\[ \int \frac {x \left (a+b \log \left (c x^n\right )\right )}{(d+e x)^7} \, dx \]
Optimal antiderivative \[ -\frac {b n}{30 e^{2} \left (e x +d \right )^{5}}+\frac {b n}{120 d \,e^{2} \left (e x +d \right )^{4}}+\frac {b n}{90 d^{2} e^{2} \left (e x +d \right )^{3}}+\frac {b n}{60 d^{3} e^{2} \left (e x +d \right )^{2}}+\frac {b n}{30 d^{4} e^{2} \left (e x +d \right )}+\frac {b n \ln \left (x \right )}{30 d^{5} e^{2}}+\frac {d \left (a +b \ln \left (c \,x^{n}\right )\right )}{6 e^{2} \left (e x +d \right )^{6}}+\frac {-a -b \ln \left (c \,x^{n}\right )}{5 e^{2} \left (e x +d \right )^{5}}-\frac {b n \ln \left (e x +d \right )}{30 d^{5} e^{2}} \]
command
integrate(x*(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 \[ \text {Timed out} \]_____________________________________________________