2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/122863We use foliations and connections on principal Lie groupoid bundles to prove various integrability results for Lie algebroids. In particular, we show, under quite general assumptions, that the semi-direct product associated to an infinitesimal action of one integrable Lie algebroid on another is integrable. This generalizes recent results of Dazord and Nistor.24 pagesDifferential GeometryMathematical PhysicsSymplectic Geometry58H05; 22A22text