Find inverse laplace transform for x(s) = (2)/(s(s+1)^2)

x(t)=

Step-by-step explanation:

The function x(s) = (2)/(s(s+1)^2) can be expressed as partial fractions:

X(s)=

2=A·(s+1)²+B·s·(s+1)+C·s

2=A·(s²+2s+1)+B·(s²+s)+C·s

2=A·s²+2sA+A+B·s²+Bs+C·s

2=s²(A+B)+s(2A+B+C)+A

So we can find the values of A, B and C by solving these equations:

A+B=0 ⇒ 2+B=0 ⇒ B= -2

2A+B+C=0 ⇒ 2·2+(-2)+C=0 ⇒ C= -2

A=2

So X(s) is expressed as:

X(s)=

Using the inverse laplace transform tables we obtain x(t):

ℒ⁻¹{X(s)}=ℒ⁻¹{}

ℒ⁻¹{X(s)}=ℒ⁻¹{}+ℒ⁻¹{}+ℒ⁻¹{}

x(t)=

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