3*(d+e*x)^4*Ei(4*(a+b*log(c*(d+e*x)^n))/(b*n))/(b*e^4*exp(4*a/(b*n))*n*(c*(d+e*x)^n)^(4/n))],
[(f+g*x)^2/(a+b*log(c*(d+e*x)^n)),x,11,(e*f-d*g)^2*(d+e*x)*Ei((a+b*log(c*(d+e*x)^n))/(b*n))/(b*e^3*exp(a/(b*n))*n*(c*(d+e*x)^n)^(1/n))+2*g*(e*f-d*g)*(d+e*x)^2*Ei(2*(a+b*log(c*(d+e*x)^n))/(b*n))/(b*e^3*exp(2*a/(b*n))*n*(c*(d+e*x)^n)^(2/n))+g^2*(d+e*x)^3*Ei(3*(a+b*log(c*(d+e*x)^n))/(b*n))/(b*e^3*exp(3*a/(b*n))*n*(c*(d+e*x)^n)^(3/n))],
[(f+g*x)/(a+b*log(c*(d+e*x)^n)),x,8,(e*f-d*g)*(d+e*x)*Ei((a+b*log(c*(d+e*x)^n))/(b*n))/(b*e^2*exp(a/(b*n))*n*(c*(d+e*x)^n)^(1/n))+g*(d+e*x)^2*Ei(2*(a+b*log(c*(d+e*x)^n))/(b*n))/(b*e^2*exp(2*a/(b*n))*n*(c*(d+e*x)^n)^(2/n))],
[1/(a+b*log(c*(d+e*x)^n)),x,3,(d+e*x)*Ei((a+b*log(c*(d+e*x)^n))/(b*n))/(b*e*exp(a/(b*n))*n*(c*(d+e*x)^n)^(1/n))],
[1/((f+g*x)*(a+b*log(c*(d+e*x)^n))),x,0,Unintegrable(1/((f+g*x)*(a+b*log(c*(d+e*x)^n))),x)],
[1/((f+g*x)^2*(a+b*log(c*(d+e*x)^n))),x,0,Unintegrable(1/((f+g*x)^2*(a+b*log(c*(d+e*x)^n))),x)],
[(f+g*x)^3/(a+b*log(c*(d+e*x)^n))^2,x,26,(e*f-d*g)^3*(d+e*x)*Ei((a+b*log(c*(d+e*x)^n))/(b*n))/(b^2*e^4*exp(a/(b*n))*n^2*(c*(d+e*x)^n)^(1/n))+6*g*(e*f-d*g)^2*(d+e*x)^2*Ei(2*(a+b*log(c*(d+e*x)^n))/(b*n))/(b^2*e^4*exp(2*a/(b*n))*n^2*(c*(d+e*x)^n)^(2/n))+9*g^2*(e*f-d*g)*(d+e*x)^3*Ei(3*(a+b*log(c*(d+e*x)^n))/(b*n))/(b^2*e^4*exp(3*a/(b*n))*n^2*(c*(d+e*x)^n)^(3/n))+4*g^3*(d+e*x)^4*Ei(4*(a+b*log(c*(d+e*x)^n))/(b*n))/(b^2*e^4*exp(4*a/(b*n))*n^2*(c*(d+e*x)^n)^(4/n))-(d+e*x)*(f+g*x)^3/(b*e*n*(a+b*log(c*(d+e*x)^n)))],
[(f+g*x)^2/(a+b*log(c*(d+e*x)^n))^2,x,20,(e*f-d*g)^2*(d+e*x)*Ei((a+b*log(c*(d+e*x)^n))/(b*n))/(b^2*e^3*exp(a/(b*n))*n^2*(c*(d+e*x)^n)^(1/n))+4*g*(e*f-d*g)*(d+e*x)^2*Ei(2*(a+b*log(c*(d+e*x)^n))/(b*n))/(b^2*e^3*exp(2*a/(b*n))*n^2*(c*(d+e*x)^n)^(2/n))+3*g^2*(d+e*x)^3*Ei(3*(a+b*log(c*(d+e*x)^n))/(b*n))/(b^2*e^3*exp(3*a/(b*n))*n^2*(c*(d+e*x)^n)^(3/n))-(d+e*x)*(f+g*x)^2/(b*e*n*(a+b*log(c*(d+e*x)^n)))],
[(f+g*x)/(a+b*log(c*(d+e*x)^n))^2,x,12,(e*f-d*g)*(d+e*x)*Ei((a+b*log(c*(d+e*x)^n))/(b*n))/(b^2*e^2*exp(a/(b*n))*n^2*(c*(d+e*x)^n)^(1/n))+2*g*(d+e*x)^2*Ei(2*(a+b*log(c*(d+e*x)^n))/(b*n))/(b^2*e^2*exp(2*a/(b*n))*n^2*(c*(d+e*x)^n)^(2/n))-(d+e*x)*(f+g*x)/(b*e*n*(a+b*log(c*(d+e*x)^n)))],
[1/(a+b*log(c*(d+e*x)^n))^2,x,4,(d+e*x)*Ei((a+b*log(c*(d+e*x)^n))/(b*n))/(b^2*e*exp(a/(b*n))*n^2*(c*(d+e*x)^n)^(1/n))+(-d-e*x)/(b*e*n*(a+b*log(c*(d+e*x)^n)))],
[1/((f+g*x)*(a+b*log(c*(d+e*x)^n))^2),x,0,Unintegrable(1/((f+g*x)*(a+b*log(c*(d+e*x)^n))^2),x)],
[1/((f+g*x)^2*(a+b*log(c*(d+e*x)^n))^2),x,0,Unintegrable(1/((f+g*x)^2*(a+b*log(c*(d+e*x)^n))^2),x)],
[(f+g*x)^2/(a+b*log(c*(d+e*x)^n))^3,x,33,1/2*(e*f-d*g)^2*(d+e*x)*Ei((a+b*log(c*(d+e*x)^n))/(b*n))/(b^3*e^3*exp(a/(b*n))*n^3*(c*(d+e*x)^n)^(1/n))+4*g*(e*f-d*g)*(d+e*x)^2*Ei(2*(a+b*log(c*(d+e*x)^n))/(b*n))/(b^3*e^3*exp(2*a/(b*n))*n^3*(c*(d+e*x)^n)^(2/n))+9/2*g^2*(d+e*x)^3*Ei(3*(a+b*log(c*(d+e*x)^n))/(b*n))/(b^3*e^3*exp(3*a/(b*n))*n^3*(c*(d+e*x)^n)^(3/n))-1/2*(d+e*x)*(f+g*x)^2/(b*e*n*(a+b*log(c*(d+e*x)^n))^2)+(e*f-d*g)*(d+e*x)*(f+g*x)/(b^2*e^2*n^2*(a+b*log(c*(d+e*x)^n)))-3/2*(d+e*x)*(f+g*x)^2/(b^2*e*n^2*(a+b*log(c*(d+e*x)^n)))],
[(f+g*x)/(a+b*log(c*(d+e*x)^n))^3,x,17,1/2*(e*f-d*g)*(d+e*x)*Ei((a+b*log(c*(d+e*x)^n))/(b*n))/(b^3*e^2*exp(a/(b*n))*n^3*(c*(d+e*x)^n)^(1/n))+2*g*(d+e*x)^2*Ei(2*(a+b*log(c*(d+e*x)^n))/(b*n))/(b^3*e^2*exp(2*a/(b*n))*n^3*(c*(d+e*x)^n)^(2/n))-1/2*(d+e*x)*(f+g*x)/(b*e*n*(a+b*log(c*(d+e*x)^n))^2)+1/2*(e*f-d*g)*(d+e*x)/(b^2*e^2*n^2*(a+b*log(c*(d+e*x)^n)))-(d+e*x)*(f+g*x)/(b^2*e*n^2*(a+b*log(c*(d+e*x)^n)))],
[1/(a+b*log(c*(d+e*x)^n))^3,x,5,1/2*(d+e*x)*Ei((a+b*log(c*(d+e*x)^n))/(b*n))/(b^3*e*exp(a/(b*n))*n^3*(c*(d+e*x)^n)^(1/n))+1/2*(-d-e*x)/(b*e*n*(a+b*log(c*(d+e*x)^n))^2)+1/2*(-d-e*x)/(b^2*e*n^2*(a+b*log(c*(d+e*x)^n)))],
[1/((f+g*x)*(a+b*log(c*(d+e*x)^n))^3),x,0,Unintegrable(1/((f+g*x)*(a+b*log(c*(d+e*x)^n))^3),x)],
[1/((f+g*x)^2*(a+b*log(c*(d+e*x)^n))^3),x,0,Unintegrable(1/((f+g*x)^2*(a+b*log(c*(d+e*x)^n))^3),x)],

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

# p>0
[(f+g*x)^2*sqrt(a+b*log(c*(d+e*x)^n)),x,17,-1/6*g^2*(d+e*x)^3*erfi(sqrt(3)*sqrt(a+b*log(c*(d+e*x)^n))/(sqrt(b)*sqrt(n)))*sqrt(b)*sqrt(n)*sqrt(1/3*Pi)/(e^3*exp(3*a/(b*n))*(c*(d+e*x)^n)^(3/n))-1/2*g*(e*f-d*g)*(d+e*x)^2*erfi(sqrt(2)*sqrt(a+b*log(c*(d+e*x)^n))/(sqrt(b)*sqrt(n)))*sqrt(b)*sqrt(n)*sqrt(1/2*Pi)/(e^3*exp(2*a/(b*n))*(c*(d+e*x)^n)^(2/n))-1/2*(e*f-d*g)^2*(d+e*x)*erfi(sqrt(a+b*log(c*(d+e*x)^n))/(sqrt(b)*sqrt(n)))*sqrt(b)*sqrt(n)*sqrt(Pi)/(e^3*exp(a/(b*n))*(c*(d+e*x)^n)^(1/n))+(e*f-d*g)^2*(d+e*x)*sqrt(a+b*log(c*(d+e*x)^n))/e^3+g*(e*f-d*g)*(d+e*x)^2*sqrt(a+b*log(c*(d+e*x)^n))/e^3+1/3*g^2*(d+e*x)^3*sqrt(a+b*log(c*(d+e*x)^n))/e^3],
[(f+g*x)*sqrt(a+b*log(c*(d+e*x)^n)),x,12,-1/4*g*(d+e*x)^2*erfi(sqrt(2)*sqrt(a+b*log(c*(d+e*x)^n))/(sqrt(b)*sqrt(n)))*sqrt(b)*sqrt(n)*sqrt(1/2*Pi)/(e^2*exp(2*a/(b*n))*(c*(d+e*x)^n)^(2/n))-1/2*(e*f-d*g)*(d+e*x)*erfi(sqrt(a+b*log(c*(d+e*x)^n))/(sqrt(b)*sqrt(n)))*sqrt(b)*sqrt(n)*sqrt(Pi)/(e^2*exp(a/(b*n))*(c*(d+e*x)^n)^(1/n))+(e*f-d*g)*(d+e*x)*sqrt(a+b*log(c*(d+e*x)^n))/e^2+1/2*g*(d+e*x)^2*sqrt(a+b*log(c*(d+e*x)^n))/e^2],
[sqrt(a+b*log(c*(d+e*x)^n)),x,5,-1/2*(d+e*x)*erfi(sqrt(a+b*log(c*(d+e*x)^n))/(sqrt(b)*sqrt(n)))*sqrt(b)*sqrt(n)*sqrt(Pi)/(e*exp(a/(b*n))*(c*(d+e*x)^n)^(1/n))+(d+e*x)*sqrt(a+b*log(c*(d+e*x)^n))/e],
[sqrt(a+b*log(c*(d+e*x)^n))/(f+g*x),x,0,Unintegrable(sqrt(a+b*log(c*(d+e*x)^n))/(f+g*x),x)],
[sqrt(a+b*log(c*(d+e*x)^n))/(f+g*x)^2,x,1,(d+e*x)*sqrt(a+b*log(c*(d+e*x)^n))/((e*f-d*g)*(f+g*x))-1/2*b*e*n*Unintegrable(1/((f+g*x)*sqrt(a+b*log(c*(d+e*x)^n))),x)/(e*f-d*g)],
[sqrt(a+b*log(c*(d+e*x)^n))/(f+g*x)^3,x,1,-1/2*sqrt(a+b*log(c*(d+e*x)^n))/(g*(f+g*x)^2)+1/4*b*e*n*Unintegrable(1/((d+e*x)*(f+g*x)^2*sqrt(a+b*log(c*(d+e*x)^n))),x)/g],
[(f+g*x)^2*(a+b*log(c*(d+e*x)^n))^(3/2),x,20,(e*f-d*g)^2*(d+e*x)*(a+b*log(c*(d+e*x)^n))^(3/2)/e^3+g*(e*f-d*g)*(d+e*x)^2*(a+b*log(c*(d+e*x)^n))^(3/2)/e^3+1/3*g^2*(d+e*x)^3*(a+b*log(c*(d+e*x)^n))^(3/2)/e^3+1/12*b^(3/2)*g^2*n^(3/2)*(d+e*x)^3*erfi(sqrt(3)*sqrt(a+b*log(c*(d+e*x)^n))/(sqrt(b)*sqrt(n)))*sqrt(1/3*Pi)/(e^3*exp(3*a/(b*n))*(c*(d+e*x)^n)^(3/n))+3/8*b^(3/2)*g*(e*f-d*g)*n^(3/2)*(d+e*x)^2*erfi(sqrt(2)*sqrt(a+b*log(c*(d+e*x)^n))/(sqrt(b)*sqrt(n)))*sqrt(1/2*Pi)/(e^3*exp(2*a/(b*n))*(c*(d+e*x)^n)^(2/n))+3/4*b^(3/2)*(e*f-d*g)^2*n^(3/2)*(d+e*x)*erfi(sqrt(a+b*log(c*(d+e*x)^n))/(sqrt(b)*sqrt(n)))*sqrt(Pi)/(e^3*exp(a/(b*n))*(c*(d+e*x)^n)^(1/n))-3/2*b*(e*f-d*g)^2*n*(d+e*x)*sqrt(a+b*log(c*(d+e*x)^n))/e^3-3/4*b*g*(e*f-d*g)*n*(d+e*x)^2*sqrt(a+b*log(c*(d+e*x)^n))/e^3-1/6*b*g^2*n*(d+e*x)^3*sqrt(a+b*log(c*(d+e*x)^n))/e^3],
[(f+g*x)*(a+b*log(c*(d+e*x)^n))^(3/2),x,14,(e*f-d*g)*(d+e*x)*(a+b*log(c*(d+e*x)^n))^(3/2)/e^2+1/2*g*(d+e*x)^2*(a+b*log(c*(d+e*x)^n))^(3/2)/e^2+3/16*b^(3/2)*g*n^(3/2)*(d+e*x)^2*erfi(sqrt(2)*sqrt(a+b*log(c*(d+e*x)^n))/(sqrt(b)*sqrt(n)))*sqrt(1/2*Pi)/(e^2*exp(2*a/(b*n))*(c*(d+e*x)^n)^(2/n))+3/4*b^(3/2)*(e*f-d*g)*n^(3/2)*(d+e*x)*erfi(sqrt(a+b*log(c*(d+e*x)^n))/(sqrt(b)*sqrt(n)))*sqrt(Pi)/(e^2*exp(a/(b*n))*(c*(d+e*x)^n)^(1/n))-3/2*b*(e*f-d*g)*n*(d+e*x)*sqrt(a+b*log(c*(d+e*x)^n))/e^2-3/8*b*g*n*(d+e*x)^2*sqrt(a+b*log(c*(d+e*x)^n))/e^2],
[(a+b*log(c*(d+e*x)^n))^(3/2),x,6,(d+e*x)*(a+b*log(c*(d+e*x)^n))^(3/2)/e+3/4*b^(3/2)*n^(3/2)*(d+e*x)*erfi(sqrt(a+b*log(c*(d+e*x)^n))/(sqrt(b)*sqrt(n)))*sqrt(Pi)/(e*exp(a/(b*n))*(c*(d+e*x)^n)^(1/n))-3/2*b*n*(d+e*x)*sqrt(a+b*log(c*(d+e*x)^n))/e],
[(a+b*log(c*(d+e*x)^n))^(3/2)/(f+g*x),x,0,Unintegrable((a+b*log(c*(d+e*x)^n))^(3/2)/(f+g*x),x)],
[(a+b*log(c*(d+e*x)^n))^(3/2)/(f+g*x)^2,x,1,(d+e*x)*(a+b*log(c*(d+e*x)^n))^(3/2)/((e*f-d*g)*(f+g*x))-3/2*b*e*n*Unintegrable(sqrt(a+b*log(c*(d+e*x)^n))/(f+g*x),x)/(e*f-d*g)],
[(a+b*log(c*(d+e*x)^n))^(3/2)/(f+g*x)^3,x,1,-1/2*(a+b*log(c*(d+e*x)^n))^(3/2)/(g*(f+g*x)^2)+3/4*b*e*n*Unintegrable(sqrt(a+b*log(c*(d+e*x)^n))/((d+e*x)*(f+g*x)^2),x)/g],
[(f+g*x)^2*(a+b*log(c*(d+e*x)^n))^(5/2),x,23,-5/2*b*(e*f-d*g)^2*n*(d+e*x)*(a+b*log(c*(d+e*x)^n))^(3/2)/e^3-5/4*b*g*(e*f-d*g)*n*(d+e*x)^2*(a+b*log(c*(d+e*x)^n))^(3/2)/e^3-5/18*b*g^2*n*(d+e*x)^3*(a+b*log(c*(d+e*x)^n))^(3/2)/e^3+(e*f-d*g)^2*(d+e*x)*(a+b*log(c*(d+e*x)^n))^(5/2)/e^3+g*(e*f-d*g)*(d+e*x)^2*(a+b*log(c*(d+e*x)^n))^(5/2)/e^3+1/3*g^2*(d+e*x)^3*(a+b*log(c*(d+e*x)^n))^(5/2)/e^3-5/72*b^(5/2)*g^2*n^(5/2)*(d+e*x)^3*erfi(sqrt(3)*sqrt(a+b*log(c*(d+e*x)^n))/(sqrt(b)*sqrt(n)))*sqrt(1/3*Pi)/(e^3*exp(3*a/(b*n))*(c*(d+e*x)^n)^(3/n))-15/32*b^(5/2)*g*(e*f-d*g)*n^(5/2)*(d+e*x)^2*erfi(sqrt(2)*sqrt(a+b*log(c*(d+e*x)^n))/(sqrt(b)*sqrt(n)))*sqrt(1/2*Pi)/(e^3*exp(2*a/(b*n))*(c*(d+e*x)^n)^(2/n))-15/8*b^(5/2)*(e*f-d*g)^2*n^(5/2)*(d+e*x)*erfi(sqrt(a+b*log(c*(d+e*x)^n))/(sqrt(b)*sqrt(n)))*sqrt(Pi)/(e^3*exp(a/(b*n))*(c*(d+e*x)^n)^(1/n))+15/4*b^2*(e*f-d*g)^2*n^2*(d+e*x)*sqrt(a+b*log(c*(d+e*x)^n))/e^3+15/16*b^2*g*(e*f-d*g)*n^2*(d+e*x)^2*sqrt(a+b*log(c*(d+e*x)^n))/e^3+5/36*b^2*g^2*n^2*(d+e*x)^3*sqrt(a+b*log(c*(d+e*x)^n))/e^3],
[(f+g*x)*(a+b*log(c*(d+e*x)^n))^(5/2),x,16,-5/2*b*(e*f-d*g)*n*(d+e*x)*(a+b*log(c*(d+e*x)^n))^(3/2)/e^2-5/8*b*g*n*(d+e*x)^2*(a+b*log(c*(d+e*x)^n))^(3/2)/e^2+(e*f-d*g)*(d+e*x)*(a+b*log(c*(d+e*x)^n))^(5/2)/e^2+1/2*g*(d+e*x)^2*(a+b*log(c*(d+e*x)^n))^(5/2)/e^2-15/64*b^(5/2)*g*n^(5/2)*(d+e*x)^2*erfi(sqrt(2)*sqrt(a+b*log(c*(d+e*x)^n))/(sqrt(b)*sqrt(n)))*sqrt(1/2*Pi)/(e^2*exp(2*a/(b*n))*(c*(d+e*x)^n)^(2/n))-15/8*b^(5/2)*(e*f-d*g)*n^(5/2)*(d+e*x)*erfi(sqrt(a+b*log(c*(d+e*x)^n))/(sqrt(b)*sqrt(n)))*sqrt(Pi)/(e^2*exp(a/(b*n))*(c*(d+e*x)^n)^(1/n))+15/4*b^2*(e*f-d*g)*n^2*(d+e*x)*sqrt(a+b*log(c*(d+e*x)^n))/e^2+15/32*b^2*g*n^2*(d+e*x)^2*sqrt(a+b*log(c*(d+e*x)^n))/e^2],
[(a+b*log(c*(d+e*x)^n))^(5/2),x,7,-5/2*b*n*(d+e*x)*(a+b*log(c*(d+e*x)^n))^(3/2)/e+(d+e*x)*(a+b*log(c*(d+e*x)^n))^(5/2)/e-15/8*b^(5/2)*n^(5/2)*(d+e*x)*erfi(sqrt(a+b*log(c*(d+e*x)^n))/(sqrt(b)*sqrt(n)))*sqrt(Pi)/(e*exp(a/(b*n))*(c*(d+e*x)^n)^(1/n))+15/4*b^2*n^2*(d+e*x)*sqrt(a+b*log(c*(d+e*x)^n))/e],
[(a+b*log(c*(d+e*x)^n))^(5/2)/(f+g*x),x,0,Unintegrable((a+b*log(c*(d+e*x)^n))^(5/2)/(f+g*x),x)],
[(a+b*log(c*(d+e*x)^n))^(5/2)/(f+g*x)^2,x,1,(d+e*x)*(a+b*log(c*(d+e*x)^n))^(5/2)/((e*f-d*g)*(f+g*x))-5/2*b*e*n*Unintegrable((a+b*log(c*(d+e*x)^n))^(3/2)/(f+g*x),x)/(e*f-d*g)],
[(a+b*log(c*(d+e*x)^n))^(5/2)/(f+g*x)^3,x,1,-1/2*(a+b*log(c*(d+e*x)^n))^(5/2)/(g*(f+g*x)^2)+5/4*b*e*n*Unintegrable((a+b*log(c*(d+e*x)^n))^(3/2)/((d+e*x)*(f+g*x)^2),x)/g],

# p<0
[(f+g*x)^3/sqrt(a+b*log(c*(d+e*x)^n)),x,18,3*g*(e*f-d*g)^2*(d+e*x)^2*erfi(sqrt(2)*sqrt(a+b*log(c*(d+e*x)^n))/(sqrt(b)*sqrt(n)))*sqrt(1/2*Pi)/(e^4*exp(2*a/(b*n))*(c*(d+e*x)^n)^(2/n)*sqrt(b)*sqrt(n))+(e*f-d*g)^3*(d+e*x)*erfi(sqrt(a+b*log(c*(d+e*x)^n))/(sqrt(b)*sqrt(n)))*sqrt(Pi)/(e^4*exp(a/(b*n))*(c*(d+e*x)^n)^(1/n)*sqrt(b)*sqrt(n))+1/2*g^3*(d+e*x)^4*erfi(2*sqrt(a+b*log(c*(d+e*x)^n))/(sqrt(b)*sqrt(n)))*sqrt(Pi)/(e^4*exp(4*a/(b*n))*(c*(d+e*x)^n)^(4/n)*sqrt(b)*sqrt(n))+g^2*(e*f-d*g)*(d+e*x)^3*erfi(sqrt(3)*sqrt(a+b*log(c*(d+e*x)^n))/(sqrt(b)*sqrt(n)))*sqrt(3*Pi)/(e^4*exp(3*a/(b*n))*(c*(d+e*x)^n)^(3/n)*sqrt(b)*sqrt(n))],
[(f+g*x)^2/sqrt(a+b*log(c*(d+e*x)^n)),x,14,g^2*(d+e*x)^3*erfi(sqrt(3)*sqrt(a+b*log(c*(d+e*x)^n))/(sqrt(b)*sqrt(n)))*sqrt(1/3*Pi)/(e^3*exp(3*a/(b*n))*(c*(d+e*x)^n)^(3/n)*sqrt(b)*sqrt(n))+(e*f-d*g)^2*(d+e*x)*erfi(sqrt(a+b*log(c*(d+e*x)^n))/(sqrt(b)*sqrt(n)))*sqrt(Pi)/(e^3*exp(a/(b*n))*(c*(d+e*x)^n)^(1/n)*sqrt(b)*sqrt(n))+g*(e*f-d*g)*(d+e*x)^2*erfi(sqrt(2)*sqrt(a+b*log(c*(d+e*x)^n))/(sqrt(b)*sqrt(n)))*sqrt(2*Pi)/(e^3*exp(2*a/(b*n))*(c*(d+e*x)^n)^(2/n)*sqrt(b)*sqrt(n))],
[(f+g*x)/sqrt(a+b*log(c*(d+e*x)^n)),x,10,g*(d+e*x)^2*erfi(sqrt(2)*sqrt(a+b*log(c*(d+e*x)^n))/(sqrt(b)*sqrt(n)))*sqrt(1/2*Pi)/(e^2*exp(2*a/(b*n))*(c*(d+e*x)^n)^(2/n)*sqrt(b)*sqrt(n))+(e*f-d*g)*(d+e*x)*erfi(sqrt(a+b*log(c*(d+e*x)^n))/(sqrt(b)*sqrt(n)))*sqrt(Pi)/(e^2*exp(a/(b*n))*(c*(d+e*x)^n)^(1/n)*sqrt(b)*sqrt(n))],
[1/sqrt(a+b*log(c*(d+e*x)^n)),x,4,(d+e*x)*erfi(sqrt(a+b*log(c*(d+e*x)^n))/(sqrt(b)*sqrt(n)))*sqrt(Pi)/(e*exp(a/(b*n))*(c*(d+e*x)^n)^(1/n)*sqrt(b)*sqrt(n))],
[1/((f+g*x)*sqrt(a+b*log(c*(d+e*x)^n))),x,0,Unintegrable(1/((f+g*x)*sqrt(a+b*log(c*(d+e*x)^n))),x)],
[(f+g*x)^3/(a+b*log(c*(d+e*x)^n))^(3/2),x,33,2*(e*f-d*g)^3*(d+e*x)*erfi(sqrt(a+b*log(c*(d+e*x)^n))/(sqrt(b)*sqrt(n)))*sqrt(Pi)/(b^(3/2)*e^4*exp(a/(b*n))*n^(3/2)*(c*(d+e*x)^n)^(1/n))+4*g^3*(d+e*x)^4*erfi(2*sqrt(a+b*log(c*(d+e*x)^n))/(sqrt(b)*sqrt(n)))*sqrt(Pi)/(b^(3/2)*e^4*exp(4*a/(b*n))*n^(3/2)*(c*(d+e*x)^n)^(4/n))+6*g*(e*f-d*g)^2*(d+e*x)^2*erfi(sqrt(2)*sqrt(a+b*log(c*(d+e*x)^n))/(sqrt(b)*sqrt(n)))*sqrt(2*Pi)/(b^(3/2)*e^4*exp(2*a/(b*n))*n^(3/2)*(c*(d+e*x)^n)^(2/n))+6*g^2*(e*f-d*g)*(d+e*x)^3*erfi(sqrt(3)*sqrt(a+b*log(c*(d+e*x)^n))/(sqrt(b)*sqrt(n)))*sqrt(3*Pi)/(b^(3/2)*e^4*exp(3*a/(b*n))*n^(3/2)*(c*(d+e*x)^n)^(3/n))-2*(d+e*x)*(f+g*x)^3/(b*e*n*sqrt(a+b*log(c*(d+e*x)^n)))],
[(f+g*x)^2/(a+b*log(c*(d+e*x)^n))^(3/2),x,25,2*(e*f-d*g)^2*(d+e*x)*erfi(sqrt(a+b*log(c*(d+e*x)^n))/(sqrt(b)*sqrt(n)))*sqrt(Pi)/(b^(3/2)*e^3*exp(a/(b*n))*n^(3/2)*(c*(d+e*x)^n)^(1/n))+4*g*(e*f-d*g)*(d+e*x)^2*erfi(sqrt(2)*sqrt(a+b*log(c*(d+e*x)^n))/(sqrt(b)*sqrt(n)))*sqrt(2*Pi)/(b^(3/2)*e^3*exp(2*a/(b*n))*n^(3/2)*(c*(d+e*x)^n)^(2/n))+2*g^2*(d+e*x)^3*erfi(sqrt(3)*sqrt(a+b*log(c*(d+e*x)^n))/(sqrt(b)*sqrt(n)))*sqrt(3*Pi)/(b^(3/2)*e^3*exp(3*a/(b*n))*n^(3/2)*(c*(d+e*x)^n)^(3/n))-2*(d+e*x)*(f+g*x)^2/(b*e*n*sqrt(a+b*log(c*(d+e*x)^n)))],
[(f+g*x)/(a+b*log(c*(d+e*x)^n))^(3/2),x,15,2*(e*f-d*g)*(d+e*x)*erfi(sqrt(a+b*log(c*(d+e*x)^n))/(sqrt(b)*sqrt(n)))*sqrt(Pi)/(b^(3/2)*e^2*exp(a/(b*n))*n^(3/2)*(c*(d+e*x)^n)^(1/n))+2*g*(d+e*x)^2*erfi(sqrt(2)*sqrt(a+b*log(c*(d+e*x)^n))/(sqrt(b)*sqrt(n)))*sqrt(2*Pi)/(b^(3/2)*e^2*exp(2*a/(b*n))*n^(3/2)*(c*(d+e*x)^n)^(2/n))-2*(d+e*x)*(f+g*x)/(b*e*n*sqrt(a+b*log(c*(d+e*x)^n)))],
[1/(a+b*log(c*(d+e*x)^n))^(3/2),x,5,2*(d+e*x)*erfi(sqrt(a+b*log(c*(d+e*x)^n))/(sqrt(b)*sqrt(n)))*sqrt(Pi)/(b^(3/2)*e*exp(a/(b*n))*n^(3/2)*(c*(d+e*x)^n)^(1/n))-2*(d+e*x)/(b*e*n*sqrt(a+b*log(c*(d+e*x)^n)))],
[1/((f+g*x)*(a+b*log(c*(d+e*x)^n))^(3/2)),x,0,Unintegrable(1/((f+g*x)*(a+b*log(c*(d+e*x)^n))^(3/2)),x)],
[(f+g*x)^3/(a+b*log(c*(d+e*x)^n))^(5/2),x,59,-2/3*(d+e*x)*(f+g*x)^3/(b*e*n*(a+b*log(c*(d+e*x)^n))^(3/2))+4/3*(e*f-d*g)^3*(d+e*x)*erfi(sqrt(a+b*log(c*(d+e*x)^n))/(sqrt(b)*sqrt(n)))*sqrt(Pi)/(b^(5/2)*e^4*exp(a/(b*n))*n^(5/2)*(c*(d+e*x)^n)^(1/n))+32/3*g^3*(d+e*x)^4*erfi(2*sqrt(a+b*log(c*(d+e*x)^n))/(sqrt(b)*sqrt(n)))*sqrt(Pi)/(b^(5/2)*e^4*exp(4*a/(b*n))*n^(5/2)*(c*(d+e*x)^n)^(4/n))+8*g*(e*f-d*g)^2*(d+e*x)^2*erfi(sqrt(2)*sqrt(a+b*log(c*(d+e*x)^n))/(sqrt(b)*sqrt(n)))*sqrt(2*Pi)/(b^(5/2)*e^4*exp(2*a/(b*n))*n^(5/2)*(c*(d+e*x)^n)^(2/n))+12*g^2*(e*f-d*g)*(d+e*x)^3*erfi(sqrt(3)*sqrt(a+b*log(c*(d+e*x)^n))/(sqrt(b)*sqrt(n)))*sqrt(3*Pi)/(b^(5/2)*e^4*exp(3*a/(b*n))*n^(5/2)*(c*(d+e*x)^n)^(3/n))+4*(e*f-d*g)*(d+e*x)*(f+g*x)^2/(b^2*e^2*n^2*sqrt(a+b*log(c*(d+e*x)^n)))-16/3*(d+e*x)*(f+g*x)^3/(b^2*e*n^2*sqrt(a+b*log(c*(d+e*x)^n)))],
[(f+g*x)^2/(a+b*log(c*(d+e*x)^n))^(5/2),x,41,-2/3*(d+e*x)*(f+g*x)^2/(b*e*n*(a+b*log(c*(d+e*x)^n))^(3/2))+4/3*(e*f-d*g)^2*(d+e*x)*erfi(sqrt(a+b*log(c*(d+e*x)^n))/(sqrt(b)*sqrt(n)))*sqrt(Pi)/(b^(5/2)*e^3*exp(a/(b*n))*n^(5/2)*(c*(d+e*x)^n)^(1/n))+16/3*g*(e*f-d*g)*(d+e*x)^2*erfi(sqrt(2)*sqrt(a+b*log(c*(d+e*x)^n))/(sqrt(b)*sqrt(n)))*sqrt(2*Pi)/(b^(5/2)*e^3*exp(2*a/(b*n))*n^(5/2)*(c*(d+e*x)^n)^(2/n))+4*g^2*(d+e*x)^3*erfi(sqrt(3)*sqrt(a+b*log(c*(d+e*x)^n))/(sqrt(b)*sqrt(n)))*sqrt(3*Pi)/(b^(5/2)*e^3*exp(3*a/(b*n))*n^(5/2)*(c*(d+e*x)^n)^(3/n))+8/3*(e*f-d*g)*(d+e*x)*(f+g*x)/(b^2*e^2*n^2*sqrt(a+b*log(c*(d+e*x)^n)))-4*(d+e*x)*(f+g*x)^2/(b^2*e*n^2*sqrt(a+b*log(c*(d+e*x)^n)))],
[(f+g*x)/(a+b*log(c*(d+e*x)^n))^(5/2),x,21,-2/3*(d+e*x)*(f+g*x)/(b*e*n*(a+b*log(c*(d+e*x)^n))^(3/2))+4/3*(e*f-d*g)*(d+e*x)*erfi(sqrt(a+b*log(c*(d+e*x)^n))/(sqrt(b)*sqrt(n)))*sqrt(Pi)/(b^(5/2)*e^2*exp(a/(b*n))*n^(5/2)*(c*(d+e*x)^n)^(1/n))+8/3*g*(d+e*x)^2*erfi(sqrt(2)*sqrt(a+b*log(c*(d+e*x)^n))/(sqrt(b)*sqrt(n)))*sqrt(2*Pi)/(b^(5/2)*e^2*exp(2*a/(b*n))*n^(5/2)*(c*(d+e*x)^n)^(2/n))+4/3*(e*f-d*g)*(d+e*x)/(b^2*e^2*n^2*sqrt(a+b*log(c*(d+e*x)^n)))-8/3*(d+e*x)*(f+g*x)/(b^2*e*n^2*sqrt(a+b*log(c*(d+e*x)^n)))],
[1/(a+b*log(c*(d+e*x)^n))^(5/2),x,6,-2/3*(d+e*x)/(b*e*n*(a+b*log(c*(d+e*x)^n))^(3/2))+4/3*(d+e*x)*erfi(sqrt(a+b*log(c*(d+e*x)^n))/(sqrt(b)*sqrt(n)))*sqrt(Pi)/(b^(5/2)*e*exp(a/(b*n))*n^(5/2)*(c*(d+e*x)^n)^(1/n))-4/3*(d+e*x)/(b^2*e*n^2*sqrt(a+b*log(c*(d+e*x)^n)))],
[1/((f+g*x)*(a+b*log(c*(d+e*x)^n))^(5/2)),x,0,Unintegrable(1/((f+g*x)*(a+b*log(c*(d+e*x)^n))^(5/2)),x)],

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

# p>0
[(f+g*x)^(3/2)*(a+b*log(c*(d+e*x)^n)),x,6,-4/15*b*(e*f-d*g)*n*(f+g*x)^(3/2)/(e*g)-4/25*b*n*(f+g*x)^(5/2)/g+4/5*b*(e*f-d*g)^(5/2)*n*arctanh(sqrt(e)*sqrt(f+g*x)/sqrt(e*f-d*g))/(e^(5/2)*g)+2/5*(f+g*x)^(5/2)*(a+b*log(c*(d+e*x)^n))/g-4/5*b*(e*f-d*g)^2*n*sqrt(f+g*x)/(e^2*g)],
[(f+g*x)^(1/2)*(a+b*log(c*(d+e*x)^n)),x,5,-4/9*b*n*(f+g*x)^(3/2)/g+4/3*b*(e*f-d*g)^(3/2)*n*arctanh(sqrt(e)*sqrt(f+g*x)/sqrt(e*f-d*g))/(e^(3/2)*g)+2/3*(f+g*x)^(3/2)*(a+b*log(c*(d+e*x)^n))/g-4/3*b*(e*f-d*g)*n*sqrt(f+g*x)/(e*g)],
[(a+b*log(c*(d+e*x)^n))/(f+g*x)^(1/2),x,4,4*b*n*arctanh(sqrt(e)*sqrt(f+g*x)/sqrt(e*f-d*g))*sqrt(e*f-d*g)/(g*sqrt(e))-4*b*n*sqrt(f+g*x)/g+2*(a+b*log(c*(d+e*x)^n))*sqrt(f+g*x)/g],
[(a+b*log(c*(d+e*x)^n))/(f+g*x)^(3/2),x,3,-4*b*n*arctanh(sqrt(e)*sqrt(f+g*x)/sqrt(e*f-d*g))*sqrt(e)/(g*sqrt(e*f-d*g))-2*(a+b*log(c*(d+e*x)^n))/(g*sqrt(f+g*x))],
[(a+b*log(c*(d+e*x)^n))/(f+g*x)^(5/2),x,4,-4/3*b*e^(3/2)*n*arctanh(sqrt(e)*sqrt(f+g*x)/sqrt(e*f-d*g))/(g*(e*f-d*g)^(3/2))-2/3*(a+b*log(c*(d+e*x)^n))/(g*(f+g*x)^(3/2))+4/3*b*e*n/(g*(e*f-d*g)*sqrt(f+g*x))],
[(a+b*log(c*(d+e*x)^n))/(f+g*x)^(7/2),x,5,4/15*b*e*n/(g*(e*f-d*g)*(f+g*x)^(3/2))-4/5*b*e^(5/2)*n*arctanh(sqrt(e)*sqrt(f+g*x)/sqrt(e*f-d*g))/(g*(e*f-d*g)^(5/2))-2/5*(a+b*log(c*(d+e*x)^n))/(g*(f+g*x)^(5/2))+4/5*b*e^2*n/(g*(e*f-d*g)^2*sqrt(f+g*x))],
[(a+b*log(c*(d+e*x)^n))/(f+g*x)^(9/2),x,6,4/35*b*e*n/(g*(e*f-d*g)*(f+g*x)^(5/2))+4/21*b*e^2*n/(g*(e*f-d*g)^2*(f+g*x)^(3/2))-4/7*b*e^(7/2)*n*arctanh(sqrt(e)*sqrt(f+g*x)/sqrt(e*f-d*g))/(g*(e*f-d*g)^(7/2))-2/7*(a+b*log(c*(d+e*x)^n))/(g*(f+g*x)^(7/2))+4/7*b*e^3*n/(g*(e*f-d*g)^3*sqrt(f+g*x))],
[(f+g*x)^(3/2)*(a+b*log(c*(d+e*x)^n))^2,x,28,128/225*b^2*(e*f-d*g)*n^2*(f+g*x)^(3/2)/(e*g)+16/125*b^2*n^2*(f+g*x)^(5/2)/g-368/75*b^2*(e*f-d*g)^(5/2)*n^2*arctanh(sqrt(e)*sqrt(f+g*x)/sqrt(e*f-d*g))/(e^(5/2)*g)-8/5*b^2*(e*f-d*g)^(5/2)*n^2*arctanh(sqrt(e)*sqrt(f+g*x)/sqrt(e*f-d*g))^2/(e^(5/2)*g)-8/15*b*(e*f-d*g)*n*(f+g*x)^(3/2)*(a+b*log(c*(d+e*x)^n))/(e*g)-8/25*b*n*(f+g*x)^(5/2)*(a+b*log(c*(d+e*x)^n))/g+8/5*b*(e*f-d*g)^(5/2)*n*arctanh(sqrt(e)*sqrt(f+g*x)/sqrt(e*f-d*g))*(a+b*log(c*(d+e*x)^n))/(e^(5/2)*g)+2/5*(f+g*x)^(5/2)*(a+b*log(c*(d+e*x)^n))^2/g+16/5*b^2*(e*f-d*g)^(5/2)*n^2*arctanh(sqrt(e)*sqrt(f+g*x)/sqrt(e*f-d*g))*log(2/(1-sqrt(e)*sqrt(f+g*x)/sqrt(e*f-d*g)))/(e^(5/2)*g)+8/5*b^2*(e*f-d*g)^(5/2)*n^2*polylog(2,1+(-2)/(1-sqrt(e)*sqrt(f+g*x)/sqrt(e*f-d*g)))/(e^(5/2)*g)+368/75*b^2*(e*f-d*g)^2*n^2*sqrt(f+g*x)/(e^2*g)-8/5*b*(e*f-d*g)^2*n*(a+b*log(c*(d+e*x)^n))*sqrt(f+g*x)/(e^2*g)],
[(f+g*x)^(1/2)*(a+b*log(c*(d+e*x)^n))^2,x,21,16/27*b^2*n^2*(f+g*x)^(3/2)/g-64/9*b^2*(e*f-d*g)^(3/2)*n^2*arctanh(sqrt(e)*sqrt(f+g*x)/sqrt(e*f-d*g))/(e^(3/2)*g)-8/3*b^2*(e*f-d*g)^(3/2)*n^2*arctanh(sqrt(e)*sqrt(f+g*x)/sqrt(e*f-d*g))^2/(e^(3/2)*g)-8/9*b*n*(f+g*x)^(3/2)*(a+b*log(c*(d+e*x)^n))/g+8/3*b*(e*f-d*g)^(3/2)*n*arctanh(sqrt(e)*sqrt(f+g*x)/sqrt(e*f-d*g))*(a+b*log(c*(d+e*x)^n))/(e^(3/2)*g)+2/3*(f+g*x)^(3/2)*(a+b*log(c*(d+e*x)^n))^2/g+16/3*b^2*(e*f-d*g)^(3/2)*n^2*arctanh(sqrt(e)*sqrt(f+g*x)/sqrt(e*f-d*g))*log(2/(1-sqrt(e)*sqrt(f+g*x)/sqrt(e*f-d*g)))/(e^(3/2)*g)+8/3*b^2*(e*f-d*g)^(3/2)*n^2*polylog(2,1+(-2)/(1-sqrt(e)*sqrt(f+g*x)/sqrt(e*f-d*g)))/(e^(3/2)*g)+64/9*b^2*(e*f-d*g)*n^2*sqrt(f+g*x)/(e*g)-8/3*b*(e*f-d*g)*n*(a+b*log(c*(d+e*x)^n))*sqrt(f+g*x)/(e*g)],
[(a+b*log(c*(d+e*x)^n))^2/(f+g*x)^(1/2),x,15,-16*b^2*n^2*arctanh(sqrt(e)*sqrt(f+g*x)/sqrt(e*f-d*g))*sqrt(e*f-d*g)/(g*sqrt(e))-8*b^2*n^2*arctanh(sqrt(e)*sqrt(f+g*x)/sqrt(e*f-d*g))^2*sqrt(e*f-d*g)/(g*sqrt(e))+8*b*n*arctanh(sqrt(e)*sqrt(f+g*x)/sqrt(e*f-d*g))*(a+b*log(c*(d+e*x)^n))*sqrt(e*f-d*g)/(g*sqrt(e))+16*b^2*n^2*arctanh(sqrt(e)*sqrt(f+g*x)/sqrt(e*f-d*g))*log(2/(1-sqrt(e)*sqrt(f+g*x)/sqrt(e*f-d*g)))*sqrt(e*f-d*g)/(g*sqrt(e))+8*b^2*n^2*polylog(2,1+(-2)/(1-sqrt(e)*sqrt(f+g*x)/sqrt(e*f-d*g)))*sqrt(e*f-d*g)/(g*sqrt(e))+16*b^2*n^2*sqrt(f+g*x)/g-8*b*n*(a+b*log(c*(d+e*x)^n))*sqrt(f+g*x)/g+2*(a+b*log(c*(d+e*x)^n))^2*sqrt(f+g*x)/g],
[(a+b*log(c*(d+e*x)^n))^2/(f+g*x)^(3/2),x,10,8*b^2*n^2*arctanh(sqrt(e)*sqrt(f+g*x)/sqrt(e*f-d*g))^2*sqrt(e)/(g*sqrt(e*f-d*g))-8*b*n*arctanh(sqrt(e)*sqrt(f+g*x)/sqrt(e*f-d*g))*(a+b*log(c*(d+e*x)^n))*sqrt(e)/(g*sqrt(e*f-d*g))-16*b^2*n^2*arctanh(sqrt(e)*sqrt(f+g*x)/sqrt(e*f-d*g))*log(2/(1-sqrt(e)*sqrt(f+g*x)/sqrt(e*f-d*g)))*sqrt(e)/(g*sqrt(e*f-d*g))-8*b^2*n^2*polylog(2,1+(-2)/(1-sqrt(e)*sqrt(f+g*x)/sqrt(e*f-d*g)))*sqrt(e)/(g*sqrt(e*f-d*g))-2*(a+b*log(c*(d+e*x)^n))^2/(g*sqrt(f+g*x))],
[(a+b*log(c*(d+e*x)^n))^2/(f+g*x)^(5/2),x,14,16/3*b^2*e^(3/2)*n^2*arctanh(sqrt(e)*sqrt(f+g*x)/sqrt(e*f-d*g))/(g*(e*f-d*g)^(3/2))+8/3*b^2*e^(3/2)*n^2*arctanh(sqrt(e)*sqrt(f+g*x)/sqrt(e*f-d*g))^2/(g*(e*f-d*g)^(3/2))-8/3*b*e^(3/2)*n*arctanh(sqrt(e)*sqrt(f+g*x)/sqrt(e*f-d*g))*(a+b*log(c*(d+e*x)^n))/(g*(e*f-d*g)^(3/2))-2/3*(a+b*log(c*(d+e*x)^n))^2/(g*(f+g*x)^(3/2))-16/3*b^2*e^(3/2)*n^2*arctanh(sqrt(e)*sqrt(f+g*x)/sqrt(e*f-d*g))*log(2/(1-sqrt(e)*sqrt(f+g*x)/sqrt(e*f-d*g)))/(g*(e*f-d*g)^(3/2))-8/3*b^2*e^(3/2)*n^2*polylog(2,1+(-2)/(1-sqrt(e)*sqrt(f+g*x)/sqrt(e*f-d*g)))/(g*(e*f-d*g)^(3/2))+8/3*b*e*n*(a+b*log(c*(d+e*x)^n))/(g*(e*f-d*g)*sqrt(f+g*x))],
[(a+b*log(c*(d+e*x)^n))^2/(f+g*x)^(7/2),x,19,64/15*b^2*e^(5/2)*n^2*arctanh(sqrt(e)*sqrt(f+g*x)/sqrt(e*f-d*g))/(g*(e*f-d*g)^(5/2))+8/5*b^2*e^(5/2)*n^2*arctanh(sqrt(e)*sqrt(f+g*x)/sqrt(e*f-d*g))^2/(g*(e*f-d*g)^(5/2))+8/15*b*e*n*(a+b*log(c*(d+e*x)^n))/(g*(e*f-d*g)*(f+g*x)^(3/2))-8/5*b*e^(5/2)*n*arctanh(sqrt(e)*sqrt(f+g*x)/sqrt(e*f-d*g))*(a+b*log(c*(d+e*x)^n))/(g*(e*f-d*g)^(5/2))-2/5*(a+b*log(c*(d+e*x)^n))^2/(g*(f+g*x)^(5/2))-16/5*b^2*e^(5/2)*n^2*arctanh(sqrt(e)*sqrt(f+g*x)/sqrt(e*f-d*g))*log(2/(1-sqrt(e)*sqrt(f+g*x)/sqrt(e*f-d*g)))/(g*(e*f-d*g)^(5/2))-8/5*b^2*e^(5/2)*n^2*polylog(2,1+(-2)/(1-sqrt(e)*sqrt(f+g*x)/sqrt(e*f-d*g)))/(g*(e*f-d*g)^(5/2))-16/15*b^2*e^2*n^2/(g*(e*f-d*g)^2*sqrt(f+g*x))+8/5*b*e^2*n*(a+b*log(c*(d+e*x)^n))/(g*(e*f-d*g)^2*sqrt(f+g*x))],
[(a+b*log(c*(d+e*x)^n))^2/(f+g*x)^(9/2),x,25,-16/105*b^2*e^2*n^2/(g*(e*f-d*g)^2*(f+g*x)^(3/2))+368/105*b^2*e^(7/2)*n^2*arctanh(sqrt(e)*sqrt(f+g*x)/sqrt(e*f-d*g))/(g*(e*f-d*g)^(7/2))+8/7*b^2*e^(7/2)*n^2*arctanh(sqrt(e)*sqrt(f+g*x)/sqrt(e*f-d*g))^2/(g*(e*f-d*g)^(7/2))+8/35*b*e*n*(a+b*log(c*(d+e*x)^n))/(g*(e*f-d*g)*(f+g*x)^(5/2))+8/21*b*e^2*n*(a+b*log(c*(d+e*x)^n))/(g*(e*f-d*g)^2*(f+g*x)^(3/2))-8/7*b*e^(7/2)*n*arctanh(sqrt(e)*sqrt(f+g*x)/sqrt(e*f-d*g))*(a+b*log(c*(d+e*x)^n))/(g*(e*f-d*g)^(7/2))-2/7*(a+b*log(c*(d+e*x)^n))^2/(g*(f+g*x)^(7/2))-16/7*b^2*e^(7/2)*n^2*arctanh(sqrt(e)*sqrt(f+g*x)/sqrt(e*f-d*g))*log(2/(1-sqrt(e)*sqrt(f+g*x)/sqrt(e*f-d*g)))/(g*(e*f-d*g)^(7/2))-8/7*b^2*e^(7/2)*n^2*polylog(2,1+(-2)/(1-sqrt(e)*sqrt(f+g*x)/sqrt(e*f-d*g)))/(g*(e*f-d*g)^(7/2))-128/105*b^2*e^3*n^2/(g*(e*f-d*g)^3*sqrt(f+g*x))+8/7*b*e^3*n*(a+b*log(c*(d+e*x)^n))/(g*(e*f-d*g)^3*sqrt(f+g*x))],

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

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

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

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

# Integrands of the form (f+g x)^q (a+b Log[c (d+e x)^n])^p when m symbolic
#  {(a + b*Log[c*(d + e*x)^n])^3*(f + g*x)^m, x, 0, (3*a^2*b*f*p*q*(f + g*x)^(2 + m)*Hypergeometric2F1[1, 2 + m, 3 + m, (f*(f + g*x))/(f*g - e*h)])/(h*(f*g - e*h)*(1 + m)*(2 + m)) + (6*a*b^2*p^2*q^2*(f + g*x)^(1 + m)*((f*(f + g*x))/(h*(e + f*x)))^(-1 - m)*HypergeometricPFQ[{-1 - m, -1 - m, -1 - m}, {-m, -m}, ((-f)*g + e*h)/(h*(e + f*x))])/(h*(1 + m)^3) - (6*b^3*p^3*q^3*(f + g*x)^(1 + m)*((f*(f + g*x))/(h*(e + f*x)))^(-1 - m)*HypergeometricPFQ[{-1 - m, -1 - m, -1 - m, -1 - m}, {-m, -m, -m}, ((-f)*g + e*h)/(h*(e + f*x))])/(h*(1 + m)^4) - (6*a*b^2*p*q*(f + g*x)^(1 + m)*((f*(f + g*x))/(h*(e + f*x)))^(-1 - m)*Hypergeometric2F1[-1 - m, -1 - m, -m, ((-f)*g + e*h)/(h*(e + f*x))]*Log[c*(d + e*x)^n])/(h*(1 + m)^2) + (6*b^3*p^2*q^2*(f + g*x)^(1 + m)*((f*(f + g*x))/(h*(e + f*x)))^(-1 - m)*HypergeometricPFQ[{-1 - m, -1 - m, -1 - m}, {-m, -m}, ((-f)*g + e*h)/(h*(e + f*x))]*Log[c*(d + e*x)^n])/(h*(1 + m)^3) - (3*b^3*p*q*(f + g*x)^(1 + m)*((f*(f + g*x))/(h*(e + f*x)))^(-1 - m)*Hypergeometric2F1[-1 - m, -1 - m, -m, ((-f)*g + e*h)/(h*(e + f*x))]*Log[c*(d + e*x)^n]^2)/(h*(1 + m)^2) + ((f + g*x)^(1 + m)*(a + b*Log[c*(d + e*x)^n])^3)/(h*(1 + m))}

# {(a + b*Log[c*(d + e*x)^n])^2*(f + g*x)^m, x, 0, (a^2*(f + g*x)^(1 + m))/(h*(1 + m)) + (2*a*b*f*p*q*(f + g*x)^(2 + m)*Hypergeometric2F1[1, 2 + m, 3 + m, (f*(f + g*x))/(f*g - e*h)])/(h*(f*g - e*h)*(1 + m)*(2 + m)) + (2*b^2*p^2*q^2*(f + g*x)^(1 + m)*((f*(f + g*x))/(h*(e + f*x)))^(-1 - m)*HypergeometricPFQ[{-1 - m, -1 - m, -1 - m}, {-m, -m}, ((-f)*g + e*h)/(h*(e + f*x))])/(h*(1 + m)^3) + (2*a*b*(f + g*x)^(1 + m)*Log[c*(d + e*x)^n])/(h*(1 + m)) - (2*b^2*p*q*(f + g*x)^(1 + m)*((f*(f + g*x))/(h*(e + f*x)))^(-1 - m)*Hypergeometric2F1[-1 - m, -1 - m, -m, ((-f)*g + e*h)/(h*(e + f*x))]*Log[c*(d + e*x)^n])/(h*(1 + m)^2) + (b^2*(f + g*x)^(1 + m)*Log[c*(d + e*x)^n]^2)/(h*(1 + m))} 
[(f+g*x)^m*(a+b*log(c*(d+e*x)^n)),x,2,b*e*n*(f+g*x)^(2+m)*hypergeom([1,2+m],[3+m],e*(f+g*x)/(e*f-d*g))/(g*(e*f-d*g)*(1+m)*(2+m))+(f+g*x)^(1+m)*(a+b*log(c*(d+e*x)^n))/(g*(1+m))],
[(f+g*x)^m/(a+b*log(c*(d+e*x)^n)),x,0,Unintegrable((f+g*x)^m/(a+b*log(c*(d+e*x)^n)),x)],
[(f+g*x)^m/(a+b*log(c*(d+e*x)^n))^2,x,0,Unintegrable((f+g*x)^m/(a+b*log(c*(d+e*x)^n))^2,x)],
[(f+g*x)^m*(a+b*log(c*(d+e*x)^n))^(3/2),x,0,Unintegrable((f+g*x)^m*(a+b*log(c*(d+e*x)^n))^(3/2),x)],
[(f+g*x)^m*(a+b*log(c*(d+e*x)^n))^(1/2),x,0,Unintegrable((f+g*x)^m*sqrt(a+b*log(c*(d+e*x)^n)),x)],
[(f+g*x)^m/(a+b*log(c*(d+e*x)^n))^(1/2),x,0,Unintegrable((f+g*x)^m/sqrt(a+b*log(c*(d+e*x)^n)),x)],
[(f+g*x)^m/(a+b*log(c*(d+e*x)^n))^(3/2),x,0,Unintegrable((f+g*x)^m/(a+b*log(c*(d+e*x)^n))^(3/2),x)],

