Find `intcos6xsqrt(1+sin6x)dx`

Explanation

To solve the integral \( \int \cos(6x) \sqrt{1 + \sin(6x)} \, dx \), we can follow these steps:

### Step 1: Substitution
Let \( t = 1 + \sin(6x) \). Then, we differentiate \( t \) with respect to \( x \):
\[ \frac{dt}{dx} = 6 \cos(6x) \]
This implies:
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