\[ \int \frac {3-x^2}{\sqrt {3+3 x^2-x^4}} \, dx \]
Optimal antiderivative \[ -\frac {\EllipticE \left (\frac {x \sqrt {2}}{\sqrt {3+\sqrt {21}}}, \frac {i \sqrt {3}}{2}+\frac {i \sqrt {7}}{2}\right ) \sqrt {-6+2 \sqrt {21}}}{2}+\EllipticF \left (\frac {x \sqrt {2}}{\sqrt {3+\sqrt {21}}}, \frac {i \sqrt {3}}{2}+\frac {i \sqrt {7}}{2}\right ) \sqrt {9+2 \sqrt {21}} \]
command
integrate((-x^2+3)/(-x^4+3*x^2+3)^(1/2),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ \frac {\sqrt {-x^{4} + 3 \, x^{2} + 3}}{x} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (\frac {\sqrt {-x^{4} + 3 \, x^{2} + 3} {\left (x^{2} - 3\right )}}{x^{4} - 3 \, x^{2} - 3}, x\right ) \]