2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/113860We evaluate certain multidimensional integrals in terms of the Lerch transcendent function $Φ$, generalizing Guillera-Sondow's formulas. As an application, we get new representations of classical constants like Euler's constant $γ$ and $\ln(4/π)$.v2: typos corrected; v3: minor corrections/changes to wordingNumber TheoryClassical Analysis and ODEs11M35; 11Y60; 33B15text