Evaluation of inverse integral transforms for undergraduate physics students

We provide a simple approach to the analytical evaluation of inverse integral transforms that does not require any knowledge of complex analysis. The central idea behind our method is to reduce the inverse transform to the solution of an ordinary differential equation. We illustrate the utility of our approach by providing examples of the evaluation of transforms without the use of tables. We also demonstrate how the method may be used to obtain a general representation of a function in the form of a series involving the Dirac delta distribution and its derivatives, which has applications in quantum mechanics, semiclassical, and nuclear physics.