Answer
$$
\int \frac{\sinh \sqrt{x}}{\sqrt{x}} d x =2 \cosh \sqrt{x}+C
$$
where $C$ is an arbitrary constant.
Work Step by Step
$$
\int \frac{\sinh \sqrt{x}}{\sqrt{x}} d x
$$
Let $u=\sqrt{x} . $ Then $d u=\frac{d x}{2 \sqrt{x}} $. and, the Substitution Rule gives
$$
\begin{aligned}
\int \frac{\sinh \sqrt{x}}{\sqrt{x}} d x & =\int \sinh u \cdot 2 d u \\
&=2 \cosh u+C\\
&=2 \cosh \sqrt{x}+C
\end{aligned}
$$
where $C$ is an arbitrary constant.