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I tried to make a partial fraction decomposition but that didn't work. Can someone show me how to do it with the residue theorem?

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    $\begingroup$ What are the poles and residues? Please show what you have done so far. $\endgroup$ – Kavi Rama Murthy Feb 23 at 8:45
  • $\begingroup$ $\cos(z)/z^2$ is even. $\endgroup$ – user10354138 Feb 23 at 8:48
  • $\begingroup$ There is a double pole at z = 0 and I think the residue is 0. (it's the first time I try to use this theorem) $\endgroup$ – syximak Feb 23 at 8:50
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By Cauchy's integral formula: $$\int_{\gamma}\frac{\cos(z)}{z^2}dz=\frac{2\pi i}{1!}\cos'(0)=0$$ where $\gamma$ is the unit circle curve.

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