I was studying Laplace transformation with handout from my prof which states
$ \displaystyle L^{-1} [\frac {2} {s+1}] = 2te^{-t}$
However no matter how many times I try I do not get $\displaystyle L[2te^{-t}](s)=\frac {2} {s+1}$ and I guess it is supposed to be
$ \displaystyle L^{-1} [\frac {2} {s+1}] = 2e^{-t}$.
Is my answer wrong or is this just prof's typo?
If the original answer is correct, could you show how I can derive $\displaystyle L[2te^{-t}](s)=\frac {2} {s+1}$?
It is the professor's typo. The function $2te^{-t}$ has a Laplace transform $\frac{2}{(s+1)^2}$