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I have learned that the inverse Laplace Transform of $ F(s) $ is defined as $$ \mathfrak{L}^{-1}(F(s)) = \frac{1}{2\pi i}\int_{\gamma-i\infty }^{\gamma+i\infty }F(s)\cdot e^{st} \ {d}s $$

What is the easiest way (avoiding lots of complex analysis if possible) to find $$ \mathfrak{L}^{-1}\left(\frac{1}{s+k}\right) $$ (where k is a constant) - I know it is $ e^{-kt}, $ but I want to know if there is a way to get this result using only the definition.

FINAL EDIT: I learned all I need to know from an answer here: Usage of inverse Laplace transform

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  • $\begingroup$ what is $$ i∞$$? $\endgroup$ – shere Feb 20 '18 at 16:13
  • $\begingroup$ Infinity on the imaginary axis. $\endgroup$ – Nick_2440 Feb 20 '18 at 16:15
  • $\begingroup$ the integral is wrong $\endgroup$ – shere Feb 20 '18 at 16:15
  • $\begingroup$ en.wikipedia.org/wiki/Inverse_Laplace_transform $\endgroup$ – shere Feb 20 '18 at 16:16
  • $\begingroup$ Not the same thing? $\endgroup$ – Nick_2440 Feb 20 '18 at 16:16

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