\[ \int \frac {x^4}{\sqrt {-1+x^4}} \, dx \]
Optimal antiderivative \[ \frac {\EllipticF \left (\frac {x \sqrt {2}}{\sqrt {x^{2}-1}}, \frac {\sqrt {2}}{2}\right ) \sqrt {x^{2}-1}\, \sqrt {x^{2}+1}\, \sqrt {2}}{6 \sqrt {x^{4}-1}}+\frac {x \sqrt {x^{4}-1}}{3} \]
command
integrate(x^4/(x^4-1)^(1/2),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ \frac {1}{3} \, \sqrt {x^{4} - 1} x - \frac {1}{3} \, {\rm ellipticF}\left (\frac {1}{x}, -1\right ) \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (\frac {x^{4}}{\sqrt {x^{4} - 1}}, x\right ) \]