\[ \int \frac {(a+b x)^{10} (A+B x)}{x^{15}} \, dx \]
Optimal antiderivative \[ -\frac {A \left (b x +a \right )^{11}}{14 a \,x^{14}}+\frac {\left (3 A b -14 a B \right ) \left (b x +a \right )^{11}}{182 a^{2} x^{13}}-\frac {b \left (3 A b -14 a B \right ) \left (b x +a \right )^{11}}{1092 a^{3} x^{12}}+\frac {b^{2} \left (3 A b -14 a B \right ) \left (b x +a \right )^{11}}{12012 a^{4} x^{11}} \]
command
integrate((b*x+a)**10*(B*x+A)/x**15,x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \text {Timed out} \]
Sympy 1.8 under Python 3.8.8 output
\[ \frac {- 858 A a^{10} - 4004 B b^{10} x^{11} + x^{10} \left (- 3003 A b^{10} - 30030 B a b^{9}\right ) + x^{9} \left (- 24024 A a b^{9} - 108108 B a^{2} b^{8}\right ) + x^{8} \left (- 90090 A a^{2} b^{8} - 240240 B a^{3} b^{7}\right ) + x^{7} \left (- 205920 A a^{3} b^{7} - 360360 B a^{4} b^{6}\right ) + x^{6} \left (- 315315 A a^{4} b^{6} - 378378 B a^{5} b^{5}\right ) + x^{5} \left (- 336336 A a^{5} b^{5} - 280280 B a^{6} b^{4}\right ) + x^{4} \left (- 252252 A a^{6} b^{4} - 144144 B a^{7} b^{3}\right ) + x^{3} \left (- 131040 A a^{7} b^{3} - 49140 B a^{8} b^{2}\right ) + x^{2} \left (- 45045 A a^{8} b^{2} - 10010 B a^{9} b\right ) + x \left (- 9240 A a^{9} b - 924 B a^{10}\right )}{12012 x^{14}} \]