\[ \int \frac {(a+b x)^{10} (A+B x)}{x^{17}} \, dx \]
Optimal antiderivative \[ -\frac {A \left (b x +a \right )^{11}}{16 a \,x^{16}}+\frac {\left (5 A b -16 a B \right ) \left (b x +a \right )^{11}}{240 a^{2} x^{15}}-\frac {b \left (5 A b -16 a B \right ) \left (b x +a \right )^{11}}{840 a^{3} x^{14}}+\frac {b^{2} \left (5 A b -16 a B \right ) \left (b x +a \right )^{11}}{3640 a^{4} x^{13}}-\frac {b^{3} \left (5 A b -16 a B \right ) \left (b x +a \right )^{11}}{21840 a^{5} x^{12}}+\frac {b^{4} \left (5 A b -16 a B \right ) \left (b x +a \right )^{11}}{240240 a^{6} x^{11}} \]
command
integrate((b*x+a)**10*(B*x+A)/x**17,x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \text {Timed out} \]
Sympy 1.8 under Python 3.8.8 output
\[ \frac {- 15015 A a^{10} - 48048 B b^{10} x^{11} + x^{10} \left (- 40040 A b^{10} - 400400 B a b^{9}\right ) + x^{9} \left (- 343200 A a b^{9} - 1544400 B a^{2} b^{8}\right ) + x^{8} \left (- 1351350 A a^{2} b^{8} - 3603600 B a^{3} b^{7}\right ) + x^{7} \left (- 3203200 A a^{3} b^{7} - 5605600 B a^{4} b^{6}\right ) + x^{6} \left (- 5045040 A a^{4} b^{6} - 6054048 B a^{5} b^{5}\right ) + x^{5} \left (- 5503680 A a^{5} b^{5} - 4586400 B a^{6} b^{4}\right ) + x^{4} \left (- 4204200 A a^{6} b^{4} - 2402400 B a^{7} b^{3}\right ) + x^{3} \left (- 2217600 A a^{7} b^{3} - 831600 B a^{8} b^{2}\right ) + x^{2} \left (- 772200 A a^{8} b^{2} - 171600 B a^{9} b\right ) + x \left (- 160160 A a^{9} b - 16016 B a^{10}\right )}{240240 x^{16}} \]