\[ \int \frac {\sqrt {3+5 x}}{(1-2 x)^{3/2} (2+3 x)^{3/2}} \, dx \]
Optimal antiderivative \[ -\frac {62 \EllipticF \left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}, \frac {\sqrt {1155}}{33}\right ) \sqrt {33}}{1617}+\frac {4 \EllipticE \left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}, \frac {\sqrt {1155}}{33}\right ) \sqrt {33}}{49}+\frac {2 \sqrt {3+5 x}}{7 \sqrt {1-2 x}\, \sqrt {2+3 x}}-\frac {12 \sqrt {1-2 x}\, \sqrt {3+5 x}}{49 \sqrt {2+3 x}} \]
command
integrate((3+5*x)^(1/2)/(1-2*x)^(3/2)/(2+3*x)^(3/2),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ -\frac {2 \, {\left (12 \, x + 1\right )} \sqrt {5 \, x + 3} \sqrt {3 \, x + 2} \sqrt {-2 \, x + 1}}{49 \, {\left (6 \, x^{2} + x - 2\right )}} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (\frac {\sqrt {5 \, x + 3} \sqrt {3 \, x + 2} \sqrt {-2 \, x + 1}}{36 \, x^{4} + 12 \, x^{3} - 23 \, x^{2} - 4 \, x + 4}, x\right ) \]