\[ \int (d+e x)^m \left (3+2 x+5 x^2\right ) \left (2+x+3 x^2-5 x^3+4 x^4\right ) \, dx \]
Optimal antiderivative \[ \frac {\left (5 d^{2}-2 d e +3 e^{2}\right ) \left (4 d^{4}+5 d^{3} e +3 d^{2} e^{2}-d \,e^{3}+2 e^{4}\right ) \left (e x +d \right )^{1+m}}{e^{7} \left (1+m \right )}-\frac {\left (120 d^{5}+85 d^{4} e +68 d^{3} e^{2}+12 d^{2} e^{3}+42 d \,e^{4}-7 e^{5}\right ) \left (e x +d \right )^{2+m}}{e^{7} \left (2+m \right )}+\frac {\left (300 d^{4}+170 d^{3} e +102 d^{2} e^{2}+12 d \,e^{3}+21 e^{4}\right ) \left (e x +d \right )^{3+m}}{e^{7} \left (3+m \right )}-\frac {2 \left (200 d^{3}+85 d^{2} e +34 d \,e^{2}+2 e^{3}\right ) \left (e x +d \right )^{4+m}}{e^{7} \left (4+m \right )}+\frac {\left (300 d^{2}+85 d e +17 e^{2}\right ) \left (e x +d \right )^{5+m}}{e^{7} \left (5+m \right )}-\frac {\left (120 d +17 e \right ) \left (e x +d \right )^{6+m}}{e^{7} \left (6+m \right )}+\frac {20 \left (e x +d \right )^{7+m}}{e^{7} \left (7+m \right )} \]
command
integrate((e*x+d)**m*(5*x**2+2*x+3)*(4*x**4-5*x**3+3*x**2+x+2),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 \[ \text {Timed out} \]_____________________________________________________