The 2-forms, \Omega and \Omega ' on a manifold M with values in vector bundles \xi \rightarrow M and \xi ' \rightarrow M are equivalent if there exist smooth fibered-linear maps U: \xi \rightarrow \xi ' and W: \xi ' \rightarrow \xi with \Omega ' = U\Omega and \Omega = W\Omega ' . It is shown that an ordinary 2-form equivalent to the curvature of a linear connection has locally a non-vanishing integrating factor at each point in the interior of the set rank (\omega) = 2 or in the set rank (\omega) > 2 . Under favorable conditions the same holds at points where the rank of \omega changes from =2 to >2. Global versions are also considered.