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