Consider the following integral. \[ \int \cos (8 x) d x \] Given the substitution $u=8 x$, find $d u$. \[ d u=(8) d x \] Rewrite the given integral in terms of $u$. \[ \int\left(\square_{x}\right) d u \] Evaluate the integral by making the given substitution. (Use $C$ for the constant of integration.)

Step 1 ：Given the substitution \(u=8x\), we find that \(du=8dx\).

Step 2 ：To rewrite the given integral in terms of \(u\), we need to replace \(dx\) with \(du/8\). So, the integral becomes: \[\int \cos(u) \frac{du}{8}\]

Step 3 ：Now, we can evaluate the integral. The integral of \(\cos(u)\) is \(\sin(u)\), so: \[\int \cos(u) \frac{du}{8} = \frac{1}{8}\sin(u) + C\]

Step 4 ：However, we need to substitute \(u\) back in terms of \(x\), so the final answer is: \[\boxed{\frac{1}{8}\sin(8x) + C}\]