\[ \int \frac {x^6 \left (a+b \log \left (c x^n\right )\right )}{(d+e x)^7} \, dx \]
Optimal antiderivative \[ -\frac {x^{6} \left (a +b \ln \left (c \,x^{n}\right )\right )}{6 e \left (e x +d \right )^{6}}-\frac {x^{5} \left (6 a +b n +6 b \ln \left (c \,x^{n}\right )\right )}{30 e^{2} \left (e x +d \right )^{5}}-\frac {x^{2} \left (20 a +19 b n +20 b \ln \left (c \,x^{n}\right )\right )}{40 e^{5} \left (e x +d \right )^{2}}-\frac {x \left (20 a +29 b n +20 b \ln \left (c \,x^{n}\right )\right )}{20 e^{6} \left (e x +d \right )}-\frac {x^{4} \left (30 a +11 b n +30 b \ln \left (c \,x^{n}\right )\right )}{120 e^{3} \left (e x +d \right )^{4}}-\frac {x^{3} \left (60 a +37 b n +60 b \ln \left (c \,x^{n}\right )\right )}{180 e^{4} \left (e x +d \right )^{3}}+\frac {\left (20 a +49 b n +20 b \ln \left (c \,x^{n}\right )\right ) \ln \left (1+\frac {e x}{d}\right )}{20 e^{7}}+\frac {b n \polylog \left (2, -\frac {e x}{d}\right )}{e^{7}} \]
command
integrate(x**6*(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 \[ \text {Timed out} \]_____________________________________________________