\[ \int \frac {x^5 \left (a+b \log \left (c x^n\right )\right )}{(d+e x)^7} \, dx \]
Optimal antiderivative \[ -\frac {b \,d^{4} n}{30 e^{6} \left (e x +d \right )^{5}}+\frac {5 b \,d^{3} n}{24 e^{6} \left (e x +d \right )^{4}}-\frac {5 b \,d^{2} n}{9 e^{6} \left (e x +d \right )^{3}}+\frac {5 b d n}{6 e^{6} \left (e x +d \right )^{2}}-\frac {5 b n}{6 e^{6} \left (e x +d \right )}+\frac {x^{6} \left (a +b \ln \left (c \,x^{n}\right )\right )}{6 d \left (e x +d \right )^{6}}-\frac {b n \ln \left (e x +d \right )}{6 d \,e^{6}} \]
command
integrate(x**5*(a+b*ln(c*x**n))/(e*x+d)**7,x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \text {output too large to display} \]
Sympy 1.8 under Python 3.8.8 output \[ \text {Timed out} \]_____________________________________________________