\[ \int \frac {\left (a+c x^2\right )^3}{(d+e x)^{10}} \, dx \]
Optimal antiderivative \[ -\frac {\left (a \,e^{2}+c \,d^{2}\right )^{3}}{9 e^{7} \left (e x +d \right )^{9}}+\frac {3 c d \left (a \,e^{2}+c \,d^{2}\right )^{2}}{4 e^{7} \left (e x +d \right )^{8}}-\frac {3 c \left (a \,e^{2}+c \,d^{2}\right ) \left (a \,e^{2}+5 c \,d^{2}\right )}{7 e^{7} \left (e x +d \right )^{7}}+\frac {2 c^{2} d \left (3 a \,e^{2}+5 c \,d^{2}\right )}{3 e^{7} \left (e x +d \right )^{6}}-\frac {3 c^{2} \left (a \,e^{2}+5 c \,d^{2}\right )}{5 e^{7} \left (e x +d \right )^{5}}+\frac {3 c^{3} d}{2 e^{7} \left (e x +d \right )^{4}}-\frac {c^{3}}{3 e^{7} \left (e x +d \right )^{3}} \]
command
integrate((c*x**2+a)**3/(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
\[ \frac {- 140 a^{3} e^{6} - 15 a^{2} c d^{2} e^{4} - 6 a c^{2} d^{4} e^{2} - 5 c^{3} d^{6} - 630 c^{3} d e^{5} x^{5} - 420 c^{3} e^{6} x^{6} + x^{4} \left (- 756 a c^{2} e^{6} - 630 c^{3} d^{2} e^{4}\right ) + x^{3} \left (- 504 a c^{2} d e^{5} - 420 c^{3} d^{3} e^{3}\right ) + x^{2} \left (- 540 a^{2} c e^{6} - 216 a c^{2} d^{2} e^{4} - 180 c^{3} d^{4} e^{2}\right ) + x \left (- 135 a^{2} c d e^{5} - 54 a c^{2} d^{3} e^{3} - 45 c^{3} d^{5} e\right )}{1260 d^{9} e^{7} + 11340 d^{8} e^{8} x + 45360 d^{7} e^{9} x^{2} + 105840 d^{6} e^{10} x^{3} + 158760 d^{5} e^{11} x^{4} + 158760 d^{4} e^{12} x^{5} + 105840 d^{3} e^{13} x^{6} + 45360 d^{2} e^{14} x^{7} + 11340 d e^{15} x^{8} + 1260 e^{16} x^{9}} \]