Inverse Laplace Transform

Question

Find the following Inverse Laplace Transform:



Answer 1

(3s + 5)/(s² - 6s + 25) = 3(s + 5/3)/[(s - 3)² + 4²] = 3(s - 3)/[(s- 3)² + 4²] + 14/[(s- 3)² + 4²] =

3(s - 3)/[(s- 3)² + 4²] + 7/2·4/[(s- 3)² + 4²] .

Then L^-1[(3s + 5)/(s² - 6s + 25)] = 3e^3xcos4x + 7/2e^3xsin4x