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There's a question I have to solve for an assignment where I need to evaluate an integral but have to use a substitution which doesn't make much sense (in my mind anyways).

$\int\sqrt{1+x^{-2/3}}dx$ using substitution $u=1+x^{2/3}$

I've been at it for ages, not even sure where to start (other than saying $\frac{du}{dx} = \frac{2}{3}x^{-1/3}$)

Any help would be greatly appreciated, thanks

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Hint. One may observe that $$ \int \sqrt{1+x^{-2/3}}\:dx=\int \sqrt{1+x^{2/3}}\cdot \frac1{x^{1/3}}\:dx $$ leading to the announced substitution.

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