\[ \int \frac {(2+3 x)^{5/2}}{(1-2 x)^{3/2} \sqrt {3+5 x}} \, dx \]
Optimal antiderivative \[ \frac {1597 \EllipticE \left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}, \frac {\sqrt {1155}}{33}\right ) \sqrt {33}}{550}+\frac {24 \EllipticF \left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}, \frac {\sqrt {1155}}{33}\right ) \sqrt {33}}{275}+\frac {7 \left (2+3 x \right )^{\frac {3}{2}} \sqrt {3+5 x}}{11 \sqrt {1-2 x}}+\frac {69 \sqrt {1-2 x}\, \sqrt {2+3 x}\, \sqrt {3+5 x}}{55} \]
command
integrate((2+3*x)^(5/2)/(1-2*x)^(3/2)/(3+5*x)^(1/2),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ \frac {{\left (33 \, x - 139\right )} \sqrt {5 \, x + 3} \sqrt {3 \, x + 2} \sqrt {-2 \, x + 1}}{55 \, {\left (2 \, x - 1\right )}} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (\frac {{\left (9 \, x^{2} + 12 \, x + 4\right )} \sqrt {5 \, x + 3} \sqrt {3 \, x + 2} \sqrt {-2 \, x + 1}}{20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3}, x\right ) \]