Elementary Laplace Transforms

$f(t)=\mathcal{L}^{-1}\{F(s)\}$	$F(s)=\mathcal{L}\{f(t)\}$
$1$	$\frac{1}{s},s>0$
$e^{at}$	$\frac{1}{s-a},s>a$
$t^n$	$\frac{n!}{s^{n+1}},s>0$
$t^p,p>-1$	$\frac{\Gamma(p+1)}{s^{p+1}},s>0$
$\sin at$	$\frac{a}{s^2+a^2},s>0$
$\cos at$	$\frac{s}{s^2+a^2},s>0$
$\sinh at$	$\frac{a}{s^2-a^2},s>\|a\|$
$\cosh at$	$\frac{s}{s^2-a^2},s>\|a\|$
$e^{at}\sin bt$	$\frac{b}{(s-a)^2+b^2},s>a$
$e^{at}\cos bt$	$\frac{s-a}{(s-a)^2+b^2},s>a$
$t^ne^{at}$	$\frac{n!}{(s-a)^{n+1}},s>a$
$u_c(t)\begin{cases}0&&t<c\\1&&t\geq c\end{cases}$	$\frac{e^{-sc}}{s},s>0$
$u_c(t)f(t-c)$	$e^{-cs}F(s)$
$e^{ct}f(t)$	$F(s-c)$
$f(ct)$	$\frac{1}{c}F(\frac{s}{c}),c>0$
$(f * g)(t)=\int_0^t f(t-\tau)g(\tau)d\tau$	$F(s)G(s)$
$\delta(t-c)$	$e^{-cs}$
$f^{(n)}(t)$	$s^n\mathcal{L}\{f(t)\}-s^{n-1}f(0)\cdots-sf^{(n-2)}(0)-f^{(n-1)}(0)$
$(-t)^nf(t)$	$F^{(n)}(s)$