Incomplete or Garbage Result When trying to Integrate.

[BrettKnoss]

Using Julia 1.10.0 on an M1 mac with BigSur, I get a garbage result for

Using Sybolics
Using SymbolicNumericIntegration

@variables x a

E(x)=(x^(3/2)/a^2)*exp(-(x/(2*a^2))) # the function provided
F(X)=integrate(E(x^2),(x,0,Inf);symbolic=true , detailed=false)
print(F(x))

should give 2a but instead gives:

[rzhli]

This answer may be correct, as x -> -∞, both x * exp(x) and exp(x) approaches to 0, thus the first and the third term vanishes, left only the 2.0a^2, which is the correct answer.
The problem is seems it didn't calculate or judge the limit value of the first and the third term, but directly output them.
BTW, why

@syms x::Real
limit(x * exp(x), x, -Inf)

fails as:

ERROR: MethodError: no method matching substitute(::SymbolicUtils.BasicSymbolic{Real}, ::Dict{SymbolicUtils.BasicSymbolic{Real}, SymbolicUtils.BasicSymbolic{Real}}, ::SymbolicUtils.BasicSymbolic{Real})
The function `substitute` exists, but no method is defined for this combination of argument types.