\[ \int \frac {1}{(1-2 x)^{5/2} (2+3 x)^{5/2} (3+5 x)^{3/2}} \, dx \]
Optimal antiderivative \[ \frac {22738708 \EllipticE \left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}, \frac {\sqrt {1155}}{33}\right ) \sqrt {33}}{9587193}+\frac {673072 \EllipticF \left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}, \frac {\sqrt {1155}}{33}\right ) \sqrt {33}}{9587193}+\frac {4}{231 \left (1-2 x \right )^{\frac {3}{2}} \left (2+3 x \right )^{\frac {3}{2}} \sqrt {3+5 x}}+\frac {1352}{17787 \left (2+3 x \right )^{\frac {3}{2}} \sqrt {1-2 x}\, \sqrt {3+5 x}}+\frac {694 \sqrt {1-2 x}}{41503 \left (2+3 x \right )^{\frac {3}{2}} \sqrt {3+5 x}}+\frac {336536 \sqrt {1-2 x}}{290521 \sqrt {2+3 x}\, \sqrt {3+5 x}}-\frac {113693540 \sqrt {1-2 x}\, \sqrt {2+3 x}}{9587193 \sqrt {3+5 x}} \]
command
integrate(1/(1-2*x)^(5/2)/(2+3*x)^(5/2)/(3+5*x)^(3/2),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ -\frac {2 \, {\left (2046483720 \, x^{4} + 615527112 \, x^{3} - 1285584962 \, x^{2} - 198573504 \, x + 215753865\right )} \sqrt {5 \, x + 3} \sqrt {3 \, x + 2} \sqrt {-2 \, x + 1}}{9587193 \, {\left (180 \, x^{5} + 168 \, x^{4} - 79 \, x^{3} - 89 \, x^{2} + 8 \, x + 12\right )}} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (-\frac {\sqrt {5 \, x + 3} \sqrt {3 \, x + 2} \sqrt {-2 \, x + 1}}{5400 \, x^{8} + 9180 \, x^{7} + 234 \, x^{6} - 6743 \, x^{5} - 2262 \, x^{4} + 1641 \, x^{3} + 754 \, x^{2} - 132 \, x - 72}, x\right ) \]