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# help with inverse laplace transform (s^2)/((s+2)^4)?!?!?!?

(s^2)/((s+2)^4)

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- kbLv 77 years agoFavorite Answer
s^2/(s+2)^4

= [(s+2) - 2]^2 / (s+2)^4

= ((s+2)^2 - 4(s+2) + 4) / (s+2)^4

= 1/(s+2)^2 - 4/(s+2)^3 + 4/(s+2)^4. (Alternately, use partial fractions to obtain this.)

Inverting term by term:

te^(-2t) - 4(t^2/2!)e^(-2t) + 4(t^3/3!)e^(-2t)

= e^(-2t) (t - 2t^2 + (2/3)t^3).

I hope this helps!

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