Chọn phương án D.

Đặt \(u=\mathrm{e}^x+2\Rightarrow\mathrm{d}u=\mathrm{e}^x\mathrm{\,d}x\).

Ta có $$\begin{aligned}
F(x)&=\displaystyle\int f(x)\mathrm{\,d}x=\displaystyle\int\dfrac{\mathrm{e}^x}{\mathrm{e}^x+2}\mathrm{\,d}x\\
&=\displaystyle\int\dfrac{1}{u}\mathrm{\,d}u=\ln|u|+C\\
&=\ln\left|\mathrm{e}^x+2\right|+C=\ln\left(\mathrm{e}^x+2\right)+C.
\end{aligned}$$