Electronics/Laplace Transform pairs

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$f(t)$	$F(s)$
$\delta (t-t_0)$	$e^{-s{t}_0}$
$u(t)$	$\frac{1}{s}$
$e^{-\alpha t}u(t)$	$\frac{1}{s+\alpha }$
$\sin (\beta t)u(t)$	$\frac{\beta }{s^2+{\beta }^2}$
$\cos (\beta t)u(t)$	$\frac{s}{s^2+{\beta }^2}$
$e^{-\alpha t}\sin (\beta t)u(t)$	$\frac{\beta }{(s+\alpha {)}^2+{\beta }^2}$
$e^{-\alpha t}\cos (\beta t)u(t)$	$\frac{s+\alpha }{(s+\alpha {)}^2+{\beta }^2}$
$2e^{\alpha t}(a\cos \beta t-b\sin \beta t)u(t)$	$\frac{a+jb}{s+\alpha -j\beta }+\frac{a-jb}{s+\alpha +j\beta }$
$t^n$	$\frac{n!}{s^{n+1}}$
$t^{n}f(t)$	$(-1{)}^n\frac{d^{n}F(s)}{d{s}^n}$
$\frac{df(t)}{dt}$	$sF(s)-f(0)$
$\underset{0}{\overset{t}{\int }}f(x)dx$	$\frac{1}{s}F(s)$
$u_{-1}(t-t_0)f(t-t_0)$	$e^{-t_{0}s}F(s),t_0\ge 0$
$h(t)*f(t)=\underset{0}{\overset{t}{\int }}h(t-\tau )f(\tau )d\tau$	$H(s)F(s)$
$f_1(t)f_2(t)$	$F_1(s)*F_2(s)$