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## Homework Statement

I am getting fooled by the this improper integral

[tex]\int_0^{\infty}\frac{cos(x)+sin(x)}{1+v^2}dv = \pi \cdot e^{-x}[/tex]

How the devil do I go about getting that result?

## The Attempt at a Solution

I end up getting the sum of the two integrals

[tex]\int_0^{1}\frac{cos(x)}{1+v^2}dv + \int_1^{\infty}\frac{sin(x)}{1+v^2}dv [/tex] but how do I proceed from there? Hints please :)