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Find the Laplace transform of (t + 2)^2 e^t.(a) 2/(s-1)^3 – 2/(s-1)^2 + 4/(s-1)(b) 2/(s-1)^3 – 2/(s-1)^2 – 4/(s-1)(c) 2/(s-1)^3 + 2/(s-1)^2 + 4/(s-1)(d) 2/(s-1)^3 + 2/(s-1)^2 – 4/(s-1)I have been asked this question during an online exam.This interesting question is from Operational Transforms in portion Intoduction to the Laplace Transform of Network Theory

Answer» RIGHT ANSWER is (C) 2/(s-1)^3 + 2/(s-1)^2 + 4/(s-1)

Best explanation: The LAPLACE transform of t^2+2t+4 is L(t^2+2t+4)=2/(s)^3 + 2/(s)^2+4/s. So the Laplace transform of (t + 2)^2 e^t is L((t + 2)^2 e^t) = 2/(s-1)^3 + 2/(s-1)^2 + 4/(s-1).


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