(i) 1/s^2(s + 1)^2 (ii) 1/(s + 1)(s^2 + 1) (iii) s/(s + 1)^2(s^2 + 1) (iv) s/(s^2 + a^2)^2

Question

Using Convolution theorem find the inverse Laplace transforms of the following functions:

(i) 1/s²(s + 1)²

(ii) 1/(s + 1)(s² + 1)

Answer 1

Then by Convolution theorem, we have

By integration by parts