Find an anti derivative (or integral) of the following functions by the method of inspection.sin 2x

Explanation

To find an antiderivative (or integral) of the function \( \sin(2x) \) using the method of inspection, we can follow these steps:

### Step 1: Identify the function and its derivative
We know that the derivative of \( \cos(2x) \) is \( -\sin(2x) \) due to the chain rule. Specifically, we have:
\[ \frac{d}{dx} \cos(2x) = -\sin(2x) \cdot \frac{d}{dx}(2x) = -\sin(2x) \cdot 2 \]
This means that:
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