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


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.


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Trying to get through college without dying. Love making apps in free time, self teaching Obj-C.

Updated on February 25, 2020


  • CoderNinja
    CoderNinja over 3 years

    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!

    • user99680
      user99680 over 9 years
      How about considering the cases $t \geq 0$ and $t<0$ separately?
  • CoderNinja
    CoderNinja over 9 years
    Thanks! This is exactly what I needed. Couldn't for the life of me figure out how to separate the abs