\[ \int \frac {1}{\sqrt {1-x} \sqrt {3-x} \sqrt {2+x}} \, dx \]
Optimal antiderivative \[ \frac {2 \EllipticF \left (\frac {\sqrt {2+x}\, \sqrt {3}}{3}, \frac {\sqrt {15}}{5}\right ) \sqrt {5}}{5} \]
command
integrate(1/(1-x)^(1/2)/(3-x)^(1/2)/(2+x)^(1/2),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ 2 \, {\rm weierstrassPInverse}\left (\frac {76}{3}, -\frac {224}{27}, x - \frac {2}{3}\right ) \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (\frac {\sqrt {x + 2} \sqrt {-x + 3} \sqrt {-x + 1}}{x^{3} - 2 \, x^{2} - 5 \, x + 6}, x\right ) \]