File:LCost halfPlus4i.png

Contour, $\cos\left({t}\right) e^{-\left({\frac 1 2 + 4i}\right)t}$.

The integrand of $\mathcal{L} \left\{{\cos \left({t}\right)}\right\}\left({\frac 1 2 + 4i}\right)$

The integral converges.