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I need help with the following integral :

Evaluate the integral : $$\int_{-\infty}^{\infty} \frac{\exp(-x^2/a)}{\cosh^4(x)} dx$$ using contour integration.

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    $\begingroup$ Welcome to this community! Please try to show what you've tried so far for the given question. $\endgroup$ – Saad Dec 31 '17 at 10:36
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    $\begingroup$ And add some context, for example where did you find it? $\endgroup$ – Shashi Dec 31 '17 at 13:38
  • $\begingroup$ This previous Question might give you some ideas about contours to try. $\endgroup$ – hardmath Dec 31 '17 at 20:24
  • $\begingroup$ Thank you for your replay. I did so much to calculate the above integral by using my experiences in residue theorem. This coming from Lagrangian method in Quantum mechanics. $\endgroup$ – Saeed Almarzoug Jan 1 '18 at 16:18