Partializing fraction with 4th power for integration

Question

How can I partialize the following fraction ? My query mainly lies with the term with 4th power . I want to use it in an integration problem .So , any clue to the dealing with integration will also be helpful...

$$\frac{2p}{(1-p)(1+p^{4})}$$

Answer 1

Hint:

$$1+p^4=(1+\sqrt 2 p+p^2)(1-\sqrt 2 p+p^2)$$can you finish now?

Answer 2

Is this what you need ? $$\frac{2p}{(1-p)(1+p^{4})}=\frac a{1-p}+\frac{b+cp+dp^2+ep ^3}{1+p^4 }$$ Cross multiply to get $$-(a+b)+ (b-c+2)p + (c-d)p^2+ (d-e)p^3+ (e-a)p^4=0$$