\[ \int (d+e x)^m \left (a+c x^2\right )^3 \, dx \]
Optimal antiderivative \[ \frac {\left (a \,e^{2}+c \,d^{2}\right )^{3} \left (e x +d \right )^{1+m}}{e^{7} \left (1+m \right )}-\frac {6 c d \left (a \,e^{2}+c \,d^{2}\right )^{2} \left (e x +d \right )^{2+m}}{e^{7} \left (2+m \right )}+\frac {3 c \left (a \,e^{2}+c \,d^{2}\right ) \left (a \,e^{2}+5 c \,d^{2}\right ) \left (e x +d \right )^{3+m}}{e^{7} \left (3+m \right )}-\frac {4 c^{2} d \left (3 a \,e^{2}+5 c \,d^{2}\right ) \left (e x +d \right )^{4+m}}{e^{7} \left (4+m \right )}+\frac {3 c^{2} \left (a \,e^{2}+5 c \,d^{2}\right ) \left (e x +d \right )^{5+m}}{e^{7} \left (5+m \right )}-\frac {6 c^{3} d \left (e x +d \right )^{6+m}}{e^{7} \left (6+m \right )}+\frac {c^{3} \left (e x +d \right )^{7+m}}{e^{7} \left (7+m \right )} \]
command
integrate((e*x+d)**m*(c*x**2+a)**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 \[ \text {Timed out} \]_____________________________________________________