\[ \int \frac {1}{(1-2 x)^{3/2} (2+3 x)^{3/2} (3+5 x)^{3/2}} \, dx \]
Optimal antiderivative \[ \frac {4636 \EllipticE \left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}, \frac {\sqrt {1155}}{33}\right ) \sqrt {33}}{5929}+\frac {124 \EllipticF \left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}, \frac {\sqrt {1155}}{33}\right ) \sqrt {33}}{5929}+\frac {4}{77 \sqrt {1-2 x}\, \sqrt {2+3 x}\, \sqrt {3+5 x}}+\frac {186 \sqrt {1-2 x}}{539 \sqrt {2+3 x}\, \sqrt {3+5 x}}-\frac {23180 \sqrt {1-2 x}\, \sqrt {2+3 x}}{5929 \sqrt {3+5 x}} \]
command
integrate(1/(1-2*x)^(3/2)/(2+3*x)^(3/2)/(3+5*x)^(3/2),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ -\frac {2 \, {\left (69540 \, x^{2} + 9544 \, x - 22003\right )} \sqrt {5 \, x + 3} \sqrt {3 \, x + 2} \sqrt {-2 \, x + 1}}{5929 \, {\left (30 \, x^{3} + 23 \, x^{2} - 7 \, x - 6\right )}} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (\frac {\sqrt {5 \, x + 3} \sqrt {3 \, x + 2} \sqrt {-2 \, x + 1}}{900 \, x^{6} + 1380 \, x^{5} + 109 \, x^{4} - 682 \, x^{3} - 227 \, x^{2} + 84 \, x + 36}, x\right ) \]