\[ \int \frac {1}{x^2 \sqrt {-1+x^4}} \, dx \]
Optimal antiderivative \[ -\frac {x \left (x^{2}+1\right )}{\sqrt {x^{4}-1}}-\frac {\EllipticF \left (\frac {x \sqrt {2}}{\sqrt {x^{2}-1}}, \frac {\sqrt {2}}{2}\right ) \sqrt {x^{2}-1}\, \sqrt {x^{2}+1}\, \sqrt {2}}{2 \sqrt {x^{4}-1}}+\frac {\EllipticE \left (\frac {x \sqrt {2}}{\sqrt {x^{2}-1}}, \frac {\sqrt {2}}{2}\right ) \sqrt {2}\, \sqrt {x^{2}-1}\, \sqrt {x^{2}+1}}{\sqrt {x^{4}-1}}+\frac {\sqrt {x^{4}-1}}{x} \]
command
integrate(1/x^2/(x^4-1)^(1/2),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ \frac {\sqrt {x^{4} - 1}}{x} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (\frac {\sqrt {x^{4} - 1}}{x^{6} - x^{2}}, x\right ) \]