Question

The Laplace transform of the function (t^2 + 4t + 2)e^3t is ___________

(a) \(\frac{2}{(s-3)} + \frac{4}{(s-3)^2}  + \frac{2}{s-3}\)

(b) \(\frac{2}{(s-3)^3}  + \frac{4}{(s-3)^2}  + \frac{2}{s-3}\)

(c) \(\frac{2}{(s-3)^3}  – \frac{4}{(s-3)^2}  + \frac{2}{s-3}\)

(d) \(\frac{2}{(s-3)^3}  – \frac{4}{(s-3)^2}  – \frac{2}{s-3}\)

This question was posed to me in quiz.

My question is from Common Laplace Transforms topic in chapter Laplace Transform and System Design of Signals and Systems

Answer 1

The correct choice is (b) \(\frac{2}{(s-3)^3}  + \frac{4}{(s-3)^2}  + \frac{2}{s-3}\)

For explanation I would say: L {(t^2 + 4t + 2)e^3t} = L {t^2 e^3t + 4te^3t + 2e^3t}

= \(\frac{2}{(s-3)^3}  + \frac{4}{(s-3)^2}  + \frac{2}{s-3}\).