a question on Laplace Transform definition

Hi. I have this problem I am quite unsure of.

For which complex values of $\displaystyle s$ is the Laplace Transform of $\displaystyle e^{-2t} cos(6t) $ defined?

What I did was simplified it and had it as

$\displaystyle \int_0^\infty e^{(-2-s)t}cos(6t) \,dt $

And from the L.T definitions, as t approaches infitinty, the function should converge to zero.

So is it right by saying $\displaystyle -2-s < 0$ and hence $\displaystyle s > 2$ ? But then again, if I take the limit of $\displaystyle e^{(-2-s)t}cos(6t)$ it doesn't converge zero, rather it is undefined.

Thanks for your help.

Thanks.