\[ \int \frac {(3+5 x)^{3/2}}{(1-2 x)^{3/2} \sqrt {2+3 x}} \, dx \]
Optimal antiderivative \[ \frac {34 \EllipticE \left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}, \frac {\sqrt {1155}}{33}\right ) \sqrt {33}}{21}+\frac {\EllipticF \left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}, \frac {\sqrt {1155}}{33}\right ) \sqrt {33}}{21}+\frac {11 \sqrt {2+3 x}\, \sqrt {3+5 x}}{7 \sqrt {1-2 x}} \]
command
integrate((3+5*x)^(3/2)/(1-2*x)^(3/2)/(2+3*x)^(1/2),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ -\frac {11 \, \sqrt {5 \, x + 3} \sqrt {3 \, x + 2} \sqrt {-2 \, x + 1}}{7 \, {\left (2 \, x - 1\right )}} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (\frac {{\left (5 \, x + 3\right )}^{\frac {3}{2}} \sqrt {3 \, x + 2} \sqrt {-2 \, x + 1}}{12 \, x^{3} - 4 \, x^{2} - 5 \, x + 2}, x\right ) \]