\[ \int \frac {1}{\sqrt {1-2 x} (2+3 x)^{3/2} (3+5 x)^{3/2}} \, dx \]
Optimal antiderivative \[ \frac {136 \EllipticE \left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}, \frac {\sqrt {1155}}{33}\right ) \sqrt {33}}{77}+\frac {4 \EllipticF \left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}, \frac {\sqrt {1155}}{33}\right ) \sqrt {33}}{77}+\frac {6 \sqrt {1-2 x}}{7 \sqrt {2+3 x}\, \sqrt {3+5 x}}-\frac {680 \sqrt {1-2 x}\, \sqrt {2+3 x}}{77 \sqrt {3+5 x}} \]
command
integrate(1/(2+3*x)^(3/2)/(3+5*x)^(3/2)/(1-2*x)^(1/2),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ -\frac {2 \, {\left (1020 \, x + 647\right )} \sqrt {5 \, x + 3} \sqrt {3 \, x + 2} \sqrt {-2 \, x + 1}}{77 \, {\left (15 \, x^{2} + 19 \, x + 6\right )}} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (-\frac {\sqrt {5 \, x + 3} \sqrt {3 \, x + 2} \sqrt {-2 \, x + 1}}{450 \, x^{5} + 915 \, x^{4} + 512 \, x^{3} - 85 \, x^{2} - 156 \, x - 36}, x\right ) \]