In the documentation https://reference.wolfram.com/language/ref/Integrate.html
in the Examples, Basic Examples, Scope, Nested Integrals, it shows
Compute the second antiderivative of a function
Integrate[a x^2+b x+c, x, x]//Expand
So try
Integrate[Ψ[x,k]^2/(16 Pi^3),k,k]
