2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/70452We remark on pseudo-elliptic integrals and on exceptional function fields, namely function fields defined over an infinite base field but nonetheless containing non-trivial units. Our emphasis is on some elementary criteria that must be satisfied by a squarefree polynomial whose square root generates a quadratic function field with non-trivial unit. We detail the genus 1 case.Submitted preprintNumber Theory11G30, 14H05 (primary), 33E05 (secondary)text