What is the Laplace Transformation of cos^2t?

[rayman123]

Homework Statement

Find a Lapalce transformation of
$$cos^2t$$

Homework Equations

The Attempt at a Solution

started like this
$$\mathcal{L}(s)=\int_0^{\infty} e^{-st}\cos^2t\mbox{d}t=\frac{1}{2}\int_0^{\infty}e^{-st}(\cos 2t+1)\mbox{d}t=\frac{1}{2}\int_0^{\infty}e^{-st}\cos 2t\mbox{d}t+\frac{1}{2}\int_0^{\infty}e^{-st}\mbox{d}t=...$$
but i wonder how much the last integral is going to be?

Homework Statement

 

[rock.freak667]

∫e^-st=(-1/s)e^-st

Now just put in the limits from ∞ to 0 and you will get the answer easily.