Evaluate the following integral: `int_0^(2pi)cos^7x\ dx`

Explanation

To evaluate the integral \( I = \int_0^{2\pi} \cos^7 x \, dx \), we can follow these steps:

### Step 1: Rewrite the integral
We can express \( \cos^7 x \) in terms of \( \cos^2 x \):
\[ I = \int_0^{2\pi} \cos^7 x \, dx = \int_0^{2\pi} \cos^2 x \cdot \cos^5 x \, dx \]

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