\[ \int \frac {\left (a^2+2 a b x+b^2 x^2\right )^2}{(d+e x)^{10}} \, dx \]
Optimal antiderivative \[ -\frac {\left (-a e +b d \right )^{4}}{9 e^{5} \left (e x +d \right )^{9}}+\frac {b \left (-a e +b d \right )^{3}}{2 e^{5} \left (e x +d \right )^{8}}-\frac {6 b^{2} \left (-a e +b d \right )^{2}}{7 e^{5} \left (e x +d \right )^{7}}+\frac {2 b^{3} \left (-a e +b d \right )}{3 e^{5} \left (e x +d \right )^{6}}-\frac {b^{4}}{5 e^{5} \left (e x +d \right )^{5}} \]
command
integrate((b**2*x**2+2*a*b*x+a**2)**2/(e*x+d)**10,x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \text {Timed out} \]
Sympy 1.8 under Python 3.8.8 output
\[ \frac {- 70 a^{4} e^{4} - 35 a^{3} b d e^{3} - 15 a^{2} b^{2} d^{2} e^{2} - 5 a b^{3} d^{3} e - b^{4} d^{4} - 126 b^{4} e^{4} x^{4} + x^{3} \left (- 420 a b^{3} e^{4} - 84 b^{4} d e^{3}\right ) + x^{2} \left (- 540 a^{2} b^{2} e^{4} - 180 a b^{3} d e^{3} - 36 b^{4} d^{2} e^{2}\right ) + x \left (- 315 a^{3} b e^{4} - 135 a^{2} b^{2} d e^{3} - 45 a b^{3} d^{2} e^{2} - 9 b^{4} d^{3} e\right )}{630 d^{9} e^{5} + 5670 d^{8} e^{6} x + 22680 d^{7} e^{7} x^{2} + 52920 d^{6} e^{8} x^{3} + 79380 d^{5} e^{9} x^{4} + 79380 d^{4} e^{10} x^{5} + 52920 d^{3} e^{11} x^{6} + 22680 d^{2} e^{12} x^{7} + 5670 d e^{13} x^{8} + 630 e^{14} x^{9}} \]