Question

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

• A. $2x^{1/2}+c$
• B. $2x^2+c$
• C. $\frac{1}{2}{x}^{1/2}+c$
• D. $\frac{1}{2}{x}^2+c$

Answer 1

The correct option is A $2x^{1/2}+c$

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

$=\int \frac{e^{{\log }_e{x}^{1/2}}}{x}dx$

$=\int \frac{x^{1/2}}{x}dx=\int x^{-1/2}dx$

$=\frac{x^{1/2}}{1/2}+c$

$=2x^{1/2}+c$