Question

Evaluate: $\int \frac{e^{\log \sqrt{x}}}{x}dx$

Answer 1

$$\begin{gathered} \int \frac{e^{\log \sqrt{x}}}{x}dx \\ =\int \frac{\sqrt{x}}{x}dx \\ =\int \frac{1}{\sqrt{x}}dx \\ =\int x^{-\frac{1}{2}}dx \\ =\left[\frac{x^{-{\displaystyle \frac{1}{2}}+1}}{-{\displaystyle \frac{1}{2}}+1}\right]+C \\ =2\sqrt{x}+C \end{gathered}$$