\[ \int \frac {1}{\sqrt {1+x} \sqrt {2+x} \sqrt {3+x}} \, dx \]
Optimal antiderivative \[ -2 \EllipticF \left (\frac {1}{\sqrt {3+x}}, \sqrt {2}\right ) \]
command
integrate(1/(1+x)^(1/2)/(2+x)^(1/2)/(3+x)^(1/2),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ 2 \, {\rm weierstrassPInverse}\left (4, 0, x + 2\right ) \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (\frac {\sqrt {x + 3} \sqrt {x + 2} \sqrt {x + 1}}{x^{3} + 6 \, x^{2} + 11 \, x + 6}, x\right ) \]