# Math Help - Finding Inverse Laplace Transform Question?

1. ## Finding Inverse Laplace Transform Question?

Hi

The following questions i don't understand how to solve:

$\mathcal{L}^{-1} [\frac{e^{-3s}}{s-3}]$

$\mathcal{L}^{-1} [\frac{e^{\pi s}}{s^2+2s+2}]$

P.S

2. $\mathcal{L}^{-1} \left[ F(s) \cdot e^{-cs} \right] = f(t-c) \, \alpha(t-c)$ where $f(t)=\mathcal{L}^{-1} [ F(s) ]$ and $\alpha$ is the unit step function.

3. In the second one, you need to complete the square

$(S+1)^2 +1$

4. Originally Posted by Ted
$\mathcal{L}^{-1} \left[ F(s) \cdot e^{-cs} \right] = f(t-c) \, \alpha(t-c)$ where $f(t)=\mathcal{L}^{-1} [ F(s) ]$ and $\alpha$ is the unit step function.
So is $\mathcal{L}^{-1}[F(s)] = \mathcal{L}^{-1}[\frac{1}{s-3}]= e^{3t}$

where t = (t-3)
$=e^{(t-3)}H_3 (t)$