LaPlace Transform Calculation

[G. Cook]

I know that Prime has a LaPlace() command to find the transform of a f(t). But, when I attempt to find the classical definite integral of 0 to infinity of e^-s*t*sin(a*t)dt the answer comes back "undefined" When I do an indefinite integral of the same and try to take a limit as the t goes to infinity, I again get an "undefined". Of course, the limit when t goes to 0 results in the correct transform. My question is why is this is happening since Prime gives e^(minus infinity)=0 correctly. How can a transform be calculated using the classical integral definition on the Prime?



















0 =0 correctly. Secondly, How can one find a transform using the classical definition integral?