# Homework Help: Lapalce transformation

1. Sep 1, 2010

### rayman123

1. The problem statement, all variables and given/known data

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

2. Relevant equations

3. 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?
1. The problem statement, all variables and given/known data

2. Sep 1, 2010

### rock.freak667

∫e-st=(-1/s)e-st

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