\[ \int \frac {x^3 \left (a+b \log \left (c x^n\right )\right )}{(d+e x)^7} \, dx \]
Optimal antiderivative \[ -\frac {b \,d^{2} n}{30 e^{4} \left (e x +d \right )^{5}}+\frac {13 b d n}{120 e^{4} \left (e x +d \right )^{4}}-\frac {19 b n}{180 e^{4} \left (e x +d \right )^{3}}+\frac {b n}{120 d \,e^{4} \left (e x +d \right )^{2}}+\frac {b n}{60 d^{2} e^{4} \left (e x +d \right )}+\frac {b n \ln \left (x \right )}{60 d^{3} e^{4}}+\frac {d^{3} \left (a +b \ln \left (c \,x^{n}\right )\right )}{6 e^{4} \left (e x +d \right )^{6}}-\frac {3 d^{2} \left (a +b \ln \left (c \,x^{n}\right )\right )}{5 e^{4} \left (e x +d \right )^{5}}+\frac {3 d \left (a +b \ln \left (c \,x^{n}\right )\right )}{4 e^{4} \left (e x +d \right )^{4}}+\frac {-a -b \ln \left (c \,x^{n}\right )}{3 e^{4} \left (e x +d \right )^{3}}-\frac {b n \ln \left (e x +d \right )}{60 d^{3} e^{4}} \]
command
integrate(x**3*(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 \[ \text {Timed out} \]_____________________________________________________