`int(1+cos4x)/(cotx-tanx)\ dx`

Explanation

To solve the integral \(\int \frac{1 + \cos 4x}{\cot x - \tan x} \, dx\), we will follow these steps:

### Step 1: Rewrite the Integral
We start with the integral:
\[ \int \frac{1 + \cos 4x}{\cot x - \tan x} \, dx \]
We know that \(\cot x = \frac{\cos x}{\sin x}\) and \(\tan x = \frac{\sin x}{\cos x}\). Thus, we can rewrite the denominator:
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