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Evaluating an Integral using Jordan's Lemma

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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.

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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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