Laplace transform of absolute sine

[Guest]

I need help determining the Laplace transform of |sin(t)|. I know the answer is 1/(s^2+1)*coth(.5*pi*s), but don't know the intermediate steps.
I got it down to the integral of e^(-s*t)*|sin(t)| dt from 0 to pi, all divided by 1-e^-pi*s), but I don't know how to proceed.

 

[royhaas]

You can drop the absolute value sign now and use integration by parts.