\[ \int \sqrt {1-2 x} (2+3 x)^{3/2} (3+5 x)^{5/2} \, dx \]
Optimal antiderivative \[ -\frac {30926081 \EllipticE \left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}, \frac {\sqrt {1155}}{33}\right ) \sqrt {33}}{3118500}-\frac {465127 \EllipticF \left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}, \frac {\sqrt {1155}}{33}\right ) \sqrt {33}}{1559250}+\frac {2 \left (2+3 x \right )^{\frac {3}{2}} \left (3+5 x \right )^{\frac {7}{2}} \sqrt {1-2 x}}{55}-\frac {7031 \left (3+5 x \right )^{\frac {3}{2}} \sqrt {1-2 x}\, \sqrt {2+3 x}}{11550}-\frac {177 \left (3+5 x \right )^{\frac {5}{2}} \sqrt {1-2 x}\, \sqrt {2+3 x}}{1925}-\frac {3 \left (3+5 x \right )^{\frac {7}{2}} \sqrt {1-2 x}\, \sqrt {2+3 x}}{275}-\frac {465127 \sqrt {1-2 x}\, \sqrt {2+3 x}\, \sqrt {3+5 x}}{103950} \]
command
integrate((2+3*x)^(3/2)*(3+5*x)^(5/2)*(1-2*x)^(1/2),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ \frac {1}{103950} \, {\left (1417500 \, x^{4} + 3354750 \, x^{3} + 2737800 \, x^{2} + 570555 \, x - 567484\right )} \sqrt {5 \, x + 3} \sqrt {3 \, x + 2} \sqrt {-2 \, x + 1} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left ({\left (75 \, x^{3} + 140 \, x^{2} + 87 \, x + 18\right )} \sqrt {5 \, x + 3} \sqrt {3 \, x + 2} \sqrt {-2 \, x + 1}, x\right ) \]