\[ \int \frac {\left (a+b x^2\right )^5 \left (A+B x^2\right )}{x^{16}} \, dx \]
Optimal antiderivative \[ -\frac {a^{5} A}{15 x^{15}}-\frac {a^{4} \left (5 A b +a B \right )}{13 x^{13}}-\frac {5 a^{3} b \left (2 A b +a B \right )}{11 x^{11}}-\frac {10 a^{2} b^{2} \left (A b +a B \right )}{9 x^{9}}-\frac {5 a \,b^{3} \left (A b +2 a B \right )}{7 x^{7}}-\frac {b^{4} \left (A b +5 a B \right )}{5 x^{5}}-\frac {b^{5} B}{3 x^{3}} \]
command
integrate((b*x**2+a)**5*(B*x**2+A)/x**16,x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \text {Timed out} \]
Sympy 1.8 under Python 3.8.8 output
\[ \frac {- 3003 A a^{5} - 15015 B b^{5} x^{12} + x^{10} \left (- 9009 A b^{5} - 45045 B a b^{4}\right ) + x^{8} \left (- 32175 A a b^{4} - 64350 B a^{2} b^{3}\right ) + x^{6} \left (- 50050 A a^{2} b^{3} - 50050 B a^{3} b^{2}\right ) + x^{4} \left (- 40950 A a^{3} b^{2} - 20475 B a^{4} b\right ) + x^{2} \left (- 17325 A a^{4} b - 3465 B a^{5}\right )}{45045 x^{15}} \]