2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/173555Beginning with Hermite's integral representation of the Hurwitz zeta function, we derive explicit expressions in terms of elementary, polygamma, and negapolygamma functions for several families of integrals of the type $\int_0^\infty f(t)K(q,t)dt$ with kernels $K(q,t)$ equal to $(e^{2πq t}-1)^{-1}$, $(e^{2πq t}+1)^{-1}$, and $(\sinh(2πq t)^{-1}$.15 pagesClassical Analysis and ODEs33B99, 11M35text