\[ \int \frac {3+5 x}{\sqrt {1-2 x} (2+3 x)^2} \, dx \]
Optimal antiderivative \[ -\frac {68 \arctanh \left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}\right ) \sqrt {21}}{441}+\frac {\sqrt {1-2 x}}{42+63 x} \]
command
integrate((3+5*x)/(2+3*x)**2/(1-2*x)**(1/2),x)
Sympy 1.10.1 under Python 3.10.4 output
\[ - \frac {4 \left (\begin {cases} \frac {\sqrt {21} \left (- \frac {\log {\left (-1 + \frac {\sqrt {21}}{3 \sqrt {1 - 2 x}} \right )}}{4} + \frac {\log {\left (1 + \frac {\sqrt {21}}{3 \sqrt {1 - 2 x}} \right )}}{4} - \frac {1}{4 \cdot \left (1 + \frac {\sqrt {21}}{3 \sqrt {1 - 2 x}}\right )} - \frac {1}{4 \left (-1 + \frac {\sqrt {21}}{3 \sqrt {1 - 2 x}}\right )}\right )}{63} & \text {for}\: \frac {1}{\sqrt {1 - 2 x}} > - \frac {\sqrt {21}}{7} \wedge \frac {1}{\sqrt {1 - 2 x}} < \frac {\sqrt {21}}{7} \end {cases}\right )}{7} + \frac {22 \left (\begin {cases} - \frac {\sqrt {21} \operatorname {acoth}{\left (\frac {\sqrt {21}}{3 \sqrt {1 - 2 x}} \right )}}{21} & \text {for}\: \frac {1}{1 - 2 x} > \frac {3}{7} \\- \frac {\sqrt {21} \operatorname {atanh}{\left (\frac {\sqrt {21}}{3 \sqrt {1 - 2 x}} \right )}}{21} & \text {for}\: \frac {1}{1 - 2 x} < \frac {3}{7} \end {cases}\right )}{7} \]
Sympy 1.8 under Python 3.8.8 output
\[ \text {Timed out} \]________________________________________________________________________________________