Integral hangs the physical Prime

[parisse]

Giac/Xcas works with fractional powers (complex-valued), not with NTHROOT. If you try to integrate an expression containing NTHROOT, the NTHROOT is replaced with a fractional power, then the CAS tries to find an antiderivative, after that it replaces back fractional powers by NTHROOT, assuming that the antiderivative for a branch is valid for another branch choice. This is the best way I know to find antiderivatives if fractional powers are involved. With an updated CAS inside the Prime, I do not see issues on the emulator for the integral of the original post.

In addition, fractional powers x^(p/q) are rewritten as (x^(1/q))^p with 0<=p<q, in order to have generalized polynomials in x^(1/q) (simplifications in a CAS always rewrite expressions in terms of a multivariate rational fraction with the lowest possible number of generalized variables, that should be algebraically independant).

As I already commented many times, if you want an approximate value for an integral inside CAS, I recommend to enter one boundary as an approx number, that will immediatly call the adaptive quadrature algorithm, avoiding all kind of possible issues with symbolic rewriting. If you are not comfortable with approx/exact representation of numbers and numeric/CAS differences, it's probably better to stay in Home.