\[ \int \frac {(1-2 x)^{5/2}}{(2+3 x)^{11/2} (3+5 x)^{3/2}} \, dx \]
Optimal antiderivative \[ \frac {683150096 \EllipticE \left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}, \frac {\sqrt {1155}}{33}\right ) \sqrt {33}}{27783}+\frac {20549264 \EllipticF \left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}, \frac {\sqrt {1155}}{33}\right ) \sqrt {33}}{27783}+\frac {14 \left (1-2 x \right )^{\frac {3}{2}}}{27 \left (2+3 x \right )^{\frac {9}{2}} \sqrt {3+5 x}}+\frac {652 \sqrt {1-2 x}}{81 \left (2+3 x \right )^{\frac {7}{2}} \sqrt {3+5 x}}+\frac {11660 \sqrt {1-2 x}}{189 \left (2+3 x \right )^{\frac {5}{2}} \sqrt {3+5 x}}+\frac {813208 \sqrt {1-2 x}}{1323 \left (2+3 x \right )^{\frac {3}{2}} \sqrt {3+5 x}}+\frac {113020952 \sqrt {1-2 x}}{9261 \sqrt {2+3 x}\, \sqrt {3+5 x}}-\frac {3415750480 \sqrt {1-2 x}\, \sqrt {2+3 x}}{27783 \sqrt {3+5 x}} \]
command
integrate((1-2*x)^(5/2)/(2+3*x)^(11/2)/(3+5*x)^(3/2),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ -\frac {2 \, {\left (138337894440 \, x^{5} + 456548966244 \, x^{4} + 602551975428 \, x^{3} + 397527527442 \, x^{2} + 131099014240 \, x + 17289178827\right )} \sqrt {5 \, x + 3} \sqrt {3 \, x + 2} \sqrt {-2 \, x + 1}}{9261 \, {\left (1215 \, x^{6} + 4779 \, x^{5} + 7830 \, x^{4} + 6840 \, x^{3} + 3360 \, x^{2} + 880 \, x + 96\right )}} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (\frac {{\left (4 \, x^{2} - 4 \, x + 1\right )} \sqrt {5 \, x + 3} \sqrt {3 \, x + 2} \sqrt {-2 \, x + 1}}{18225 \, x^{8} + 94770 \, x^{7} + 215541 \, x^{6} + 280044 \, x^{5} + 227340 \, x^{4} + 118080 \, x^{3} + 38320 \, x^{2} + 7104 \, x + 576}, x\right ) \]