\[ \int \frac {x^4 \left (a+b \log \left (c x^n\right )\right )}{(d+e x)^7} \, dx \]
Optimal antiderivative \[ -\frac {b n \,x^{5}}{30 d^{2} \left (e x +d \right )^{5}}+\frac {b \,d^{2} n}{120 e^{5} \left (e x +d \right )^{4}}-\frac {2 b d n}{45 e^{5} \left (e x +d \right )^{3}}+\frac {b n}{10 e^{5} \left (e x +d \right )^{2}}-\frac {2 b n}{15 d \,e^{5} \left (e x +d \right )}+\frac {x^{5} \left (a +b \ln \left (c \,x^{n}\right )\right )}{6 d \left (e x +d \right )^{6}}+\frac {x^{5} \left (a +b \ln \left (c \,x^{n}\right )\right )}{30 d^{2} \left (e x +d \right )^{5}}-\frac {b n \ln \left (e x +d \right )}{30 d^{2} e^{5}} \]
command
integrate(x**4*(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 \[ \text {Timed out} \]_____________________________________________________