Laplace Transform: The Definition

Find the Laplace transform using the definition.

1. \( f(t) = e^{3t} \)        solution

2. \( f(t) = 2t+5 \)       solution

3. \( f(t) = t^2 \)     solution

4. \( f(t) = \sin (at) \)       solution I   solution II

5. \(f(t) = \cosh (bt) \)      solution I   solution II