\[ \int \frac {1}{\sqrt {4-x} \sqrt {5-x} \sqrt {-3+x}} \, dx \]
Optimal antiderivative \[ \EllipticF \left (\sqrt {-3+x}, \frac {\sqrt {2}}{2}\right ) \sqrt {2} \]
command
integrate(1/(4-x)^(1/2)/(5-x)^(1/2)/(-3+x)^(1/2),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ 2 \, {\rm weierstrassPInverse}\left (4, 0, x - 4\right ) \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (\frac {\sqrt {x - 3} \sqrt {-x + 5} \sqrt {-x + 4}}{x^{3} - 12 \, x^{2} + 47 \, x - 60}, x\right ) \]