  We solve the integration problem for generalized complex manifolds, obtaining
as the natural integrating object a weakly holomorphic symplectic groupoid,
which is a real symplectic groupoid with a compatible complex structure defined
only on the associated stack, i.e., only up to Morita equivalence. We explain
how such objects differentiate to give generalized complex manifolds, and we
show that a generalized complex manifold is integrable in this sense if and
only if its underlying real Poisson structure is integrable. Crucial to our
solution are several new technical tools which are of independent interest,
namely, a reduction procedure for Lie groupoid actions on Courant algebroids,
as well as certain local-to-global extension results for multiplicative forms
on local Lie groupoids. Finally, we implement our generalized complex
integration procedure in several concrete examples.
