Finding Inverse Laplace Transforms with Residue Method

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Homework Statement

Inverse laplace transforms

F(s)=\frac{5s-2}{s^{2}(s-1)(s+2)}

Homework Equations

Residue technique

The Attempt at a Solution

F(s)=\frac{5s-2}{s^{2}(s-1)(s+2)} = \frac{k1}{s^{2}} + \frac{k2}{s-1} + \frac{k3}{s+2}

I solved for K1,K2, and K3, which all came to be 1.

answer=e^{t}+e^{-2t}+t
textbook answer = e^{t}+e^{-2t}+t -2

Can someone explain to me how did the -2 come?

 

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It is very important that I know this. I was told that there was a k4 at the end but for problems we did in control theory class k4 was said to be 0 always and we took it as a rule.

So I need to know where this -2 came from.