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## Homework Statement

I have three inverse laplace transforms I can't solve, they are,

i)

(s-1)/(s^2 + 8s + 17)

ii)

(s+3)/(s^2 + 4s)

iii)

2/[(s+1)*(s^2 + 1)]

## Homework Equations

The laplace transform table,

http://en.wikipedia.org/wiki/Laplace_transform#Table_of_selected_Laplace_transforms

## The Attempt at a Solution

i) I completed the square and got,

(s-1)/(s^2 + 8s + 17)

-->(s-1)/[(s+4)^2 -1]

then split up into, s/[(s+4)^2 -1] and -1/[(s+4)^2 -1]

my answer was e^-4t *cos(t) - e^-4t *sin(t)

but the answer is e^-4t *cos(t) - 5e^-4t *sin(t) , I do not know where the 5 has come from ?

ii) I'm not sure where to start on this one

(s+3)/(s^2 + 4s) , I have taken out a factor of 1/s but im not sure were to go from there.

iii) For this one, I'm not having problem with the actual laplace but rather partial fractions, what I have done,

2/[(s+1)*(s^2 + 1)] = A/(s+1) + B/(s^2 + 1)

A(s^2 + 1) + B(s+1) = 2

for s=-1 I found A= 1

but I'm stuck at finding B, how do I make (s^2 + 1) = 0

Thanks a lot in advance !