# Maple integration test file: "3 Logarithms\3.1.2 (d x)^m (a+b log(c x^n))^p.txt"

lst:=[

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

# Integrands of the form x^m Log[c x]^p

# p>0
[x^3*log(c*x),x,1,-1/16*x^4+1/4*x^4*log(c*x)],
[x^2*log(c*x),x,1,-1/9*x^3+1/3*x^3*log(c*x)],
[x*log(c*x),x,1,-1/4*x^2+1/2*x^2*log(c*x)],
[log(c*x),x,1,-x+x*log(c*x)],
[log(c*x)/x,x,1,1/2*log(c*x)^2],
[log(c*x)/x^2,x,1,(-1)/x-log(c*x)/x],
[log(c*x)/x^3,x,1,(-1/4)/x^2-1/2*log(c*x)/x^2],
[x^3*log(c*x)^2,x,2,1/32*x^4-1/8*x^4*log(c*x)+1/4*x^4*log(c*x)^2],
[x^2*log(c*x)^2,x,2,2/27*x^3-2/9*x^3*log(c*x)+1/3*x^3*log(c*x)^2],
[x*log(c*x)^2,x,2,1/4*x^2-1/2*x^2*log(c*x)+1/2*x^2*log(c*x)^2],
[log(c*x)^2,x,2,2*x-2*x*log(c*x)+x*log(c*x)^2],
[log(c*x)^2/x,x,2,1/3*log(c*x)^3],
[log(c*x)^2/x^2,x,2,(-2)/x-2*log(c*x)/x-log(c*x)^2/x],
[log(c*x)^2/x^3,x,2,(-1/4)/x^2-1/2*log(c*x)/x^2-1/2*log(c*x)^2/x^2],
[x^3*log(c*x)^3,x,3,-3/128*x^4+3/32*x^4*log(c*x)-3/16*x^4*log(c*x)^2+1/4*x^4*log(c*x)^3],
[x^2*log(c*x)^3,x,3,-2/27*x^3+2/9*x^3*log(c*x)-1/3*x^3*log(c*x)^2+1/3*x^3*log(c*x)^3],
[x*log(c*x)^3,x,3,-3/8*x^2+3/4*x^2*log(c*x)-3/4*x^2*log(c*x)^2+1/2*x^2*log(c*x)^3],
[log(c*x)^3,x,3,-6*x+6*x*log(c*x)-3*x*log(c*x)^2+x*log(c*x)^3],
[log(c*x)^3/x,x,2,1/4*log(c*x)^4],
[log(c*x)^3/x^2,x,3,(-6)/x-6*log(c*x)/x-3*log(c*x)^2/x-log(c*x)^3/x],
[log(c*x)^3/x^3,x,3,(-3/8)/x^2-3/4*log(c*x)/x^2-3/4*log(c*x)^2/x^2-1/2*log(c*x)^3/x^2],

# p<0
[x^3/log(c*x),x,2,Ei(4*log(c*x))/c^4],
[x^2/log(c*x),x,2,Ei(3*log(c*x))/c^3],
[x/log(c*x),x,2,Ei(2*log(c*x))/c^2],
[1/log(c*x),x,1,Li(c*x)/c],
[1/(x*log(c*x)),x,2,log(log(c*x))],
[1/(x^2*log(c*x)),x,2,c*Ei(-log(c*x))],
[1/(x^3*log(c*x)),x,2,c^2*Ei(-2*log(c*x))],
[x^3/log(c*x)^2,x,3,4*Ei(4*log(c*x))/c^4-x^4/log(c*x)],
[x^2/log(c*x)^2,x,3,3*Ei(3*log(c*x))/c^3-x^3/log(c*x)],
[x/log(c*x)^2,x,3,2*Ei(2*log(c*x))/c^2-x^2/log(c*x)],
[1/log(c*x)^2,x,2,Li(c*x)/c-x/log(c*x)],
[1/(x*log(c*x)^2),x,2,(-1)/log(c*x)],
[1/(x^2*log(c*x)^2),x,3,-c*Ei(-log(c*x))+(-1)/(x*log(c*x))],
[1/(x^3*log(c*x)^2),x,3,-2*c^2*Ei(-2*log(c*x))+(-1)/(x^2*log(c*x))],
[x^3/log(c*x)^3,x,4,8*Ei(4*log(c*x))/c^4-1/2*x^4/log(c*x)^2-2*x^4/log(c*x)],
[x^2/log(c*x)^3,x,4,9/2*Ei(3*log(c*x))/c^3-1/2*x^3/log(c*x)^2-3/2*x^3/log(c*x)],
[x/log(c*x)^3,x,4,2*Ei(2*log(c*x))/c^2-1/2*x^2/log(c*x)^2-x^2/log(c*x)],
[1/log(c*x)^3,x,3,1/2*Li(c*x)/c-1/2*x/log(c*x)^2-1/2*x/log(c*x)],
[1/(x*log(c*x)^3),x,2,(-1/2)/log(c*x)^2],
[1/(x^2*log(c*x)^3),x,4,1/2*c*Ei(-log(c*x))+(-1/2)/(x*log(c*x)^2)+1/2/(x*log(c*x))],
[1/(x^3*log(c*x)^3),x,4,2*c^2*Ei(-2*log(c*x))+(-1/2)/(x^2*log(c*x)^2)+1/(x^2*log(c*x))],

