Laplace Transform/Graphical Interpretation/Examples/Cosine t of 3 - 9 i

Example of Graphical Interpretation of Laplace Transforms

For $\map {\laptrans {\map \cos t} } {3 - 9 i}$, notice how the contour spirals towards the origin.

Intuitively, the integral converges because as $t$ increases without bound, the contour "shrinks" as it continues its path into the origin.