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