\[ \int \left (a+\frac {b}{x}\right )^{3/2} x^{9/2} \, dx \]
Optimal antiderivative \[ -\frac {32 b^{3} \left (a +\frac {b}{x}\right )^{\frac {5}{2}} x^{\frac {5}{2}}}{1155 a^{4}}+\frac {16 b^{2} \left (a +\frac {b}{x}\right )^{\frac {5}{2}} x^{\frac {7}{2}}}{231 a^{3}}-\frac {4 b \left (a +\frac {b}{x}\right )^{\frac {5}{2}} x^{\frac {9}{2}}}{33 a^{2}}+\frac {2 \left (a +\frac {b}{x}\right )^{\frac {5}{2}} x^{\frac {11}{2}}}{11 a} \]
command
integrate((a+b/x)**(3/2)*x**(9/2),x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \text {Exception raised: SystemError} \]
Sympy 1.8 under Python 3.8.8 output
\[ \frac {210 a^{8} b^{\frac {19}{2}} x^{8} \sqrt {\frac {a x}{b} + 1}}{1155 a^{7} b^{9} x^{3} + 3465 a^{6} b^{10} x^{2} + 3465 a^{5} b^{11} x + 1155 a^{4} b^{12}} + \frac {910 a^{7} b^{\frac {21}{2}} x^{7} \sqrt {\frac {a x}{b} + 1}}{1155 a^{7} b^{9} x^{3} + 3465 a^{6} b^{10} x^{2} + 3465 a^{5} b^{11} x + 1155 a^{4} b^{12}} + \frac {1480 a^{6} b^{\frac {23}{2}} x^{6} \sqrt {\frac {a x}{b} + 1}}{1155 a^{7} b^{9} x^{3} + 3465 a^{6} b^{10} x^{2} + 3465 a^{5} b^{11} x + 1155 a^{4} b^{12}} + \frac {1068 a^{5} b^{\frac {25}{2}} x^{5} \sqrt {\frac {a x}{b} + 1}}{1155 a^{7} b^{9} x^{3} + 3465 a^{6} b^{10} x^{2} + 3465 a^{5} b^{11} x + 1155 a^{4} b^{12}} + \frac {290 a^{4} b^{\frac {27}{2}} x^{4} \sqrt {\frac {a x}{b} + 1}}{1155 a^{7} b^{9} x^{3} + 3465 a^{6} b^{10} x^{2} + 3465 a^{5} b^{11} x + 1155 a^{4} b^{12}} - \frac {10 a^{3} b^{\frac {29}{2}} x^{3} \sqrt {\frac {a x}{b} + 1}}{1155 a^{7} b^{9} x^{3} + 3465 a^{6} b^{10} x^{2} + 3465 a^{5} b^{11} x + 1155 a^{4} b^{12}} - \frac {60 a^{2} b^{\frac {31}{2}} x^{2} \sqrt {\frac {a x}{b} + 1}}{1155 a^{7} b^{9} x^{3} + 3465 a^{6} b^{10} x^{2} + 3465 a^{5} b^{11} x + 1155 a^{4} b^{12}} - \frac {80 a b^{\frac {33}{2}} x \sqrt {\frac {a x}{b} + 1}}{1155 a^{7} b^{9} x^{3} + 3465 a^{6} b^{10} x^{2} + 3465 a^{5} b^{11} x + 1155 a^{4} b^{12}} - \frac {32 b^{\frac {35}{2}} \sqrt {\frac {a x}{b} + 1}}{1155 a^{7} b^{9} x^{3} + 3465 a^{6} b^{10} x^{2} + 3465 a^{5} b^{11} x + 1155 a^{4} b^{12}} \]