\[ \int \frac {(a+b x)^{10} (A+B x)}{x^{16}} \, dx \]
Optimal antiderivative \[ -\frac {A \left (b x +a \right )^{11}}{15 a \,x^{15}}+\frac {\left (4 A b -15 a B \right ) \left (b x +a \right )^{11}}{210 a^{2} x^{14}}-\frac {b \left (4 A b -15 a B \right ) \left (b x +a \right )^{11}}{910 a^{3} x^{13}}+\frac {b^{2} \left (4 A b -15 a B \right ) \left (b x +a \right )^{11}}{5460 a^{4} x^{12}}-\frac {b^{3} \left (4 A b -15 a B \right ) \left (b x +a \right )^{11}}{60060 a^{5} x^{11}} \]
command
integrate((b*x+a)**10*(B*x+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
\[ \frac {- 4004 A a^{10} - 15015 B b^{10} x^{11} + x^{10} \left (- 12012 A b^{10} - 120120 B a b^{9}\right ) + x^{9} \left (- 100100 A a b^{9} - 450450 B a^{2} b^{8}\right ) + x^{8} \left (- 386100 A a^{2} b^{8} - 1029600 B a^{3} b^{7}\right ) + x^{7} \left (- 900900 A a^{3} b^{7} - 1576575 B a^{4} b^{6}\right ) + x^{6} \left (- 1401400 A a^{4} b^{6} - 1681680 B a^{5} b^{5}\right ) + x^{5} \left (- 1513512 A a^{5} b^{5} - 1261260 B a^{6} b^{4}\right ) + x^{4} \left (- 1146600 A a^{6} b^{4} - 655200 B a^{7} b^{3}\right ) + x^{3} \left (- 600600 A a^{7} b^{3} - 225225 B a^{8} b^{2}\right ) + x^{2} \left (- 207900 A a^{8} b^{2} - 46200 B a^{9} b\right ) + x \left (- 42900 A a^{9} b - 4290 B a^{10}\right )}{60060 x^{15}} \]