I have been doing revision on integration lately, and came across a question that need to resolve (1+u(adsbygoogle = window.adsbygoogle || []).push({}); ^{2})/(1+u^{4}) in partial fraction before I can proceed.

1+u^{4}= (u^{2}-2u+2)(x^{2}+2u+2)

therefore 1+u^{2}= (Au+B)(x^{2}+2u+2) + (Cu+D)(u^{2}-2u+2)

and I need to find out A, B, C and D

But wait, the next step in my textbook contains something like (1+sqrt(2)u+u^{2}) and (1-sqrt(2)+u^{2}) in denominators, so what is the problem and where does sqrt(2) come from ?

PS

original question:

[inte]dx/[(1+x^{2})(sqrt(1-x^{2}))]

and the substitution used is :

u=sqrt[(1-x)/(1+x)]

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# Partial fraction

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