Evaluate: `int1/(sqrt(3)sinx+cosx)\ dx`

Explanation

To evaluate the integral \( I = \int \frac{1}{\sqrt{3} \sin x + \cos x} \, dx \), we can follow these steps:

### Step 1: Rewrite the Denominator
We start by rewriting the denominator to make it easier to integrate. We can factor out a constant from the denominator:
\[ I = \int \frac{1}{\sqrt{3} \sin x + \cos x} \, dx = \int \frac{1}{2 \left( \frac{1}{2} \cos x + \frac{\sqrt{3}}{2} \sin x \right)} \, dx \]

...