Help show that Laplace transform exists

[bengaltiger14]

Homework Statement

Show that f(t)=e^(5t) sin(t) satisfies the condition for the LaPlace transform to exist

I can solve the Laplace and get 2/((s-5)^2 + 4)

How do I show that the conditions exist? If it is solvable using the table, shouldn't that be enough?

 

[jambaugh]

You must show that the improper integral defining the Laplace transform of the function exists. Recall that you define the value of an improper integral as the limit of a regular definite integral as the limit of integration approaches the singular value (in this case the upper limit of integration approaching infinity).