  The integral $\int_{-\infty}^{\infty} e^{- x^2 - g x^4} dx $ is used as an
introductory learning tool in the study of Quantum Field Theory and path
integrals. Typically it is analysed via perturbation theory. Close form
solutions have been quoted but it is not clear how they were derived. So I set
about deriving the close form solution on my own and using the same methodology
obtain closed form expressions for the even positive integer moments.
