\[ \int \left (2+x^2-x^4\right )^{3/2} \, dx \]
Optimal antiderivative \[ \frac {x \left (-x^{4}+x^{2}+2\right )^{\frac {3}{2}}}{7}+\frac {34 \EllipticE \left (\frac {x \sqrt {2}}{2}, i \sqrt {2}\right )}{35}+\frac {48 \EllipticF \left (\frac {x \sqrt {2}}{2}, i \sqrt {2}\right )}{35}+\frac {x \left (3 x^{2}+19\right ) \sqrt {-x^{4}+x^{2}+2}}{35} \]
command
integrate((-x^4+x^2+2)^(3/2),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ -\frac {{\left (5 \, x^{6} - 8 \, x^{4} - 29 \, x^{2} + 34\right )} \sqrt {-x^{4} + x^{2} + 2}}{35 \, x} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left ({\left (-x^{4} + x^{2} + 2\right )}^{\frac {3}{2}}, x\right ) \]