`int1/(1+cos3x)dx`

Explanation

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

### Step 1: Multiply by the Conjugate
We start by multiplying the numerator and denominator by the conjugate of the denominator, which is \(1 - \cos 3x\):

\[ \int \frac{1 - \cos 3x}{(1 + \cos 3x)(1 - \cos 3x)} \, dx \]
...