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KNUCK7ES
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Homework Statement
I =[itex]\int \frac{cosx}{x^{2}-2x+2}dx[/itex] the integral runs from -inf to inf
evaluate the integral using the calculus of residues.
Homework Equations
shown in my attempt
The Attempt at a Solution
Re [itex]\oint\frac{e^{iz}}{z^{2}-2z+2}[/itex]
with singularities at z=1+i and z-i they are both simple poles since we can turn
[itex]z^{2}-2z+2[/itex]
to
[itex](z-2)z+2[/itex]
now all we need to do is find the residues
residue=(z-pole)f(z)
the problem is i get an answer with imaginary numbers.
my contour uses a semi circle above the real axis, so i only need to use the 1+i pole.