\[ \int \frac {3-x^2}{\sqrt {3+x^2-x^4}} \, dx \]
Optimal antiderivative \[ -\frac {\EllipticE \left (\frac {x \sqrt {2}}{\sqrt {1+\sqrt {13}}}, \frac {i \sqrt {3}}{6}+\frac {i \sqrt {39}}{6}\right ) \sqrt {-2+2 \sqrt {13}}}{2}+\EllipticF \left (\frac {x \sqrt {2}}{\sqrt {1+\sqrt {13}}}, \frac {i \sqrt {3}}{6}+\frac {i \sqrt {39}}{6}\right ) \sqrt {7+2 \sqrt {13}} \]
command
integrate((-x^2+3)/(-x^4+x^2+3)^(1/2),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ \frac {\sqrt {-x^{4} + x^{2} + 3}}{x} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (\frac {\sqrt {-x^{4} + x^{2} + 3} {\left (x^{2} - 3\right )}}{x^{4} - x^{2} - 3}, x\right ) \]