(i) s/9s^2 + 4 (ii) 1/16s^2 - 9 (iii) (s + 2)^3/s^6 (iv) (2s + 18)/(s^2 + 25) (v) (8 - 6s)/(16s^2 + 9) (vi) 1/s^3/2.

Question

Find the inverse Laplace transforms of the following functions:

(i) s/9s² + 4

(ii) 1/16s² - 9

(iii) (s + 2)³/s⁶

(iv) (2s + 18)/(s² + 25)

(v) (8 - 6s)/(16s² + 9)

(vi) 1/s^3/2.

Answer 1

(i) L^-1{s/9s² + 4} = 1/9L^-1{s/s² + (2/3)²}