\[ \int \frac {x^4}{\sqrt {-1+x^3}} \, dx \]
Optimal antiderivative \[ \frac {2 x^{2} \sqrt {x^{3}-1}}{7}-\frac {8 \sqrt {x^{3}-1}}{7 \left (1-x -\sqrt {3}\right )}-\frac {8 \left (1-x \right ) \EllipticF \left (\frac {1-x +\sqrt {3}}{1-x -\sqrt {3}}, 2 i-i \sqrt {3}\right ) \sqrt {2}\, \sqrt {\frac {x^{2}+x +1}{\left (1-x -\sqrt {3}\right )^{2}}}\, 3^{\frac {3}{4}}}{21 \sqrt {x^{3}-1}\, \sqrt {\frac {-1+x}{\left (1-x -\sqrt {3}\right )^{2}}}}+\frac {4 \,3^{\frac {1}{4}} \left (1-x \right ) \EllipticE \left (\frac {1-x +\sqrt {3}}{1-x -\sqrt {3}}, 2 i-i \sqrt {3}\right ) \sqrt {\frac {x^{2}+x +1}{\left (1-x -\sqrt {3}\right )^{2}}}\, \left (\frac {\sqrt {6}}{2}+\frac {\sqrt {2}}{2}\right )}{7 \sqrt {x^{3}-1}\, \sqrt {\frac {-1+x}{\left (1-x -\sqrt {3}\right )^{2}}}} \]
command
integrate(x^4/(x^3-1)^(1/2),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ \frac {2}{7} \, \sqrt {x^{3} - 1} x^{2} - \frac {8}{7} \, {\rm weierstrassZeta}\left (0, 4, {\rm weierstrassPInverse}\left (0, 4, x\right )\right ) \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (\frac {x^{4}}{\sqrt {x^{3} - 1}}, x\right ) \]