Hi guys if i have to transform $e^{t-1}u(t-1)$ , why the result is $\frac{e^{-s}}{(s-1)}$ and not $\frac{e^{-(s-1)}}{(s-1)}$ if the $e^{t-1}$ multiply all the "function" ?
2026-03-27 07:11:39.1774595499
Laplace transform and delay
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$${\cal L}\left(u(t-c)f(t-c)\right)=e^{-cs}{\cal L}(f)$$ now let $c=1$: $${\cal L}\left(u(t-1)e^{t-1}\right)=e^{-s}\dfrac{1}{s-1}$$