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...
$$\frac{2p}{(1-p)(1+p^{4})}$$
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@SiongThyeGoh...Thank you. I've understood it.But , can you tell me how can I integrate the term with the 4th power...It would be helpful if you include it in your answer. – Nehal Samee Feb 15 '18 at 08:26
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Hint:
$$1+p^4=(1+\sqrt 2 p+p^2)(1-\sqrt 2 p+p^2)$$can you finish now?
Mostafa Ayaz
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1Sure!$$1+p^4=1+p^4+2p^2-2p^2\=(1+p^2)^2-(\sqrt 2 p)^2\=(1+\sqrt 2 p+p^2)(1-\sqrt 2 p+p^2)$$ – Mostafa Ayaz Feb 15 '18 at 08:31
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There you can write $1+p^4=(p+s_1)(p+s_2)(p+s_3)(p+s_4)$ where $s_j=e^{i(\frac{\pi}{4}+j\frac{\pi}{2})}$ – Mostafa Ayaz Feb 15 '18 at 08:36
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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 $$-(a+b)+ (b-c+2)p + (c-d)p^2+ (d-e)p^3+ (e-a)p^4=0$$
Claude Leibovici
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@ClaudeLeibovici...How can I integrate the partialized fraction...It would be helpful for me ... – Nehal Samee Feb 15 '18 at 08:34
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@NehalSamee. You must in fact use what Mostafa Ayaz answered. – Claude Leibovici Feb 15 '18 at 08:36
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