Residue calculus

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Verify the integral formula with the aid of residues.

1.) Show that the p.v. of the integral of (x^2+1)/(x^4+1) from 0 to infinite =
(pi)/(sqrt 2).

Note: p.v.=principal value; pi is approximately 3.14; sqrt 2=square root of 2

Please show all work and explain the steps, especially how you found the zeros of the function.

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Solution Preview

Please see the attachment.

Proof:
Since is an even function, then .
Now we compute ...

Solution Summary

This shows how to verify an integral formula using residues.

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