# Integrands of the form (f+g x)^q (a+b Log[c (d+e x)^n])^p when n symbolic
[(f+g*x)^m*(a+b*log(c*(d+e*x)^n))^n,x,0,Unintegrable((f+g*x)^m*(a+b*log(c*(d+e*x)^n))^n,x)],
[(f+g*x)^3*(a+b*log(c*(d+e*x)^n))^n,x,14,4^(-1-n)*g^3*(d+e*x)^4*GAMMA(1+n,-4*(a+b*log(c*(d+e*x)^n))/(b*n))*(a+b*log(c*(d+e*x)^n))^n/(e^4*exp(4*a/(b*n))*(c*(d+e*x)^n)^(4/n)*((-a-b*log(c*(d+e*x)^n))/(b*n))^n)+g^2*(e*f-d*g)*(d+e*x)^3*GAMMA(1+n,-3*(a+b*log(c*(d+e*x)^n))/(b*n))*(a+b*log(c*(d+e*x)^n))^n/(3^n*e^4*exp(3*a/(b*n))*(c*(d+e*x)^n)^(3/n)*((-a-b*log(c*(d+e*x)^n))/(b*n))^n)+3*2^(-1-n)*g*(e*f-d*g)^2*(d+e*x)^2*GAMMA(1+n,-2*(a+b*log(c*(d+e*x)^n))/(b*n))*(a+b*log(c*(d+e*x)^n))^n/(e^4*exp(2*a/(b*n))*(c*(d+e*x)^n)^(2/n)*((-a-b*log(c*(d+e*x)^n))/(b*n))^n)+(e*f-d*g)^3*(d+e*x)*GAMMA(1+n,(-a-b*log(c*(d+e*x)^n))/(b*n))*(a+b*log(c*(d+e*x)^n))^n/(e^4*exp(a/(b*n))*(c*(d+e*x)^n)^(1/n)*((-a-b*log(c*(d+e*x)^n))/(b*n))^n)],
[(f+g*x)^2*(a+b*log(c*(d+e*x)^n))^n,x,11,3^(-1-n)*g^2*(d+e*x)^3*GAMMA(1+n,-3*(a+b*log(c*(d+e*x)^n))/(b*n))*(a+b*log(c*(d+e*x)^n))^n/(e^3*exp(3*a/(b*n))*(c*(d+e*x)^n)^(3/n)*((-a-b*log(c*(d+e*x)^n))/(b*n))^n)+g*(e*f-d*g)*(d+e*x)^2*GAMMA(1+n,-2*(a+b*log(c*(d+e*x)^n))/(b*n))*(a+b*log(c*(d+e*x)^n))^n/(2^n*e^3*exp(2*a/(b*n))*(c*(d+e*x)^n)^(2/n)*((-a-b*log(c*(d+e*x)^n))/(b*n))^n)+(e*f-d*g)^2*(d+e*x)*GAMMA(1+n,(-a-b*log(c*(d+e*x)^n))/(b*n))*(a+b*log(c*(d+e*x)^n))^n/(e^3*exp(a/(b*n))*(c*(d+e*x)^n)^(1/n)*((-a-b*log(c*(d+e*x)^n))/(b*n))^n)],
[(f+g*x)*(a+b*log(c*(d+e*x)^n))^n,x,8,2^(-1-n)*g*(d+e*x)^2*GAMMA(1+n,-2*(a+b*log(c*(d+e*x)^n))/(b*n))*(a+b*log(c*(d+e*x)^n))^n/(e^2*exp(2*a/(b*n))*(c*(d+e*x)^n)^(2/n)*((-a-b*log(c*(d+e*x)^n))/(b*n))^n)+(e*f-d*g)*(d+e*x)*GAMMA(1+n,(-a-b*log(c*(d+e*x)^n))/(b*n))*(a+b*log(c*(d+e*x)^n))^n/(e^2*exp(a/(b*n))*(c*(d+e*x)^n)^(1/n)*((-a-b*log(c*(d+e*x)^n))/(b*n))^n)],
[(a+b*log(c*(d+e*x)^n))^n,x,3,(d+e*x)*GAMMA(1+n,(-a-b*log(c*(d+e*x)^n))/(b*n))*(a+b*log(c*(d+e*x)^n))^n/(e*exp(a/(b*n))*(c*(d+e*x)^n)^(1/n)*((-a-b*log(c*(d+e*x)^n))/(b*n))^n)],
[(a+b*log(c*(d+e*x)^n))^n/(f+g*x),x,0,Unintegrable((a+b*log(c*(d+e*x)^n))^n/(f+g*x),x)],

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

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

# p>0
[(h+i*x)^4*(a+b*log(c*(e+f*x)))/(d*e+d*f*x),x,8,-4*b*i*(f*h-e*i)^3*x/(d*f^4)-3/2*b*i^2*(f*h-e*i)^2*(e+f*x)^2/(d*f^5)-4/9*b*i^3*(f*h-e*i)*(e+f*x)^3/(d*f^5)-1/16*b*i^4*(e+f*x)^4/(d*f^5)-1/2*b*(f*h-e*i)^4*log(e+f*x)^2/(d*f^5)+4*i*(f*h-e*i)^3*(e+f*x)*(a+b*log(c*(e+f*x)))/(d*f^5)+3*i^2*(f*h-e*i)^2*(e+f*x)^2*(a+b*log(c*(e+f*x)))/(d*f^5)+4/3*i^3*(f*h-e*i)*(e+f*x)^3*(a+b*log(c*(e+f*x)))/(d*f^5)+1/4*i^4*(e+f*x)^4*(a+b*log(c*(e+f*x)))/(d*f^5)+(f*h-e*i)^4*log(e+f*x)*(a+b*log(c*(e+f*x)))/(d*f^5)],
[(h+i*x)^3*(a+b*log(c*(e+f*x)))/(d*e+d*f*x),x,8,-3*b*i*(f*h-e*i)^2*x/(d*f^3)-3/4*b*i^2*(f*h-e*i)*(e+f*x)^2/(d*f^4)-1/9*b*i^3*(e+f*x)^3/(d*f^4)-1/2*b*(f*h-e*i)^3*log(e+f*x)^2/(d*f^4)+3*i*(f*h-e*i)^2*(e+f*x)*(a+b*log(c*(e+f*x)))/(d*f^4)+3/2*i^2*(f*h-e*i)*(e+f*x)^2*(a+b*log(c*(e+f*x)))/(d*f^4)+1/3*i^3*(e+f*x)^3*(a+b*log(c*(e+f*x)))/(d*f^4)+(f*h-e*i)^3*log(e+f*x)*(a+b*log(c*(e+f*x)))/(d*f^4)],
[(h+i*x)^2*(a+b*log(c*(e+f*x)))/(d*e+d*f*x),x,7,-1/4*b*(4*f*h-3*e*i+f*i*x)^2/(d*f^3)-1/2*b*(f*h-e*i)^2*log(e+f*x)^2/(d*f^3)+2*i*(f*h-e*i)*(e+f*x)*(a+b*log(c*(e+f*x)))/(d*f^3)+1/2*i^2*(e+f*x)^2*(a+b*log(c*(e+f*x)))/(d*f^3)+(f*h-e*i)^2*log(e+f*x)*(a+b*log(c*(e+f*x)))/(d*f^3)],
[(h+i*x)*(a+b*log(c*(e+f*x)))/(d*e+d*f*x),x,6,a*i*x/(d*f)-b*i*x/(d*f)+b*i*(e+f*x)*log(c*(e+f*x))/(d*f^2)+1/2*(f*h-e*i)*(a+b*log(c*(e+f*x)))^2/(b*d*f^2)],
[(a+b*log(c*(e+f*x)))/(d*e+d*f*x),x,3,1/2*(a+b*log(c*(e+f*x)))^2/(b*d*f)],
[(a+b*log(c*(e+f*x)))/((d*e+d*f*x)*(h+i*x)),x,4,-(a+b*log(c*(e+f*x)))*log(1+(f*h-e*i)/(i*(e+f*x)))/(d*(f*h-e*i))+b*polylog(2,(-f*h+e*i)/(i*(e+f*x)))/(d*(f*h-e*i))],
[(a+b*log(c*(e+f*x)))/((d*e+d*f*x)*(h+i*x)^2),x,7,-i*(e+f*x)*(a+b*log(c*(e+f*x)))/(d*(f*h-e*i)^2*(h+i*x))+b*f*log(h+i*x)/(d*(f*h-e*i)^2)-f*(a+b*log(c*(e+f*x)))*log(1+(f*h-e*i)/(i*(e+f*x)))/(d*(f*h-e*i)^2)+b*f*polylog(2,(-f*h+e*i)/(i*(e+f*x)))/(d*(f*h-e*i)^2)],
[(a+b*log(c*(e+f*x)))/((d*e+d*f*x)*(h+i*x)^3),x,11,-1/2*b*f/(d*(f*h-e*i)^2*(h+i*x))-1/2*b*f^2*log(e+f*x)/(d*(f*h-e*i)^3)+1/2*(a+b*log(c*(e+f*x)))/(d*(f*h-e*i)*(h+i*x)^2)-f*i*(e+f*x)*(a+b*log(c*(e+f*x)))/(d*(f*h-e*i)^3*(h+i*x))+3/2*b*f^2*log(h+i*x)/(d*(f*h-e*i)^3)-f^2*(a+b*log(c*(e+f*x)))*log(1+(f*h-e*i)/(i*(e+f*x)))/(d*(f*h-e*i)^3)+b*f^2*polylog(2,(-f*h+e*i)/(i*(e+f*x)))/(d*(f*h-e*i)^3)],
[(h+i*x)^4*(a+b*log(c*(e+f*x)))^2/(d*e+d*f*x),x,32,-4*a*b*i*(f*h-e*i)^3*x/(d*f^4)+8*b^2*i*(f*h-e*i)^3*x/(d*f^4)+3/2*b^2*i^2*(f*h-e*i)^2*(e+f*x)^2/(d*f^5)+8/27*b^2*i^3*(f*h-e*i)*(e+f*x)^3/(d*f^5)+1/32*b^2*i^4*(e+f*x)^4/(d*f^5)+7/12*b^2*(f*h-e*i)^4*log(e+f*x)^2/(d*f^5)-4*b^2*i*(f*h-e*i)^3*(e+f*x)*log(c*(e+f*x))/(d*f^5)-4*b*i*(f*h-e*i)^3*(e+f*x)*(a+b*log(c*(e+f*x)))/(d*f^5)-3*b*i^2*(f*h-e*i)^2*(e+f*x)^2*(a+b*log(c*(e+f*x)))/(d*f^5)-8/9*b*i^3*(f*h-e*i)*(e+f*x)^3*(a+b*log(c*(e+f*x)))/(d*f^5)-1/8*b*i^4*(e+f*x)^4*(a+b*log(c*(e+f*x)))/(d*f^5)-7/6*b*(f*h-e*i)^4*log(e+f*x)*(a+b*log(c*(e+f*x)))/(d*f^5)+2*i*(f*h-e*i)^3*(e+f*x)*(a+b*log(c*(e+f*x)))^2/(d*f^5)+1/2*i^2*(f*h-e*i)^2*(e+f*x)^2*(a+b*log(c*(e+f*x)))^2/(d*f^5)+1/3*(f*h-e*i)*(h+i*x)^3*(a+b*log(c*(e+f*x)))^2/(d*f^2)+1/4*(h+i*x)^4*(a+b*log(c*(e+f*x)))^2/(d*f)+1/3*(f*h-e*i)^4*(a+b*log(c*(e+f*x)))^3/(b*d*f^5)],
[(h+i*x)^3*(a+b*log(c*(e+f*x)))^2/(d*e+d*f*x),x,24,-4*a*b*i*(f*h-e*i)^2*x/(d*f^3)+6*b^2*i*(f*h-e*i)^2*x/(d*f^3)+3/4*b^2*i^2*(f*h-e*i)*(e+f*x)^2/(d*f^4)+2/27*b^2*i^3*(e+f*x)^3/(d*f^4)+1/3*b^2*(f*h-e*i)^3*log(e+f*x)^2/(d*f^4)-4*b^2*i*(f*h-e*i)^2*(e+f*x)*log(c*(e+f*x))/(d*f^4)-2*b*i*(f*h-e*i)^2*(e+f*x)*(a+b*log(c*(e+f*x)))/(d*f^4)-3/2*b*i^2*(f*h-e*i)*(e+f*x)^2*(a+b*log(c*(e+f*x)))/(d*f^4)-2/9*b*i^3*(e+f*x)^3*(a+b*log(c*(e+f*x)))/(d*f^4)-2/3*b*(f*h-e*i)^3*log(e+f*x)*(a+b*log(c*(e+f*x)))/(d*f^4)+2*i*(f*h-e*i)^2*(e+f*x)*(a+b*log(c*(e+f*x)))^2/(d*f^4)+1/2*i^2*(f*h-e*i)*(e+f*x)^2*(a+b*log(c*(e+f*x)))^2/(d*f^4)+1/3*(h+i*x)^3*(a+b*log(c*(e+f*x)))^2/(d*f)+1/3*(f*h-e*i)^3*(a+b*log(c*(e+f*x)))^3/(b*d*f^4)],
[(h+i*x)^2*(a+b*log(c*(e+f*x)))^2/(d*e+d*f*x),x,16,-4*a*b*i*(f*h-e*i)*x/(d*f^2)+4*b^2*i*(f*h-e*i)*x/(d*f^2)+1/4*b^2*i^2*(e+f*x)^2/(d*f^3)-4*b^2*i*(f*h-e*i)*(e+f*x)*log(c*(e+f*x))/(d*f^3)-1/2*b*i^2*(e+f*x)^2*(a+b*log(c*(e+f*x)))/(d*f^3)+2*i*(f*h-e*i)*(e+f*x)*(a+b*log(c*(e+f*x)))^2/(d*f^3)+1/2*i^2*(e+f*x)^2*(a+b*log(c*(e+f*x)))^2/(d*f^3)+1/3*(f*h-e*i)^2*(a+b*log(c*(e+f*x)))^3/(b*d*f^3)],
[(h+i*x)*(a+b*log(c*(e+f*x)))^2/(d*e+d*f*x),x,8,-2*a*b*i*x/(d*f)+2*b^2*i*x/(d*f)-2*b^2*i*(e+f*x)*log(c*(e+f*x))/(d*f^2)+i*(e+f*x)*(a+b*log(c*(e+f*x)))^2/(d*f^2)+1/3*(f*h-e*i)*(a+b*log(c*(e+f*x)))^3/(b*d*f^2)],
[(a+b*log(c*(e+f*x)))^2/(d*e+d*f*x),x,4,1/3*(a+b*log(c*(e+f*x)))^3/(b*d*f)],
[(a+b*log(c*(e+f*x)))^2/((d*e+d*f*x)*(h+i*x)),x,5,-(a+b*log(c*(e+f*x)))^2*log(1+(f*h-e*i)/(i*(e+f*x)))/(d*(f*h-e*i))+2*b*(a+b*log(c*(e+f*x)))*polylog(2,(-f*h+e*i)/(i*(e+f*x)))/(d*(f*h-e*i))+2*b^2*polylog(3,(-f*h+e*i)/(i*(e+f*x)))/(d*(f*h-e*i))],
[(a+b*log(c*(e+f*x)))^2/((d*e+d*f*x)*(h+i*x)^2),x,9,-i*(e+f*x)*(a+b*log(c*(e+f*x)))^2/(d*(f*h-e*i)^2*(h+i*x))+2*b*f*(a+b*log(c*(e+f*x)))*log(f*(h+i*x)/(f*h-e*i))/(d*(f*h-e*i)^2)-f*(a+b*log(c*(e+f*x)))^2*log(1+(f*h-e*i)/(i*(e+f*x)))/(d*(f*h-e*i)^2)+2*b*f*(a+b*log(c*(e+f*x)))*polylog(2,(-f*h+e*i)/(i*(e+f*x)))/(d*(f*h-e*i)^2)+2*b^2*f*polylog(2,-i*(e+f*x)/(f*h-e*i))/(d*(f*h-e*i)^2)+2*b^2*f*polylog(3,(-f*h+e*i)/(i*(e+f*x)))/(d*(f*h-e*i)^2)],
[(a+b*log(c*(e+f*x)))^2/((d*e+d*f*x)*(h+i*x)^3),x,16,b*f*i*(e+f*x)*(a+b*log(c*(e+f*x)))/(d*(f*h-e*i)^3*(h+i*x))+1/2*(a+b*log(c*(e+f*x)))^2/(d*(f*h-e*i)*(h+i*x)^2)-f*i*(e+f*x)*(a+b*log(c*(e+f*x)))^2/(d*(f*h-e*i)^3*(h+i*x))-b^2*f^2*log(h+i*x)/(d*(f*h-e*i)^3)+2*b*f^2*(a+b*log(c*(e+f*x)))*log(f*(h+i*x)/(f*h-e*i))/(d*(f*h-e*i)^3)+b*f^2*(a+b*log(c*(e+f*x)))*log(1+(f*h-e*i)/(i*(e+f*x)))/(d*(f*h-e*i)^3)-f^2*(a+b*log(c*(e+f*x)))^2*log(1+(f*h-e*i)/(i*(e+f*x)))/(d*(f*h-e*i)^3)-b^2*f^2*polylog(2,(-f*h+e*i)/(i*(e+f*x)))/(d*(f*h-e*i)^3)+2*b*f^2*(a+b*log(c*(e+f*x)))*polylog(2,(-f*h+e*i)/(i*(e+f*x)))/(d*(f*h-e*i)^3)+2*b^2*f^2*polylog(2,-i*(e+f*x)/(f*h-e*i))/(d*(f*h-e*i)^3)+2*b^2*f^2*polylog(3,(-f*h+e*i)/(i*(e+f*x)))/(d*(f*h-e*i)^3)],

# p<0
[(h+i*x)^4/((d*e+d*f*x)*(a+b*log(c*(e+f*x)))),x,14,4*i*(f*h-e*i)^3*Ei((a+b*log(c*(e+f*x)))/b)/(b*c*d*exp(a/b)*f^5)+6*i^2*(f*h-e*i)^2*Ei(2*(a+b*log(c*(e+f*x)))/b)/(b*c^2*d*exp(2*a/b)*f^5)+4*i^3*(f*h-e*i)*Ei(3*(a+b*log(c*(e+f*x)))/b)/(b*c^3*d*exp(3*a/b)*f^5)+i^4*Ei(4*(a+b*log(c*(e+f*x)))/b)/(b*c^4*d*exp(4*a/b)*f^5)+(f*h-e*i)^4*log(a+b*log(c*(e+f*x)))/(b*d*f^5)],
[(h+i*x)^3/((d*e+d*f*x)*(a+b*log(c*(e+f*x)))),x,12,3*i*(f*h-e*i)^2*Ei((a+b*log(c*(e+f*x)))/b)/(b*c*d*exp(a/b)*f^4)+3*i^2*(f*h-e*i)*Ei(2*(a+b*log(c*(e+f*x)))/b)/(b*c^2*d*exp(2*a/b)*f^4)+i^3*Ei(3*(a+b*log(c*(e+f*x)))/b)/(b*c^3*d*exp(3*a/b)*f^4)+(f*h-e*i)^3*log(a+b*log(c*(e+f*x)))/(b*d*f^4)],
[(h+i*x)^2/((d*e+d*f*x)*(a+b*log(c*(e+f*x)))),x,10,2*i*(f*h-e*i)*Ei((a+b*log(c*(e+f*x)))/b)/(b*c*d*exp(a/b)*f^3)+i^2*Ei(2*(a+b*log(c*(e+f*x)))/b)/(b*c^2*d*exp(2*a/b)*f^3)+(f*h-e*i)^2*log(a+b*log(c*(e+f*x)))/(b*d*f^3)],
[(h+i*x)/((d*e+d*f*x)*(a+b*log(c*(e+f*x)))),x,8,i*Ei((a+b*log(c*(e+f*x)))/b)/(b*c*d*exp(a/b)*f^2)+(f*h-e*i)*log(a+b*log(c*(e+f*x)))/(b*d*f^2)],
[1/((d*e+d*f*x)*(a+b*log(c*(e+f*x)))),x,4,log(a+b*log(c*(e+f*x)))/(b*d*f)],
[1/((d*e+d*f*x)*(h+i*x)*(a+b*log(c*(e+f*x)))),x,5,log(a+b*log(c*(e+f*x)))/(b*d*(f*h-e*i))-i*Unintegrable(1/((h+i*x)*(a+b*log(c*(e+f*x)))),x)/(d*(f*h-e*i))],
[1/((d*e+d*f*x)*(h+i*x)^2*(a+b*log(c*(e+f*x)))),x,5,f*log(a+b*log(c*(e+f*x)))/(b*d*(f*h-e*i)^2)-i*Unintegrable(1/((h+i*x)^2*(a+b*log(c*(e+f*x)))),x)/(d*(f*h-e*i))-f*i*Unintegrable(1/((h+i*x)*(a+b*log(c*(e+f*x)))),x)/(d*(f*h-e*i)^2)],

# Integrands of the form (g+h x)^(m/2) (a+b Log[c (d+e x)^n])^p / (e+f x)
[(f+g*x)^(5/2)*(a+b*log(c*(d+e*x)^n))/(d+e*x),x,27,-32/45*b*(e*f-d*g)*n*(f+g*x)^(3/2)/e^2-4/25*b*n*(f+g*x)^(5/2)/e+92/15*b*(e*f-d*g)^(5/2)*n*arctanh(sqrt(e)*sqrt(f+g*x)/sqrt(e*f-d*g))/e^(7/2)+2*b*(e*f-d*g)^(5/2)*n*arctanh(sqrt(e)*sqrt(f+g*x)/sqrt(e*f-d*g))^2/e^(7/2)+2/3*(e*f-d*g)*(f+g*x)^(3/2)*(a+b*log(c*(d+e*x)^n))/e^2+2/5*(f+g*x)^(5/2)*(a+b*log(c*(d+e*x)^n))/e-2*(e*f-d*g)^(5/2)*arctanh(sqrt(e)*sqrt(f+g*x)/sqrt(e*f-d*g))*(a+b*log(c*(d+e*x)^n))/e^(7/2)-4*b*(e*f-d*g)^(5/2)*n*arctanh(sqrt(e)*sqrt(f+g*x)/sqrt(e*f-d*g))*log(2/(1-sqrt(e)*sqrt(f+g*x)/sqrt(e*f-d*g)))/e^(7/2)-2*b*(e*f-d*g)^(5/2)*n*polylog(2,1+(-2)/(1-sqrt(e)*sqrt(f+g*x)/sqrt(e*f-d*g)))/e^(7/2)-92/15*b*(e*f-d*g)^2*n*sqrt(f+g*x)/e^3+2*(e*f-d*g)^2*(a+b*log(c*(d+e*x)^n))*sqrt(f+g*x)/e^3],
[(f+g*x)^(3/2)*(a+b*log(c*(d+e*x)^n))/(d+e*x),x,20,-4/9*b*n*(f+g*x)^(3/2)/e+16/3*b*(e*f-d*g)^(3/2)*n*arctanh(sqrt(e)*sqrt(f+g*x)/sqrt(e*f-d*g))/e^(5/2)+2*b*(e*f-d*g)^(3/2)*n*arctanh(sqrt(e)*sqrt(f+g*x)/sqrt(e*f-d*g))^2/e^(5/2)+2/3*(f+g*x)^(3/2)*(a+b*log(c*(d+e*x)^n))/e-2*(e*f-d*g)^(3/2)*arctanh(sqrt(e)*sqrt(f+g*x)/sqrt(e*f-d*g))*(a+b*log(c*(d+e*x)^n))/e^(5/2)-4*b*(e*f-d*g)^(3/2)*n*arctanh(sqrt(e)*sqrt(f+g*x)/sqrt(e*f-d*g))*log(2/(1-sqrt(e)*sqrt(f+g*x)/sqrt(e*f-d*g)))/e^(5/2)-2*b*(e*f-d*g)^(3/2)*n*polylog(2,1+(-2)/(1-sqrt(e)*sqrt(f+g*x)/sqrt(e*f-d*g)))/e^(5/2)-16/3*b*(e*f-d*g)*n*sqrt(f+g*x)/e^2+2*(e*f-d*g)*(a+b*log(c*(d+e*x)^n))*sqrt(f+g*x)/e^2],
[(f+g*x)^(1/2)*(a+b*log(c*(d+e*x)^n))/(d+e*x),x,14,4*b*n*arctanh(sqrt(e)*sqrt(f+g*x)/sqrt(e*f-d*g))*sqrt(e*f-d*g)/e^(3/2)+2*b*n*arctanh(sqrt(e)*sqrt(f+g*x)/sqrt(e*f-d*g))^2*sqrt(e*f-d*g)/e^(3/2)-2*arctanh(sqrt(e)*sqrt(f+g*x)/sqrt(e*f-d*g))*(a+b*log(c*(d+e*x)^n))*sqrt(e*f-d*g)/e^(3/2)-4*b*n*arctanh(sqrt(e)*sqrt(f+g*x)/sqrt(e*f-d*g))*log(2/(1-sqrt(e)*sqrt(f+g*x)/sqrt(e*f-d*g)))*sqrt(e*f-d*g)/e^(3/2)-2*b*n*polylog(2,1+(-2)/(1-sqrt(e)*sqrt(f+g*x)/sqrt(e*f-d*g)))*sqrt(e*f-d*g)/e^(3/2)-4*b*n*sqrt(f+g*x)/e+2*(a+b*log(c*(d+e*x)^n))*sqrt(f+g*x)/e],
[(a+b*log(c*(d+e*x)^n))/((d+e*x)*(f+g*x)^(1/2)),x,9,2*b*n*arctanh(sqrt(e)*sqrt(f+g*x)/sqrt(e*f-d*g))^2/(sqrt(e)*sqrt(e*f-d*g))-2*arctanh(sqrt(e)*sqrt(f+g*x)/sqrt(e*f-d*g))*(a+b*log(c*(d+e*x)^n))/(sqrt(e)*sqrt(e*f-d*g))-4*b*n*arctanh(sqrt(e)*sqrt(f+g*x)/sqrt(e*f-d*g))*log(2/(1-sqrt(e)*sqrt(f+g*x)/sqrt(e*f-d*g)))/(sqrt(e)*sqrt(e*f-d*g))-2*b*n*polylog(2,1+(-2)/(1-sqrt(e)*sqrt(f+g*x)/sqrt(e*f-d*g)))/(sqrt(e)*sqrt(e*f-d*g))],
[(a+b*log(c*(d+e*x)^n))/((d+e*x)*(f+g*x)^(3/2)),x,13,4*b*n*arctanh(sqrt(e)*sqrt(f+g*x)/sqrt(e*f-d*g))*sqrt(e)/(e*f-d*g)^(3/2)+2*b*n*arctanh(sqrt(e)*sqrt(f+g*x)/sqrt(e*f-d*g))^2*sqrt(e)/(e*f-d*g)^(3/2)-2*arctanh(sqrt(e)*sqrt(f+g*x)/sqrt(e*f-d*g))*(a+b*log(c*(d+e*x)^n))*sqrt(e)/(e*f-d*g)^(3/2)-4*b*n*arctanh(sqrt(e)*sqrt(f+g*x)/sqrt(e*f-d*g))*log(2/(1-sqrt(e)*sqrt(f+g*x)/sqrt(e*f-d*g)))*sqrt(e)/(e*f-d*g)^(3/2)-2*b*n*polylog(2,1+(-2)/(1-sqrt(e)*sqrt(f+g*x)/sqrt(e*f-d*g)))*sqrt(e)/(e*f-d*g)^(3/2)+2*(a+b*log(c*(d+e*x)^n))/((e*f-d*g)*sqrt(f+g*x))],
[(a+b*log(c*(d+e*x)^n))/((d+e*x)*(f+g*x)^(5/2)),x,18,16/3*b*e^(3/2)*n*arctanh(sqrt(e)*sqrt(f+g*x)/sqrt(e*f-d*g))/(e*f-d*g)^(5/2)+2*b*e^(3/2)*n*arctanh(sqrt(e)*sqrt(f+g*x)/sqrt(e*f-d*g))^2/(e*f-d*g)^(5/2)+2/3*(a+b*log(c*(d+e*x)^n))/((e*f-d*g)*(f+g*x)^(3/2))-2*e^(3/2)*arctanh(sqrt(e)*sqrt(f+g*x)/sqrt(e*f-d*g))*(a+b*log(c*(d+e*x)^n))/(e*f-d*g)^(5/2)-4*b*e^(3/2)*n*arctanh(sqrt(e)*sqrt(f+g*x)/sqrt(e*f-d*g))*log(2/(1-sqrt(e)*sqrt(f+g*x)/sqrt(e*f-d*g)))/(e*f-d*g)^(5/2)-2*b*e^(3/2)*n*polylog(2,1+(-2)/(1-sqrt(e)*sqrt(f+g*x)/sqrt(e*f-d*g)))/(e*f-d*g)^(5/2)-4/3*b*e*n/((e*f-d*g)^2*sqrt(f+g*x))+2*e*(a+b*log(c*(d+e*x)^n))/((e*f-d*g)^2*sqrt(f+g*x))],

#  These special cases of the above form formerly caused infinite recursion! 
[(d+e*x)^(3/2)*log(a+b*x)/(a+b*x),x,20,-4/9*(d+e*x)^(3/2)/b+16/3*(b*d-a*e)^(3/2)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/b^(5/2)+2*(b*d-a*e)^(3/2)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))^2/b^(5/2)+2/3*(d+e*x)^(3/2)*log(a+b*x)/b-2*(b*d-a*e)^(3/2)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*log(a+b*x)/b^(5/2)-4*(b*d-a*e)^(3/2)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*log(2/(1-sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e)))/b^(5/2)-2*(b*d-a*e)^(3/2)*polylog(2,1+(-2)/(1-sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e)))/b^(5/2)-16/3*(b*d-a*e)*sqrt(d+e*x)/b^2+2*(b*d-a*e)*log(a+b*x)*sqrt(d+e*x)/b^2],
[(d+e*x)^(1/2)*log(a+b*x)/(a+b*x),x,14,4*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b*d-a*e)/b^(3/2)+2*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))^2*sqrt(b*d-a*e)/b^(3/2)-2*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*log(a+b*x)*sqrt(b*d-a*e)/b^(3/2)-4*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*log(2/(1-sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e)))*sqrt(b*d-a*e)/b^(3/2)-2*polylog(2,1+(-2)/(1-sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e)))*sqrt(b*d-a*e)/b^(3/2)-4*sqrt(d+e*x)/b+2*log(a+b*x)*sqrt(d+e*x)/b],
[log(a+b*x)/((a+b*x)*(d+e*x)^(1/2)),x,9,2*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))^2/(sqrt(b)*sqrt(b*d-a*e))-2*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*log(a+b*x)/(sqrt(b)*sqrt(b*d-a*e))-4*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*log(2/(1-sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e)))/(sqrt(b)*sqrt(b*d-a*e))-2*polylog(2,1+(-2)/(1-sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e)))/(sqrt(b)*sqrt(b*d-a*e))],
[log(a+b*x)/((a+b*x)*(d+e*x)^(3/2)),x,13,4*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b)/(b*d-a*e)^(3/2)+2*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))^2*sqrt(b)/(b*d-a*e)^(3/2)-2*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*log(a+b*x)*sqrt(b)/(b*d-a*e)^(3/2)-4*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*log(2/(1-sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e)))*sqrt(b)/(b*d-a*e)^(3/2)-2*polylog(2,1+(-2)/(1-sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e)))*sqrt(b)/(b*d-a*e)^(3/2)+2*log(a+b*x)/((b*d-a*e)*sqrt(d+e*x))],
[log(a+b*x)/((a+b*x)*(d+e*x)^(5/2)),x,18,16/3*b^(3/2)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b*d-a*e)^(5/2)+2*b^(3/2)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))^2/(b*d-a*e)^(5/2)+2/3*log(a+b*x)/((b*d-a*e)*(d+e*x)^(3/2))-2*b^(3/2)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*log(a+b*x)/(b*d-a*e)^(5/2)-4*b^(3/2)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*log(2/(1-sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e)))/(b*d-a*e)^(5/2)-2*b^(3/2)*polylog(2,1+(-2)/(1-sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e)))/(b*d-a*e)^(5/2)-4/3*b/((b*d-a*e)^2*sqrt(d+e*x))+2*b*log(a+b*x)/((b*d-a*e)^2*sqrt(d+e*x))],

# Integrands of the form (f+g x)^q (a+b Log[c (d+e x)^n])^p / (e+f x) with q symbolic
#  {(h + i*x)^m*(a + b*Log[c*(e + f*x)])^2/(d*e + d*f*x), x, 0, -((a^2*(h + i*x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, (f*(h + i*x))/(f*i - e*j)])/(d*(f*i - e*j)*(1 + m))) - (2*a*b*(h + i*x)^m*HypergeometricPFQ[{-m, -m, -m}, {1 - m, 1 - m}, ((-f)*i + e*j)/(j*(e + f*x))])/(((f*(h + i*x))/(j*(e + f*x)))^m*(d*f*m^2)) + (2*b^2*(h + i*x)^m*HypergeometricPFQ[{-m, -m, -m, -m}, {1 - m, 1 - m, 1 - m}, ((-f)*i + e*j)/(j*(e + f*x))])/(((f*(h + i*x))/(j*(e + f*x)))^m*(d*f*m^3)) + (2*a*b*(h + i*x)^m*Hypergeometric2F1[-m, -m, 1 - m, ((-f)*i + e*j)/(j*(e + f*x))]*Log[c*(e + f*x)])/(((f*(h + i*x))/(j*(e + f*x)))^m*(d*f*m)) - (2*b^2*(h + i*x)^m*HypergeometricPFQ[{-m, -m, -m}, {1 - m, 1 - m}, ((-f)*i + e*j)/(j*(e + f*x))]*Log[c*(e + f*x)])/(((f*(h + i*x))/(j*(e + f*x)))^m*(d*f*m^2)) + (b^2*(h + i*x)^m*Hypergeometric2F1[-m, -m, 1 - m, ((-f)*i + e*j)/(j*(e + f*x))]*Log[c*(e + f*x)]^2)/(((f*(h + i*x))/(j*(e + f*x)))^m*(d*f*m))}

# {(h + i*x)^m*(a + b*Log[c*(e + f*x)])^1/(d*e + d*f*x), x, 0, -((a*(h + i*x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, (f*(h + i*x))/(f*i - e*j)])/(d*(f*i - e*j)*(1 + m))) - (b*(h + i*x)^m*HypergeometricPFQ[{-m, -m, -m}, {1 - m, 1 - m}, ((-f)*i + e*j)/(j*(e + f*x))])/(((f*(h + i*x))/(j*(e + f*x)))^m*(d*f*m^2)) + (b*(h + i*x)^m*Hypergeometric2F1[-m, -m, 1 - m, ((-f)*i + e*j)/(j*(e + f*x))]*Log[c*(e + f*x)])/(((f*(h + i*x))/(j*(e + f*x)))^m*(d*f*m))} 

# Integrands of the form (f+g x)^q (a+b Log[c (d+e x)^n])^p / (e+f x) with p symbolic
[(h+i*x)^q*(a+b*log(c*(e+f*x)))^p/(d*e+d*f*x),x,0,Unintegrable((h+i*x)^q*(a+b*log(c*(e+f*x)))^p/(d*e+d*f*x),x)],
[(h+i*x)^3*(a+b*log(c*(e+f*x)))^p/(d*e+d*f*x),x,12,(f*h-e*i)^3*(a+b*log(c*(e+f*x)))^(1+p)/(b*d*f^4*(1+p))+3^(-1-p)*i^3*GAMMA(1+p,-3*(a+b*log(c*(e+f*x)))/b)*(a+b*log(c*(e+f*x)))^p/(c^3*d*exp(3*a/b)*f^4*((-a-b*log(c*(e+f*x)))/b)^p)+3*2^(-1-p)*i^2*(f*h-e*i)*GAMMA(1+p,-2*(a+b*log(c*(e+f*x)))/b)*(a+b*log(c*(e+f*x)))^p/(c^2*d*exp(2*a/b)*f^4*((-a-b*log(c*(e+f*x)))/b)^p)+3*i*(f*h-e*i)^2*GAMMA(1+p,(-a-b*log(c*(e+f*x)))/b)*(a+b*log(c*(e+f*x)))^p/(c*d*exp(a/b)*f^4*((-a-b*log(c*(e+f*x)))/b)^p)],
[(h+i*x)^2*(a+b*log(c*(e+f*x)))^p/(d*e+d*f*x),x,10,(f*h-e*i)^2*(a+b*log(c*(e+f*x)))^(1+p)/(b*d*f^3*(1+p))+2^(-1-p)*i^2*GAMMA(1+p,-2*(a+b*log(c*(e+f*x)))/b)*(a+b*log(c*(e+f*x)))^p/(c^2*d*exp(2*a/b)*f^3*((-a-b*log(c*(e+f*x)))/b)^p)+2*i*(f*h-e*i)*GAMMA(1+p,(-a-b*log(c*(e+f*x)))/b)*(a+b*log(c*(e+f*x)))^p/(c*d*exp(a/b)*f^3*((-a-b*log(c*(e+f*x)))/b)^p)],
[(h+i*x)*(a+b*log(c*(e+f*x)))^p/(d*e+d*f*x),x,8,(f*h-e*i)*(a+b*log(c*(e+f*x)))^(1+p)/(b*d*f^2*(1+p))+i*GAMMA(1+p,(-a-b*log(c*(e+f*x)))/b)*(a+b*log(c*(e+f*x)))^p/(c*d*exp(a/b)*f^2*((-a-b*log(c*(e+f*x)))/b)^p)],
[(a+b*log(c*(e+f*x)))^p/(d*e+d*f*x),x,4,(a+b*log(c*(e+f*x)))^(1+p)/(b*d*f*(1+p))],
[(a+b*log(c*(e+f*x)))^p/((d*e+d*f*x)*(h+i*x)),x,0,Unintegrable((a+b*log(c*(e+f*x)))^p/((d*e+d*f*x)*(h+i*x)),x)],
[(a+b*log(c*(e+f*x)))^p/((d*e+d*f*x)*(h+i*x)^2),x,0,Unintegrable((a+b*log(c*(e+f*x)))^p/((d*e+d*f*x)*(h+i*x)^2),x)],
[(a+b*log(c*(e+f*x)))^p/((d*e+d*f*x)*(h+i*x)^3),x,0,Unintegrable((a+b*log(c*(e+f*x)))^p/((d*e+d*f*x)*(h+i*x)^3),x)],

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

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

# p>0
[(h+i*x)^3*(a+b*log(c*(d+e*x)^n))/(f+g*x),x,14,a*i*(g*h-f*i)^2*x/g^3-1/3*b*i*(e*h-d*i)^2*n*x/(e^2*g)-1/2*b*i*(e*h-d*i)*(g*h-f*i)*n*x/(e*g^2)-b*i*(g*h-f*i)^2*n*x/g^3-1/6*b*(e*h-d*i)*n*(h+i*x)^2/(e*g)-1/4*b*(g*h-f*i)*n*(h+i*x)^2/g^2-1/9*b*n*(h+i*x)^3/g-1/3*b*(e*h-d*i)^3*n*log(d+e*x)/(e^3*g)-1/2*b*(e*h-d*i)^2*(g*h-f*i)*n*log(d+e*x)/(e^2*g^2)+b*i*(g*h-f*i)^2*(d+e*x)*log(c*(d+e*x)^n)/(e*g^3)+1/2*(g*h-f*i)*(h+i*x)^2*(a+b*log(c*(d+e*x)^n))/g^2+1/3*(h+i*x)^3*(a+b*log(c*(d+e*x)^n))/g+(g*h-f*i)^3*(a+b*log(c*(d+e*x)^n))*log(e*(f+g*x)/(e*f-d*g))/g^4+b*(g*h-f*i)^3*n*polylog(2,-g*(d+e*x)/(e*f-d*g))/g^4],
[(h+i*x)^2*(a+b*log(c*(d+e*x)^n))/(f+g*x),x,11,a*i*(g*h-f*i)*x/g^2-1/2*b*i*(e*h-d*i)*n*x/(e*g)-b*i*(g*h-f*i)*n*x/g^2-1/4*b*n*(h+i*x)^2/g-1/2*b*(e*h-d*i)^2*n*log(d+e*x)/(e^2*g)+b*i*(g*h-f*i)*(d+e*x)*log(c*(d+e*x)^n)/(e*g^2)+1/2*(h+i*x)^2*(a+b*log(c*(d+e*x)^n))/g+(g*h-f*i)^2*(a+b*log(c*(d+e*x)^n))*log(e*(f+g*x)/(e*f-d*g))/g^3+b*(g*h-f*i)^2*n*polylog(2,-g*(d+e*x)/(e*f-d*g))/g^3],
[(h+i*x)*(a+b*log(c*(d+e*x)^n))/(f+g*x),x,8,a*i*x/g-b*i*n*x/g+b*i*(d+e*x)*log(c*(d+e*x)^n)/(e*g)+(g*h-f*i)*(a+b*log(c*(d+e*x)^n))*log(e*(f+g*x)/(e*f-d*g))/g^2+b*(g*h-f*i)*n*polylog(2,-g*(d+e*x)/(e*f-d*g))/g^2],
[(a+b*log(c*(d+e*x)^n))/(f+g*x),x,3,(a+b*log(c*(d+e*x)^n))*log(e*(f+g*x)/(e*f-d*g))/g+b*n*polylog(2,-g*(d+e*x)/(e*f-d*g))/g],
[(a+b*log(c*(d+e*x)^n))/((f+g*x)*(h+i*x)),x,8,(a+b*log(c*(d+e*x)^n))*log(e*(f+g*x)/(e*f-d*g))/(g*h-f*i)-(a+b*log(c*(d+e*x)^n))*log(e*(h+i*x)/(e*h-d*i))/(g*h-f*i)+b*n*polylog(2,-g*(d+e*x)/(e*f-d*g))/(g*h-f*i)-b*n*polylog(2,-i*(d+e*x)/(e*h-d*i))/(g*h-f*i)],
[(a+b*log(c*(d+e*x)^n))/((f+g*x)*(h+i*x)^2),x,12,-b*e*n*log(d+e*x)/((e*h-d*i)*(g*h-f*i))+(a+b*log(c*(d+e*x)^n))/((g*h-f*i)*(h+i*x))+g*(a+b*log(c*(d+e*x)^n))*log(e*(f+g*x)/(e*f-d*g))/(g*h-f*i)^2+b*e*n*log(h+i*x)/((e*h-d*i)*(g*h-f*i))-g*(a+b*log(c*(d+e*x)^n))*log(e*(h+i*x)/(e*h-d*i))/(g*h-f*i)^2+b*g*n*polylog(2,-g*(d+e*x)/(e*f-d*g))/(g*h-f*i)^2-b*g*n*polylog(2,-i*(d+e*x)/(e*h-d*i))/(g*h-f*i)^2],
[(a+b*log(c*(d+e*x)^n))/((f+g*x)*(h+i*x)^3),x,15,-1/2*b*e*n/((e*h-d*i)*(g*h-f*i)*(h+i*x))-b*e*g*n*log(d+e*x)/((e*h-d*i)*(g*h-f*i)^2)-1/2*b*e^2*n*log(d+e*x)/((e*h-d*i)^2*(g*h-f*i))+1/2*(a+b*log(c*(d+e*x)^n))/((g*h-f*i)*(h+i*x)^2)+g*(a+b*log(c*(d+e*x)^n))/((g*h-f*i)^2*(h+i*x))+g^2*(a+b*log(c*(d+e*x)^n))*log(e*(f+g*x)/(e*f-d*g))/(g*h-f*i)^3+b*e*g*n*log(h+i*x)/((e*h-d*i)*(g*h-f*i)^2)+1/2*b*e^2*n*log(h+i*x)/((e*h-d*i)^2*(g*h-f*i))-g^2*(a+b*log(c*(d+e*x)^n))*log(e*(h+i*x)/(e*h-d*i))/(g*h-f*i)^3+b*g^2*n*polylog(2,-g*(d+e*x)/(e*f-d*g))/(g*h-f*i)^3-b*g^2*n*polylog(2,-i*(d+e*x)/(e*h-d*i))/(g*h-f*i)^3],
[(h+i*x)^2*(a+b*log(c*(d+e*x)^n))^2/(f+g*x),x,19,-2*a*b*i*(e*h-d*i)*n*x/(e*g)-2*a*b*i*(g*h-f*i)*n*x/g^2+2*b^2*i*(e*h-d*i)*n^2*x/(e*g)+2*b^2*i*(g*h-f*i)*n^2*x/g^2+1/4*b^2*i^2*n^2*(d+e*x)^2/(e^2*g)-2*b^2*i*(e*h-d*i)*n*(d+e*x)*log(c*(d+e*x)^n)/(e^2*g)-2*b^2*i*(g*h-f*i)*n*(d+e*x)*log(c*(d+e*x)^n)/(e*g^2)-1/2*b*i^2*n*(d+e*x)^2*(a+b*log(c*(d+e*x)^n))/(e^2*g)+i*(e*h-d*i)*(d+e*x)*(a+b*log(c*(d+e*x)^n))^2/(e^2*g)+i*(g*h-f*i)*(d+e*x)*(a+b*log(c*(d+e*x)^n))^2/(e*g^2)+1/2*i^2*(d+e*x)^2*(a+b*log(c*(d+e*x)^n))^2/(e^2*g)+(g*h-f*i)^2*(a+b*log(c*(d+e*x)^n))^2*log(e*(f+g*x)/(e*f-d*g))/g^3+2*b*(g*h-f*i)^2*n*(a+b*log(c*(d+e*x)^n))*polylog(2,-g*(d+e*x)/(e*f-d*g))/g^3-2*b^2*(g*h-f*i)^2*n^2*polylog(3,-g*(d+e*x)/(e*f-d*g))/g^3],
[(h+i*x)*(a+b*log(c*(d+e*x)^n))^2/(f+g*x),x,10,-2*a*b*i*n*x/g+2*b^2*i*n^2*x/g-2*b^2*i*n*(d+e*x)*log(c*(d+e*x)^n)/(e*g)+i*(d+e*x)*(a+b*log(c*(d+e*x)^n))^2/(e*g)+(g*h-f*i)*(a+b*log(c*(d+e*x)^n))^2*log(e*(f+g*x)/(e*f-d*g))/g^2+2*b*(g*h-f*i)*n*(a+b*log(c*(d+e*x)^n))*polylog(2,-g*(d+e*x)/(e*f-d*g))/g^2-2*b^2*(g*h-f*i)*n^2*polylog(3,-g*(d+e*x)/(e*f-d*g))/g^2],
[(a+b*log(c*(d+e*x)^n))^2/(f+g*x),x,4,(a+b*log(c*(d+e*x)^n))^2*log(e*(f+g*x)/(e*f-d*g))/g+2*b*n*(a+b*log(c*(d+e*x)^n))*polylog(2,-g*(d+e*x)/(e*f-d*g))/g-2*b^2*n^2*polylog(3,-g*(d+e*x)/(e*f-d*g))/g],
[(a+b*log(c*(d+e*x)^n))^2/((f+g*x)*(h+i*x)),x,10,(a+b*log(c*(d+e*x)^n))^2*log(e*(f+g*x)/(e*f-d*g))/(g*h-f*i)-(a+b*log(c*(d+e*x)^n))^2*log(e*(h+i*x)/(e*h-d*i))/(g*h-f*i)+2*b*n*(a+b*log(c*(d+e*x)^n))*polylog(2,-g*(d+e*x)/(e*f-d*g))/(g*h-f*i)-2*b*n*(a+b*log(c*(d+e*x)^n))*polylog(2,-i*(d+e*x)/(e*h-d*i))/(g*h-f*i)-2*b^2*n^2*polylog(3,-g*(d+e*x)/(e*f-d*g))/(g*h-f*i)+2*b^2*n^2*polylog(3,-i*(d+e*x)/(e*h-d*i))/(g*h-f*i)],
[(a+b*log(c*(d+e*x)^n))^2/((f+g*x)*(h+i*x)^2),x,14,-i*(d+e*x)*(a+b*log(c*(d+e*x)^n))^2/((e*h-d*i)*(g*h-f*i)*(h+i*x))+g*(a+b*log(c*(d+e*x)^n))^2*log(e*(f+g*x)/(e*f-d*g))/(g*h-f*i)^2+2*b*e*n*(a+b*log(c*(d+e*x)^n))*log(e*(h+i*x)/(e*h-d*i))/((e*h-d*i)*(g*h-f*i))-g*(a+b*log(c*(d+e*x)^n))^2*log(e*(h+i*x)/(e*h-d*i))/(g*h-f*i)^2+2*b*g*n*(a+b*log(c*(d+e*x)^n))*polylog(2,-g*(d+e*x)/(e*f-d*g))/(g*h-f*i)^2+2*b^2*e*n^2*polylog(2,-i*(d+e*x)/(e*h-d*i))/((e*h-d*i)*(g*h-f*i))-2*b*g*n*(a+b*log(c*(d+e*x)^n))*polylog(2,-i*(d+e*x)/(e*h-d*i))/(g*h-f*i)^2-2*b^2*g*n^2*polylog(3,-g*(d+e*x)/(e*f-d*g))/(g*h-f*i)^2+2*b^2*g*n^2*polylog(3,-i*(d+e*x)/(e*h-d*i))/(g*h-f*i)^2],
[(h+i*x)^2*(a+b*log(c*(d+e*x)^n))^3/(f+g*x),x,23,6*a*b^2*i*(e*h-d*i)*n^2*x/(e*g)+6*a*b^2*i*(g*h-f*i)*n^2*x/g^2-6*b^3*i*(e*h-d*i)*n^3*x/(e*g)-6*b^3*i*(g*h-f*i)*n^3*x/g^2-3/8*b^3*i^2*n^3*(d+e*x)^2/(e^2*g)+6*b^3*i*(e*h-d*i)*n^2*(d+e*x)*log(c*(d+e*x)^n)/(e^2*g)+6*b^3*i*(g*h-f*i)*n^2*(d+e*x)*log(c*(d+e*x)^n)/(e*g^2)+3/4*b^2*i^2*n^2*(d+e*x)^2*(a+b*log(c*(d+e*x)^n))/(e^2*g)-3*b*i*(e*h-d*i)*n*(d+e*x)*(a+b*log(c*(d+e*x)^n))^2/(e^2*g)-3*b*i*(g*h-f*i)*n*(d+e*x)*(a+b*log(c*(d+e*x)^n))^2/(e*g^2)-3/4*b*i^2*n*(d+e*x)^2*(a+b*log(c*(d+e*x)^n))^2/(e^2*g)+i*(e*h-d*i)*(d+e*x)*(a+b*log(c*(d+e*x)^n))^3/(e^2*g)+i*(g*h-f*i)*(d+e*x)*(a+b*log(c*(d+e*x)^n))^3/(e*g^2)+1/2*i^2*(d+e*x)^2*(a+b*log(c*(d+e*x)^n))^3/(e^2*g)+(g*h-f*i)^2*(a+b*log(c*(d+e*x)^n))^3*log(e*(f+g*x)/(e*f-d*g))/g^3+3*b*(g*h-f*i)^2*n*(a+b*log(c*(d+e*x)^n))^2*polylog(2,-g*(d+e*x)/(e*f-d*g))/g^3-6*b^2*(g*h-f*i)^2*n^2*(a+b*log(c*(d+e*x)^n))*polylog(3,-g*(d+e*x)/(e*f-d*g))/g^3+6*b^3*(g*h-f*i)^2*n^3*polylog(4,-g*(d+e*x)/(e*f-d*g))/g^3],
[(h+i*x)*(a+b*log(c*(d+e*x)^n))^3/(f+g*x),x,12,6*a*b^2*i*n^2*x/g-6*b^3*i*n^3*x/g+6*b^3*i*n^2*(d+e*x)*log(c*(d+e*x)^n)/(e*g)-3*b*i*n*(d+e*x)*(a+b*log(c*(d+e*x)^n))^2/(e*g)+i*(d+e*x)*(a+b*log(c*(d+e*x)^n))^3/(e*g)+(g*h-f*i)*(a+b*log(c*(d+e*x)^n))^3*log(e*(f+g*x)/(e*f-d*g))/g^2+3*b*(g*h-f*i)*n*(a+b*log(c*(d+e*x)^n))^2*polylog(2,-g*(d+e*x)/(e*f-d*g))/g^2-6*b^2*(g*h-f*i)*n^2*(a+b*log(c*(d+e*x)^n))*polylog(3,-g*(d+e*x)/(e*f-d*g))/g^2+6*b^3*(g*h-f*i)*n^3*polylog(4,-g*(d+e*x)/(e*f-d*g))/g^2],
[(a+b*log(c*(d+e*x)^n))^3/(f+g*x),x,5,(a+b*log(c*(d+e*x)^n))^3*log(e*(f+g*x)/(e*f-d*g))/g+3*b*n*(a+b*log(c*(d+e*x)^n))^2*polylog(2,-g*(d+e*x)/(e*f-d*g))/g-6*b^2*n^2*(a+b*log(c*(d+e*x)^n))*polylog(3,-g*(d+e*x)/(e*f-d*g))/g+6*b^3*n^3*polylog(4,-g*(d+e*x)/(e*f-d*g))/g],
[(a+b*log(c*(d+e*x)^n))^3/((f+g*x)*(h+i*x)),x,12,(a+b*log(c*(d+e*x)^n))^3*log(e*(f+g*x)/(e*f-d*g))/(g*h-f*i)-(a+b*log(c*(d+e*x)^n))^3*log(e*(h+i*x)/(e*h-d*i))/(g*h-f*i)+3*b*n*(a+b*log(c*(d+e*x)^n))^2*polylog(2,-g*(d+e*x)/(e*f-d*g))/(g*h-f*i)-3*b*n*(a+b*log(c*(d+e*x)^n))^2*polylog(2,-i*(d+e*x)/(e*h-d*i))/(g*h-f*i)-6*b^2*n^2*(a+b*log(c*(d+e*x)^n))*polylog(3,-g*(d+e*x)/(e*f-d*g))/(g*h-f*i)+6*b^2*n^2*(a+b*log(c*(d+e*x)^n))*polylog(3,-i*(d+e*x)/(e*h-d*i))/(g*h-f*i)+6*b^3*n^3*polylog(4,-g*(d+e*x)/(e*f-d*g))/(g*h-f*i)-6*b^3*n^3*polylog(4,-i*(d+e*x)/(e*h-d*i))/(g*h-f*i)],
[(a+b*log(c*(d+e*x)^n))^3/((f+g*x)*(h+i*x)^2),x,17,-i*(d+e*x)*(a+b*log(c*(d+e*x)^n))^3/((e*h-d*i)*(g*h-f*i)*(h+i*x))+g*(a+b*log(c*(d+e*x)^n))^3*log(e*(f+g*x)/(e*f-d*g))/(g*h-f*i)^2+3*b*e*n*(a+b*log(c*(d+e*x)^n))^2*log(e*(h+i*x)/(e*h-d*i))/((e*h-d*i)*(g*h-f*i))-g*(a+b*log(c*(d+e*x)^n))^3*log(e*(h+i*x)/(e*h-d*i))/(g*h-f*i)^2+3*b*g*n*(a+b*log(c*(d+e*x)^n))^2*polylog(2,-g*(d+e*x)/(e*f-d*g))/(g*h-f*i)^2+6*b^2*e*n^2*(a+b*log(c*(d+e*x)^n))*polylog(2,-i*(d+e*x)/(e*h-d*i))/((e*h-d*i)*(g*h-f*i))-3*b*g*n*(a+b*log(c*(d+e*x)^n))^2*polylog(2,-i*(d+e*x)/(e*h-d*i))/(g*h-f*i)^2-6*b^2*g*n^2*(a+b*log(c*(d+e*x)^n))*polylog(3,-g*(d+e*x)/(e*f-d*g))/(g*h-f*i)^2-6*b^3*e*n^3*polylog(3,-i*(d+e*x)/(e*h-d*i))/((e*h-d*i)*(g*h-f*i))+6*b^2*g*n^2*(a+b*log(c*(d+e*x)^n))*polylog(3,-i*(d+e*x)/(e*h-d*i))/(g*h-f*i)^2+6*b^3*g*n^3*polylog(4,-g*(d+e*x)/(e*f-d*g))/(g*h-f*i)^2-6*b^3*g*n^3*polylog(4,-i*(d+e*x)/(e*h-d*i))/(g*h-f*i)^2],

