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

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... –  Guess who it is. Aug 15 '12 at 17:15
Yes, [the answer](wolframalpha.com/input/… is not a nice one. –  process91 Aug 15 '12 at 17:23