\[ \int (f x)^{-1+m} \left (d+e x^m\right )^2 \left (a+b \log \left (c x^n\right )\right ) \, dx \]
Optimal antiderivative \[ -\frac {b \,d^{2} n x \left (f x \right )^{-1+m}}{m^{2}}-\frac {b d e n \,x^{1+m} \left (f x \right )^{-1+m}}{2 m^{2}}-\frac {b \,e^{2} n \,x^{1+2 m} \left (f x \right )^{-1+m}}{9 m^{2}}-\frac {b \,d^{3} n \,x^{1-m} \left (f x \right )^{-1+m} \ln \left (x \right )}{3 e m}+\frac {x^{1-m} \left (f x \right )^{-1+m} \left (d +e \,x^{m}\right )^{3} \left (a +b \ln \left (c \,x^{n}\right )\right )}{3 e m} \]
command
integrate((f*x)**(-1+m)*(d+e*x**m)**2*(a+b*ln(c*x**n)),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 \[ \text {Timed out} \]_____________________________________________________