Integerate `(1)/(4+5sinx)`

Explanation

To solve the integral \( I = \int \frac{1}{4 + 5 \sin x} \, dx \), we can use a substitution method. Here’s a step-by-step solution:

### Step 1: Use a substitution
Let \( t = \tan\left(\frac{x}{2}\right) \). Then, we can use the following identities:
- \( \sin x = \frac{2t}{1 + t^2} \)
- \( dx = \frac{2}{1 + t^2} \, dt \)

### Step 2: Substitute into the integral
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