\[ \int (d+e x)^m \left (3+2 x+5 x^2\right )^3 \left (2+x+3 x^2-5 x^3+4 x^4\right ) \, dx \]
Optimal antiderivative \[ \frac {\left (5 d^{2}-2 d e +3 e^{2}\right )^{3} \left (4 d^{4}+5 d^{3} e +3 d^{2} e^{2}-d \,e^{3}+2 e^{4}\right ) \left (e x +d \right )^{1+m}}{e^{11} \left (1+m \right )}-\frac {\left (5 d^{2}-2 d e +3 e^{2}\right )^{2} \left (200 d^{5}+169 d^{4} e +108 d^{3} e^{2}-20 d^{2} e^{3}+86 d \,e^{4}-15 e^{5}\right ) \left (e x +d \right )^{2+m}}{e^{11} \left (2+m \right )}+\frac {3 \left (5 d^{2}-2 d e +3 e^{2}\right ) \left (1500 d^{6}+660 d^{5} e +792 d^{4} e^{2}+58 d^{3} e^{3}+547 d^{2} e^{4}-156 d \,e^{5}+53 e^{6}\right ) \left (e x +d \right )^{3+m}}{e^{11} \left (3+m \right )}-\frac {2 \left (30000 d^{7}+1050 d^{6} e +21420 d^{5} e^{2}+1715 d^{4} e^{3}+9990 d^{3} e^{4}-2550 d^{2} e^{5}+2218 d \,e^{6}-287 e^{7}\right ) \left (e x +d \right )^{4+m}}{e^{11} \left (4+m \right )}+\frac {\left (105000 d^{6}+3150 d^{5} e +53550 d^{4} e^{2}+3430 d^{3} e^{3}+14985 d^{2} e^{4}-2550 d \,e^{5}+1109 e^{6}\right ) \left (e x +d \right )^{5+m}}{e^{11} \left (5+m \right )}-\frac {6 \left (21000 d^{5}+525 d^{4} e +7140 d^{3} e^{2}+343 d^{2} e^{3}+999 d \,e^{4}-85 e^{5}\right ) \left (e x +d \right )^{6+m}}{e^{11} \left (6+m \right )}+\frac {\left (105000 d^{4}+2100 d^{3} e +21420 d^{2} e^{2}+686 d \,e^{3}+999 e^{4}\right ) \left (e x +d \right )^{7+m}}{e^{11} \left (7+m \right )}-\frac {2 \left (30000 d^{3}+450 d^{2} e +3060 d \,e^{2}+49 e^{3}\right ) \left (e x +d \right )^{8+m}}{e^{11} \left (8+m \right )}+\frac {45 \left (500 d^{2}+5 d e +17 e^{2}\right ) \left (e x +d \right )^{9+m}}{e^{11} \left (9+m \right )}-\frac {25 \left (200 d +e \right ) \left (e x +d \right )^{10+m}}{e^{11} \left (10+m \right )}+\frac {500 \left (e x +d \right )^{11+m}}{e^{11} \left (11+m \right )} \]
command
integrate((e*x+d)**m*(5*x**2+2*x+3)**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 \[ \text {Timed out} \]_____________________________________________________