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

# Integrands of the form (i+j x)^(m/2) (a+b Log[c (d+e x)^n])^p / (g+h x)

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

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

# q>0

# q>0
[x^3*(a+b*log(c*(d+e*x)^n))/(f+g*x),x,14,a*f^2*x/g^3-b*f^2*n*x/g^3-1/2*b*d*f*n*x/(e*g^2)-1/3*b*d^2*n*x/(e^2*g)+1/4*b*f*n*x^2/g^2+1/6*b*d*n*x^2/(e*g)-1/9*b*n*x^3/g+1/2*b*d^2*f*n*log(d+e*x)/(e^2*g^2)+1/3*b*d^3*n*log(d+e*x)/(e^3*g)+b*f^2*(d+e*x)*log(c*(d+e*x)^n)/(e*g^3)-1/2*f*x^2*(a+b*log(c*(d+e*x)^n))/g^2+1/3*x^3*(a+b*log(c*(d+e*x)^n))/g-f^3*(a+b*log(c*(d+e*x)^n))*log(e*(f+g*x)/(e*f-d*g))/g^4-b*f^3*n*polylog(2,-g*(d+e*x)/(e*f-d*g))/g^4],
[x^2*(a+b*log(c*(d+e*x)^n))/(f+g*x),x,11,-a*f*x/g^2+b*f*n*x/g^2+1/2*b*d*n*x/(e*g)-1/4*b*n*x^2/g-1/2*b*d^2*n*log(d+e*x)/(e^2*g)-b*f*(d+e*x)*log(c*(d+e*x)^n)/(e*g^2)+1/2*x^2*(a+b*log(c*(d+e*x)^n))/g+f^2*(a+b*log(c*(d+e*x)^n))*log(e*(f+g*x)/(e*f-d*g))/g^3+b*f^2*n*polylog(2,-g*(d+e*x)/(e*f-d*g))/g^3],
[x*(a+b*log(c*(d+e*x)^n))/(f+g*x),x,8,a*x/g-b*n*x/g+b*(d+e*x)*log(c*(d+e*x)^n)/(e*g)-f*(a+b*log(c*(d+e*x)^n))*log(e*(f+g*x)/(e*f-d*g))/g^2-b*f*n*polylog(2,-g*(d+e*x)/(e*f-d*g))/g^2],
[(a+b*log(c*(d+e*x)^n))/(f+g*x),x,3,(a+b*log(c*(d+e*x)^n))*log(e*(f+g*x)/(e*f-d*g))/g+b*n*polylog(2,-g*(d+e*x)/(e*f-d*g))/g],
[(a+b*log(c*(d+e*x)^n))/(x*(f+g*x)),x,7,log(-e*x/d)*(a+b*log(c*(d+e*x)^n))/f-(a+b*log(c*(d+e*x)^n))*log(e*(f+g*x)/(e*f-d*g))/f-b*n*polylog(2,-g*(d+e*x)/(e*f-d*g))/f+b*n*polylog(2,1+e*x/d)/f],
[(a+b*log(c*(d+e*x)^n))/(x^2*(f+g*x)),x,11,b*e*n*log(x)/(d*f)-b*e*n*log(d+e*x)/(d*f)+(-a-b*log(c*(d+e*x)^n))/(f*x)-g*log(-e*x/d)*(a+b*log(c*(d+e*x)^n))/f^2+g*(a+b*log(c*(d+e*x)^n))*log(e*(f+g*x)/(e*f-d*g))/f^2+b*g*n*polylog(2,-g*(d+e*x)/(e*f-d*g))/f^2-b*g*n*polylog(2,1+e*x/d)/f^2],
[(a+b*log(c*(d+e*x)^n))/(x^3*(f+g*x)),x,14,-1/2*b*e*n/(d*f*x)-1/2*b*e^2*n*log(x)/(d^2*f)-b*e*g*n*log(x)/(d*f^2)+1/2*b*e^2*n*log(d+e*x)/(d^2*f)+b*e*g*n*log(d+e*x)/(d*f^2)+1/2*(-a-b*log(c*(d+e*x)^n))/(f*x^2)+g*(a+b*log(c*(d+e*x)^n))/(f^2*x)+g^2*log(-e*x/d)*(a+b*log(c*(d+e*x)^n))/f^3-g^2*(a+b*log(c*(d+e*x)^n))*log(e*(f+g*x)/(e*f-d*g))/f^3-b*g^2*n*polylog(2,-g*(d+e*x)/(e*f-d*g))/f^3+b*g^2*n*polylog(2,1+e*x/d)/f^3],
[x^3*(a+b*log(c*(d+e*x)^n))/(f+g*x)^2,x,15,-2*a*f*x/g^3+2*b*f*n*x/g^3+1/2*b*d*n*x/(e*g^2)-1/4*b*n*x^2/g^2-1/2*b*d^2*n*log(d+e*x)/(e^2*g^2)-b*e*f^3*n*log(d+e*x)/(g^4*(e*f-d*g))-2*b*f*(d+e*x)*log(c*(d+e*x)^n)/(e*g^3)+1/2*x^2*(a+b*log(c*(d+e*x)^n))/g^2+f^3*(a+b*log(c*(d+e*x)^n))/(g^4*(f+g*x))+b*e*f^3*n*log(f+g*x)/(g^4*(e*f-d*g))+3*f^2*(a+b*log(c*(d+e*x)^n))*log(e*(f+g*x)/(e*f-d*g))/g^4+3*b*f^2*n*polylog(2,-g*(d+e*x)/(e*f-d*g))/g^4],
[x^2*(a+b*log(c*(d+e*x)^n))/(f+g*x)^2,x,12,a*x/g^2-b*n*x/g^2+b*e*f^2*n*log(d+e*x)/(g^3*(e*f-d*g))+b*(d+e*x)*log(c*(d+e*x)^n)/(e*g^2)-f^2*(a+b*log(c*(d+e*x)^n))/(g^3*(f+g*x))-b*e*f^2*n*log(f+g*x)/(g^3*(e*f-d*g))-2*f*(a+b*log(c*(d+e*x)^n))*log(e*(f+g*x)/(e*f-d*g))/g^3-2*b*f*n*polylog(2,-g*(d+e*x)/(e*f-d*g))/g^3],
[x*(a+b*log(c*(d+e*x)^n))/(f+g*x)^2,x,9,-b*e*f*n*log(d+e*x)/(g^2*(e*f-d*g))+f*(a+b*log(c*(d+e*x)^n))/(g^2*(f+g*x))+b*e*f*n*log(f+g*x)/(g^2*(e*f-d*g))+(a+b*log(c*(d+e*x)^n))*log(e*(f+g*x)/(e*f-d*g))/g^2+b*n*polylog(2,-g*(d+e*x)/(e*f-d*g))/g^2],
[(a+b*log(c*(d+e*x)^n))/(f+g*x)^2,x,4,b*e*n*log(d+e*x)/(g*(e*f-d*g))+(-a-b*log(c*(d+e*x)^n))/(g*(f+g*x))-b*e*n*log(f+g*x)/(g*(e*f-d*g))],
[(a+b*log(c*(d+e*x)^n))/(x*(f+g*x)^2),x,11,-b*e*n*log(d+e*x)/(f*(e*f-d*g))+(a+b*log(c*(d+e*x)^n))/(f*(f+g*x))+log(-e*x/d)*(a+b*log(c*(d+e*x)^n))/f^2+b*e*n*log(f+g*x)/(f*(e*f-d*g))-(a+b*log(c*(d+e*x)^n))*log(e*(f+g*x)/(e*f-d*g))/f^2-b*n*polylog(2,-g*(d+e*x)/(e*f-d*g))/f^2+b*n*polylog(2,1+e*x/d)/f^2],
[(a+b*log(c*(d+e*x)^n))/(x^2*(f+g*x)^2),x,15,b*e*n*log(x)/(d*f^2)-b*e*n*log(d+e*x)/(d*f^2)+b*e*g*n*log(d+e*x)/(f^2*(e*f-d*g))+(-a-b*log(c*(d+e*x)^n))/(f^2*x)-g*(a+b*log(c*(d+e*x)^n))/(f^2*(f+g*x))-2*g*log(-e*x/d)*(a+b*log(c*(d+e*x)^n))/f^3-b*e*g*n*log(f+g*x)/(f^2*(e*f-d*g))+2*g*(a+b*log(c*(d+e*x)^n))*log(e*(f+g*x)/(e*f-d*g))/f^3+2*b*g*n*polylog(2,-g*(d+e*x)/(e*f-d*g))/f^3-2*b*g*n*polylog(2,1+e*x/d)/f^3],
[(a+b*log(c*(d+e*x)^n))/(x^3*(f+g*x)^2),x,18,-1/2*b*e*n/(d*f^2*x)-1/2*b*e^2*n*log(x)/(d^2*f^2)-2*b*e*g*n*log(x)/(d*f^3)+1/2*b*e^2*n*log(d+e*x)/(d^2*f^2)+2*b*e*g*n*log(d+e*x)/(d*f^3)-b*e*g^2*n*log(d+e*x)/(f^3*(e*f-d*g))+1/2*(-a-b*log(c*(d+e*x)^n))/(f^2*x^2)+2*g*(a+b*log(c*(d+e*x)^n))/(f^3*x)+g^2*(a+b*log(c*(d+e*x)^n))/(f^3*(f+g*x))+3*g^2*log(-e*x/d)*(a+b*log(c*(d+e*x)^n))/f^4+b*e*g^2*n*log(f+g*x)/(f^3*(e*f-d*g))-3*g^2*(a+b*log(c*(d+e*x)^n))*log(e*(f+g*x)/(e*f-d*g))/f^4-3*b*g^2*n*polylog(2,-g*(d+e*x)/(e*f-d*g))/f^4+3*b*g^2*n*polylog(2,1+e*x/d)/f^4],

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

# q>0

# q>0
[x^5*(a+b*log(c*(d+e*x)^n))/(f+g*x^2),x,16,-1/2*b*d*f*n*x/(e*g^2)+1/4*b*d^3*n*x/(e^3*g)+1/4*b*f*n*x^2/g^2-1/8*b*d^2*n*x^2/(e^2*g)+1/12*b*d*n*x^3/(e*g)-1/16*b*n*x^4/g+1/2*b*d^2*f*n*log(d+e*x)/(e^2*g^2)-1/4*b*d^4*n*log(d+e*x)/(e^4*g)-1/2*f*x^2*(a+b*log(c*(d+e*x)^n))/g^2+1/4*x^4*(a+b*log(c*(d+e*x)^n))/g+1/2*f^2*(a+b*log(c*(d+e*x)^n))*log(e*(sqrt(-f)-x*sqrt(g))/(e*sqrt(-f)+d*sqrt(g)))/g^3+1/2*f^2*(a+b*log(c*(d+e*x)^n))*log(e*(sqrt(-f)+x*sqrt(g))/(e*sqrt(-f)-d*sqrt(g)))/g^3+1/2*b*f^2*n*polylog(2,-(d+e*x)*sqrt(g)/(e*sqrt(-f)-d*sqrt(g)))/g^3+1/2*b*f^2*n*polylog(2,(d+e*x)*sqrt(g)/(e*sqrt(-f)+d*sqrt(g)))/g^3],
[x^3*(a+b*log(c*(d+e*x)^n))/(f+g*x^2),x,13,1/2*b*d*n*x/(e*g)-1/4*b*n*x^2/g-1/2*b*d^2*n*log(d+e*x)/(e^2*g)+1/2*x^2*(a+b*log(c*(d+e*x)^n))/g-1/2*f*(a+b*log(c*(d+e*x)^n))*log(e*(sqrt(-f)-x*sqrt(g))/(e*sqrt(-f)+d*sqrt(g)))/g^2-1/2*f*(a+b*log(c*(d+e*x)^n))*log(e*(sqrt(-f)+x*sqrt(g))/(e*sqrt(-f)-d*sqrt(g)))/g^2-1/2*b*f*n*polylog(2,-(d+e*x)*sqrt(g)/(e*sqrt(-f)-d*sqrt(g)))/g^2-1/2*b*f*n*polylog(2,(d+e*x)*sqrt(g)/(e*sqrt(-f)+d*sqrt(g)))/g^2],
[x*(a+b*log(c*(d+e*x)^n))/(f+g*x^2),x,8,1/2*(a+b*log(c*(d+e*x)^n))*log(e*(sqrt(-f)-x*sqrt(g))/(e*sqrt(-f)+d*sqrt(g)))/g+1/2*(a+b*log(c*(d+e*x)^n))*log(e*(sqrt(-f)+x*sqrt(g))/(e*sqrt(-f)-d*sqrt(g)))/g+1/2*b*n*polylog(2,-(d+e*x)*sqrt(g)/(e*sqrt(-f)-d*sqrt(g)))/g+1/2*b*n*polylog(2,(d+e*x)*sqrt(g)/(e*sqrt(-f)+d*sqrt(g)))/g],
[(a+b*log(c*(d+e*x)^n))/(x*(f+g*x^2)),x,12,log(-e*x/d)*(a+b*log(c*(d+e*x)^n))/f-1/2*(a+b*log(c*(d+e*x)^n))*log(e*(sqrt(-f)-x*sqrt(g))/(e*sqrt(-f)+d*sqrt(g)))/f-1/2*(a+b*log(c*(d+e*x)^n))*log(e*(sqrt(-f)+x*sqrt(g))/(e*sqrt(-f)-d*sqrt(g)))/f+b*n*polylog(2,1+e*x/d)/f-1/2*b*n*polylog(2,-(d+e*x)*sqrt(g)/(e*sqrt(-f)-d*sqrt(g)))/f-1/2*b*n*polylog(2,(d+e*x)*sqrt(g)/(e*sqrt(-f)+d*sqrt(g)))/f],
[(a+b*log(c*(d+e*x)^n))/(x^3*(f+g*x^2)),x,15,-1/2*b*e*n/(d*f*x)-1/2*b*e^2*n*log(x)/(d^2*f)+1/2*b*e^2*n*log(d+e*x)/(d^2*f)+1/2*(-a-b*log(c*(d+e*x)^n))/(f*x^2)-g*log(-e*x/d)*(a+b*log(c*(d+e*x)^n))/f^2+1/2*g*(a+b*log(c*(d+e*x)^n))*log(e*(sqrt(-f)-x*sqrt(g))/(e*sqrt(-f)+d*sqrt(g)))/f^2+1/2*g*(a+b*log(c*(d+e*x)^n))*log(e*(sqrt(-f)+x*sqrt(g))/(e*sqrt(-f)-d*sqrt(g)))/f^2-b*g*n*polylog(2,1+e*x/d)/f^2+1/2*b*g*n*polylog(2,-(d+e*x)*sqrt(g)/(e*sqrt(-f)-d*sqrt(g)))/f^2+1/2*b*g*n*polylog(2,(d+e*x)*sqrt(g)/(e*sqrt(-f)+d*sqrt(g)))/f^2],
[x^4*(a+b*log(c*(d+e*x)^n))/(f+g*x^2),x,16,-a*f*x/g^2+b*f*n*x/g^2-1/3*b*d^2*n*x/(e^2*g)+1/6*b*d*n*x^2/(e*g)-1/9*b*n*x^3/g+1/3*b*d^3*n*log(d+e*x)/(e^3*g)-b*f*(d+e*x)*log(c*(d+e*x)^n)/(e*g^2)+1/3*x^3*(a+b*log(c*(d+e*x)^n))/g+1/2*(-f)^(3/2)*(a+b*log(c*(d+e*x)^n))*log(e*(sqrt(-f)-x*sqrt(g))/(e*sqrt(-f)+d*sqrt(g)))/g^(5/2)-1/2*(-f)^(3/2)*(a+b*log(c*(d+e*x)^n))*log(e*(sqrt(-f)+x*sqrt(g))/(e*sqrt(-f)-d*sqrt(g)))/g^(5/2)-1/2*b*(-f)^(3/2)*n*polylog(2,-(d+e*x)*sqrt(g)/(e*sqrt(-f)-d*sqrt(g)))/g^(5/2)+1/2*b*(-f)^(3/2)*n*polylog(2,(d+e*x)*sqrt(g)/(e*sqrt(-f)+d*sqrt(g)))/g^(5/2)],
[x^2*(a+b*log(c*(d+e*x)^n))/(f+g*x^2),x,13,a*x/g-b*n*x/g+b*(d+e*x)*log(c*(d+e*x)^n)/(e*g)+1/2*(a+b*log(c*(d+e*x)^n))*log(e*(sqrt(-f)-x*sqrt(g))/(e*sqrt(-f)+d*sqrt(g)))*sqrt(-f)/g^(3/2)-1/2*(a+b*log(c*(d+e*x)^n))*log(e*(sqrt(-f)+x*sqrt(g))/(e*sqrt(-f)-d*sqrt(g)))*sqrt(-f)/g^(3/2)-1/2*b*n*polylog(2,-(d+e*x)*sqrt(g)/(e*sqrt(-f)-d*sqrt(g)))*sqrt(-f)/g^(3/2)+1/2*b*n*polylog(2,(d+e*x)*sqrt(g)/(e*sqrt(-f)+d*sqrt(g)))*sqrt(-f)/g^(3/2)],
[(a+b*log(c*(d+e*x)^n))/(f+g*x^2),x,8,1/2*(a+b*log(c*(d+e*x)^n))*log(e*(sqrt(-f)-x*sqrt(g))/(e*sqrt(-f)+d*sqrt(g)))/(sqrt(-f)*sqrt(g))-1/2*(a+b*log(c*(d+e*x)^n))*log(e*(sqrt(-f)+x*sqrt(g))/(e*sqrt(-f)-d*sqrt(g)))/(sqrt(-f)*sqrt(g))-1/2*b*n*polylog(2,-(d+e*x)*sqrt(g)/(e*sqrt(-f)-d*sqrt(g)))/(sqrt(-f)*sqrt(g))+1/2*b*n*polylog(2,(d+e*x)*sqrt(g)/(e*sqrt(-f)+d*sqrt(g)))/(sqrt(-f)*sqrt(g))],
[(a+b*log(c*(d+e*x)^n))/(x^2*(f+g*x^2)),x,14,b*e*n*log(x)/(d*f)-b*e*n*log(d+e*x)/(d*f)+(-a-b*log(c*(d+e*x)^n))/(f*x)+1/2*(a+b*log(c*(d+e*x)^n))*log(e*(sqrt(-f)-x*sqrt(g))/(e*sqrt(-f)+d*sqrt(g)))*sqrt(g)/(-f)^(3/2)-1/2*(a+b*log(c*(d+e*x)^n))*log(e*(sqrt(-f)+x*sqrt(g))/(e*sqrt(-f)-d*sqrt(g)))*sqrt(g)/(-f)^(3/2)-1/2*b*n*polylog(2,-(d+e*x)*sqrt(g)/(e*sqrt(-f)-d*sqrt(g)))*sqrt(g)/(-f)^(3/2)+1/2*b*n*polylog(2,(d+e*x)*sqrt(g)/(e*sqrt(-f)+d*sqrt(g)))*sqrt(g)/(-f)^(3/2)],
[(a+b*log(c*(d+e*x)^n))/(x^4*(f+g*x^2)),x,17,-1/6*b*e*n/(d*f*x^2)+1/3*b*e^2*n/(d^2*f*x)+1/3*b*e^3*n*log(x)/(d^3*f)-b*e*g*n*log(x)/(d*f^2)-1/3*b*e^3*n*log(d+e*x)/(d^3*f)+b*e*g*n*log(d+e*x)/(d*f^2)+1/3*(-a-b*log(c*(d+e*x)^n))/(f*x^3)+g*(a+b*log(c*(d+e*x)^n))/(f^2*x)+1/2*g^(3/2)*(a+b*log(c*(d+e*x)^n))*log(e*(sqrt(-f)-x*sqrt(g))/(e*sqrt(-f)+d*sqrt(g)))/(-f)^(5/2)-1/2*g^(3/2)*(a+b*log(c*(d+e*x)^n))*log(e*(sqrt(-f)+x*sqrt(g))/(e*sqrt(-f)-d*sqrt(g)))/(-f)^(5/2)-1/2*b*g^(3/2)*n*polylog(2,-(d+e*x)*sqrt(g)/(e*sqrt(-f)-d*sqrt(g)))/(-f)^(5/2)+1/2*b*g^(3/2)*n*polylog(2,(d+e*x)*sqrt(g)/(e*sqrt(-f)+d*sqrt(g)))/(-f)^(5/2)],
[x^5*(a+b*log(c*(d+e*x)^n))/(f+g*x^2)^2,x,19,1/2*b*d*n*x/(e*g^2)-1/4*b*n*x^2/g^2+1/2*b*d*e*f^(3/2)*n*arctan(x*sqrt(g)/sqrt(f))/(g^(5/2)*(e^2*f+d^2*g))-1/2*b*d^2*n*log(d+e*x)/(e^2*g^2)+1/2*b*e^2*f^2*n*log(d+e*x)/(g^3*(e^2*f+d^2*g))+1/2*x^2*(a+b*log(c*(d+e*x)^n))/g^2-1/2*f^2*(a+b*log(c*(d+e*x)^n))/(g^3*(f+g*x^2))-1/4*b*e^2*f^2*n*log(f+g*x^2)/(g^3*(e^2*f+d^2*g))-f*(a+b*log(c*(d+e*x)^n))*log(e*(sqrt(-f)-x*sqrt(g))/(e*sqrt(-f)+d*sqrt(g)))/g^3-f*(a+b*log(c*(d+e*x)^n))*log(e*(sqrt(-f)+x*sqrt(g))/(e*sqrt(-f)-d*sqrt(g)))/g^3-b*f*n*polylog(2,-(d+e*x)*sqrt(g)/(e*sqrt(-f)-d*sqrt(g)))/g^3-b*f*n*polylog(2,(d+e*x)*sqrt(g)/(e*sqrt(-f)+d*sqrt(g)))/g^3],
[x^3*(a+b*log(c*(d+e*x)^n))/(f+g*x^2)^2,x,16,-1/2*b*e^2*f*n*log(d+e*x)/(g^2*(e^2*f+d^2*g))+1/2*f*(a+b*log(c*(d+e*x)^n))/(g^2*(f+g*x^2))+1/4*b*e^2*f*n*log(f+g*x^2)/(g^2*(e^2*f+d^2*g))+1/2*(a+b*log(c*(d+e*x)^n))*log(e*(sqrt(-f)-x*sqrt(g))/(e*sqrt(-f)+d*sqrt(g)))/g^2+1/2*(a+b*log(c*(d+e*x)^n))*log(e*(sqrt(-f)+x*sqrt(g))/(e*sqrt(-f)-d*sqrt(g)))/g^2+1/2*b*n*polylog(2,-(d+e*x)*sqrt(g)/(e*sqrt(-f)-d*sqrt(g)))/g^2+1/2*b*n*polylog(2,(d+e*x)*sqrt(g)/(e*sqrt(-f)+d*sqrt(g)))/g^2-1/2*b*d*e*n*arctan(x*sqrt(g)/sqrt(f))*sqrt(f)/(g^(3/2)*(e^2*f+d^2*g))],
[x*(a+b*log(c*(d+e*x)^n))/(f+g*x^2)^2,x,6,1/2*b*e^2*n*log(d+e*x)/(g*(e^2*f+d^2*g))+1/2*(-a-b*log(c*(d+e*x)^n))/(g*(f+g*x^2))-1/4*b*e^2*n*log(f+g*x^2)/(g*(e^2*f+d^2*g))+1/2*b*d*e*n*arctan(x*sqrt(g)/sqrt(f))/((e^2*f+d^2*g)*sqrt(f)*sqrt(g))],
[(a+b*log(c*(d+e*x)^n))/(x*(f+g*x^2)^2),x,18,-1/2*b*e^2*n*log(d+e*x)/(f*(e^2*f+d^2*g))+1/2*(a+b*log(c*(d+e*x)^n))/(f*(f+g*x^2))+log(-e*x/d)*(a+b*log(c*(d+e*x)^n))/f^2+1/4*b*e^2*n*log(f+g*x^2)/(f*(e^2*f+d^2*g))-1/2*(a+b*log(c*(d+e*x)^n))*log(e*(sqrt(-f)-x*sqrt(g))/(e*sqrt(-f)+d*sqrt(g)))/f^2-1/2*(a+b*log(c*(d+e*x)^n))*log(e*(sqrt(-f)+x*sqrt(g))/(e*sqrt(-f)-d*sqrt(g)))/f^2+b*n*polylog(2,1+e*x/d)/f^2-1/2*b*n*polylog(2,-(d+e*x)*sqrt(g)/(e*sqrt(-f)-d*sqrt(g)))/f^2-1/2*b*n*polylog(2,(d+e*x)*sqrt(g)/(e*sqrt(-f)+d*sqrt(g)))/f^2-1/2*b*d*e*n*arctan(x*sqrt(g)/sqrt(f))*sqrt(g)/(f^(3/2)*(e^2*f+d^2*g))],
[(a+b*log(c*(d+e*x)^n))/(x^3*(f+g*x^2)^2),x,21,-1/2*b*e*n/(d*f^2*x)+1/2*b*d*e*g^(3/2)*n*arctan(x*sqrt(g)/sqrt(f))/(f^(5/2)*(e^2*f+d^2*g))-1/2*b*e^2*n*log(x)/(d^2*f^2)+1/2*b*e^2*n*log(d+e*x)/(d^2*f^2)+1/2*b*e^2*g*n*log(d+e*x)/(f^2*(e^2*f+d^2*g))+1/2*(-a-b*log(c*(d+e*x)^n))/(f^2*x^2)-1/2*g*(a+b*log(c*(d+e*x)^n))/(f^2*(f+g*x^2))-2*g*log(-e*x/d)*(a+b*log(c*(d+e*x)^n))/f^3-1/4*b*e^2*g*n*log(f+g*x^2)/(f^2*(e^2*f+d^2*g))+g*(a+b*log(c*(d+e*x)^n))*log(e*(sqrt(-f)-x*sqrt(g))/(e*sqrt(-f)+d*sqrt(g)))/f^3+g*(a+b*log(c*(d+e*x)^n))*log(e*(sqrt(-f)+x*sqrt(g))/(e*sqrt(-f)-d*sqrt(g)))/f^3-2*b*g*n*polylog(2,1+e*x/d)/f^3+b*g*n*polylog(2,-(d+e*x)*sqrt(g)/(e*sqrt(-f)-d*sqrt(g)))/f^3+b*g*n*polylog(2,(d+e*x)*sqrt(g)/(e*sqrt(-f)+d*sqrt(g)))/f^3],
[x^4*(a+b*log(c*(d+e*x)^n))/(f+g*x^2)^2,x,31,a*x/g^2-b*n*x/g^2+b*(d+e*x)*log(c*(d+e*x)^n)/(e*g^2)+3/4*(a+b*log(c*(d+e*x)^n))*log(e*(sqrt(-f)-x*sqrt(g))/(e*sqrt(-f)+d*sqrt(g)))*sqrt(-f)/g^(5/2)-3/4*(a+b*log(c*(d+e*x)^n))*log(e*(sqrt(-f)+x*sqrt(g))/(e*sqrt(-f)-d*sqrt(g)))*sqrt(-f)/g^(5/2)-3/4*b*n*polylog(2,-(d+e*x)*sqrt(g)/(e*sqrt(-f)-d*sqrt(g)))*sqrt(-f)/g^(5/2)+3/4*b*n*polylog(2,(d+e*x)*sqrt(g)/(e*sqrt(-f)+d*sqrt(g)))*sqrt(-f)/g^(5/2)-1/4*b*e*f*n*log(d+e*x)/(g^(5/2)*(e*sqrt(-f)-d*sqrt(g)))+1/4*b*e*f*n*log(sqrt(-f)+x*sqrt(g))/(g^(5/2)*(e*sqrt(-f)-d*sqrt(g)))+1/4*b*e*f*n*log(d+e*x)/(g^(5/2)*(e*sqrt(-f)+d*sqrt(g)))-1/4*b*e*f*n*log(sqrt(-f)-x*sqrt(g))/(g^(5/2)*(e*sqrt(-f)+d*sqrt(g)))-1/4*f*(a+b*log(c*(d+e*x)^n))/(g^(5/2)*(sqrt(-f)-x*sqrt(g)))+1/4*f*(a+b*log(c*(d+e*x)^n))/(g^(5/2)*(sqrt(-f)+x*sqrt(g)))],
[x^2*(a+b*log(c*(d+e*x)^n))/(f+g*x^2)^2,x,28,1/4*(a+b*log(c*(d+e*x)^n))*log(e*(sqrt(-f)-x*sqrt(g))/(e*sqrt(-f)+d*sqrt(g)))/(g^(3/2)*sqrt(-f))-1/4*(a+b*log(c*(d+e*x)^n))*log(e*(sqrt(-f)+x*sqrt(g))/(e*sqrt(-f)-d*sqrt(g)))/(g^(3/2)*sqrt(-f))-1/4*b*n*polylog(2,-(d+e*x)*sqrt(g)/(e*sqrt(-f)-d*sqrt(g)))/(g^(3/2)*sqrt(-f))+1/4*b*n*polylog(2,(d+e*x)*sqrt(g)/(e*sqrt(-f)+d*sqrt(g)))/(g^(3/2)*sqrt(-f))+1/4*b*e*n*log(d+e*x)/(g^(3/2)*(e*sqrt(-f)-d*sqrt(g)))-1/4*b*e*n*log(sqrt(-f)+x*sqrt(g))/(g^(3/2)*(e*sqrt(-f)-d*sqrt(g)))-1/4*b*e*n*log(d+e*x)/(g^(3/2)*(e*sqrt(-f)+d*sqrt(g)))+1/4*b*e*n*log(sqrt(-f)-x*sqrt(g))/(g^(3/2)*(e*sqrt(-f)+d*sqrt(g)))+1/4*(a+b*log(c*(d+e*x)^n))/(g^(3/2)*(sqrt(-f)-x*sqrt(g)))+1/4*(-a-b*log(c*(d+e*x)^n))/(g^(3/2)*(sqrt(-f)+x*sqrt(g)))],
[(a+b*log(c*(d+e*x)^n))/(f+g*x^2)^2,x,18,-1/4*(a+b*log(c*(d+e*x)^n))*log(e*(sqrt(-f)-x*sqrt(g))/(e*sqrt(-f)+d*sqrt(g)))/((-f)^(3/2)*sqrt(g))+1/4*(a+b*log(c*(d+e*x)^n))*log(e*(sqrt(-f)+x*sqrt(g))/(e*sqrt(-f)-d*sqrt(g)))/((-f)^(3/2)*sqrt(g))+1/4*b*n*polylog(2,-(d+e*x)*sqrt(g)/(e*sqrt(-f)-d*sqrt(g)))/((-f)^(3/2)*sqrt(g))-1/4*b*n*polylog(2,(d+e*x)*sqrt(g)/(e*sqrt(-f)+d*sqrt(g)))/((-f)^(3/2)*sqrt(g))+1/4*b*e*n*log(d+e*x)/(f*sqrt(g)*(e*sqrt(-f)+d*sqrt(g)))-1/4*b*e*n*log(sqrt(-f)-x*sqrt(g))/(f*sqrt(g)*(e*sqrt(-f)+d*sqrt(g)))+1/4*b*e*n*log(d+e*x)/(sqrt(g)*(e*(-f)^(3/2)+d*f*sqrt(g)))-1/4*b*e*n*log(sqrt(-f)+x*sqrt(g))/(sqrt(g)*(e*(-f)^(3/2)+d*f*sqrt(g)))+1/4*(-a-b*log(c*(d+e*x)^n))/(f*sqrt(g)*(sqrt(-f)-x*sqrt(g)))+1/4*(a+b*log(c*(d+e*x)^n))/(f*sqrt(g)*(sqrt(-f)+x*sqrt(g)))],
[(a+b*log(c*(d+e*x)^n))/(x^2*(f+g*x^2)^2),x,32,b*e*n*log(x)/(d*f^2)-b*e*n*log(d+e*x)/(d*f^2)+(-a-b*log(c*(d+e*x)^n))/(f^2*x)-3/4*(a+b*log(c*(d+e*x)^n))*log(e*(sqrt(-f)-x*sqrt(g))/(e*sqrt(-f)+d*sqrt(g)))*sqrt(g)/(-f)^(5/2)+3/4*(a+b*log(c*(d+e*x)^n))*log(e*(sqrt(-f)+x*sqrt(g))/(e*sqrt(-f)-d*sqrt(g)))*sqrt(g)/(-f)^(5/2)+3/4*b*n*polylog(2,-(d+e*x)*sqrt(g)/(e*sqrt(-f)-d*sqrt(g)))*sqrt(g)/(-f)^(5/2)-3/4*b*n*polylog(2,(d+e*x)*sqrt(g)/(e*sqrt(-f)+d*sqrt(g)))*sqrt(g)/(-f)^(5/2)-1/4*b*e*n*log(d+e*x)*sqrt(g)/(f^2*(e*sqrt(-f)+d*sqrt(g)))+1/4*b*e*n*log(sqrt(-f)-x*sqrt(g))*sqrt(g)/(f^2*(e*sqrt(-f)+d*sqrt(g)))-1/4*b*e*n*log(d+e*x)*sqrt(g)/(f*(e*(-f)^(3/2)+d*f*sqrt(g)))+1/4*b*e*n*log(sqrt(-f)+x*sqrt(g))*sqrt(g)/(f*(e*(-f)^(3/2)+d*f*sqrt(g)))+1/4*(a+b*log(c*(d+e*x)^n))*sqrt(g)/(f^2*(sqrt(-f)-x*sqrt(g)))-1/4*(a+b*log(c*(d+e*x)^n))*sqrt(g)/(f^2*(sqrt(-f)+x*sqrt(g)))],
[(a+b*log(c*(d+e*x)^n))/sqrt(2+g*x^2),x,10,1/2*b*n*arcsinh(x*sqrt(g)/sqrt(2))^2/sqrt(g)+arcsinh(x*sqrt(g)/sqrt(2))*(a+b*log(c*(d+e*x)^n))/sqrt(g)-b*n*arcsinh(x*sqrt(g)/sqrt(2))*log(1+e*exp(arcsinh(x*sqrt(g)/sqrt(2)))*sqrt(2)/(d*sqrt(g)-sqrt(2*e^2+d^2*g)))/sqrt(g)-b*n*arcsinh(x*sqrt(g)/sqrt(2))*log(1+e*exp(arcsinh(x*sqrt(g)/sqrt(2)))*sqrt(2)/(d*sqrt(g)+sqrt(2*e^2+d^2*g)))/sqrt(g)-b*n*polylog(2,-e*exp(arcsinh(x*sqrt(g)/sqrt(2)))*sqrt(2)/(d*sqrt(g)-sqrt(2*e^2+d^2*g)))/sqrt(g)-b*n*polylog(2,-e*exp(arcsinh(x*sqrt(g)/sqrt(2)))*sqrt(2)/(d*sqrt(g)+sqrt(2*e^2+d^2*g)))/sqrt(g)],
[(a+b*log(c*(d+e*x)^n))/sqrt(f+g*x^2),x,11,1/2*b*n*arcsinh(x*sqrt(g)/sqrt(f))^2*sqrt(f)*sqrt(1+g*x^2/f)/(sqrt(g)*sqrt(f+g*x^2))+arcsinh(x*sqrt(g)/sqrt(f))*(a+b*log(c*(d+e*x)^n))*sqrt(f)*sqrt(1+g*x^2/f)/(sqrt(g)*sqrt(f+g*x^2))-b*n*arcsinh(x*sqrt(g)/sqrt(f))*log(1+e*exp(arcsinh(x*sqrt(g)/sqrt(f)))*sqrt(f)/(d*sqrt(g)-sqrt(e^2*f+d^2*g)))*sqrt(f)*sqrt(1+g*x^2/f)/(sqrt(g)*sqrt(f+g*x^2))-b*n*arcsinh(x*sqrt(g)/sqrt(f))*log(1+e*exp(arcsinh(x*sqrt(g)/sqrt(f)))*sqrt(f)/(d*sqrt(g)+sqrt(e^2*f+d^2*g)))*sqrt(f)*sqrt(1+g*x^2/f)/(sqrt(g)*sqrt(f+g*x^2))-b*n*polylog(2,-e*exp(arcsinh(x*sqrt(g)/sqrt(f)))*sqrt(f)/(d*sqrt(g)-sqrt(e^2*f+d^2*g)))*sqrt(f)*sqrt(1+g*x^2/f)/(sqrt(g)*sqrt(f+g*x^2))-b*n*polylog(2,-e*exp(arcsinh(x*sqrt(g)/sqrt(f)))*sqrt(f)/(d*sqrt(g)+sqrt(e^2*f+d^2*g)))*sqrt(f)*sqrt(1+g*x^2/f)/(sqrt(g)*sqrt(f+g*x^2))],
[(a+b*log(c*(d+e*x)^n))/(sqrt(2-g*x)*sqrt(2+g*x)),x,9,1/2*I*b*n*arcsin(1/2*g*x)^2/g+arcsin(1/2*g*x)*(a+b*log(c*(d+e*x)^n))/g-b*n*arcsin(1/2*g*x)*log(1+2*e*exp(I*arcsin(1/2*g*x))/(I*d*g-sqrt(4*e^2-d^2*g^2)))/g-b*n*arcsin(1/2*g*x)*log(1+2*e*exp(I*arcsin(1/2*g*x))/(I*d*g+sqrt(4*e^2-d^2*g^2)))/g+I*b*n*polylog(2,-2*e*exp(I*arcsin(1/2*g*x))/(I*d*g-sqrt(4*e^2-d^2*g^2)))/g+I*b*n*polylog(2,-2*e*exp(I*arcsin(1/2*g*x))/(I*d*g+sqrt(4*e^2-d^2*g^2)))/g],
[(a+b*log(c*(d+e*x)^n))/(sqrt(f-g*x)*sqrt(f+g*x)),x,11,1/2*I*b*f*n*arcsin(g*x/f)^2*sqrt(1-g^2*x^2/f^2)/(g*sqrt(f-g*x)*sqrt(f+g*x))+f*arcsin(g*x/f)*(a+b*log(c*(d+e*x)^n))*sqrt(1-g^2*x^2/f^2)/(g*sqrt(f-g*x)*sqrt(f+g*x))-b*f*n*arcsin(g*x/f)*log(1+e*exp(I*arcsin(g*x/f))*f/(I*d*g-sqrt(e^2*f^2-d^2*g^2)))*sqrt(1-g^2*x^2/f^2)/(g*sqrt(f-g*x)*sqrt(f+g*x))-b*f*n*arcsin(g*x/f)*log(1+e*exp(I*arcsin(g*x/f))*f/(I*d*g+sqrt(e^2*f^2-d^2*g^2)))*sqrt(1-g^2*x^2/f^2)/(g*sqrt(f-g*x)*sqrt(f+g*x))+I*b*f*n*polylog(2,-e*exp(I*arcsin(g*x/f))*f/(I*d*g-sqrt(e^2*f^2-d^2*g^2)))*sqrt(1-g^2*x^2/f^2)/(g*sqrt(f-g*x)*sqrt(f+g*x))+I*b*f*n*polylog(2,-e*exp(I*arcsin(g*x/f))*f/(I*d*g+sqrt(e^2*f^2-d^2*g^2)))*sqrt(1-g^2*x^2/f^2)/(g*sqrt(f-g*x)*sqrt(f+g*x))],
[log(2*e/(e+f*x))/(e^2-f^2*x^2),x,2,1/2*polylog(2,1-2*e/(e+f*x))/(e*f)],
[log(e/(e+f*x))/(e^2-f^2*x^2),x,4,-arctanh(f*x/e)*log(2)/(e*f)+1/2*polylog(2,1-2*e/(e+f*x))/(e*f)],
[(a+b*log(2*e/(e+f*x)))/(e^2-f^2*x^2),x,4,a*arctanh(f*x/e)/(e*f)+1/2*b*polylog(2,1-2*e/(e+f*x))/(e*f)],
[(a+b*log(e/(e+f*x)))/(e^2-f^2*x^2),x,4,arctanh(f*x/e)*(a-b*log(2))/(e*f)+1/2*b*polylog(2,1-2*e/(e+f*x))/(e*f)],

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

# q>0

# q<0
[x^5*log(c+d*x)/(a+b*x^3),x,16,-1/3*c^2*x/(b*d^2)+1/6*c*x^2/(b*d)-1/9*x^3/b+1/3*c^3*log(c+d*x)/(b*d^3)+1/3*x^3*log(c+d*x)/b-1/3*a*log(-d*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*c-a^(1/3)*d))*log(c+d*x)/b^2-1/3*a*log(-d*((-1)^(2/3)*a^(1/3)+b^(1/3)*x)/(b^(1/3)*c-(-1)^(2/3)*a^(1/3)*d))*log(c+d*x)/b^2-1/3*a*log((-1)^(1/3)*d*(a^(1/3)+(-1)^(2/3)*b^(1/3)*x)/(b^(1/3)*c+(-1)^(1/3)*a^(1/3)*d))*log(c+d*x)/b^2-1/3*a*polylog(2,b^(1/3)*(c+d*x)/(b^(1/3)*c-a^(1/3)*d))/b^2-1/3*a*polylog(2,b^(1/3)*(c+d*x)/(b^(1/3)*c+(-1)^(1/3)*a^(1/3)*d))/b^2-1/3*a*polylog(2,b^(1/3)*(c+d*x)/(b^(1/3)*c-(-1)^(2/3)*a^(1/3)*d))/b^2],
[x^2*log(c+d*x)/(a+b*x^3),x,11,1/3*log(-d*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*c-a^(1/3)*d))*log(c+d*x)/b+1/3*log(-d*((-1)^(2/3)*a^(1/3)+b^(1/3)*x)/(b^(1/3)*c-(-1)^(2/3)*a^(1/3)*d))*log(c+d*x)/b+1/3*log((-1)^(1/3)*d*(a^(1/3)+(-1)^(2/3)*b^(1/3)*x)/(b^(1/3)*c+(-1)^(1/3)*a^(1/3)*d))*log(c+d*x)/b+1/3*polylog(2,b^(1/3)*(c+d*x)/(b^(1/3)*c-a^(1/3)*d))/b+1/3*polylog(2,b^(1/3)*(c+d*x)/(b^(1/3)*c+(-1)^(1/3)*a^(1/3)*d))/b+1/3*polylog(2,b^(1/3)*(c+d*x)/(b^(1/3)*c-(-1)^(2/3)*a^(1/3)*d))/b],
[log(c+d*x)/(x*(a+b*x^3)),x,15,log(-d*x/c)*log(c+d*x)/a-1/3*log(-d*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*c-a^(1/3)*d))*log(c+d*x)/a-1/3*log(-d*((-1)^(2/3)*a^(1/3)+b^(1/3)*x)/(b^(1/3)*c-(-1)^(2/3)*a^(1/3)*d))*log(c+d*x)/a-1/3*log((-1)^(1/3)*d*(a^(1/3)+(-1)^(2/3)*b^(1/3)*x)/(b^(1/3)*c+(-1)^(1/3)*a^(1/3)*d))*log(c+d*x)/a-1/3*polylog(2,b^(1/3)*(c+d*x)/(b^(1/3)*c-a^(1/3)*d))/a-1/3*polylog(2,b^(1/3)*(c+d*x)/(b^(1/3)*c+(-1)^(1/3)*a^(1/3)*d))/a-1/3*polylog(2,b^(1/3)*(c+d*x)/(b^(1/3)*c-(-1)^(2/3)*a^(1/3)*d))/a+polylog(2,1+d*x/c)/a],
[log(c+d*x)/(x^4*(a+b*x^3)),x,18,-1/6*d/(a*c*x^2)+1/3*d^2/(a*c^2*x)+1/3*d^3*log(x)/(a*c^3)-1/3*d^3*log(c+d*x)/(a*c^3)-1/3*log(c+d*x)/(a*x^3)-b*log(-d*x/c)*log(c+d*x)/a^2+1/3*b*log(-d*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*c-a^(1/3)*d))*log(c+d*x)/a^2+1/3*b*log(-d*((-1)^(2/3)*a^(1/3)+b^(1/3)*x)/(b^(1/3)*c-(-1)^(2/3)*a^(1/3)*d))*log(c+d*x)/a^2+1/3*b*log((-1)^(1/3)*d*(a^(1/3)+(-1)^(2/3)*b^(1/3)*x)/(b^(1/3)*c+(-1)^(1/3)*a^(1/3)*d))*log(c+d*x)/a^2+1/3*b*polylog(2,b^(1/3)*(c+d*x)/(b^(1/3)*c-a^(1/3)*d))/a^2+1/3*b*polylog(2,b^(1/3)*(c+d*x)/(b^(1/3)*c+(-1)^(1/3)*a^(1/3)*d))/a^2+1/3*b*polylog(2,b^(1/3)*(c+d*x)/(b^(1/3)*c-(-1)^(2/3)*a^(1/3)*d))/a^2-b*polylog(2,1+d*x/c)/a^2],
[x^4*log(c+d*x)/(a+b*x^3),x,16,1/2*c*x/(b*d)-1/4*x^2/b-1/2*c^2*log(c+d*x)/(b*d^2)+1/2*x^2*log(c+d*x)/b+1/3*a^(2/3)*log(-d*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*c-a^(1/3)*d))*log(c+d*x)/b^(5/3)-1/3*(-1)^(1/3)*a^(2/3)*log(d*(a^(1/3)-(-1)^(1/3)*b^(1/3)*x)/((-1)^(1/3)*b^(1/3)*c+a^(1/3)*d))*log(c+d*x)/b^(5/3)+1/3*(-1)^(2/3)*a^(2/3)*log(-d*(a^(1/3)+(-1)^(2/3)*b^(1/3)*x)/((-1)^(2/3)*b^(1/3)*c-a^(1/3)*d))*log(c+d*x)/b^(5/3)+1/3*a^(2/3)*polylog(2,b^(1/3)*(c+d*x)/(b^(1/3)*c-a^(1/3)*d))/b^(5/3)+1/3*(-1)^(2/3)*a^(2/3)*polylog(2,(-1)^(2/3)*b^(1/3)*(c+d*x)/((-1)^(2/3)*b^(1/3)*c-a^(1/3)*d))/b^(5/3)-1/3*(-1)^(1/3)*a^(2/3)*polylog(2,(-1)^(1/3)*b^(1/3)*(c+d*x)/((-1)^(1/3)*b^(1/3)*c+a^(1/3)*d))/b^(5/3)],
[x^3*log(c+d*x)/(a+b*x^3),x,15,-x/b+(c+d*x)*log(c+d*x)/(b*d)-1/3*a^(1/3)*log(-d*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*c-a^(1/3)*d))*log(c+d*x)/b^(4/3)-1/3*(-1)^(2/3)*a^(1/3)*log(d*(a^(1/3)-(-1)^(1/3)*b^(1/3)*x)/((-1)^(1/3)*b^(1/3)*c+a^(1/3)*d))*log(c+d*x)/b^(4/3)+1/3*(-1)^(1/3)*a^(1/3)*log(-d*(a^(1/3)+(-1)^(2/3)*b^(1/3)*x)/((-1)^(2/3)*b^(1/3)*c-a^(1/3)*d))*log(c+d*x)/b^(4/3)-1/3*a^(1/3)*polylog(2,b^(1/3)*(c+d*x)/(b^(1/3)*c-a^(1/3)*d))/b^(4/3)+1/3*(-1)^(1/3)*a^(1/3)*polylog(2,(-1)^(2/3)*b^(1/3)*(c+d*x)/((-1)^(2/3)*b^(1/3)*c-a^(1/3)*d))/b^(4/3)-1/3*(-1)^(2/3)*a^(1/3)*polylog(2,(-1)^(1/3)*b^(1/3)*(c+d*x)/((-1)^(1/3)*b^(1/3)*c+a^(1/3)*d))/b^(4/3)],
[x*log(c+d*x)/(a+b*x^3),x,11,-1/3*log(-d*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*c-a^(1/3)*d))*log(c+d*x)/(a^(1/3)*b^(2/3))+1/3*(-1)^(1/3)*log(d*(a^(1/3)-(-1)^(1/3)*b^(1/3)*x)/((-1)^(1/3)*b^(1/3)*c+a^(1/3)*d))*log(c+d*x)/(a^(1/3)*b^(2/3))-1/3*(-1)^(2/3)*log(-d*(a^(1/3)+(-1)^(2/3)*b^(1/3)*x)/((-1)^(2/3)*b^(1/3)*c-a^(1/3)*d))*log(c+d*x)/(a^(1/3)*b^(2/3))-1/3*polylog(2,b^(1/3)*(c+d*x)/(b^(1/3)*c-a^(1/3)*d))/(a^(1/3)*b^(2/3))-1/3*(-1)^(2/3)*polylog(2,(-1)^(2/3)*b^(1/3)*(c+d*x)/((-1)^(2/3)*b^(1/3)*c-a^(1/3)*d))/(a^(1/3)*b^(2/3))+1/3*(-1)^(1/3)*polylog(2,(-1)^(1/3)*b^(1/3)*(c+d*x)/((-1)^(1/3)*b^(1/3)*c+a^(1/3)*d))/(a^(1/3)*b^(2/3))],
[log(c+d*x)/(a+b*x^3),x,11,1/3*log(-d*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*c-a^(1/3)*d))*log(c+d*x)/(a^(2/3)*b^(1/3))+1/3*(-1)^(2/3)*log(d*(a^(1/3)-(-1)^(1/3)*b^(1/3)*x)/((-1)^(1/3)*b^(1/3)*c+a^(1/3)*d))*log(c+d*x)/(a^(2/3)*b^(1/3))-1/3*(-1)^(1/3)*log(-d*(a^(1/3)+(-1)^(2/3)*b^(1/3)*x)/((-1)^(2/3)*b^(1/3)*c-a^(1/3)*d))*log(c+d*x)/(a^(2/3)*b^(1/3))+1/3*polylog(2,b^(1/3)*(c+d*x)/(b^(1/3)*c-a^(1/3)*d))/(a^(2/3)*b^(1/3))-1/3*(-1)^(1/3)*polylog(2,(-1)^(2/3)*b^(1/3)*(c+d*x)/((-1)^(2/3)*b^(1/3)*c-a^(1/3)*d))/(a^(2/3)*b^(1/3))+1/3*(-1)^(2/3)*polylog(2,(-1)^(1/3)*b^(1/3)*(c+d*x)/((-1)^(1/3)*b^(1/3)*c+a^(1/3)*d))/(a^(2/3)*b^(1/3))],
[log(c+d*x)/(x^2*(a+b*x^3)),x,17,d*log(x)/(a*c)-d*log(c+d*x)/(a*c)-log(c+d*x)/(a*x)+1/3*b^(1/3)*log(-d*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*c-a^(1/3)*d))*log(c+d*x)/a^(4/3)-1/3*(-1)^(1/3)*b^(1/3)*log(d*(a^(1/3)-(-1)^(1/3)*b^(1/3)*x)/((-1)^(1/3)*b^(1/3)*c+a^(1/3)*d))*log(c+d*x)/a^(4/3)+1/3*(-1)^(2/3)*b^(1/3)*log(-d*(a^(1/3)+(-1)^(2/3)*b^(1/3)*x)/((-1)^(2/3)*b^(1/3)*c-a^(1/3)*d))*log(c+d*x)/a^(4/3)+1/3*b^(1/3)*polylog(2,b^(1/3)*(c+d*x)/(b^(1/3)*c-a^(1/3)*d))/a^(4/3)+1/3*(-1)^(2/3)*b^(1/3)*polylog(2,(-1)^(2/3)*b^(1/3)*(c+d*x)/((-1)^(2/3)*b^(1/3)*c-a^(1/3)*d))/a^(4/3)-1/3*(-1)^(1/3)*b^(1/3)*polylog(2,(-1)^(1/3)*b^(1/3)*(c+d*x)/((-1)^(1/3)*b^(1/3)*c+a^(1/3)*d))/a^(4/3)],
[log(c+d*x)/(x^3*(a+b*x^3)),x,16,-1/2*d/(a*c*x)-1/2*d^2*log(x)/(a*c^2)+1/2*d^2*log(c+d*x)/(a*c^2)-1/2*log(c+d*x)/(a*x^2)-1/3*b^(2/3)*log(-d*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*c-a^(1/3)*d))*log(c+d*x)/a^(5/3)-1/3*(-1)^(2/3)*b^(2/3)*log(d*(a^(1/3)-(-1)^(1/3)*b^(1/3)*x)/((-1)^(1/3)*b^(1/3)*c+a^(1/3)*d))*log(c+d*x)/a^(5/3)+1/3*(-1)^(1/3)*b^(2/3)*log(-d*(a^(1/3)+(-1)^(2/3)*b^(1/3)*x)/((-1)^(2/3)*b^(1/3)*c-a^(1/3)*d))*log(c+d*x)/a^(5/3)-1/3*b^(2/3)*polylog(2,b^(1/3)*(c+d*x)/(b^(1/3)*c-a^(1/3)*d))/a^(5/3)+1/3*(-1)^(1/3)*b^(2/3)*polylog(2,(-1)^(2/3)*b^(1/3)*(c+d*x)/((-1)^(2/3)*b^(1/3)*c-a^(1/3)*d))/a^(5/3)-1/3*(-1)^(2/3)*b^(2/3)*polylog(2,(-1)^(1/3)*b^(1/3)*(c+d*x)/((-1)^(1/3)*b^(1/3)*c+a^(1/3)*d))/a^(5/3)],

