MHB Rieman inversion formula in Laplace transform

[lucad93]

Hello everybody! I'm sorry if it's not the right section to post in. I'm trying to solve this exercise:
$$\frac{1}{2i\pi}*\int_{8-i\infty}^{8+i\infty}\frac{e^{s(t-5)}}{(s+4)^2}ds$$
The request is to find the result in function of $$t$$
I know i must use the Riemann inversion formula, and so the request would be to anti-transform this $$\frac{e^{-5s}}{(s+4)^{2}}$$. First question: Am I right? I haven't found a transform that fit with this, how can I do?
ThankYou! :)

 

[Euge]

Hi lucad93,

Welcome! (Smile) What you're trying to find here is the inverse Laplace transform of the function

$$F(s) = \frac{1}{(s + 4)^2}$$

at $t-5$. Do you have to compute this using residue calculus, or using certain properties of the Laplace transform (e.g., $\mathcal{L}(t^a)(s) = \Gamma(a+1)/s^{a+1}, a > -1$, etc.)?