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

# p>0
[x^3*(a+b*log(c*x^n)),x,1,-1/16*b*n*x^4+1/4*x^4*(a+b*log(c*x^n))],
[x^2*(a+b*log(c*x^n)),x,1,-1/9*b*n*x^3+1/3*x^3*(a+b*log(c*x^n))],
[x*(a+b*log(c*x^n)),x,1,-1/4*b*n*x^2+1/2*x^2*(a+b*log(c*x^n))],
[a+b*log(c*x^n),x,2,a*x-b*n*x+b*x*log(c*x^n)],
[(a+b*log(c*x^n))/x,x,1,1/2*(a+b*log(c*x^n))^2/(b*n)],
[(a+b*log(c*x^n))/x^2,x,1,-b*n/x+(-a-b*log(c*x^n))/x],
[(a+b*log(c*x^n))/x^3,x,1,-1/4*b*n/x^2+1/2*(-a-b*log(c*x^n))/x^2],
[x^3*(a+b*log(c*x^n))^2,x,2,1/32*b^2*n^2*x^4-1/8*b*n*x^4*(a+b*log(c*x^n))+1/4*x^4*(a+b*log(c*x^n))^2],
[x^2*(a+b*log(c*x^n))^2,x,2,2/27*b^2*n^2*x^3-2/9*b*n*x^3*(a+b*log(c*x^n))+1/3*x^3*(a+b*log(c*x^n))^2],
[x*(a+b*log(c*x^n))^2,x,2,1/4*b^2*n^2*x^2-1/2*b*n*x^2*(a+b*log(c*x^n))+1/2*x^2*(a+b*log(c*x^n))^2],
[(a+b*log(c*x^n))^2,x,3,-2*a*b*n*x+2*b^2*n^2*x-2*b^2*n*x*log(c*x^n)+x*(a+b*log(c*x^n))^2],
[(a+b*log(c*x^n))^2/x,x,2,1/3*(a+b*log(c*x^n))^3/(b*n)],
[(a+b*log(c*x^n))^2/x^2,x,2,-2*b^2*n^2/x-2*b*n*(a+b*log(c*x^n))/x-(a+b*log(c*x^n))^2/x],
[(a+b*log(c*x^n))^2/x^3,x,2,-1/4*b^2*n^2/x^2-1/2*b*n*(a+b*log(c*x^n))/x^2-1/2*(a+b*log(c*x^n))^2/x^2],
[x^3*(a+b*log(c*x^n))^3,x,3,-3/128*b^3*n^3*x^4+3/32*b^2*n^2*x^4*(a+b*log(c*x^n))-3/16*b*n*x^4*(a+b*log(c*x^n))^2+1/4*x^4*(a+b*log(c*x^n))^3],
[x^2*(a+b*log(c*x^n))^3,x,3,-2/27*b^3*n^3*x^3+2/9*b^2*n^2*x^3*(a+b*log(c*x^n))-1/3*b*n*x^3*(a+b*log(c*x^n))^2+1/3*x^3*(a+b*log(c*x^n))^3],
[x*(a+b*log(c*x^n))^3,x,3,-3/8*b^3*n^3*x^2+3/4*b^2*n^2*x^2*(a+b*log(c*x^n))-3/4*b*n*x^2*(a+b*log(c*x^n))^2+1/2*x^2*(a+b*log(c*x^n))^3],
[(a+b*log(c*x^n))^3,x,4,6*a*b^2*n^2*x-6*b^3*n^3*x+6*b^3*n^2*x*log(c*x^n)-3*b*n*x*(a+b*log(c*x^n))^2+x*(a+b*log(c*x^n))^3],
[(a+b*log(c*x^n))^3/x,x,2,1/4*(a+b*log(c*x^n))^4/(b*n)],
[(a+b*log(c*x^n))^3/x^2,x,3,-6*b^3*n^3/x-6*b^2*n^2*(a+b*log(c*x^n))/x-3*b*n*(a+b*log(c*x^n))^2/x-(a+b*log(c*x^n))^3/x],
[(a+b*log(c*x^n))^3/x^3,x,3,-3/8*b^3*n^3/x^2-3/4*b^2*n^2*(a+b*log(c*x^n))/x^2-3/4*b*n*(a+b*log(c*x^n))^2/x^2-1/2*(a+b*log(c*x^n))^3/x^2],
[(a+b*log(c*x^n))^3/x^4,x,3,-2/27*b^3*n^3/x^3-2/9*b^2*n^2*(a+b*log(c*x^n))/x^3-1/3*b*n*(a+b*log(c*x^n))^2/x^3-1/3*(a+b*log(c*x^n))^3/x^3],

