Laplace transform of $\frac{sin(t)}{t}$ How to compute the Laplace transform $\mathcal{L}\frac{sin(t)}{t}$? I can't use the shifting theorem because of the $t^{-1}$? 
Thank you.

HINT:
Note that if $F(s)=\int_0^\infty \frac{\sin(t)}{t}e^{-st}\,dt$, then
$$F'(s)=-\int_0^\infty \sin(t) e^{-st}\,dt=-\frac{1}{s^2+1}$$
Now integrate $F'(s)$ and apply $\lim_{s\to \infty}F(s)=0$.
