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