\[ \int \frac {(1-2 x)^{5/2}}{(2+3 x)^{3/2} (3+5 x)^{3/2}} \, dx \]
Optimal antiderivative \[ \frac {4636 \EllipticE \left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}, \frac {\sqrt {1155}}{33}\right ) \sqrt {33}}{225}+\frac {124 \EllipticF \left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}, \frac {\sqrt {1155}}{33}\right ) \sqrt {33}}{225}+\frac {14 \left (1-2 x \right )^{\frac {3}{2}}}{3 \sqrt {2+3 x}\, \sqrt {3+5 x}}-\frac {1496 \sqrt {1-2 x}\, \sqrt {2+3 x}}{15 \sqrt {3+5 x}} \]
command
integrate((1-2*x)^(5/2)/(2+3*x)^(3/2)/(3+5*x)^(3/2),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ -\frac {2 \, {\left (2314 \, x + 1461\right )} \sqrt {5 \, x + 3} \sqrt {3 \, x + 2} \sqrt {-2 \, x + 1}}{15 \, {\left (15 \, x^{2} + 19 \, x + 6\right )}} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (\frac {{\left (4 \, x^{2} - 4 \, x + 1\right )} \sqrt {5 \, x + 3} \sqrt {3 \, x + 2} \sqrt {-2 \, x + 1}}{225 \, x^{4} + 570 \, x^{3} + 541 \, x^{2} + 228 \, x + 36}, x\right ) \]