\[ \int \frac {1}{(1-2 x)^{3/2} (2+3 x)^{5/2} (3+5 x)^{3/2}} \, dx \]
Optimal antiderivative \[ \frac {220076 \EllipticE \left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}, \frac {\sqrt {1155}}{33}\right ) \sqrt {33}}{41503}+\frac {6584 \EllipticF \left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}, \frac {\sqrt {1155}}{33}\right ) \sqrt {33}}{41503}+\frac {4}{77 \left (2+3 x \right )^{\frac {3}{2}} \sqrt {1-2 x}\, \sqrt {3+5 x}}+\frac {54 \sqrt {1-2 x}}{539 \left (2+3 x \right )^{\frac {3}{2}} \sqrt {3+5 x}}+\frac {9876 \sqrt {1-2 x}}{3773 \sqrt {2+3 x}\, \sqrt {3+5 x}}-\frac {1100380 \sqrt {1-2 x}\, \sqrt {2+3 x}}{41503 \sqrt {3+5 x}} \]
command
integrate(1/(1-2*x)^(3/2)/(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
\[ -\frac {2 \, {\left (9903420 \, x^{3} + 7926942 \, x^{2} - 2259236 \, x - 2088967\right )} \sqrt {5 \, x + 3} \sqrt {3 \, x + 2} \sqrt {-2 \, x + 1}}{41503 \, {\left (90 \, x^{4} + 129 \, x^{3} + 25 \, x^{2} - 32 \, x - 12\right )}} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (\frac {\sqrt {5 \, x + 3} \sqrt {3 \, x + 2} \sqrt {-2 \, x + 1}}{2700 \, x^{7} + 5940 \, x^{6} + 3087 \, x^{5} - 1828 \, x^{4} - 2045 \, x^{3} - 202 \, x^{2} + 276 \, x + 72}, x\right ) \]