find the Laplace transform of f (t).f(t)=\frac{e^t-e^{-t}}{t}

Rui Baldwin

Rui Baldwin

Answered question

2021-09-08

find the Laplace transform of f (t).
f(t)=etett

Answer & Explanation

Nathanael Webber

Nathanael Webber

Skilled2021-09-09Added 117 answers

Step 1
Laplace transform of common function:
L{eatf(t)}=F(sa)
L{f(t)t}=sF(s)ds
Step 2
f(t)=etett
F(s)=sL{etet}ds
=s(1s11s+1)ds
=s1s1dss1s+1ds
F(s)=[ln(s1)ln(s+1)]s
F(s)=[ln(s1s+1)]s
F(s)=ln1ln(s1s+1)
F(s)=ln(s+1s1)(lna=ln1a)

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