Renormalization of Logarithmic divergences

[zetafunction]

how can logarithmic divergences be renormalized ?

for example if i have $$\int_{0}^{\infty} \frac{log^{n}(x)dx}{x+a}$$ differentiation with respect to 'a' and integration over 'x' gives finite result for example

$$\int_{0}^{\infty} \frac{dx}{x+a}=-log(a)+C$$

here 'C' would be an extra parameter in our theory to be measured, are there another methods to regularize logarithmic divergencies, for example if ONLY the logarithmic divergences were RELEVANT how could we get rid of them ??

 

[muppet]

There's loads of different ways of renormalising a theory- which books have you tried looking at?