8.58 Problem number 1856

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

Optimal antiderivative \[ \frac {2528082 \arctanh \left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}\right ) \sqrt {21}}{343}-\frac {551075 \arctanh \left (\frac {\sqrt {55}\, \sqrt {1-2 x}}{11}\right ) \sqrt {55}}{121}-\frac {182335 \sqrt {1-2 x}}{294 \left (3+5 x \right )^{2}}+\frac {\sqrt {1-2 x}}{3 \left (2+3 x \right )^{3} \left (3+5 x \right )^{2}}+\frac {29 \sqrt {1-2 x}}{7 \left (2+3 x \right )^{2} \left (3+5 x \right )^{2}}+\frac {4042 \sqrt {1-2 x}}{49 \left (2+3 x \right ) \left (3+5 x \right )^{2}}+\frac {4031135 \sqrt {1-2 x}}{1078 \left (3+5 x \right )} \]

command

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