\[ \int \frac {(2+3 x)^{5/2} \sqrt {3+5 x}}{\sqrt {1-2 x}} \, dx \]
Optimal antiderivative \[ -\frac {5057 \EllipticF \left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}, \frac {\sqrt {1155}}{33}\right ) \sqrt {33}}{26250}-\frac {56041 \EllipticE \left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}, \frac {\sqrt {1155}}{33}\right ) \sqrt {33}}{8750}-\frac {104 \left (2+3 x \right )^{\frac {3}{2}} \sqrt {1-2 x}\, \sqrt {3+5 x}}{175}-\frac {\left (2+3 x \right )^{\frac {5}{2}} \sqrt {1-2 x}\, \sqrt {3+5 x}}{7}-\frac {4839 \sqrt {1-2 x}\, \sqrt {2+3 x}\, \sqrt {3+5 x}}{1750} \]
command
integrate((2+3*x)^(5/2)*(3+5*x)^(1/2)/(1-2*x)^(1/2),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ -\frac {1}{1750} \, {\left (2250 \, x^{2} + 6120 \, x + 7919\right )} \sqrt {5 \, x + 3} \sqrt {3 \, x + 2} \sqrt {-2 \, x + 1} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (-\frac {{\left (9 \, x^{2} + 12 \, x + 4\right )} \sqrt {5 \, x + 3} \sqrt {3 \, x + 2} \sqrt {-2 \, x + 1}}{2 \, x - 1}, x\right ) \]