How do you use partial fraction decomposition to break up $1/(s+4)^2$?

Question

How do you use partial fraction decomposition to break up $1/(s+4)^2$?

The usual method isn't giving me an answer.

Answer 1

Hint: You have a double root. The equation is

$$f(s)=\frac{1}{(s+4)^2}=\frac{A}{(s+4)}+\frac{B}{(s+4)^2}$$

Now it is easy to calculate A and B.

Remark:

If you want to integrate $f(s)$, you don't need to look for partial fractions.

$\int \frac{1}{(s+4)^2} \ dx=\int (s+4)^{-2} \ dx=-(s+4)^{-2+1}+C$

Answer 2

You are already done. You would write $\frac 1{(s+4)^2}=\frac A{s+4}+\frac B{(s+4)^2}$. Clearly $A=0, B=1$ is the solution.

Answer 3

The unicity of partial fraction decomposition gives the answer: it is $\;\dfrac1{(s+4)^2}$.