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