\[ \int \frac {1}{\sqrt {(2-x) x \left (4-2 x+x^2\right )}} \, dx \]
Optimal antiderivative \[ \frac {\EllipticF \left (-1+x , \frac {i \sqrt {3}}{3}\right ) \sqrt {3}}{3} \]
command
integrate(1/((2-x)*x*(x^2-2*x+4))^(1/2),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ -\frac {1}{2} \, \sqrt {2} {\rm weierstrassPInverse}\left (-\frac {2}{3}, \frac {7}{54}, -\frac {x - 3}{3 \, x}\right ) \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (-\frac {\sqrt {-x^{4} + 4 \, x^{3} - 8 \, x^{2} + 8 \, x}}{x^{4} - 4 \, x^{3} + 8 \, x^{2} - 8 \, x}, x\right ) \]