Question

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

Answer 1

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