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Tabla de la transformada de Laplace
δ
(
t
)
\delta(t)
δ
(
t
)
1
1
1
1
(
θ
(
t
)
)
1\quad(\theta(t))
1
(
θ
(
t
))
1
s
\dfrac{1}{s}
s
1
t
t
t
1
s
2
\dfrac{1}{s^{2}}
s
2
1
t
n
t^{n}
t
n
n
!
s
n
+
1
\dfrac{n!}{s^{\,n+1}}
s
n
+
1
n
!
t
\sqrt{t}
t
π
2
s
3
/
2
\dfrac{\sqrt{\pi}}{2\,s^{3/2}}
2
s
3/2
π
e
−
a
t
e^{-at}
e
−
a
t
1
s
+
a
\dfrac{1}{s+a}
s
+
a
1
t
e
−
a
t
t\,e^{-at}
t
e
−
a
t
1
(
s
+
a
)
2
\dfrac{1}{(s+a)^{2}}
(
s
+
a
)
2
1
sin
(
a
t
)
\sin(at)
sin
(
a
t
)
a
s
2
+
a
2
\dfrac{a}{s^{2}+a^{2}}
s
2
+
a
2
a
cos
(
a
t
)
\cos(at)
cos
(
a
t
)
s
s
2
+
a
2
\dfrac{s}{s^{2}+a^{2}}
s
2
+
a
2
s
e
−
a
t
sin
(
b
t
)
e^{-at}\sin(bt)
e
−
a
t
sin
(
b
t
)
b
(
s
+
a
)
2
+
b
2
\dfrac{b}{(s+a)^{2}+b^{2}}
(
s
+
a
)
2
+
b
2
b
e
−
a
t
cos
(
b
t
)
e^{-at}\cos(bt)
e
−
a
t
cos
(
b
t
)
s
+
a
(
s
+
a
)
2
+
b
2
\dfrac{s+a}{(s+a)^{2}+b^{2}}
(
s
+
a
)
2
+
b
2
s
+
a
sinh
(
a
t
)
\sinh(at)
sinh
(
a
t
)
a
s
2
−
a
2
\dfrac{a}{s^{2}-a^{2}}
s
2
−
a
2
a
cosh
(
a
t
)
\cosh(at)
cosh
(
a
t
)
s
s
2
−
a
2
\dfrac{s}{s^{2}-a^{2}}
s
2
−
a
2
s
θ
(
t
−
a
)
\theta(t-a)
θ
(
t
−
a
)
e
−
a
s
s
\dfrac{e^{-as}}{s}
s
e
−
a
s