\[ \int \frac {(3+5 x)^{5/2}}{\sqrt {1-2 x} \sqrt {2+3 x}} \, dx \]
Optimal antiderivative \[ -\frac {4141 \EllipticE \left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}, \frac {\sqrt {1155}}{33}\right ) \sqrt {33}}{810}-\frac {62 \EllipticF \left (\frac {\sqrt {21}\, \sqrt {1-2 x}}{7}, \frac {\sqrt {1155}}{33}\right ) \sqrt {33}}{405}-\frac {\left (3+5 x \right )^{\frac {3}{2}} \sqrt {1-2 x}\, \sqrt {2+3 x}}{3}-\frac {62 \sqrt {1-2 x}\, \sqrt {2+3 x}\, \sqrt {3+5 x}}{27} \]
command
integrate((3+5*x)^(5/2)/(1-2*x)^(1/2)/(2+3*x)^(1/2),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ -\frac {1}{27} \, {\left (45 \, x + 89\right )} \sqrt {5 \, x + 3} \sqrt {3 \, x + 2} \sqrt {-2 \, x + 1} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (-\frac {{\left (25 \, x^{2} + 30 \, x + 9\right )} \sqrt {5 \, x + 3} \sqrt {3 \, x + 2} \sqrt {-2 \, x + 1}}{6 \, x^{2} + x - 2}, x\right ) \]