Inverse Laplace Transformation Simple Question

Question

I'm new to Inverse Laplace Transformation so, I need to know whether the following question is correctly solved or not..

Question:

1/(s+2)^3

Solution:

Multiplying and dividing by 2;

= 2/2(s+2)^3

now, since 2=2! so;

= 2!/2(s+2)^3

now, using formula n!/(s-a)^n+1

here taking a's value in minus i.e a = -2 and n's value is 2

= 2!/2(s-(-2))^2+1

= t^(2)e^(-2t) [since n!/(s-a)^n+1 = t^(n)e^(at)]

Answer 1

Very close, you want:

$$\mathscr{L}^{-1}\left( \dfrac{1}{(s+2)^3}\right) = \dfrac{1}{2}t^2e^{-2t}$$

You must leave the $\dfrac{1}{2}$ term because you need it there to eliminate the $2!$ term. In other words, take the result I wrote and the result you wrote and find the Laplace Transform. What happens? Clear?