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

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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.