2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/59993We study the planar three-body problem and prove the absence of a complete set of complex meromorphic first integrals in a neighborhood of the Lagrangian solution. We use the Ziglin's method and study the monodromy group of the corresponding normal variational equations.17 pages, submitted to Crelle's JournalDynamical Systems37K10text