Table of LaPlace Transforms
()ft
L
{ ( )} ( )f t F s
1. 1
1
s
2. t
2
1
s
3.
n
t
1
!
n
n
s
, n is a positive integer
4.
1/2
t
s
5.
1/2
t
3/2
2s
6.
t
1
( 1) ,1
s
7.
sinkt
22
k
sk
8.
coskt
22
s
sk
9.
2
sin kt
2
22
2
( 4 )
k
s s k
10.
2
cos kt
22
22
2
( 4 )
sk
s s k
11.
at
e
1
sa
12.
sinhkt
22
k
sk
13.
coshkt
22
s
sk
()ft
L
{ ( )} ( )f t F s
14.
2
sinh kt
2
22
2
( 4 )
k
s s k
15.
2
cosh kt
22
22
2
( 4 )
sk
s s k
16.
at
te
2
1
()sa
17.
n at
te
1
!
n
n
sa
, n is a positive integer
18.
sin
at
e kt
22
()
k
s a k
19.
cos
at
e kt
22
()
sa
s a k
20.
sinh
at
e kt
22
()
k
s a k
21.
cosh
at
e kt
22
()
sa
s a k
22.
sint kt
2 2 2
2
()
ks
sk
23.
cost kt
22
2 2 2
()
sk
sk
24.
sin coskt kt kt
2
2 2 2
2
()
ks
sk
25.
sin coskt kt kt
3
2 2 2
2
()
ks
sk
26.
sinht kt
2 2 2
2
()
ks
sk
()ft
L
{ ( )} ( )f t F s
27.
cosht kt
22
2 2 2
()
sk
sk
28.
at bt
ee
ab
1
( )( )s a s b
29.
at bt
ae be
ab
( )( )
s
s a s b
30.
1 coskt
2
22
()
k
s s k
31.
sinkt kt
3
2 2 2
()
k
s s k
32.
22
sin sin
()
a bt b at
ab a b
2 2 2 2
1
( )( )s a s b
33.
22
cos cosbt at
ab
2 2 2 2
( )( )
s
s a s b
34.
sin sinhkt kt
2
44
2
4
ks
sk
35.
sin coshkt kt
22
44
( 2 )
4
k s k
sk
36.
cos sinhkt kt
22
44
( 2 )
4
k s k
sk
37.
cos coshkt kt
3
44
4
s
sk
38.
0()J kt
22
1
sk
39.
bt at
ee
t
ln sa
sb
