in the sense of distribution how do i calculate the following integral
$$ \int _{0}^{\infty} \frac{f(x)}{|x-a|} $$
I saw something like this
$$ \int _{0}^{a}\frac{f(x)-f(a)}{|x-a|}+ \int _{a}^{\infty}\frac{f(x)}{|x-a|}$$
but not sure about this split of the integration limits and if the integration limits are correct, is this valid also when $ a=0 4 4 thanks.