Integrate $1/x$ in the sense of distribution, with non-symmetric excluded neighborhood of zero

I'm kind of confused with this question because of the boundary terms. for a test function $\phi$ define: $ u(\phi) = \lim_{\epsilon \rightarrow 0+} \int_{x\notin(-3\epsilon,5\epsilon)} \phi(x) x^{-1} dx $

Find a locally integrable function $v$ such that $v'=u$ in the sense of distributions.

How can I deal with boundary terms to find the correct distribution?