Compute the Laplace transform. Your answer should be a function of the variable $s$:

$\displaystyle \mathcal{L}\,\biggl\lbrace 2 + u_{7/2}(t)e^{t}\cos\!\left(\pi t\right) \biggr\rbrace =$

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You may find the following formulas useful:
$\qquad\displaystyle\begin{aligned}\cos(bt+\pi) &= -\cos(bt) \\ \sin(bt+\pi) &= -\sin(bt) \\ \cos(bt+\tfrac{\pi}{2}) &= -\sin(bt) \\ \sin(bt+\tfrac{\pi}{2}) &= \cos(bt) \\ \end{aligned}$

If you don't get this in 2 tries, you can get a hint.

Hint: