Chapter 5 - Review - Exercises - Page 423: 31

$\int \frac{e^{\sqrt{x}}}{\sqrt{x}}~dx = 2e^{\sqrt{x}}+C$

$\int \frac{e^{\sqrt{x}}}{\sqrt{x}}~dx$ Let $u = \sqrt{x}$ $\frac{du}{dx} = \frac{1}{2\sqrt{x}}$ $dx = 2\sqrt{x}~du$ $\int (\frac{e^u}{\sqrt{x}})~(2\sqrt{x}~du)$ $=\int 2e^u~du$ $=2e^u+C$ $=2e^{\sqrt{x}}+C$