8.63 Problem number 2046

\[ \int \frac {1}{\sqrt {1-2 x} (2+3 x)^5 (3+5 x)} \, dx \]

Optimal antiderivative \[ \frac {36045 \arctanh \left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}\right ) \sqrt {21}}{196}-\frac {1250 \arctanh \left (\frac {\sqrt {55}\, \sqrt {1-2 x}}{11}\right ) \sqrt {55}}{11}+\frac {3 \sqrt {1-2 x}}{28 \left (2+3 x \right )^{4}}+\frac {3 \sqrt {1-2 x}}{4 \left (2+3 x \right )^{3}}+\frac {45 \sqrt {1-2 x}}{8 \left (2+3 x \right )^{2}}+\frac {3135 \sqrt {1-2 x}}{56 \left (2+3 x \right )} \]

command

integrate(1/(2+3*x)**5/(3+5*x)/(1-2*x)**(1/2),x)

Sympy 1.10.1 under Python 3.10.4 output

\[ \text {output too large to display} \]

Sympy 1.8 under Python 3.8.8 output \[ \text {Timed out} \]_____________________________________________________