\[ \int \frac {1}{(1-2 x)^{5/2} \sqrt {2+3 x} \sqrt {3+5 x}} \, dx \]
Optimal antiderivative \[ \frac {272 \EllipticE \left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}, \frac {\sqrt {1155}}{33}\right ) \sqrt {33}}{17787}-\frac {202 \EllipticF \left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}, \frac {\sqrt {1155}}{33}\right ) \sqrt {33}}{17787}+\frac {4 \sqrt {2+3 x}\, \sqrt {3+5 x}}{231 \left (1-2 x \right )^{\frac {3}{2}}}+\frac {544 \sqrt {2+3 x}\, \sqrt {3+5 x}}{17787 \sqrt {1-2 x}} \]
command
integrate(1/(1-2*x)^(5/2)/(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
\[ -\frac {4 \, {\left (272 \, x - 213\right )} \sqrt {5 \, x + 3} \sqrt {3 \, x + 2} \sqrt {-2 \, x + 1}}{17787 \, {\left (4 \, x^{2} - 4 \, x + 1\right )}} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (-\frac {\sqrt {5 \, x + 3} \sqrt {3 \, x + 2} \sqrt {-2 \, x + 1}}{120 \, x^{5} - 28 \, x^{4} - 90 \, x^{3} + 27 \, x^{2} + 17 \, x - 6}, x\right ) \]