\[ \int \frac {1}{\sqrt {1-2 x} (2+3 x)^{7/2} (3+5 x)^{3/2}} \, dx \]
Optimal antiderivative \[ \frac {1344984 \EllipticE \left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}, \frac {\sqrt {1155}}{33}\right ) \sqrt {33}}{18865}+\frac {40456 \EllipticF \left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}, \frac {\sqrt {1155}}{33}\right ) \sqrt {33}}{18865}+\frac {6 \sqrt {1-2 x}}{35 \left (2+3 x \right )^{\frac {5}{2}} \sqrt {3+5 x}}+\frac {436 \sqrt {1-2 x}}{245 \left (2+3 x \right )^{\frac {3}{2}} \sqrt {3+5 x}}+\frac {60684 \sqrt {1-2 x}}{1715 \sqrt {2+3 x}\, \sqrt {3+5 x}}-\frac {1344984 \sqrt {1-2 x}\, \sqrt {2+3 x}}{3773 \sqrt {3+5 x}} \]
command
integrate(1/(2+3*x)^(7/2)/(3+5*x)^(3/2)/(1-2*x)^(1/2),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ -\frac {2 \, {\left (90786420 \, x^{3} + 178568982 \, x^{2} + 116993058 \, x + 25529443\right )} \sqrt {5 \, x + 3} \sqrt {3 \, x + 2} \sqrt {-2 \, x + 1}}{18865 \, {\left (135 \, x^{4} + 351 \, x^{3} + 342 \, x^{2} + 148 \, x + 24\right )}} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (-\frac {\sqrt {5 \, x + 3} \sqrt {3 \, x + 2} \sqrt {-2 \, x + 1}}{4050 \, x^{7} + 13635 \, x^{6} + 17388 \, x^{5} + 9039 \, x^{4} - 376 \, x^{3} - 2536 \, x^{2} - 1056 \, x - 144}, x\right ) \]