Question

Derive the Laplace Transform for:
f(t)=1/k(1-e^-kt)

Answer 1

Have you tried using the definition? Write down the integral of the transform and try and evaluate it.

Answer 2

\[ L[f(t)] = \int_0^\infty \frac{1}{k(1-e^{-kt})} e^{-st} \ dt \]
Now to evaluate that, write that fraction as an infinite sum using
\[ \frac{1}{1-x} = x + x^2 + x^3 + .... \]

Answer 3

\[ \frac{1}{1-x} = \sum_{i=0}^\infty x^i \] I forgot the constant term above.