\[ \int \frac {\sqrt {3+5 x}}{\sqrt {1-2 x} (2+3 x)^{7/2}} \, dx \]
Optimal antiderivative \[ -\frac {68 \EllipticF \left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}, \frac {\sqrt {1155}}{33}\right ) \sqrt {33}}{5145}-\frac {584 \EllipticE \left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}, \frac {\sqrt {1155}}{33}\right ) \sqrt {33}}{1715}-\frac {2 \sqrt {1-2 x}\, \sqrt {3+5 x}}{35 \left (2+3 x \right )^{\frac {5}{2}}}+\frac {18 \sqrt {1-2 x}\, \sqrt {3+5 x}}{245 \left (2+3 x \right )^{\frac {3}{2}}}+\frac {1752 \sqrt {1-2 x}\, \sqrt {3+5 x}}{1715 \sqrt {2+3 x}} \]
command
integrate((3+5*x)^(1/2)/(2+3*x)^(7/2)/(1-2*x)^(1/2),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ \frac {2 \, {\left (7884 \, x^{2} + 10701 \, x + 3581\right )} \sqrt {5 \, x + 3} \sqrt {3 \, x + 2} \sqrt {-2 \, x + 1}}{1715 \, {\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )}} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (-\frac {\sqrt {5 \, x + 3} \sqrt {3 \, x + 2} \sqrt {-2 \, x + 1}}{162 \, x^{5} + 351 \, x^{4} + 216 \, x^{3} - 24 \, x^{2} - 64 \, x - 16}, x\right ) \]