Page 150 - Schaum's Outline of Theory and Problems of Signals and Systems

CHAP. 31 LAPLACE TRANSFORM AND CONTINUOUS-TIME LTI SYSTEMS

Thus,

The ROC of X(s) is Re(s) > 0. Thus, x(t) is a right-sided signal and from Table 3-1 we obtain

into the above expression, after simple computations we obtain

Alternate Solution:
We can write X(s) as

As before, by Eq. (3.30) we obtain

Then we have

Thus,

Then from Table 3-1 we obtain

3.19. Find the inverse Laplace transform of

We see that X(s) has one simple pole at s = - 3 and one multiple pole at s = -5 with
multiplicity 2. Then by Eqs. (3.29) and (3.31) we have