Answer
$$\frac{2}{3}x\sqrt x + C$$
Work Step by Step
$$\eqalign{
& \int {{e^{\ln \sqrt x }}} dx \cr
& {\text{Use the inverse property }}{e^{\ln f\left( x \right)}} = f\left( x \right).{\text{ Then }}{e^{\ln \sqrt x }} = \sqrt x \cr
& \int {{e^{\ln \sqrt x }}} dx = \int {\sqrt x } dx \cr
& {\text{write }}\sqrt x {\text{ as }}{x^{1/2}} \cr
& = \int {{x^{1/2}}} dx \cr
& {\text{integrating by the power rule, we get}} \cr
& = \frac{{{x^{3/2}}}}{{3/2}} + C \cr
& = \frac{2}{3}{x^{3/2}} + C \cr
& = \frac{2}{3}x\sqrt x + C \cr} $$
