1549312215-Complex_Analysis_for_Mathematics_and_Engineering_5th_edition__Mathews

12.9 • INVER.TlNG THE LAPLACE TR.ANSFORM 5 6 9

Figure 12. 27 The contour f R·

• EXAMPLE 12. 28 Find the inverse Laplace transform of the function given
  by

F() 8 4s+ 3

= s3+2s^2 +s+2·

Solution Here we have P (s) = 4s + 3 and Q (s) = (s + 2) (s^2 + 1) so that Q

has simple zeros located at the points s 1 = - 2, s2 = i, and s3 = -i. When we