Evaluate: `int1/(5+4cosx)\ dx`

Explanation

To evaluate the integral \( \int \frac{1}{5 + 4 \cos x} \, dx \), we can use a substitution based on the trigonometric identity for cosine. Here’s a step-by-step solution:

### Step 1: Use the trigonometric identity
We know that:
\[ \cos x = \frac{1 - \tan^2\left(\frac{x}{2}\right)}{1 + \tan^2\left(\frac{x}{2}\right)} \]
Substituting this into the integral gives:
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