\[ \int (1-2 x)^{5/2} (2+3 x)^3 \sqrt {3+5 x} \, dx \]
Optimal antiderivative \[ -\frac {3 \left (1-2 x \right )^{\frac {7}{2}} \left (2+3 x \right )^{2} \left (3+5 x \right )^{\frac {3}{2}}}{70}-\frac {3 \left (1-2 x \right )^{\frac {7}{2}} \left (3+5 x \right )^{\frac {3}{2}} \left (33857+26700 x \right )}{280000}+\frac {3735929329 \arcsin \left (\frac {\sqrt {22}\, \sqrt {3+5 x}}{11}\right ) \sqrt {10}}{2560000000}+\frac {30875449 \left (1-2 x \right )^{\frac {3}{2}} \sqrt {3+5 x}}{76800000}+\frac {2806859 \left (1-2 x \right )^{\frac {5}{2}} \sqrt {3+5 x}}{19200000}-\frac {255169 \left (1-2 x \right )^{\frac {7}{2}} \sqrt {3+5 x}}{640000}+\frac {339629939 \sqrt {1-2 x}\, \sqrt {3+5 x}}{256000000} \]
command
integrate((1-2*x)**(5/2)*(2+3*x)**3*(3+5*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 \[ \text {Timed out} \]_____________________________________________________