\[ \int \frac {t^3}{\sqrt {4+t^3}} \, dt \]
Optimal antiderivative \[ \frac {2 t \sqrt {t^{3}+4}}{5}-\frac {8 \,2^{\frac {2}{3}} \left (2^{\frac {2}{3}}+t \right ) \EllipticF \left (\frac {t +2^{\frac {2}{3}} \left (1-\sqrt {3}\right )}{t +2^{\frac {2}{3}} \left (1+\sqrt {3}\right )}, i \sqrt {3}+2 i\right ) \left (\frac {\sqrt {6}}{2}+\frac {\sqrt {2}}{2}\right ) \sqrt {\frac {2 \,2^{\frac {1}{3}}-2^{\frac {2}{3}} t +t^{2}}{\left (t +2^{\frac {2}{3}} \left (1+\sqrt {3}\right )\right )^{2}}}\, 3^{\frac {3}{4}}}{15 \sqrt {t^{3}+4}\, \sqrt {\frac {2^{\frac {2}{3}}+t}{\left (t +2^{\frac {2}{3}} \left (1+\sqrt {3}\right )\right )^{2}}}} \]
command
integrate(t^3/(t^3+4)^(1/2),t, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ \frac {2}{5} \, \sqrt {t^{3} + 4} t - \frac {16}{5} \, {\rm weierstrassPInverse}\left (0, -16, t\right ) \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (\frac {t^{3}}{\sqrt {t^{3} + 4}}, t\right ) \]