\[ \int \frac {(1-2 x)^{3/2}}{(2+3 x)^{9/2} (3+5 x)^{3/2}} \, dx \]
Optimal antiderivative \[ \frac {10312712 \EllipticE \left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}, \frac {\sqrt {1155}}{33}\right ) \sqrt {33}}{5145}+\frac {310208 \EllipticF \left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}, \frac {\sqrt {1155}}{33}\right ) \sqrt {33}}{5145}+\frac {2 \sqrt {1-2 x}}{3 \left (2+3 x \right )^{\frac {7}{2}} \sqrt {3+5 x}}+\frac {176 \sqrt {1-2 x}}{35 \left (2+3 x \right )^{\frac {5}{2}} \sqrt {3+5 x}}+\frac {12276 \sqrt {1-2 x}}{245 \left (2+3 x \right )^{\frac {3}{2}} \sqrt {3+5 x}}+\frac {1706144 \sqrt {1-2 x}}{1715 \sqrt {2+3 x}\, \sqrt {3+5 x}}-\frac {10312712 \sqrt {1-2 x}\, \sqrt {2+3 x}}{1029 \sqrt {3+5 x}} \]
command
integrate((1-2*x)^(3/2)/(2+3*x)^(9/2)/(3+5*x)^(3/2),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ -\frac {2 \, {\left (696108060 \, x^{4} + 1833255216 \, x^{3} + 1809835578 \, x^{2} + 793777840 \, x + 130497191\right )} \sqrt {5 \, x + 3} \sqrt {3 \, x + 2} \sqrt {-2 \, x + 1}}{1715 \, {\left (405 \, x^{5} + 1323 \, x^{4} + 1728 \, x^{3} + 1128 \, x^{2} + 368 \, x + 48\right )}} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (\frac {\sqrt {5 \, x + 3} \sqrt {3 \, x + 2} {\left (-2 \, x + 1\right )}^{\frac {3}{2}}}{6075 \, x^{7} + 27540 \, x^{6} + 53487 \, x^{5} + 57690 \, x^{4} + 37320 \, x^{3} + 14480 \, x^{2} + 3120 \, x + 288}, x\right ) \]