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Homework Statement
Find [tex]\int_{0}^{\infty} \frac{\cos(\pi x)}{1-4x^2} dx[/tex]
Homework Equations
The residue theorem
The Attempt at a Solution
The residue of this function at $$x=\pm\frac{1}{2}$$ is zero. Therefore shouldn't the integral be zero, if you take a closed path as a hemisphere in the upper half of the complex plane? Yet the integral evaluates to $$\pi/4$$
I am completely lost.
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