\[ \int \frac {\left (a+b x^2\right )^5 \left (A+B x^2\right )}{x^{19}} \, dx \]
Optimal antiderivative \[ -\frac {a^{5} A}{18 x^{18}}-\frac {a^{4} \left (5 A b +a B \right )}{16 x^{16}}-\frac {5 a^{3} b \left (2 A b +a B \right )}{14 x^{14}}-\frac {5 a^{2} b^{2} \left (A b +a B \right )}{6 x^{12}}-\frac {a \,b^{3} \left (A b +2 a B \right )}{2 x^{10}}-\frac {b^{4} \left (A b +5 a B \right )}{8 x^{8}}-\frac {b^{5} B}{6 x^{6}} \]
command
integrate((b*x**2+a)**5*(B*x**2+A)/x**19,x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \text {Timed out} \]
Sympy 1.8 under Python 3.8.8 output
\[ \frac {- 56 A a^{5} - 168 B b^{5} x^{12} + x^{10} \left (- 126 A b^{5} - 630 B a b^{4}\right ) + x^{8} \left (- 504 A a b^{4} - 1008 B a^{2} b^{3}\right ) + x^{6} \left (- 840 A a^{2} b^{3} - 840 B a^{3} b^{2}\right ) + x^{4} \left (- 720 A a^{3} b^{2} - 360 B a^{4} b\right ) + x^{2} \left (- 315 A a^{4} b - 63 B a^{5}\right )}{1008 x^{18}} \]