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