How do you use partial fraction decomposition to break up $1/(s+4)^2$? How do you use partial fraction decomposition to break up $1/(s+4)^2$?
The usual method isn't giving me an answer.

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