  We provide explicit formulas for integrating multiplicative forms on local
Lie groupoids in terms of infinitesimal data. Combined with our previous work
[8], which constructs the local Lie groupoid of a Lie algebroid, these formulas
produce concrete integrations of several geometric stuctures defined
infinitesimally. In particular, we obtain local integrations and non-degenerate
realizations of Poisson, Nijenhuis-Poisson, Dirac, and Jacobi structures by
local symplectic, symplectic-Nijenhuis, presymplectic, and contact groupoids,
respectively.

Differential Geometry;Symplectic Geometry