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Table of Laplace Transform

√
e −a/s cos 2 at
√ √
s πt
√
e −a/s sin 2 at
√ √
s s πa
√ 2
e −a s e −a /4t
√ (a > 0) √
s πt
√ ( )
e −a s (a > 0) erfc √
a
s 2 t
e −as (a > 0) δ (t)
a
e −as (a > 0) u (t)
s 2 a 2
2
e s /4 erfc s √ e −t
2 π
t
1 = e −as [ ] ([t] - greatest integer ≤ t)
as
s(e −1) s(1−e −as ) a
[t]
1 (a ̸= 1) a −1
s
s(e −a) a−1
s
e −1 a [t]
s
s(e −a)
log s+a e −bt −e −at
s+b t
−(log s+γ) (γ : Euler constant) log t
s
log s −(log t + γ)
s
( 2 2 )
log s +a 2 (cos bt − cos at)
s +b 2 t
2

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