\[ \int \frac {(1-2 x)^{3/2}}{\sqrt {2+3 x} \sqrt {3+5 x}} \, dx \]
Optimal antiderivative \[ \frac {272 \EllipticE \left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}, \frac {\sqrt {1155}}{33}\right ) \sqrt {33}}{675}-\frac {202 \EllipticF \left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}, \frac {\sqrt {1155}}{33}\right ) \sqrt {33}}{675}-\frac {4 \sqrt {1-2 x}\, \sqrt {2+3 x}\, \sqrt {3+5 x}}{45} \]
command
integrate((1-2*x)^(3/2)/(2+3*x)^(1/2)/(3+5*x)^(1/2),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ -\frac {4}{45} \, \sqrt {5 \, x + 3} \sqrt {3 \, x + 2} \sqrt {-2 \, x + 1} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (\frac {\sqrt {5 \, x + 3} \sqrt {3 \, x + 2} {\left (-2 \, x + 1\right )}^{\frac {3}{2}}}{15 \, x^{2} + 19 \, x + 6}, x\right ) \]