Munasinghe, R. M2023-02-122023-02-122023-0224058440https://rda.sliit.lk/handle/123456789/3274The integral ∫−∞∞e−xdx is used as an introductory learning tool in the study of Quantum Field Theory and path integrals. Typically, it is analyzed via perturbation theory. Closed-form solutions have been quoted for which I could not find any derivation. Using a simple and elegant transformation, the close form solutions for the integral and its even positive integer moments can be obtained in terms of Bessel functions.en0-dimensional quartic anharmonic oscillator0-dimensional φ4-field theoryBessel functionsClosed-form solutionPerturbation theorySolvable quantum field theoryArticle10.1016/j.heliyon.2023.e13168