Laplace transform in ODE Use any method to find the laplace transform of coshbt
Looking to get help with this example for my exam review

The laplace transformations of $coshbt$ is the following
$$\int_0^\infty cosh({bt})e^{-st} dt$$
$$= \int_0^\infty \frac{(e^bt + e^{-bt})e^{-st}}{2} dt$$
$$= \frac{1}{2} \int_0^\infty e^{-st + bt} + e^{-st - bt} dt $$
$$= \frac{1}{2} \int_0^\infty e^{(-s + b)t} + e^{(-s - b)t} dt$$
$$=\frac{1}{2} \begin{bmatrix} \frac {e^{(-s+ b)t}}{-s+b} + \frac{e^{-st - bt}}{-s-b} \end{bmatrix}^\infty_0$$
You can probably take it from here.
