\[ \int \frac {(1-2 x)^{5/2}}{(2+3 x)^{9/2} \sqrt {3+5 x}} \, dx \]
Optimal antiderivative \[ -\frac {703480 \EllipticE \left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}, \frac {\sqrt {1155}}{33}\right ) \sqrt {33}}{3969}-\frac {21160 \EllipticF \left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}, \frac {\sqrt {1155}}{33}\right ) \sqrt {33}}{3969}+\frac {2 \left (1-2 x \right )^{\frac {3}{2}} \sqrt {3+5 x}}{3 \left (2+3 x \right )^{\frac {7}{2}}}+\frac {76 \sqrt {1-2 x}\, \sqrt {3+5 x}}{9 \left (2+3 x \right )^{\frac {5}{2}}}+\frac {10124 \sqrt {1-2 x}\, \sqrt {3+5 x}}{189 \left (2+3 x \right )^{\frac {3}{2}}}+\frac {703480 \sqrt {1-2 x}\, \sqrt {3+5 x}}{1323 \sqrt {2+3 x}} \]
command
integrate((1-2*x)^(5/2)/(2+3*x)^(9/2)/(3+5*x)^(1/2),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ \frac {2 \, {\left (9496980 \, x^{3} + 19312866 \, x^{2} + 13103724 \, x + 2967269\right )} \sqrt {5 \, x + 3} \sqrt {3 \, x + 2} \sqrt {-2 \, x + 1}}{1323 \, {\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )}} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (\frac {{\left (4 \, x^{2} - 4 \, x + 1\right )} \sqrt {5 \, x + 3} \sqrt {3 \, x + 2} \sqrt {-2 \, x + 1}}{1215 \, x^{6} + 4779 \, x^{5} + 7830 \, x^{4} + 6840 \, x^{3} + 3360 \, x^{2} + 880 \, x + 96}, x\right ) \]