# p<0
[x^3/(a+b*log(c*x^n)),x,2,x^4*Ei(4*(a+b*log(c*x^n))/(b*n))/(b*exp(4*a/(b*n))*n*(c*x^n)^(4/n))],
[x^2/(a+b*log(c*x^n)),x,2,x^3*Ei(3*(a+b*log(c*x^n))/(b*n))/(b*exp(3*a/(b*n))*n*(c*x^n)^(3/n))],
[x/(a+b*log(c*x^n)),x,2,x^2*Ei(2*(a+b*log(c*x^n))/(b*n))/(b*exp(2*a/(b*n))*n*(c*x^n)^(2/n))],
[1/(a+b*log(c*x^n)),x,2,x*Ei((a+b*log(c*x^n))/(b*n))/(b*exp(a/(b*n))*n*(c*x^n)^(1/n))],
[1/(x*(a+b*log(c*x^n))),x,2,log(a+b*log(c*x^n))/(b*n)],
[1/(x^2*(a+b*log(c*x^n))),x,2,exp(a/(b*n))*(c*x^n)^(1/n)*Ei((-a-b*log(c*x^n))/(b*n))/(b*n*x)],
[1/(x^3*(a+b*log(c*x^n))),x,2,exp(2*a/(b*n))*(c*x^n)^(2/n)*Ei(-2*(a+b*log(c*x^n))/(b*n))/(b*n*x^2)],
[1/(x^4*(a+b*log(c*x^n))),x,2,exp(3*a/(b*n))*(c*x^n)^(3/n)*Ei(-3*(a+b*log(c*x^n))/(b*n))/(b*n*x^3)],
[x^3/(a+b*log(c*x^n))^2,x,3,4*x^4*Ei(4*(a+b*log(c*x^n))/(b*n))/(b^2*exp(4*a/(b*n))*n^2*(c*x^n)^(4/n))-x^4/(b*n*(a+b*log(c*x^n)))],
[x^2/(a+b*log(c*x^n))^2,x,3,3*x^3*Ei(3*(a+b*log(c*x^n))/(b*n))/(b^2*exp(3*a/(b*n))*n^2*(c*x^n)^(3/n))-x^3/(b*n*(a+b*log(c*x^n)))],
[x/(a+b*log(c*x^n))^2,x,3,2*x^2*Ei(2*(a+b*log(c*x^n))/(b*n))/(b^2*exp(2*a/(b*n))*n^2*(c*x^n)^(2/n))-x^2/(b*n*(a+b*log(c*x^n)))],
[1/(a+b*log(c*x^n))^2,x,3,x*Ei((a+b*log(c*x^n))/(b*n))/(b^2*exp(a/(b*n))*n^2*(c*x^n)^(1/n))-x/(b*n*(a+b*log(c*x^n)))],
[1/(x*(a+b*log(c*x^n))^2),x,2,(-1)/(b*n*(a+b*log(c*x^n)))],
[1/(x^2*(a+b*log(c*x^n))^2),x,3,-exp(a/(b*n))*(c*x^n)^(1/n)*Ei((-a-b*log(c*x^n))/(b*n))/(b^2*n^2*x)+(-1)/(b*n*x*(a+b*log(c*x^n)))],
[1/(x^3*(a+b*log(c*x^n))^2),x,3,-2*exp(2*a/(b*n))*(c*x^n)^(2/n)*Ei(-2*(a+b*log(c*x^n))/(b*n))/(b^2*n^2*x^2)+(-1)/(b*n*x^2*(a+b*log(c*x^n)))],
[1/(x^4*(a+b*log(c*x^n))^2),x,3,-3*exp(3*a/(b*n))*(c*x^n)^(3/n)*Ei(-3*(a+b*log(c*x^n))/(b*n))/(b^2*n^2*x^3)+(-1)/(b*n*x^3*(a+b*log(c*x^n)))],
[x^3/(a+b*log(c*x^n))^3,x,4,8*x^4*Ei(4*(a+b*log(c*x^n))/(b*n))/(b^3*exp(4*a/(b*n))*n^3*(c*x^n)^(4/n))-1/2*x^4/(b*n*(a+b*log(c*x^n))^2)-2*x^4/(b^2*n^2*(a+b*log(c*x^n)))],
[x^2/(a+b*log(c*x^n))^3,x,4,9/2*x^3*Ei(3*(a+b*log(c*x^n))/(b*n))/(b^3*exp(3*a/(b*n))*n^3*(c*x^n)^(3/n))-1/2*x^3/(b*n*(a+b*log(c*x^n))^2)-3/2*x^3/(b^2*n^2*(a+b*log(c*x^n)))],
[x/(a+b*log(c*x^n))^3,x,4,2*x^2*Ei(2*(a+b*log(c*x^n))/(b*n))/(b^3*exp(2*a/(b*n))*n^3*(c*x^n)^(2/n))-1/2*x^2/(b*n*(a+b*log(c*x^n))^2)-x^2/(b^2*n^2*(a+b*log(c*x^n)))],
[1/(a+b*log(c*x^n))^3,x,4,1/2*x*Ei((a+b*log(c*x^n))/(b*n))/(b^3*exp(a/(b*n))*n^3*(c*x^n)^(1/n))-1/2*x/(b*n*(a+b*log(c*x^n))^2)-1/2*x/(b^2*n^2*(a+b*log(c*x^n)))],
[1/(x*(a+b*log(c*x^n))^3),x,2,(-1/2)/(b*n*(a+b*log(c*x^n))^2)],
[1/(x^2*(a+b*log(c*x^n))^3),x,4,1/2*exp(a/(b*n))*(c*x^n)^(1/n)*Ei((-a-b*log(c*x^n))/(b*n))/(b^3*n^3*x)+(-1/2)/(b*n*x*(a+b*log(c*x^n))^2)+1/2/(b^2*n^2*x*(a+b*log(c*x^n)))],
[1/(x^3*(a+b*log(c*x^n))^3),x,4,2*exp(2*a/(b*n))*(c*x^n)^(2/n)*Ei(-2*(a+b*log(c*x^n))/(b*n))/(b^3*n^3*x^2)+(-1/2)/(b*n*x^2*(a+b*log(c*x^n))^2)+1/(b^2*n^2*x^2*(a+b*log(c*x^n)))],
[1/(x^4*(a+b*log(c*x^n))^3),x,4,9/2*exp(3*a/(b*n))*(c*x^n)^(3/n)*Ei(-3*(a+b*log(c*x^n))/(b*n))/(b^3*n^3*x^3)+(-1/2)/(b*n*x^3*(a+b*log(c*x^n))^2)+3/2/(b^2*n^2*x^3*(a+b*log(c*x^n)))],

