# Evaluate $\int_{-\infty}^{\infty} \frac{\exp(-x^2/a)}{\cosh(x)^4} dx$ using contour integration. [closed]

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.

• Welcome to this community! Please try to show what you've tried so far for the given question. – Saad Dec 31 '17 at 10:36
• And add some context, for example where did you find it? – Shashi Dec 31 '17 at 13:38
• This previous Question might give you some ideas about contours to try. – hardmath Dec 31 '17 at 20:24
• 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. – Saeed Almarzoug Jan 1 '18 at 16:18