Common Laplace Transforms

n=positive integer
f(t)F(s)
1
1-----
s
1
eat-----
s-a
n!
tn-----
sn+1
a
sin(at)-----
s2+a2
s
cos(at)-----
s2+a2
a
sinh(at)-----
s2-a2
s
cosh(at)-----
s2-a2
b
eatsin(bt)-----
(s-a)2+b2
s-a
eatcos(bt)-----
(s-a)2+b2
n!
tneat-----
(s-a)n+1
e-cs
uc(t)-----
s
uc(t)f(t-c)e-csF(s)
uc(t)f(t)F(s-c)
f(ct)(1/c)F(s/c)
f(n)(t)snF(s)-sn-1f(0)-...-f(n-1)(0)
(-t)nf(t)F(n)(s)