\[ \int \frac {1}{x^8 \sqrt {1-x^4}} \, dx \]
Optimal antiderivative \[ \frac {5 \EllipticF \left (x , i\right )}{21}-\frac {\sqrt {-x^{4}+1}}{7 x^{7}}-\frac {5 \sqrt {-x^{4}+1}}{21 x^{3}} \]
command
integrate(1/x^8/(-x^4+1)^(1/2),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ \frac {5 \, x^{7} {\rm ellipticF}\left (x, -1\right ) - {\left (5 \, x^{4} + 3\right )} \sqrt {-x^{4} + 1}}{21 \, x^{7}} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (-\frac {\sqrt {-x^{4} + 1}}{x^{12} - x^{8}}, x\right ) \]