\[ \int x^5 \left (d+e x^r\right )^2 \left (a+b \log \left (c x^n\right )\right ) \, dx \]
Optimal antiderivative \[ -\frac {b \,d^{2} n \,x^{6}}{36}-\frac {b \,e^{2} n \,x^{6+2 r}}{4 \left (3+r \right )^{2}}-\frac {2 b d e n \,x^{6+r}}{\left (6+r \right )^{2}}+\frac {\left (d^{2} x^{6}+\frac {3 e^{2} x^{6+2 r}}{3+r}+\frac {12 d e \,x^{6+r}}{6+r}\right ) \left (a +b \ln \left (c \,x^{n}\right )\right )}{6} \]
command
integrate(x**5*(d+e*x**r)**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 \[ \text {Timed out} \]_____________________________________________________