\[ \int \frac {\sqrt {1-x^2}}{\sqrt {2+3 x^2}} \, dx \]
Optimal antiderivative \[ \frac {5 \EllipticF \left (x , \frac {i \sqrt {6}}{2}\right ) \sqrt {2}}{6}-\frac {\EllipticE \left (x , \frac {i \sqrt {6}}{2}\right ) \sqrt {2}}{3} \]
command
integrate((-x^2+1)^(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
\[ \frac {\sqrt {3 \, x^{2} + 2} \sqrt {-x^{2} + 1}}{3 \, x} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (\frac {\sqrt {-x^{2} + 1}}{\sqrt {3 \, x^{2} + 2}}, x\right ) \]