`int1/(cosx+sqrt(3)sinx)\ dx` is equal to `logtan(pi/3+x/2)+C` (b) `logtan(x/2-pi/3)+C` (c) `1/2logtan(x/2+pi/3)+C` (d) none of these

Explanation

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

### Step 1: Rewrite the Denominator
We notice that the expression in the denominator can be rewritten using trigonometric identities. Specifically, we can express \( \cos x + \sqrt{3} \sin x \) in a different form.

We can factor out a constant and rewrite it as:
\[
\cos x + \sqrt{3} \sin x = 2 \left( \frac{1}{2} \cos x + \frac{\sqrt{3}}{2} \sin x \right)
...