Let F=U $\times$ (U $\times$ x), where x is the position vector and U a uniform vector field. By using the divergence theorem, find the surface integral $\int_S $ F $\cdot$ dS, where S is the closed surface of the cube with verices $(\pm1,\pm1, \pm1)$.
By the divergence theorem $\int_S $ F $\cdot$ dS= $\int_V \nabla \cdot$ F dV.
$\nabla \cdot F = \nabla \cdot (U \times( U\times x))=(\nabla \times U)(U \times x)-U(\nabla(U \times x))=(\nabla \times U)(U \times x) -U((\nabla \times U)x-U(\nabla \times x))$
Because $U$ is a uniform vector field, I know $\nabla \times U = 0$ and $\nabla \cdot U = 0$, but I'm not sure if $ \nabla \times x=0$, because that would imply $\nabla \cdot F = 0$ and the question wouldn't make sense.
Where am I wrong?
Also, how should I interpret the gradients, $\nabla F$ and $\nabla x$?