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I have been trying to find an integral ## \int_{-\infty}^{+\infty} \frac{ e^{-\sqrt{(x^2 + 1)}}}{(x^2 + 1)^2} dx ##.

I initially posted this question in the complex analysis forum since I felt it might be done using contour integration. However now I realize it might not be the best way to go about as the integral over the curve in complex space does not converge to zero as the radius of the curve tends to infinity.

Any suggestions on how I can get this integral done?

Thanks!

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# Computing an integral -- any method

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