Pagano's theorem. A generalized form of the Dirichlet integral involving Laplace Transforms techniques

10 PAGES (1591 WORDS) Mathematics Paper

The problem of integration technique over integrands of the form f(t)/t^n, can be solved by differentiation(n times)  by using Leibniz's rule to get rid of t^n, that leads to integrate back (n times) to end the game which it's harder than the original problem.This work focuses on the derivation of the formula (Pagano's Theorem) which is a perfect tool to avoid that hard task. It allows to change the difficult n iterated integrals  into a more outstanding easier problem which consists of n -1 derivatives.The Pagano's Theorem is a generalization of the Dirichlet integral