We can sometimes use trigonometric identities to transform integrals. The integral formulas for `sin^(2)x and cos^(2)x` arise frequently in applications. Evaluate:
`intcos^(2)xdx`

Explanation

To evaluate the integral \( \int \cos^2 x \, dx \), we can use a trigonometric identity to simplify the expression. Here are the steps to solve the integral:

### Step 1: Use the Trigonometric Identity
We know from trigonometric identities that:
\[ \cos^2 x = \frac{1 + \cos(2x)}{2} \]
This identity allows us to express \( \cos^2 x \) in a form that is easier to integrate.
...