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