# Integrands of the form x^m (f+g x^4)^q (a+b Log[c (d+e x)^n])

# q>0

# q<0
[x^7*log(c+d*x)/(a+b*x^4),x,23,1/4*c^3*x/(b*d^3)-1/8*c^2*x^2/(b*d^2)+1/12*c*x^3/(b*d)-1/16*x^4/b-1/4*c^4*log(c+d*x)/(b*d^4)+1/4*x^4*log(c+d*x)/b-1/4*a*log(d*((-a)^(1/4)-b^(1/4)*x)/(b^(1/4)*c+(-a)^(1/4)*d))*log(c+d*x)/b^2-1/4*a*log(-d*((-a)^(1/4)+b^(1/4)*x)/(b^(1/4)*c-(-a)^(1/4)*d))*log(c+d*x)/b^2-1/4*a*log(c+d*x)*log(-d*(b^(1/4)*x+sqrt(-sqrt(-a)))/(b^(1/4)*c-d*sqrt(-sqrt(-a))))/b^2-1/4*a*log(c+d*x)*log(d*(-b^(1/4)*x+sqrt(-sqrt(-a)))/(b^(1/4)*c+d*sqrt(-sqrt(-a))))/b^2-1/4*a*polylog(2,b^(1/4)*(c+d*x)/(b^(1/4)*c-(-a)^(1/4)*d))/b^2-1/4*a*polylog(2,b^(1/4)*(c+d*x)/(b^(1/4)*c+(-a)^(1/4)*d))/b^2-1/4*a*polylog(2,b^(1/4)*(c+d*x)/(b^(1/4)*c-d*sqrt(-sqrt(-a))))/b^2-1/4*a*polylog(2,b^(1/4)*(c+d*x)/(b^(1/4)*c+d*sqrt(-sqrt(-a))))/b^2],
[x^3*log(c+d*x)/(a+b*x^4),x,18,1/4*log(d*((-a)^(1/4)-b^(1/4)*x)/(b^(1/4)*c+(-a)^(1/4)*d))*log(c+d*x)/b+1/4*log(-d*((-a)^(1/4)+b^(1/4)*x)/(b^(1/4)*c-(-a)^(1/4)*d))*log(c+d*x)/b+1/4*log(c+d*x)*log(-d*(b^(1/4)*x+sqrt(-sqrt(-a)))/(b^(1/4)*c-d*sqrt(-sqrt(-a))))/b+1/4*log(c+d*x)*log(d*(-b^(1/4)*x+sqrt(-sqrt(-a)))/(b^(1/4)*c+d*sqrt(-sqrt(-a))))/b+1/4*polylog(2,b^(1/4)*(c+d*x)/(b^(1/4)*c-(-a)^(1/4)*d))/b+1/4*polylog(2,b^(1/4)*(c+d*x)/(b^(1/4)*c+(-a)^(1/4)*d))/b+1/4*polylog(2,b^(1/4)*(c+d*x)/(b^(1/4)*c-d*sqrt(-sqrt(-a))))/b+1/4*polylog(2,b^(1/4)*(c+d*x)/(b^(1/4)*c+d*sqrt(-sqrt(-a))))/b],
[log(c+d*x)/(x*(a+b*x^4)),x,22,log(-d*x/c)*log(c+d*x)/a-1/4*log(d*((-a)^(1/4)-b^(1/4)*x)/(b^(1/4)*c+(-a)^(1/4)*d))*log(c+d*x)/a-1/4*log(-d*((-a)^(1/4)+b^(1/4)*x)/(b^(1/4)*c-(-a)^(1/4)*d))*log(c+d*x)/a-1/4*log(c+d*x)*log(-d*(b^(1/4)*x+sqrt(-sqrt(-a)))/(b^(1/4)*c-d*sqrt(-sqrt(-a))))/a-1/4*log(c+d*x)*log(d*(-b^(1/4)*x+sqrt(-sqrt(-a)))/(b^(1/4)*c+d*sqrt(-sqrt(-a))))/a-1/4*polylog(2,b^(1/4)*(c+d*x)/(b^(1/4)*c-(-a)^(1/4)*d))/a-1/4*polylog(2,b^(1/4)*(c+d*x)/(b^(1/4)*c+(-a)^(1/4)*d))/a+polylog(2,1+d*x/c)/a-1/4*polylog(2,b^(1/4)*(c+d*x)/(b^(1/4)*c-d*sqrt(-sqrt(-a))))/a-1/4*polylog(2,b^(1/4)*(c+d*x)/(b^(1/4)*c+d*sqrt(-sqrt(-a))))/a],
[x^5*log(c+d*x)/(a+b*x^4),x,23,1/2*c*x/(b*d)-1/4*x^2/b-1/2*c^2*log(c+d*x)/(b*d^2)+1/2*x^2*log(c+d*x)/b+1/4*log(d*((-a)^(1/4)-b^(1/4)*x)/(b^(1/4)*c+(-a)^(1/4)*d))*log(c+d*x)*sqrt(-a)/b^(3/2)+1/4*log(-d*((-a)^(1/4)+b^(1/4)*x)/(b^(1/4)*c-(-a)^(1/4)*d))*log(c+d*x)*sqrt(-a)/b^(3/2)-1/4*log(c+d*x)*log(-d*(b^(1/4)*x+sqrt(-sqrt(-a)))/(b^(1/4)*c-d*sqrt(-sqrt(-a))))*sqrt(-a)/b^(3/2)-1/4*log(c+d*x)*log(d*(-b^(1/4)*x+sqrt(-sqrt(-a)))/(b^(1/4)*c+d*sqrt(-sqrt(-a))))*sqrt(-a)/b^(3/2)+1/4*polylog(2,b^(1/4)*(c+d*x)/(b^(1/4)*c-(-a)^(1/4)*d))*sqrt(-a)/b^(3/2)+1/4*polylog(2,b^(1/4)*(c+d*x)/(b^(1/4)*c+(-a)^(1/4)*d))*sqrt(-a)/b^(3/2)-1/4*polylog(2,b^(1/4)*(c+d*x)/(b^(1/4)*c-d*sqrt(-sqrt(-a))))*sqrt(-a)/b^(3/2)-1/4*polylog(2,b^(1/4)*(c+d*x)/(b^(1/4)*c+d*sqrt(-sqrt(-a))))*sqrt(-a)/b^(3/2)],
[x*log(c+d*x)/(a+b*x^4),x,18,1/4*log(d*((-a)^(1/4)-b^(1/4)*x)/(b^(1/4)*c+(-a)^(1/4)*d))*log(c+d*x)/(sqrt(-a)*sqrt(b))+1/4*log(-d*((-a)^(1/4)+b^(1/4)*x)/(b^(1/4)*c-(-a)^(1/4)*d))*log(c+d*x)/(sqrt(-a)*sqrt(b))-1/4*log(c+d*x)*log(-d*(b^(1/4)*x+sqrt(-sqrt(-a)))/(b^(1/4)*c-d*sqrt(-sqrt(-a))))/(sqrt(-a)*sqrt(b))-1/4*log(c+d*x)*log(d*(-b^(1/4)*x+sqrt(-sqrt(-a)))/(b^(1/4)*c+d*sqrt(-sqrt(-a))))/(sqrt(-a)*sqrt(b))+1/4*polylog(2,b^(1/4)*(c+d*x)/(b^(1/4)*c-(-a)^(1/4)*d))/(sqrt(-a)*sqrt(b))+1/4*polylog(2,b^(1/4)*(c+d*x)/(b^(1/4)*c+(-a)^(1/4)*d))/(sqrt(-a)*sqrt(b))-1/4*polylog(2,b^(1/4)*(c+d*x)/(b^(1/4)*c-d*sqrt(-sqrt(-a))))/(sqrt(-a)*sqrt(b))-1/4*polylog(2,b^(1/4)*(c+d*x)/(b^(1/4)*c+d*sqrt(-sqrt(-a))))/(sqrt(-a)*sqrt(b))],
[log(c+d*x)/(x^3*(a+b*x^4)),x,23,-1/2*d/(a*c*x)-1/2*d^2*log(x)/(a*c^2)+1/2*d^2*log(c+d*x)/(a*c^2)-1/2*log(c+d*x)/(a*x^2)+1/4*log(d*((-a)^(1/4)-b^(1/4)*x)/(b^(1/4)*c+(-a)^(1/4)*d))*log(c+d*x)*sqrt(b)/(-a)^(3/2)+1/4*log(-d*((-a)^(1/4)+b^(1/4)*x)/(b^(1/4)*c-(-a)^(1/4)*d))*log(c+d*x)*sqrt(b)/(-a)^(3/2)-1/4*log(c+d*x)*log(-d*(b^(1/4)*x+sqrt(-sqrt(-a)))/(b^(1/4)*c-d*sqrt(-sqrt(-a))))*sqrt(b)/(-a)^(3/2)-1/4*log(c+d*x)*log(d*(-b^(1/4)*x+sqrt(-sqrt(-a)))/(b^(1/4)*c+d*sqrt(-sqrt(-a))))*sqrt(b)/(-a)^(3/2)+1/4*polylog(2,b^(1/4)*(c+d*x)/(b^(1/4)*c-(-a)^(1/4)*d))*sqrt(b)/(-a)^(3/2)+1/4*polylog(2,b^(1/4)*(c+d*x)/(b^(1/4)*c+(-a)^(1/4)*d))*sqrt(b)/(-a)^(3/2)-1/4*polylog(2,b^(1/4)*(c+d*x)/(b^(1/4)*c-d*sqrt(-sqrt(-a))))*sqrt(b)/(-a)^(3/2)-1/4*polylog(2,b^(1/4)*(c+d*x)/(b^(1/4)*c+d*sqrt(-sqrt(-a))))*sqrt(b)/(-a)^(3/2)],
[x^4*log(c+d*x)/(a+b*x^4),x,22,-x/b+(c+d*x)*log(c+d*x)/(b*d)+1/4*(-a)^(1/4)*log(d*((-a)^(1/4)-b^(1/4)*x)/(b^(1/4)*c+(-a)^(1/4)*d))*log(c+d*x)/b^(5/4)-1/4*(-a)^(1/4)*log(-d*((-a)^(1/4)+b^(1/4)*x)/(b^(1/4)*c-(-a)^(1/4)*d))*log(c+d*x)/b^(5/4)-1/4*(-a)^(1/4)*polylog(2,b^(1/4)*(c+d*x)/(b^(1/4)*c-(-a)^(1/4)*d))/b^(5/4)+1/4*(-a)^(1/4)*polylog(2,b^(1/4)*(c+d*x)/(b^(1/4)*c+(-a)^(1/4)*d))/b^(5/4)-1/4*log(c+d*x)*log(-d*(b^(1/4)*x+sqrt(-sqrt(-a)))/(b^(1/4)*c-d*sqrt(-sqrt(-a))))*sqrt(-sqrt(-a))/b^(5/4)+1/4*log(c+d*x)*log(d*(-b^(1/4)*x+sqrt(-sqrt(-a)))/(b^(1/4)*c+d*sqrt(-sqrt(-a))))*sqrt(-sqrt(-a))/b^(5/4)-1/4*polylog(2,b^(1/4)*(c+d*x)/(b^(1/4)*c-d*sqrt(-sqrt(-a))))*sqrt(-sqrt(-a))/b^(5/4)+1/4*polylog(2,b^(1/4)*(c+d*x)/(b^(1/4)*c+d*sqrt(-sqrt(-a))))*sqrt(-sqrt(-a))/b^(5/4)],
[x^2*log(c+d*x)/(a+b*x^4),x,18,1/4*log(d*((-a)^(1/4)-b^(1/4)*x)/(b^(1/4)*c+(-a)^(1/4)*d))*log(c+d*x)/((-a)^(1/4)*b^(3/4))-1/4*log(-d*((-a)^(1/4)+b^(1/4)*x)/(b^(1/4)*c-(-a)^(1/4)*d))*log(c+d*x)/((-a)^(1/4)*b^(3/4))-1/4*polylog(2,b^(1/4)*(c+d*x)/(b^(1/4)*c-(-a)^(1/4)*d))/((-a)^(1/4)*b^(3/4))+1/4*polylog(2,b^(1/4)*(c+d*x)/(b^(1/4)*c+(-a)^(1/4)*d))/((-a)^(1/4)*b^(3/4))-1/4*log(c+d*x)*log(-d*(b^(1/4)*x+sqrt(-sqrt(-a)))/(b^(1/4)*c-d*sqrt(-sqrt(-a))))/(b^(3/4)*sqrt(-sqrt(-a)))+1/4*log(c+d*x)*log(d*(-b^(1/4)*x+sqrt(-sqrt(-a)))/(b^(1/4)*c+d*sqrt(-sqrt(-a))))/(b^(3/4)*sqrt(-sqrt(-a)))-1/4*polylog(2,b^(1/4)*(c+d*x)/(b^(1/4)*c-d*sqrt(-sqrt(-a))))/(b^(3/4)*sqrt(-sqrt(-a)))+1/4*polylog(2,b^(1/4)*(c+d*x)/(b^(1/4)*c+d*sqrt(-sqrt(-a))))/(b^(3/4)*sqrt(-sqrt(-a)))],
[log(c+d*x)/(a+b*x^4),x,18,1/4*log(d*((-a)^(1/4)-b^(1/4)*x)/(b^(1/4)*c+(-a)^(1/4)*d))*log(c+d*x)/((-a)^(3/4)*b^(1/4))-1/4*log(-d*((-a)^(1/4)+b^(1/4)*x)/(b^(1/4)*c-(-a)^(1/4)*d))*log(c+d*x)/((-a)^(3/4)*b^(1/4))-1/4*polylog(2,b^(1/4)*(c+d*x)/(b^(1/4)*c-(-a)^(1/4)*d))/((-a)^(3/4)*b^(1/4))+1/4*polylog(2,b^(1/4)*(c+d*x)/(b^(1/4)*c+(-a)^(1/4)*d))/((-a)^(3/4)*b^(1/4))-1/4*log(c+d*x)*log(-d*(b^(1/4)*x+sqrt(-sqrt(-a)))/(b^(1/4)*c-d*sqrt(-sqrt(-a))))/(b^(1/4)*(-sqrt(-a))^(3/2))+1/4*log(c+d*x)*log(d*(-b^(1/4)*x+sqrt(-sqrt(-a)))/(b^(1/4)*c+d*sqrt(-sqrt(-a))))/(b^(1/4)*(-sqrt(-a))^(3/2))-1/4*polylog(2,b^(1/4)*(c+d*x)/(b^(1/4)*c-d*sqrt(-sqrt(-a))))/(b^(1/4)*(-sqrt(-a))^(3/2))+1/4*polylog(2,b^(1/4)*(c+d*x)/(b^(1/4)*c+d*sqrt(-sqrt(-a))))/(b^(1/4)*(-sqrt(-a))^(3/2))],
[log(c+d*x)/(x^2*(a+b*x^4)),x,24,d*log(x)/(a*c)-d*log(c+d*x)/(a*c)-log(c+d*x)/(a*x)+1/4*b^(1/4)*log(d*((-a)^(1/4)-b^(1/4)*x)/(b^(1/4)*c+(-a)^(1/4)*d))*log(c+d*x)/(-a)^(5/4)-1/4*b^(1/4)*log(-d*((-a)^(1/4)+b^(1/4)*x)/(b^(1/4)*c-(-a)^(1/4)*d))*log(c+d*x)/(-a)^(5/4)-1/4*b^(1/4)*polylog(2,b^(1/4)*(c+d*x)/(b^(1/4)*c-(-a)^(1/4)*d))/(-a)^(5/4)+1/4*b^(1/4)*polylog(2,b^(1/4)*(c+d*x)/(b^(1/4)*c+(-a)^(1/4)*d))/(-a)^(5/4)-1/4*b^(1/4)*log(c+d*x)*log(-d*(b^(1/4)*x+sqrt(-sqrt(-a)))/(b^(1/4)*c-d*sqrt(-sqrt(-a))))/(-sqrt(-a))^(5/2)+1/4*b^(1/4)*log(c+d*x)*log(d*(-b^(1/4)*x+sqrt(-sqrt(-a)))/(b^(1/4)*c+d*sqrt(-sqrt(-a))))/(-sqrt(-a))^(5/2)-1/4*b^(1/4)*polylog(2,b^(1/4)*(c+d*x)/(b^(1/4)*c-d*sqrt(-sqrt(-a))))/(-sqrt(-a))^(5/2)+1/4*b^(1/4)*polylog(2,b^(1/4)*(c+d*x)/(b^(1/4)*c+d*sqrt(-sqrt(-a))))/(-sqrt(-a))^(5/2)],

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

# q>0
[(f+g/x)*x*(a+b*log(c*(d+e*x)^n)),x,4,1/2*b*(d*f-e*g)*n*x/e-1/4*b*n*(g+f*x)^2/f-1/2*b*(d*f-e*g)^2*n*log(d+e*x)/(e^2*f)+1/2*(g+f*x)^2*(a+b*log(c*(d+e*x)^n))/f],
[(f+g/x)^2*x^2*(a+b*log(c*(d+e*x)^n)),x,4,-1/3*b*(d*f-e*g)^2*n*x/e^2+1/6*b*(d*f-e*g)*n*(g+f*x)^2/(e*f)-1/9*b*n*(g+f*x)^3/f+1/3*b*(d*f-e*g)^3*n*log(d+e*x)/(e^3*f)+1/3*(g+f*x)^3*(a+b*log(c*(d+e*x)^n))/f],
[(f+g/x)^3*x^3*(a+b*log(c*(d+e*x)^n)),x,4,1/4*b*(d*f-e*g)^3*n*x/e^3-1/8*b*(d*f-e*g)^2*n*(g+f*x)^2/(e^2*f)+1/12*b*(d*f-e*g)*n*(g+f*x)^3/(e*f)-1/16*b*n*(g+f*x)^4/f-1/4*b*(d*f-e*g)^4*n*log(d+e*x)/(e^4*f)+1/4*(g+f*x)^4*(a+b*log(c*(d+e*x)^n))/f],

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

# Integrands of the form x^m (f+g / x^2)^q (a+b Log[c (d+e x)^n])
[log(a+b*x)/(c+d/x^2),x,12,-x/c+(a+b*x)*log(a+b*x)/(b*c)+1/2*log(a+b*x)*log(-b*(x*sqrt(-c)+sqrt(d))/(a*sqrt(-c)-b*sqrt(d)))*sqrt(d)/(-c)^(3/2)-1/2*log(a+b*x)*log(b*(-x*sqrt(-c)+sqrt(d))/(a*sqrt(-c)+b*sqrt(d)))*sqrt(d)/(-c)^(3/2)+1/2*polylog(2,(a+b*x)*sqrt(-c)/(a*sqrt(-c)-b*sqrt(d)))*sqrt(d)/(-c)^(3/2)-1/2*polylog(2,(a+b*x)*sqrt(-c)/(a*sqrt(-c)+b*sqrt(d)))*sqrt(d)/(-c)^(3/2)],

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

# q>0

# q>0
[x^5*(a+b*log(c*(d+e*x)^n))^2/(f+g*x^2),x,28,-2*a*b*d*f*n*x/(e*g^2)+2*b^2*d*f*n^2*x/(e*g^2)-2*b^2*d^3*n^2*x/(e^3*g)-1/4*b^2*f*n^2*(d+e*x)^2/(e^2*g^2)+3/4*b^2*d^2*n^2*(d+e*x)^2/(e^4*g)-2/9*b^2*d*n^2*(d+e*x)^3/(e^4*g)+1/32*b^2*n^2*(d+e*x)^4/(e^4*g)+1/4*b^2*d^4*n^2*log(d+e*x)^2/(e^4*g)-2*b^2*d*f*n*(d+e*x)*log(c*(d+e*x)^n)/(e^2*g^2)+2*b*d^3*n*(d+e*x)*(a+b*log(c*(d+e*x)^n))/(e^4*g)+1/2*b*f*n*(d+e*x)^2*(a+b*log(c*(d+e*x)^n))/(e^2*g^2)-3/2*b*d^2*n*(d+e*x)^2*(a+b*log(c*(d+e*x)^n))/(e^4*g)+2/3*b*d*n*(d+e*x)^3*(a+b*log(c*(d+e*x)^n))/(e^4*g)-1/8*b*n*(d+e*x)^4*(a+b*log(c*(d+e*x)^n))/(e^4*g)-1/2*b*d^4*n*log(d+e*x)*(a+b*log(c*(d+e*x)^n))/(e^4*g)+1/4*x^4*(a+b*log(c*(d+e*x)^n))^2/g+d*f*(d+e*x)*(a+b*log(c*(d+e*x)^n))^2/(e^2*g^2)-1/2*f*(d+e*x)^2*(a+b*log(c*(d+e*x)^n))^2/(e^2*g^2)+1/2*f^2*(a+b*log(c*(d+e*x)^n))^2*log(e*(sqrt(-f)-x*sqrt(g))/(e*sqrt(-f)+d*sqrt(g)))/g^3+1/2*f^2*(a+b*log(c*(d+e*x)^n))^2*log(e*(sqrt(-f)+x*sqrt(g))/(e*sqrt(-f)-d*sqrt(g)))/g^3+b*f^2*n*(a+b*log(c*(d+e*x)^n))*polylog(2,-(d+e*x)*sqrt(g)/(e*sqrt(-f)-d*sqrt(g)))/g^3+b*f^2*n*(a+b*log(c*(d+e*x)^n))*polylog(2,(d+e*x)*sqrt(g)/(e*sqrt(-f)+d*sqrt(g)))/g^3-b^2*f^2*n^2*polylog(3,-(d+e*x)*sqrt(g)/(e*sqrt(-f)-d*sqrt(g)))/g^3-b^2*f^2*n^2*polylog(3,(d+e*x)*sqrt(g)/(e*sqrt(-f)+d*sqrt(g)))/g^3],
[x^3*(a+b*log(c*(d+e*x)^n))^2/(f+g*x^2),x,21,2*a*b*d*n*x/(e*g)-2*b^2*d*n^2*x/(e*g)+1/4*b^2*n^2*(d+e*x)^2/(e^2*g)+2*b^2*d*n*(d+e*x)*log(c*(d+e*x)^n)/(e^2*g)-1/2*b*n*(d+e*x)^2*(a+b*log(c*(d+e*x)^n))/(e^2*g)-d*(d+e*x)*(a+b*log(c*(d+e*x)^n))^2/(e^2*g)+1/2*(d+e*x)^2*(a+b*log(c*(d+e*x)^n))^2/(e^2*g)-1/2*f*(a+b*log(c*(d+e*x)^n))^2*log(e*(sqrt(-f)-x*sqrt(g))/(e*sqrt(-f)+d*sqrt(g)))/g^2-1/2*f*(a+b*log(c*(d+e*x)^n))^2*log(e*(sqrt(-f)+x*sqrt(g))/(e*sqrt(-f)-d*sqrt(g)))/g^2-b*f*n*(a+b*log(c*(d+e*x)^n))*polylog(2,-(d+e*x)*sqrt(g)/(e*sqrt(-f)-d*sqrt(g)))/g^2-b*f*n*(a+b*log(c*(d+e*x)^n))*polylog(2,(d+e*x)*sqrt(g)/(e*sqrt(-f)+d*sqrt(g)))/g^2+b^2*f*n^2*polylog(3,-(d+e*x)*sqrt(g)/(e*sqrt(-f)-d*sqrt(g)))/g^2+b^2*f*n^2*polylog(3,(d+e*x)*sqrt(g)/(e*sqrt(-f)+d*sqrt(g)))/g^2],
[x*(a+b*log(c*(d+e*x)^n))^2/(f+g*x^2),x,10,1/2*(a+b*log(c*(d+e*x)^n))^2*log(e*(sqrt(-f)-x*sqrt(g))/(e*sqrt(-f)+d*sqrt(g)))/g+1/2*(a+b*log(c*(d+e*x)^n))^2*log(e*(sqrt(-f)+x*sqrt(g))/(e*sqrt(-f)-d*sqrt(g)))/g+b*n*(a+b*log(c*(d+e*x)^n))*polylog(2,-(d+e*x)*sqrt(g)/(e*sqrt(-f)-d*sqrt(g)))/g+b*n*(a+b*log(c*(d+e*x)^n))*polylog(2,(d+e*x)*sqrt(g)/(e*sqrt(-f)+d*sqrt(g)))/g-b^2*n^2*polylog(3,-(d+e*x)*sqrt(g)/(e*sqrt(-f)-d*sqrt(g)))/g-b^2*n^2*polylog(3,(d+e*x)*sqrt(g)/(e*sqrt(-f)+d*sqrt(g)))/g],
[(a+b*log(c*(d+e*x)^n))^2/(x*(f+g*x^2)),x,16,log(-e*x/d)*(a+b*log(c*(d+e*x)^n))^2/f-1/2*(a+b*log(c*(d+e*x)^n))^2*log(e*(sqrt(-f)-x*sqrt(g))/(e*sqrt(-f)+d*sqrt(g)))/f-1/2*(a+b*log(c*(d+e*x)^n))^2*log(e*(sqrt(-f)+x*sqrt(g))/(e*sqrt(-f)-d*sqrt(g)))/f+2*b*n*(a+b*log(c*(d+e*x)^n))*polylog(2,1+e*x/d)/f-b*n*(a+b*log(c*(d+e*x)^n))*polylog(2,-(d+e*x)*sqrt(g)/(e*sqrt(-f)-d*sqrt(g)))/f-b*n*(a+b*log(c*(d+e*x)^n))*polylog(2,(d+e*x)*sqrt(g)/(e*sqrt(-f)+d*sqrt(g)))/f-2*b^2*n^2*polylog(3,1+e*x/d)/f+b^2*n^2*polylog(3,-(d+e*x)*sqrt(g)/(e*sqrt(-f)-d*sqrt(g)))/f+b^2*n^2*polylog(3,(d+e*x)*sqrt(g)/(e*sqrt(-f)+d*sqrt(g)))/f],
[(a+b*log(c*(d+e*x)^n))^2/(x^3*(f+g*x^2)),x,23,b^2*e^2*n^2*log(x)/(d^2*f)-b*e*n*(d+e*x)*(a+b*log(c*(d+e*x)^n))/(d^2*f*x)-1/2*(a+b*log(c*(d+e*x)^n))^2/(f*x^2)-g*log(-e*x/d)*(a+b*log(c*(d+e*x)^n))^2/f^2-b*e^2*n*(a+b*log(c*(d+e*x)^n))*log(1-d/(d+e*x))/(d^2*f)+1/2*g*(a+b*log(c*(d+e*x)^n))^2*log(e*(sqrt(-f)-x*sqrt(g))/(e*sqrt(-f)+d*sqrt(g)))/f^2+1/2*g*(a+b*log(c*(d+e*x)^n))^2*log(e*(sqrt(-f)+x*sqrt(g))/(e*sqrt(-f)-d*sqrt(g)))/f^2+b^2*e^2*n^2*polylog(2,d/(d+e*x))/(d^2*f)-2*b*g*n*(a+b*log(c*(d+e*x)^n))*polylog(2,1+e*x/d)/f^2+b*g*n*(a+b*log(c*(d+e*x)^n))*polylog(2,-(d+e*x)*sqrt(g)/(e*sqrt(-f)-d*sqrt(g)))/f^2+b*g*n*(a+b*log(c*(d+e*x)^n))*polylog(2,(d+e*x)*sqrt(g)/(e*sqrt(-f)+d*sqrt(g)))/f^2+2*b^2*g*n^2*polylog(3,1+e*x/d)/f^2-b^2*g*n^2*polylog(3,-(d+e*x)*sqrt(g)/(e*sqrt(-f)-d*sqrt(g)))/f^2-b^2*g*n^2*polylog(3,(d+e*x)*sqrt(g)/(e*sqrt(-f)+d*sqrt(g)))/f^2],
[x^4*(a+b*log(c*(d+e*x)^n))^2/(f+g*x^2),x,23,2*a*b*f*n*x/g^2-2*b^2*f*n^2*x/g^2+2*b^2*d^2*n^2*x/(e^2*g)-1/2*b^2*d*n^2*(d+e*x)^2/(e^3*g)+2/27*b^2*n^2*(d+e*x)^3/(e^3*g)-1/3*b^2*d^3*n^2*log(d+e*x)^2/(e^3*g)+2*b^2*f*n*(d+e*x)*log(c*(d+e*x)^n)/(e*g^2)-2*b*d^2*n*(d+e*x)*(a+b*log(c*(d+e*x)^n))/(e^3*g)+b*d*n*(d+e*x)^2*(a+b*log(c*(d+e*x)^n))/(e^3*g)-2/9*b*n*(d+e*x)^3*(a+b*log(c*(d+e*x)^n))/(e^3*g)+2/3*b*d^3*n*log(d+e*x)*(a+b*log(c*(d+e*x)^n))/(e^3*g)+1/3*x^3*(a+b*log(c*(d+e*x)^n))^2/g-f*(d+e*x)*(a+b*log(c*(d+e*x)^n))^2/(e*g^2)+1/2*(-f)^(3/2)*(a+b*log(c*(d+e*x)^n))^2*log(e*(sqrt(-f)-x*sqrt(g))/(e*sqrt(-f)+d*sqrt(g)))/g^(5/2)-1/2*(-f)^(3/2)*(a+b*log(c*(d+e*x)^n))^2*log(e*(sqrt(-f)+x*sqrt(g))/(e*sqrt(-f)-d*sqrt(g)))/g^(5/2)-b*(-f)^(3/2)*n*(a+b*log(c*(d+e*x)^n))*polylog(2,-(d+e*x)*sqrt(g)/(e*sqrt(-f)-d*sqrt(g)))/g^(5/2)+b*(-f)^(3/2)*n*(a+b*log(c*(d+e*x)^n))*polylog(2,(d+e*x)*sqrt(g)/(e*sqrt(-f)+d*sqrt(g)))/g^(5/2)+b^2*(-f)^(3/2)*n^2*polylog(3,-(d+e*x)*sqrt(g)/(e*sqrt(-f)-d*sqrt(g)))/g^(5/2)-b^2*(-f)^(3/2)*n^2*polylog(3,(d+e*x)*sqrt(g)/(e*sqrt(-f)+d*sqrt(g)))/g^(5/2)],
[x^2*(a+b*log(c*(d+e*x)^n))^2/(f+g*x^2),x,16,-2*a*b*n*x/g+2*b^2*n^2*x/g-2*b^2*n*(d+e*x)*log(c*(d+e*x)^n)/(e*g)+(d+e*x)*(a+b*log(c*(d+e*x)^n))^2/(e*g)+1/2*(a+b*log(c*(d+e*x)^n))^2*log(e*(sqrt(-f)-x*sqrt(g))/(e*sqrt(-f)+d*sqrt(g)))*sqrt(-f)/g^(3/2)-1/2*(a+b*log(c*(d+e*x)^n))^2*log(e*(sqrt(-f)+x*sqrt(g))/(e*sqrt(-f)-d*sqrt(g)))*sqrt(-f)/g^(3/2)-b*n*(a+b*log(c*(d+e*x)^n))*polylog(2,-(d+e*x)*sqrt(g)/(e*sqrt(-f)-d*sqrt(g)))*sqrt(-f)/g^(3/2)+b*n*(a+b*log(c*(d+e*x)^n))*polylog(2,(d+e*x)*sqrt(g)/(e*sqrt(-f)+d*sqrt(g)))*sqrt(-f)/g^(3/2)+b^2*n^2*polylog(3,-(d+e*x)*sqrt(g)/(e*sqrt(-f)-d*sqrt(g)))*sqrt(-f)/g^(3/2)-b^2*n^2*polylog(3,(d+e*x)*sqrt(g)/(e*sqrt(-f)+d*sqrt(g)))*sqrt(-f)/g^(3/2)],
[(a+b*log(c*(d+e*x)^n))^2/(f+g*x^2),x,10,1/2*(a+b*log(c*(d+e*x)^n))^2*log(e*(sqrt(-f)-x*sqrt(g))/(e*sqrt(-f)+d*sqrt(g)))/(sqrt(-f)*sqrt(g))-1/2*(a+b*log(c*(d+e*x)^n))^2*log(e*(sqrt(-f)+x*sqrt(g))/(e*sqrt(-f)-d*sqrt(g)))/(sqrt(-f)*sqrt(g))-b*n*(a+b*log(c*(d+e*x)^n))*polylog(2,-(d+e*x)*sqrt(g)/(e*sqrt(-f)-d*sqrt(g)))/(sqrt(-f)*sqrt(g))+b*n*(a+b*log(c*(d+e*x)^n))*polylog(2,(d+e*x)*sqrt(g)/(e*sqrt(-f)+d*sqrt(g)))/(sqrt(-f)*sqrt(g))+b^2*n^2*polylog(3,-(d+e*x)*sqrt(g)/(e*sqrt(-f)-d*sqrt(g)))/(sqrt(-f)*sqrt(g))-b^2*n^2*polylog(3,(d+e*x)*sqrt(g)/(e*sqrt(-f)+d*sqrt(g)))/(sqrt(-f)*sqrt(g))],
[(a+b*log(c*(d+e*x)^n))^2/(x^2*(f+g*x^2)),x,15,2*b*e*n*log(-e*x/d)*(a+b*log(c*(d+e*x)^n))/(d*f)-(d+e*x)*(a+b*log(c*(d+e*x)^n))^2/(d*f*x)+2*b^2*e*n^2*polylog(2,1+e*x/d)/(d*f)+1/2*(a+b*log(c*(d+e*x)^n))^2*log(e*(sqrt(-f)-x*sqrt(g))/(e*sqrt(-f)+d*sqrt(g)))*sqrt(g)/(-f)^(3/2)-1/2*(a+b*log(c*(d+e*x)^n))^2*log(e*(sqrt(-f)+x*sqrt(g))/(e*sqrt(-f)-d*sqrt(g)))*sqrt(g)/(-f)^(3/2)-b*n*(a+b*log(c*(d+e*x)^n))*polylog(2,-(d+e*x)*sqrt(g)/(e*sqrt(-f)-d*sqrt(g)))*sqrt(g)/(-f)^(3/2)+b*n*(a+b*log(c*(d+e*x)^n))*polylog(2,(d+e*x)*sqrt(g)/(e*sqrt(-f)+d*sqrt(g)))*sqrt(g)/(-f)^(3/2)+b^2*n^2*polylog(3,-(d+e*x)*sqrt(g)/(e*sqrt(-f)-d*sqrt(g)))*sqrt(g)/(-f)^(3/2)-b^2*n^2*polylog(3,(d+e*x)*sqrt(g)/(e*sqrt(-f)+d*sqrt(g)))*sqrt(g)/(-f)^(3/2)],
[(a+b*log(c*(d+e*x)^n))^2/(x^4*(f+g*x^2)),x,26,-1/3*b^2*e^2*n^2/(d^2*f*x)-b^2*e^3*n^2*log(x)/(d^3*f)+1/3*b^2*e^3*n^2*log(d+e*x)/(d^3*f)-1/3*b*e*n*(a+b*log(c*(d+e*x)^n))/(d*f*x^2)+2/3*b*e^2*n*(d+e*x)*(a+b*log(c*(d+e*x)^n))/(d^3*f*x)-2*b*e*g*n*log(-e*x/d)*(a+b*log(c*(d+e*x)^n))/(d*f^2)-1/3*(a+b*log(c*(d+e*x)^n))^2/(f*x^3)+g*(d+e*x)*(a+b*log(c*(d+e*x)^n))^2/(d*f^2*x)+2/3*b*e^3*n*(a+b*log(c*(d+e*x)^n))*log(1-d/(d+e*x))/(d^3*f)+1/2*g^(3/2)*(a+b*log(c*(d+e*x)^n))^2*log(e*(sqrt(-f)-x*sqrt(g))/(e*sqrt(-f)+d*sqrt(g)))/(-f)^(5/2)-1/2*g^(3/2)*(a+b*log(c*(d+e*x)^n))^2*log(e*(sqrt(-f)+x*sqrt(g))/(e*sqrt(-f)-d*sqrt(g)))/(-f)^(5/2)-2/3*b^2*e^3*n^2*polylog(2,d/(d+e*x))/(d^3*f)-2*b^2*e*g*n^2*polylog(2,1+e*x/d)/(d*f^2)-b*g^(3/2)*n*(a+b*log(c*(d+e*x)^n))*polylog(2,-(d+e*x)*sqrt(g)/(e*sqrt(-f)-d*sqrt(g)))/(-f)^(5/2)+b*g^(3/2)*n*(a+b*log(c*(d+e*x)^n))*polylog(2,(d+e*x)*sqrt(g)/(e*sqrt(-f)+d*sqrt(g)))/(-f)^(5/2)+b^2*g^(3/2)*n^2*polylog(3,-(d+e*x)*sqrt(g)/(e*sqrt(-f)-d*sqrt(g)))/(-f)^(5/2)-b^2*g^(3/2)*n^2*polylog(3,(d+e*x)*sqrt(g)/(e*sqrt(-f)+d*sqrt(g)))/(-f)^(5/2)],
[x^5*(a+b*log(c*(d+e*x)^n))^2/(f+g*x^2)^2,x,34,2*a*b*d*n*x/(e*g^2)-2*b^2*d*n^2*x/(e*g^2)+1/4*b^2*n^2*(d+e*x)^2/(e^2*g^2)+2*b^2*d*n*(d+e*x)*log(c*(d+e*x)^n)/(e^2*g^2)-1/2*b*n*(d+e*x)^2*(a+b*log(c*(d+e*x)^n))/(e^2*g^2)+1/2*e^2*f^2*(a+b*log(c*(d+e*x)^n))^2/(g^3*(e^2*f+d^2*g))-d*(d+e*x)*(a+b*log(c*(d+e*x)^n))^2/(e^2*g^2)+1/2*(d+e*x)^2*(a+b*log(c*(d+e*x)^n))^2/(e^2*g^2)-1/2*f^2*(a+b*log(c*(d+e*x)^n))^2/(g^3*(f+g*x^2))-f*(a+b*log(c*(d+e*x)^n))^2*log(e*(sqrt(-f)-x*sqrt(g))/(e*sqrt(-f)+d*sqrt(g)))/g^3-f*(a+b*log(c*(d+e*x)^n))^2*log(e*(sqrt(-f)+x*sqrt(g))/(e*sqrt(-f)-d*sqrt(g)))/g^3-2*b*f*n*(a+b*log(c*(d+e*x)^n))*polylog(2,-(d+e*x)*sqrt(g)/(e*sqrt(-f)-d*sqrt(g)))/g^3-2*b*f*n*(a+b*log(c*(d+e*x)^n))*polylog(2,(d+e*x)*sqrt(g)/(e*sqrt(-f)+d*sqrt(g)))/g^3+2*b^2*f*n^2*polylog(3,-(d+e*x)*sqrt(g)/(e*sqrt(-f)-d*sqrt(g)))/g^3+2*b^2*f*n^2*polylog(3,(d+e*x)*sqrt(g)/(e*sqrt(-f)+d*sqrt(g)))/g^3-1/2*b^2*e*(-f)^(3/2)*n^2*polylog(2,(d+e*x)*sqrt(g)/(e*sqrt(-f)+d*sqrt(g)))*(e*sqrt(-f)-d*sqrt(g))/(g^3*(e^2*f+d^2*g))-1/2*b*e*(-f)^(3/2)*n*(a+b*log(c*(d+e*x)^n))*log(e*(sqrt(-f)+x*sqrt(g))/(e*sqrt(-f)-d*sqrt(g)))*(e*sqrt(-f)+d*sqrt(g))/(g^3*(e^2*f+d^2*g))-1/2*b^2*e*(-f)^(3/2)*n^2*polylog(2,-(d+e*x)*sqrt(g)/(e*sqrt(-f)-d*sqrt(g)))*(e*sqrt(-f)+d*sqrt(g))/(g^3*(e^2*f+d^2*g))-1/2*b*e*f*n*(a+b*log(c*(d+e*x)^n))*log(e*(sqrt(-f)-x*sqrt(g))/(e*sqrt(-f)+d*sqrt(g)))*(e*f+d*sqrt(-f)*sqrt(g))/(g^3*(e^2*f+d^2*g))],
[x^3*(a+b*log(c*(d+e*x)^n))^2/(f+g*x^2)^2,x,25,-1/2*e^2*f*(a+b*log(c*(d+e*x)^n))^2/(g^2*(e^2*f+d^2*g))+1/2*f*(a+b*log(c*(d+e*x)^n))^2/(g^2*(f+g*x^2))+1/2*(a+b*log(c*(d+e*x)^n))^2*log(e*(sqrt(-f)-x*sqrt(g))/(e*sqrt(-f)+d*sqrt(g)))/g^2+1/2*(a+b*log(c*(d+e*x)^n))^2*log(e*(sqrt(-f)+x*sqrt(g))/(e*sqrt(-f)-d*sqrt(g)))/g^2+b*n*(a+b*log(c*(d+e*x)^n))*polylog(2,-(d+e*x)*sqrt(g)/(e*sqrt(-f)-d*sqrt(g)))/g^2+b*n*(a+b*log(c*(d+e*x)^n))*polylog(2,(d+e*x)*sqrt(g)/(e*sqrt(-f)+d*sqrt(g)))/g^2-b^2*n^2*polylog(3,-(d+e*x)*sqrt(g)/(e*sqrt(-f)-d*sqrt(g)))/g^2-b^2*n^2*polylog(3,(d+e*x)*sqrt(g)/(e*sqrt(-f)+d*sqrt(g)))/g^2-1/2*b^2*e*n^2*polylog(2,-(d+e*x)*sqrt(g)/(e*sqrt(-f)-d*sqrt(g)))*sqrt(-f)*(e*sqrt(-f)+d*sqrt(g))/(g^2*(e^2*f+d^2*g))+1/2*b*e*n*(a+b*log(c*(d+e*x)^n))*log(e*(sqrt(-f)+x*sqrt(g))/(e*sqrt(-f)-d*sqrt(g)))*(e*f-d*sqrt(-f)*sqrt(g))/(g^2*(e^2*f+d^2*g))+1/2*b*e*n*(a+b*log(c*(d+e*x)^n))*log(e*(sqrt(-f)-x*sqrt(g))/(e*sqrt(-f)+d*sqrt(g)))*(e*f+d*sqrt(-f)*sqrt(g))/(g^2*(e^2*f+d^2*g))+1/2*b^2*e*n^2*polylog(2,(d+e*x)*sqrt(g)/(e*sqrt(-f)+d*sqrt(g)))*(e*f+d*sqrt(-f)*sqrt(g))/(g^2*(e^2*f+d^2*g))],
[x*(a+b*log(c*(d+e*x)^n))^2/(f+g*x^2)^2,x,13,1/2*e^2*(a+b*log(c*(d+e*x)^n))^2/(g*(e^2*f+d^2*g))-1/2*(a+b*log(c*(d+e*x)^n))^2/(g*(f+g*x^2))-1/2*b^2*e*n^2*polylog(2,-(d+e*x)*sqrt(g)/(e*sqrt(-f)-d*sqrt(g)))*(e*sqrt(-f)+d*sqrt(g))/(g*(e^2*f+d^2*g)*sqrt(-f))-1/2*b*e*n*(a+b*log(c*(d+e*x)^n))*log(e*(sqrt(-f)+x*sqrt(g))/(e*sqrt(-f)-d*sqrt(g)))*(e*f-d*sqrt(-f)*sqrt(g))/(f*g*(e^2*f+d^2*g))-1/2*b*e*n*(a+b*log(c*(d+e*x)^n))*log(e*(sqrt(-f)-x*sqrt(g))/(e*sqrt(-f)+d*sqrt(g)))*(e*f+d*sqrt(-f)*sqrt(g))/(f*g*(e^2*f+d^2*g))-1/2*b^2*e*n^2*polylog(2,(d+e*x)*sqrt(g)/(e*sqrt(-f)+d*sqrt(g)))*(e*f+d*sqrt(-f)*sqrt(g))/(f*g*(e^2*f+d^2*g))],
[(a+b*log(c*(d+e*x)^n))^2/(x*(f+g*x^2)^2),x,29,-1/2*e^2*(a+b*log(c*(d+e*x)^n))^2/(f*(e^2*f+d^2*g))+1/2*(a+b*log(c*(d+e*x)^n))^2/(f*(f+g*x^2))+log(-e*x/d)*(a+b*log(c*(d+e*x)^n))^2/f^2-1/2*(a+b*log(c*(d+e*x)^n))^2*log(e*(sqrt(-f)-x*sqrt(g))/(e*sqrt(-f)+d*sqrt(g)))/f^2-1/2*(a+b*log(c*(d+e*x)^n))^2*log(e*(sqrt(-f)+x*sqrt(g))/(e*sqrt(-f)-d*sqrt(g)))/f^2+2*b*n*(a+b*log(c*(d+e*x)^n))*polylog(2,1+e*x/d)/f^2-b*n*(a+b*log(c*(d+e*x)^n))*polylog(2,-(d+e*x)*sqrt(g)/(e*sqrt(-f)-d*sqrt(g)))/f^2-b*n*(a+b*log(c*(d+e*x)^n))*polylog(2,(d+e*x)*sqrt(g)/(e*sqrt(-f)+d*sqrt(g)))/f^2-2*b^2*n^2*polylog(3,1+e*x/d)/f^2+b^2*n^2*polylog(3,-(d+e*x)*sqrt(g)/(e*sqrt(-f)-d*sqrt(g)))/f^2+b^2*n^2*polylog(3,(d+e*x)*sqrt(g)/(e*sqrt(-f)+d*sqrt(g)))/f^2-1/2*b^2*e*n^2*polylog(2,-(d+e*x)*sqrt(g)/(e*sqrt(-f)-d*sqrt(g)))*(e*sqrt(-f)+d*sqrt(g))/((-f)^(3/2)*(e^2*f+d^2*g))+1/2*b*e*n*(a+b*log(c*(d+e*x)^n))*log(e*(sqrt(-f)+x*sqrt(g))/(e*sqrt(-f)-d*sqrt(g)))*(e*f-d*sqrt(-f)*sqrt(g))/(f^2*(e^2*f+d^2*g))+1/2*b*e*n*(a+b*log(c*(d+e*x)^n))*log(e*(sqrt(-f)-x*sqrt(g))/(e*sqrt(-f)+d*sqrt(g)))*(e*f+d*sqrt(-f)*sqrt(g))/(f^2*(e^2*f+d^2*g))+1/2*b^2*e*n^2*polylog(2,(d+e*x)*sqrt(g)/(e*sqrt(-f)+d*sqrt(g)))*(e*f+d*sqrt(-f)*sqrt(g))/(f^2*(e^2*f+d^2*g))],
[(a+b*log(c*(d+e*x)^n))^2/(x^3*(f+g*x^2)^2),x,36,b^2*e^2*n^2*log(x)/(d^2*f^2)-b*e*n*(d+e*x)*(a+b*log(c*(d+e*x)^n))/(d^2*f^2*x)+1/2*e^2*g*(a+b*log(c*(d+e*x)^n))^2/(f^2*(e^2*f+d^2*g))-1/2*(a+b*log(c*(d+e*x)^n))^2/(f^2*x^2)-1/2*g*(a+b*log(c*(d+e*x)^n))^2/(f^2*(f+g*x^2))-2*g*log(-e*x/d)*(a+b*log(c*(d+e*x)^n))^2/f^3-b*e^2*n*(a+b*log(c*(d+e*x)^n))*log(1-d/(d+e*x))/(d^2*f^2)+g*(a+b*log(c*(d+e*x)^n))^2*log(e*(sqrt(-f)-x*sqrt(g))/(e*sqrt(-f)+d*sqrt(g)))/f^3+g*(a+b*log(c*(d+e*x)^n))^2*log(e*(sqrt(-f)+x*sqrt(g))/(e*sqrt(-f)-d*sqrt(g)))/f^3+b^2*e^2*n^2*polylog(2,d/(d+e*x))/(d^2*f^2)-4*b*g*n*(a+b*log(c*(d+e*x)^n))*polylog(2,1+e*x/d)/f^3+2*b*g*n*(a+b*log(c*(d+e*x)^n))*polylog(2,-(d+e*x)*sqrt(g)/(e*sqrt(-f)-d*sqrt(g)))/f^3+2*b*g*n*(a+b*log(c*(d+e*x)^n))*polylog(2,(d+e*x)*sqrt(g)/(e*sqrt(-f)+d*sqrt(g)))/f^3+4*b^2*g*n^2*polylog(3,1+e*x/d)/f^3-2*b^2*g*n^2*polylog(3,-(d+e*x)*sqrt(g)/(e*sqrt(-f)-d*sqrt(g)))/f^3-2*b^2*g*n^2*polylog(3,(d+e*x)*sqrt(g)/(e*sqrt(-f)+d*sqrt(g)))/f^3-1/2*b^2*e*g*n^2*polylog(2,-(d+e*x)*sqrt(g)/(e*sqrt(-f)-d*sqrt(g)))*(e*sqrt(-f)+d*sqrt(g))/((-f)^(5/2)*(e^2*f+d^2*g))-1/2*b*e*g*n*(a+b*log(c*(d+e*x)^n))*log(e*(sqrt(-f)+x*sqrt(g))/(e*sqrt(-f)-d*sqrt(g)))*(e*f-d*sqrt(-f)*sqrt(g))/(f^3*(e^2*f+d^2*g))-1/2*b*e*g*n*(a+b*log(c*(d+e*x)^n))*log(e*(sqrt(-f)-x*sqrt(g))/(e*sqrt(-f)+d*sqrt(g)))*(e*f+d*sqrt(-f)*sqrt(g))/(f^3*(e^2*f+d^2*g))-1/2*b^2*e*g*n^2*polylog(2,(d+e*x)*sqrt(g)/(e*sqrt(-f)+d*sqrt(g)))*(e*f+d*sqrt(-f)*sqrt(g))/(f^3*(e^2*f+d^2*g))],
[x^4*(a+b*log(c*(d+e*x)^n))^2/(f+g*x^2)^2,x,36,-2*a*b*n*x/g^2+2*b^2*n^2*x/g^2-2*b^2*n*(d+e*x)*log(c*(d+e*x)^n)/(e*g^2)+(d+e*x)*(a+b*log(c*(d+e*x)^n))^2/(e*g^2)+3/4*(a+b*log(c*(d+e*x)^n))^2*log(e*(sqrt(-f)-x*sqrt(g))/(e*sqrt(-f)+d*sqrt(g)))*sqrt(-f)/g^(5/2)-3/4*(a+b*log(c*(d+e*x)^n))^2*log(e*(sqrt(-f)+x*sqrt(g))/(e*sqrt(-f)-d*sqrt(g)))*sqrt(-f)/g^(5/2)-3/2*b*n*(a+b*log(c*(d+e*x)^n))*polylog(2,-(d+e*x)*sqrt(g)/(e*sqrt(-f)-d*sqrt(g)))*sqrt(-f)/g^(5/2)+3/2*b*n*(a+b*log(c*(d+e*x)^n))*polylog(2,(d+e*x)*sqrt(g)/(e*sqrt(-f)+d*sqrt(g)))*sqrt(-f)/g^(5/2)+3/2*b^2*n^2*polylog(3,-(d+e*x)*sqrt(g)/(e*sqrt(-f)-d*sqrt(g)))*sqrt(-f)/g^(5/2)-3/2*b^2*n^2*polylog(3,(d+e*x)*sqrt(g)/(e*sqrt(-f)+d*sqrt(g)))*sqrt(-f)/g^(5/2)+1/2*b*e*f*n*(a+b*log(c*(d+e*x)^n))*log(e*(sqrt(-f)+x*sqrt(g))/(e*sqrt(-f)-d*sqrt(g)))/(g^(5/2)*(e*sqrt(-f)-d*sqrt(g)))+1/2*b^2*e*f*n^2*polylog(2,-(d+e*x)*sqrt(g)/(e*sqrt(-f)-d*sqrt(g)))/(g^(5/2)*(e*sqrt(-f)-d*sqrt(g)))-1/2*b*e*f*n*(a+b*log(c*(d+e*x)^n))*log(e*(sqrt(-f)-x*sqrt(g))/(e*sqrt(-f)+d*sqrt(g)))/(g^(5/2)*(e*sqrt(-f)+d*sqrt(g)))-1/2*b^2*e*f*n^2*polylog(2,(d+e*x)*sqrt(g)/(e*sqrt(-f)+d*sqrt(g)))/(g^(5/2)*(e*sqrt(-f)+d*sqrt(g)))-1/4*f*(d+e*x)*(a+b*log(c*(d+e*x)^n))^2/(g^2*(e*sqrt(-f)+d*sqrt(g))*(sqrt(-f)-x*sqrt(g)))-1/4*f*(d+e*x)*(a+b*log(c*(d+e*x)^n))^2/(g^2*(e*sqrt(-f)-d*sqrt(g))*(sqrt(-f)+x*sqrt(g)))],
[x^2*(a+b*log(c*(d+e*x)^n))^2/(f+g*x^2)^2,x,32,1/4*(a+b*log(c*(d+e*x)^n))^2*log(e*(sqrt(-f)-x*sqrt(g))/(e*sqrt(-f)+d*sqrt(g)))/(g^(3/2)*sqrt(-f))-1/4*(a+b*log(c*(d+e*x)^n))^2*log(e*(sqrt(-f)+x*sqrt(g))/(e*sqrt(-f)-d*sqrt(g)))/(g^(3/2)*sqrt(-f))-1/2*b*n*(a+b*log(c*(d+e*x)^n))*polylog(2,-(d+e*x)*sqrt(g)/(e*sqrt(-f)-d*sqrt(g)))/(g^(3/2)*sqrt(-f))+1/2*b*n*(a+b*log(c*(d+e*x)^n))*polylog(2,(d+e*x)*sqrt(g)/(e*sqrt(-f)+d*sqrt(g)))/(g^(3/2)*sqrt(-f))+1/2*b^2*n^2*polylog(3,-(d+e*x)*sqrt(g)/(e*sqrt(-f)-d*sqrt(g)))/(g^(3/2)*sqrt(-f))-1/2*b^2*n^2*polylog(3,(d+e*x)*sqrt(g)/(e*sqrt(-f)+d*sqrt(g)))/(g^(3/2)*sqrt(-f))-1/2*b*e*n*(a+b*log(c*(d+e*x)^n))*log(e*(sqrt(-f)+x*sqrt(g))/(e*sqrt(-f)-d*sqrt(g)))/(g^(3/2)*(e*sqrt(-f)-d*sqrt(g)))-1/2*b^2*e*n^2*polylog(2,-(d+e*x)*sqrt(g)/(e*sqrt(-f)-d*sqrt(g)))/(g^(3/2)*(e*sqrt(-f)-d*sqrt(g)))+1/2*b*e*n*(a+b*log(c*(d+e*x)^n))*log(e*(sqrt(-f)-x*sqrt(g))/(e*sqrt(-f)+d*sqrt(g)))/(g^(3/2)*(e*sqrt(-f)+d*sqrt(g)))+1/2*b^2*e*n^2*polylog(2,(d+e*x)*sqrt(g)/(e*sqrt(-f)+d*sqrt(g)))/(g^(3/2)*(e*sqrt(-f)+d*sqrt(g)))+1/4*(d+e*x)*(a+b*log(c*(d+e*x)^n))^2/(g*(e*sqrt(-f)+d*sqrt(g))*(sqrt(-f)-x*sqrt(g)))+1/4*(d+e*x)*(a+b*log(c*(d+e*x)^n))^2/(g*(e*sqrt(-f)-d*sqrt(g))*(sqrt(-f)+x*sqrt(g)))],
[(a+b*log(c*(d+e*x)^n))^2/(f+g*x^2)^2,x,20,-1/4*(a+b*log(c*(d+e*x)^n))^2*log(e*(sqrt(-f)-x*sqrt(g))/(e*sqrt(-f)+d*sqrt(g)))/((-f)^(3/2)*sqrt(g))+1/4*(a+b*log(c*(d+e*x)^n))^2*log(e*(sqrt(-f)+x*sqrt(g))/(e*sqrt(-f)-d*sqrt(g)))/((-f)^(3/2)*sqrt(g))+1/2*b*n*(a+b*log(c*(d+e*x)^n))*polylog(2,-(d+e*x)*sqrt(g)/(e*sqrt(-f)-d*sqrt(g)))/((-f)^(3/2)*sqrt(g))-1/2*b*n*(a+b*log(c*(d+e*x)^n))*polylog(2,(d+e*x)*sqrt(g)/(e*sqrt(-f)+d*sqrt(g)))/((-f)^(3/2)*sqrt(g))-1/2*b^2*n^2*polylog(3,-(d+e*x)*sqrt(g)/(e*sqrt(-f)-d*sqrt(g)))/((-f)^(3/2)*sqrt(g))+1/2*b^2*n^2*polylog(3,(d+e*x)*sqrt(g)/(e*sqrt(-f)+d*sqrt(g)))/((-f)^(3/2)*sqrt(g))-1/2*b*e*n*(a+b*log(c*(d+e*x)^n))*log(e*(sqrt(-f)-x*sqrt(g))/(e*sqrt(-f)+d*sqrt(g)))/(f*sqrt(g)*(e*sqrt(-f)+d*sqrt(g)))-1/2*b^2*e*n^2*polylog(2,(d+e*x)*sqrt(g)/(e*sqrt(-f)+d*sqrt(g)))/(f*sqrt(g)*(e*sqrt(-f)+d*sqrt(g)))-1/2*b*e*n*(a+b*log(c*(d+e*x)^n))*log(e*(sqrt(-f)+x*sqrt(g))/(e*sqrt(-f)-d*sqrt(g)))/(sqrt(g)*(e*(-f)^(3/2)+d*f*sqrt(g)))-1/2*b^2*e*n^2*polylog(2,-(d+e*x)*sqrt(g)/(e*sqrt(-f)-d*sqrt(g)))/(sqrt(g)*(e*(-f)^(3/2)+d*f*sqrt(g)))-1/4*(d+e*x)*(a+b*log(c*(d+e*x)^n))^2/(f*(e*sqrt(-f)+d*sqrt(g))*(sqrt(-f)-x*sqrt(g)))-1/4*(d+e*x)*(a+b*log(c*(d+e*x)^n))^2/(f*(e*sqrt(-f)-d*sqrt(g))*(sqrt(-f)+x*sqrt(g)))],
[(a+b*log(c*(d+e*x)^n))^2/(x^2*(f+g*x^2)^2),x,35,2*b*e*n*log(-e*x/d)*(a+b*log(c*(d+e*x)^n))/(d*f^2)-(d+e*x)*(a+b*log(c*(d+e*x)^n))^2/(d*f^2*x)+2*b^2*e*n^2*polylog(2,1+e*x/d)/(d*f^2)-3/4*(a+b*log(c*(d+e*x)^n))^2*log(e*(sqrt(-f)-x*sqrt(g))/(e*sqrt(-f)+d*sqrt(g)))*sqrt(g)/(-f)^(5/2)+3/4*(a+b*log(c*(d+e*x)^n))^2*log(e*(sqrt(-f)+x*sqrt(g))/(e*sqrt(-f)-d*sqrt(g)))*sqrt(g)/(-f)^(5/2)+3/2*b*n*(a+b*log(c*(d+e*x)^n))*polylog(2,-(d+e*x)*sqrt(g)/(e*sqrt(-f)-d*sqrt(g)))*sqrt(g)/(-f)^(5/2)-3/2*b*n*(a+b*log(c*(d+e*x)^n))*polylog(2,(d+e*x)*sqrt(g)/(e*sqrt(-f)+d*sqrt(g)))*sqrt(g)/(-f)^(5/2)-3/2*b^2*n^2*polylog(3,-(d+e*x)*sqrt(g)/(e*sqrt(-f)-d*sqrt(g)))*sqrt(g)/(-f)^(5/2)+3/2*b^2*n^2*polylog(3,(d+e*x)*sqrt(g)/(e*sqrt(-f)+d*sqrt(g)))*sqrt(g)/(-f)^(5/2)+1/2*b*e*n*(a+b*log(c*(d+e*x)^n))*log(e*(sqrt(-f)-x*sqrt(g))/(e*sqrt(-f)+d*sqrt(g)))*sqrt(g)/(f^2*(e*sqrt(-f)+d*sqrt(g)))+1/2*b^2*e*n^2*polylog(2,(d+e*x)*sqrt(g)/(e*sqrt(-f)+d*sqrt(g)))*sqrt(g)/(f^2*(e*sqrt(-f)+d*sqrt(g)))+1/2*b*e*n*(a+b*log(c*(d+e*x)^n))*log(e*(sqrt(-f)+x*sqrt(g))/(e*sqrt(-f)-d*sqrt(g)))*sqrt(g)/(f*(e*(-f)^(3/2)+d*f*sqrt(g)))+1/2*b^2*e*n^2*polylog(2,-(d+e*x)*sqrt(g)/(e*sqrt(-f)-d*sqrt(g)))*sqrt(g)/(f*(e*(-f)^(3/2)+d*f*sqrt(g)))+1/4*g*(d+e*x)*(a+b*log(c*(d+e*x)^n))^2/(f^2*(e*sqrt(-f)+d*sqrt(g))*(sqrt(-f)-x*sqrt(g)))+1/4*g*(d+e*x)*(a+b*log(c*(d+e*x)^n))^2/(f^2*(e*sqrt(-f)-d*sqrt(g))*(sqrt(-f)+x*sqrt(g)))],

