How to Find the Inverse Laplace Transform for a Given Function?

[mr.engineer]

""Invers laplace transformation""

Homework Statement

Find invers laplace transform f(t) for F(s)= s /((s+a)^2 +w^2)) ?

Homework Equations

The Attempt at a Solution

i have the final answer but i need the steps to know how i can do it exactly
the final answer is :
f(t) = t^k sin(wt) e^-at

 

[Inferior89]

I am curious where the k comes from. It is not in your transform.

 

[mr.engineer]

yeah your notation is good,i there is something missing in my function
the true function is F(s)= s/((s+a)^2+w^2)^n , there is power n on the denominator.
t^k is just the power of t term causes by n maybe its the same gap with me..

 

[Inferior89]

Your F(s) or answer seems wrong.

http://www.wolframalpha.com/input/?i=inverse+laplace+s+/((s+a)^2++w^2)

I don't want to explain the steps if the F(s) is wrongly written which it seems to be since the answer is wrong.