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