Laplace transformation of f(t) = e^(at)

[asdf1]

for this question:
f(t)=e^(at), when t>0, a is constant. find the laplace transformation.

my question:
for the integration part, what happens if s-a<0?

 

[Tide]

If s < a then the integral diverges. There are conditions on f(t) for the existence of the transform.

 

[asdf1]

thank you very much!