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[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?