8.66 Problem number 2068

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

Optimal antiderivative \[ \frac {7852680 \arctanh \left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}\right ) \sqrt {21}}{2401}-\frac {2689875 \arctanh \left (\frac {\sqrt {55}\, \sqrt {1-2 x}}{11}\right ) \sqrt {55}}{1331}-\frac {2076675 \sqrt {1-2 x}}{7546 \left (3+5 x \right )^{2}}+\frac {\sqrt {1-2 x}}{7 \left (2+3 x \right )^{3} \left (3+5 x \right )^{2}}+\frac {90 \sqrt {1-2 x}}{49 \left (2+3 x \right )^{2} \left (3+5 x \right )^{2}}+\frac {12555 \sqrt {1-2 x}}{343 \left (2+3 x \right ) \left (3+5 x \right )^{2}}+\frac {137735775 \sqrt {1-2 x}}{83006 \left (3+5 x \right )} \]

command

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