\[ \int \frac {\left (a+b x^3\right )^5 \left (A+B x^3\right )}{x^{16}} \, dx \]
Optimal antiderivative \[ -\frac {a^{5} A}{15 x^{15}}-\frac {a^{4} \left (5 A b +a B \right )}{12 x^{12}}-\frac {5 a^{3} b \left (2 A b +a B \right )}{9 x^{9}}-\frac {5 a^{2} b^{2} \left (A b +a B \right )}{3 x^{6}}-\frac {5 a \,b^{3} \left (A b +2 a B \right )}{3 x^{3}}+\frac {b^{5} B \,x^{3}}{3}+b^{4} \left (A b +5 a B \right ) \ln \! \left (x \right ) \]
command
integrate((b*x**3+a)**5*(B*x**3+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
\[ \frac {B b^{5} x^{3}}{3} + b^{4} \left (A b + 5 B a\right ) \log {\left (x \right )} + \frac {- 12 A a^{5} + x^{12} \left (- 300 A a b^{4} - 600 B a^{2} b^{3}\right ) + x^{9} \left (- 300 A a^{2} b^{3} - 300 B a^{3} b^{2}\right ) + x^{6} \left (- 200 A a^{3} b^{2} - 100 B a^{4} b\right ) + x^{3} \left (- 75 A a^{4} b - 15 B a^{5}\right )}{180 x^{15}} \]