\[ \int \frac {(2+3 x)^{5/2}}{\sqrt {1-2 x} (3+5 x)^{3/2}} \, dx \]
Optimal antiderivative \[ -\frac {438 \EllipticE \left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}, \frac {\sqrt {1155}}{33}\right ) \sqrt {33}}{1375}-\frac {17 \EllipticF \left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}, \frac {\sqrt {1155}}{33}\right ) \sqrt {33}}{1375}-\frac {2 \left (2+3 x \right )^{\frac {3}{2}} \sqrt {1-2 x}}{55 \sqrt {3+5 x}}-\frac {27 \sqrt {1-2 x}\, \sqrt {2+3 x}\, \sqrt {3+5 x}}{275} \]
command
integrate((2+3*x)^(5/2)/(3+5*x)^(3/2)/(1-2*x)^(1/2),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ -\frac {{\left (165 \, x + 101\right )} \sqrt {3 \, x + 2} \sqrt {-2 \, x + 1}}{275 \, \sqrt {5 \, x + 3}} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (-\frac {{\left (9 \, x^{2} + 12 \, x + 4\right )} \sqrt {5 \, x + 3} \sqrt {3 \, x + 2} \sqrt {-2 \, x + 1}}{50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9}, x\right ) \]