Evaluate $ \int_0^\infty \cos(x)/\cosh(x) dx $

Asked Oct 16 '14 at 18:08

Active Oct 16 '14 at 18:12

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I need to evaluate $$\int_0^\infty \frac{\cos(x)}{\cosh(x)} dx $$ through Residue Theory, but it has an infinite number of poles in x=(2n+1)pi/2, I couldn't find the way to the solution that is $$\frac{\pi\ }{2 \cosh \ (\pi\ /2)}.$$

I tried also the Method of the Fourier Integral, but couldn't find the answer too. I'm in this question for over 1.5h and have a test tomorrow, can someone help me?

edited Oct 16 '14 at 18:12

Joonas Ilmavirta

26,345

asked Oct 16 '14 at 18:08

Aquele Mesmo

1

http://math.stackexchange.com/questions/171073/how-to-evaluate-these-integrals-by-hand – Ron Gordon Oct 16 '14 at 18:18
Thanks man, I wasn't abble to find a question like this. Thank you – Aquele Mesmo Oct 16 '14 at 18:20
https://answers.yahoo.com/question/index?qid=20091007162254AAZXzt5 – Dr. Sonnhard Graubner Oct 16 '14 at 18:21

Evaluate $ \int_0^\infty \cos(x)/\cosh(x) dx $

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