What is the Laplace transform of x (t) = – e2t u(t)*

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What is the Laplace transform of x (t) = – e^2t u(t)^* (tu(t)) ?

1. - 1
  s²(s + 2)
2. - 1
  s²(s - 2)
3. 1
  s²(s - 2)
4. - 1
  s(s - 2)

Correct Option: B

X(s) = L[- e^-2t u(t)] . L[tu(t)]
Using l[x₁(t) * X₂(t)] = X₁(s). X₂(s), we get

X(s) =	- 1	.	1	= -	1
	(s - 2)		s²		s²(s - 2)