Here is something to get you started:
$ \mathcal{L}[f(t)]=\int_0^\infty e^{-st}f(t)\ dt $
$ \mathcal{L}[f'(t)]= sF(s)-f(0) $
p. 226: 1.
$ \mathcal{L}[t^2-2t]= \frac{2}{s^3}-2\frac{1}{s^2} $
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