Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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

share|cite|improve this question
up vote 4 down vote accepted

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

share|cite|improve this answer
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... – J. M. Aug 15 '12 at 17:15
Yes, [the answer](… is not a nice one. – process91 Aug 15 '12 at 17:23

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.