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## Homework Statement

Decide the inverse laplace transform of the problem below:

F(s)= [itex]\frac{4s-5}{s^2-4s+8}[/itex]

You're allowed to use s shifting.

## Homework Equations

## The Attempt at a Solution

By looking at the denominator, I see that it might be factorized easily, so I try that.

I end up struggling and realizing that it's a complex root. Complex roots and inverse laplace transform isn't something we've learned yet, but I'm keen to solve this problem regardless.

So the denominator can be written like this:

##s^2 - 4s +8 = 2+/- 2i##

Looking at my laplace transform table, I can't recognize the pattern to try solving this.

Can I use polynomial division?

Any help here is greatly appreciated.