How can I find the Laplace of
$f(t) = \cos^2(t)$
$f(t) = \sin3t\cos3t$
$f(t) = te^{t}$
$f(t) = t\cos(2t)$
What about inverse transform for
$F(s) = \frac{5-3s}{2^s+9}$
$F(s) = \frac{10s-3}{25-s^2}$
$F(s) = 2s^{-1}e^{-3s}$
Is there a general method used when you're multiplying two functions together, or have what appears to be a combination in the inverse Laplace? I was hoping I could look them up on a table of transforms, but I'm not exactly sure how to deal with them.