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

# p>0
[(d*x)^(5/2)*(a+b*log(c*x^n)),x,1,-4/49*b*n*(d*x)^(7/2)/d+2/7*(d*x)^(7/2)*(a+b*log(c*x^n))/d],
[(d*x)^(3/2)*(a+b*log(c*x^n)),x,1,-4/25*b*n*(d*x)^(5/2)/d+2/5*(d*x)^(5/2)*(a+b*log(c*x^n))/d],
[(d*x)^(1/2)*(a+b*log(c*x^n)),x,1,-4/9*b*n*(d*x)^(3/2)/d+2/3*(d*x)^(3/2)*(a+b*log(c*x^n))/d],
[(a+b*log(c*x^n))/(d*x)^(1/2),x,1,-4*b*n*sqrt(d*x)/d+2*(a+b*log(c*x^n))*sqrt(d*x)/d],
[(a+b*log(c*x^n))/(d*x)^(3/2),x,1,-4*b*n/(d*sqrt(d*x))-2*(a+b*log(c*x^n))/(d*sqrt(d*x))],
[(a+b*log(c*x^n))/(d*x)^(5/2),x,1,-4/9*b*n/(d*(d*x)^(3/2))-2/3*(a+b*log(c*x^n))/(d*(d*x)^(3/2))],
[(d*x)^(5/2)*(a+b*log(c*x^n))^2,x,2,16/343*b^2*n^2*(d*x)^(7/2)/d-8/49*b*n*(d*x)^(7/2)*(a+b*log(c*x^n))/d+2/7*(d*x)^(7/2)*(a+b*log(c*x^n))^2/d],
[(d*x)^(3/2)*(a+b*log(c*x^n))^2,x,2,16/125*b^2*n^2*(d*x)^(5/2)/d-8/25*b*n*(d*x)^(5/2)*(a+b*log(c*x^n))/d+2/5*(d*x)^(5/2)*(a+b*log(c*x^n))^2/d],
[(d*x)^(1/2)*(a+b*log(c*x^n))^2,x,2,16/27*b^2*n^2*(d*x)^(3/2)/d-8/9*b*n*(d*x)^(3/2)*(a+b*log(c*x^n))/d+2/3*(d*x)^(3/2)*(a+b*log(c*x^n))^2/d],
[(a+b*log(c*x^n))^2/(d*x)^(1/2),x,2,16*b^2*n^2*sqrt(d*x)/d-8*b*n*(a+b*log(c*x^n))*sqrt(d*x)/d+2*(a+b*log(c*x^n))^2*sqrt(d*x)/d],
[(a+b*log(c*x^n))^2/(d*x)^(3/2),x,2,-16*b^2*n^2/(d*sqrt(d*x))-8*b*n*(a+b*log(c*x^n))/(d*sqrt(d*x))-2*(a+b*log(c*x^n))^2/(d*sqrt(d*x))],
[(a+b*log(c*x^n))^2/(d*x)^(5/2),x,2,-16/27*b^2*n^2/(d*(d*x)^(3/2))-8/9*b*n*(a+b*log(c*x^n))/(d*(d*x)^(3/2))-2/3*(a+b*log(c*x^n))^2/(d*(d*x)^(3/2))],

