The general integration by parts formula in multiple dimensions is given by

$\displaystyle \int_{\Omega} \nabla u \cdot \mathbf{v} = \int_{\partial\Omega} (u \mathbf{v})\cdot n-\int_\Omega u \nabla\cdot\mathbf{v}$

Is there a good reference that details the derivation of this formula? More specifically, I'm looking for a derivation of the above result that does not use differential forms.

Thanks.