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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