Showing that $\int_{\Bbb R^n} \mathop{\rm div} u\,dx =0$

Question

If $\frac{\partial u}{\partial x_i}\in L^1(\Bbb R^n)$ for each $i$. How to show that $\int_{\Bbb R^n} \mathop{\rm div} u\,dx =0$?

It might help to use Gauss theorem. But it is not a bounded domain with smooth boundary.