- #1

- 986

- 9

## Homework Statement

.......find the inverse transform of the given function.

F(s)= (2s+2)/(s

^{2}+4s+5)

## Homework Equations

On another page, I see these 2:

f(t)=e

^{at}sin(bt)--------->F(s)=b/[(s-a)

^{2}+b

^{2})

f(t)=e

^{at}cos(bt)--------->F(s)=(s-a)/[(s-a)

^{2}+b

^{2})

## The Attempt at a Solution

This is my first time doing anything with Laplace transforms.

I can change the denominator to (s+2)

^{2}+ 1 and factor a -2 out of the numerator. Then it looks like the relevant equations.

-2((s-1/2)/((s+2)

^{2}+1))

But I don't understand where to go from here. The -2, of course, is just a constant that can chill out front. Judging from the answer in the back of the book, I use a combination of both relevant equations. Explain the algebra involved here.