\[ \int \frac {x^2}{\sqrt {1-4 x^2} \sqrt {2+3 x^2}} \, dx \]
Optimal antiderivative \[ \frac {\EllipticE \left (2 x , \frac {i \sqrt {6}}{4}\right ) \sqrt {2}}{6}-\frac {\EllipticF \left (2 x , \frac {i \sqrt {6}}{4}\right ) \sqrt {2}}{6} \]
command
integrate(x^2/(-4*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
\[ -\frac {\sqrt {3 \, x^{2} + 2} \sqrt {-4 \, x^{2} + 1}}{12 \, x} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (-\frac {\sqrt {3 \, x^{2} + 2} \sqrt {-4 \, x^{2} + 1} x^{2}}{12 \, x^{4} + 5 \, x^{2} - 2}, x\right ) \]