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)