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

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

# p>0
[(a+b*log(c*x^n))^(1/2),x,4,-1/2*x*erfi(sqrt(a+b*log(c*x^n))/(sqrt(b)*sqrt(n)))*sqrt(b)*sqrt(n)*sqrt(Pi)/(exp(a/(b*n))*(c*x^n)^(1/n))+x*sqrt(a+b*log(c*x^n))],
[x^3*sqrt(log(a*x^n)),x,4,-1/16*x^4*erfi(2*sqrt(log(a*x^n))/sqrt(n))*sqrt(n)*sqrt(Pi)/(a*x^n)^(4/n)+1/4*x^4*sqrt(log(a*x^n))],
[x^2*sqrt(log(a*x^n)),x,4,-1/6*x^3*erfi(sqrt(3)*sqrt(log(a*x^n))/sqrt(n))*sqrt(n)*sqrt(1/3*Pi)/(a*x^n)^(3/n)+1/3*x^3*sqrt(log(a*x^n))],
[x*sqrt(log(a*x^n)),x,4,-1/4*x^2*erfi(sqrt(2)*sqrt(log(a*x^n))/sqrt(n))*sqrt(n)*sqrt(1/2*Pi)/(a*x^n)^(2/n)+1/2*x^2*sqrt(log(a*x^n))],
[sqrt(log(a*x^n)),x,4,-1/2*x*erfi(sqrt(log(a*x^n))/sqrt(n))*sqrt(n)*sqrt(Pi)/(a*x^n)^(1/n)+x*sqrt(log(a*x^n))],
[sqrt(log(a*x^n))/x,x,2,2/3*log(a*x^n)^(3/2)/n],
[sqrt(log(a*x^n))/x^2,x,4,1/2*(a*x^n)^(1/n)*erf(sqrt(log(a*x^n))/sqrt(n))*sqrt(n)*sqrt(Pi)/x-sqrt(log(a*x^n))/x],
[sqrt(log(a*x^n))/x^3,x,4,1/4*(a*x^n)^(2/n)*erf(sqrt(2)*sqrt(log(a*x^n))/sqrt(n))*sqrt(n)*sqrt(1/2*Pi)/x^2-1/2*sqrt(log(a*x^n))/x^2],
[x^3*log(a*x^n)^(3/2),x,5,1/4*x^4*log(a*x^n)^(3/2)+3/128*n^(3/2)*x^4*erfi(2*sqrt(log(a*x^n))/sqrt(n))*sqrt(Pi)/(a*x^n)^(4/n)-3/32*n*x^4*sqrt(log(a*x^n))],
[x^2*log(a*x^n)^(3/2),x,5,1/3*x^3*log(a*x^n)^(3/2)+1/12*n^(3/2)*x^3*erfi(sqrt(3)*sqrt(log(a*x^n))/sqrt(n))*sqrt(1/3*Pi)/(a*x^n)^(3/n)-1/6*n*x^3*sqrt(log(a*x^n))],
[x*log(a*x^n)^(3/2),x,5,1/2*x^2*log(a*x^n)^(3/2)+3/16*n^(3/2)*x^2*erfi(sqrt(2)*sqrt(log(a*x^n))/sqrt(n))*sqrt(1/2*Pi)/(a*x^n)^(2/n)-3/8*n*x^2*sqrt(log(a*x^n))],
[log(a*x^n)^(3/2),x,5,x*log(a*x^n)^(3/2)+3/4*n^(3/2)*x*erfi(sqrt(log(a*x^n))/sqrt(n))*sqrt(Pi)/(a*x^n)^(1/n)-3/2*n*x*sqrt(log(a*x^n))],
[log(a*x^n)^(3/2)/x,x,2,2/5*log(a*x^n)^(5/2)/n],
[log(a*x^n)^(3/2)/x^2,x,5,-log(a*x^n)^(3/2)/x+3/4*n^(3/2)*(a*x^n)^(1/n)*erf(sqrt(log(a*x^n))/sqrt(n))*sqrt(Pi)/x-3/2*n*sqrt(log(a*x^n))/x],
[log(a*x^n)^(3/2)/x^3,x,5,-1/2*log(a*x^n)^(3/2)/x^2+3/16*n^(3/2)*(a*x^n)^(2/n)*erf(sqrt(2)*sqrt(log(a*x^n))/sqrt(n))*sqrt(1/2*Pi)/x^2-3/8*n*sqrt(log(a*x^n))/x^2],

