\[ \int \sqrt {1-2 x} (2+3 x)^4 (3+5 x)^{3/2} \, dx \]
Optimal antiderivative \[ -\frac {52760369 \left (1-2 x \right )^{\frac {3}{2}} \left (3+5 x \right )^{\frac {3}{2}}}{7680000}-\frac {403 \left (1-2 x \right )^{\frac {3}{2}} \left (2+3 x \right )^{2} \left (3+5 x \right )^{\frac {5}{2}}}{2800}-\frac {3 \left (1-2 x \right )^{\frac {3}{2}} \left (2+3 x \right )^{3} \left (3+5 x \right )^{\frac {5}{2}}}{70}-\frac {\left (1-2 x \right )^{\frac {3}{2}} \left (3+5 x \right )^{\frac {5}{2}} \left (1480103+874608 x \right )}{640000}+\frac {70224051139 \arcsin \left (\frac {\sqrt {22}\, \sqrt {3+5 x}}{11}\right ) \sqrt {10}}{2048000000}-\frac {580364059 \left (1-2 x \right )^{\frac {3}{2}} \sqrt {3+5 x}}{20480000}+\frac {6384004649 \sqrt {1-2 x}\, \sqrt {3+5 x}}{204800000} \]
command
integrate((2+3*x)**4*(3+5*x)**(3/2)*(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 \[ \text {Timed out} \]_____________________________________________________