- Thread starter
- #1

\[

\mathcal{L}\{e^{-at}\} = \frac{1}{s + a}.

\]

When it comes to the inverse Laplace transform, I can only find the tables to remember in a book. However, if we go back to the Laplace transform, we can always do

\[

\int_0^{\infty}f(t)e^{-st}dt

\]

to determine the transform with out a table. Is there an inverse analog? What if I can't remember the inverse Laplace of \(\mathcal{L}^{-1}\big\{\frac{s}{s^2 + a^2}\big\}\)? Can I work it like I could with Laplace transform?