Question

# find the inverse Laplace transform of the given function F(s)=frac{e^{-2}+e^{-2s}-e^{-3s}-e^{-4s}}{s}

Laplace transform
find the inverse Laplace transform of the given function
$$F(s)=\frac{e^{-2}+e^{-2s}-e^{-3s}-e^{-4s}}{s}$$

2020-10-29
$$\text{Step 1}$$
$$\text{We have to find the inverse Laplace transform of the given function:}$$
$$F(s)=\frac{e^{-2}+e^{-2s}-e^{-3s}-e^{-4s}}{s}$$
$$\text{Step 2}$$
$$L^{-1}\left\{F\right\}=L^{-1}\left\{\frac{e^{-s}}{s}\right\}+L^{-1}\left\{\frac{e^{-2s}}{s}\right\}-L^{-1}\left\{\frac{e^{-3s}}{s}\right\}-L^{-1}\left\{\frac{e^{-4s}}{s}\right\}=u(t-1)+u(t-2)-u(t-3)-u(t-4)$$
$$\text{Step 3}$$
$$\text{Hence, the final answer is: }$$
$$u(t-1)+u(t-2)+u(t-3)+u(t-4)$$