INTEGRALS WITH POWERS OF THE ARCTAN FUNCTION VIA EULER SUMS

We undertake an investigation into families of integrals containing powers of the inverse tangent and log functions. It will be shown that Euler sums play an important part in the evaluation of these integrals. In a special case of the parameters, our analysis generalizes an arctan integral studied by Ramanujan [11]. In another special case, we prove that the corresponding log tangent integral can be represented as a linear combination of the product of zeta functions and the Dirichlet beta function. We also deduce formulas for log-sine and log-cosine integrals.