Answer
$${e^{x + 2}} + C$$
Work Step by Step
$$\eqalign{
& \int {{e^{x + 2}}} dx \cr
& {\text{property }}{e^{a + b}} = {e^a}{e^b} \cr
& = \int {{e^2}{e^x}} dx \cr
& = {e^2}\int {{e^x}} dx \cr
& {\text{integrate}} \cr
& = {e^2}\left( {{e^x}} \right) + C \cr
& = {e^{x + 2}} + C \cr
& {\text{check by differentiation}} \cr
& {\text{ = }}\frac{d}{{dx}}\left( {{e^{x + 2}} + C} \right) \cr
& {\text{ = }}\frac{d}{{dx}}\left( {{e^{x + 2}}} \right) + \frac{d}{{dx}}\left( C \right) \cr
& {\text{ = }}{e^2}\frac{d}{{dx}}\left( {{e^x}} \right) + \frac{d}{{dx}}\left( C \right) \cr
& {\text{ = }}{e^2}\left( {{e^x}} \right) + 0 \cr
& = {e^{x + 2}} \cr} $$
