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Evaluating an Integral using Jordan's Lemma

The problem is to find the value of the integral from 0 to INF of [(ln x)^2]/(x^2 +9).

We are to use f(z)= [(Log z)^2]/(z^2 +9), where
-pi/2 < Log z < 3pi/2. We are to use the curve C from -R to -p along the real axis, -p to p around 0, p to R along the real axis, and the curve Cr from 0 to pi.

I am having several problems with this one, including:

**finding the residue at 3i.
**figuring out how to set up and equate the four integrals to 2pi(i) times the residue at 3i.

Solution Summary

An integral is evaluated using Jordan's Lemma. The solution is detailed and well presented. A diagram is included.

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