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