8.65 Problem number 2057

\[ \int \frac {1}{\sqrt {1-2 x} (2+3 x)^4 (3+5 x)^2} \, dx \]

Optimal antiderivative \[ -\frac {1051695 \arctanh \left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}\right ) \sqrt {21}}{2401}+\frac {32750 \arctanh \left (\frac {\sqrt {55}\, \sqrt {1-2 x}}{11}\right ) \sqrt {55}}{121}-\frac {1676975 \sqrt {1-2 x}}{7546 \left (3+5 x \right )}+\frac {\sqrt {1-2 x}}{7 \left (2+3 x \right )^{3} \left (3+5 x \right )}+\frac {145 \sqrt {1-2 x}}{98 \left (2+3 x \right )^{2} \left (3+5 x \right )}+\frac {7585 \sqrt {1-2 x}}{343 \left (2+3 x \right ) \left (3+5 x \right )} \]

command

integrate(1/(2+3*x)**4/(3+5*x)**2/(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 \[ \text {Timed out} \]_____________________________________________________