\[ \int \frac {2+3 x}{\sqrt {1-2 x} (3+5 x)^2} \, dx \]
Optimal antiderivative \[ -\frac {68 \arctanh \left (\frac {\sqrt {55}\, \sqrt {1-2 x}}{11}\right ) \sqrt {55}}{3025}-\frac {\sqrt {1-2 x}}{55 \left (3+5 x \right )} \]
command
integrate((2+3*x)/(3+5*x)**2/(1-2*x)**(1/2),x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \frac {4 \left (\begin {cases} \frac {\sqrt {55} \left (- \frac {\log {\left (-1 + \frac {\sqrt {55}}{5 \sqrt {1 - 2 x}} \right )}}{4} + \frac {\log {\left (1 + \frac {\sqrt {55}}{5 \sqrt {1 - 2 x}} \right )}}{4} - \frac {1}{4 \cdot \left (1 + \frac {\sqrt {55}}{5 \sqrt {1 - 2 x}}\right )} - \frac {1}{4 \left (-1 + \frac {\sqrt {55}}{5 \sqrt {1 - 2 x}}\right )}\right )}{275} & \text {for}\: \frac {1}{\sqrt {1 - 2 x}} > - \frac {\sqrt {55}}{11} \wedge \frac {1}{\sqrt {1 - 2 x}} < \frac {\sqrt {55}}{11} \end {cases}\right )}{11} + \frac {14 \left (\begin {cases} - \frac {\sqrt {55} \operatorname {acoth}{\left (\frac {\sqrt {55}}{5 \sqrt {1 - 2 x}} \right )}}{55} & \text {for}\: \frac {1}{1 - 2 x} > \frac {5}{11} \\- \frac {\sqrt {55} \operatorname {atanh}{\left (\frac {\sqrt {55}}{5 \sqrt {1 - 2 x}} \right )}}{55} & \text {for}\: \frac {1}{1 - 2 x} < \frac {5}{11} \end {cases}\right )}{11} \]
Sympy 1.8 under Python 3.8.8 output
\[ \text {Timed out} \]________________________________________________________________________________________