# Evaluate an Inverse Laplace Transform using its definition

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

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