My textbook says that any rational function can be integrated using partial fraction expansion. So I was eager to try this out. But I got stuck with my very first example. How do I integrate $\frac{8x^2}{(x^2+1)^3}$ using partial fraction expansion?
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Can you perform the expansion ? – Oct 17 '17 at 09:37
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May help https://math.stackexchange.com/a/1776522/108128. – Nosrati Oct 17 '17 at 09:38
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Yep. $\frac{8}{(x^2+1)^2}-\frac{8}{(x^2+1)^3}$ – Adam Oct 17 '17 at 09:44
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@Adam Over complex factors ? – Oct 17 '17 at 09:55
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We didn't learn about that... – Adam Oct 17 '17 at 09:57
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@Adam Then you are stuck with the partial fraction that you got in your last comment. – Oct 17 '17 at 10:01
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time to learn it, I guess... – Adam Oct 17 '17 at 10:03
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@Adam If you to solve this question then make $x = \tan \theta$ substitution. – Oct 17 '17 at 10:09
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I know, I already solved it using this. But I wanted to try using partial fraction expansion. – Adam Oct 17 '17 at 10:21
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See here: https://math.stackexchange.com/a/689932/1242 – Hans Lundmark Oct 17 '17 at 11:27