\[ \int (d+e x)^m \left (3+2 x+5 x^2\right )^2 \left (2+x+3 x^2-5 x^3+4 x^4\right ) \, dx \]
Optimal antiderivative \[ \frac {\left (5 d^{2}-2 d e +3 e^{2}\right )^{2} \left (4 d^{4}+5 d^{3} e +3 d^{2} e^{2}-d \,e^{3}+2 e^{4}\right ) \left (e x +d \right )^{1+m}}{e^{9} \left (1+m \right )}-\frac {\left (5 d^{2}-2 d e +3 e^{2}\right ) \left (160 d^{5}+127 d^{4} e +88 d^{3} e^{2}-4 d^{2} e^{3}+64 d \,e^{4}-11 e^{5}\right ) \left (e x +d \right )^{2+m}}{e^{9} \left (2+m \right )}+\frac {\left (2800 d^{6}+945 d^{5} e +1665 d^{4} e^{2}+370 d^{3} e^{3}+888 d^{2} e^{4}-195 d \,e^{5}+107 e^{6}\right ) \left (e x +d \right )^{3+m}}{e^{9} \left (3+m \right )}-\frac {\left (5600 d^{5}+1575 d^{4} e +2220 d^{3} e^{2}+370 d^{2} e^{3}+592 d \,e^{4}-65 e^{5}\right ) \left (e x +d \right )^{4+m}}{e^{9} \left (4+m \right )}+\frac {\left (7000 d^{4}+1575 d^{3} e +1665 d^{2} e^{2}+185 d \,e^{3}+148 e^{4}\right ) \left (e x +d \right )^{5+m}}{e^{9} \left (5+m \right )}-\frac {\left (5600 d^{3}+945 d^{2} e +666 d \,e^{2}+37 e^{3}\right ) \left (e x +d \right )^{6+m}}{e^{9} \left (6+m \right )}+\frac {\left (2800 d^{2}+315 d e +111 e^{2}\right ) \left (e x +d \right )^{7+m}}{e^{9} \left (7+m \right )}-\frac {5 \left (160 d +9 e \right ) \left (e x +d \right )^{8+m}}{e^{9} \left (8+m \right )}+\frac {100 \left (e x +d \right )^{9+m}}{e^{9} \left (9+m \right )} \]
command
integrate((e*x+d)**m*(5*x**2+2*x+3)**2*(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 \[ \text {Timed out} \]_____________________________________________________