8.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{094b3c91-1460-44a2-b9d6-4de90d3adfa0-15_590_855_210_548}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{figure}
The curve \(C\), shown in Figure 2, has equation
$$y = 2 x ^ { \frac { 1 } { 2 } } , \quad 1 \leqslant x \leqslant 8$$
- Show that the length \(s\) of curve \(C\) is given by the equation
$$s = \int _ { 1 } ^ { 8 } \sqrt { } \left( 1 + \frac { 1 } { x } \right) \mathrm { d } x$$
- Using the substitution \(x = \sinh ^ { 2 } u\), or otherwise, find an exact value for \(s\).
Give your answer in the form \(a \sqrt { } 2 + \ln ( b + c \sqrt { } 2 )\) where \(a , b\) and \(c\) are integers.