Integration technique using Laplace Transforms. A generalized form of the Dirichlet integral.
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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 (Espil'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 Espil's Theorem is a generalization of the Dirichlet integral
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Federico, E (2019). Integration technique using Laplace Transforms. A generalized form of the Dirichlet integral.. Afribary.com: Retrieved February 25, 2021, from https://afribary.com/works/integration-technique-using-laplace-transforms-a-generalized-form-of-the-dirichlet-integral
Espil, Federico. "Integration technique using Laplace Transforms. A generalized form of the Dirichlet integral." Afribary.com. Afribary.com, 23 Apr. 2019, https://afribary.com/works/integration-technique-using-laplace-transforms-a-generalized-form-of-the-dirichlet-integral . Accessed 25 Feb. 2021.
Espil, Federico. "Integration technique using Laplace Transforms. A generalized form of the Dirichlet integral.". Afribary.com, Afribary.com, 23 Apr. 2019. Web. 25 Feb. 2021. < https://afribary.com/works/integration-technique-using-laplace-transforms-a-generalized-form-of-the-dirichlet-integral >.
Espil, Federico. "Integration technique using Laplace Transforms. A generalized form of the Dirichlet integral." Afribary.com (2019). Accessed February 25, 2021. https://afribary.com/works/integration-technique-using-laplace-transforms-a-generalized-form-of-the-dirichlet-integral