# p<0
[x^3/sqrt(log(a*x^n)),x,3,1/2*x^4*erfi(2*sqrt(log(a*x^n))/sqrt(n))*sqrt(Pi)/((a*x^n)^(4/n)*sqrt(n))],
[x^2/sqrt(log(a*x^n)),x,3,x^3*erfi(sqrt(3)*sqrt(log(a*x^n))/sqrt(n))*sqrt(1/3*Pi)/((a*x^n)^(3/n)*sqrt(n))],
[x/sqrt(log(a*x^n)),x,3,x^2*erfi(sqrt(2)*sqrt(log(a*x^n))/sqrt(n))*sqrt(1/2*Pi)/((a*x^n)^(2/n)*sqrt(n))],
[1/sqrt(log(a*x^n)),x,3,x*erfi(sqrt(log(a*x^n))/sqrt(n))*sqrt(Pi)/((a*x^n)^(1/n)*sqrt(n))],
[1/(x*sqrt(log(a*x^n))),x,2,2*sqrt(log(a*x^n))/n],
[1/(x^2*sqrt(log(a*x^n))),x,3,(a*x^n)^(1/n)*erf(sqrt(log(a*x^n))/sqrt(n))*sqrt(Pi)/(x*sqrt(n))],
[1/(x^3*sqrt(log(a*x^n))),x,3,(a*x^n)^(2/n)*erf(sqrt(2)*sqrt(log(a*x^n))/sqrt(n))*sqrt(1/2*Pi)/(x^2*sqrt(n))],
[x^3/log(a*x^n)^(3/2),x,4,4*x^4*erfi(2*sqrt(log(a*x^n))/sqrt(n))*sqrt(Pi)/(n^(3/2)*(a*x^n)^(4/n))-2*x^4/(n*sqrt(log(a*x^n)))],
[x^2/log(a*x^n)^(3/2),x,4,2*x^3*erfi(sqrt(3)*sqrt(log(a*x^n))/sqrt(n))*sqrt(3*Pi)/(n^(3/2)*(a*x^n)^(3/n))-2*x^3/(n*sqrt(log(a*x^n)))],
[x/log(a*x^n)^(3/2),x,4,2*x^2*erfi(sqrt(2)*sqrt(log(a*x^n))/sqrt(n))*sqrt(2*Pi)/(n^(3/2)*(a*x^n)^(2/n))-2*x^2/(n*sqrt(log(a*x^n)))],
[1/log(a*x^n)^(3/2),x,4,2*x*erfi(sqrt(log(a*x^n))/sqrt(n))*sqrt(Pi)/(n^(3/2)*(a*x^n)^(1/n))-2*x/(n*sqrt(log(a*x^n)))],
[1/(x*log(a*x^n)^(3/2)),x,2,(-2)/(n*sqrt(log(a*x^n)))],
[1/(x^2*log(a*x^n)^(3/2)),x,4,-2*(a*x^n)^(1/n)*erf(sqrt(log(a*x^n))/sqrt(n))*sqrt(Pi)/(n^(3/2)*x)+(-2)/(n*x*sqrt(log(a*x^n)))],
[1/(x^3*log(a*x^n)^(3/2)),x,4,-2*(a*x^n)^(2/n)*erf(sqrt(2)*sqrt(log(a*x^n))/sqrt(n))*sqrt(2*Pi)/(n^(3/2)*x^2)+(-2)/(n*x^2*sqrt(log(a*x^n)))],
[x^3/log(a*x^n)^(5/2),x,5,-2/3*x^4/(n*log(a*x^n)^(3/2))+32/3*x^4*erfi(2*sqrt(log(a*x^n))/sqrt(n))*sqrt(Pi)/(n^(5/2)*(a*x^n)^(4/n))-16/3*x^4/(n^2*sqrt(log(a*x^n)))],
[x^2/log(a*x^n)^(5/2),x,5,-2/3*x^3/(n*log(a*x^n)^(3/2))+4*x^3*erfi(sqrt(3)*sqrt(log(a*x^n))/sqrt(n))*sqrt(3*Pi)/(n^(5/2)*(a*x^n)^(3/n))-4*x^3/(n^2*sqrt(log(a*x^n)))],
[x/log(a*x^n)^(5/2),x,5,-2/3*x^2/(n*log(a*x^n)^(3/2))+8/3*x^2*erfi(sqrt(2)*sqrt(log(a*x^n))/sqrt(n))*sqrt(2*Pi)/(n^(5/2)*(a*x^n)^(2/n))-8/3*x^2/(n^2*sqrt(log(a*x^n)))],
[1/log(a*x^n)^(5/2),x,5,-2/3*x/(n*log(a*x^n)^(3/2))+4/3*x*erfi(sqrt(log(a*x^n))/sqrt(n))*sqrt(Pi)/(n^(5/2)*(a*x^n)^(1/n))-4/3*x/(n^2*sqrt(log(a*x^n)))],
[1/(x*log(a*x^n)^(5/2)),x,2,(-2/3)/(n*log(a*x^n)^(3/2))],
[1/(x^2*log(a*x^n)^(5/2)),x,5,(-2/3)/(n*x*log(a*x^n)^(3/2))+4/3*(a*x^n)^(1/n)*erf(sqrt(log(a*x^n))/sqrt(n))*sqrt(Pi)/(n^(5/2)*x)+4/3/(n^2*x*sqrt(log(a*x^n)))],
[1/(x^3*log(a*x^n)^(5/2)),x,5,(-2/3)/(n*x^2*log(a*x^n)^(3/2))+8/3*(a*x^n)^(2/n)*erf(sqrt(2)*sqrt(log(a*x^n))/sqrt(n))*sqrt(2*Pi)/(n^(5/2)*x^2)+8/3/(n^2*x^2*sqrt(log(a*x^n)))],

