\begin{equation*} 	\int \! \frac{\left(e^{x} + 1\right)^2}{\sqrt{e^{x}}} \cdot dx 		= \int e^{3x/2} \cdot dx + 2\,\int e^{x/2} \cdot dx + \int e^{-x/2} \cdot dx 		= \frac{2}{3}\,e^{3x/2} + 4\,e^{x/2} - 2\,e^{-x/2} + C \end{equation*}