How to take the laplace of $e^{-|t|}$

Question

I seem to be having some trouble trying to compute the laplace transform of this function. I looked on Wolfram and it said the answer was simply $$\dfrac{1}{s+1}$$ but I highly doubt that is the correct answer. How should I go about trying to simplify the absolute value? Thanks for your time!

Answer 1

You are interested in two-sided Laplace transform probably:

$\mathcal{L}(e^{-|t|})= \int_{-\infty}^0e^t\cdot e^{-st} dt+\int_{0}^{\infty}e^{-t}\cdot e^{-st} dt$

From here you may go on.