\[ \int \frac {1}{(1-2 x)^{3/2} (2+3 x)^{7/2} (3+5 x)^{5/2}} \, dx \]
Optimal antiderivative \[ -\frac {12071114168 \EllipticE \left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}, \frac {\sqrt {1155}}{33}\right ) \sqrt {33}}{47935965}-\frac {363103712 \EllipticF \left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}, \frac {\sqrt {1155}}{33}\right ) \sqrt {33}}{47935965}+\frac {4}{77 \left (2+3 x \right )^{\frac {5}{2}} \left (3+5 x \right )^{\frac {3}{2}} \sqrt {1-2 x}}+\frac {138 \sqrt {1-2 x}}{2695 \left (2+3 x \right )^{\frac {5}{2}} \left (3+5 x \right )^{\frac {3}{2}}}+\frac {19548 \sqrt {1-2 x}}{18865 \left (2+3 x \right )^{\frac {3}{2}} \left (3+5 x \right )^{\frac {3}{2}}}+\frac {4115652 \sqrt {1-2 x}}{132055 \left (3+5 x \right )^{\frac {3}{2}} \sqrt {2+3 x}}-\frac {181551856 \sqrt {1-2 x}\, \sqrt {2+3 x}}{871563 \left (3+5 x \right )^{\frac {3}{2}}}+\frac {12071114168 \sqrt {1-2 x}\, \sqrt {2+3 x}}{9587193 \sqrt {3+5 x}} \]
command
integrate(1/(1-2*x)^(3/2)/(2+3*x)^(7/2)/(3+5*x)^(5/2),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ \frac {2 \, {\left (8148002063400 \, x^{5} + 16841199826980 \, x^{4} + 9658241620704 \, x^{3} - 1466692421066 \, x^{2} - 2920885694212 \, x - 687365548973\right )} \sqrt {5 \, x + 3} \sqrt {3 \, x + 2} \sqrt {-2 \, x + 1}}{47935965 \, {\left (1350 \, x^{6} + 3645 \, x^{5} + 3366 \, x^{4} + 769 \, x^{3} - 638 \, x^{2} - 420 \, x - 72\right )}} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (\frac {\sqrt {5 \, x + 3} \sqrt {3 \, x + 2} \sqrt {-2 \, x + 1}}{40500 \, x^{9} + 140400 \, x^{8} + 175365 \, x^{7} + 66873 \, x^{6} - 46885 \, x^{5} - 52853 \, x^{4} - 11968 \, x^{3} + 5112 \, x^{2} + 3024 \, x + 432}, x\right ) \]