Integral NA in home, CAS

[parisse]

The "exact" answer from the Prime is not correct in the negative x direction, it's just too complicated to track the algebraic branches from fractional powers and sqrt correctly during symbolic integration. The numeric answer can be obtained by splitting in 2 parts
int (sqrt (1+x^(-2/3)),x,-1.0,0)+int (sqrt (1+x^(-2/3)),x,0,1.0)
If I keep it in one integral, I get undef, probably because of the singularity at x=0. This is really a hard integral, that's why I wondered where it comes from.