A_Table_of_Laplace_Transforms.pdf
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TableofLaplaceTransforms
F(x) f(t),t
0
1 (t)
1
s
1(t)
s
2
t
2!
s
3
t
2
3!
s
4
t
3
m!
s
m
+1
t
m
1
s+a
e
−
at
1
(s+a)
2
te
−
at
1
(s+a)
3
2!
t
2
e
−
at
1
(s+a)
m
(m
−
1)!
t
m
−
1
e
−
at
a
s(s+a)
1
−
e
−
at
a
s
2
(s+a)
a
(at
−
1+e
−
at
)
(s+a)(s+b)
e
−
at
−
e
−
bt
(s+a)
2
(1
−
at)e
−
at
s(s+a)
2
1
−
e
−
at
(1+at)
(b
−
a)s
(s+a)(s+b)
be
−
bt
−
ae
−
at
s
2
+a
2
sinat
s
s
2
+a
2
cosat
s+a
(s+a)
2
+b
2
e
−
at
cosbt
b
(s+a)
2
+b
2
e
−
at
sinbt
s[(s+a)
2
+b
2
]
1
−
e
at
a
2
+b
2
cosbt+
a
b
sinbt
1
1
1
1
b
−
a
s
a
2
a
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