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## Homework Statement

find the inverse Laplace transform of the given function by

using the convolution theorem

## Homework Equations

F(s) = s/((s+1)(s

^{2})+4)

The theorem : Lap{(f*g)(t)} = F(s)*G(s)

## The Attempt at a Solution

I know how to find it the answer is :

we have 1/(s+1) * s/(s+4) and the inverse of each of these functions are : e

^{-t}* cos(2t)

further the answer is : ∫(e

^{(-(t-τ))}*cos(τ)dτ)

But if I try to solve this problem without convolution theorem; and with partial fraction I get :

s/((s+1)(s

^{2}+4)) = (1/5) ( (1/(s+1) + s/(s

^{2}+4) + 4/(s

^{2}+4) )

and the inverse of this function is :

(1/5) (cos(2t) - e

^{-t}+2sin(2t))

MY QUESTION IS :

∫(e

^{(-(t-τ))}*cos(τ)dτ) = (1/5) (cos(2t) - e

^{-t}+2sin(2t)) is this right ?