Let $F$ be a distribution and let $f$ be a locally summable function. The distribution $F(f)$ is defined as the neutrix limit of the sequence $\{F_n(f)\}$, where $F_n(x)=F(x)*\delta_n(x)$ and $\{\delta_n(x)\}$ is a certain sequence of infinitely differentiable functions converging to the Dirac delta-function $\delta(x)$. The distributions $(x^r_+)^{-1}$ and $(x^r_-)^{-1}$ are evaluated for $r=1,2,\dots$.