\[ \int x^m (d+e x) \left (1+2 x+x^2\right )^5 \, dx \]
Optimal antiderivative \[ \frac {d \,x^{1+m}}{1+m}+\frac {\left (10 d +e \right ) x^{2+m}}{2+m}+\frac {5 \left (9 d +2 e \right ) x^{3+m}}{3+m}+\frac {15 \left (8 d +3 e \right ) x^{4+m}}{4+m}+\frac {30 \left (7 d +4 e \right ) x^{5+m}}{5+m}+\frac {42 \left (6 d +5 e \right ) x^{6+m}}{6+m}+\frac {42 \left (5 d +6 e \right ) x^{7+m}}{7+m}+\frac {30 \left (4 d +7 e \right ) x^{8+m}}{8+m}+\frac {15 \left (3 d +8 e \right ) x^{9+m}}{9+m}+\frac {5 \left (2 d +9 e \right ) x^{10+m}}{10+m}+\frac {\left (d +10 e \right ) x^{11+m}}{11+m}+\frac {e \,x^{12+m}}{12+m} \]
command
integrate(x**m*(e*x+d)*(x**2+2*x+1)**5,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 \[ \text {Timed out} \]_____________________________________________________