\[ \int \frac {x^2}{\sqrt {2-3 x^2} \sqrt {1+4 x^2}} \, dx \]
Optimal antiderivative \[ \frac {\EllipticE \left (\frac {x \sqrt {6}}{2}, \frac {2 i \sqrt {6}}{3}\right ) \sqrt {3}}{12}-\frac {\EllipticF \left (\frac {x \sqrt {6}}{2}, \frac {2 i \sqrt {6}}{3}\right ) \sqrt {3}}{12} \]
command
integrate(x^2/(-3*x^2+2)^(1/2)/(4*x^2+1)^(1/2),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ -\frac {\sqrt {4 \, x^{2} + 1} \sqrt {-3 \, x^{2} + 2}}{12 \, x} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (-\frac {\sqrt {4 \, x^{2} + 1} \sqrt {-3 \, x^{2} + 2} x^{2}}{12 \, x^{4} - 5 \, x^{2} - 2}, x\right ) \]