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