So, we can rewrite the Laplace transform as:
$$
F(s) = \int_0^\pi e^{-st} \cos t dt
$$
Now, we can integrate by parts. Let $u = e^{-st}$ and $dv = \cos t dt$. Then, $du = -se^{-st} dt$ and $v = \sin t$. Applying integration by parts, we get:
$$
F(s) = \left[
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