\[ \int (e x)^m \left (A+B x^n\right ) \left (c+d x^n\right )^3 \, dx \]
Optimal antiderivative \[ \frac {c^{2} \left (3 A d +B c \right ) x^{1+n} \left (e x \right )^{m}}{1+m +n}+\frac {3 c d \left (A d +B c \right ) x^{1+2 n} \left (e x \right )^{m}}{1+m +2 n}+\frac {d^{2} \left (A d +3 B c \right ) x^{1+3 n} \left (e x \right )^{m}}{1+m +3 n}+\frac {B \,d^{3} x^{1+4 n} \left (e x \right )^{m}}{1+m +4 n}+\frac {A \,c^{3} \left (e x \right )^{1+m}}{e \left (1+m \right )} \]
command
integrate((e*x)**m*(A+B*x**n)*(c+d*x**n)**3,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 \[ \text {Timed out} \]_____________________________________________________