\int \frac{1}{4 + \sqrt{x} } \, dx
Let u = x^{1/2} \Rightarrow u^2 = x
\begin{align*}
u^2 &= x \\
\text{Differentiate both sides with respect to $x$} \\
\frac{d}{dx} (u^2) &= \frac{d}{dx}x \,\, \text{Apply chain rule to LHS} \\
\frac{d}{du} (u^2) \frac{du}{dx } &= 1 \\
2u...