\[ \int \frac {(1-2 x)^{3/2}}{(2+3 x)^{7/2} (3+5 x)^{5/2}} \, dx \]
Optimal antiderivative \[ -\frac {33232 \EllipticF \left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}, \frac {\sqrt {1155}}{33}\right ) \sqrt {33}}{385}-\frac {301304 \EllipticE \left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}, \frac {\sqrt {1155}}{33}\right ) \sqrt {33}}{105}+\frac {14 \sqrt {1-2 x}}{15 \left (2+3 x \right )^{\frac {5}{2}} \left (3+5 x \right )^{\frac {3}{2}}}+\frac {536 \sqrt {1-2 x}}{45 \left (2+3 x \right )^{\frac {3}{2}} \left (3+5 x \right )^{\frac {3}{2}}}+\frac {111884 \sqrt {1-2 x}}{315 \left (3+5 x \right )^{\frac {3}{2}} \sqrt {2+3 x}}-\frac {16616 \sqrt {1-2 x}\, \sqrt {2+3 x}}{7 \left (3+5 x \right )^{\frac {3}{2}}}+\frac {301304 \sqrt {1-2 x}\, \sqrt {2+3 x}}{21 \sqrt {3+5 x}} \]
command
integrate((1-2*x)^(3/2)/(2+3*x)^(7/2)/(3+5*x)^(5/2),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ \frac {2 \, {\left (101690100 \, x^{4} + 261029520 \, x^{3} + 251053266 \, x^{2} + 107221804 \, x + 17157169\right )} \sqrt {5 \, x + 3} \sqrt {3 \, x + 2} \sqrt {-2 \, x + 1}}{105 \, {\left (675 \, x^{5} + 2160 \, x^{4} + 2763 \, x^{3} + 1766 \, x^{2} + 564 \, x + 72\right )}} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (\frac {\sqrt {5 \, x + 3} \sqrt {3 \, x + 2} {\left (-2 \, x + 1\right )}^{\frac {3}{2}}}{10125 \, x^{7} + 45225 \, x^{6} + 86535 \, x^{5} + 91947 \, x^{4} + 58592 \, x^{3} + 22392 \, x^{2} + 4752 \, x + 432}, x\right ) \]