\[ \int \frac {2+3 x}{(1-2 x)^{5/2} (3+5 x)^2} \, dx \]
Optimal antiderivative \[ \frac {76}{1815 \left (1-2 x \right )^{\frac {3}{2}}}-\frac {1}{55 \left (1-2 x \right )^{\frac {3}{2}} \left (3+5 x \right )}-\frac {76 \arctanh \left (\frac {\sqrt {55}\, \sqrt {1-2 x}}{11}\right ) \sqrt {55}}{14641}+\frac {76}{1331 \sqrt {1-2 x}} \]
command
integrate((2+3*x)/(1-2*x)**(5/2)/(3+5*x)**2,x)
Sympy 1.10.1 under Python 3.10.4 output
\[ - \frac {20 \left (\begin {cases} \frac {\sqrt {55} \left (- \frac {\log {\left (\frac {\sqrt {55} \sqrt {1 - 2 x}}{11} - 1 \right )}}{4} + \frac {\log {\left (\frac {\sqrt {55} \sqrt {1 - 2 x}}{11} + 1 \right )}}{4} - \frac {1}{4 \left (\frac {\sqrt {55} \sqrt {1 - 2 x}}{11} + 1\right )} - \frac {1}{4 \left (\frac {\sqrt {55} \sqrt {1 - 2 x}}{11} - 1\right )}\right )}{605} & \text {for}\: \sqrt {1 - 2 x} > - \frac {\sqrt {55}}{5} \wedge \sqrt {1 - 2 x} < \frac {\sqrt {55}}{5} \end {cases}\right )}{121} + \frac {370 \left (\begin {cases} - \frac {\sqrt {55} \operatorname {acoth}{\left (\frac {\sqrt {55} \sqrt {1 - 2 x}}{11} \right )}}{55} & \text {for}\: x < - \frac {3}{5} \\- \frac {\sqrt {55} \operatorname {atanh}{\left (\frac {\sqrt {55} \sqrt {1 - 2 x}}{11} \right )}}{55} & \text {for}\: x > - \frac {3}{5} \end {cases}\right )}{1331} + \frac {74}{1331 \sqrt {1 - 2 x}} + \frac {14}{363 \left (1 - 2 x\right )^{\frac {3}{2}}} \]
Sympy 1.8 under Python 3.8.8 output
\[ \text {Timed out} \]________________________________________________________________________________________