\[ \int \frac {3+5 x}{(1-2 x)^{5/2} (2+3 x)^2} \, dx \]
Optimal antiderivative \[ \frac {20}{147 \left (1-2 x \right )^{\frac {3}{2}}}+\frac {1}{21 \left (1-2 x \right )^{\frac {3}{2}} \left (2+3 x \right )}-\frac {60 \arctanh \left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}\right ) \sqrt {21}}{2401}+\frac {60}{343 \sqrt {1-2 x}} \]
command
integrate((3+5*x)/(1-2*x)**(5/2)/(2+3*x)**2,x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \frac {12 \left (\begin {cases} \frac {\sqrt {21} \left (- \frac {\log {\left (\frac {\sqrt {21} \sqrt {1 - 2 x}}{7} - 1 \right )}}{4} + \frac {\log {\left (\frac {\sqrt {21} \sqrt {1 - 2 x}}{7} + 1 \right )}}{4} - \frac {1}{4 \left (\frac {\sqrt {21} \sqrt {1 - 2 x}}{7} + 1\right )} - \frac {1}{4 \left (\frac {\sqrt {21} \sqrt {1 - 2 x}}{7} - 1\right )}\right )}{147} & \text {for}\: \sqrt {1 - 2 x} > - \frac {\sqrt {21}}{3} \wedge \sqrt {1 - 2 x} < \frac {\sqrt {21}}{3} \end {cases}\right )}{49} + \frac {186 \left (\begin {cases} - \frac {\sqrt {21} \operatorname {acoth}{\left (\frac {\sqrt {21} \sqrt {1 - 2 x}}{7} \right )}}{21} & \text {for}\: x < - \frac {2}{3} \\- \frac {\sqrt {21} \operatorname {atanh}{\left (\frac {\sqrt {21} \sqrt {1 - 2 x}}{7} \right )}}{21} & \text {for}\: x > - \frac {2}{3} \end {cases}\right )}{343} + \frac {62}{343 \sqrt {1 - 2 x}} + \frac {22}{147 \left (1 - 2 x\right )^{\frac {3}{2}}} \]
Sympy 1.8 under Python 3.8.8 output
\[ \text {Timed out} \]________________________________________________________________________________________