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    Evaluating an Integral using Jordan's Lemma

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    The problem is:

    Evaluate the integral from 0 to INF of:
    [(x^(1/3))*(ln x)]/(x^2 +9) dx

    by using f(z)= [(z^(1/3))*(Log z)]/(z^2 +9), with
    -pi/2 < Log z < 3pi/2.
    Also, with z^(1/3)= e^[(1/3)Log z].

    We are to use the curve C:
    from -R to -p, -p to p around origin, p to R, and Cr from 0 to pi.

    Many thanks in advance for your help. This is TOUGH one!

    © BrainMass Inc. brainmass.com December 24, 2021, 4:57 pm ad1c9bdddf

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    Let , we use the following figure:

    Since , ...

    Solution Summary

    An integral is evaluated using Jordan's lemma. A diagrm is included in this well presented solution.