Using convolution theorem for Laplace theorem,, show that
inverse Laplace transform (1/(S^3/2*(s-1)) = (2*e^t)/Pi^1/2 intregral (from 0 to t) e^-x*x^1/2dx.
The Attempt at a Solution
The inverse Laplace above is a product of 1/s^3/2 and 1/(s-1)
and both terms are the Laplace transform of 2/Pi^1/2*t^1/2 and e^t respectively.
changing variable t = u gives:2/Pi^1/2*u^1/2 and e^u
using convolution: integral (from 0 to infinity) e^-st integral (from 0 to t)
(2/Pi^1/2*u^1/2 )(e^u)du dt.
I dont know how to go about with the integral from here onwards..Help!