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

# q>0

# q<0
[log(c*(a+b*x)^n)^3/(d+e*x^2),x,12,1/2*log(c*(a+b*x)^n)^3*log(b*(sqrt(-d)-x*sqrt(e))/(b*sqrt(-d)+a*sqrt(e)))/(sqrt(-d)*sqrt(e))-1/2*log(c*(a+b*x)^n)^3*log(b*(sqrt(-d)+x*sqrt(e))/(b*sqrt(-d)-a*sqrt(e)))/(sqrt(-d)*sqrt(e))-3/2*n*log(c*(a+b*x)^n)^2*polylog(2,-(a+b*x)*sqrt(e)/(b*sqrt(-d)-a*sqrt(e)))/(sqrt(-d)*sqrt(e))+3/2*n*log(c*(a+b*x)^n)^2*polylog(2,(a+b*x)*sqrt(e)/(b*sqrt(-d)+a*sqrt(e)))/(sqrt(-d)*sqrt(e))+3*n^2*log(c*(a+b*x)^n)*polylog(3,-(a+b*x)*sqrt(e)/(b*sqrt(-d)-a*sqrt(e)))/(sqrt(-d)*sqrt(e))-3*n^2*log(c*(a+b*x)^n)*polylog(3,(a+b*x)*sqrt(e)/(b*sqrt(-d)+a*sqrt(e)))/(sqrt(-d)*sqrt(e))-3*n^3*polylog(4,-(a+b*x)*sqrt(e)/(b*sqrt(-d)-a*sqrt(e)))/(sqrt(-d)*sqrt(e))+3*n^3*polylog(4,(a+b*x)*sqrt(e)/(b*sqrt(-d)+a*sqrt(e)))/(sqrt(-d)*sqrt(e))],
[log(c*(a+b*x)^n)^2/(d+e*x^2),x,10,1/2*log(c*(a+b*x)^n)^2*log(b*(sqrt(-d)-x*sqrt(e))/(b*sqrt(-d)+a*sqrt(e)))/(sqrt(-d)*sqrt(e))-1/2*log(c*(a+b*x)^n)^2*log(b*(sqrt(-d)+x*sqrt(e))/(b*sqrt(-d)-a*sqrt(e)))/(sqrt(-d)*sqrt(e))-n*log(c*(a+b*x)^n)*polylog(2,-(a+b*x)*sqrt(e)/(b*sqrt(-d)-a*sqrt(e)))/(sqrt(-d)*sqrt(e))+n*log(c*(a+b*x)^n)*polylog(2,(a+b*x)*sqrt(e)/(b*sqrt(-d)+a*sqrt(e)))/(sqrt(-d)*sqrt(e))+n^2*polylog(3,-(a+b*x)*sqrt(e)/(b*sqrt(-d)-a*sqrt(e)))/(sqrt(-d)*sqrt(e))-n^2*polylog(3,(a+b*x)*sqrt(e)/(b*sqrt(-d)+a*sqrt(e)))/(sqrt(-d)*sqrt(e))],
[log(c*(a+b*x)^n)/(d+e*x^2),x,8,1/2*log(c*(a+b*x)^n)*log(b*(sqrt(-d)-x*sqrt(e))/(b*sqrt(-d)+a*sqrt(e)))/(sqrt(-d)*sqrt(e))-1/2*log(c*(a+b*x)^n)*log(b*(sqrt(-d)+x*sqrt(e))/(b*sqrt(-d)-a*sqrt(e)))/(sqrt(-d)*sqrt(e))-1/2*n*polylog(2,-(a+b*x)*sqrt(e)/(b*sqrt(-d)-a*sqrt(e)))/(sqrt(-d)*sqrt(e))+1/2*n*polylog(2,(a+b*x)*sqrt(e)/(b*sqrt(-d)+a*sqrt(e)))/(sqrt(-d)*sqrt(e))],
[1/((d+e*x^2)*log(c*(a+b*x)^n)),x,2,-1/2*Unintegrable(1/(log(c*(a+b*x)^n)*(sqrt(-d)-x*sqrt(e))),x)/sqrt(-d)-1/2*Unintegrable(1/(log(c*(a+b*x)^n)*(sqrt(-d)+x*sqrt(e))),x)/sqrt(-d)],

# Integrands of the form (h+i x)^m (f+g x^r)^q (a+b Log[c (d+e x)^n])^p
[log(c-a*(1-c)/(b*x^m))/(x*(a+b*x^m)),x,4,polylog(2,(1-c)*(b+a/x^m)/b)/(a*m)],
[log((-a+a*c+b*c*x^m)/(b*x^m))/(x*(a+b*x^m)),x,5,polylog(2,(1-c)*(b+a/x^m)/b)/(a*m)],
[log(c*(a+(-d+a*c*d)/(c*e*x^m)))/(x*(d+e*x^m)),x,4,polylog(2,(1-a*c)*(e+d/x^m)/e)/(d*m)],
[log((-d+a*c*d+a*c*e*x^m)/(e*x^m))/(x*(d+e*x^m)),x,5,polylog(2,(1-a*c)*(e+d/x^m)/e)/(d*m)],
[log(2*a/(a+b*x))/(a^2-b^2*x^2),x,2,1/2*polylog(2,1-2*a/(a+b*x))/(a*b)],
[log(2*a/(a+b*x))/((a-b*x)*(a+b*x)),x,4,1/2*polylog(2,1-2*a/(a+b*x))/(a*b)],
[log((a*(1-c)+b*(1+c)*x)/(a+b*x))/(a^2-b^2*x^2),x,1,1/2*polylog(2,1+(-a*(1-c)-b*(1+c)*x)/(a+b*x))/(a*b)],
[log((a*(1-c)+b*(1+c)*x)/(a+b*x))/((a-b*x)*(a+b*x)),x,2,1/2*polylog(2,c*(a-b*x)/(a+b*x))/(a*b)],
[log(1-c*(a-b*x)/(a+b*x))/(a^2-b^2*x^2),x,1,1/2*polylog(2,c*(a-b*x)/(a+b*x))/(a*b)],
[log(1-c*(a-b*x)/(a+b*x))/((a-b*x)*(a+b*x)),x,3,1/2*polylog(2,c*(a-b*x)/(a+b*x))/(a*b)],

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

# Integrands of the form Log[c (a+b x)^n]^p / (d + e x + f x^2)
[log(c*(a+b*x)^n)^3/(d*x+e*x^2),x,13,log(-b*x/a)*log(c*(a+b*x)^n)^3/d-log(c*(a+b*x)^n)^3*log(b*(d+e*x)/(b*d-a*e))/d-3*n*log(c*(a+b*x)^n)^2*polylog(2,-e*(a+b*x)/(b*d-a*e))/d+3*n*log(c*(a+b*x)^n)^2*polylog(2,1+b*x/a)/d+6*n^2*log(c*(a+b*x)^n)*polylog(3,-e*(a+b*x)/(b*d-a*e))/d-6*n^2*log(c*(a+b*x)^n)*polylog(3,1+b*x/a)/d-6*n^3*polylog(4,-e*(a+b*x)/(b*d-a*e))/d+6*n^3*polylog(4,1+b*x/a)/d],
[log(c*(a+b*x)^n)^2/(d*x+e*x^2),x,11,log(-b*x/a)*log(c*(a+b*x)^n)^2/d-log(c*(a+b*x)^n)^2*log(b*(d+e*x)/(b*d-a*e))/d-2*n*log(c*(a+b*x)^n)*polylog(2,-e*(a+b*x)/(b*d-a*e))/d+2*n*log(c*(a+b*x)^n)*polylog(2,1+b*x/a)/d+2*n^2*polylog(3,-e*(a+b*x)/(b*d-a*e))/d-2*n^2*polylog(3,1+b*x/a)/d],
[log(c*(a+b*x)^n)/(d*x+e*x^2),x,8,log(-b*x/a)*log(c*(a+b*x)^n)/d-log(c*(a+b*x)^n)*log(b*(d+e*x)/(b*d-a*e))/d-n*polylog(2,-e*(a+b*x)/(b*d-a*e))/d+n*polylog(2,1+b*x/a)/d],
[1/((d*x+e*x^2)*log(c*(a+b*x)^n)),x,3,Unintegrable(1/(x*log(c*(a+b*x)^n)),x)/d-e*Unintegrable(1/((d+e*x)*log(c*(a+b*x)^n)),x)/d],
[log(c*(a+b*x)^n)^3/(d+e*x+f*x^2),x,12,log(c*(a+b*x)^n)^3*log(-b*(e+2*f*x-sqrt(e^2-4*d*f))/(2*a*f-b*(e-sqrt(e^2-4*d*f))))/sqrt(e^2-4*d*f)-log(c*(a+b*x)^n)^3*log(-b*(e+2*f*x+sqrt(e^2-4*d*f))/(2*a*f-b*(e+sqrt(e^2-4*d*f))))/sqrt(e^2-4*d*f)+3*n*log(c*(a+b*x)^n)^2*polylog(2,2*f*(a+b*x)/(2*a*f-b*(e-sqrt(e^2-4*d*f))))/sqrt(e^2-4*d*f)-3*n*log(c*(a+b*x)^n)^2*polylog(2,2*f*(a+b*x)/(2*a*f-b*(e+sqrt(e^2-4*d*f))))/sqrt(e^2-4*d*f)-6*n^2*log(c*(a+b*x)^n)*polylog(3,2*f*(a+b*x)/(2*a*f-b*(e-sqrt(e^2-4*d*f))))/sqrt(e^2-4*d*f)+6*n^2*log(c*(a+b*x)^n)*polylog(3,2*f*(a+b*x)/(2*a*f-b*(e+sqrt(e^2-4*d*f))))/sqrt(e^2-4*d*f)+6*n^3*polylog(4,2*f*(a+b*x)/(2*a*f-b*(e-sqrt(e^2-4*d*f))))/sqrt(e^2-4*d*f)-6*n^3*polylog(4,2*f*(a+b*x)/(2*a*f-b*(e+sqrt(e^2-4*d*f))))/sqrt(e^2-4*d*f)],
[log(c*(a+b*x)^n)^2/(d+e*x+f*x^2),x,10,log(c*(a+b*x)^n)^2*log(-b*(e+2*f*x-sqrt(e^2-4*d*f))/(2*a*f-b*(e-sqrt(e^2-4*d*f))))/sqrt(e^2-4*d*f)-log(c*(a+b*x)^n)^2*log(-b*(e+2*f*x+sqrt(e^2-4*d*f))/(2*a*f-b*(e+sqrt(e^2-4*d*f))))/sqrt(e^2-4*d*f)+2*n*log(c*(a+b*x)^n)*polylog(2,2*f*(a+b*x)/(2*a*f-b*(e-sqrt(e^2-4*d*f))))/sqrt(e^2-4*d*f)-2*n*log(c*(a+b*x)^n)*polylog(2,2*f*(a+b*x)/(2*a*f-b*(e+sqrt(e^2-4*d*f))))/sqrt(e^2-4*d*f)-2*n^2*polylog(3,2*f*(a+b*x)/(2*a*f-b*(e-sqrt(e^2-4*d*f))))/sqrt(e^2-4*d*f)+2*n^2*polylog(3,2*f*(a+b*x)/(2*a*f-b*(e+sqrt(e^2-4*d*f))))/sqrt(e^2-4*d*f)],
[log(c*(a+b*x)^n)/(d+e*x+f*x^2),x,8,log(c*(a+b*x)^n)*log(-b*(e+2*f*x-sqrt(e^2-4*d*f))/(2*a*f-b*(e-sqrt(e^2-4*d*f))))/sqrt(e^2-4*d*f)-log(c*(a+b*x)^n)*log(-b*(e+2*f*x+sqrt(e^2-4*d*f))/(2*a*f-b*(e+sqrt(e^2-4*d*f))))/sqrt(e^2-4*d*f)+n*polylog(2,2*f*(a+b*x)/(2*a*f-b*(e-sqrt(e^2-4*d*f))))/sqrt(e^2-4*d*f)-n*polylog(2,2*f*(a+b*x)/(2*a*f-b*(e+sqrt(e^2-4*d*f))))/sqrt(e^2-4*d*f)],
[1/((d+e*x+f*x^2)*log(c*(a+b*x)^n)),x,2,2*f*Unintegrable(1/(log(c*(a+b*x)^n)*(e+2*f*x-sqrt(e^2-4*d*f))),x)/sqrt(e^2-4*d*f)-2*f*Unintegrable(1/(log(c*(a+b*x)^n)*(e+2*f*x+sqrt(e^2-4*d*f))),x)/sqrt(e^2-4*d*f)],
[x^3*log(x)/(a+b*x+c*x^2),x,10,b*x/c^2-1/4*x^2/c-b*x*log(x)/c^2+1/2*x^2*log(x)/c+1/2*log(x)*log(1+2*c*x/(b-sqrt(b^2-4*a*c)))*(b^2-a*c-b*(b^2-3*a*c)/sqrt(b^2-4*a*c))/c^3+1/2*polylog(2,-2*c*x/(b-sqrt(b^2-4*a*c)))*(b^2-a*c-b*(b^2-3*a*c)/sqrt(b^2-4*a*c))/c^3+1/2*log(x)*log(1+2*c*x/(b+sqrt(b^2-4*a*c)))*(b^2-a*c+b*(b^2-3*a*c)/sqrt(b^2-4*a*c))/c^3+1/2*polylog(2,-2*c*x/(b+sqrt(b^2-4*a*c)))*(b^2-a*c+b*(b^2-3*a*c)/sqrt(b^2-4*a*c))/c^3],
[x^2*log(x)/(a+b*x+c*x^2),x,9,-x/c+x*log(x)/c-1/2*log(x)*log(1+2*c*x/(b-sqrt(b^2-4*a*c)))*(b+(-b^2+2*a*c)/sqrt(b^2-4*a*c))/c^2-1/2*polylog(2,-2*c*x/(b-sqrt(b^2-4*a*c)))*(b+(-b^2+2*a*c)/sqrt(b^2-4*a*c))/c^2-1/2*log(x)*log(1+2*c*x/(b+sqrt(b^2-4*a*c)))*(b+(b^2-2*a*c)/sqrt(b^2-4*a*c))/c^2-1/2*polylog(2,-2*c*x/(b+sqrt(b^2-4*a*c)))*(b+(b^2-2*a*c)/sqrt(b^2-4*a*c))/c^2],
[x*log(x)/(a+b*x+c*x^2),x,6,1/2*log(x)*log(1+2*c*x/(b-sqrt(b^2-4*a*c)))*(1-b/sqrt(b^2-4*a*c))/c+1/2*polylog(2,-2*c*x/(b-sqrt(b^2-4*a*c)))*(1-b/sqrt(b^2-4*a*c))/c+1/2*log(x)*log(1+2*c*x/(b+sqrt(b^2-4*a*c)))*(1+b/sqrt(b^2-4*a*c))/c+1/2*polylog(2,-2*c*x/(b+sqrt(b^2-4*a*c)))*(1+b/sqrt(b^2-4*a*c))/c],
[log(x)/(a+b*x+c*x^2),x,6,log(x)*log(1+2*c*x/(b-sqrt(b^2-4*a*c)))/sqrt(b^2-4*a*c)-log(x)*log(1+2*c*x/(b+sqrt(b^2-4*a*c)))/sqrt(b^2-4*a*c)+polylog(2,-2*c*x/(b-sqrt(b^2-4*a*c)))/sqrt(b^2-4*a*c)-polylog(2,-2*c*x/(b+sqrt(b^2-4*a*c)))/sqrt(b^2-4*a*c)],
[log(x)/(x*(a+b*x+c*x^2)),x,9,1/2*log(x)^2/a-1/2*log(x)*log(1+2*c*x/(b+sqrt(b^2-4*a*c)))*(1-b/sqrt(b^2-4*a*c))/a-1/2*polylog(2,-2*c*x/(b+sqrt(b^2-4*a*c)))*(1-b/sqrt(b^2-4*a*c))/a-1/2*log(x)*log(1+2*c*x/(b-sqrt(b^2-4*a*c)))*(1+b/sqrt(b^2-4*a*c))/a-1/2*polylog(2,-2*c*x/(b-sqrt(b^2-4*a*c)))*(1+b/sqrt(b^2-4*a*c))/a],
[log(x)/(x^2*(a+b*x+c*x^2)),x,10,(-1)/(a*x)-log(x)/(a*x)-1/2*b*log(x)^2/a^2+1/2*log(x)*log(1+2*c*x/(b+sqrt(b^2-4*a*c)))*(b+(-b^2+2*a*c)/sqrt(b^2-4*a*c))/a^2+1/2*polylog(2,-2*c*x/(b+sqrt(b^2-4*a*c)))*(b+(-b^2+2*a*c)/sqrt(b^2-4*a*c))/a^2+1/2*log(x)*log(1+2*c*x/(b-sqrt(b^2-4*a*c)))*(b+(b^2-2*a*c)/sqrt(b^2-4*a*c))/a^2+1/2*polylog(2,-2*c*x/(b-sqrt(b^2-4*a*c)))*(b+(b^2-2*a*c)/sqrt(b^2-4*a*c))/a^2],
[log(x)/(x^3*(a+b*x+c*x^2)),x,11,(-1/4)/(a*x^2)+b/(a^2*x)-1/2*log(x)/(a*x^2)+b*log(x)/(a^2*x)+1/2*(b^2-a*c)*log(x)^2/a^3-1/2*log(x)*log(1+2*c*x/(b+sqrt(b^2-4*a*c)))*(b^2-a*c-b*(b^2-3*a*c)/sqrt(b^2-4*a*c))/a^3-1/2*polylog(2,-2*c*x/(b+sqrt(b^2-4*a*c)))*(b^2-a*c-b*(b^2-3*a*c)/sqrt(b^2-4*a*c))/a^3-1/2*log(x)*log(1+2*c*x/(b-sqrt(b^2-4*a*c)))*(b^2-a*c+b*(b^2-3*a*c)/sqrt(b^2-4*a*c))/a^3-1/2*polylog(2,-2*c*x/(b-sqrt(b^2-4*a*c)))*(b^2-a*c+b*(b^2-3*a*c)/sqrt(b^2-4*a*c))/a^3],

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

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

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

# p>0
[x^3*log(f*x^m)*(a+b*log(c*(d+e*x)^n)),x,11,-5/16*b*d^3*m*n*x/e^3+3/32*b*d^2*m*n*x^2/e^2-7/144*b*d*m*n*x^3/e+1/32*b*m*n*x^4+1/4*b*d^3*n*x*log(f*x^m)/e^3-1/8*b*d^2*n*x^2*log(f*x^m)/e^2+1/12*b*d*n*x^3*log(f*x^m)/e-1/16*b*n*x^4*log(f*x^m)+1/16*b*d^4*m*n*log(d+e*x)/e^4-1/16*(m*x^4-4*x^4*log(f*x^m))*(a+b*log(c*(d+e*x)^n))-1/4*b*d^4*n*log(f*x^m)*log(1+e*x/d)/e^4-1/4*b*d^4*m*n*polylog(2,-e*x/d)/e^4],
[x^2*log(f*x^m)*(a+b*log(c*(d+e*x)^n)),x,10,4/9*b*d^2*m*n*x/e^2-5/36*b*d*m*n*x^2/e+2/27*b*m*n*x^3-1/3*b*d^2*n*x*log(f*x^m)/e^2+1/6*b*d*n*x^2*log(f*x^m)/e-1/9*b*n*x^3*log(f*x^m)-1/9*b*d^3*m*n*log(d+e*x)/e^3-1/9*(m*x^3-3*x^3*log(f*x^m))*(a+b*log(c*(d+e*x)^n))+1/3*b*d^3*n*log(f*x^m)*log(1+e*x/d)/e^3+1/3*b*d^3*m*n*polylog(2,-e*x/d)/e^3],
[x*log(f*x^m)*(a+b*log(c*(d+e*x)^n)),x,9,-3/4*b*d*m*n*x/e+1/4*b*m*n*x^2+1/2*b*d*n*x*log(f*x^m)/e-1/4*b*n*x^2*log(f*x^m)+1/4*b*d^2*m*n*log(d+e*x)/e^2-1/4*(m*x^2-2*x^2*log(f*x^m))*(a+b*log(c*(d+e*x)^n))-1/2*b*d^2*n*log(f*x^m)*log(1+e*x/d)/e^2-1/2*b*d^2*m*n*polylog(2,-e*x/d)/e^2],
[log(f*x^m)*(a+b*log(c*(d+e*x)^n)),x,8,2*b*m*n*x-b*n*x*log(f*x^m)-b*d*m*n*log(d+e*x)/e-x*(m-log(f*x^m))*(a+b*log(c*(d+e*x)^n))+b*d*n*log(f*x^m)*log(1+e*x/d)/e+b*d*m*n*polylog(2,-e*x/d)/e],
[log(f*x^m)*(a+b*log(c*(d+e*x)^n))/x,x,4,1/2*log(f*x^m)^2*(a+b*log(c*(d+e*x)^n))/m-1/2*b*n*log(f*x^m)^2*log(1+e*x/d)/m-b*n*log(f*x^m)*polylog(2,-e*x/d)+b*m*n*polylog(3,-e*x/d)],
[log(f*x^m)*(a+b*log(c*(d+e*x)^n))/x^2,x,6,b*e*m*n*log(x)/d-b*e*n*log(1+d/(e*x))*log(f*x^m)/d-b*e*m*n*log(d+e*x)/d-(m/x+log(f*x^m)/x)*(a+b*log(c*(d+e*x)^n))+b*e*m*n*polylog(2,-d/(e*x))/d],
[log(f*x^m)*(a+b*log(c*(d+e*x)^n))/x^3,x,7,-3/4*b*e*m*n/(d*x)-1/4*b*e^2*m*n*log(x)/d^2-1/2*b*e*n*log(f*x^m)/(d*x)+1/2*b*e^2*n*log(1+d/(e*x))*log(f*x^m)/d^2+1/4*b*e^2*m*n*log(d+e*x)/d^2-1/4*(m/x^2+2*log(f*x^m)/x^2)*(a+b*log(c*(d+e*x)^n))-1/2*b*e^2*m*n*polylog(2,-d/(e*x))/d^2],
[log(f*x^m)*(a+b*log(c*(d+e*x)^n))/x^4,x,9,-5/36*b*e*m*n/(d*x^2)+4/9*b*e^2*m*n/(d^2*x)+1/9*b*e^3*m*n*log(x)/d^3-1/6*b*e*n*log(f*x^m)/(d*x^2)+1/3*b*e^2*n*log(f*x^m)/(d^2*x)-1/3*b*e^3*n*log(1+d/(e*x))*log(f*x^m)/d^3-1/9*b*e^3*m*n*log(d+e*x)/d^3-1/9*(m/x^3+3*log(f*x^m)/x^3)*(a+b*log(c*(d+e*x)^n))+1/3*b*e^3*m*n*polylog(2,-d/(e*x))/d^3],
[log(f*x^m)*(a+b*log(c*(d+e*x)^n))/x^5,x,11,-7/144*b*e*m*n/(d*x^3)+3/32*b*e^2*m*n/(d^2*x^2)-5/16*b*e^3*m*n/(d^3*x)-1/16*b*e^4*m*n*log(x)/d^4-1/12*b*e*n*log(f*x^m)/(d*x^3)+1/8*b*e^2*n*log(f*x^m)/(d^2*x^2)-1/4*b*e^3*n*log(f*x^m)/(d^3*x)+1/4*b*e^4*n*log(1+d/(e*x))*log(f*x^m)/d^4+1/16*b*e^4*m*n*log(d+e*x)/d^4-1/16*(m/x^4+4*log(f*x^m)/x^4)*(a+b*log(c*(d+e*x)^n))-1/4*b*e^4*m*n*polylog(2,-d/(e*x))/d^4],
[x^2*log(f*x^m)*(a+b*log(c*(d+e*x)^n))^2,x,52,2/9*a*b*d^2*m*n*x/e^2-71/54*b^2*d^2*m*n^2*x/e^2+1/9*b*d^2*m*n*(6*a-11*b*n)*x/e^2+19/54*b^2*d*m*n^2*x^2/e-2/27*b^2*m*n^2*x^3-2/3*a*b*d^2*n*x*log(f*x^m)/e^2+11/9*b^2*d^2*n^2*x*log(f*x^m)/e^2-5/18*b^2*d*n^2*x^2*log(f*x^m)/e+2/27*b^2*n^2*x^3*log(f*x^m)+23/54*b^2*d^3*m*n^2*log(d+e*x)/e^3+5/9*b^2*d^3*m*n^2*log(-e*x/d)*log(d+e*x)/e^3-5/9*b^2*d^3*n^2*log(f*x^m)*log(d+e*x)/e^3+8/9*b^2*d^2*m*n*(d+e*x)*log(c*(d+e*x)^n)/e^3+2/3*b^2*d^3*m*n*log(-e*x/d)*log(c*(d+e*x)^n)/e^3-2/3*b^2*d^2*n*(d+e*x)*log(f*x^m)*log(c*(d+e*x)^n)/e^3-5/18*b*d*m*n*x^2*(a+b*log(c*(d+e*x)^n))/e+4/27*b*m*n*x^3*(a+b*log(c*(d+e*x)^n))+1/3*b*d*n*x^2*log(f*x^m)*(a+b*log(c*(d+e*x)^n))/e-2/9*b*n*x^3*log(f*x^m)*(a+b*log(c*(d+e*x)^n))-1/9*d^3*m*(a+b*log(c*(d+e*x)^n))^2/e^3-1/9*m*x^3*(a+b*log(c*(d+e*x)^n))^2-1/3*d^3*m*log(-e*x/d)*(a+b*log(c*(d+e*x)^n))^2/e^3+1/3*d^3*log(f*x^m)*(a+b*log(c*(d+e*x)^n))^2/e^3+1/3*x^3*log(f*x^m)*(a+b*log(c*(d+e*x)^n))^2+11/9*b^2*d^3*m*n^2*polylog(2,1+e*x/d)/e^3-2/3*b*d^3*m*n*(a+b*log(c*(d+e*x)^n))*polylog(2,1+e*x/d)/e^3+2/3*b^2*d^3*m*n^2*polylog(3,1+e*x/d)/e^3,11/9*a*b*d^2*m*n*x/e^2-28/9*b^2*d^2*m*n^2*x/e^2+5/36*b^2*d*m*n^2*x^2/e-2/81*b^2*m*n^2*x^3+13/36*b^2*d*m*n^2*(d+e*x)^2/e^3-4/81*b^2*m*n^2*(d+e*x)^3/e^3+23/54*b^2*d^3*m*n^2*log(x)/e^3+2*b^2*d^2*n^2*x*log(f*x^m)/e^2-1/2*b^2*d*n^2*(d+e*x)^2*log(f*x^m)/e^3+2/27*b^2*n^2*(d+e*x)^3*log(f*x^m)/e^3+1/9*b^2*d^3*m*n^2*log(d+e*x)^2/e^3+1/3*b^2*d^3*m*n^2*log(x)*log(d+e*x)^2/e^3-1/3*b^2*d^3*n^2*log(f*x^m)*log(d+e*x)^2/e^3+11/9*b^2*d^2*m*n*(d+e*x)*log(c*(d+e*x)^n)/e^3+2/3*b*d^2*m*n*(d+e*x)*(a+b*log(c*(d+e*x)^n))/e^3-13/18*b*d*m*n*(d+e*x)^2*(a+b*log(c*(d+e*x)^n))/e^3+4/27*b*m*n*(d+e*x)^3*(a+b*log(c*(d+e*x)^n))/e^3+11/9*b*d^3*m*n*log(-e*x/d)*(a+b*log(c*(d+e*x)^n))/e^3-2*b*d^2*n*(d+e*x)*log(f*x^m)*(a+b*log(c*(d+e*x)^n))/e^3+b*d*n*(d+e*x)^2*log(f*x^m)*(a+b*log(c*(d+e*x)^n))/e^3-2/9*b*n*(d+e*x)^3*log(f*x^m)*(a+b*log(c*(d+e*x)^n))/e^3-2/9*b*d^3*m*n*log(d+e*x)*(a+b*log(c*(d+e*x)^n))/e^3-2/3*b*d^3*m*n*log(x)*log(d+e*x)*(a+b*log(c*(d+e*x)^n))/e^3+2/3*b*d^3*n*log(f*x^m)*log(d+e*x)*(a+b*log(c*(d+e*x)^n))/e^3-1/9*m*x^3*(a+b*log(c*(d+e*x)^n))^2+1/3*d^3*m*log(x)*(a+b*log(c*(d+e*x)^n))^2/e^3-1/3*d^3*m*log(-e*x/d)*(a+b*log(c*(d+e*x)^n))^2/e^3+1/3*x^3*log(f*x^m)*(a+b*log(c*(d+e*x)^n))^2+11/9*b^2*d^3*m*n^2*polylog(2,1+e*x/d)/e^3-2/3*b*d^3*m*n*(a+b*log(c*(d+e*x)^n))*polylog(2,1+e*x/d)/e^3+2/3*b^2*d^3*m*n^2*polylog(3,1+e*x/d)/e^3],
[x*log(f*x^m)*(a+b*log(c*(d+e*x)^n))^2,x,38,-1/2*a*b*d*m*n*x/e+2*b^2*d*m*n^2*x/e-2*b*d*m*n*(a-b*n)*x/e-1/8*b^2*m*n^2*x^2-1/4*b^2*m*n^2*(d+e*x)^2/e^2-1/4*b^2*d^2*m*n^2*log(x)/e^2+2*a*b*d*n*x*log(f*x^m)/e-2*b^2*d*n^2*x*log(f*x^m)/e+1/4*b^2*n^2*(d+e*x)^2*log(f*x^m)/e^2-5/2*b^2*d*m*n*(d+e*x)*log(c*(d+e*x)^n)/e^2-2*b^2*d^2*m*n*log(-e*x/d)*log(c*(d+e*x)^n)/e^2+2*b^2*d*n*(d+e*x)*log(f*x^m)*log(c*(d+e*x)^n)/e^2+1/2*b*m*n*(d+e*x)^2*(a+b*log(c*(d+e*x)^n))/e^2+1/2*b*d^2*m*n*log(-e*x/d)*(a+b*log(c*(d+e*x)^n))/e^2-1/2*b*n*(d+e*x)^2*log(f*x^m)*(a+b*log(c*(d+e*x)^n))/e^2+1/2*d*m*(d+e*x)*(a+b*log(c*(d+e*x)^n))^2/e^2-1/4*m*(d+e*x)^2*(a+b*log(c*(d+e*x)^n))^2/e^2+1/2*d^2*m*log(-e*x/d)*(a+b*log(c*(d+e*x)^n))^2/e^2-d*(d+e*x)*log(f*x^m)*(a+b*log(c*(d+e*x)^n))^2/e^2+1/2*(d+e*x)^2*log(f*x^m)*(a+b*log(c*(d+e*x)^n))^2/e^2-3/2*b^2*d^2*m*n^2*polylog(2,1+e*x/d)/e^2+b*d^2*m*n*(a+b*log(c*(d+e*x)^n))*polylog(2,1+e*x/d)/e^2-b^2*d^2*m*n^2*polylog(3,1+e*x/d)/e^2],
[log(f*x^m)*(a+b*log(c*(d+e*x)^n))^2,x,17,2*a*b*m*n*x-4*b^2*m*n^2*x+2*b*m*n*(a-b*n)*x-2*a*b*n*x*log(f*x^m)+2*b^2*n^2*x*log(f*x^m)+4*b^2*m*n*(d+e*x)*log(c*(d+e*x)^n)/e+2*b^2*d*m*n*log(-e*x/d)*log(c*(d+e*x)^n)/e-2*b^2*n*(d+e*x)*log(f*x^m)*log(c*(d+e*x)^n)/e-m*(d+e*x)*(a+b*log(c*(d+e*x)^n))^2/e-d*m*log(-e*x/d)*(a+b*log(c*(d+e*x)^n))^2/e+(d+e*x)*log(f*x^m)*(a+b*log(c*(d+e*x)^n))^2/e+2*b^2*d*m*n^2*polylog(2,1+e*x/d)/e-2*b*d*m*n*(a+b*log(c*(d+e*x)^n))*polylog(2,1+e*x/d)/e+2*b^2*d*m*n^2*polylog(3,1+e*x/d)/e],
[log(f*x^m)*(a+b*log(c*(d+e*x)^n))^2/x,x,-1,1/2*m*log(x)^2*(a-b*n*log(d+e*x)+b*log(c*(d+e*x)^n))^2+log(x)*(-m*log(x)+log(f*x^m))*(a-b*n*log(d+e*x)+b*log(c*(d+e*x)^n))^2+2*b*n*(-m*log(x)+log(f*x^m))*(a-b*n*log(d+e*x)+b*log(c*(d+e*x)^n))*(log(x)*(log(d+e*x)-log(1+e*x/d))-polylog(2,-e*x/d))+2*b*m*n*(a-b*n*log(d+e*x)+b*log(c*(d+e*x)^n))*(1/2*log(x)^2*(log(d+e*x)-log(1+e*x/d))-log(x)*polylog(2,-e*x/d)+polylog(3,-e*x/d))-b^2*n^2*(m*log(x)-log(f*x^m))*(log(-e*x/d)*log(d+e*x)^2+2*log(d+e*x)*polylog(2,1+e*x/d)-2*polylog(3,1+e*x/d))+1/12*b^2*m*n^2*(log(-e*x/d)^4+6*log(-e*x/d)^2*log(-e*x/(d+e*x))^2-4*(log(-e*x/d)+log(d/(d+e*x)))*log(-e*x/(d+e*x))^3+log(-e*x/(d+e*x))^4+6*log(x)^2*log(d+e*x)^2+4*(2*log(-e*x/d)^3-3*log(x)^2*log(d+e*x))*log(1+e*x/d)+6*(log(x)-log(-e*x/d))*(log(x)+3*log(-e*x/d))*log(1+e*x/d)^2-4*log(-e*x/d)^2*log(-e*x/(d+e*x))*(log(-e*x/d)+3*log(1+e*x/d))+12*(log(-e*x/d)^2-2*log(-e*x/d)*(log(-e*x/(d+e*x))+log(1+e*x/d))+2*log(x)*(-log(d+e*x)+log(1+e*x/d)))*polylog(2,-e*x/d)-12*log(-e*x/(d+e*x))^2*polylog(2,e*x/(d+e*x))+12*(log(-e*x/d)-log(-e*x/(d+e*x)))^2*polylog(2,1+e*x/d)+24*(log(x)-log(-e*x/d))*log(1+e*x/d)*polylog(2,1+e*x/d)+24*(log(-e*x/(d+e*x))+log(d+e*x))*polylog(3,-e*x/d)+24*log(-e*x/(d+e*x))*polylog(3,e*x/(d+e*x))+24*(-log(x)+log(-e*x/(d+e*x)))*polylog(3,1+e*x/d)-24*(polylog(4,-e*x/d)+polylog(4,e*x/(d+e*x))-polylog(4,1+e*x/d)))],
[log(f*x^m)*(a+b*log(c*(d+e*x)^n))^2/x^2,x,-1,-b^2*e*m*n^2*log(x)^2*log(d+e*x)/d+2*b^2*e*m*n^2*log(-e*x/d)*log(d+e*x)/d+2*b^2*e*n^2*log(x)*log(f*x^m)*log(d+e*x)/d-b^2*e*m*n^2*log(d+e*x)^2/d-b^2*m*n^2*log(d+e*x)^2/x+b^2*e*m*n^2*log(-e*x/d)*log(d+e*x)^2/d-b^2*e*n^2*log(f*x^m)*log(d+e*x)^2/d-b^2*n^2*log(f*x^m)*log(d+e*x)^2/x-2*b*n*(m*log(x)-log(f*x^m))*(e*x*log(-e*x/d)-(d+e*x)*log(d+e*x))*(a-b*n*log(d+e*x)+b*log(c*(d+e*x)^n))/(d*x)-m*log(x)*(a-b*n*log(d+e*x)+b*log(c*(d+e*x)^n))^2/x-(m-m*log(x)+log(f*x^m))*(a-b*n*log(d+e*x)+b*log(c*(d+e*x)^n))^2/x+b^2*e*m*n^2*log(x)^2*log(1+e*x/d)/d-2*b^2*e*n^2*log(x)*log(f*x^m)*log(1+e*x/d)/d-2*b^2*e*n^2*log(f*x^m)*polylog(2,-e*x/d)/d+b*m*n*(a-b*n*log(d+e*x)+b*log(c*(d+e*x)^n))*(2*e*x*log(-e*x/d)-2*(d+e*x)*log(d+e*x)-2*d*log(x)*log(d+e*x)+e*x*(log(x)^2-2*(log(x)*log(1+e*x/d)+polylog(2,-e*x/d))))/(d*x)+2*b^2*e*m*n^2*(1+log(d+e*x))*polylog(2,1+e*x/d)/d+2*b^2*e*m*n^2*polylog(3,-e*x/d)/d-2*b^2*e*m*n^2*polylog(3,1+e*x/d)/d],
[log(f*x^m)*(a+b*log(c*(d+e*x)^n))^2/x^3,x,-1,b^2*e^2*m*n^2*log(x)/d^2-1/2*b^2*e^2*m*n^2*log(x)^2/d^2+1/2*b^2*e^2*m*n^2*log(-e*x/d)/d^2+b^2*e^2*n^2*log(x)*log(f*x^m)/d^2-3/2*b^2*e^2*m*n^2*log(d+e*x)/d^2-3/2*b^2*e*m*n^2*log(d+e*x)/(d*x)+b^2*e^2*m*n^2*log(x)*log(d+e*x)/d^2+1/2*b^2*e^2*m*n^2*log(x)^2*log(d+e*x)/d^2-1/2*b^2*e^2*m*n^2*log(-e*x/d)*log(d+e*x)/d^2-b^2*e^2*n^2*log(f*x^m)*log(d+e*x)/d^2-b^2*e*n^2*log(f*x^m)*log(d+e*x)/(d*x)-b^2*e^2*n^2*log(x)*log(f*x^m)*log(d+e*x)/d^2+1/4*b^2*e^2*m*n^2*log(d+e*x)^2/d^2-1/4*b^2*m*n^2*log(d+e*x)^2/x^2-1/2*b^2*e^2*m*n^2*log(-e*x/d)*log(d+e*x)^2/d^2+1/2*b^2*e^2*n^2*log(f*x^m)*log(d+e*x)^2/d^2-1/2*b^2*n^2*log(f*x^m)*log(d+e*x)^2/x^2+b*n*(m*log(x)-log(f*x^m))*(e^2*x^2*log(-e*x/d)+(d+e*x)*(e*x+(d-e*x)*log(d+e*x)))*(a-b*n*log(d+e*x)+b*log(c*(d+e*x)^n))/(d^2*x^2)-1/2*m*log(x)*(a-b*n*log(d+e*x)+b*log(c*(d+e*x)^n))^2/x^2-1/4*(m-2*m*log(x)+2*log(f*x^m))*(a-b*n*log(d+e*x)+b*log(c*(d+e*x)^n))^2/x^2-b^2*e^2*m*n^2*log(x)*log(1+e*x/d)/d^2-1/2*b^2*e^2*m*n^2*log(x)^2*log(1+e*x/d)/d^2+b^2*e^2*n^2*log(x)*log(f*x^m)*log(1+e*x/d)/d^2-b^2*e^2*n^2*(m-log(f*x^m))*polylog(2,-e*x/d)/d^2-1/2*b*m*n*(a-b*n*log(d+e*x)+b*log(c*(d+e*x)^n))*(e*x*(d+e*x)+e^2*x^2*log(-e*x/d)+(d^2-e^2*x^2)*log(d+e*x)+2*d^2*log(x)*log(d+e*x)+e*x*(e*x*log(x)^2+2*d*(1+log(x))-2*e*x*(log(x)*log(1+e*x/d)+polylog(2,-e*x/d))))/(d^2*x^2)-1/2*b^2*e^2*m*n^2*(1+2*log(d+e*x))*polylog(2,1+e*x/d)/d^2-b^2*e^2*m*n^2*polylog(3,-e*x/d)/d^2+b^2*e^2*m*n^2*polylog(3,1+e*x/d)/d^2],
[log(f*x^m)*(a+b*log(c*(d+e*x)^n))^3,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+6*a*b^2*n^2*x*log(f*x^m)-6*b^3*n^3*x*log(f*x^m)-18*b^3*m*n^2*(d+e*x)*log(c*(d+e*x)^n)/e-6*b^3*d*m*n^2*log(-e*x/d)*log(c*(d+e*x)^n)/e+6*b^3*n^2*(d+e*x)*log(f*x^m)*log(c*(d+e*x)^n)/e+6*b*m*n*(d+e*x)*(a+b*log(c*(d+e*x)^n))^2/e+3*b*d*m*n*log(-e*x/d)*(a+b*log(c*(d+e*x)^n))^2/e-3*b*n*(d+e*x)*log(f*x^m)*(a+b*log(c*(d+e*x)^n))^2/e-m*(d+e*x)*(a+b*log(c*(d+e*x)^n))^3/e-d*m*log(-e*x/d)*(a+b*log(c*(d+e*x)^n))^3/e+(d+e*x)*log(f*x^m)*(a+b*log(c*(d+e*x)^n))^3/e-6*b^3*d*m*n^3*polylog(2,1+e*x/d)/e+6*b^2*d*m*n^2*(a+b*log(c*(d+e*x)^n))*polylog(2,1+e*x/d)/e-3*b*d*m*n*(a+b*log(c*(d+e*x)^n))^2*polylog(2,1+e*x/d)/e-6*b^3*d*m*n^3*polylog(3,1+e*x/d)/e+6*b^2*d*m*n^2*(a+b*log(c*(d+e*x)^n))*polylog(3,1+e*x/d)/e-6*b^3*d*m*n^3*polylog(4,1+e*x/d)/e],
[log(x)*log(a+b*x)^2/x,x,-1,1/12*(log(-b*x/a)^4+6*log(-b*x/a)^2*log(-b*x/(a+b*x))^2-4*(log(-b*x/a)+log(a/(a+b*x)))*log(-b*x/(a+b*x))^3+log(-b*x/(a+b*x))^4+6*log(x)^2*log(a+b*x)^2+4*(2*log(-b*x/a)^3-3*log(x)^2*log(a+b*x))*log(1+b*x/a)+6*(log(x)-log(-b*x/a))*(log(x)+3*log(-b*x/a))*log(1+b*x/a)^2-4*log(-b*x/a)^2*log(-b*x/(a+b*x))*(log(-b*x/a)+3*log(1+b*x/a))+12*(log(-b*x/a)^2-2*log(-b*x/a)*(log(-b*x/(a+b*x))+log(1+b*x/a))+2*log(x)*(-log(a+b*x)+log(1+b*x/a)))*polylog(2,-b*x/a)-12*log(-b*x/(a+b*x))^2*polylog(2,b*x/(a+b*x))+12*(log(-b*x/a)-log(-b*x/(a+b*x)))^2*polylog(2,1+b*x/a)+24*(log(x)-log(-b*x/a))*log(1+b*x/a)*polylog(2,1+b*x/a)+24*(log(-b*x/(a+b*x))+log(a+b*x))*polylog(3,-b*x/a)+24*log(-b*x/(a+b*x))*polylog(3,b*x/(a+b*x))+24*(-log(x)+log(-b*x/(a+b*x)))*polylog(3,1+b*x/a)-24*(polylog(4,-b*x/a)+polylog(4,b*x/(a+b*x))-polylog(4,1+b*x/a)))],

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

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

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

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

# Integrands of the form x^m (a+b Log[c (d+e x)^n]) (f+g Log[c (d+e x)^n])
[x^2*(a+b*log(c*(d+e*x)^n))*(f+g*log(c*(d+e*x)^n)),x,7,2*b*d^2*g*n^2*x/e^2-1/2*b*d*g*n^2*(d+e*x)^2/e^3+2/27*b*g*n^2*(d+e*x)^3/e^3-1/3*b*d^3*g*n^2*log(d+e*x)^2/e^3+1/3*x^3*(a+b*log(c*(d+e*x)^n))*(f+g*log(c*(d+e*x)^n))-d^2*n*(d+e*x)*(b*f+a*g+2*b*g*log(c*(d+e*x)^n))/e^3+1/2*d*n*(d+e*x)^2*(b*f+a*g+2*b*g*log(c*(d+e*x)^n))/e^3-1/9*n*(d+e*x)^3*(b*f+a*g+2*b*g*log(c*(d+e*x)^n))/e^3+1/3*d^3*n*log(d+e*x)*(b*f+a*g+2*b*g*log(c*(d+e*x)^n))/e^3],
[x*(a+b*log(c*(d+e*x)^n))*(f+g*log(c*(d+e*x)^n)),x,7,-2*b*d*g*n^2*x/e+1/4*b*g*n^2*(d+e*x)^2/e^2+1/2*b*d^2*g*n^2*log(d+e*x)^2/e^2+1/2*x^2*(a+b*log(c*(d+e*x)^n))*(f+g*log(c*(d+e*x)^n))+d*n*(d+e*x)*(b*f+a*g+2*b*g*log(c*(d+e*x)^n))/e^2-1/4*n*(d+e*x)^2*(b*f+a*g+2*b*g*log(c*(d+e*x)^n))/e^2-1/2*d^2*n*log(d+e*x)*(b*f+a*g+2*b*g*log(c*(d+e*x)^n))/e^2],
[(a+b*log(c*(d+e*x)^n))*(f+g*log(c*(d+e*x)^n)),x,6,-(b*f+a*g)*n*x+2*b*g*n^2*x-2*b*g*n*(d+e*x)*log(c*(d+e*x)^n)/e+x*(a+b*log(c*(d+e*x)^n))*(f+g*log(c*(d+e*x)^n))+1/4*d*(b*f+a*g+2*b*g*log(c*(d+e*x)^n))^2/(b*e*g)],
[(a+b*log(c*(d+e*x)^n))*(f+g*log(c*(d+e*x)^n))/x,x,6,log(x)*(a+b*log(c*(d+e*x)^n))*(f+g*log(c*(d+e*x)^n))-1/4*log(x)*(b*f+a*g+2*b*g*log(c*(d+e*x)^n))^2/(b*g)+1/4*log(-e*x/d)*(b*f+a*g+2*b*g*log(c*(d+e*x)^n))^2/(b*g)+n*(b*f+a*g+2*b*g*log(c*(d+e*x)^n))*polylog(2,1+e*x/d)-2*b*g*n^2*polylog(3,1+e*x/d)],
[(a+b*log(c*(d+e*x)^n))*(f+g*log(c*(d+e*x)^n))/x^2,x,4,-(a+b*log(c*(d+e*x)^n))*(f+g*log(c*(d+e*x)^n))/x+e*n*(b*f+a*g+2*b*g*log(c*(d+e*x)^n))*log(1-d/(d+e*x))/d-2*b*e*g*n^2*polylog(2,d/(d+e*x))/d],
[(a+b*log(c*(d+e*x)^n))*(f+g*log(c*(d+e*x)^n))/x^3,x,7,b*e^2*g*n^2*log(x)/d^2-1/2*(a+b*log(c*(d+e*x)^n))*(f+g*log(c*(d+e*x)^n))/x^2-1/2*e*n*(d+e*x)*(b*f+a*g+2*b*g*log(c*(d+e*x)^n))/(d^2*x)-1/2*e^2*n*(b*f+a*g+2*b*g*log(c*(d+e*x)^n))*log(1-d/(d+e*x))/d^2+b*e^2*g*n^2*polylog(2,d/(d+e*x))/d^2],
[(a+b*log(c*(d+e*x)^n))*(f+g*log(c*(d+e*x)^n))/x^4,x,11,-1/3*b*e^2*g*n^2/(d^2*x)-b*e^3*g*n^2*log(x)/d^3+1/3*b*e^3*g*n^2*log(d+e*x)/d^3-1/3*(a+b*log(c*(d+e*x)^n))*(f+g*log(c*(d+e*x)^n))/x^3-1/6*e*n*(b*f+a*g+2*b*g*log(c*(d+e*x)^n))/(d*x^2)+1/3*e^2*n*(d+e*x)*(b*f+a*g+2*b*g*log(c*(d+e*x)^n))/(d^3*x)+1/3*e^3*n*(b*f+a*g+2*b*g*log(c*(d+e*x)^n))*log(1-d/(d+e*x))/d^3-2/3*b*e^3*g*n^2*polylog(2,d/(d+e*x))/d^3],

