\[ \int \frac {(3+5 x)^{3/2}}{\sqrt {1-2 x} (2+3 x)^{5/2}} \, dx \]
Optimal antiderivative \[ \frac {272 \EllipticE \left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}, \frac {\sqrt {1155}}{33}\right ) \sqrt {33}}{1323}-\frac {202 \EllipticF \left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}, \frac {\sqrt {1155}}{33}\right ) \sqrt {33}}{1323}+\frac {2 \sqrt {1-2 x}\, \sqrt {3+5 x}}{63 \left (2+3 x \right )^{\frac {3}{2}}}-\frac {272 \sqrt {1-2 x}\, \sqrt {3+5 x}}{441 \sqrt {2+3 x}} \]
command
integrate((3+5*x)^(3/2)/(2+3*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
\[ -\frac {2 \, {\left (408 \, x + 265\right )} \sqrt {5 \, x + 3} \sqrt {3 \, x + 2} \sqrt {-2 \, x + 1}}{441 \, {\left (9 \, x^{2} + 12 \, x + 4\right )}} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (-\frac {{\left (5 \, x + 3\right )}^{\frac {3}{2}} \sqrt {3 \, x + 2} \sqrt {-2 \, x + 1}}{54 \, x^{4} + 81 \, x^{3} + 18 \, x^{2} - 20 \, x - 8}, x\right ) \]