\[ \int \frac {1}{(1-2 x)^{5/2} (2+3 x)^{5/2} (3+5 x)^{5/2}} \, dx \]
Optimal antiderivative \[ \frac {4}{231 \left (1-2 x \right )^{\frac {3}{2}} \left (2+3 x \right )^{\frac {3}{2}} \left (3+5 x \right )^{\frac {3}{2}}}-\frac {1446357824 \EllipticE \left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}, \frac {\sqrt {1155}}{33}\right ) \sqrt {33}}{105459123}-\frac {43537016 \EllipticF \left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}, \frac {\sqrt {1155}}{33}\right ) \sqrt {33}}{105459123}+\frac {544}{5929 \left (2+3 x \right )^{\frac {3}{2}} \left (3+5 x \right )^{\frac {3}{2}} \sqrt {1-2 x}}+\frac {414 \sqrt {1-2 x}}{41503 \left (2+3 x \right )^{\frac {3}{2}} \left (3+5 x \right )^{\frac {3}{2}}}+\frac {488436 \sqrt {1-2 x}}{290521 \left (3+5 x \right )^{\frac {3}{2}} \sqrt {2+3 x}}-\frac {108842540 \sqrt {1-2 x}\, \sqrt {2+3 x}}{9587193 \left (3+5 x \right )^{\frac {3}{2}}}+\frac {7231789120 \sqrt {1-2 x}\, \sqrt {2+3 x}}{105459123 \sqrt {3+5 x}} \]
command
integrate(1/(1-2*x)^(5/2)/(2+3*x)^(5/2)/(3+5*x)^(5/2),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ \frac {2 \, {\left (650861020800 \, x^{5} + 585919463160 \, x^{4} - 291775464272 \, x^{3} - 308398535118 \, x^{2} + 30866656614 \, x + 41179778225\right )} \sqrt {5 \, x + 3} \sqrt {3 \, x + 2} \sqrt {-2 \, x + 1}}{105459123 \, {\left (900 \, x^{6} + 1380 \, x^{5} + 109 \, x^{4} - 682 \, x^{3} - 227 \, x^{2} + 84 \, x + 36\right )}} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (-\frac {\sqrt {5 \, x + 3} \sqrt {3 \, x + 2} \sqrt {-2 \, x + 1}}{27000 \, x^{9} + 62100 \, x^{8} + 28710 \, x^{7} - 33013 \, x^{6} - 31539 \, x^{5} + 1419 \, x^{4} + 8693 \, x^{3} + 1602 \, x^{2} - 756 \, x - 216}, x\right ) \]