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

# p>0
[x^3*(a+b*log(c*(d+e*x)^n))*(f+g*log(h*(i+j*x)^m)),x,35,1/4*a*g*i^3*m*x/j^3+1/4*b*d^3*f*n*x/e^3-5/16*b*d^3*g*m*n*x/e^3-5/16*b*g*i^3*m*n*x/j^3-5/24*b*d*g*i^2*m*n*x/(e*j^2)-5/24*b*d^2*g*i*m*n*x/(e^2*j)+3/32*b*d^2*g*m*n*x^2/e^2+3/32*b*g*i^2*m*n*x^2/j^2+1/12*b*d*g*i*m*n*x^2/(e*j)-7/144*b*d*g*m*n*x^3/e-7/144*b*g*i*m*n*x^3/j+1/32*b*g*m*n*x^4+1/16*b*d^4*g*m*n*log(d+e*x)/e^4+1/8*b*d^2*g*i^2*m*n*log(d+e*x)/(e^2*j^2)+1/12*b*d^3*g*i*m*n*log(d+e*x)/(e^3*j)+1/4*b*g*i^3*m*(d+e*x)*log(c*(d+e*x)^n)/(e*j^3)-1/8*g*i^2*m*x^2*(a+b*log(c*(d+e*x)^n))/j^2+1/12*g*i*m*x^3*(a+b*log(c*(d+e*x)^n))/j-1/16*g*m*x^4*(a+b*log(c*(d+e*x)^n))+1/16*b*g*i^4*m*n*log(i+j*x)/j^4+1/12*b*d*g*i^3*m*n*log(i+j*x)/(e*j^3)+1/8*b*d^2*g*i^2*m*n*log(i+j*x)/(e^2*j^2)-1/4*g*i^4*m*(a+b*log(c*(d+e*x)^n))*log(e*(i+j*x)/(e*i-d*j))/j^4+1/4*b*d^3*g*n*(i+j*x)*log(h*(i+j*x)^m)/(e^3*j)-1/8*b*d^2*n*x^2*(f+g*log(h*(i+j*x)^m))/e^2+1/12*b*d*n*x^3*(f+g*log(h*(i+j*x)^m))/e-1/16*b*n*x^4*(f+g*log(h*(i+j*x)^m))-1/4*b*d^4*n*log(-j*(d+e*x)/(e*i-d*j))*(f+g*log(h*(i+j*x)^m))/e^4+1/4*x^4*(a+b*log(c*(d+e*x)^n))*(f+g*log(h*(i+j*x)^m))-1/4*b*g*i^4*m*n*polylog(2,-j*(d+e*x)/(e*i-d*j))/j^4-1/4*b*d^4*g*m*n*polylog(2,e*(i+j*x)/(e*i-d*j))/e^4],
[x^2*(a+b*log(c*(d+e*x)^n))*(f+g*log(h*(i+j*x)^m)),x,29,-1/3*a*g*i^2*m*x/j^2-1/3*b*d^2*f*n*x/e^2+4/9*b*d^2*g*m*n*x/e^2+4/9*b*g*i^2*m*n*x/j^2+1/3*b*d*g*i*m*n*x/(e*j)-5/36*b*d*g*m*n*x^2/e-5/36*b*g*i*m*n*x^2/j+2/27*b*g*m*n*x^3-1/9*b*d^3*g*m*n*log(d+e*x)/e^3-1/6*b*d^2*g*i*m*n*log(d+e*x)/(e^2*j)-1/3*b*g*i^2*m*(d+e*x)*log(c*(d+e*x)^n)/(e*j^2)+1/6*g*i*m*x^2*(a+b*log(c*(d+e*x)^n))/j-1/9*g*m*x^3*(a+b*log(c*(d+e*x)^n))-1/9*b*g*i^3*m*n*log(i+j*x)/j^3-1/6*b*d*g*i^2*m*n*log(i+j*x)/(e*j^2)+1/3*g*i^3*m*(a+b*log(c*(d+e*x)^n))*log(e*(i+j*x)/(e*i-d*j))/j^3-1/3*b*d^2*g*n*(i+j*x)*log(h*(i+j*x)^m)/(e^2*j)+1/6*b*d*n*x^2*(f+g*log(h*(i+j*x)^m))/e-1/9*b*n*x^3*(f+g*log(h*(i+j*x)^m))+1/3*b*d^3*n*log(-j*(d+e*x)/(e*i-d*j))*(f+g*log(h*(i+j*x)^m))/e^3+1/3*x^3*(a+b*log(c*(d+e*x)^n))*(f+g*log(h*(i+j*x)^m))+1/3*b*g*i^3*m*n*polylog(2,-j*(d+e*x)/(e*i-d*j))/j^3+1/3*b*d^3*g*m*n*polylog(2,e*(i+j*x)/(e*i-d*j))/e^3],
[x*(a+b*log(c*(d+e*x)^n))*(f+g*log(h*(i+j*x)^m)),x,23,1/2*a*g*i*m*x/j+1/2*b*d*f*n*x/e-3/4*b*d*g*m*n*x/e-3/4*b*g*i*m*n*x/j+1/4*b*g*m*n*x^2+1/4*b*d^2*g*m*n*log(d+e*x)/e^2+1/2*b*g*i*m*(d+e*x)*log(c*(d+e*x)^n)/(e*j)-1/4*g*m*x^2*(a+b*log(c*(d+e*x)^n))+1/4*b*g*i^2*m*n*log(i+j*x)/j^2-1/2*g*i^2*m*(a+b*log(c*(d+e*x)^n))*log(e*(i+j*x)/(e*i-d*j))/j^2+1/2*b*d*g*n*(i+j*x)*log(h*(i+j*x)^m)/(e*j)-1/4*b*n*x^2*(f+g*log(h*(i+j*x)^m))-1/2*b*d^2*n*log(-j*(d+e*x)/(e*i-d*j))*(f+g*log(h*(i+j*x)^m))/e^2+1/2*x^2*(a+b*log(c*(d+e*x)^n))*(f+g*log(h*(i+j*x)^m))-1/2*b*g*i^2*m*n*polylog(2,-j*(d+e*x)/(e*i-d*j))/j^2-1/2*b*d^2*g*m*n*polylog(2,e*(i+j*x)/(e*i-d*j))/e^2],
[(a+b*log(c*(d+e*x)^n))*(f+g*log(h*(i+j*x)^m)),x,17,-a*g*m*x-b*f*n*x+2*b*g*m*n*x-b*g*m*(d+e*x)*log(c*(d+e*x)^n)/e+g*i*m*(a+b*log(c*(d+e*x)^n))*log(e*(i+j*x)/(e*i-d*j))/j-b*g*n*(i+j*x)*log(h*(i+j*x)^m)/j+b*d*n*log(-j*(d+e*x)/(e*i-d*j))*(f+g*log(h*(i+j*x)^m))/e+x*(a+b*log(c*(d+e*x)^n))*(f+g*log(h*(i+j*x)^m))+b*g*i*m*n*polylog(2,-j*(d+e*x)/(e*i-d*j))/j+b*d*g*m*n*polylog(2,e*(i+j*x)/(e*i-d*j))/e],
[(a+b*log(c*(d+e*x)^n))*(f+g*log(h*(i+j*x)^m))/x,x,13,f*log(-e*x/d)*(a+b*log(c*(d+e*x)^n))+b*g*m*n*log(-e*x/d)*log(d+e*x)*log(i+j*x)-b*g*m*log(-j*x/i)*(n*log(d+e*x)-log(c*(d+e*x)^n))*log(i+j*x)+1/2*b*g*m*n*(log(-e*x/d)+log((e*i-d*j)/(e*(i+j*x)))-log(-(e*i-d*j)*x/(d*(i+j*x))))*log(d*(i+j*x)/(i*(d+e*x)))^2-1/2*b*g*m*n*(log(-e*x/d)-log(-j*x/i))*(log(d+e*x)+log(d*(i+j*x)/(i*(d+e*x))))^2-b*g*log(-e*x/d)*log(c*(d+e*x)^n)*(m*log(i+j*x)-log(h*(i+j*x)^m))+a*g*log(-j*x/i)*log(h*(i+j*x)^m)+b*f*n*polylog(2,1+e*x/d)+b*g*m*n*(log(i+j*x)-log(d*(i+j*x)/(i*(d+e*x))))*polylog(2,1+e*x/d)-b*g*n*(m*log(i+j*x)-log(h*(i+j*x)^m))*polylog(2,1+e*x/d)+b*g*m*n*log(d*(i+j*x)/(i*(d+e*x)))*polylog(2,i*(d+e*x)/(d*(i+j*x)))-b*g*m*n*log(d*(i+j*x)/(i*(d+e*x)))*polylog(2,j*(d+e*x)/(e*(i+j*x)))+a*g*m*polylog(2,1+j*x/i)-b*g*m*(n*log(d+e*x)-log(c*(d+e*x)^n))*polylog(2,1+j*x/i)+b*g*m*n*(log(d+e*x)+log(d*(i+j*x)/(i*(d+e*x))))*polylog(2,1+j*x/i)-b*g*m*n*polylog(3,1+e*x/d)+b*g*m*n*polylog(3,i*(d+e*x)/(d*(i+j*x)))-b*g*m*n*polylog(3,j*(d+e*x)/(e*(i+j*x)))-b*g*m*n*polylog(3,1+j*x/i)],
[(a+b*log(c*(d+e*x)^n))*(f+g*log(h*(i+j*x)^m))/x^2,x,15,g*j*m*log(-e*x/d)*(a+b*log(c*(d+e*x)^n))/i-g*j*m*(a+b*log(c*(d+e*x)^n))*log(e*(i+j*x)/(e*i-d*j))/i+b*e*n*log(-j*x/i)*(f+g*log(h*(i+j*x)^m))/d-b*e*n*log(-j*(d+e*x)/(e*i-d*j))*(f+g*log(h*(i+j*x)^m))/d-(a+b*log(c*(d+e*x)^n))*(f+g*log(h*(i+j*x)^m))/x-b*g*j*m*n*polylog(2,-j*(d+e*x)/(e*i-d*j))/i+b*g*j*m*n*polylog(2,1+e*x/d)/i-b*e*g*m*n*polylog(2,e*(i+j*x)/(e*i-d*j))/d+b*e*g*m*n*polylog(2,1+j*x/i)/d],
[(a+b*log(c*(d+e*x)^n))*(f+g*log(h*(i+j*x)^m))/x^3,x,23,b*e*g*j*m*n*log(x)/(d*i)-1/2*b*e*g*j*m*n*log(d+e*x)/(d*i)-1/2*g*j*m*(a+b*log(c*(d+e*x)^n))/(i*x)-1/2*g*j^2*m*log(-e*x/d)*(a+b*log(c*(d+e*x)^n))/i^2-1/2*b*e*g*j*m*n*log(i+j*x)/(d*i)+1/2*g*j^2*m*(a+b*log(c*(d+e*x)^n))*log(e*(i+j*x)/(e*i-d*j))/i^2-1/2*b*e*n*(f+g*log(h*(i+j*x)^m))/(d*x)-1/2*b*e^2*n*log(-j*x/i)*(f+g*log(h*(i+j*x)^m))/d^2+1/2*b*e^2*n*log(-j*(d+e*x)/(e*i-d*j))*(f+g*log(h*(i+j*x)^m))/d^2-1/2*(a+b*log(c*(d+e*x)^n))*(f+g*log(h*(i+j*x)^m))/x^2+1/2*b*g*j^2*m*n*polylog(2,-j*(d+e*x)/(e*i-d*j))/i^2-1/2*b*g*j^2*m*n*polylog(2,1+e*x/d)/i^2+1/2*b*e^2*g*m*n*polylog(2,e*(i+j*x)/(e*i-d*j))/d^2-1/2*b*e^2*g*m*n*polylog(2,1+j*x/i)/d^2],

#  {x^3*(a + b*Log[c*(d + e*x)^n])^2*(f + g*Log[h*(i + j*x)^m]), x, 157, (2*a*b*d^3*f*n*x)/e^3 - (a*b*d^3*g*m*n*x)/e^3 - (5*a*b*g*i^3*m*n*x)/(8*j^3) - (2*a*b*d*g*i^2*m*n*x)/(3*e*j^2) - (3*a*b*d^2*g*i*m*n*x)/(4*e^2*j) - (2*b^2*d^3*f*n^2*x)/e^3 + (649*b^2*d^3*g*m*n^2*x)/(288*e^3) + (21*b^2*g*i^3*m*n^2*x)/(32*j^3) + (119*b^2*d*g*i^2*m*n^2*x)/(144*e*j^2) + (55*b^2*d^2*g*i*m*n^2*x)/(48*e^2*j) - (139*b^2*d^2*g*m*n^2*x^2)/(576*e^2) - (3*b^2*g*i^2*m*n^2*x^2)/(64*j^2) - (b^2*d*g*i*m*n^2*x^2)/(9*e*j) + (53*b^2*d*g*m*n^2*x^3)/(864*e) + (7*b^2*g*i*m*n^2*x^3)/(288*j) - (1/64)*b^2*g*m*n^2*x^4 + (3*b^2*d^2*f*n^2*(d + e*x)^2)/(4*e^4) - (3*b^2*d^2*g*m*n^2*(d + e*x)^2)/(16*e^4) - (b^2*g*i^2*m*n^2*(d + e*x)^2)/(16*e^2*j^2) - (b^2*d*g*i*m*n^2*(d + e*x)^2)/(8*e^3*j) - (2*b^2*d*f*n^2*(d + e*x)^3)/(9*e^4) + (b^2*d*g*m*n^2*(d + e*x)^3)/(18*e^4) + (b^2*g*i*m*n^2*(d + e*x)^3)/(54*e^3*j) + (b^2*f*n^2*(d + e*x)^4)/(32*e^4) - (b^2*g*m*n^2*(d + e*x)^4)/(128*e^4) - (61*b^2*d^4*g*m*n^2*Log[d + e*x])/(288*e^4) - (b^2*d^2*g*i^2*m*n^2*Log[d + e*x])/(16*e^2*j^2) - (b^2*d^3*g*i*m*n^2*Log[d + e*x])/(8*e^3*j) + (2*b^2*d^3*f*n*(d + e*x)*Log[c*(d + e*x)^n])/e^4 - (b^2*d^3*g*m*n*(d + e*x)*Log[c*(d + e*x)^n])/e^4 - (5*b^2*g*i^3*m*n*(d + e*x)*Log[c*(d + e*x)^n])/(8*e*j^3) - (2*b^2*d*g*i^2*m*n*(d + e*x)*Log[c*(d + e*x)^n])/(3*e^2*j^2) - (3*b^2*d^2*g*i*m*n*(d + e*x)*Log[c*(d + e*x)^n])/(4*e^3*j) + (b*d^2*g*m*n*x^2*(a + b*Log[c*(d + e*x)^n]))/(8*e^2) + (b*g*i^2*m*n*x^2*(a + b*Log[c*(d + e*x)^n]))/(16*j^2) + (b*d*g*i*m*n*x^2*(a + b*Log[c*(d + e*x)^n]))/(12*e*j) - (b*d*g*m*n*x^3*(a + b*Log[c*(d + e*x)^n]))/(18*e) - (b*g*i*m*n*x^3*(a + b*Log[c*(d + e*x)^n]))/(24*j) + (1/32)*b*g*m*n*x^4*(a + b*Log[c*(d + e*x)^n]) - (3*b*d^2*f*n*(d + e*x)^2*(a + b*Log[c*(d + e*x)^n]))/(2*e^4) + (3*b*d^2*g*m*n*(d + e*x)^2*(a + b*Log[c*(d + e*x)^n]))/(8*e^4) + (b*g*i^2*m*n*(d + e*x)^2*(a + b*Log[c*(d + e*x)^n]))/(8*e^2*j^2) + (b*d*g*i*m*n*(d + e*x)^2*(a + b*Log[c*(d + e*x)^n]))/(4*e^3*j) + (2*b*d*f*n*(d + e*x)^3*(a + b*Log[c*(d + e*x)^n]))/(3*e^4) - (b*d*g*m*n*(d + e*x)^3*(a + b*Log[c*(d + e*x)^n]))/(6*e^4) - (b*g*i*m*n*(d + e*x)^3*(a + b*Log[c*(d + e*x)^n]))/(18*e^3*j) - (b*f*n*(d + e*x)^4*(a + b*Log[c*(d + e*x)^n]))/(8*e^4) + (b*g*m*n*(d + e*x)^4*(a + b*Log[c*(d + e*x)^n]))/(32*e^4) - (d^4*f*(a + b*Log[c*(d + e*x)^n])^2)/(4*e^4) + (d^4*g*m*(a + b*Log[c*(d + e*x)^n])^2)/(16*e^4) + (d^3*g*i*m*(a + b*Log[c*(d + e*x)^n])^2)/(12*e^3*j) + (g*i*m*x^3*(a + b*Log[c*(d + e*x)^n])^2)/(12*j) - (1/16)*g*m*x^4*(a + b*Log[c*(d + e*x)^n])^2 + (g*i^3*m*(d + e*x)*(a + b*Log[c*(d + e*x)^n])^2)/(4*e*j^3) + (d*g*i^2*m*(d + e*x)*(a + b*Log[c*(d + e*x)^n])^2)/(4*e^2*j^2) - (g*i^2*m*(d + e*x)^2*(a + b*Log[c*(d + e*x)^n])^2)/(8*e^2*j^2) - (b^2*g*i^4*m*n^2*Log[i + j*x])/(32*j^4) - (7*b^2*d*g*i^3*m*n^2*Log[i + j*x])/(72*e*j^3) - (13*b^2*d^2*g*i^2*m*n^2*Log[i + j*x])/(48*e^2*j^2) + (b*g*i^4*m*n*(a + b*Log[c*(d + e*x)^n])*Log[(e*(i + j*x))/(e*i - d*j)])/(8*j^4) + (b*d*g*i^3*m*n*(a + b*Log[c*(d + e*x)^n])*Log[(e*(i + j*x))/(e*i - d*j)])/(6*e*j^3) + (b*d^2*g*i^2*m*n*(a + b*Log[c*(d + e*x)^n])*Log[(e*(i + j*x))/(e*i - d*j)])/(4*e^2*j^2) + (b*d^3*g*i*m*n*(a + b*Log[c*(d + e*x)^n])*Log[(e*(i + j*x))/(e*i - d*j)])/(2*e^3*j) + (d^4*g*m*(a + b*Log[c*(d + e*x)^n])^2*Log[(e*(i + j*x))/(e*i - d*j)])/(4*e^4) - (g*i^4*m*(a + b*Log[c*(d + e*x)^n])^2*Log[(e*(i + j*x))/(e*i - d*j)])/(4*j^4) + (13*b^2*d^2*g*n^2*x^2*Log[h*(i + j*x)^m])/(48*e^2) - (7*b^2*d*g*n^2*x^3*Log[h*(i + j*x)^m])/(72*e) + (1/32)*b^2*g*n^2*x^4*Log[h*(i + j*x)^m] - (25*b^2*d^3*g*n^2*(i + j*x)*Log[h*(i + j*x)^m])/(24*e^3*j) + (25*b^2*d^4*g*n^2*Log[-((j*(d + e*x))/(e*i - d*j))]*Log[h*(i + j*x)^m])/(24*e^4) + (b*d^3*g*n*x*(a + b*Log[c*(d + e*x)^n])*Log[h*(i + j*x)^m])/(2*e^3) - (b*d^2*g*n*x^2*(a + b*Log[c*(d + e*x)^n])*Log[h*(i + j*x)^m])/(4*e^2) + (b*d*g*n*x^3*(a + b*Log[c*(d + e*x)^n])*Log[h*(i + j*x)^m])/(6*e) - (1/8)*b*g*n*x^4*(a + b*Log[c*(d + e*x)^n])*Log[h*(i + j*x)^m] - (d^4*g*(a + b*Log[c*(d + e*x)^n])^2*Log[h*(i + j*x)^m])/(4*e^4) + (1/4)*x^4*(a + b*Log[c*(d + e*x)^n])^2*(f + g*Log[h*(i + j*x)^m]) + (b^2*g*i^4*m*n^2*PolyLog[2, -((j*(d + e*x))/(e*i - d*j))])/(8*j^4) + (b^2*d*g*i^3*m*n^2*PolyLog[2, -((j*(d + e*x))/(e*i - d*j))])/(6*e*j^3) + (b^2*d^2*g*i^2*m*n^2*PolyLog[2, -((j*(d + e*x))/(e*i - d*j))])/(4*e^2*j^2) + (b^2*d^3*g*i*m*n^2*PolyLog[2, -((j*(d + e*x))/(e*i - d*j))])/(2*e^3*j) + (b*d^4*g*m*n*(a + b*Log[c*(d + e*x)^n])*PolyLog[2, -((j*(d + e*x))/(e*i - d*j))])/(2*e^4) - (b*g*i^4*m*n*(a + b*Log[c*(d + e*x)^n])*PolyLog[2, -((j*(d + e*x))/(e*i - d*j))])/(2*j^4) + (25*b^2*d^4*g*m*n^2*PolyLog[2, (e*(i + j*x))/(e*i - d*j)])/(24*e^4) - (b^2*d^4*g*m*n^2*PolyLog[3, -((j*(d + e*x))/(e*i - d*j))])/(2*e^4) + (b^2*g*i^4*m*n^2*PolyLog[3, -((j*(d + e*x))/(e*i - d*j))])/(2*j^4)} 

#  {x^2*(a + b*Log[c*(d + e*x)^n])^2*(f + g*Log[h*(i + j*x)^m]), x, 108, (2*a*b*d^2*g*m*n*x)/(3*e^2) + (8*a*b*g*i^2*m*n*x)/(9*j^2) + (a*b*d*g*i*m*n*x)/(e*j) + (2*b^2*d^2*f*n^2*x)/e^2 - (151*b^2*d^2*g*m*n^2*x)/(54*e^2) - (26*b^2*g*i^2*m*n^2*x)/(27*j^2) - (25*b^2*d*g*i*m*n^2*x)/(18*e*j) + (7*b^2*d*g*m*n^2*x^2)/(27*e) + (5*b^2*g*i*m*n^2*x^2)/(54*j) - (4/81)*b^2*g*m*n^2*x^3 - (b^2*d*f*n^2*(d + e*x)^2)/(2*e^3) + (b^2*d*g*m*n^2*(d + e*x)^2)/(6*e^3) + (b^2*g*i*m*n^2*(d + e*x)^2)/(12*e^2*j) + (2*b^2*f*n^2*(d + e*x)^3)/(27*e^3) - (2*b^2*g*m*n^2*(d + e*x)^3)/(81*e^3) + (13*b^2*d^3*g*m*n^2*Log[d + e*x])/(54*e^3) + (b^2*d^2*g*i*m*n^2*Log[d + e*x])/(9*e^2*j) - (b^2*d^3*f*n^2*Log[d + e*x]^2)/(3*e^3) + (b^2*d^3*g*m*n^2*Log[d + e*x]^2)/(9*e^3) + (2*b^2*d^2*g*m*n*(d + e*x)*Log[c*(d + e*x)^n])/(3*e^3) + (8*b^2*g*i^2*m*n*(d + e*x)*Log[c*(d + e*x)^n])/(9*e*j^2) + (b^2*d*g*i*m*n*(d + e*x)*Log[c*(d + e*x)^n])/(e^2*j) - (b*d*g*m*n*x^2*(a + b*Log[c*(d + e*x)^n]))/(6*e) - (b*g*i*m*n*x^2*(a + b*Log[c*(d + e*x)^n]))/(9*j) + (2/27)*b*g*m*n*x^3*(a + b*Log[c*(d + e*x)^n]) - (b*g*i*m*n*(d + e*x)^2*(a + b*Log[c*(d + e*x)^n]))/(6*e^2*j) - (1/9)*b*f*n*((18*d^2*(d + e*x))/e^3 - (9*d*(d + e*x)^2)/e^3 + (2*(d + e*x)^3)/e^3 - (6*d^3*Log[d + e*x])/e^3)*(a + b*Log[c*(d + e*x)^n]) + (1/27)*b*g*m*n*((18*d^2*(d + e*x))/e^3 - (9*d*(d + e*x)^2)/e^3 + (2*(d + e*x)^3)/e^3 - (6*d^3*Log[d + e*x])/e^3)*(a + b*Log[c*(d + e*x)^n]) - (1/9)*g*m*x^3*(a + b*Log[c*(d + e*x)^n])^2 - (g*i^2*m*(d + e*x)*(a + b*Log[c*(d + e*x)^n])^2)/(3*e*j^2) - (d*g*i*m*(d + e*x)*(a + b*Log[c*(d + e*x)^n])^2)/(3*e^2*j) + (g*i*m*(d + e*x)^2*(a + b*Log[c*(d + e*x)^n])^2)/(6*e^2*j) + (2*b^2*g*i^3*m*n^2*Log[i + j*x])/(27*j^3) + (5*b^2*d*g*i^2*m*n^2*Log[i + j*x])/(18*e*j^2) - (2*b*g*i^3*m*n*(a + b*Log[c*(d + e*x)^n])*Log[(e*(i + j*x))/(e*i - d*j)])/(9*j^3) - (b*d*g*i^2*m*n*(a + b*Log[c*(d + e*x)^n])*Log[(e*(i + j*x))/(e*i - d*j)])/(3*e*j^2) - (2*b*d^2*g*i*m*n*(a + b*Log[c*(d + e*x)^n])*Log[(e*(i + j*x))/(e*i - d*j)])/(3*e^2*j) - (d^3*g*m*(a + b*Log[c*(d + e*x)^n])^2*Log[(e*(i + j*x))/(e*i - d*j)])/(3*e^3) + (g*i^3*m*(a + b*Log[c*(d + e*x)^n])^2*Log[(e*(i + j*x))/(e*i - d*j)])/(3*j^3) - (5*b^2*d*g*n^2*x^2*Log[h*(i + j*x)^m])/(18*e) + (2/27)*b^2*g*n^2*x^3*Log[h*(i + j*x)^m] + (11*b^2*d^2*g*n^2*(i + j*x)*Log[h*(i + j*x)^m])/(9*e^2*j) - (11*b^2*d^3*g*n^2*Log[-((j*(d + e*x))/(e*i - d*j))]*Log[h*(i + j*x)^m])/(9*e^3) - (2*b*d^2*g*n*x*(a + b*Log[c*(d + e*x)^n])*Log[h*(i + j*x)^m])/(3*e^2) + (b*d*g*n*x^2*(a + b*Log[c*(d + e*x)^n])*Log[h*(i + j*x)^m])/(3*e) - (2/9)*b*g*n*x^3*(a + b*Log[c*(d + e*x)^n])*Log[h*(i + j*x)^m] + (d^3*g*(a + b*Log[c*(d + e*x)^n])^2*Log[h*(i + j*x)^m])/(3*e^3) + (1/3)*x^3*(a + b*Log[c*(d + e*x)^n])^2*(f + g*Log[h*(i + j*x)^m]) - (2*b^2*g*i^3*m*n^2*PolyLog[2, -((j*(d + e*x))/(e*i - d*j))])/(9*j^3) - (b^2*d*g*i^2*m*n^2*PolyLog[2, -((j*(d + e*x))/(e*i - d*j))])/(3*e*j^2) - (2*b^2*d^2*g*i*m*n^2*PolyLog[2, -((j*(d + e*x))/(e*i - d*j))])/(3*e^2*j) - (2*b*d^3*g*m*n*(a + b*Log[c*(d + e*x)^n])*PolyLog[2, -((j*(d + e*x))/(e*i - d*j))])/(3*e^3) + (2*b*g*i^3*m*n*(a + b*Log[c*(d + e*x)^n])*PolyLog[2, -((j*(d + e*x))/(e*i - d*j))])/(3*j^3) - (11*b^2*d^3*g*m*n^2*PolyLog[2, (e*(i + j*x))/(e*i - d*j)])/(9*e^3) + (2*b^2*d^3*g*m*n^2*PolyLog[3, -((j*(d + e*x))/(e*i - d*j))])/(3*e^3) - (2*b^2*g*i^3*m*n^2*PolyLog[3, -((j*(d + e*x))/(e*i - d*j))])/(3*j^3)} 
[x*(a+b*log(c*(d+e*x)^n))^2*(f+g*log(h*(i+j*x)^m)),x,73,-2*a*b*d*g*m*n*x/e-3/2*a*b*g*i*m*n*x/j-2*b^2*d*f*n^2*x/e+15/4*b^2*d*g*m*n^2*x/e+7/4*b^2*g*i*m*n^2*x/j-1/4*b^2*g*m*n^2*x^2+1/4*b^2*f*n^2*(d+e*x)^2/e^2-1/8*b^2*g*m*n^2*(d+e*x)^2/e^2-1/4*b^2*d^2*g*m*n^2*log(d+e*x)/e^2+1/2*b^2*d^2*f*n^2*log(d+e*x)^2/e^2-2*b^2*d*g*m*n*(d+e*x)*log(c*(d+e*x)^n)/e^2-3/2*b^2*g*i*m*n*(d+e*x)*log(c*(d+e*x)^n)/(e*j)+1/4*b*g*m*n*x^2*(a+b*log(c*(d+e*x)^n))+2*b*d*f*n*(d+e*x)*(a+b*log(c*(d+e*x)^n))/e^2-1/2*b*f*n*(d+e*x)^2*(a+b*log(c*(d+e*x)^n))/e^2+1/4*b*g*m*n*(d+e*x)^2*(a+b*log(c*(d+e*x)^n))/e^2-b*d^2*f*n*log(d+e*x)*(a+b*log(c*(d+e*x)^n))/e^2+1/2*d*g*m*(d+e*x)*(a+b*log(c*(d+e*x)^n))^2/e^2+1/2*g*i*m*(d+e*x)*(a+b*log(c*(d+e*x)^n))^2/(e*j)-1/4*g*m*(d+e*x)^2*(a+b*log(c*(d+e*x)^n))^2/e^2-1/4*b^2*g*i^2*m*n^2*log(i+j*x)/j^2+1/2*b*g*i^2*m*n*(a+b*log(c*(d+e*x)^n))*log(e*(i+j*x)/(e*i-d*j))/j^2+b*d*g*i*m*n*(a+b*log(c*(d+e*x)^n))*log(e*(i+j*x)/(e*i-d*j))/(e*j)+1/2*d^2*g*m*(a+b*log(c*(d+e*x)^n))^2*log(e*(i+j*x)/(e*i-d*j))/e^2-1/2*g*i^2*m*(a+b*log(c*(d+e*x)^n))^2*log(e*(i+j*x)/(e*i-d*j))/j^2+1/4*b^2*g*n^2*x^2*log(h*(i+j*x)^m)-3/2*b^2*d*g*n^2*(i+j*x)*log(h*(i+j*x)^m)/(e*j)+3/2*b^2*d^2*g*n^2*log(-j*(d+e*x)/(e*i-d*j))*log(h*(i+j*x)^m)/e^2+b*d*g*n*x*(a+b*log(c*(d+e*x)^n))*log(h*(i+j*x)^m)/e-1/2*b*g*n*x^2*(a+b*log(c*(d+e*x)^n))*log(h*(i+j*x)^m)-1/2*d^2*g*(a+b*log(c*(d+e*x)^n))^2*log(h*(i+j*x)^m)/e^2+1/2*x^2*(a+b*log(c*(d+e*x)^n))^2*(f+g*log(h*(i+j*x)^m))+1/2*b^2*g*i^2*m*n^2*polylog(2,-j*(d+e*x)/(e*i-d*j))/j^2+b^2*d*g*i*m*n^2*polylog(2,-j*(d+e*x)/(e*i-d*j))/(e*j)+b*d^2*g*m*n*(a+b*log(c*(d+e*x)^n))*polylog(2,-j*(d+e*x)/(e*i-d*j))/e^2-b*g*i^2*m*n*(a+b*log(c*(d+e*x)^n))*polylog(2,-j*(d+e*x)/(e*i-d*j))/j^2+3/2*b^2*d^2*g*m*n^2*polylog(2,e*(i+j*x)/(e*i-d*j))/e^2-b^2*d^2*g*m*n^2*polylog(3,-j*(d+e*x)/(e*i-d*j))/e^2+b^2*g*i^2*m*n^2*polylog(3,-j*(d+e*x)/(e*i-d*j))/j^2],
[(a+b*log(c*(d+e*x)^n))^2*(f+g*log(h*(i+j*x)^m)),x,41,-2*a*b*f*n*x+4*a*b*g*m*n*x+2*b^2*f*n^2*x-6*b^2*g*m*n^2*x-2*b^2*f*n*(d+e*x)*log(c*(d+e*x)^n)/e+4*b^2*g*m*n*(d+e*x)*log(c*(d+e*x)^n)/e+d*f*(a+b*log(c*(d+e*x)^n))^2/e-g*m*(d+e*x)*(a+b*log(c*(d+e*x)^n))^2/e-2*b*g*i*m*n*(a+b*log(c*(d+e*x)^n))*log(e*(i+j*x)/(e*i-d*j))/j-d*g*m*(a+b*log(c*(d+e*x)^n))^2*log(e*(i+j*x)/(e*i-d*j))/e+g*i*m*(a+b*log(c*(d+e*x)^n))^2*log(e*(i+j*x)/(e*i-d*j))/j+2*b^2*g*n^2*(i+j*x)*log(h*(i+j*x)^m)/j-2*b^2*d*g*n^2*log(-j*(d+e*x)/(e*i-d*j))*log(h*(i+j*x)^m)/e-2*b*g*n*x*(a+b*log(c*(d+e*x)^n))*log(h*(i+j*x)^m)+d*g*(a+b*log(c*(d+e*x)^n))^2*log(h*(i+j*x)^m)/e+x*(a+b*log(c*(d+e*x)^n))^2*(f+g*log(h*(i+j*x)^m))-2*b^2*g*i*m*n^2*polylog(2,-j*(d+e*x)/(e*i-d*j))/j-2*b*d*g*m*n*(a+b*log(c*(d+e*x)^n))*polylog(2,-j*(d+e*x)/(e*i-d*j))/e+2*b*g*i*m*n*(a+b*log(c*(d+e*x)^n))*polylog(2,-j*(d+e*x)/(e*i-d*j))/j-2*b^2*d*g*m*n^2*polylog(2,e*(i+j*x)/(e*i-d*j))/e+2*b^2*d*g*m*n^2*polylog(3,-j*(d+e*x)/(e*i-d*j))/e-2*b^2*g*i*m*n^2*polylog(3,-j*(d+e*x)/(e*i-d*j))/j],
[(a+b*log(c*(d+e*x)^n))^2*(f+g*log(h*(i+j*x)^m))/x,x,0,Unintegrable((a+b*log(c*(d+e*x)^n))^2*(f+g*log(h*(i+j*x)^m))/x,x)],
[(a+b*log(c*(d+e*x)^n))^2*(f+g*log(h*(i+j*x)^m))/x^2,x,0,Unintegrable((a+b*log(c*(d+e*x)^n))^2*(f+g*log(h*(i+j*x)^m))/x^2,x)],

#  {x^2*(a + b*Log[c*(d + e*x)^n])^3*(f + g*Log[h*(i + j*x)^m]), x, 262, (6*a*b^2*d^2*f*n^2*x)/e^2 - (28*a*b^2*d^2*g*m*n^2*x)/(3*e^2) - (26*a*b^2*g*i^2*m*n^2*x)/(9*j^2) - (9*a*b^2*d*g*i*m*n^2*x)/(2*e*j) - (6*b^3*d^2*f*n^3*x)/e^2 + (1571*b^3*d^2*g*m*n^3*x)/(108*e^2) + (80*b^3*g*i^2*m*n^3*x)/(27*j^2) + (185*b^3*d*g*i*m*n^3*x)/(36*e*j) - (55*b^3*d*g*m*n^3*x^2)/(108*e) - (5*b^3*g*i*m*n^3*x^2)/(54*j) + (4/81)*b^3*g*m*n^3*x^3 + (3*b^3*d*f*n^3*(d + e*x)^2)/(4*e^3) - (13*b^3*d*g*m*n^3*(d + e*x)^2)/(24*e^3) - (5*b^3*g*i*m*n^3*(d + e*x)^2)/(24*e^2*j) - (2*b^3*f*n^3*(d + e*x)^3)/(27*e^3) + (4*b^3*g*m*n^3*(d + e*x)^3)/(81*e^3) - (53*b^3*d^3*g*m*n^3*Log[d + e*x])/(108*e^3) - (b^3*d^2*g*i*m*n^3*Log[d + e*x])/(9*e^2*j) + (6*b^3*d^2*f*n^2*(d + e*x)*Log[c*(d + e*x)^n])/e^3 - (28*b^3*d^2*g*m*n^2*(d + e*x)*Log[c*(d + e*x)^n])/(3*e^3) - (26*b^3*g*i^2*m*n^2*(d + e*x)*Log[c*(d + e*x)^n])/(9*e*j^2) - (9*b^3*d*g*i*m*n^2*(d + e*x)*Log[c*(d + e*x)^n])/(2*e^2*j) + (5*b^2*d*g*m*n^2*x^2*(a + b*Log[c*(d + e*x)^n]))/(12*e) + (b^2*g*i*m*n^2*x^2*(a + b*Log[c*(d + e*x)^n]))/(9*j) - (2/27)*b^2*g*m*n^2*x^3*(a + b*Log[c*(d + e*x)^n]) - (3*b^2*d*f*n^2*(d + e*x)^2*(a + b*Log[c*(d + e*x)^n]))/(2*e^3) + (13*b^2*d*g*m*n^2*(d + e*x)^2*(a + b*Log[c*(d + e*x)^n]))/(12*e^3) + (5*b^2*g*i*m*n^2*(d + e*x)^2*(a + b*Log[c*(d + e*x)^n]))/(12*e^2*j) + (2*b^2*f*n^2*(d + e*x)^3*(a + b*Log[c*(d + e*x)^n]))/(9*e^3) - (4*b^2*g*m*n^2*(d + e*x)^3*(a + b*Log[c*(d + e*x)^n]))/(27*e^3) + (b*d^3*g*m*n*(a + b*Log[c*(d + e*x)^n])^2)/(9*e^3) + (1/9)*b*g*m*n*x^3*(a + b*Log[c*(d + e*x)^n])^2 - (3*b*d^2*f*n*(d + e*x)*(a + b*Log[c*(d + e*x)^n])^2)/e^3 + (5*b*d^2*g*m*n*(d + e*x)*(a + b*Log[c*(d + e*x)^n])^2)/(2*e^3) + (4*b*g*i^2*m*n*(d + e*x)*(a + b*Log[c*(d + e*x)^n])^2)/(3*e*j^2) + (11*b*d*g*i*m*n*(d + e*x)*(a + b*Log[c*(d + e*x)^n])^2)/(6*e^2*j) + (3*b*d*f*n*(d + e*x)^2*(a + b*Log[c*(d + e*x)^n])^2)/(2*e^3) - (3*b*d*g*m*n*(d + e*x)^2*(a + b*Log[c*(d + e*x)^n])^2)/(4*e^3) - (5*b*g*i*m*n*(d + e*x)^2*(a + b*Log[c*(d + e*x)^n])^2)/(12*e^2*j) - (b*f*n*(d + e*x)^3*(a + b*Log[c*(d + e*x)^n])^2)/(3*e^3) + (b*g*m*n*(d + e*x)^3*(a + b*Log[c*(d + e*x)^n])^2)/(9*e^3) + (d^3*f*(a + b*Log[c*(d + e*x)^n])^3)/(3*e^3) - (d^2*g*m*(d + e*x)*(a + b*Log[c*(d + e*x)^n])^3)/(3*e^3) - (g*i^2*m*(d + e*x)*(a + b*Log[c*(d + e*x)^n])^3)/(3*e*j^2) - (d*g*i*m*(d + e*x)*(a + b*Log[c*(d + e*x)^n])^3)/(3*e^2*j) + (d*g*m*(d + e*x)^2*(a + b*Log[c*(d + e*x)^n])^3)/(3*e^3) + (g*i*m*(d + e*x)^2*(a + b*Log[c*(d + e*x)^n])^3)/(6*e^2*j) - (g*m*(d + e*x)^3*(a + b*Log[c*(d + e*x)^n])^3)/(9*e^3) - (2*b^3*g*i^3*m*n^3*Log[i + j*x])/(27*j^3) - (19*b^3*d*g*i^2*m*n^3*Log[i + j*x])/(36*e*j^2) + (2*b^2*g*i^3*m*n^2*(a + b*Log[c*(d + e*x)^n])*Log[(e*(i + j*x))/(e*i - d*j)])/(9*j^3) + (5*b^2*d*g*i^2*m*n^2*(a + b*Log[c*(d + e*x)^n])*Log[(e*(i + j*x))/(e*i - d*j)])/(6*e*j^2) + (11*b^2*d^2*g*i*m*n^2*(a + b*Log[c*(d + e*x)^n])*Log[(e*(i + j*x))/(e*i - d*j)])/(3*e^2*j) + (11*b*d^3*g*m*n*(a + b*Log[c*(d + e*x)^n])^2*Log[(e*(i + j*x))/(e*i - d*j)])/(6*e^3) - (b*g*i^3*m*n*(a + b*Log[c*(d + e*x)^n])^2*Log[(e*(i + j*x))/(e*i - d*j)])/(3*j^3) - (b*d*g*i^2*m*n*(a + b*Log[c*(d + e*x)^n])^2*Log[(e*(i + j*x))/(e*i - d*j)])/(2*e*j^2) - (b*d^2*g*i*m*n*(a + b*Log[c*(d + e*x)^n])^2*Log[(e*(i + j*x))/(e*i - d*j)])/(e^2*j) - (d^3*g*m*(a + b*Log[c*(d + e*x)^n])^3*Log[(e*(i + j*x))/(e*i - d*j)])/(3*e^3) + (g*i^3*m*(a + b*Log[c*(d + e*x)^n])^3*Log[(e*(i + j*x))/(e*i - d*j)])/(3*j^3) + (19*b^3*d*g*n^3*x^2*Log[h*(i + j*x)^m])/(36*e) - (2/27)*b^3*g*n^3*x^3*Log[h*(i + j*x)^m] - (85*b^3*d^2*g*n^3*(i + j*x)*Log[h*(i + j*x)^m])/(18*e^2*j) + (85*b^3*d^3*g*n^3*Log[-((j*(d + e*x))/(e*i - d*j))]*Log[h*(i + j*x)^m])/(18*e^3) + (11*b^2*d^2*g*n^2*x*(a + b*Log[c*(d + e*x)^n])*Log[h*(i + j*x)^m])/(3*e^2) - (5*b^2*d*g*n^2*x^2*(a + b*Log[c*(d + e*x)^n])*Log[h*(i + j*x)^m])/(6*e) + (2/9)*b^2*g*n^2*x^3*(a + b*Log[c*(d + e*x)^n])*Log[h*(i + j*x)^m] - (11*b*d^3*g*n*(a + b*Log[c*(d + e*x)^n])^2*Log[h*(i + j*x)^m])/(6*e^3) - (b*d^2*g*n*x*(a + b*Log[c*(d + e*x)^n])^2*Log[h*(i + j*x)^m])/e^2 + (b*d*g*n*x^2*(a + b*Log[c*(d + e*x)^n])^2*Log[h*(i + j*x)^m])/(2*e) - (1/3)*b*g*n*x^3*(a + b*Log[c*(d + e*x)^n])^2*Log[h*(i + j*x)^m] + (d^3*g*(a + b*Log[c*(d + e*x)^n])^3*Log[h*(i + j*x)^m])/(3*e^3) + (1/3)*x^3*(a + b*Log[c*(d + e*x)^n])^3*(f + g*Log[h*(i + j*x)^m]) + (2*b^3*g*i^3*m*n^3*PolyLog[2, -((j*(d + e*x))/(e*i - d*j))])/(9*j^3) + (5*b^3*d*g*i^2*m*n^3*PolyLog[2, -((j*(d + e*x))/(e*i - d*j))])/(6*e*j^2) + (11*b^3*d^2*g*i*m*n^3*PolyLog[2, -((j*(d + e*x))/(e*i - d*j))])/(3*e^2*j) + (11*b^2*d^3*g*m*n^2*(a + b*Log[c*(d + e*x)^n])*PolyLog[2, -((j*(d + e*x))/(e*i - d*j))])/(3*e^3) - (2*b^2*g*i^3*m*n^2*(a + b*Log[c*(d + e*x)^n])*PolyLog[2, -((j*(d + e*x))/(e*i - d*j))])/(3*j^3) - (b^2*d*g*i^2*m*n^2*(a + b*Log[c*(d + e*x)^n])*PolyLog[2, -((j*(d + e*x))/(e*i - d*j))])/(e*j^2) - (2*b^2*d^2*g*i*m*n^2*(a + b*Log[c*(d + e*x)^n])*PolyLog[2, -((j*(d + e*x))/(e*i - d*j))])/(e^2*j) - (b*d^3*g*m*n*(a + b*Log[c*(d + e*x)^n])^2*PolyLog[2, -((j*(d + e*x))/(e*i - d*j))])/e^3 + (b*g*i^3*m*n*(a + b*Log[c*(d + e*x)^n])^2*PolyLog[2, -((j*(d + e*x))/(e*i - d*j))])/j^3 + (85*b^3*d^3*g*m*n^3*PolyLog[2, (e*(i + j*x))/(e*i - d*j)])/(18*e^3) - (11*b^3*d^3*g*m*n^3*PolyLog[3, -((j*(d + e*x))/(e*i - d*j))])/(3*e^3) + (2*b^3*g*i^3*m*n^3*PolyLog[3, -((j*(d + e*x))/(e*i - d*j))])/(3*j^3) + (b^3*d*g*i^2*m*n^3*PolyLog[3, -((j*(d + e*x))/(e*i - d*j))])/(e*j^2) + (2*b^3*d^2*g*i*m*n^3*PolyLog[3, -((j*(d + e*x))/(e*i - d*j))])/(e^2*j) + (2*b^2*d^3*g*m*n^2*(a + b*Log[c*(d + e*x)^n])*PolyLog[3, -((j*(d + e*x))/(e*i - d*j))])/e^3 - (2*b^2*g*i^3*m*n^2*(a + b*Log[c*(d + e*x)^n])*PolyLog[3, -((j*(d + e*x))/(e*i - d*j))])/j^3 - (2*b^3*d^3*g*m*n^3*PolyLog[4, -((j*(d + e*x))/(e*i - d*j))])/e^3 + (2*b^3*g*i^3*m*n^3*PolyLog[4, -((j*(d + e*x))/(e*i - d*j))])/j^3} 
[x*(a+b*log(c*(d+e*x)^n))^3*(f+g*log(h*(i+j*x)^m)),x,148,-6*a*b^2*d*f*n^2*x/e+12*a*b^2*d*g*m*n^2*x/e+21/4*a*b^2*g*i*m*n^2*x/j+6*b^3*d*f*n^3*x/e-141/8*b^3*d*g*m*n^3*x/e-45/8*b^3*g*i*m*n^3*x/j+3/8*b^3*g*m*n^3*x^2-3/8*b^3*f*n^3*(d+e*x)^2/e^2+3/8*b^3*g*m*n^3*(d+e*x)^2/e^2+3/8*b^3*d^2*g*m*n^3*log(d+e*x)/e^2-6*b^3*d*f*n^2*(d+e*x)*log(c*(d+e*x)^n)/e^2+12*b^3*d*g*m*n^2*(d+e*x)*log(c*(d+e*x)^n)/e^2+21/4*b^3*g*i*m*n^2*(d+e*x)*log(c*(d+e*x)^n)/(e*j)-3/8*b^2*g*m*n^2*x^2*(a+b*log(c*(d+e*x)^n))+3/4*b^2*f*n^2*(d+e*x)^2*(a+b*log(c*(d+e*x)^n))/e^2-3/4*b^2*g*m*n^2*(d+e*x)^2*(a+b*log(c*(d+e*x)^n))/e^2+3*b*d*f*n*(d+e*x)*(a+b*log(c*(d+e*x)^n))^2/e^2-15/4*b*d*g*m*n*(d+e*x)*(a+b*log(c*(d+e*x)^n))^2/e^2-9/4*b*g*i*m*n*(d+e*x)*(a+b*log(c*(d+e*x)^n))^2/(e*j)-3/4*b*f*n*(d+e*x)^2*(a+b*log(c*(d+e*x)^n))^2/e^2+3/4*b*g*m*n*(d+e*x)^2*(a+b*log(c*(d+e*x)^n))^2/e^2-1/2*d^2*f*(a+b*log(c*(d+e*x)^n))^3/e^2+1/2*d*g*m*(d+e*x)*(a+b*log(c*(d+e*x)^n))^3/e^2+1/2*g*i*m*(d+e*x)*(a+b*log(c*(d+e*x)^n))^3/(e*j)-1/4*g*m*(d+e*x)^2*(a+b*log(c*(d+e*x)^n))^3/e^2+3/8*b^3*g*i^2*m*n^3*log(i+j*x)/j^2-3/4*b^2*g*i^2*m*n^2*(a+b*log(c*(d+e*x)^n))*log(e*(i+j*x)/(e*i-d*j))/j^2-9/2*b^2*d*g*i*m*n^2*(a+b*log(c*(d+e*x)^n))*log(e*(i+j*x)/(e*i-d*j))/(e*j)-9/4*b*d^2*g*m*n*(a+b*log(c*(d+e*x)^n))^2*log(e*(i+j*x)/(e*i-d*j))/e^2+3/4*b*g*i^2*m*n*(a+b*log(c*(d+e*x)^n))^2*log(e*(i+j*x)/(e*i-d*j))/j^2+3/2*b*d*g*i*m*n*(a+b*log(c*(d+e*x)^n))^2*log(e*(i+j*x)/(e*i-d*j))/(e*j)+1/2*d^2*g*m*(a+b*log(c*(d+e*x)^n))^3*log(e*(i+j*x)/(e*i-d*j))/e^2-1/2*g*i^2*m*(a+b*log(c*(d+e*x)^n))^3*log(e*(i+j*x)/(e*i-d*j))/j^2-3/8*b^3*g*n^3*x^2*log(h*(i+j*x)^m)+21/4*b^3*d*g*n^3*(i+j*x)*log(h*(i+j*x)^m)/(e*j)-21/4*b^3*d^2*g*n^3*log(-j*(d+e*x)/(e*i-d*j))*log(h*(i+j*x)^m)/e^2-9/2*b^2*d*g*n^2*x*(a+b*log(c*(d+e*x)^n))*log(h*(i+j*x)^m)/e+3/4*b^2*g*n^2*x^2*(a+b*log(c*(d+e*x)^n))*log(h*(i+j*x)^m)+9/4*b*d^2*g*n*(a+b*log(c*(d+e*x)^n))^2*log(h*(i+j*x)^m)/e^2+3/2*b*d*g*n*x*(a+b*log(c*(d+e*x)^n))^2*log(h*(i+j*x)^m)/e-3/4*b*g*n*x^2*(a+b*log(c*(d+e*x)^n))^2*log(h*(i+j*x)^m)-1/2*d^2*g*(a+b*log(c*(d+e*x)^n))^3*log(h*(i+j*x)^m)/e^2+1/2*x^2*(a+b*log(c*(d+e*x)^n))^3*(f+g*log(h*(i+j*x)^m))-3/4*b^3*g*i^2*m*n^3*polylog(2,-j*(d+e*x)/(e*i-d*j))/j^2-9/2*b^3*d*g*i*m*n^3*polylog(2,-j*(d+e*x)/(e*i-d*j))/(e*j)-9/2*b^2*d^2*g*m*n^2*(a+b*log(c*(d+e*x)^n))*polylog(2,-j*(d+e*x)/(e*i-d*j))/e^2+3/2*b^2*g*i^2*m*n^2*(a+b*log(c*(d+e*x)^n))*polylog(2,-j*(d+e*x)/(e*i-d*j))/j^2+3*b^2*d*g*i*m*n^2*(a+b*log(c*(d+e*x)^n))*polylog(2,-j*(d+e*x)/(e*i-d*j))/(e*j)+3/2*b*d^2*g*m*n*(a+b*log(c*(d+e*x)^n))^2*polylog(2,-j*(d+e*x)/(e*i-d*j))/e^2-3/2*b*g*i^2*m*n*(a+b*log(c*(d+e*x)^n))^2*polylog(2,-j*(d+e*x)/(e*i-d*j))/j^2-21/4*b^3*d^2*g*m*n^3*polylog(2,e*(i+j*x)/(e*i-d*j))/e^2+9/2*b^3*d^2*g*m*n^3*polylog(3,-j*(d+e*x)/(e*i-d*j))/e^2-3/2*b^3*g*i^2*m*n^3*polylog(3,-j*(d+e*x)/(e*i-d*j))/j^2-3*b^3*d*g*i*m*n^3*polylog(3,-j*(d+e*x)/(e*i-d*j))/(e*j)-3*b^2*d^2*g*m*n^2*(a+b*log(c*(d+e*x)^n))*polylog(3,-j*(d+e*x)/(e*i-d*j))/e^2+3*b^2*g*i^2*m*n^2*(a+b*log(c*(d+e*x)^n))*polylog(3,-j*(d+e*x)/(e*i-d*j))/j^2+3*b^3*d^2*g*m*n^3*polylog(4,-j*(d+e*x)/(e*i-d*j))/e^2-3*b^3*g*i^2*m*n^3*polylog(4,-j*(d+e*x)/(e*i-d*j))/j^2],
[(a+b*log(c*(d+e*x)^n))^3*(f+g*log(h*(i+j*x)^m)),x,64,6*a*b^2*f*n^2*x-18*a*b^2*g*m*n^2*x-6*b^3*f*n^3*x+24*b^3*g*m*n^3*x+6*b^3*f*n^2*(d+e*x)*log(c*(d+e*x)^n)/e-18*b^3*g*m*n^2*(d+e*x)*log(c*(d+e*x)^n)/e-3*b*f*n*(d+e*x)*(a+b*log(c*(d+e*x)^n))^2/e+6*b*g*m*n*(d+e*x)*(a+b*log(c*(d+e*x)^n))^2/e+d*f*(a+b*log(c*(d+e*x)^n))^3/e-g*m*(d+e*x)*(a+b*log(c*(d+e*x)^n))^3/e+6*b^2*g*i*m*n^2*(a+b*log(c*(d+e*x)^n))*log(e*(i+j*x)/(e*i-d*j))/j+3*b*d*g*m*n*(a+b*log(c*(d+e*x)^n))^2*log(e*(i+j*x)/(e*i-d*j))/e-3*b*g*i*m*n*(a+b*log(c*(d+e*x)^n))^2*log(e*(i+j*x)/(e*i-d*j))/j-d*g*m*(a+b*log(c*(d+e*x)^n))^3*log(e*(i+j*x)/(e*i-d*j))/e+g*i*m*(a+b*log(c*(d+e*x)^n))^3*log(e*(i+j*x)/(e*i-d*j))/j-6*b^3*g*n^3*(i+j*x)*log(h*(i+j*x)^m)/j+6*b^3*d*g*n^3*log(-j*(d+e*x)/(e*i-d*j))*log(h*(i+j*x)^m)/e+6*b^2*g*n^2*x*(a+b*log(c*(d+e*x)^n))*log(h*(i+j*x)^m)-3*b*d*g*n*(a+b*log(c*(d+e*x)^n))^2*log(h*(i+j*x)^m)/e-3*b*g*n*x*(a+b*log(c*(d+e*x)^n))^2*log(h*(i+j*x)^m)+d*g*(a+b*log(c*(d+e*x)^n))^3*log(h*(i+j*x)^m)/e+x*(a+b*log(c*(d+e*x)^n))^3*(f+g*log(h*(i+j*x)^m))+6*b^3*g*i*m*n^3*polylog(2,-j*(d+e*x)/(e*i-d*j))/j+6*b^2*d*g*m*n^2*(a+b*log(c*(d+e*x)^n))*polylog(2,-j*(d+e*x)/(e*i-d*j))/e-6*b^2*g*i*m*n^2*(a+b*log(c*(d+e*x)^n))*polylog(2,-j*(d+e*x)/(e*i-d*j))/j-3*b*d*g*m*n*(a+b*log(c*(d+e*x)^n))^2*polylog(2,-j*(d+e*x)/(e*i-d*j))/e+3*b*g*i*m*n*(a+b*log(c*(d+e*x)^n))^2*polylog(2,-j*(d+e*x)/(e*i-d*j))/j+6*b^3*d*g*m*n^3*polylog(2,e*(i+j*x)/(e*i-d*j))/e-6*b^3*d*g*m*n^3*polylog(3,-j*(d+e*x)/(e*i-d*j))/e+6*b^3*g*i*m*n^3*polylog(3,-j*(d+e*x)/(e*i-d*j))/j+6*b^2*d*g*m*n^2*(a+b*log(c*(d+e*x)^n))*polylog(3,-j*(d+e*x)/(e*i-d*j))/e-6*b^2*g*i*m*n^2*(a+b*log(c*(d+e*x)^n))*polylog(3,-j*(d+e*x)/(e*i-d*j))/j-6*b^3*d*g*m*n^3*polylog(4,-j*(d+e*x)/(e*i-d*j))/e+6*b^3*g*i*m*n^3*polylog(4,-j*(d+e*x)/(e*i-d*j))/j],
[(a+b*log(c*(d+e*x)^n))^3*(f+g*log(h*(i+j*x)^m))/x,x,0,Unintegrable((a+b*log(c*(d+e*x)^n))^3*(f+g*log(h*(i+j*x)^m))/x,x)],
[(a+b*log(c*(d+e*x)^n))^3*(f+g*log(h*(i+j*x)^m))/x^2,x,0,Unintegrable((a+b*log(c*(d+e*x)^n))^3*(f+g*log(h*(i+j*x)^m))/x^2,x)],

