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Contour integral with absolute value

  1. Jan 29, 2012 #1

    hunt_mat

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    Suppose I want to compute tthe integral:
    [tex]
    \int_{-\infty}^{\infty}\frac{\textrm{sech}\hspace{0.1cm} x}{x^{2}-2|x|+1}dx
    [/tex]
    Can I compute this integral via contour integration? The only way that I have thought of is to split up the domain:
    [tex]
    \int_{-\infty}^{\infty}\frac{\textrm{sech}\hspace{0.1cm} x}{x^{2}-2|x|+1}dx=\int_{-\infty}^{0}\frac{\textrm{sech}\hspace{0.1cm} x}{x^{2}+2x+1}dx+\int_{0}^{\infty}\frac{\textrm{sech}\hspace{0.1cm} x}{x^{2}-2x+1}dx
    [/tex]
    Is this the best way I can go about things for is there a better way?
     
  2. jcsd
  3. Jan 29, 2012 #2

    mathman

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    Gold Member

    So far OK, but you have singularities at |x|=1.
     
  4. Jan 30, 2012 #3

    hunt_mat

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    I am aware of the singularities, this was just an example. The other integral doesn't have singularities, I just wanted to get my ideas accross.
     
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