16.139 Problem number 970

\[ \int \frac {x^2}{\sqrt {16-x^4}} \, dx \]

Optimal antiderivative \[ 2 \EllipticE \left (\frac {x}{2}, i\right )-2 \EllipticF \left (\frac {x}{2}, i\right ) \]

command

integrate(x^2/(-x^4+16)^(1/2),x, algorithm="fricas")

Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output

\[ -\frac {\sqrt {-x^{4} + 16}}{x} \]

Fricas 1.3.7 via sagemath 9.3 output

\[ {\rm integral}\left (-\frac {\sqrt {-x^{4} + 16} x^{2}}{x^{4} - 16}, x\right ) \]