\[ \int \sqrt {1-2 x} (2+3 x)^3 (3+5 x)^{5/2} \, dx \]
Optimal antiderivative \[ -\frac {3262963 \left (1-2 x \right )^{\frac {3}{2}} \left (3+5 x \right )^{\frac {3}{2}}}{307200}-\frac {296633 \left (1-2 x \right )^{\frac {3}{2}} \left (3+5 x \right )^{\frac {5}{2}}}{128000}-\frac {3 \left (1-2 x \right )^{\frac {3}{2}} \left (2+3 x \right )^{2} \left (3+5 x \right )^{\frac {7}{2}}}{70}-\frac {3 \left (1-2 x \right )^{\frac {3}{2}} \left (3+5 x \right )^{\frac {7}{2}} \left (1963+1140 x \right )}{8000}+\frac {4343003753 \arcsin \left (\frac {\sqrt {22}\, \sqrt {3+5 x}}{11}\right ) \sqrt {10}}{81920000}-\frac {35892593 \left (1-2 x \right )^{\frac {3}{2}} \sqrt {3+5 x}}{819200}+\frac {394818523 \sqrt {1-2 x}\, \sqrt {3+5 x}}{8192000} \]
command
integrate((2+3*x)**3*(3+5*x)**(5/2)*(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 \[ \text {Timed out} \]_____________________________________________________