Find the inverse Laplace transform of frac{e^{-s}}{s(s+1)}

Chardonnay Felix 2021-02-19 Answered
Find the inverse Laplace transform of
ess(s+1)
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Expert Answer

tabuordy
Answered 2021-02-20 Author has 91 answers

Step 1
To determine : The inverse Laplace transform of
(ess(s+1))
Step 2
Solution :
Using Heaviside step function
,if [L1[F(s)]=f(t) then L1[easF(s)]=f(ta)u(ta) for any a0 where u(ta) is the step function.
The given function is ess(s+1)
Here, F(s)=1s(s+1) and a=1
Now, u(t1)L11s(s+1)(t1)
Using L1[F(s)]=f(t) ,then L1(F(s)s)=0tf(t)dt
L1(1s(s+1))=0tetdt
L1(1s(s+1))=[et1]0t=[ete0]=[et1]=1et
Hence, the Inverse Laplace transform is u(t1)(1e(t1))

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