# Integrands of the form (d x)^m (a+b Log[c x^n])^p with m symbolic
[(d*x)^m*(a+a*(1+m)*log(c*x^n)/n),x,1,a*(d*x)^(1+m)*log(c*x^n)/(d*n)],
[(d*x)^m*(a+b*log(c*x^n))^3,x,3,-6*b^3*n^3*(d*x)^(1+m)/(d*(1+m)^4)+6*b^2*n^2*(d*x)^(1+m)*(a+b*log(c*x^n))/(d*(1+m)^3)-3*b*n*(d*x)^(1+m)*(a+b*log(c*x^n))^2/(d*(1+m)^2)+(d*x)^(1+m)*(a+b*log(c*x^n))^3/(d*(1+m))],
[(d*x)^m*(a+b*log(c*x^n))^2,x,2,2*b^2*n^2*(d*x)^(1+m)/(d*(1+m)^3)-2*b*n*(d*x)^(1+m)*(a+b*log(c*x^n))/(d*(1+m)^2)+(d*x)^(1+m)*(a+b*log(c*x^n))^2/(d*(1+m))],
[(d*x)^m*(a+b*log(c*x^n)),x,1,-b*n*(d*x)^(1+m)/(d*(1+m)^2)+(d*x)^(1+m)*(a+b*log(c*x^n))/(d*(1+m))],
[(d*x)^m/(a+b*log(c*x^n)),x,2,(d*x)^(1+m)*Ei((1+m)*(a+b*log(c*x^n))/(b*n))/(b*d*exp(a*(1+m)/(b*n))*n*(c*x^n)^((1+m)/n))],
[(d*x)^m/(a+b*log(c*x^n))^2,x,3,(1+m)*(d*x)^(1+m)*Ei((1+m)*(a+b*log(c*x^n))/(b*n))/(b^2*d*exp(a*(1+m)/(b*n))*n^2*(c*x^n)^((1+m)/n))-(d*x)^(1+m)/(b*d*n*(a+b*log(c*x^n)))],
[(d*x)^m/(a+b*log(c*x^n))^3,x,4,1/2*(1+m)^2*(d*x)^(1+m)*Ei((1+m)*(a+b*log(c*x^n))/(b*n))/(b^3*d*exp(a*(1+m)/(b*n))*n^3*(c*x^n)^((1+m)/n))-1/2*(d*x)^(1+m)/(b*d*n*(a+b*log(c*x^n))^2)-1/2*(1+m)*(d*x)^(1+m)/(b^2*d*n^2*(a+b*log(c*x^n)))],
[(d*x)^(-1+n)*log(c*x^n)^3,x,3,-6*(d*x)^n/(d*n)+6*(d*x)^n*log(c*x^n)/(d*n)-3*(d*x)^n*log(c*x^n)^2/(d*n)+(d*x)^n*log(c*x^n)^3/(d*n)],
[(d*x)^(-1+n)*log(c*x^n)^2,x,2,2*(d*x)^n/(d*n)-2*(d*x)^n*log(c*x^n)/(d*n)+(d*x)^n*log(c*x^n)^2/(d*n)],
[(d*x)^(-1+n)*log(c*x^n),x,1,-(d*x)^n/(d*n)+(d*x)^n*log(c*x^n)/(d*n)],
[(d*x)^(-1+n)/log(c*x^n),x,3,x^(1-n)*(d*x)^(-1+n)*Li(c*x^n)/(c*n)],
[(d*x)^(-1+n)/log(c*x^n)^2,x,4,x^(1-n)*(d*x)^(-1+n)*Li(c*x^n)/(c*n)-(d*x)^n/(d*n*log(c*x^n))],
