\[ \int \frac {x^7}{\left (2+x^6\right )^{3/2}} \, dx \]
Optimal antiderivative \[ -\frac {x^{2}}{3 \sqrt {x^{6}+2}}+\frac {2^{\frac {5}{6}} \left (2^{\frac {1}{3}}+x^{2}\right ) \EllipticF \left (\frac {x^{2}+2^{\frac {1}{3}} \left (1-\sqrt {3}\right )}{x^{2}+2^{\frac {1}{3}} \left (1+\sqrt {3}\right )}, i \sqrt {3}+2 i\right ) \left (\frac {\sqrt {6}}{2}+\frac {\sqrt {2}}{2}\right ) \sqrt {\frac {2^{\frac {2}{3}}-2^{\frac {1}{3}} x^{2}+x^{4}}{\left (x^{2}+2^{\frac {1}{3}} \left (1+\sqrt {3}\right )\right )^{2}}}\, 3^{\frac {3}{4}}}{9 \sqrt {x^{6}+2}\, \sqrt {\frac {2^{\frac {1}{3}}+x^{2}}{\left (x^{2}+2^{\frac {1}{3}} \left (1+\sqrt {3}\right )\right )^{2}}}} \]
command
integrate(x^7/(x^6+2)^(3/2),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ -\frac {\sqrt {x^{6} + 2} x^{2} - 2 \, {\left (x^{6} + 2\right )} {\rm weierstrassPInverse}\left (0, -8, x^{2}\right )}{3 \, {\left (x^{6} + 2\right )}} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (\frac {\sqrt {x^{6} + 2} x^{7}}{x^{12} + 4 \, x^{6} + 4}, x\right ) \]