Example 2. Find the integral $\int \sqrt{x+4} d x$.
Solution. According to transformation 1,

$$
d x=d(x+4)
$$

Applying formula (9.5') for the case when $u=x+4$ and $\alpha=\frac{1}{2}$, we get

$$
\begin{gathered}
\int \sqrt{x+4} d x=\int(x+4)^{\frac{1}{2}} d(x+4)=\frac{(x+4)^{\frac{1}{2}+1}}{\frac{1}{2}+1}+C= \\
=\frac{2}{3}(x+4)^{\frac{3}{2}}+C=\frac{2}{3}(x+4) \sqrt{x+4}+C
\end{gathered}
$$