\[ \int \frac {(1-2 x)^{5/2}}{(2+3 x)^{11/2} \sqrt {3+5 x}} \, dx \]
Optimal antiderivative \[ -\frac {66055016 \EllipticE \left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}, \frac {\sqrt {1155}}{33}\right ) \sqrt {33}}{83349}-\frac {1986944 \EllipticF \left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}, \frac {\sqrt {1155}}{33}\right ) \sqrt {33}}{83349}+\frac {14 \left (1-2 x \right )^{\frac {3}{2}} \sqrt {3+5 x}}{27 \left (2+3 x \right )^{\frac {9}{2}}}+\frac {512 \sqrt {1-2 x}\, \sqrt {3+5 x}}{81 \left (2+3 x \right )^{\frac {7}{2}}}+\frac {20420 \sqrt {1-2 x}\, \sqrt {3+5 x}}{567 \left (2+3 x \right )^{\frac {5}{2}}}+\frac {950584 \sqrt {1-2 x}\, \sqrt {3+5 x}}{3969 \left (2+3 x \right )^{\frac {3}{2}}}+\frac {66055016 \sqrt {1-2 x}\, \sqrt {3+5 x}}{27783 \sqrt {2+3 x}} \]
command
integrate((1-2*x)^(5/2)/(2+3*x)^(11/2)/(3+5*x)^(1/2),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ \frac {2 \, {\left (2675228148 \, x^{4} + 7223771916 \, x^{3} + 7318104714 \, x^{2} + 3296666850 \, x + 557240459\right )} \sqrt {5 \, x + 3} \sqrt {3 \, x + 2} \sqrt {-2 \, x + 1}}{27783 \, {\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )}} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (\frac {{\left (4 \, x^{2} - 4 \, x + 1\right )} \sqrt {5 \, x + 3} \sqrt {3 \, x + 2} \sqrt {-2 \, x + 1}}{3645 \, x^{7} + 16767 \, x^{6} + 33048 \, x^{5} + 36180 \, x^{4} + 23760 \, x^{3} + 9360 \, x^{2} + 2048 \, x + 192}, x\right ) \]