\[ \int \frac {(1-2 x)^{5/2}}{\sqrt {2+3 x} (3+5 x)^{5/2}} \, dx \]
Optimal antiderivative \[ -\frac {68 \EllipticF \left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}, \frac {\sqrt {1155}}{33}\right ) \sqrt {33}}{375}-\frac {584 \EllipticE \left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}, \frac {\sqrt {1155}}{33}\right ) \sqrt {33}}{125}-\frac {22 \left (1-2 x \right )^{\frac {3}{2}} \sqrt {2+3 x}}{15 \left (3+5 x \right )^{\frac {3}{2}}}+\frac {572 \sqrt {1-2 x}\, \sqrt {2+3 x}}{25 \sqrt {3+5 x}} \]
command
integrate((1-2*x)^(5/2)/(3+5*x)^(5/2)/(2+3*x)^(1/2),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ \frac {22 \, {\left (400 \, x + 229\right )} \sqrt {5 \, x + 3} \sqrt {3 \, x + 2} \sqrt {-2 \, x + 1}}{75 \, {\left (25 \, x^{2} + 30 \, x + 9\right )}} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (\frac {{\left (4 \, x^{2} - 4 \, x + 1\right )} \sqrt {5 \, x + 3} \sqrt {3 \, x + 2} \sqrt {-2 \, x + 1}}{375 \, x^{4} + 925 \, x^{3} + 855 \, x^{2} + 351 \, x + 54}, x\right ) \]