Definite integral of the logarithm hyperbolic secant function in terms of the Hurwitz zeta function - Reynolds, Robert; Stauffer, Allan (AIMS mathematics, 2021)
We evaluate definite integrals of the form given by $\int_{0}^{∞}R(a, x)\log (\cos (α) \text{sech}(x)+1)dx$. The function $R(a, x)$ is a rational function with general complex number parameters. Definite integrals of this form yield closed forms for famous integrals in the books of Bierens de Haan [4] and Gradshteyn and Ryzhik [ 5 ].