I need to find the partial decomposition of a fraction which contains an arbitrary constant. This is the final step, or close to final, on a larger non-linear differential equation problem. I need to integrate...
$$\int\frac{1}{y^4-K^4}dy$$
Where $K$ is an arbitrary constant. I'm prettry sure I need to break this fraction up with partial fractions. It's been a long while since I've used partial fractions, and I've tried to brush up, but I can't figure out how to split the fraction up into partials with the unknown constant. I know how I would do it if $K$ where an actual known number, and I've tried just going forward with the way that I know, but I'm getting nowhere. How would I go about splitting...
$$\frac{1}{y^4-K^4}$$
into partial fractions so that I can integrate it?