\[ \int \frac {1}{\left ((2-x) x \left (4-2 x+x^2\right )\right )^{3/2}} \, dx \]
Optimal antiderivative \[ -\frac {\EllipticE \left (-1+x , \frac {i \sqrt {3}}{3}\right ) \sqrt {3}}{24}+\frac {\EllipticF \left (-1+x , \frac {i \sqrt {3}}{3}\right ) \sqrt {3}}{12}+\frac {\left (5+\left (-1+x \right )^{2}\right ) \left (-1+x \right )}{24 \sqrt {3-2 \left (-1+x \right )^{2}-\left (-1+x \right )^{4}}} \]
command
integrate(1/((2-x)*x*(x^2-2*x+4))^(3/2),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ -\frac {5 \, \sqrt {2} {\left (x^{4} - 4 \, x^{3} + 8 \, x^{2} - 8 \, x\right )} {\rm weierstrassPInverse}\left (-\frac {2}{3}, \frac {7}{54}, -\frac {x - 3}{3 \, x}\right ) - 6 \, \sqrt {2} {\left (x^{4} - 4 \, x^{3} + 8 \, x^{2} - 8 \, x\right )} {\rm weierstrassZeta}\left (-\frac {2}{3}, \frac {7}{54}, {\rm weierstrassPInverse}\left (-\frac {2}{3}, \frac {7}{54}, -\frac {x - 3}{3 \, x}\right )\right ) + 3 \, \sqrt {-x^{4} + 4 \, x^{3} - 8 \, x^{2} + 8 \, x} {\left (x^{2} + 2\right )}}{72 \, {\left (x^{4} - 4 \, x^{3} + 8 \, x^{2} - 8 \, x\right )}} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (\frac {\sqrt {-x^{4} + 4 \, x^{3} - 8 \, x^{2} + 8 \, x}}{x^{8} - 8 \, x^{7} + 32 \, x^{6} - 80 \, x^{5} + 128 \, x^{4} - 128 \, x^{3} + 64 \, x^{2}}, x\right ) \]