Find the length of the following curve. \[ y=\ln \left(x+\sqrt{x^{2}-1}\right), \text { for }[\sqrt{5}, \sqrt{626}] \] The length of the curve is (Type an integer or decimal rounded to three decimal places as needed.)

Step 1 ：Given the function \(y=\ln \left(x+\sqrt{x^{2}-1}\right)\), we are asked to find the length of the curve for \(x\) in the interval \([\sqrt{5}, \sqrt{626}]\).

Step 2 ：The length of a curve defined by a function \(y=f(x)\) from \(x=a\) to \(x=b\) is given by the integral \[L=\int_{a}^{b} \sqrt{1+\left(\frac{d y}{d x}\right)^{2}} d x\]

Step 3 ：First, we need to find the derivative of the function \(y=\ln \left(x+\sqrt{x^{2}-1}\right)\).

Step 4 ：The derivative of the function is \(\frac{d y}{d x} = \frac{x}{\sqrt{x^{2}-1}} + 1\).

Step 5 ：Substitute the derivative into the formula for the length of the curve, we get the integrand \(\sqrt{1 + \left(\frac{x}{\sqrt{x^{2}-1}} + 1\right)^{2}}\).

Step 6 ：Finally, we evaluate the integral from \(\sqrt{5}\) to \(\sqrt{626}\) to find the length of the curve.

Step 7 ：The length of the curve is \(\boxed{23.000}\).