\[ \int \frac {1}{(1-x)^{7/2} x^5} \, dx \]
Optimal antiderivative \[ \frac {3003}{320 \left (1-x \right )^{\frac {5}{2}}}+\frac {1001}{64 \left (1-x \right )^{\frac {3}{2}}}-\frac {1}{4 \left (1-x \right )^{\frac {5}{2}} x^{4}}-\frac {13}{24 \left (1-x \right )^{\frac {5}{2}} x^{3}}-\frac {143}{96 \left (1-x \right )^{\frac {5}{2}} x^{2}}-\frac {429}{64 \left (1-x \right )^{\frac {5}{2}} x}-\frac {3003 \arctanh \! \left (\sqrt {1-x}\right )}{64}+\frac {3003}{64 \sqrt {1-x}} \]
command
integrate(1/(1-x)**(7/2)/x**5,x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \text {Timed out} \]
Sympy 1.8 under Python 3.8.8 output
\[ \begin {cases} - \frac {45045 i x^{7} \operatorname {asin}{\left (\frac {1}{\sqrt {x}} \right )}}{- 960 x^{7} + 2880 x^{6} - 2880 x^{5} + 960 x^{4}} + \frac {45045 i x^{6} \sqrt {x - 1}}{- 960 x^{7} + 2880 x^{6} - 2880 x^{5} + 960 x^{4}} + \frac {135135 i x^{6} \operatorname {asin}{\left (\frac {1}{\sqrt {x}} \right )}}{- 960 x^{7} + 2880 x^{6} - 2880 x^{5} + 960 x^{4}} - \frac {105105 i x^{5} \sqrt {x - 1}}{- 960 x^{7} + 2880 x^{6} - 2880 x^{5} + 960 x^{4}} - \frac {135135 i x^{5} \operatorname {asin}{\left (\frac {1}{\sqrt {x}} \right )}}{- 960 x^{7} + 2880 x^{6} - 2880 x^{5} + 960 x^{4}} + \frac {69069 i x^{4} \sqrt {x - 1}}{- 960 x^{7} + 2880 x^{6} - 2880 x^{5} + 960 x^{4}} + \frac {45045 i x^{4} \operatorname {asin}{\left (\frac {1}{\sqrt {x}} \right )}}{- 960 x^{7} + 2880 x^{6} - 2880 x^{5} + 960 x^{4}} - \frac {6435 i x^{3} \sqrt {x - 1}}{- 960 x^{7} + 2880 x^{6} - 2880 x^{5} + 960 x^{4}} - \frac {1430 i x^{2} \sqrt {x - 1}}{- 960 x^{7} + 2880 x^{6} - 2880 x^{5} + 960 x^{4}} - \frac {520 i x \sqrt {x - 1}}{- 960 x^{7} + 2880 x^{6} - 2880 x^{5} + 960 x^{4}} - \frac {240 i \sqrt {x - 1}}{- 960 x^{7} + 2880 x^{6} - 2880 x^{5} + 960 x^{4}} & \text {for}\: \left |{x}\right | > 1 \\- \frac {45045 x^{7} \log {\left (x \right )}}{- 1920 x^{7} + 5760 x^{6} - 5760 x^{5} + 1920 x^{4}} + \frac {90090 x^{7} \log {\left (\sqrt {1 - x} + 1 \right )}}{- 1920 x^{7} + 5760 x^{6} - 5760 x^{5} + 1920 x^{4}} - \frac {45045 i \pi x^{7}}{- 1920 x^{7} + 5760 x^{6} - 5760 x^{5} + 1920 x^{4}} + \frac {90090 x^{6} \sqrt {1 - x}}{- 1920 x^{7} + 5760 x^{6} - 5760 x^{5} + 1920 x^{4}} + \frac {135135 x^{6} \log {\left (x \right )}}{- 1920 x^{7} + 5760 x^{6} - 5760 x^{5} + 1920 x^{4}} - \frac {270270 x^{6} \log {\left (\sqrt {1 - x} + 1 \right )}}{- 1920 x^{7} + 5760 x^{6} - 5760 x^{5} + 1920 x^{4}} + \frac {135135 i \pi x^{6}}{- 1920 x^{7} + 5760 x^{6} - 5760 x^{5} + 1920 x^{4}} - \frac {210210 x^{5} \sqrt {1 - x}}{- 1920 x^{7} + 5760 x^{6} - 5760 x^{5} + 1920 x^{4}} - \frac {135135 x^{5} \log {\left (x \right )}}{- 1920 x^{7} + 5760 x^{6} - 5760 x^{5} + 1920 x^{4}} + \frac {270270 x^{5} \log {\left (\sqrt {1 - x} + 1 \right )}}{- 1920 x^{7} + 5760 x^{6} - 5760 x^{5} + 1920 x^{4}} - \frac {135135 i \pi x^{5}}{- 1920 x^{7} + 5760 x^{6} - 5760 x^{5} + 1920 x^{4}} + \frac {138138 x^{4} \sqrt {1 - x}}{- 1920 x^{7} + 5760 x^{6} - 5760 x^{5} + 1920 x^{4}} + \frac {45045 x^{4} \log {\left (x \right )}}{- 1920 x^{7} + 5760 x^{6} - 5760 x^{5} + 1920 x^{4}} - \frac {90090 x^{4} \log {\left (\sqrt {1 - x} + 1 \right )}}{- 1920 x^{7} + 5760 x^{6} - 5760 x^{5} + 1920 x^{4}} + \frac {45045 i \pi x^{4}}{- 1920 x^{7} + 5760 x^{6} - 5760 x^{5} + 1920 x^{4}} - \frac {12870 x^{3} \sqrt {1 - x}}{- 1920 x^{7} + 5760 x^{6} - 5760 x^{5} + 1920 x^{4}} - \frac {2860 x^{2} \sqrt {1 - x}}{- 1920 x^{7} + 5760 x^{6} - 5760 x^{5} + 1920 x^{4}} - \frac {1040 x \sqrt {1 - x}}{- 1920 x^{7} + 5760 x^{6} - 5760 x^{5} + 1920 x^{4}} - \frac {480 \sqrt {1 - x}}{- 1920 x^{7} + 5760 x^{6} - 5760 x^{5} + 1920 x^{4}} & \text {otherwise} \end {cases} \]