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QUESTION

Find the inverse Laplace transform of the function
$\ds\frac{1}{s^2+2s+2}$

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ANSWER


$\ds{\cal{L}}^{-1}\left\{\frac{1}{s^2+2s+2}\right\}={\cal{L}}^{-1}\left\{\frac{1}{(s+1)^2+1}\right\}=e^{-t}\sin
(t)$



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