How Do You Transform and Simplify the Inverse Laplace Function 1/[s(2s^2+2s+1)]?

[fern518]

Hey everyone.

I've got through most of a problem that involves finding an inverse laplace transform, but I am stuck at one part that requires algebraic manipulation. The function is

1/[s(2s²+2s+1)]

So far I have modified it too look like .5/[s(s+.5)² +.5²](1/.5)

I'm not sure how to modify the function with that extra s in the denominator.

I had seen that the function could be transformed into (1/s) - [(s+.5)+.5]/[(s+.5)²+.5² and then from that the inverse Laplace could be easily obtained, but I am not sure how this transformation was done. I am sure there is a property I'm not thinking of, but any help on this would be greatly appreciated!

 

[n.karthick]

You can consider like this
$$\frac{1}{s(s+a)^2}=\frac{A}{s}+\frac{Bs+C}{(s+a)^2}$$
From the above equation find A, B and C values by substituting different values of s.