Find the Laplace Transform Could anyone enlighten me on how to find the Laplace Transform of
$$\frac{1-\cos (t)}{t}$$

$$
f(t)=\frac{g(t)}{t}=\frac{1-\cos t}{t}
$$
thus the Laplace transform is
$$
  F(s)=\int_s^\infty G(z)\,\mathrm dz=\int_s^\infty \left[\frac{1}{z}-\frac{z}{z^2+1}\right]\,\mathrm dz=\left[\log{z}-\log\left(\sqrt{z^2+1}\right)\right]_s^\infty=\log\left(\tfrac{\sqrt{s^2+1}}{s}\right)
$$
