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I want to integrate

\[\frac{x^2}{1-x^2},\]

what I have try is trigonometric substitution and partition function and integration by part

but still cannot solve it

Thx for your reading!

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    @JavierBadia I could not understand what you claimed here. I meant only to use the theorem of changes of variables in elementary calculus. Why does this make no sense here? Moreover, $(lny)/4=ln(y^{1/4})$, right?2013-01-30

2 Answers 2

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$\frac{x^2}{1-x^2} = -\frac{x^2}{x^2 - 1} = -\frac{x^2 - 1 + 1}{x^2 - 1} = -1 - \frac{1}{x^2 - 1}$ Can you take it from here?

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    @DaveUM: Agree. Students usually like algorithms, and rational functions and their relatives give one of the few opportunities.2013-01-26
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And going a little further,

$\frac{1}{x^2-1} = \frac{1}{(x-1)(x+1)} =\frac{1}{2}\left(\frac{1}{x-1}-\frac{1}{x+1}\right) $

At this point, even I can integrate it.