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Possible Duplicate:
Help evaluating $\int \frac{dx}{(x^2 + a^2)^2}$

How to I begin this integration problem?

$\begin{align}\int_{0}^{1} \frac{dx}{{\left(x^2 + 1\right)}^{2}}\end{align}$

I'm not really sure how setup the triangle to do trigonometric substitution for this problem, since I am squaring the bottom, not taking the square root of it.

Could someone please demonstrate/explain how I could do this?

Thank you for your time.

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    What a coincidence that this question was posted on the same day as mine. Wonder if we're working from the book, at the same time, (from the same school, in the same class)? lol Thank you, Sivaram2012-03-12
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    @SivaramAmbikasaran: Since this is a definite integral, we might potentially have different solutions, so I am not so sure we should close this as a dupe.2012-03-12
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    @Aryabhata Once we have the indefinite integral, it is just a question of plugging in the limits and hence I voted to close it. The OP too seems to acknowledge this.2012-03-12
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    @SivaramAmbikasaran: Yes, but that does not mean there aren't other solutions. For instance if the limits were $0$ to $\infty$, a substitution of $x = \frac{1}{t}$ and adding gives us the answer easily.2012-03-12
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    @Aryabhata True. I get it. I concede. Is there any way I can undo?2012-03-12
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    @SivaramAmbikasaran: Unfortunately there isn't. Of course, OP seems to have tagged it indefinite-integral... (though I am not sure that was intended).2012-03-12
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    Whoops, fixed. ;)2012-03-12

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