Copied Residue theory Show that \[ \int_0^\infty \frac{\cos(2x)}{(1+x^2)^2}\,dx=\frac{3\pi e^{-2}}{4}. \] **(a)** Raw LaTeX Residue theory Show that \[\int_0^\infty \frac{\cos(2x)}{(1+x^2)^2}\,dx=\frac{3\pi e^{-2}}{4}.\] \item Topic Tags Contour Integration and Residue Calculus Isolated Singularities and Residues Real Integral Evaluation by Complex Methods