New two-parameter integral formulas proved via the digamma function

Abstract

This paper presents new integral formulas involving two parameters: an integer parameter and a real parameter. These formulas are notable for their generality, as well as for the method of proof, which relies on the properties of the digamma function. Detailed derivations are provided, offering a fresh perspective compared to more conventional techniques. Additionally, the paper proposes an open problem concerning the possibility of proving these results using standard integral calculus methods.