Evaluation of an Integral

TL;DR

This paper generalizes the Moll-Arias de Reyna integral, providing a broader class of integrals and calculating multiple specific values, enhancing understanding of this mathematical family.

Contribution

The paper introduces a generalization of the Moll-Arias de Reyna integral and computes several specific values, expanding the integral's applicability.

Findings

Generalized the Moll-Arias de Reyna integral

Calculated multiple specific integral values

Enhanced understanding of this class of integrals

Abstract

The Moll-Arias de Reyna integral [1] $$\int_0^{\infty}\frac{dx}{(x^2+1)^{3/2}}\frac{1}{\sqrt{\varphi(x)+\sqrt{\varphi(x)}}}$$ $$\varphi(x)=1+\frac{4}{3}\left(\frac{x}{x^2+1}\right)^2$$ is generalised and several values are given.