\(\begin{equation} \text { Tính nguyên hàm } I=\int \frac{1}{2 x+x \sqrt{x}+\sqrt{x}} \mathrm{~d} x \text { . } \end{equation}\)

\(\begin{equation}
\begin{array}{l}
\text { Ta có } I=\int \frac{1}{2 x+x \sqrt{x}+\sqrt{x}} \mathrm{~d} x=\int \frac{\mathrm{d} x}{\sqrt{x}(2 \sqrt{x}+x+1)} . \\
\text { Đặt } t=\sqrt{x} \Rightarrow 2 \mathrm{~d} t=\frac{\mathrm{d} x}{\sqrt{x}} \\
\text { Khi đó } I=2 \int \frac{\mathrm{d} t}{2 t+t^{2}+1}=2 \int \frac{\mathrm{d} t}{(t+1)^{2}}=-\frac{2}{t+1}+C=-\frac{2}{\sqrt{x}+1}+C
\end{array}
\end{equation}\)