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Differential Equations

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Help Joe to Finish the Decomposition

DIFFEQ-OWQKSN

Joe wants to take the inverse Laplace Transform of:

$$\frac{s^4+s^3+s^2+s+2}{(s+1)(s^2+1)}$$

He knows that the partial fraction decomposition should be taken first, but he has trouble doing it. Can you help him find the partial fraction decomposition?

A

$s+\cfrac{1}{s+1}+\frac{1-s}{s^2+1}$

B

$\cfrac{1}{s+1}-\frac{-s+1}{s^2+1}$

C

$\cfrac{1}{s+1}+\frac{1-s}{s^2+1}$

D

$s+\cfrac{1}{s+1}-\frac{-s+1}{s^2+1}$