$($b$)$ Now, let's evaluate the same integral using a power series. First, find the power series for the function $f(x)=\frac{32}{x^{2}4}.$ Then, integrate it from $0$ to $2,$ and call the result $S.S$ should be an infinite series.

What are the first few terms of $S?$

$a_0=$

$a_1=$

$a_2=$

$a_3=$

$a_4=$