New Theorems in Solving Families of Improper Integrals

Abstract

Many improper integrals appear in the classical table of integrals by I. S. Gradshteyn and I. M. Ryzhik. It is a challenge for some researchers to determine the method in which these integrations are formed or solved. In this article, we present some new theorems to solve different families of improper integrals. In addition, we establish new formulas of integrations that cannot be solved by mathematical software such as Mathematica or Maple. In this article, we present three main theorems that are essential in generating new formulas for solving improper integrals. To show the efficiency and the simplicity of the presented techniques, we present some applications and examples on integrations that cannot be solved by regular methods. Furthermore, we acquire new results for integrations and compare them to that obtained in the classical table of integrations. Some previous results, become special cases of our outcomes or generalizations to acquire new integrals.

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