\[ \int \frac {\sqrt {3+5 x}}{(1-2 x)^{5/2} (2+3 x)^{7/2}} \, dx \]
Optimal antiderivative \[ -\frac {2092 \EllipticF \left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}, \frac {\sqrt {1155}}{33}\right ) \sqrt {33}}{252105}-\frac {189368 \EllipticE \left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}, \frac {\sqrt {1155}}{33}\right ) \sqrt {33}}{2773155}+\frac {2 \sqrt {3+5 x}}{21 \left (1-2 x \right )^{\frac {3}{2}} \left (2+3 x \right )^{\frac {5}{2}}}+\frac {458 \sqrt {3+5 x}}{1617 \left (2+3 x \right )^{\frac {5}{2}} \sqrt {1-2 x}}-\frac {2818 \sqrt {1-2 x}\, \sqrt {3+5 x}}{18865 \left (2+3 x \right )^{\frac {5}{2}}}-\frac {5438 \sqrt {1-2 x}\, \sqrt {3+5 x}}{132055 \left (2+3 x \right )^{\frac {3}{2}}}+\frac {189368 \sqrt {1-2 x}\, \sqrt {3+5 x}}{924385 \sqrt {2+3 x}} \]
command
integrate((3+5*x)^(1/2)/(1-2*x)^(5/2)/(2+3*x)^(7/2),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ \frac {2 \, {\left (10225872 \, x^{4} + 2723436 \, x^{3} - 7133292 \, x^{2} - 807691 \, x + 1339677\right )} \sqrt {5 \, x + 3} \sqrt {3 \, x + 2} \sqrt {-2 \, x + 1}}{2773155 \, {\left (108 \, x^{5} + 108 \, x^{4} - 45 \, x^{3} - 58 \, x^{2} + 4 \, x + 8\right )}} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (-\frac {\sqrt {5 \, x + 3} \sqrt {3 \, x + 2} \sqrt {-2 \, x + 1}}{648 \, x^{7} + 756 \, x^{6} - 378 \, x^{5} - 609 \, x^{4} + 56 \, x^{3} + 168 \, x^{2} - 16}, x\right ) \]