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So I'm trying to do the laplace transform of unit step functions. From the laplace table in my book it says :
$ \mathcal{L}(u_c(t)f(t-c)) = e^{-cs}F(s) $

So my problem asks for the laplace transform of:
$ tu_8(t) $

So should I did the following:
$ (t-8)u_8(t) + 8u_8(t) $
$ \mathcal{L}((t-8)u_8(t) + 8u_8(t)) = e^{-8s}F(s) +\frac{8e^{-8s}}{s} $

So I have two questions:
1.) Is my attempt to solve the problem correct or am I completely off?
2.) What will the F(s) be?

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up vote 1 down vote accepted

$$ F(s)=\frac{1}{s^2}=\mathscr{L}\{t\}. $$ Everything else is OK.

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