\[ \int \frac {1}{(1-2 x)^{5/2} (2+3 x)^{3/2} (3+5 x)^{5/2}} \, dx \]
Optimal antiderivative \[ -\frac {19885156 \EllipticE \left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}, \frac {\sqrt {1155}}{33}\right ) \sqrt {33}}{15065589}-\frac {609304 \EllipticF \left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}, \frac {\sqrt {1155}}{33}\right ) \sqrt {33}}{15065589}+\frac {4}{231 \left (1-2 x \right )^{\frac {3}{2}} \left (3+5 x \right )^{\frac {3}{2}} \sqrt {2+3 x}}+\frac {456}{5929 \left (3+5 x \right )^{\frac {3}{2}} \sqrt {1-2 x}\, \sqrt {2+3 x}}+\frac {5034 \sqrt {1-2 x}}{41503 \left (3+5 x \right )^{\frac {3}{2}} \sqrt {2+3 x}}-\frac {1523260 \sqrt {1-2 x}\, \sqrt {2+3 x}}{1369599 \left (3+5 x \right )^{\frac {3}{2}}}+\frac {99425780 \sqrt {1-2 x}\, \sqrt {2+3 x}}{15065589 \sqrt {3+5 x}} \]
command
integrate(1/(1-2*x)^(5/2)/(2+3*x)^(3/2)/(3+5*x)^(5/2),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ \frac {2 \, {\left (2982773400 \, x^{4} + 694871080 \, x^{3} - 1802210526 \, x^{2} - 211488180 \, x + 283144937\right )} \sqrt {5 \, x + 3} \sqrt {3 \, x + 2} \sqrt {-2 \, x + 1}}{15065589 \, {\left (300 \, x^{5} + 260 \, x^{4} - 137 \, x^{3} - 136 \, x^{2} + 15 \, x + 18\right )}} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (-\frac {\sqrt {5 \, x + 3} \sqrt {3 \, x + 2} \sqrt {-2 \, x + 1}}{9000 \, x^{8} + 14700 \, x^{7} - 230 \, x^{6} - 10851 \, x^{5} - 3279 \, x^{4} + 2659 \, x^{3} + 1125 \, x^{2} - 216 \, x - 108}, x\right ) \]