\[ \int \frac {\left (a+b x^2\right )^5 \left (A+B x^2\right )}{x^{14}} \, dx \]
Optimal antiderivative \[ -\frac {a^{5} A}{13 x^{13}}-\frac {a^{4} \left (5 A b +a B \right )}{11 x^{11}}-\frac {5 a^{3} b \left (2 A b +a B \right )}{9 x^{9}}-\frac {10 a^{2} b^{2} \left (A b +a B \right )}{7 x^{7}}-\frac {a \,b^{3} \left (A b +2 a B \right )}{x^{5}}-\frac {b^{4} \left (A b +5 a B \right )}{3 x^{3}}-\frac {b^{5} B}{x} \]
command
integrate((b*x**2+a)**5*(B*x**2+A)/x**14,x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \text {Timed out} \]
Sympy 1.8 under Python 3.8.8 output
\[ \frac {- 693 A a^{5} - 9009 B b^{5} x^{12} + x^{10} \left (- 3003 A b^{5} - 15015 B a b^{4}\right ) + x^{8} \left (- 9009 A a b^{4} - 18018 B a^{2} b^{3}\right ) + x^{6} \left (- 12870 A a^{2} b^{3} - 12870 B a^{3} b^{2}\right ) + x^{4} \left (- 10010 A a^{3} b^{2} - 5005 B a^{4} b\right ) + x^{2} \left (- 4095 A a^{4} b - 819 B a^{5}\right )}{9009 x^{13}} \]