Find $\int \frac{\mathrm dx}{\sqrt{x}+\sqrt[3]{x}}$
I substituted $t = \sqrt x$ so $x = t^2$ and $\mathrm dx = 2t \mathrm dt$. I got to the
$ 2\int \frac{dt}{1+t^{-\frac13}} $
I'm not sure, if that is right. I still do lots of mistakes, but even if it would be right, I don't know, what to do next.