Integral NA in home, CAS

[parisse]

Indeed, I see your point. Then as you said, it's fairly easy to use the fact that the function is even and get the real value.
For a more general function, it is a good idea to split the interval at the point where the fractional power is singular.
int(sqrt (1+(x^2)^(-1/3)),x,-1,0)+int(sqrt (1+(x^2)^(-1/3)),x,0,1)