to find the inverse Laplace transform of the given function. F(s)=\frac{2^{n+1}n!}{s^{n+1}}

opatovaL 2021-09-18 Answered
to find the inverse Laplace transform of the given function.
F(s)=2n+1n!sn+1
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Answers (1)

delilnaT
Answered 2021-09-19 Author has 94 answers

Step 1: Consider the provided function,
F(s)=2n+1n!sn+1
Step 2: Further simplify,
Consider the function from the provided function is G(s)=n!sn+1
The inverse Laplace transform of the function G(s)=n!sn+1  is  g(t)=tn
So, G(s2)=2n+1n!sn+1=F(s)
Then,
L{g(2t)}=12G(s2)
2L{g(2t)}=G(s2)=F(s)
2g(2t)=L1{F(s)}
2(2t)n=L1{F(s)}=f(t)
f(t)=2n+1tn
Hence , the inverse Laplace transform is f(t)=2n+1tn

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