# p<0

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

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

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

# Integrands of the form (a+b Log[c (d (e+f x)^m)^n])^p
[(a+b*log(c*(d*(e+f*x)^m)^n))^4,x,7,-24*a*b^3*m^3*n^3*x+24*b^4*m^4*n^4*x-24*b^4*m^3*n^3*(e+f*x)*log(c*(d*(e+f*x)^m)^n)/f+12*b^2*m^2*n^2*(e+f*x)*(a+b*log(c*(d*(e+f*x)^m)^n))^2/f-4*b*m*n*(e+f*x)*(a+b*log(c*(d*(e+f*x)^m)^n))^3/f+(e+f*x)*(a+b*log(c*(d*(e+f*x)^m)^n))^4/f],
[(a+b*log(c*(d*(e+f*x)^m)^n))^3,x,6,6*a*b^2*m^2*n^2*x-6*b^3*m^3*n^3*x+6*b^3*m^2*n^2*(e+f*x)*log(c*(d*(e+f*x)^m)^n)/f-3*b*m*n*(e+f*x)*(a+b*log(c*(d*(e+f*x)^m)^n))^2/f+(e+f*x)*(a+b*log(c*(d*(e+f*x)^m)^n))^3/f],
[(a+b*log(c*(d*(e+f*x)^m)^n))^2,x,5,-2*a*b*m*n*x+2*b^2*m^2*n^2*x-2*b^2*m*n*(e+f*x)*log(c*(d*(e+f*x)^m)^n)/f+(e+f*x)*(a+b*log(c*(d*(e+f*x)^m)^n))^2/f],
[a+b*log(c*(d*(e+f*x)^m)^n),x,4,a*x-b*m*n*x+b*(e+f*x)*log(c*(d*(e+f*x)^m)^n)/f],
[1/(a+b*log(c*(d*(e+f*x)^m)^n)),x,4,(e+f*x)*Ei((a+b*log(c*(d*(e+f*x)^m)^n))/(b*m*n))/(b*exp(a/(b*m*n))*f*m*n*(c*(d*(e+f*x)^m)^n)^(1/(m*n)))],
[1/(a+b*log(c*(d*(e+f*x)^m)^n))^2,x,5,(e+f*x)*Ei((a+b*log(c*(d*(e+f*x)^m)^n))/(b*m*n))/(b^2*exp(a/(b*m*n))*f*m^2*n^2*(c*(d*(e+f*x)^m)^n)^(1/(m*n)))+(-e-f*x)/(b*f*m*n*(a+b*log(c*(d*(e+f*x)^m)^n)))],
[1/(a+b*log(c*(d*(e+f*x)^m)^n))^3,x,6,1/2*(e+f*x)*Ei((a+b*log(c*(d*(e+f*x)^m)^n))/(b*m*n))/(b^3*exp(a/(b*m*n))*f*m^3*n^3*(c*(d*(e+f*x)^m)^n)^(1/(m*n)))+1/2*(-e-f*x)/(b*f*m*n*(a+b*log(c*(d*(e+f*x)^m)^n))^2)+1/2*(-e-f*x)/(b^2*f*m^2*n^2*(a+b*log(c*(d*(e+f*x)^m)^n)))],

# Integrands of the form (a+b Log[c (d (e+f x)^m)^n])^(p/2)
[(a+b*log(c*(d*(e+f*x)^m)^n))^(5/2),x,8,-5/2*b*m*n*(e+f*x)*(a+b*log(c*(d*(e+f*x)^m)^n))^(3/2)/f+(e+f*x)*(a+b*log(c*(d*(e+f*x)^m)^n))^(5/2)/f-15/8*b^(5/2)*m^(5/2)*n^(5/2)*(e+f*x)*erfi(sqrt(a+b*log(c*(d*(e+f*x)^m)^n))/(sqrt(b)*sqrt(m)*sqrt(n)))*sqrt(Pi)/(exp(a/(b*m*n))*f*(c*(d*(e+f*x)^m)^n)^(1/(m*n)))+15/4*b^2*m^2*n^2*(e+f*x)*sqrt(a+b*log(c*(d*(e+f*x)^m)^n))/f],
[(a+b*log(c*(d*(e+f*x)^m)^n))^(3/2),x,7,(e+f*x)*(a+b*log(c*(d*(e+f*x)^m)^n))^(3/2)/f+3/4*b^(3/2)*m^(3/2)*n^(3/2)*(e+f*x)*erfi(sqrt(a+b*log(c*(d*(e+f*x)^m)^n))/(sqrt(b)*sqrt(m)*sqrt(n)))*sqrt(Pi)/(exp(a/(b*m*n))*f*(c*(d*(e+f*x)^m)^n)^(1/(m*n)))-3/2*b*m*n*(e+f*x)*sqrt(a+b*log(c*(d*(e+f*x)^m)^n))/f],
[(a+b*log(c*(d*(e+f*x)^m)^n))^(1/2),x,6,-1/2*(e+f*x)*erfi(sqrt(a+b*log(c*(d*(e+f*x)^m)^n))/(sqrt(b)*sqrt(m)*sqrt(n)))*sqrt(b)*sqrt(m)*sqrt(n)*sqrt(Pi)/(exp(a/(b*m*n))*f*(c*(d*(e+f*x)^m)^n)^(1/(m*n)))+(e+f*x)*sqrt(a+b*log(c*(d*(e+f*x)^m)^n))/f],
[1/(a+b*log(c*(d*(e+f*x)^m)^n))^(1/2),x,5,(e+f*x)*erfi(sqrt(a+b*log(c*(d*(e+f*x)^m)^n))/(sqrt(b)*sqrt(m)*sqrt(n)))*sqrt(Pi)/(exp(a/(b*m*n))*f*(c*(d*(e+f*x)^m)^n)^(1/(m*n))*sqrt(b)*sqrt(m)*sqrt(n))],
[1/(a+b*log(c*(d*(e+f*x)^m)^n))^(3/2),x,6,2*(e+f*x)*erfi(sqrt(a+b*log(c*(d*(e+f*x)^m)^n))/(sqrt(b)*sqrt(m)*sqrt(n)))*sqrt(Pi)/(b^(3/2)*exp(a/(b*m*n))*f*m^(3/2)*n^(3/2)*(c*(d*(e+f*x)^m)^n)^(1/(m*n)))-2*(e+f*x)/(b*f*m*n*sqrt(a+b*log(c*(d*(e+f*x)^m)^n)))],
[1/(a+b*log(c*(d*(e+f*x)^m)^n))^(5/2),x,7,-2/3*(e+f*x)/(b*f*m*n*(a+b*log(c*(d*(e+f*x)^m)^n))^(3/2))+4/3*(e+f*x)*erfi(sqrt(a+b*log(c*(d*(e+f*x)^m)^n))/(sqrt(b)*sqrt(m)*sqrt(n)))*sqrt(Pi)/(b^(5/2)*exp(a/(b*m*n))*f*m^(5/2)*n^(5/2)*(c*(d*(e+f*x)^m)^n)^(1/(m*n)))-4/3*(e+f*x)/(b^2*f*m^2*n^2*sqrt(a+b*log(c*(d*(e+f*x)^m)^n)))],
[1/(a+b*log(c*(d*(e+f*x)^m)^n))^(7/2),x,8,-2/5*(e+f*x)/(b*f*m*n*(a+b*log(c*(d*(e+f*x)^m)^n))^(5/2))-4/15*(e+f*x)/(b^2*f*m^2*n^2*(a+b*log(c*(d*(e+f*x)^m)^n))^(3/2))+8/15*(e+f*x)*erfi(sqrt(a+b*log(c*(d*(e+f*x)^m)^n))/(sqrt(b)*sqrt(m)*sqrt(n)))*sqrt(Pi)/(b^(7/2)*exp(a/(b*m*n))*f*m^(7/2)*n^(7/2)*(c*(d*(e+f*x)^m)^n)^(1/(m*n)))-8/15*(e+f*x)/(b^3*f*m^3*n^3*sqrt(a+b*log(c*(d*(e+f*x)^m)^n)))],

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

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

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

# p>0
[(g+h*x)^3*(a+b*log(c*(d*(e+f*x)^p)^q)),x,4,-1/4*b*(f*g-e*h)^3*p*q*x/f^3-1/8*b*(f*g-e*h)^2*p*q*(g+h*x)^2/(f^2*h)-1/12*b*(f*g-e*h)*p*q*(g+h*x)^3/(f*h)-1/16*b*p*q*(g+h*x)^4/h-1/4*b*(f*g-e*h)^4*p*q*log(e+f*x)/(f^4*h)+1/4*(g+h*x)^4*(a+b*log(c*(d*(e+f*x)^p)^q))/h],
[(g+h*x)^2*(a+b*log(c*(d*(e+f*x)^p)^q)),x,4,-1/3*b*(f*g-e*h)^2*p*q*x/f^2-1/6*b*(f*g-e*h)*p*q*(g+h*x)^2/(f*h)-1/9*b*p*q*(g+h*x)^3/h-1/3*b*(f*g-e*h)^3*p*q*log(e+f*x)/(f^3*h)+1/3*(g+h*x)^3*(a+b*log(c*(d*(e+f*x)^p)^q))/h],
[(g+h*x)*(a+b*log(c*(d*(e+f*x)^p)^q)),x,4,-1/2*b*(f*g-e*h)*p*q*x/f-1/4*b*p*q*(g+h*x)^2/h-1/2*b*(f*g-e*h)^2*p*q*log(e+f*x)/(f^2*h)+1/2*(g+h*x)^2*(a+b*log(c*(d*(e+f*x)^p)^q))/h],
[a+b*log(c*(d*(e+f*x)^p)^q),x,4,a*x-b*p*q*x+b*(e+f*x)*log(c*(d*(e+f*x)^p)^q)/f],
[(a+b*log(c*(d*(e+f*x)^p)^q))/(g+h*x),x,4,(a+b*log(c*(d*(e+f*x)^p)^q))*log(f*(g+h*x)/(f*g-e*h))/h+b*p*q*polylog(2,-h*(e+f*x)/(f*g-e*h))/h],
[(a+b*log(c*(d*(e+f*x)^p)^q))/(g+h*x)^2,x,5,b*f*p*q*log(e+f*x)/(h*(f*g-e*h))+(-a-b*log(c*(d*(e+f*x)^p)^q))/(h*(g+h*x))-b*f*p*q*log(g+h*x)/(h*(f*g-e*h))],
[(a+b*log(c*(d*(e+f*x)^p)^q))/(g+h*x)^3,x,4,1/2*b*f*p*q/(h*(f*g-e*h)*(g+h*x))+1/2*b*f^2*p*q*log(e+f*x)/(h*(f*g-e*h)^2)+1/2*(-a-b*log(c*(d*(e+f*x)^p)^q))/(h*(g+h*x)^2)-1/2*b*f^2*p*q*log(g+h*x)/(h*(f*g-e*h)^2)],
[(a+b*log(c*(d*(e+f*x)^p)^q))/(g+h*x)^4,x,4,1/6*b*f*p*q/(h*(f*g-e*h)*(g+h*x)^2)+1/3*b*f^2*p*q/(h*(f*g-e*h)^2*(g+h*x))+1/3*b*f^3*p*q*log(e+f*x)/(h*(f*g-e*h)^3)+1/3*(-a-b*log(c*(d*(e+f*x)^p)^q))/(h*(g+h*x)^3)-1/3*b*f^3*p*q*log(g+h*x)/(h*(f*g-e*h)^3)],
[(g+h*x)^3*(a+b*log(c*(d*(e+f*x)^p)^q))^2,x,9,2*b^2*(f*g-e*h)^3*p^2*q^2*x/f^3+3/4*b^2*h*(f*g-e*h)^2*p^2*q^2*(e+f*x)^2/f^4+2/9*b^2*h^2*(f*g-e*h)*p^2*q^2*(e+f*x)^3/f^4+1/32*b^2*h^3*p^2*q^2*(e+f*x)^4/f^4+1/4*b^2*(f*g-e*h)^4*p^2*q^2*log(e+f*x)^2/(f^4*h)-2*b*(f*g-e*h)^3*p*q*(e+f*x)*(a+b*log(c*(d*(e+f*x)^p)^q))/f^4-3/2*b*h*(f*g-e*h)^2*p*q*(e+f*x)^2*(a+b*log(c*(d*(e+f*x)^p)^q))/f^4-2/3*b*h^2*(f*g-e*h)*p*q*(e+f*x)^3*(a+b*log(c*(d*(e+f*x)^p)^q))/f^4-1/8*b*h^3*p*q*(e+f*x)^4*(a+b*log(c*(d*(e+f*x)^p)^q))/f^4-1/2*b*(f*g-e*h)^4*p*q*log(e+f*x)*(a+b*log(c*(d*(e+f*x)^p)^q))/(f^4*h)+1/4*(g+h*x)^4*(a+b*log(c*(d*(e+f*x)^p)^q))^2/h],
[(g+h*x)^2*(a+b*log(c*(d*(e+f*x)^p)^q))^2,x,9,2*b^2*(f*g-e*h)^2*p^2*q^2*x/f^2+1/2*b^2*h*(f*g-e*h)*p^2*q^2*(e+f*x)^2/f^3+2/27*b^2*h^2*p^2*q^2*(e+f*x)^3/f^3+1/3*b^2*(f*g-e*h)^3*p^2*q^2*log(e+f*x)^2/(f^3*h)-2*b*(f*g-e*h)^2*p*q*(e+f*x)*(a+b*log(c*(d*(e+f*x)^p)^q))/f^3-b*h*(f*g-e*h)*p*q*(e+f*x)^2*(a+b*log(c*(d*(e+f*x)^p)^q))/f^3-2/9*b*h^2*p*q*(e+f*x)^3*(a+b*log(c*(d*(e+f*x)^p)^q))/f^3-2/3*b*(f*g-e*h)^3*p*q*log(e+f*x)*(a+b*log(c*(d*(e+f*x)^p)^q))/(f^3*h)+1/3*(g+h*x)^3*(a+b*log(c*(d*(e+f*x)^p)^q))^2/h],
[(g+h*x)*(a+b*log(c*(d*(e+f*x)^p)^q))^2,x,10,-2*a*b*(f*g-e*h)*p*q*x/f+2*b^2*(f*g-e*h)*p^2*q^2*x/f+1/4*b^2*h*p^2*q^2*(e+f*x)^2/f^2-2*b^2*(f*g-e*h)*p*q*(e+f*x)*log(c*(d*(e+f*x)^p)^q)/f^2-1/2*b*h*p*q*(e+f*x)^2*(a+b*log(c*(d*(e+f*x)^p)^q))/f^2+(f*g-e*h)*(e+f*x)*(a+b*log(c*(d*(e+f*x)^p)^q))^2/f^2+1/2*h*(e+f*x)^2*(a+b*log(c*(d*(e+f*x)^p)^q))^2/f^2],
[(a+b*log(c*(d*(e+f*x)^p)^q))^2,x,5,-2*a*b*p*q*x+2*b^2*p^2*q^2*x-2*b^2*p*q*(e+f*x)*log(c*(d*(e+f*x)^p)^q)/f+(e+f*x)*(a+b*log(c*(d*(e+f*x)^p)^q))^2/f],
[(a+b*log(c*(d*(e+f*x)^p)^q))^2/(g+h*x),x,5,(a+b*log(c*(d*(e+f*x)^p)^q))^2*log(f*(g+h*x)/(f*g-e*h))/h+2*b*p*q*(a+b*log(c*(d*(e+f*x)^p)^q))*polylog(2,-h*(e+f*x)/(f*g-e*h))/h-2*b^2*p^2*q^2*polylog(3,-h*(e+f*x)/(f*g-e*h))/h],
[(a+b*log(c*(d*(e+f*x)^p)^q))^2/(g+h*x)^2,x,5,(e+f*x)*(a+b*log(c*(d*(e+f*x)^p)^q))^2/((f*g-e*h)*(g+h*x))-2*b*f*p*q*(a+b*log(c*(d*(e+f*x)^p)^q))*log(f*(g+h*x)/(f*g-e*h))/(h*(f*g-e*h))-2*b^2*f*p^2*q^2*polylog(2,-h*(e+f*x)/(f*g-e*h))/(h*(f*g-e*h))],
[(a+b*log(c*(d*(e+f*x)^p)^q))^2/(g+h*x)^3,x,8,-b*f*p*q*(e+f*x)*(a+b*log(c*(d*(e+f*x)^p)^q))/((f*g-e*h)^2*(g+h*x))-1/2*(a+b*log(c*(d*(e+f*x)^p)^q))^2/(h*(g+h*x)^2)+b^2*f^2*p^2*q^2*log(g+h*x)/(h*(f*g-e*h)^2)-b*f^2*p*q*(a+b*log(c*(d*(e+f*x)^p)^q))*log(1+(f*g-e*h)/(h*(e+f*x)))/(h*(f*g-e*h)^2)+b^2*f^2*p^2*q^2*polylog(2,(-f*g+e*h)/(h*(e+f*x)))/(h*(f*g-e*h)^2)],
[(g+h*x)^2*(a+b*log(c*(d*(e+f*x)^p)^q))^3,x,16,6*a*b^2*(f*g-e*h)^2*p^2*q^2*x/f^2-6*b^3*(f*g-e*h)^2*p^3*q^3*x/f^2-3/4*b^3*h*(f*g-e*h)*p^3*q^3*(e+f*x)^2/f^3-2/27*b^3*h^2*p^3*q^3*(e+f*x)^3/f^3+6*b^3*(f*g-e*h)^2*p^2*q^2*(e+f*x)*log(c*(d*(e+f*x)^p)^q)/f^3+3/2*b^2*h*(f*g-e*h)*p^2*q^2*(e+f*x)^2*(a+b*log(c*(d*(e+f*x)^p)^q))/f^3+2/9*b^2*h^2*p^2*q^2*(e+f*x)^3*(a+b*log(c*(d*(e+f*x)^p)^q))/f^3-3*b*(f*g-e*h)^2*p*q*(e+f*x)*(a+b*log(c*(d*(e+f*x)^p)^q))^2/f^3-3/2*b*h*(f*g-e*h)*p*q*(e+f*x)^2*(a+b*log(c*(d*(e+f*x)^p)^q))^2/f^3-1/3*b*h^2*p*q*(e+f*x)^3*(a+b*log(c*(d*(e+f*x)^p)^q))^2/f^3+(f*g-e*h)^2*(e+f*x)*(a+b*log(c*(d*(e+f*x)^p)^q))^3/f^3+h*(f*g-e*h)*(e+f*x)^2*(a+b*log(c*(d*(e+f*x)^p)^q))^3/f^3+1/3*h^2*(e+f*x)^3*(a+b*log(c*(d*(e+f*x)^p)^q))^3/f^3],
[(g+h*x)*(a+b*log(c*(d*(e+f*x)^p)^q))^3,x,12,6*a*b^2*(f*g-e*h)*p^2*q^2*x/f-6*b^3*(f*g-e*h)*p^3*q^3*x/f-3/8*b^3*h*p^3*q^3*(e+f*x)^2/f^2+6*b^3*(f*g-e*h)*p^2*q^2*(e+f*x)*log(c*(d*(e+f*x)^p)^q)/f^2+3/4*b^2*h*p^2*q^2*(e+f*x)^2*(a+b*log(c*(d*(e+f*x)^p)^q))/f^2-3*b*(f*g-e*h)*p*q*(e+f*x)*(a+b*log(c*(d*(e+f*x)^p)^q))^2/f^2-3/4*b*h*p*q*(e+f*x)^2*(a+b*log(c*(d*(e+f*x)^p)^q))^2/f^2+(f*g-e*h)*(e+f*x)*(a+b*log(c*(d*(e+f*x)^p)^q))^3/f^2+1/2*h*(e+f*x)^2*(a+b*log(c*(d*(e+f*x)^p)^q))^3/f^2],
[(a+b*log(c*(d*(e+f*x)^p)^q))^3,x,6,6*a*b^2*p^2*q^2*x-6*b^3*p^3*q^3*x+6*b^3*p^2*q^2*(e+f*x)*log(c*(d*(e+f*x)^p)^q)/f-3*b*p*q*(e+f*x)*(a+b*log(c*(d*(e+f*x)^p)^q))^2/f+(e+f*x)*(a+b*log(c*(d*(e+f*x)^p)^q))^3/f],
[(a+b*log(c*(d*(e+f*x)^p)^q))^3/(g+h*x),x,6,(a+b*log(c*(d*(e+f*x)^p)^q))^3*log(f*(g+h*x)/(f*g-e*h))/h+3*b*p*q*(a+b*log(c*(d*(e+f*x)^p)^q))^2*polylog(2,-h*(e+f*x)/(f*g-e*h))/h-6*b^2*p^2*q^2*(a+b*log(c*(d*(e+f*x)^p)^q))*polylog(3,-h*(e+f*x)/(f*g-e*h))/h+6*b^3*p^3*q^3*polylog(4,-h*(e+f*x)/(f*g-e*h))/h],
[(a+b*log(c*(d*(e+f*x)^p)^q))^3/(g+h*x)^2,x,6,(e+f*x)*(a+b*log(c*(d*(e+f*x)^p)^q))^3/((f*g-e*h)*(g+h*x))-3*b*f*p*q*(a+b*log(c*(d*(e+f*x)^p)^q))^2*log(f*(g+h*x)/(f*g-e*h))/(h*(f*g-e*h))-6*b^2*f*p^2*q^2*(a+b*log(c*(d*(e+f*x)^p)^q))*polylog(2,-h*(e+f*x)/(f*g-e*h))/(h*(f*g-e*h))+6*b^3*f*p^3*q^3*polylog(3,-h*(e+f*x)/(f*g-e*h))/(h*(f*g-e*h))],
[(a+b*log(c*(d*(e+f*x)^p)^q))^3/(g+h*x)^3,x,10,-3/2*b*f*p*q*(e+f*x)*(a+b*log(c*(d*(e+f*x)^p)^q))^2/((f*g-e*h)^2*(g+h*x))-1/2*(a+b*log(c*(d*(e+f*x)^p)^q))^3/(h*(g+h*x)^2)+3*b^2*f^2*p^2*q^2*(a+b*log(c*(d*(e+f*x)^p)^q))*log(f*(g+h*x)/(f*g-e*h))/(h*(f*g-e*h)^2)-3/2*b*f^2*p*q*(a+b*log(c*(d*(e+f*x)^p)^q))^2*log(1+(f*g-e*h)/(h*(e+f*x)))/(h*(f*g-e*h)^2)+3*b^2*f^2*p^2*q^2*(a+b*log(c*(d*(e+f*x)^p)^q))*polylog(2,(-f*g+e*h)/(h*(e+f*x)))/(h*(f*g-e*h)^2)+3*b^3*f^2*p^3*q^3*polylog(2,-h*(e+f*x)/(f*g-e*h))/(h*(f*g-e*h)^2)+3*b^3*f^2*p^3*q^3*polylog(3,(-f*g+e*h)/(h*(e+f*x)))/(h*(f*g-e*h)^2)],
[(a+b*log(c*(d*(e+f*x)^p)^q))^4,x,7,-24*a*b^3*p^3*q^3*x+24*b^4*p^4*q^4*x-24*b^4*p^3*q^3*(e+f*x)*log(c*(d*(e+f*x)^p)^q)/f+12*b^2*p^2*q^2*(e+f*x)*(a+b*log(c*(d*(e+f*x)^p)^q))^2/f-4*b*p*q*(e+f*x)*(a+b*log(c*(d*(e+f*x)^p)^q))^3/f+(e+f*x)*(a+b*log(c*(d*(e+f*x)^p)^q))^4/f],
[(a+b*log(c*(d*(e+f*x)^p)^q))^4/(g+h*x),x,7,(a+b*log(c*(d*(e+f*x)^p)^q))^4*log(f*(g+h*x)/(f*g-e*h))/h+4*b*p*q*(a+b*log(c*(d*(e+f*x)^p)^q))^3*polylog(2,-h*(e+f*x)/(f*g-e*h))/h-12*b^2*p^2*q^2*(a+b*log(c*(d*(e+f*x)^p)^q))^2*polylog(3,-h*(e+f*x)/(f*g-e*h))/h+24*b^3*p^3*q^3*(a+b*log(c*(d*(e+f*x)^p)^q))*polylog(4,-h*(e+f*x)/(f*g-e*h))/h-24*b^4*p^4*q^4*polylog(5,-h*(e+f*x)/(f*g-e*h))/h],
[(a+b*log(c*(d*(e+f*x)^p)^q))^4/(g+h*x)^2,x,7,(e+f*x)*(a+b*log(c*(d*(e+f*x)^p)^q))^4/((f*g-e*h)*(g+h*x))-4*b*f*p*q*(a+b*log(c*(d*(e+f*x)^p)^q))^3*log(f*(g+h*x)/(f*g-e*h))/(h*(f*g-e*h))-12*b^2*f*p^2*q^2*(a+b*log(c*(d*(e+f*x)^p)^q))^2*polylog(2,-h*(e+f*x)/(f*g-e*h))/(h*(f*g-e*h))+24*b^3*f*p^3*q^3*(a+b*log(c*(d*(e+f*x)^p)^q))*polylog(3,-h*(e+f*x)/(f*g-e*h))/(h*(f*g-e*h))-24*b^4*f*p^4*q^4*polylog(4,-h*(e+f*x)/(f*g-e*h))/(h*(f*g-e*h))],
[log(c*(d*(e+f*x)^p)^q),x,3,-p*q*x+(e+f*x)*log(c*(d*(e+f*x)^p)^q)/f],

# p<0
[(g+h*x)^2/(a+b*log(c*(d*(e+f*x)^p)^q)),x,12,(f*g-e*h)^2*(e+f*x)*Ei((a+b*log(c*(d*(e+f*x)^p)^q))/(b*p*q))/(b*exp(a/(b*p*q))*f^3*p*q*(c*(d*(e+f*x)^p)^q)^(1/(p*q)))+2*h*(f*g-e*h)*(e+f*x)^2*Ei(2*(a+b*log(c*(d*(e+f*x)^p)^q))/(b*p*q))/(b*exp(2*a/(b*p*q))*f^3*p*q*(c*(d*(e+f*x)^p)^q)^(2/(p*q)))+h^2*(e+f*x)^3*Ei(3*(a+b*log(c*(d*(e+f*x)^p)^q))/(b*p*q))/(b*exp(3*a/(b*p*q))*f^3*p*q*(c*(d*(e+f*x)^p)^q)^(3/(p*q)))],
[(g+h*x)/(a+b*log(c*(d*(e+f*x)^p)^q)),x,9,(f*g-e*h)*(e+f*x)*Ei((a+b*log(c*(d*(e+f*x)^p)^q))/(b*p*q))/(b*exp(a/(b*p*q))*f^2*p*q*(c*(d*(e+f*x)^p)^q)^(1/(p*q)))+h*(e+f*x)^2*Ei(2*(a+b*log(c*(d*(e+f*x)^p)^q))/(b*p*q))/(b*exp(2*a/(b*p*q))*f^2*p*q*(c*(d*(e+f*x)^p)^q)^(2/(p*q)))],
[1/(a+b*log(c*(d*(e+f*x)^p)^q)),x,4,(e+f*x)*Ei((a+b*log(c*(d*(e+f*x)^p)^q))/(b*p*q))/(b*exp(a/(b*p*q))*f*p*q*(c*(d*(e+f*x)^p)^q)^(1/(p*q)))],
[1/((g+h*x)*(a+b*log(c*(d*(e+f*x)^p)^q))),x,0,Unintegrable(1/((g+h*x)*(a+b*log(c*(d*(e+f*x)^p)^q))),x)],
[1/((g+h*x)^2*(a+b*log(c*(d*(e+f*x)^p)^q))),x,0,Unintegrable(1/((g+h*x)^2*(a+b*log(c*(d*(e+f*x)^p)^q))),x)],
[(g+h*x)^2/(a+b*log(c*(d*(e+f*x)^p)^q))^2,x,21,(f*g-e*h)^2*(e+f*x)*Ei((a+b*log(c*(d*(e+f*x)^p)^q))/(b*p*q))/(b^2*exp(a/(b*p*q))*f^3*p^2*q^2*(c*(d*(e+f*x)^p)^q)^(1/(p*q)))+4*h*(f*g-e*h)*(e+f*x)^2*Ei(2*(a+b*log(c*(d*(e+f*x)^p)^q))/(b*p*q))/(b^2*exp(2*a/(b*p*q))*f^3*p^2*q^2*(c*(d*(e+f*x)^p)^q)^(2/(p*q)))+3*h^2*(e+f*x)^3*Ei(3*(a+b*log(c*(d*(e+f*x)^p)^q))/(b*p*q))/(b^2*exp(3*a/(b*p*q))*f^3*p^2*q^2*(c*(d*(e+f*x)^p)^q)^(3/(p*q)))-(e+f*x)*(g+h*x)^2/(b*f*p*q*(a+b*log(c*(d*(e+f*x)^p)^q)))],
[(g+h*x)/(a+b*log(c*(d*(e+f*x)^p)^q))^2,x,13,(f*g-e*h)*(e+f*x)*Ei((a+b*log(c*(d*(e+f*x)^p)^q))/(b*p*q))/(b^2*exp(a/(b*p*q))*f^2*p^2*q^2*(c*(d*(e+f*x)^p)^q)^(1/(p*q)))+2*h*(e+f*x)^2*Ei(2*(a+b*log(c*(d*(e+f*x)^p)^q))/(b*p*q))/(b^2*exp(2*a/(b*p*q))*f^2*p^2*q^2*(c*(d*(e+f*x)^p)^q)^(2/(p*q)))-(e+f*x)*(g+h*x)/(b*f*p*q*(a+b*log(c*(d*(e+f*x)^p)^q)))],
[1/(a+b*log(c*(d*(e+f*x)^p)^q))^2,x,5,(e+f*x)*Ei((a+b*log(c*(d*(e+f*x)^p)^q))/(b*p*q))/(b^2*exp(a/(b*p*q))*f*p^2*q^2*(c*(d*(e+f*x)^p)^q)^(1/(p*q)))+(-e-f*x)/(b*f*p*q*(a+b*log(c*(d*(e+f*x)^p)^q)))],
[1/((g+h*x)*(a+b*log(c*(d*(e+f*x)^p)^q))^2),x,0,Unintegrable(1/((g+h*x)*(a+b*log(c*(d*(e+f*x)^p)^q))^2),x)],
[1/((g+h*x)^2*(a+b*log(c*(d*(e+f*x)^p)^q))^2),x,0,Unintegrable(1/((g+h*x)^2*(a+b*log(c*(d*(e+f*x)^p)^q))^2),x)],
[(g+h*x)^2/(a+b*log(c*(d*(e+f*x)^p)^q))^3,x,34,1/2*(f*g-e*h)^2*(e+f*x)*Ei((a+b*log(c*(d*(e+f*x)^p)^q))/(b*p*q))/(b^3*exp(a/(b*p*q))*f^3*p^3*q^3*(c*(d*(e+f*x)^p)^q)^(1/(p*q)))+4*h*(f*g-e*h)*(e+f*x)^2*Ei(2*(a+b*log(c*(d*(e+f*x)^p)^q))/(b*p*q))/(b^3*exp(2*a/(b*p*q))*f^3*p^3*q^3*(c*(d*(e+f*x)^p)^q)^(2/(p*q)))+9/2*h^2*(e+f*x)^3*Ei(3*(a+b*log(c*(d*(e+f*x)^p)^q))/(b*p*q))/(b^3*exp(3*a/(b*p*q))*f^3*p^3*q^3*(c*(d*(e+f*x)^p)^q)^(3/(p*q)))-1/2*(e+f*x)*(g+h*x)^2/(b*f*p*q*(a+b*log(c*(d*(e+f*x)^p)^q))^2)+(f*g-e*h)*(e+f*x)*(g+h*x)/(b^2*f^2*p^2*q^2*(a+b*log(c*(d*(e+f*x)^p)^q)))-3/2*(e+f*x)*(g+h*x)^2/(b^2*f*p^2*q^2*(a+b*log(c*(d*(e+f*x)^p)^q)))],
[(g+h*x)/(a+b*log(c*(d*(e+f*x)^p)^q))^3,x,18,1/2*(f*g-e*h)*(e+f*x)*Ei((a+b*log(c*(d*(e+f*x)^p)^q))/(b*p*q))/(b^3*exp(a/(b*p*q))*f^2*p^3*q^3*(c*(d*(e+f*x)^p)^q)^(1/(p*q)))+2*h*(e+f*x)^2*Ei(2*(a+b*log(c*(d*(e+f*x)^p)^q))/(b*p*q))/(b^3*exp(2*a/(b*p*q))*f^2*p^3*q^3*(c*(d*(e+f*x)^p)^q)^(2/(p*q)))-1/2*(e+f*x)*(g+h*x)/(b*f*p*q*(a+b*log(c*(d*(e+f*x)^p)^q))^2)+1/2*(f*g-e*h)*(e+f*x)/(b^2*f^2*p^2*q^2*(a+b*log(c*(d*(e+f*x)^p)^q)))-(e+f*x)*(g+h*x)/(b^2*f*p^2*q^2*(a+b*log(c*(d*(e+f*x)^p)^q)))],
[1/(a+b*log(c*(d*(e+f*x)^p)^q))^3,x,6,1/2*(e+f*x)*Ei((a+b*log(c*(d*(e+f*x)^p)^q))/(b*p*q))/(b^3*exp(a/(b*p*q))*f*p^3*q^3*(c*(d*(e+f*x)^p)^q)^(1/(p*q)))+1/2*(-e-f*x)/(b*f*p*q*(a+b*log(c*(d*(e+f*x)^p)^q))^2)+1/2*(-e-f*x)/(b^2*f*p^2*q^2*(a+b*log(c*(d*(e+f*x)^p)^q)))],
[1/((g+h*x)*(a+b*log(c*(d*(e+f*x)^p)^q))^3),x,0,Unintegrable(1/((g+h*x)*(a+b*log(c*(d*(e+f*x)^p)^q))^3),x)],
[1/((g+h*x)^2*(a+b*log(c*(d*(e+f*x)^p)^q))^3),x,0,Unintegrable(1/((g+h*x)^2*(a+b*log(c*(d*(e+f*x)^p)^q))^3),x)],

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

# p>0
[(g+h*x)^2*sqrt(a+b*log(c*(d*(e+f*x)^p)^q)),x,18,-1/6*h^2*(e+f*x)^3*erfi(sqrt(3)*sqrt(a+b*log(c*(d*(e+f*x)^p)^q))/(sqrt(b)*sqrt(p)*sqrt(q)))*sqrt(b)*sqrt(p)*sqrt(1/3*Pi)*sqrt(q)/(exp(3*a/(b*p*q))*f^3*(c*(d*(e+f*x)^p)^q)^(3/(p*q)))-1/2*h*(f*g-e*h)*(e+f*x)^2*erfi(sqrt(2)*sqrt(a+b*log(c*(d*(e+f*x)^p)^q))/(sqrt(b)*sqrt(p)*sqrt(q)))*sqrt(b)*sqrt(p)*sqrt(1/2*Pi)*sqrt(q)/(exp(2*a/(b*p*q))*f^3*(c*(d*(e+f*x)^p)^q)^(2/(p*q)))-1/2*(f*g-e*h)^2*(e+f*x)*erfi(sqrt(a+b*log(c*(d*(e+f*x)^p)^q))/(sqrt(b)*sqrt(p)*sqrt(q)))*sqrt(b)*sqrt(p)*sqrt(Pi)*sqrt(q)/(exp(a/(b*p*q))*f^3*(c*(d*(e+f*x)^p)^q)^(1/(p*q)))+(f*g-e*h)^2*(e+f*x)*sqrt(a+b*log(c*(d*(e+f*x)^p)^q))/f^3+h*(f*g-e*h)*(e+f*x)^2*sqrt(a+b*log(c*(d*(e+f*x)^p)^q))/f^3+1/3*h^2*(e+f*x)^3*sqrt(a+b*log(c*(d*(e+f*x)^p)^q))/f^3],
[(g+h*x)*sqrt(a+b*log(c*(d*(e+f*x)^p)^q)),x,13,-1/4*h*(e+f*x)^2*erfi(sqrt(2)*sqrt(a+b*log(c*(d*(e+f*x)^p)^q))/(sqrt(b)*sqrt(p)*sqrt(q)))*sqrt(b)*sqrt(p)*sqrt(1/2*Pi)*sqrt(q)/(exp(2*a/(b*p*q))*f^2*(c*(d*(e+f*x)^p)^q)^(2/(p*q)))-1/2*(f*g-e*h)*(e+f*x)*erfi(sqrt(a+b*log(c*(d*(e+f*x)^p)^q))/(sqrt(b)*sqrt(p)*sqrt(q)))*sqrt(b)*sqrt(p)*sqrt(Pi)*sqrt(q)/(exp(a/(b*p*q))*f^2*(c*(d*(e+f*x)^p)^q)^(1/(p*q)))+(f*g-e*h)*(e+f*x)*sqrt(a+b*log(c*(d*(e+f*x)^p)^q))/f^2+1/2*h*(e+f*x)^2*sqrt(a+b*log(c*(d*(e+f*x)^p)^q))/f^2],
[sqrt(a+b*log(c*(d*(e+f*x)^p)^q)),x,6,-1/2*(e+f*x)*erfi(sqrt(a+b*log(c*(d*(e+f*x)^p)^q))/(sqrt(b)*sqrt(p)*sqrt(q)))*sqrt(b)*sqrt(p)*sqrt(Pi)*sqrt(q)/(exp(a/(b*p*q))*f*(c*(d*(e+f*x)^p)^q)^(1/(p*q)))+(e+f*x)*sqrt(a+b*log(c*(d*(e+f*x)^p)^q))/f],
[sqrt(a+b*log(c*(d*(e+f*x)^p)^q))/(g+h*x),x,0,Unintegrable(sqrt(a+b*log(c*(d*(e+f*x)^p)^q))/(g+h*x),x)],
[sqrt(a+b*log(c*(d*(e+f*x)^p)^q))/(g+h*x)^2,x,0,Unintegrable(sqrt(a+b*log(c*(d*(e+f*x)^p)^q))/(g+h*x)^2,x)],
[(g+h*x)^2*(a+b*log(c*(d*(e+f*x)^p)^q))^(3/2),x,21,(f*g-e*h)^2*(e+f*x)*(a+b*log(c*(d*(e+f*x)^p)^q))^(3/2)/f^3+h*(f*g-e*h)*(e+f*x)^2*(a+b*log(c*(d*(e+f*x)^p)^q))^(3/2)/f^3+1/3*h^2*(e+f*x)^3*(a+b*log(c*(d*(e+f*x)^p)^q))^(3/2)/f^3+1/12*b^(3/2)*h^2*p^(3/2)*q^(3/2)*(e+f*x)^3*erfi(sqrt(3)*sqrt(a+b*log(c*(d*(e+f*x)^p)^q))/(sqrt(b)*sqrt(p)*sqrt(q)))*sqrt(1/3*Pi)/(exp(3*a/(b*p*q))*f^3*(c*(d*(e+f*x)^p)^q)^(3/(p*q)))+3/8*b^(3/2)*h*(f*g-e*h)*p^(3/2)*q^(3/2)*(e+f*x)^2*erfi(sqrt(2)*sqrt(a+b*log(c*(d*(e+f*x)^p)^q))/(sqrt(b)*sqrt(p)*sqrt(q)))*sqrt(1/2*Pi)/(exp(2*a/(b*p*q))*f^3*(c*(d*(e+f*x)^p)^q)^(2/(p*q)))+3/4*b^(3/2)*(f*g-e*h)^2*p^(3/2)*q^(3/2)*(e+f*x)*erfi(sqrt(a+b*log(c*(d*(e+f*x)^p)^q))/(sqrt(b)*sqrt(p)*sqrt(q)))*sqrt(Pi)/(exp(a/(b*p*q))*f^3*(c*(d*(e+f*x)^p)^q)^(1/(p*q)))-3/2*b*(f*g-e*h)^2*p*q*(e+f*x)*sqrt(a+b*log(c*(d*(e+f*x)^p)^q))/f^3-3/4*b*h*(f*g-e*h)*p*q*(e+f*x)^2*sqrt(a+b*log(c*(d*(e+f*x)^p)^q))/f^3-1/6*b*h^2*p*q*(e+f*x)^3*sqrt(a+b*log(c*(d*(e+f*x)^p)^q))/f^3],
[(g+h*x)*(a+b*log(c*(d*(e+f*x)^p)^q))^(3/2),x,15,(f*g-e*h)*(e+f*x)*(a+b*log(c*(d*(e+f*x)^p)^q))^(3/2)/f^2+1/2*h*(e+f*x)^2*(a+b*log(c*(d*(e+f*x)^p)^q))^(3/2)/f^2+3/16*b^(3/2)*h*p^(3/2)*q^(3/2)*(e+f*x)^2*erfi(sqrt(2)*sqrt(a+b*log(c*(d*(e+f*x)^p)^q))/(sqrt(b)*sqrt(p)*sqrt(q)))*sqrt(1/2*Pi)/(exp(2*a/(b*p*q))*f^2*(c*(d*(e+f*x)^p)^q)^(2/(p*q)))+3/4*b^(3/2)*(f*g-e*h)*p^(3/2)*q^(3/2)*(e+f*x)*erfi(sqrt(a+b*log(c*(d*(e+f*x)^p)^q))/(sqrt(b)*sqrt(p)*sqrt(q)))*sqrt(Pi)/(exp(a/(b*p*q))*f^2*(c*(d*(e+f*x)^p)^q)^(1/(p*q)))-3/2*b*(f*g-e*h)*p*q*(e+f*x)*sqrt(a+b*log(c*(d*(e+f*x)^p)^q))/f^2-3/8*b*h*p*q*(e+f*x)^2*sqrt(a+b*log(c*(d*(e+f*x)^p)^q))/f^2],
[(a+b*log(c*(d*(e+f*x)^p)^q))^(3/2),x,7,(e+f*x)*(a+b*log(c*(d*(e+f*x)^p)^q))^(3/2)/f+3/4*b^(3/2)*p^(3/2)*q^(3/2)*(e+f*x)*erfi(sqrt(a+b*log(c*(d*(e+f*x)^p)^q))/(sqrt(b)*sqrt(p)*sqrt(q)))*sqrt(Pi)/(exp(a/(b*p*q))*f*(c*(d*(e+f*x)^p)^q)^(1/(p*q)))-3/2*b*p*q*(e+f*x)*sqrt(a+b*log(c*(d*(e+f*x)^p)^q))/f],
[(a+b*log(c*(d*(e+f*x)^p)^q))^(3/2)/(g+h*x),x,0,Unintegrable((a+b*log(c*(d*(e+f*x)^p)^q))^(3/2)/(g+h*x),x)],
[(a+b*log(c*(d*(e+f*x)^p)^q))^(3/2)/(g+h*x)^2,x,0,Unintegrable((a+b*log(c*(d*(e+f*x)^p)^q))^(3/2)/(g+h*x)^2,x)],

# p<0
[(g+h*x)^2/sqrt(a+b*log(c*(d*(e+f*x)^p)^q)),x,15,h^2*(e+f*x)^3*erfi(sqrt(3)*sqrt(a+b*log(c*(d*(e+f*x)^p)^q))/(sqrt(b)*sqrt(p)*sqrt(q)))*sqrt(1/3*Pi)/(exp(3*a/(b*p*q))*f^3*(c*(d*(e+f*x)^p)^q)^(3/(p*q))*sqrt(b)*sqrt(p)*sqrt(q))+(f*g-e*h)^2*(e+f*x)*erfi(sqrt(a+b*log(c*(d*(e+f*x)^p)^q))/(sqrt(b)*sqrt(p)*sqrt(q)))*sqrt(Pi)/(exp(a/(b*p*q))*f^3*(c*(d*(e+f*x)^p)^q)^(1/(p*q))*sqrt(b)*sqrt(p)*sqrt(q))+h*(f*g-e*h)*(e+f*x)^2*erfi(sqrt(2)*sqrt(a+b*log(c*(d*(e+f*x)^p)^q))/(sqrt(b)*sqrt(p)*sqrt(q)))*sqrt(2*Pi)/(exp(2*a/(b*p*q))*f^3*(c*(d*(e+f*x)^p)^q)^(2/(p*q))*sqrt(b)*sqrt(p)*sqrt(q))],
[(g+h*x)/sqrt(a+b*log(c*(d*(e+f*x)^p)^q)),x,11,h*(e+f*x)^2*erfi(sqrt(2)*sqrt(a+b*log(c*(d*(e+f*x)^p)^q))/(sqrt(b)*sqrt(p)*sqrt(q)))*sqrt(1/2*Pi)/(exp(2*a/(b*p*q))*f^2*(c*(d*(e+f*x)^p)^q)^(2/(p*q))*sqrt(b)*sqrt(p)*sqrt(q))+(f*g-e*h)*(e+f*x)*erfi(sqrt(a+b*log(c*(d*(e+f*x)^p)^q))/(sqrt(b)*sqrt(p)*sqrt(q)))*sqrt(Pi)/(exp(a/(b*p*q))*f^2*(c*(d*(e+f*x)^p)^q)^(1/(p*q))*sqrt(b)*sqrt(p)*sqrt(q))],
[1/sqrt(a+b*log(c*(d*(e+f*x)^p)^q)),x,5,(e+f*x)*erfi(sqrt(a+b*log(c*(d*(e+f*x)^p)^q))/(sqrt(b)*sqrt(p)*sqrt(q)))*sqrt(Pi)/(exp(a/(b*p*q))*f*(c*(d*(e+f*x)^p)^q)^(1/(p*q))*sqrt(b)*sqrt(p)*sqrt(q))],
[1/((g+h*x)*sqrt(a+b*log(c*(d*(e+f*x)^p)^q))),x,0,Unintegrable(1/((g+h*x)*sqrt(a+b*log(c*(d*(e+f*x)^p)^q))),x)],
[(g+h*x)^2/(a+b*log(c*(d*(e+f*x)^p)^q))^(3/2),x,26,2*(f*g-e*h)^2*(e+f*x)*erfi(sqrt(a+b*log(c*(d*(e+f*x)^p)^q))/(sqrt(b)*sqrt(p)*sqrt(q)))*sqrt(Pi)/(b^(3/2)*exp(a/(b*p*q))*f^3*p^(3/2)*q^(3/2)*(c*(d*(e+f*x)^p)^q)^(1/(p*q)))+4*h*(f*g-e*h)*(e+f*x)^2*erfi(sqrt(2)*sqrt(a+b*log(c*(d*(e+f*x)^p)^q))/(sqrt(b)*sqrt(p)*sqrt(q)))*sqrt(2*Pi)/(b^(3/2)*exp(2*a/(b*p*q))*f^3*p^(3/2)*q^(3/2)*(c*(d*(e+f*x)^p)^q)^(2/(p*q)))+2*h^2*(e+f*x)^3*erfi(sqrt(3)*sqrt(a+b*log(c*(d*(e+f*x)^p)^q))/(sqrt(b)*sqrt(p)*sqrt(q)))*sqrt(3*Pi)/(b^(3/2)*exp(3*a/(b*p*q))*f^3*p^(3/2)*q^(3/2)*(c*(d*(e+f*x)^p)^q)^(3/(p*q)))-2*(e+f*x)*(g+h*x)^2/(b*f*p*q*sqrt(a+b*log(c*(d*(e+f*x)^p)^q)))],
[(g+h*x)/(a+b*log(c*(d*(e+f*x)^p)^q))^(3/2),x,16,2*(f*g-e*h)*(e+f*x)*erfi(sqrt(a+b*log(c*(d*(e+f*x)^p)^q))/(sqrt(b)*sqrt(p)*sqrt(q)))*sqrt(Pi)/(b^(3/2)*exp(a/(b*p*q))*f^2*p^(3/2)*q^(3/2)*(c*(d*(e+f*x)^p)^q)^(1/(p*q)))+2*h*(e+f*x)^2*erfi(sqrt(2)*sqrt(a+b*log(c*(d*(e+f*x)^p)^q))/(sqrt(b)*sqrt(p)*sqrt(q)))*sqrt(2*Pi)/(b^(3/2)*exp(2*a/(b*p*q))*f^2*p^(3/2)*q^(3/2)*(c*(d*(e+f*x)^p)^q)^(2/(p*q)))-2*(e+f*x)*(g+h*x)/(b*f*p*q*sqrt(a+b*log(c*(d*(e+f*x)^p)^q)))],
[1/(a+b*log(c*(d*(e+f*x)^p)^q))^(3/2),x,6,2*(e+f*x)*erfi(sqrt(a+b*log(c*(d*(e+f*x)^p)^q))/(sqrt(b)*sqrt(p)*sqrt(q)))*sqrt(Pi)/(b^(3/2)*exp(a/(b*p*q))*f*p^(3/2)*q^(3/2)*(c*(d*(e+f*x)^p)^q)^(1/(p*q)))-2*(e+f*x)/(b*f*p*q*sqrt(a+b*log(c*(d*(e+f*x)^p)^q)))],
[1/((g+h*x)*(a+b*log(c*(d*(e+f*x)^p)^q))^(3/2)),x,0,Unintegrable(1/((g+h*x)*(a+b*log(c*(d*(e+f*x)^p)^q))^(3/2)),x)],
[(g+h*x)^2/(a+b*log(c*(d*(e+f*x)^p)^q))^(5/2),x,42,-2/3*(e+f*x)*(g+h*x)^2/(b*f*p*q*(a+b*log(c*(d*(e+f*x)^p)^q))^(3/2))+4/3*(f*g-e*h)^2*(e+f*x)*erfi(sqrt(a+b*log(c*(d*(e+f*x)^p)^q))/(sqrt(b)*sqrt(p)*sqrt(q)))*sqrt(Pi)/(b^(5/2)*exp(a/(b*p*q))*f^3*p^(5/2)*q^(5/2)*(c*(d*(e+f*x)^p)^q)^(1/(p*q)))+16/3*h*(f*g-e*h)*(e+f*x)^2*erfi(sqrt(2)*sqrt(a+b*log(c*(d*(e+f*x)^p)^q))/(sqrt(b)*sqrt(p)*sqrt(q)))*sqrt(2*Pi)/(b^(5/2)*exp(2*a/(b*p*q))*f^3*p^(5/2)*q^(5/2)*(c*(d*(e+f*x)^p)^q)^(2/(p*q)))+4*h^2*(e+f*x)^3*erfi(sqrt(3)*sqrt(a+b*log(c*(d*(e+f*x)^p)^q))/(sqrt(b)*sqrt(p)*sqrt(q)))*sqrt(3*Pi)/(b^(5/2)*exp(3*a/(b*p*q))*f^3*p^(5/2)*q^(5/2)*(c*(d*(e+f*x)^p)^q)^(3/(p*q)))+8/3*(f*g-e*h)*(e+f*x)*(g+h*x)/(b^2*f^2*p^2*q^2*sqrt(a+b*log(c*(d*(e+f*x)^p)^q)))-4*(e+f*x)*(g+h*x)^2/(b^2*f*p^2*q^2*sqrt(a+b*log(c*(d*(e+f*x)^p)^q)))],
[(g+h*x)/(a+b*log(c*(d*(e+f*x)^p)^q))^(5/2),x,22,-2/3*(e+f*x)*(g+h*x)/(b*f*p*q*(a+b*log(c*(d*(e+f*x)^p)^q))^(3/2))+4/3*(f*g-e*h)*(e+f*x)*erfi(sqrt(a+b*log(c*(d*(e+f*x)^p)^q))/(sqrt(b)*sqrt(p)*sqrt(q)))*sqrt(Pi)/(b^(5/2)*exp(a/(b*p*q))*f^2*p^(5/2)*q^(5/2)*(c*(d*(e+f*x)^p)^q)^(1/(p*q)))+8/3*h*(e+f*x)^2*erfi(sqrt(2)*sqrt(a+b*log(c*(d*(e+f*x)^p)^q))/(sqrt(b)*sqrt(p)*sqrt(q)))*sqrt(2*Pi)/(b^(5/2)*exp(2*a/(b*p*q))*f^2*p^(5/2)*q^(5/2)*(c*(d*(e+f*x)^p)^q)^(2/(p*q)))+4/3*(f*g-e*h)*(e+f*x)/(b^2*f^2*p^2*q^2*sqrt(a+b*log(c*(d*(e+f*x)^p)^q)))-8/3*(e+f*x)*(g+h*x)/(b^2*f*p^2*q^2*sqrt(a+b*log(c*(d*(e+f*x)^p)^q)))],
[1/(a+b*log(c*(d*(e+f*x)^p)^q))^(5/2),x,7,-2/3*(e+f*x)/(b*f*p*q*(a+b*log(c*(d*(e+f*x)^p)^q))^(3/2))+4/3*(e+f*x)*erfi(sqrt(a+b*log(c*(d*(e+f*x)^p)^q))/(sqrt(b)*sqrt(p)*sqrt(q)))*sqrt(Pi)/(b^(5/2)*exp(a/(b*p*q))*f*p^(5/2)*q^(5/2)*(c*(d*(e+f*x)^p)^q)^(1/(p*q)))-4/3*(e+f*x)/(b^2*f*p^2*q^2*sqrt(a+b*log(c*(d*(e+f*x)^p)^q)))],
[1/((g+h*x)*(a+b*log(c*(d*(e+f*x)^p)^q))^(5/2)),x,0,Unintegrable(1/((g+h*x)*(a+b*log(c*(d*(e+f*x)^p)^q))^(5/2)),x)],

