\[ \int \frac {a+b \log \left (c x^n\right )}{x \left (d+e x^r\right )} \, dx \]
Optimal antiderivative \[ -\frac {\left (a +b \ln \left (c \,x^{n}\right )\right ) \ln \left (1+\frac {d \,x^{-r}}{e}\right )}{d r}+\frac {b n \polylog \left (2, -\frac {d \,x^{-r}}{e}\right )}{d \,r^{2}} \]
command
integrate((a+b*ln(c*x**n))/x/(d+e*x**r),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 \[ \text {Timed out} \]_____________________________________________________