This is related to a fluids HW: Let $u(x)$ be incompressible vector field on n-D space, $x\in \Omega\subset R^n$ and let $\theta(x)$ be a scalar field s.t. $\int_{\Omega} \theta(x)dx=0$, $\nabla.u=0$
$\Omega$ is boundary-less (say n-Torus). This is crucial since this means there are no boundary terms while doing integration by parts.
Let $\theta=\Delta f$
Prove that: $\int_{\Omega}(\theta) (u.\nabla f)dx =\int_{\Omega}\nabla f.\nabla u.\nabla f dx$