\[ \int \frac {1}{\sqrt {-3-x} \sqrt {-2-x} \sqrt {-1+x}} \, dx \]
Optimal antiderivative \[ -\frac {2 i \EllipticK \left (4\right ) \sqrt {2+x}}{\sqrt {-2-x}}+\frac {\EllipticK \left (\frac {3}{4}\right ) \sqrt {3+x}}{\sqrt {-3-x}}-\frac {\EllipticF \left (\frac {2}{\sqrt {3+x}}, \frac {1}{2}\right ) \sqrt {2+x}\, \sqrt {3+x}}{\sqrt {-3-x}\, \sqrt {-2-x}} \]
command
integrate(1/(-3-x)^(1/2)/(-2-x)^(1/2)/(-1+x)^(1/2),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ 2 \, {\rm weierstrassPInverse}\left (\frac {52}{3}, \frac {280}{27}, x + \frac {4}{3}\right ) \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (\frac {\sqrt {x - 1} \sqrt {-x - 2} \sqrt {-x - 3}}{x^{3} + 4 \, x^{2} + x - 6}, x\right ) \]