Definite Integral to Infinity of x by Sine m x over x Squared plus a Squared/Proof 2

Proof
From Definite Integral to Infinity of $\dfrac {\cos m x} {x^2 + a^2}$:


 * $\ds \int_0^\infty \frac {\cos m x} {x^2 + a^2} \rd x = \frac \pi {2 a} e^{-m a}$

We have:

So: