Evaluate $ \ \int_{- \infty}^{\infty} \frac{x \sin (3x)}{x^2 +4}\,dx \ $ using Jordan's Lemma How to to evaluate 
$
\
\int_{- \infty}^{\infty} \frac{x \sin (3x)}{x^2 +4}\,dx 
\
$ using Jordan's Lemma?

Hint:
Consider the complex integral
$$ \int_{C} \frac{ z\,{\rm e}^{3 i z}  }{ (z^2 + 4)} dz \,.$$
See here for the contour $C$.
