Answer
$$
\int \frac{e^{\sqrt{x}}}{\sqrt{x}} d x=2 e^{\sqrt{x}}+C
$$
where $C$ is an arbitrary constant.
Work Step by Step
$$
\int \frac{e^{\sqrt{x}}}{\sqrt{x}} d x
$$
$$\text { Let } u=\sqrt{x} . \text { Then } d u=\frac{d x}{2 \sqrt{x}}
$$
substituting in the given integral we have :
$$
\begin{aligned}
\int \frac{e^{\sqrt{x}}}{\sqrt{x}} d x &=2 \int e^{u} d u \\
&=2 e^{u}+C\\
&=2 e^{\sqrt{x}}+C
\end{aligned}
$$
where $C$ is an arbitrary constant.