Contour integral with absolute value

  • Thread starter hunt_mat
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  • #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?
 

Answers and Replies

  • #2
mathman
Science Advisor
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So far OK, but you have singularities at |x|=1.
 
  • #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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