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

# p>0
[(g+h*x)^(3/2)*(a+b*log(c*(d*(e+f*x)^p)^q)),x,7,-4/15*b*(f*g-e*h)*p*q*(g+h*x)^(3/2)/(f*h)-4/25*b*p*q*(g+h*x)^(5/2)/h+4/5*b*(f*g-e*h)^(5/2)*p*q*arctanh(sqrt(f)*sqrt(g+h*x)/sqrt(f*g-e*h))/(f^(5/2)*h)+2/5*(g+h*x)^(5/2)*(a+b*log(c*(d*(e+f*x)^p)^q))/h-4/5*b*(f*g-e*h)^2*p*q*sqrt(g+h*x)/(f^2*h)],
[(g+h*x)^(1/2)*(a+b*log(c*(d*(e+f*x)^p)^q)),x,6,-4/9*b*p*q*(g+h*x)^(3/2)/h+4/3*b*(f*g-e*h)^(3/2)*p*q*arctanh(sqrt(f)*sqrt(g+h*x)/sqrt(f*g-e*h))/(f^(3/2)*h)+2/3*(g+h*x)^(3/2)*(a+b*log(c*(d*(e+f*x)^p)^q))/h-4/3*b*(f*g-e*h)*p*q*sqrt(g+h*x)/(f*h)],
[(a+b*log(c*(d*(e+f*x)^p)^q))/(g+h*x)^(1/2),x,5,4*b*p*q*arctanh(sqrt(f)*sqrt(g+h*x)/sqrt(f*g-e*h))*sqrt(f*g-e*h)/(h*sqrt(f))-4*b*p*q*sqrt(g+h*x)/h+2*(a+b*log(c*(d*(e+f*x)^p)^q))*sqrt(g+h*x)/h],
[(a+b*log(c*(d*(e+f*x)^p)^q))/(g+h*x)^(3/2),x,4,-4*b*p*q*arctanh(sqrt(f)*sqrt(g+h*x)/sqrt(f*g-e*h))*sqrt(f)/(h*sqrt(f*g-e*h))-2*(a+b*log(c*(d*(e+f*x)^p)^q))/(h*sqrt(g+h*x))],
[(a+b*log(c*(d*(e+f*x)^p)^q))/(g+h*x)^(5/2),x,5,-4/3*b*f^(3/2)*p*q*arctanh(sqrt(f)*sqrt(g+h*x)/sqrt(f*g-e*h))/(h*(f*g-e*h)^(3/2))-2/3*(a+b*log(c*(d*(e+f*x)^p)^q))/(h*(g+h*x)^(3/2))+4/3*b*f*p*q/(h*(f*g-e*h)*sqrt(g+h*x))],
[(a+b*log(c*(d*(e+f*x)^p)^q))/(g+h*x)^(7/2),x,6,4/15*b*f*p*q/(h*(f*g-e*h)*(g+h*x)^(3/2))-4/5*b*f^(5/2)*p*q*arctanh(sqrt(f)*sqrt(g+h*x)/sqrt(f*g-e*h))/(h*(f*g-e*h)^(5/2))-2/5*(a+b*log(c*(d*(e+f*x)^p)^q))/(h*(g+h*x)^(5/2))+4/5*b*f^2*p*q/(h*(f*g-e*h)^2*sqrt(g+h*x))],
[(a+b*log(c*(d*(e+f*x)^p)^q))/(g+h*x)^(9/2),x,7,4/35*b*f*p*q/(h*(f*g-e*h)*(g+h*x)^(5/2))+4/21*b*f^2*p*q/(h*(f*g-e*h)^2*(g+h*x)^(3/2))-4/7*b*f^(7/2)*p*q*arctanh(sqrt(f)*sqrt(g+h*x)/sqrt(f*g-e*h))/(h*(f*g-e*h)^(7/2))-2/7*(a+b*log(c*(d*(e+f*x)^p)^q))/(h*(g+h*x)^(7/2))+4/7*b*f^3*p*q/(h*(f*g-e*h)^3*sqrt(g+h*x))],
[(g+h*x)^(3/2)*(a+b*log(c*(d*(e+f*x)^p)^q))^2,x,29,128/225*b^2*(f*g-e*h)*p^2*q^2*(g+h*x)^(3/2)/(f*h)+16/125*b^2*p^2*q^2*(g+h*x)^(5/2)/h-368/75*b^2*(f*g-e*h)^(5/2)*p^2*q^2*arctanh(sqrt(f)*sqrt(g+h*x)/sqrt(f*g-e*h))/(f^(5/2)*h)-8/5*b^2*(f*g-e*h)^(5/2)*p^2*q^2*arctanh(sqrt(f)*sqrt(g+h*x)/sqrt(f*g-e*h))^2/(f^(5/2)*h)-8/15*b*(f*g-e*h)*p*q*(g+h*x)^(3/2)*(a+b*log(c*(d*(e+f*x)^p)^q))/(f*h)-8/25*b*p*q*(g+h*x)^(5/2)*(a+b*log(c*(d*(e+f*x)^p)^q))/h+8/5*b*(f*g-e*h)^(5/2)*p*q*arctanh(sqrt(f)*sqrt(g+h*x)/sqrt(f*g-e*h))*(a+b*log(c*(d*(e+f*x)^p)^q))/(f^(5/2)*h)+2/5*(g+h*x)^(5/2)*(a+b*log(c*(d*(e+f*x)^p)^q))^2/h+16/5*b^2*(f*g-e*h)^(5/2)*p^2*q^2*arctanh(sqrt(f)*sqrt(g+h*x)/sqrt(f*g-e*h))*log(2/(1-sqrt(f)*sqrt(g+h*x)/sqrt(f*g-e*h)))/(f^(5/2)*h)+8/5*b^2*(f*g-e*h)^(5/2)*p^2*q^2*polylog(2,1+(-2)/(1-sqrt(f)*sqrt(g+h*x)/sqrt(f*g-e*h)))/(f^(5/2)*h)+368/75*b^2*(f*g-e*h)^2*p^2*q^2*sqrt(g+h*x)/(f^2*h)-8/5*b*(f*g-e*h)^2*p*q*(a+b*log(c*(d*(e+f*x)^p)^q))*sqrt(g+h*x)/(f^2*h)],
[(g+h*x)^(1/2)*(a+b*log(c*(d*(e+f*x)^p)^q))^2,x,22,16/27*b^2*p^2*q^2*(g+h*x)^(3/2)/h-64/9*b^2*(f*g-e*h)^(3/2)*p^2*q^2*arctanh(sqrt(f)*sqrt(g+h*x)/sqrt(f*g-e*h))/(f^(3/2)*h)-8/3*b^2*(f*g-e*h)^(3/2)*p^2*q^2*arctanh(sqrt(f)*sqrt(g+h*x)/sqrt(f*g-e*h))^2/(f^(3/2)*h)-8/9*b*p*q*(g+h*x)^(3/2)*(a+b*log(c*(d*(e+f*x)^p)^q))/h+8/3*b*(f*g-e*h)^(3/2)*p*q*arctanh(sqrt(f)*sqrt(g+h*x)/sqrt(f*g-e*h))*(a+b*log(c*(d*(e+f*x)^p)^q))/(f^(3/2)*h)+2/3*(g+h*x)^(3/2)*(a+b*log(c*(d*(e+f*x)^p)^q))^2/h+16/3*b^2*(f*g-e*h)^(3/2)*p^2*q^2*arctanh(sqrt(f)*sqrt(g+h*x)/sqrt(f*g-e*h))*log(2/(1-sqrt(f)*sqrt(g+h*x)/sqrt(f*g-e*h)))/(f^(3/2)*h)+8/3*b^2*(f*g-e*h)^(3/2)*p^2*q^2*polylog(2,1+(-2)/(1-sqrt(f)*sqrt(g+h*x)/sqrt(f*g-e*h)))/(f^(3/2)*h)+64/9*b^2*(f*g-e*h)*p^2*q^2*sqrt(g+h*x)/(f*h)-8/3*b*(f*g-e*h)*p*q*(a+b*log(c*(d*(e+f*x)^p)^q))*sqrt(g+h*x)/(f*h)],
[(a+b*log(c*(d*(e+f*x)^p)^q))^2/(g+h*x)^(1/2),x,16,-16*b^2*p^2*q^2*arctanh(sqrt(f)*sqrt(g+h*x)/sqrt(f*g-e*h))*sqrt(f*g-e*h)/(h*sqrt(f))-8*b^2*p^2*q^2*arctanh(sqrt(f)*sqrt(g+h*x)/sqrt(f*g-e*h))^2*sqrt(f*g-e*h)/(h*sqrt(f))+8*b*p*q*arctanh(sqrt(f)*sqrt(g+h*x)/sqrt(f*g-e*h))*(a+b*log(c*(d*(e+f*x)^p)^q))*sqrt(f*g-e*h)/(h*sqrt(f))+16*b^2*p^2*q^2*arctanh(sqrt(f)*sqrt(g+h*x)/sqrt(f*g-e*h))*log(2/(1-sqrt(f)*sqrt(g+h*x)/sqrt(f*g-e*h)))*sqrt(f*g-e*h)/(h*sqrt(f))+8*b^2*p^2*q^2*polylog(2,1+(-2)/(1-sqrt(f)*sqrt(g+h*x)/sqrt(f*g-e*h)))*sqrt(f*g-e*h)/(h*sqrt(f))+16*b^2*p^2*q^2*sqrt(g+h*x)/h-8*b*p*q*(a+b*log(c*(d*(e+f*x)^p)^q))*sqrt(g+h*x)/h+2*(a+b*log(c*(d*(e+f*x)^p)^q))^2*sqrt(g+h*x)/h],
[(a+b*log(c*(d*(e+f*x)^p)^q))^2/(g+h*x)^(3/2),x,11,8*b^2*p^2*q^2*arctanh(sqrt(f)*sqrt(g+h*x)/sqrt(f*g-e*h))^2*sqrt(f)/(h*sqrt(f*g-e*h))-8*b*p*q*arctanh(sqrt(f)*sqrt(g+h*x)/sqrt(f*g-e*h))*(a+b*log(c*(d*(e+f*x)^p)^q))*sqrt(f)/(h*sqrt(f*g-e*h))-16*b^2*p^2*q^2*arctanh(sqrt(f)*sqrt(g+h*x)/sqrt(f*g-e*h))*log(2/(1-sqrt(f)*sqrt(g+h*x)/sqrt(f*g-e*h)))*sqrt(f)/(h*sqrt(f*g-e*h))-8*b^2*p^2*q^2*polylog(2,1+(-2)/(1-sqrt(f)*sqrt(g+h*x)/sqrt(f*g-e*h)))*sqrt(f)/(h*sqrt(f*g-e*h))-2*(a+b*log(c*(d*(e+f*x)^p)^q))^2/(h*sqrt(g+h*x))],
[(a+b*log(c*(d*(e+f*x)^p)^q))^2/(g+h*x)^(5/2),x,15,16/3*b^2*f^(3/2)*p^2*q^2*arctanh(sqrt(f)*sqrt(g+h*x)/sqrt(f*g-e*h))/(h*(f*g-e*h)^(3/2))+8/3*b^2*f^(3/2)*p^2*q^2*arctanh(sqrt(f)*sqrt(g+h*x)/sqrt(f*g-e*h))^2/(h*(f*g-e*h)^(3/2))-8/3*b*f^(3/2)*p*q*arctanh(sqrt(f)*sqrt(g+h*x)/sqrt(f*g-e*h))*(a+b*log(c*(d*(e+f*x)^p)^q))/(h*(f*g-e*h)^(3/2))-2/3*(a+b*log(c*(d*(e+f*x)^p)^q))^2/(h*(g+h*x)^(3/2))-16/3*b^2*f^(3/2)*p^2*q^2*arctanh(sqrt(f)*sqrt(g+h*x)/sqrt(f*g-e*h))*log(2/(1-sqrt(f)*sqrt(g+h*x)/sqrt(f*g-e*h)))/(h*(f*g-e*h)^(3/2))-8/3*b^2*f^(3/2)*p^2*q^2*polylog(2,1+(-2)/(1-sqrt(f)*sqrt(g+h*x)/sqrt(f*g-e*h)))/(h*(f*g-e*h)^(3/2))+8/3*b*f*p*q*(a+b*log(c*(d*(e+f*x)^p)^q))/(h*(f*g-e*h)*sqrt(g+h*x))],
[(a+b*log(c*(d*(e+f*x)^p)^q))^2/(g+h*x)^(7/2),x,20,64/15*b^2*f^(5/2)*p^2*q^2*arctanh(sqrt(f)*sqrt(g+h*x)/sqrt(f*g-e*h))/(h*(f*g-e*h)^(5/2))+8/5*b^2*f^(5/2)*p^2*q^2*arctanh(sqrt(f)*sqrt(g+h*x)/sqrt(f*g-e*h))^2/(h*(f*g-e*h)^(5/2))+8/15*b*f*p*q*(a+b*log(c*(d*(e+f*x)^p)^q))/(h*(f*g-e*h)*(g+h*x)^(3/2))-8/5*b*f^(5/2)*p*q*arctanh(sqrt(f)*sqrt(g+h*x)/sqrt(f*g-e*h))*(a+b*log(c*(d*(e+f*x)^p)^q))/(h*(f*g-e*h)^(5/2))-2/5*(a+b*log(c*(d*(e+f*x)^p)^q))^2/(h*(g+h*x)^(5/2))-16/5*b^2*f^(5/2)*p^2*q^2*arctanh(sqrt(f)*sqrt(g+h*x)/sqrt(f*g-e*h))*log(2/(1-sqrt(f)*sqrt(g+h*x)/sqrt(f*g-e*h)))/(h*(f*g-e*h)^(5/2))-8/5*b^2*f^(5/2)*p^2*q^2*polylog(2,1+(-2)/(1-sqrt(f)*sqrt(g+h*x)/sqrt(f*g-e*h)))/(h*(f*g-e*h)^(5/2))-16/15*b^2*f^2*p^2*q^2/(h*(f*g-e*h)^2*sqrt(g+h*x))+8/5*b*f^2*p*q*(a+b*log(c*(d*(e+f*x)^p)^q))/(h*(f*g-e*h)^2*sqrt(g+h*x))],
[(a+b*log(c*(d*(e+f*x)^p)^q))^2/(g+h*x)^(9/2),x,26,-16/105*b^2*f^2*p^2*q^2/(h*(f*g-e*h)^2*(g+h*x)^(3/2))+368/105*b^2*f^(7/2)*p^2*q^2*arctanh(sqrt(f)*sqrt(g+h*x)/sqrt(f*g-e*h))/(h*(f*g-e*h)^(7/2))+8/7*b^2*f^(7/2)*p^2*q^2*arctanh(sqrt(f)*sqrt(g+h*x)/sqrt(f*g-e*h))^2/(h*(f*g-e*h)^(7/2))+8/35*b*f*p*q*(a+b*log(c*(d*(e+f*x)^p)^q))/(h*(f*g-e*h)*(g+h*x)^(5/2))+8/21*b*f^2*p*q*(a+b*log(c*(d*(e+f*x)^p)^q))/(h*(f*g-e*h)^2*(g+h*x)^(3/2))-8/7*b*f^(7/2)*p*q*arctanh(sqrt(f)*sqrt(g+h*x)/sqrt(f*g-e*h))*(a+b*log(c*(d*(e+f*x)^p)^q))/(h*(f*g-e*h)^(7/2))-2/7*(a+b*log(c*(d*(e+f*x)^p)^q))^2/(h*(g+h*x)^(7/2))-16/7*b^2*f^(7/2)*p^2*q^2*arctanh(sqrt(f)*sqrt(g+h*x)/sqrt(f*g-e*h))*log(2/(1-sqrt(f)*sqrt(g+h*x)/sqrt(f*g-e*h)))/(h*(f*g-e*h)^(7/2))-8/7*b^2*f^(7/2)*p^2*q^2*polylog(2,1+(-2)/(1-sqrt(f)*sqrt(g+h*x)/sqrt(f*g-e*h)))/(h*(f*g-e*h)^(7/2))-128/105*b^2*f^3*p^2*q^2/(h*(f*g-e*h)^3*sqrt(g+h*x))+8/7*b*f^3*p*q*(a+b*log(c*(d*(e+f*x)^p)^q))/(h*(f*g-e*h)^3*sqrt(g+h*x))],

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

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

# p>0
[sqrt(g+h*x)*sqrt(a+b*log(c*(d*(e+f*x)^p)^q)),x,0,Unintegrable(sqrt(g+h*x)*sqrt(a+b*log(c*(d*(e+f*x)^p)^q)),x)],
[sqrt(a+b*log(c*(d*(e+f*x)^p)^q))/sqrt(g+h*x),x,0,Unintegrable(sqrt(a+b*log(c*(d*(e+f*x)^p)^q))/sqrt(g+h*x),x)],
[sqrt(a+b*log(c*(d*(e+f*x)^p)^q))/(g+h*x)^(3/2),x,0,Unintegrable(sqrt(a+b*log(c*(d*(e+f*x)^p)^q))/(g+h*x)^(3/2),x)],

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

# Integrands of the form (g+h x)^q (a+b Log[c (d (e+f x)^m)^n])^p when q symbolic
#  {(a + b*Log[c*(d*(e + f*x)^p)^q])^3*(g + h*x)^m, x, 0, (3*a^2*b*f*p*q*(g + h*x)^(2 + m)*Hypergeometric2F1[1, 2 + m, 3 + m, (f*(g + h*x))/(f*g - e*h)])/(h*(f*g - e*h)*(1 + m)*(2 + m)) + (6*a*b^2*p^2*q^2*(g + h*x)^(1 + m)*((f*(g + h*x))/(h*(e + f*x)))^(-1 - m)*HypergeometricPFQ[{-1 - m, -1 - m, -1 - m}, {-m, -m}, -((f*g - e*h)/(h*(e + f*x)))])/(h*(1 + m)^3) - (6*b^3*p^3*q^3*(g + h*x)^(1 + m)*((f*(g + h*x))/(h*(e + f*x)))^(-1 - m)*HypergeometricPFQ[{-1 - m, -1 - m, -1 - m, -1 - m}, {-m, -m, -m}, -((f*g - e*h)/(h*(e + f*x)))])/(h*(1 + m)^4) - (6*a*b^2*p*q*(g + h*x)^(1 + m)*((f*(g + h*x))/(h*(e + f*x)))^(-1 - m)*Hypergeometric2F1[-1 - m, -1 - m, -m, -((f*g - e*h)/(h*(e + f*x)))]*Log[c*(d*(e + f*x)^p)^q])/(h*(1 + m)^2) + (6*b^3*p^2*q^2*(g + h*x)^(1 + m)*((f*(g + h*x))/(h*(e + f*x)))^(-1 - m)*HypergeometricPFQ[{-1 - m, -1 - m, -1 - m}, {-m, -m}, -((f*g - e*h)/(h*(e + f*x)))]*Log[c*(d*(e + f*x)^p)^q])/(h*(1 + m)^3) - (3*b^3*p*q*(g + h*x)^(1 + m)*((f*(g + h*x))/(h*(e + f*x)))^(-1 - m)*Hypergeometric2F1[-1 - m, -1 - m, -m, -((f*g - e*h)/(h*(e + f*x)))]*Log[c*(d*(e + f*x)^p)^q]^2)/(h*(1 + m)^2) + ((g + h*x)^(1 + m)*(a + b*Log[c*(d*(e + f*x)^p)^q])^3)/(h*(1 + m))}

# {(a + b*Log[c*(d*(e + f*x)^p)^q])^2*(g + h*x)^m, x, 0, (a^2*(g + h*x)^(1 + m))/(h*(1 + m)) + (2*a*b*f*p*q*(g + h*x)^(2 + m)*Hypergeometric2F1[1, 2 + m, 3 + m, (f*(g + h*x))/(f*g - e*h)])/(h*(f*g - e*h)*(1 + m)*(2 + m)) + (2*b^2*p^2*q^2*(g + h*x)^(1 + m)*((f*(g + h*x))/(h*(e + f*x)))^(-1 - m)*HypergeometricPFQ[{-1 - m, -1 - m, -1 - m}, {-m, -m}, -((f*g - e*h)/(h*(e + f*x)))])/(h*(1 + m)^3) + (2*a*b*(g + h*x)^(1 + m)*Log[c*(d*(e + f*x)^p)^q])/(h*(1 + m)) - (2*b^2*p*q*(g + h*x)^(1 + m)*((f*(g + h*x))/(h*(e + f*x)))^(-1 - m)*Hypergeometric2F1[-1 - m, -1 - m, -m, -((f*g - e*h)/(h*(e + f*x)))]*Log[c*(d*(e + f*x)^p)^q])/(h*(1 + m)^2) + (b^2*(g + h*x)^(1 + m)*Log[c*(d*(e + f*x)^p)^q]^2)/(h*(1 + m))} 
[(g+h*x)^m*(a+b*log(c*(d*(e+f*x)^p)^q)),x,3,b*f*p*q*(g+h*x)^(2+m)*hypergeom([1,2+m],[3+m],f*(g+h*x)/(f*g-e*h))/(h*(f*g-e*h)*(1+m)*(2+m))+(g+h*x)^(1+m)*(a+b*log(c*(d*(e+f*x)^p)^q))/(h*(1+m))],
[(g+h*x)^m/(a+b*log(c*(d*(e+f*x)^p)^q)),x,0,Unintegrable((g+h*x)^m/(a+b*log(c*(d*(e+f*x)^p)^q)),x)],
[(g+h*x)^m/(a+b*log(c*(d*(e+f*x)^p)^q))^2,x,0,Unintegrable((g+h*x)^m/(a+b*log(c*(d*(e+f*x)^p)^q))^2,x)],
[(g+h*x)^m*(a+b*log(c*(d*(e+f*x)^p)^q))^(3/2),x,0,Unintegrable((g+h*x)^m*(a+b*log(c*(d*(e+f*x)^p)^q))^(3/2),x)],
[(g+h*x)^m*(a+b*log(c*(d*(e+f*x)^p)^q))^(1/2),x,0,Unintegrable((g+h*x)^m*sqrt(a+b*log(c*(d*(e+f*x)^p)^q)),x)],
[(g+h*x)^m/(a+b*log(c*(d*(e+f*x)^p)^q))^(1/2),x,0,Unintegrable((g+h*x)^m/sqrt(a+b*log(c*(d*(e+f*x)^p)^q)),x)],
[(g+h*x)^m/(a+b*log(c*(d*(e+f*x)^p)^q))^(3/2),x,0,Unintegrable((g+h*x)^m/(a+b*log(c*(d*(e+f*x)^p)^q))^(3/2),x)],

# Integrands of the form (g+h x)^q (a+b Log[c (d (e+f x)^m)^n])^p when p symbolic
[(g+h*x)^m*(a+b*log(c*(d*(e+f*x)^p)^q))^n,x,0,Unintegrable((g+h*x)^m*(a+b*log(c*(d*(e+f*x)^p)^q))^n,x)],
[(g+h*x)^2*(a+b*log(c*(d*(e+f*x)^p)^q))^n,x,12,3^(-1-n)*h^2*(e+f*x)^3*GAMMA(1+n,-3*(a+b*log(c*(d*(e+f*x)^p)^q))/(b*p*q))*(a+b*log(c*(d*(e+f*x)^p)^q))^n/(exp(3*a/(b*p*q))*f^3*(c*(d*(e+f*x)^p)^q)^(3/(p*q))*((-a-b*log(c*(d*(e+f*x)^p)^q))/(b*p*q))^n)+h*(f*g-e*h)*(e+f*x)^2*GAMMA(1+n,-2*(a+b*log(c*(d*(e+f*x)^p)^q))/(b*p*q))*(a+b*log(c*(d*(e+f*x)^p)^q))^n/(2^n*exp(2*a/(b*p*q))*f^3*(c*(d*(e+f*x)^p)^q)^(2/(p*q))*((-a-b*log(c*(d*(e+f*x)^p)^q))/(b*p*q))^n)+(f*g-e*h)^2*(e+f*x)*GAMMA(1+n,(-a-b*log(c*(d*(e+f*x)^p)^q))/(b*p*q))*(a+b*log(c*(d*(e+f*x)^p)^q))^n/(exp(a/(b*p*q))*f^3*(c*(d*(e+f*x)^p)^q)^(1/(p*q))*((-a-b*log(c*(d*(e+f*x)^p)^q))/(b*p*q))^n)],
[(g+h*x)*(a+b*log(c*(d*(e+f*x)^p)^q))^n,x,9,2^(-1-n)*h*(e+f*x)^2*GAMMA(1+n,-2*(a+b*log(c*(d*(e+f*x)^p)^q))/(b*p*q))*(a+b*log(c*(d*(e+f*x)^p)^q))^n/(exp(2*a/(b*p*q))*f^2*(c*(d*(e+f*x)^p)^q)^(2/(p*q))*((-a-b*log(c*(d*(e+f*x)^p)^q))/(b*p*q))^n)+(f*g-e*h)*(e+f*x)*GAMMA(1+n,(-a-b*log(c*(d*(e+f*x)^p)^q))/(b*p*q))*(a+b*log(c*(d*(e+f*x)^p)^q))^n/(exp(a/(b*p*q))*f^2*(c*(d*(e+f*x)^p)^q)^(1/(p*q))*((-a-b*log(c*(d*(e+f*x)^p)^q))/(b*p*q))^n)],
[(a+b*log(c*(d*(e+f*x)^p)^q))^n,x,4,(e+f*x)*GAMMA(1+n,(-a-b*log(c*(d*(e+f*x)^p)^q))/(b*p*q))*(a+b*log(c*(d*(e+f*x)^p)^q))^n/(exp(a/(b*p*q))*f*(c*(d*(e+f*x)^p)^q)^(1/(p*q))*((-a-b*log(c*(d*(e+f*x)^p)^q))/(b*p*q))^n)],
[(a+b*log(c*(d*(e+f*x)^p)^q))^n/(g+h*x),x,0,Unintegrable((a+b*log(c*(d*(e+f*x)^p)^q))^n/(g+h*x),x)],

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

# Integrands of the form (g+h x^2)^q (a+b Log[c (d (e+f x)^m)^n])
[(a+b*log(c*(d*(e+f*x)^p)^q))/(g+h*x^2),x,9,1/2*(a+b*log(c*(d*(e+f*x)^p)^q))*log(f*(sqrt(-g)-x*sqrt(h))/(f*sqrt(-g)+e*sqrt(h)))/(sqrt(-g)*sqrt(h))-1/2*(a+b*log(c*(d*(e+f*x)^p)^q))*log(f*(sqrt(-g)+x*sqrt(h))/(f*sqrt(-g)-e*sqrt(h)))/(sqrt(-g)*sqrt(h))-1/2*b*p*q*polylog(2,-(e+f*x)*sqrt(h)/(f*sqrt(-g)-e*sqrt(h)))/(sqrt(-g)*sqrt(h))+1/2*b*p*q*polylog(2,(e+f*x)*sqrt(h)/(f*sqrt(-g)+e*sqrt(h)))/(sqrt(-g)*sqrt(h))],
[(a+b*log(c*(d*(e+f*x)^p)^q))/sqrt(2+h*x^2),x,11,1/2*b*p*q*arcsinh(x*sqrt(h)/sqrt(2))^2/sqrt(h)+arcsinh(x*sqrt(h)/sqrt(2))*(a+b*log(c*(d*(e+f*x)^p)^q))/sqrt(h)-b*p*q*arcsinh(x*sqrt(h)/sqrt(2))*log(1+exp(arcsinh(x*sqrt(h)/sqrt(2)))*f*sqrt(2)/(e*sqrt(h)-sqrt(2*f^2+e^2*h)))/sqrt(h)-b*p*q*arcsinh(x*sqrt(h)/sqrt(2))*log(1+exp(arcsinh(x*sqrt(h)/sqrt(2)))*f*sqrt(2)/(e*sqrt(h)+sqrt(2*f^2+e^2*h)))/sqrt(h)-b*p*q*polylog(2,-exp(arcsinh(x*sqrt(h)/sqrt(2)))*f*sqrt(2)/(e*sqrt(h)-sqrt(2*f^2+e^2*h)))/sqrt(h)-b*p*q*polylog(2,-exp(arcsinh(x*sqrt(h)/sqrt(2)))*f*sqrt(2)/(e*sqrt(h)+sqrt(2*f^2+e^2*h)))/sqrt(h)],
[(a+b*log(c*(d*(e+f*x)^p)^q))/sqrt(g+h*x^2),x,12,1/2*b*p*q*arcsinh(x*sqrt(h)/sqrt(g))^2*sqrt(g)*sqrt(1+h*x^2/g)/(sqrt(h)*sqrt(g+h*x^2))+arcsinh(x*sqrt(h)/sqrt(g))*(a+b*log(c*(d*(e+f*x)^p)^q))*sqrt(g)*sqrt(1+h*x^2/g)/(sqrt(h)*sqrt(g+h*x^2))-b*p*q*arcsinh(x*sqrt(h)/sqrt(g))*log(1+exp(arcsinh(x*sqrt(h)/sqrt(g)))*f*sqrt(g)/(e*sqrt(h)-sqrt(f^2*g+e^2*h)))*sqrt(g)*sqrt(1+h*x^2/g)/(sqrt(h)*sqrt(g+h*x^2))-b*p*q*arcsinh(x*sqrt(h)/sqrt(g))*log(1+exp(arcsinh(x*sqrt(h)/sqrt(g)))*f*sqrt(g)/(e*sqrt(h)+sqrt(f^2*g+e^2*h)))*sqrt(g)*sqrt(1+h*x^2/g)/(sqrt(h)*sqrt(g+h*x^2))-b*p*q*polylog(2,-exp(arcsinh(x*sqrt(h)/sqrt(g)))*f*sqrt(g)/(e*sqrt(h)-sqrt(f^2*g+e^2*h)))*sqrt(g)*sqrt(1+h*x^2/g)/(sqrt(h)*sqrt(g+h*x^2))-b*p*q*polylog(2,-exp(arcsinh(x*sqrt(h)/sqrt(g)))*f*sqrt(g)/(e*sqrt(h)+sqrt(f^2*g+e^2*h)))*sqrt(g)*sqrt(1+h*x^2/g)/(sqrt(h)*sqrt(g+h*x^2))],
[(a+b*log(c*(d*(e+f*x)^p)^q))/(sqrt(2-h*x)*sqrt(2+h*x)),x,10,1/2*I*b*p*q*arcsin(1/2*h*x)^2/h+arcsin(1/2*h*x)*(a+b*log(c*(d*(e+f*x)^p)^q))/h-b*p*q*arcsin(1/2*h*x)*log(1+2*exp(I*arcsin(1/2*h*x))*f/(I*e*h-sqrt(4*f^2-e^2*h^2)))/h-b*p*q*arcsin(1/2*h*x)*log(1+2*exp(I*arcsin(1/2*h*x))*f/(I*e*h+sqrt(4*f^2-e^2*h^2)))/h+I*b*p*q*polylog(2,-2*exp(I*arcsin(1/2*h*x))*f/(I*e*h-sqrt(4*f^2-e^2*h^2)))/h+I*b*p*q*polylog(2,-2*exp(I*arcsin(1/2*h*x))*f/(I*e*h+sqrt(4*f^2-e^2*h^2)))/h],
[(a+b*log(c*(d*(e+f*x)^p)^q))/(sqrt(g-h*x)*sqrt(g+h*x)),x,12,1/2*I*b*g*p*q*arcsin(h*x/g)^2*sqrt(1-h^2*x^2/g^2)/(h*sqrt(g-h*x)*sqrt(g+h*x))+g*arcsin(h*x/g)*(a+b*log(c*(d*(e+f*x)^p)^q))*sqrt(1-h^2*x^2/g^2)/(h*sqrt(g-h*x)*sqrt(g+h*x))-b*g*p*q*arcsin(h*x/g)*log(1+exp(I*arcsin(h*x/g))*f*g/(I*e*h-sqrt(f^2*g^2-e^2*h^2)))*sqrt(1-h^2*x^2/g^2)/(h*sqrt(g-h*x)*sqrt(g+h*x))-b*g*p*q*arcsin(h*x/g)*log(1+exp(I*arcsin(h*x/g))*f*g/(I*e*h+sqrt(f^2*g^2-e^2*h^2)))*sqrt(1-h^2*x^2/g^2)/(h*sqrt(g-h*x)*sqrt(g+h*x))+I*b*g*p*q*polylog(2,-exp(I*arcsin(h*x/g))*f*g/(I*e*h-sqrt(f^2*g^2-e^2*h^2)))*sqrt(1-h^2*x^2/g^2)/(h*sqrt(g-h*x)*sqrt(g+h*x))+I*b*g*p*q*polylog(2,-exp(I*arcsin(h*x/g))*f*g/(I*e*h+sqrt(f^2*g^2-e^2*h^2)))*sqrt(1-h^2*x^2/g^2)/(h*sqrt(g-h*x)*sqrt(g+h*x))],

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

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

# p>0
[(i+j*x)^3*(a+b*log(c*(d*(e+f*x)^p)^q))/(g+h*x),x,15,a*j*(h*i-g*j)^2*x/h^3-1/3*b*j*(f*i-e*j)^2*p*q*x/(f^2*h)-1/2*b*j*(f*i-e*j)*(h*i-g*j)*p*q*x/(f*h^2)-b*j*(h*i-g*j)^2*p*q*x/h^3-1/6*b*(f*i-e*j)*p*q*(i+j*x)^2/(f*h)-1/4*b*(h*i-g*j)*p*q*(i+j*x)^2/h^2-1/9*b*p*q*(i+j*x)^3/h-1/3*b*(f*i-e*j)^3*p*q*log(e+f*x)/(f^3*h)-1/2*b*(f*i-e*j)^2*(h*i-g*j)*p*q*log(e+f*x)/(f^2*h^2)+b*j*(h*i-g*j)^2*(e+f*x)*log(c*(d*(e+f*x)^p)^q)/(f*h^3)+1/2*(h*i-g*j)*(i+j*x)^2*(a+b*log(c*(d*(e+f*x)^p)^q))/h^2+1/3*(i+j*x)^3*(a+b*log(c*(d*(e+f*x)^p)^q))/h+(h*i-g*j)^3*(a+b*log(c*(d*(e+f*x)^p)^q))*log(f*(g+h*x)/(f*g-e*h))/h^4+b*(h*i-g*j)^3*p*q*polylog(2,-h*(e+f*x)/(f*g-e*h))/h^4],
[(i+j*x)^2*(a+b*log(c*(d*(e+f*x)^p)^q))/(g+h*x),x,12,a*j*(h*i-g*j)*x/h^2-1/2*b*j*(f*i-e*j)*p*q*x/(f*h)-b*j*(h*i-g*j)*p*q*x/h^2-1/4*b*p*q*(i+j*x)^2/h-1/2*b*(f*i-e*j)^2*p*q*log(e+f*x)/(f^2*h)+b*j*(h*i-g*j)*(e+f*x)*log(c*(d*(e+f*x)^p)^q)/(f*h^2)+1/2*(i+j*x)^2*(a+b*log(c*(d*(e+f*x)^p)^q))/h+(h*i-g*j)^2*(a+b*log(c*(d*(e+f*x)^p)^q))*log(f*(g+h*x)/(f*g-e*h))/h^3+b*(h*i-g*j)^2*p*q*polylog(2,-h*(e+f*x)/(f*g-e*h))/h^3],
[(i+j*x)*(a+b*log(c*(d*(e+f*x)^p)^q))/(g+h*x),x,9,a*j*x/h-b*j*p*q*x/h+b*j*(e+f*x)*log(c*(d*(e+f*x)^p)^q)/(f*h)+(h*i-g*j)*(a+b*log(c*(d*(e+f*x)^p)^q))*log(f*(g+h*x)/(f*g-e*h))/h^2+b*(h*i-g*j)*p*q*polylog(2,-h*(e+f*x)/(f*g-e*h))/h^2],
[(a+b*log(c*(d*(e+f*x)^p)^q))/(g+h*x),x,4,(a+b*log(c*(d*(e+f*x)^p)^q))*log(f*(g+h*x)/(f*g-e*h))/h+b*p*q*polylog(2,-h*(e+f*x)/(f*g-e*h))/h],
[(a+b*log(c*(d*(e+f*x)^p)^q))/((g+h*x)*(i+j*x)),x,9,(a+b*log(c*(d*(e+f*x)^p)^q))*log(f*(g+h*x)/(f*g-e*h))/(h*i-g*j)-(a+b*log(c*(d*(e+f*x)^p)^q))*log(f*(i+j*x)/(f*i-e*j))/(h*i-g*j)+b*p*q*polylog(2,-h*(e+f*x)/(f*g-e*h))/(h*i-g*j)-b*p*q*polylog(2,-j*(e+f*x)/(f*i-e*j))/(h*i-g*j)],
[(a+b*log(c*(d*(e+f*x)^p)^q))/((g+h*x)*(i+j*x)^2),x,13,-b*f*p*q*log(e+f*x)/((f*i-e*j)*(h*i-g*j))+(a+b*log(c*(d*(e+f*x)^p)^q))/((h*i-g*j)*(i+j*x))+h*(a+b*log(c*(d*(e+f*x)^p)^q))*log(f*(g+h*x)/(f*g-e*h))/(h*i-g*j)^2+b*f*p*q*log(i+j*x)/((f*i-e*j)*(h*i-g*j))-h*(a+b*log(c*(d*(e+f*x)^p)^q))*log(f*(i+j*x)/(f*i-e*j))/(h*i-g*j)^2+b*h*p*q*polylog(2,-h*(e+f*x)/(f*g-e*h))/(h*i-g*j)^2-b*h*p*q*polylog(2,-j*(e+f*x)/(f*i-e*j))/(h*i-g*j)^2],
[(a+b*log(c*(d*(e+f*x)^p)^q))/((g+h*x)*(i+j*x)^3),x,16,-1/2*b*f*p*q/((f*i-e*j)*(h*i-g*j)*(i+j*x))-b*f*h*p*q*log(e+f*x)/((f*i-e*j)*(h*i-g*j)^2)-1/2*b*f^2*p*q*log(e+f*x)/((f*i-e*j)^2*(h*i-g*j))+1/2*(a+b*log(c*(d*(e+f*x)^p)^q))/((h*i-g*j)*(i+j*x)^2)+h*(a+b*log(c*(d*(e+f*x)^p)^q))/((h*i-g*j)^2*(i+j*x))+h^2*(a+b*log(c*(d*(e+f*x)^p)^q))*log(f*(g+h*x)/(f*g-e*h))/(h*i-g*j)^3+b*f*h*p*q*log(i+j*x)/((f*i-e*j)*(h*i-g*j)^2)+1/2*b*f^2*p*q*log(i+j*x)/((f*i-e*j)^2*(h*i-g*j))-h^2*(a+b*log(c*(d*(e+f*x)^p)^q))*log(f*(i+j*x)/(f*i-e*j))/(h*i-g*j)^3+b*h^2*p*q*polylog(2,-h*(e+f*x)/(f*g-e*h))/(h*i-g*j)^3-b*h^2*p*q*polylog(2,-j*(e+f*x)/(f*i-e*j))/(h*i-g*j)^3],
[(i+j*x)^2*(a+b*log(c*(d*(e+f*x)^p)^q))^2/(g+h*x),x,20,-2*a*b*j*(f*i-e*j)*p*q*x/(f*h)-2*a*b*j*(h*i-g*j)*p*q*x/h^2+2*b^2*j*(f*i-e*j)*p^2*q^2*x/(f*h)+2*b^2*j*(h*i-g*j)*p^2*q^2*x/h^2+1/4*b^2*j^2*p^2*q^2*(e+f*x)^2/(f^2*h)-2*b^2*j*(f*i-e*j)*p*q*(e+f*x)*log(c*(d*(e+f*x)^p)^q)/(f^2*h)-2*b^2*j*(h*i-g*j)*p*q*(e+f*x)*log(c*(d*(e+f*x)^p)^q)/(f*h^2)-1/2*b*j^2*p*q*(e+f*x)^2*(a+b*log(c*(d*(e+f*x)^p)^q))/(f^2*h)+j*(f*i-e*j)*(e+f*x)*(a+b*log(c*(d*(e+f*x)^p)^q))^2/(f^2*h)+j*(h*i-g*j)*(e+f*x)*(a+b*log(c*(d*(e+f*x)^p)^q))^2/(f*h^2)+1/2*j^2*(e+f*x)^2*(a+b*log(c*(d*(e+f*x)^p)^q))^2/(f^2*h)+(h*i-g*j)^2*(a+b*log(c*(d*(e+f*x)^p)^q))^2*log(f*(g+h*x)/(f*g-e*h))/h^3+2*b*(h*i-g*j)^2*p*q*(a+b*log(c*(d*(e+f*x)^p)^q))*polylog(2,-h*(e+f*x)/(f*g-e*h))/h^3-2*b^2*(h*i-g*j)^2*p^2*q^2*polylog(3,-h*(e+f*x)/(f*g-e*h))/h^3],
[(i+j*x)*(a+b*log(c*(d*(e+f*x)^p)^q))^2/(g+h*x),x,11,-2*a*b*j*p*q*x/h+2*b^2*j*p^2*q^2*x/h-2*b^2*j*p*q*(e+f*x)*log(c*(d*(e+f*x)^p)^q)/(f*h)+j*(e+f*x)*(a+b*log(c*(d*(e+f*x)^p)^q))^2/(f*h)+(h*i-g*j)*(a+b*log(c*(d*(e+f*x)^p)^q))^2*log(f*(g+h*x)/(f*g-e*h))/h^2+2*b*(h*i-g*j)*p*q*(a+b*log(c*(d*(e+f*x)^p)^q))*polylog(2,-h*(e+f*x)/(f*g-e*h))/h^2-2*b^2*(h*i-g*j)*p^2*q^2*polylog(3,-h*(e+f*x)/(f*g-e*h))/h^2],
[(a+b*log(c*(d*(e+f*x)^p)^q))^2/(g+h*x),x,5,(a+b*log(c*(d*(e+f*x)^p)^q))^2*log(f*(g+h*x)/(f*g-e*h))/h+2*b*p*q*(a+b*log(c*(d*(e+f*x)^p)^q))*polylog(2,-h*(e+f*x)/(f*g-e*h))/h-2*b^2*p^2*q^2*polylog(3,-h*(e+f*x)/(f*g-e*h))/h],
[(a+b*log(c*(d*(e+f*x)^p)^q))^2/((g+h*x)*(i+j*x)),x,11,(a+b*log(c*(d*(e+f*x)^p)^q))^2*log(f*(g+h*x)/(f*g-e*h))/(h*i-g*j)-(a+b*log(c*(d*(e+f*x)^p)^q))^2*log(f*(i+j*x)/(f*i-e*j))/(h*i-g*j)+2*b*p*q*(a+b*log(c*(d*(e+f*x)^p)^q))*polylog(2,-h*(e+f*x)/(f*g-e*h))/(h*i-g*j)-2*b*p*q*(a+b*log(c*(d*(e+f*x)^p)^q))*polylog(2,-j*(e+f*x)/(f*i-e*j))/(h*i-g*j)-2*b^2*p^2*q^2*polylog(3,-h*(e+f*x)/(f*g-e*h))/(h*i-g*j)+2*b^2*p^2*q^2*polylog(3,-j*(e+f*x)/(f*i-e*j))/(h*i-g*j)],
[(a+b*log(c*(d*(e+f*x)^p)^q))^2/((g+h*x)*(i+j*x)^2),x,15,-j*(e+f*x)*(a+b*log(c*(d*(e+f*x)^p)^q))^2/((f*i-e*j)*(h*i-g*j)*(i+j*x))+h*(a+b*log(c*(d*(e+f*x)^p)^q))^2*log(f*(g+h*x)/(f*g-e*h))/(h*i-g*j)^2+2*b*f*p*q*(a+b*log(c*(d*(e+f*x)^p)^q))*log(f*(i+j*x)/(f*i-e*j))/((f*i-e*j)*(h*i-g*j))-h*(a+b*log(c*(d*(e+f*x)^p)^q))^2*log(f*(i+j*x)/(f*i-e*j))/(h*i-g*j)^2+2*b*h*p*q*(a+b*log(c*(d*(e+f*x)^p)^q))*polylog(2,-h*(e+f*x)/(f*g-e*h))/(h*i-g*j)^2+2*b^2*f*p^2*q^2*polylog(2,-j*(e+f*x)/(f*i-e*j))/((f*i-e*j)*(h*i-g*j))-2*b*h*p*q*(a+b*log(c*(d*(e+f*x)^p)^q))*polylog(2,-j*(e+f*x)/(f*i-e*j))/(h*i-g*j)^2-2*b^2*h*p^2*q^2*polylog(3,-h*(e+f*x)/(f*g-e*h))/(h*i-g*j)^2+2*b^2*h*p^2*q^2*polylog(3,-j*(e+f*x)/(f*i-e*j))/(h*i-g*j)^2],
[(i+j*x)^2*(a+b*log(c*(d*(e+f*x)^p)^q))^3/(g+h*x),x,24,6*a*b^2*j*(f*i-e*j)*p^2*q^2*x/(f*h)+6*a*b^2*j*(h*i-g*j)*p^2*q^2*x/h^2-6*b^3*j*(f*i-e*j)*p^3*q^3*x/(f*h)-6*b^3*j*(h*i-g*j)*p^3*q^3*x/h^2-3/8*b^3*j^2*p^3*q^3*(e+f*x)^2/(f^2*h)+6*b^3*j*(f*i-e*j)*p^2*q^2*(e+f*x)*log(c*(d*(e+f*x)^p)^q)/(f^2*h)+6*b^3*j*(h*i-g*j)*p^2*q^2*(e+f*x)*log(c*(d*(e+f*x)^p)^q)/(f*h^2)+3/4*b^2*j^2*p^2*q^2*(e+f*x)^2*(a+b*log(c*(d*(e+f*x)^p)^q))/(f^2*h)-3*b*j*(f*i-e*j)*p*q*(e+f*x)*(a+b*log(c*(d*(e+f*x)^p)^q))^2/(f^2*h)-3*b*j*(h*i-g*j)*p*q*(e+f*x)*(a+b*log(c*(d*(e+f*x)^p)^q))^2/(f*h^2)-3/4*b*j^2*p*q*(e+f*x)^2*(a+b*log(c*(d*(e+f*x)^p)^q))^2/(f^2*h)+j*(f*i-e*j)*(e+f*x)*(a+b*log(c*(d*(e+f*x)^p)^q))^3/(f^2*h)+j*(h*i-g*j)*(e+f*x)*(a+b*log(c*(d*(e+f*x)^p)^q))^3/(f*h^2)+1/2*j^2*(e+f*x)^2*(a+b*log(c*(d*(e+f*x)^p)^q))^3/(f^2*h)+(h*i-g*j)^2*(a+b*log(c*(d*(e+f*x)^p)^q))^3*log(f*(g+h*x)/(f*g-e*h))/h^3+3*b*(h*i-g*j)^2*p*q*(a+b*log(c*(d*(e+f*x)^p)^q))^2*polylog(2,-h*(e+f*x)/(f*g-e*h))/h^3-6*b^2*(h*i-g*j)^2*p^2*q^2*(a+b*log(c*(d*(e+f*x)^p)^q))*polylog(3,-h*(e+f*x)/(f*g-e*h))/h^3+6*b^3*(h*i-g*j)^2*p^3*q^3*polylog(4,-h*(e+f*x)/(f*g-e*h))/h^3],
[(i+j*x)*(a+b*log(c*(d*(e+f*x)^p)^q))^3/(g+h*x),x,13,6*a*b^2*j*p^2*q^2*x/h-6*b^3*j*p^3*q^3*x/h+6*b^3*j*p^2*q^2*(e+f*x)*log(c*(d*(e+f*x)^p)^q)/(f*h)-3*b*j*p*q*(e+f*x)*(a+b*log(c*(d*(e+f*x)^p)^q))^2/(f*h)+j*(e+f*x)*(a+b*log(c*(d*(e+f*x)^p)^q))^3/(f*h)+(h*i-g*j)*(a+b*log(c*(d*(e+f*x)^p)^q))^3*log(f*(g+h*x)/(f*g-e*h))/h^2+3*b*(h*i-g*j)*p*q*(a+b*log(c*(d*(e+f*x)^p)^q))^2*polylog(2,-h*(e+f*x)/(f*g-e*h))/h^2-6*b^2*(h*i-g*j)*p^2*q^2*(a+b*log(c*(d*(e+f*x)^p)^q))*polylog(3,-h*(e+f*x)/(f*g-e*h))/h^2+6*b^3*(h*i-g*j)*p^3*q^3*polylog(4,-h*(e+f*x)/(f*g-e*h))/h^2],
[(a+b*log(c*(d*(e+f*x)^p)^q))^3/(g+h*x),x,6,(a+b*log(c*(d*(e+f*x)^p)^q))^3*log(f*(g+h*x)/(f*g-e*h))/h+3*b*p*q*(a+b*log(c*(d*(e+f*x)^p)^q))^2*polylog(2,-h*(e+f*x)/(f*g-e*h))/h-6*b^2*p^2*q^2*(a+b*log(c*(d*(e+f*x)^p)^q))*polylog(3,-h*(e+f*x)/(f*g-e*h))/h+6*b^3*p^3*q^3*polylog(4,-h*(e+f*x)/(f*g-e*h))/h],
[(a+b*log(c*(d*(e+f*x)^p)^q))^3/((g+h*x)*(i+j*x)),x,13,(a+b*log(c*(d*(e+f*x)^p)^q))^3*log(f*(g+h*x)/(f*g-e*h))/(h*i-g*j)-(a+b*log(c*(d*(e+f*x)^p)^q))^3*log(f*(i+j*x)/(f*i-e*j))/(h*i-g*j)+3*b*p*q*(a+b*log(c*(d*(e+f*x)^p)^q))^2*polylog(2,-h*(e+f*x)/(f*g-e*h))/(h*i-g*j)-3*b*p*q*(a+b*log(c*(d*(e+f*x)^p)^q))^2*polylog(2,-j*(e+f*x)/(f*i-e*j))/(h*i-g*j)-6*b^2*p^2*q^2*(a+b*log(c*(d*(e+f*x)^p)^q))*polylog(3,-h*(e+f*x)/(f*g-e*h))/(h*i-g*j)+6*b^2*p^2*q^2*(a+b*log(c*(d*(e+f*x)^p)^q))*polylog(3,-j*(e+f*x)/(f*i-e*j))/(h*i-g*j)+6*b^3*p^3*q^3*polylog(4,-h*(e+f*x)/(f*g-e*h))/(h*i-g*j)-6*b^3*p^3*q^3*polylog(4,-j*(e+f*x)/(f*i-e*j))/(h*i-g*j)],
[(a+b*log(c*(d*(e+f*x)^p)^q))^3/((g+h*x)*(i+j*x)^2),x,18,-j*(e+f*x)*(a+b*log(c*(d*(e+f*x)^p)^q))^3/((f*i-e*j)*(h*i-g*j)*(i+j*x))+h*(a+b*log(c*(d*(e+f*x)^p)^q))^3*log(f*(g+h*x)/(f*g-e*h))/(h*i-g*j)^2+3*b*f*p*q*(a+b*log(c*(d*(e+f*x)^p)^q))^2*log(f*(i+j*x)/(f*i-e*j))/((f*i-e*j)*(h*i-g*j))-h*(a+b*log(c*(d*(e+f*x)^p)^q))^3*log(f*(i+j*x)/(f*i-e*j))/(h*i-g*j)^2+3*b*h*p*q*(a+b*log(c*(d*(e+f*x)^p)^q))^2*polylog(2,-h*(e+f*x)/(f*g-e*h))/(h*i-g*j)^2+6*b^2*f*p^2*q^2*(a+b*log(c*(d*(e+f*x)^p)^q))*polylog(2,-j*(e+f*x)/(f*i-e*j))/((f*i-e*j)*(h*i-g*j))-3*b*h*p*q*(a+b*log(c*(d*(e+f*x)^p)^q))^2*polylog(2,-j*(e+f*x)/(f*i-e*j))/(h*i-g*j)^2-6*b^2*h*p^2*q^2*(a+b*log(c*(d*(e+f*x)^p)^q))*polylog(3,-h*(e+f*x)/(f*g-e*h))/(h*i-g*j)^2-6*b^3*f*p^3*q^3*polylog(3,-j*(e+f*x)/(f*i-e*j))/((f*i-e*j)*(h*i-g*j))+6*b^2*h*p^2*q^2*(a+b*log(c*(d*(e+f*x)^p)^q))*polylog(3,-j*(e+f*x)/(f*i-e*j))/(h*i-g*j)^2+6*b^3*h*p^3*q^3*polylog(4,-h*(e+f*x)/(f*g-e*h))/(h*i-g*j)^2-6*b^3*h*p^3*q^3*polylog(4,-j*(e+f*x)/(f*i-e*j))/(h*i-g*j)^2],

# p<0
[(i+j*x)/((g+h*x)*(a+b*log(c*(d*(e+f*x)^p)^q))),x,0,Unintegrable((i+j*x)/((g+h*x)*(a+b*log(c*(d*(e+f*x)^p)^q))),x)],
[1/((g+h*x)*(a+b*log(c*(d*(e+f*x)^p)^q))),x,0,Unintegrable(1/((g+h*x)*(a+b*log(c*(d*(e+f*x)^p)^q))),x)],
[1/((g+h*x)*(i+j*x)*(a+b*log(c*(d*(e+f*x)^p)^q))),x,0,Unintegrable(1/((g+h*x)*(i+j*x)*(a+b*log(c*(d*(e+f*x)^p)^q))),x)],
[1/((g+h*x)*(i+j*x)^2*(a+b*log(c*(d*(e+f*x)^p)^q))),x,0,Unintegrable(1/((g+h*x)*(i+j*x)^2*(a+b*log(c*(d*(e+f*x)^p)^q))),x)],
[(i+j*x)/((g+h*x)*(a+b*log(c*(d*(e+f*x)^p)^q))^2),x,0,Unintegrable((i+j*x)/((g+h*x)*(a+b*log(c*(d*(e+f*x)^p)^q))^2),x)],
[1/((g+h*x)*(a+b*log(c*(d*(e+f*x)^p)^q))^2),x,0,Unintegrable(1/((g+h*x)*(a+b*log(c*(d*(e+f*x)^p)^q))^2),x)],
[1/((g+h*x)*(i+j*x)*(a+b*log(c*(d*(e+f*x)^p)^q))^2),x,0,Unintegrable(1/((g+h*x)*(i+j*x)*(a+b*log(c*(d*(e+f*x)^p)^q))^2),x)],
[1/((g+h*x)*(i+j*x)^2*(a+b*log(c*(d*(e+f*x)^p)^q))^2),x,0,Unintegrable(1/((g+h*x)*(i+j*x)^2*(a+b*log(c*(d*(e+f*x)^p)^q))^2),x)]]:
