Solution
= Solution
For $\operatorname{Re}s>0$,
$$
\boxed{
\mathcal L\{H(t-t_0)\}(s)
=\int_{t_0}^{\infty}e^{-st}\,dt
=\frac{e^{-st_0}}s}.
$$
This is the <Laplace transform time-shift rule> in its simplest form.
= Solution
For $\operatorname{Re}s>0$,
$$
\boxed{
\mathcal L\{H(t-t_0)\}(s)
=\int_{t_0}^{\infty}e^{-st}\,dt
=\frac{e^{-st_0}}s}.
$$
This is the <Laplace transform time-shift rule> in its simplest form.