How Does Renormalization Address Divergences in Integrals?

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eljose
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for a divergent series i can write an expression in the form:

\int_{R}dxC(x)w(x)e^{-ax}

where a is a divegent quantity in the form a=ln\epsilon

the qeustion is how i would apply renormalization?..in fact if we apply functional differentiation respect to e^{-ax} we get

C(x)w(x) the divergent term magically disappears
 
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