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How do I integrate this expression: $\displaystyle\int{2x\,dx\over x^3+x^{2/3}}$?

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Let $u=x^{1/3}$, then $u^3=x$ so $dx=3u^2 du$ and now your integrand is a rational function.

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    On that note: $u^7+1=(u+1)(u^6-u^5+u^4-u^3+u^2-u+1)$. I wish the OP luck with his integration...2012-08-15
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    Yes, [the answer](http://www.wolframalpha.com/input/?i=integrate%202x%20%2F%20(x%5E3%20%2B%20x%5E\(2%2F3\)\)%20dx&t=crmtb01) is not a nice one.2012-08-15