I would like to apply the Kramers Kronig relations on measurements of the dispersive electromagnetic materials. But the big restriction is the upper value of the integral which is at infinity as in the equation below $$\int_{x=0}^\infty \frac{(xIm(x)-wIm(w))}{x^2-w^2}dx $$
When I solve this equation, I get undefined value of the integral at infinity which is $$\lim_{x\to \infty}\ln(x^2-w^2)$$ This part will give infinity and therefore will give an error in the measurement, so how can I overcome the upper part of the integral?