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Residue theorem for real integrals

  1. Sep 21, 2011 #1
    The question asks to show using the residue theorem that

    [itex]\int[/itex] cos(x)/(x2+1)2 dx = [itex]\pi[/itex]/e
    (the terminals of the integral are -[itex]\infty[/itex] to [itex]\infty[/itex] but i didnt know the code to write that)

    I found the singularities at -i and +i

    so i think we can then say

    [itex]\int[/itex]cos (z) / (z+i)2(z-i)2 dz

    and if we take that integral over a closed contour then we will be left with the residue

    and i know that once we have found the residue you can multiply this by 2[itex]\pi[/itex]i and sum all the residues together.

    BUT...

    i dont know how to find the residues for this question. the cos on the top line is causing me trouble. maybe i need to expand the cos as a series? but im not sure

    thanks
     
  2. jcsd
  3. Sep 21, 2011 #2

    Hootenanny

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  4. Sep 21, 2011 #3
    ive looked on that page and stared at it for ages...

    will both methods work? and am i correct with what i have done so far? (ie poles at +i and -i)???
     
  5. Sep 21, 2011 #4

    Hootenanny

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    Yes, both methods will work and you are indeed correct in what you have done so far.
     
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