Integral of $ \int \frac{dx}{2 + \sqrt{x}} $ Can someone show me how to get the following integral please. I'm not sure how to approach this problem
$$ \int \frac{dx}{2 + \sqrt{x}} $$

Try making the following substitution: 
$$\sqrt x = u \implies x = u^2 \text{ and } dx = 2u\,du$$
That gives you the integral $$\begin{align} \int \frac{dx}{2 + \sqrt x} & = \int \frac{2u\;du}{2+u}\tag{substitution $u = \sqrt x$} \\ \\ & = \int \left(2 - \frac{4}{2+u}\right)\,du\tag{polynomial division}\end{align}$$
