16.108 Problem number 885

\[ \int \frac {x^4}{\sqrt {1-x^4}} \, dx \]

Optimal antiderivative \[ \frac {\EllipticF \left (x , i\right )}{3}-\frac {x \sqrt {-x^{4}+1}}{3} \]

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

\[ -\frac {1}{3} \, \sqrt {-x^{4} + 1} x \]

Fricas 1.3.7 via sagemath 9.3 output

\[ {\rm integral}\left (-\frac {\sqrt {-x^{4} + 1} x^{4}}{x^{4} - 1}, x\right ) \]