\[ \int \frac {(2+3 x)^{3/2} \sqrt {3+5 x}}{(1-2 x)^{3/2}} \, dx \]
Optimal antiderivative \[ \frac {139 \EllipticE \left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}, \frac {\sqrt {1155}}{33}\right ) \sqrt {33}}{30}+\frac {23 \EllipticF \left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}, \frac {\sqrt {1155}}{33}\right ) \sqrt {33}}{165}+\frac {\left (2+3 x \right )^{\frac {3}{2}} \sqrt {3+5 x}}{\sqrt {1-2 x}}+2 \sqrt {1-2 x}\, \sqrt {2+3 x}\, \sqrt {3+5 x} \]
command
integrate((2+3*x)^(3/2)*(3+5*x)^(1/2)/(1-2*x)^(3/2),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ \frac {\sqrt {5 \, x + 3} \sqrt {3 \, x + 2} {\left (x - 4\right )} \sqrt {-2 \, x + 1}}{2 \, x - 1} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (\frac {\sqrt {5 \, x + 3} {\left (3 \, x + 2\right )}^{\frac {3}{2}} \sqrt {-2 \, x + 1}}{4 \, x^{2} - 4 \, x + 1}, x\right ) \]