
28.2. Tables of Inverse Laplace Transforms 1473
No.
Laplace transform,
e
f
(p)
Inverse transform, f(x) =
1
2πi
Z
c+i∞
c−i∞
e
px
e
f(p) dp
20
p
(p + a)(p + b)(p + c)
a(b −c)e
−ax
+ b(c − a)e
−bx
+ c(a − b)e
−cx
(a − b)(b − c)(c − a)
21
p
2
(p + a)(p + b)(p + c)
a
2
(c − b)e
−ax
+ b
2
(a − c)e
−bx
+ c
2
(b −a)e
−cx
(a − b)(b − c)( c − a)
22
1
(p + a)(p + b)
2
1
(a − b)
2
e
−ax
− e
−bx
+ (a − b)xe
−bx
23
p
(p + a)(p + b)
2
1
(a − b)
2
−ae
−ax
+ [a + b(b −a)x
e
−bx
24
p
2
(p + a)(p + b)
2
1
(a − b)
2
a
2
e
−ax
+ b(b − 2a −b
2
x + abx)e
−bx
25
1
(p + a)
3
1
2
x
2
e
−ax
26
p
(p + a)
3
x
1 −
1
2
ax
e
−ax
27
p
2
(p + a)
3
1 −2ax +
1
2
a
2
x
2
e
−ax
28
1
p(p
2
+ a
2
)
1
a
2
1 − cos(ax)
29
1
p
(p + b)
2
+ a
2
1
a
2
+ b
2
1 − e
−bx
h
cos(ax) +
b
a
sin(ax)
i
30
1
(p + a)(p
2
+ b
2
)
1
a
2
+