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$$\int \frac{x^2+1}{x^5-1}dx$$

I am unable to integrate it, nothing works. Yes, I can use partial fraction but who remembers factorization of $x^5-1$, I need a better way of doing this.

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    You don't have to "remember" the factorization of $x^5-1$. Notice that $x=1$ is a solution and use long division to see that $x^5-1=(x-1)(x^4+x^3+x^2+x+1)$.2012-04-14
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    @chris: Long division? Geometric sum formula bro.2012-04-14
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    @anon: That works too. It's useful to know that, in general, if you can spot a solution then long division is a way to get the factorization of the polynomial though.2012-04-14
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    If this is homework problem, you have a cruel instructor. (Unless there is a smart way of doing this that I haven't figured out yet)2012-04-14
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    If this is a first course in integration at a "less-than-undergrad-level" (I live in Quebec, and we call this CEGEP, but I don't know how it works in other places...), then the instructor is really cruel. But in a context where complex numbers have been explained, this is really not that hard.2012-04-14
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    @Patrick: In my experience standard undergraduate calculus doesn’t assume knowledge of complex numbers.2012-04-14
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    Very cruel indeed; this results in an unholy mass of arctangents and logarithms...2012-04-14

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