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    Residual calculus

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    Use residue theory to compute the integral:

    Use residue theory to compute the integral:

    I know that the singular points are 4i and -4i, and that I need to integrate from -R to R and then around the half circle from 0 to pi. Only 4i is in this half-circle, so I need to calculate the residue for 4i. This is where I get stuck and then I need to know how to put it all together at the end. Please advise, and show each step. Thanks!

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    Solution Preview

    Please see the attachment.

    Let's consider the integral , where and is consist of the half circle and the line segment from ...

    Solution Summary

    This shows how to use residue theory to compute the integral. The expert calculates the residues for half-circles.