Chapter 5 - Logarithmic, Exponential, and Other Transcendental Functions - 5.4 Exercises - Page 354: 97

$2e^{\sqrt{x}}+C$

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