Integrate e^{0.5x^2}

I am trying to integrate an exp function without sucess, as follows:

using Symbolics, SymbolicNumericIntegration
@variables x
integrate(exp(0.5*x^2), x)

Which returns (0, exp(0.5(x^2)), Inf).

However, when I try to integrate a similar function, the package works fine:

using Symbolics, SymbolicNumericIntegration
@variables x
integrate(exp(x^2), x)

Which returns (0.7071067811865478SymbolicNumericIntegration.Erfi(x), 0, 1.958577713602137e-12).

Is this type of function not supported in the package, or is there something I'm doing wrong?

Start with the Julia examples using SymbolicNumericIntegration.integrate for exp(0.5*x^2) and exp(x^2), comparing the returned tuples and the differing coefficient. Trace the integration entry point to determine whether the first expression is unsupported or handled incorrectly; done means the behavior is explained and the issue has a verified resolution.