Answer
$$ -\frac{2}{1+\sqrt{x}}+\frac{1}{(1+\sqrt{x})^{2}}+C $$
Work Step by Step
Given $$ \int \frac{d x}{(1+\sqrt{x})^{3}}$$
Let $$ u=1+\sqrt{x}\ \ \ \ \Rightarrow \ \ du =\frac{dx}{2\sqrt{x}} $$
Then
\begin{aligned} \int \frac{d x}{(1+\sqrt{x})^{3}} &=2 \int \frac{u-1}{u^{3}} d u \\ &=2 \int\left(u^{-2}-u^{-3}\right) d u \\ &=-\frac{2}{u}+\frac{1}{u^{2}}+C \\
&= -\frac{2}{1+\sqrt{x}}+\frac{1}{(1+\sqrt{x})^{2}}+C
\end{aligned}
