8.50 Problem number 1837

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

Optimal antiderivative \[ \frac {11656955 \arctanh \left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}\right ) \sqrt {21}}{28812}-250 \arctanh \left (\frac {\sqrt {55}\, \sqrt {1-2 x}}{11}\right ) \sqrt {55}+\frac {\sqrt {1-2 x}}{4 \left (2+3 x \right )^{4}}+\frac {139 \sqrt {1-2 x}}{84 \left (2+3 x \right )^{3}}+\frac {14555 \sqrt {1-2 x}}{1176 \left (2+3 x \right )^{2}}+\frac {337955 \sqrt {1-2 x}}{2744 \left (2+3 x \right )} \]

command

integrate((1-2*x)**(1/2)/(2+3*x)**5/(3+5*x),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 \[ \text {Timed out} \]_____________________________________________________