\[ \int \left (a+b x^n\right )^2 \left (d+e x^n\right )^3 \, dx \]
Optimal antiderivative \[ a^{2} d^{3} x +\frac {a \,d^{2} \left (3 a e +2 b d \right ) x^{1+n}}{1+n}+\frac {d \left (3 a^{2} e^{2}+6 a b d e +b^{2} d^{2}\right ) x^{1+2 n}}{1+2 n}+\frac {e \left (a^{2} e^{2}+6 a b d e +3 b^{2} d^{2}\right ) x^{1+3 n}}{1+3 n}+\frac {b \,e^{2} \left (2 a e +3 b d \right ) x^{1+4 n}}{1+4 n}+\frac {b^{2} e^{3} x^{1+5 n}}{1+5 n} \]
command
integrate((a+b*x**n)**2*(d+e*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 \[ \text {Timed out} \]_____________________________________________________