\[ \int \frac {1}{\sqrt {1-2 x} (2+3 x)^{3/2} (3+5 x)^{5/2}} \, dx \]
Optimal antiderivative \[ -\frac {17804 \EllipticE \left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}, \frac {\sqrt {1155}}{33}\right ) \sqrt {33}}{2541}-\frac {536 \EllipticF \left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}, \frac {\sqrt {1155}}{33}\right ) \sqrt {33}}{2541}+\frac {6 \sqrt {1-2 x}}{7 \left (3+5 x \right )^{\frac {3}{2}} \sqrt {2+3 x}}-\frac {1340 \sqrt {1-2 x}\, \sqrt {2+3 x}}{231 \left (3+5 x \right )^{\frac {3}{2}}}+\frac {89020 \sqrt {1-2 x}\, \sqrt {2+3 x}}{2541 \sqrt {3+5 x}} \]
command
integrate(1/(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
\[ \frac {2 \, {\left (667650 \, x^{2} + 823580 \, x + 253409\right )} \sqrt {5 \, x + 3} \sqrt {3 \, x + 2} \sqrt {-2 \, x + 1}}{2541 \, {\left (75 \, x^{3} + 140 \, x^{2} + 87 \, x + 18\right )}} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (-\frac {\sqrt {5 \, x + 3} \sqrt {3 \, x + 2} \sqrt {-2 \, x + 1}}{2250 \, x^{6} + 5925 \, x^{5} + 5305 \, x^{4} + 1111 \, x^{3} - 1035 \, x^{2} - 648 \, x - 108}, x\right ) \]