The Inverse Tangent Integral and its Association with Euler Sums

Abstract

In the existing literature, integrals that involve the inverse tangent integral in their integrands are not commonly found. However, in this paper, we delve into specific families of integrals that do contain the inverse tangent integral and reveal that their expressions are closely linked to certain variants of Euler harmonic sums. Furthermore, we provide explicit demonstrations of certain particular cases of our primary findings.