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
Pagano, F. (2020). Pagano's theorem. A generalized form of the Dirichlet integral involving Laplace Transforms techniques. Afribary. Retrieved from https://track.afribary.com/works/pagano-se-theorem-a-generalized-form-of-the-dirichlet-integral-involving-laplace-transforms-techniques
Pagano, Federico "Pagano's theorem. A generalized form of the Dirichlet integral involving Laplace Transforms techniques" Afribary. Afribary, 30 Aug. 2020, https://track.afribary.com/works/pagano-se-theorem-a-generalized-form-of-the-dirichlet-integral-involving-laplace-transforms-techniques. Accessed 20 Nov. 2024.
Pagano, Federico . "Pagano's theorem. A generalized form of the Dirichlet integral involving Laplace Transforms techniques". Afribary, Afribary, 30 Aug. 2020. Web. 20 Nov. 2024. < https://track.afribary.com/works/pagano-se-theorem-a-generalized-form-of-the-dirichlet-integral-involving-laplace-transforms-techniques >.
Pagano, Federico . "Pagano's theorem. A generalized form of the Dirichlet integral involving Laplace Transforms techniques" Afribary (2020). Accessed November 20, 2024. https://track.afribary.com/works/pagano-se-theorem-a-generalized-form-of-the-dirichlet-integral-involving-laplace-transforms-techniques