I have the function $\frac{x^4}{(x^2+1)^5}$ but I can't remember how to calculate the fractions residues. I know that you can calculate the residues when the root is real and have multiplicity (r) >1 by using $b_{k}$ = $\frac{1}{(r-k)!}$ $\frac{d^{r-k}}{ds^{r-k}}$ ($\frac{N(s)}{D(s)}(s+a)^r)$ with 1<=k<=r
Is there a similar way as above for complex roots with r>1? For example, something like $\beta_{k}s+\beta_{l}$ = $\frac{1}{(r-k)!}$ $\frac{d^{r-k}}{ds^{r-k}}$ ($\frac{N(s)}{D(s)}((s+a)(s-a))^r)$
$$x^4=((x^2+1)-1)^2=(x^2+1)^2-2(x^2+1)+1$$
should reduce your expression to friendlier looking fractions.