Chapter 7 - Section 7.1 - The Logarithm Defined as an Integral - Exercises - Page 401: 15

$2 e^{\sqrt r} +c$

Solve $\int e^{\sqrt r} \dfrac{1}{\sqrt r}dr$ Let us $p=\sqrt r$ and $dp=\dfrac{1}{2 \sqrt r}dr$ This implies $\int e^{\sqrt r} \dfrac{1}{\sqrt r}dr=2\int e^p dp $ $=2 e^{p} +c$ $=2 e^{\sqrt r} +c$ Hence, $\int e^{\sqrt r} \dfrac{1}{\sqrt r}dr=2 e^{\sqrt r} +c$