Compute the line integral \(\int_{C} f(x, y) d s\) for the given function and path or curve.

\(f(x, y, z)=e^{x}-\frac{y}{2 \sqrt{2} z}, \quad\) the path \(\mathbf{r}(t)=\left\langle\ln t, \sqrt{2} t, \frac{1}{2} t^{2}ightangle\) for \(1 \leq t \leq 2\)