\[ \int \frac {a+b \log \left (c x^n\right )}{(d+e x)^7} \, dx \]
Optimal antiderivative \[ \frac {b n}{30 d e \left (e x +d \right )^{5}}+\frac {b n}{24 d^{2} e \left (e x +d \right )^{4}}+\frac {b n}{18 d^{3} e \left (e x +d \right )^{3}}+\frac {b n}{12 d^{4} e \left (e x +d \right )^{2}}+\frac {b n}{6 d^{5} e \left (e x +d \right )}+\frac {b n \ln \left (x \right )}{6 d^{6} e}+\frac {-a -b \ln \left (c \,x^{n}\right )}{6 e \left (e x +d \right )^{6}}-\frac {b n \ln \left (e x +d \right )}{6 d^{6} e} \]
command
integrate((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 \[ \text {Timed out} \]_____________________________________________________