\[ \int \frac {x}{\sqrt {2+x^6}} \, dx \]
Optimal antiderivative \[ \frac {2^{\frac {5}{6}} \left (2^{\frac {1}{3}}+x^{2}\right ) \EllipticF \left (\frac {x^{2}+2^{\frac {1}{3}} \left (1-\sqrt {3}\right )}{x^{2}+2^{\frac {1}{3}} \left (1+\sqrt {3}\right )}, i \sqrt {3}+2 i\right ) \left (\frac {\sqrt {6}}{2}+\frac {\sqrt {2}}{2}\right ) \sqrt {\frac {2^{\frac {2}{3}}-2^{\frac {1}{3}} x^{2}+x^{4}}{\left (x^{2}+2^{\frac {1}{3}} \left (1+\sqrt {3}\right )\right )^{2}}}\, 3^{\frac {3}{4}}}{6 \sqrt {x^{6}+2}\, \sqrt {\frac {2^{\frac {1}{3}}+x^{2}}{\left (x^{2}+2^{\frac {1}{3}} \left (1+\sqrt {3}\right )\right )^{2}}}} \]
command
integrate(x/(x^6+2)^(1/2),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ {\rm weierstrassPInverse}\left (0, -8, x^{2}\right ) \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (\frac {x}{\sqrt {x^{6} + 2}}, x\right ) \]