\[ \int \frac {x^4 \sqrt {-1+3 x^2}}{\sqrt {2-3 x^2}} \, dx \]
Optimal antiderivative \[ -\frac {8 \sqrt {x^{2}}\, \EllipticE \left (\frac {\sqrt {-6 x^{2}+4}}{2}, \sqrt {2}\right ) \sqrt {3}}{135 x}-\frac {2 \sqrt {x^{2}}\, \EllipticF \left (\frac {\sqrt {-6 x^{2}+4}}{2}, \sqrt {2}\right ) \sqrt {3}}{81 x}-\frac {7 x \sqrt {-3 x^{2}+2}\, \sqrt {3 x^{2}-1}}{135}-\frac {x^{3} \sqrt {-3 x^{2}+2}\, \sqrt {3 x^{2}-1}}{15} \]
command
integrate(x^4*(3*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
\[ -\frac {{\left (9 \, x^{4} + 7 \, x^{2} + 8\right )} \sqrt {3 \, x^{2} - 1} \sqrt {-3 \, x^{2} + 2}}{135 \, x} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (-\frac {\sqrt {3 \, x^{2} - 1} \sqrt {-3 \, x^{2} + 2} x^{4}}{3 \, x^{2} - 2}, x\right ) \]