[(d*x)^(-1+n)/log(c*x^n)^3,x,5,1/2*x^(1-n)*(d*x)^(-1+n)*Li(c*x^n)/(c*n)-1/2*(d*x)^n/(d*n*log(c*x^n)^2)-1/2*(d*x)^n/(d*n*log(c*x^n))],
[x^m*log(a*x^n)^(3/2),x,5,x^(1+m)*log(a*x^n)^(3/2)/(1+m)+3/4*n^(3/2)*x^(1+m)*erfi(sqrt(1+m)*sqrt(log(a*x^n))/sqrt(n))*sqrt(Pi)/((1+m)^(5/2)*(a*x^n)^((1+m)/n))-3/2*n*x^(1+m)*sqrt(log(a*x^n))/(1+m)^2],
[x^m*log(a*x^n)^(1/2),x,4,-1/2*x^(1+m)*erfi(sqrt(1+m)*sqrt(log(a*x^n))/sqrt(n))*sqrt(n)*sqrt(Pi)/((1+m)^(3/2)*(a*x^n)^((1+m)/n))+x^(1+m)*sqrt(log(a*x^n))/(1+m)],
[x^m/log(a*x^n)^(1/2),x,3,x^(1+m)*erfi(sqrt(1+m)*sqrt(log(a*x^n))/sqrt(n))*sqrt(Pi)/((a*x^n)^((1+m)/n)*sqrt(1+m)*sqrt(n))],
[x^m/log(a*x^n)^(3/2),x,4,2*x^(1+m)*erfi(sqrt(1+m)*sqrt(log(a*x^n))/sqrt(n))*sqrt(1+m)*sqrt(Pi)/(n^(3/2)*(a*x^n)^((1+m)/n))-2*x^(1+m)/(n*sqrt(log(a*x^n)))],
[x^m/log(a*x^n)^(5/2),x,5,-2/3*x^(1+m)/(n*log(a*x^n)^(3/2))+4/3*(1+m)^(3/2)*x^(1+m)*erfi(sqrt(1+m)*sqrt(log(a*x^n))/sqrt(n))*sqrt(Pi)/(n^(5/2)*(a*x^n)^((1+m)/n))-4/3*(1+m)*x^(1+m)/(n^2*sqrt(log(a*x^n)))],

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

# Integrands of the form (d x^q)^m (a+b Log[c x^n])^p
[(d*x^q)^m*(a+b*log(c*x^n))^p,x,3,x*(d*x^q)^m*GAMMA(1+p,-(1+m*q)*(a+b*log(c*x^n))/(b*n))*(a+b*log(c*x^n))^p/(exp((a+a*m*q)/(b*n))*(1+m*q)*(c*x^n)^((1+m*q)/n)*(-(1+m*q)*(a+b*log(c*x^n))/(b*n))^p)],
[(d1*x^q1)^m1*(d2*x^q2)^m2*(a+b*log(c*x^n))^p,x,4,x*(d1*x^q1)^m1*(d2*x^q2)^m2*GAMMA(1+p,-(1+m1*q1+m2*q2)*(a+b*log(c*x^n))/(b*n))*(a+b*log(c*x^n))^p/(exp(a*(1+m1*q1+m2*q2)/(b*n))*(1+m1*q1+m2*q2)*(c*x^n)^((1+m1*q1+m2*q2)/n)*(-(1+m1*q1+m2*q2)*(a+b*log(c*x^n))/(b*n))^p)]]:
