Question

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 1

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).