Write an antiderivative for each of functions using the method of inspection :`sin2x`

Explanation

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

### Step-by-Step Solution:

1. **Identify the Derivative**: We know that the derivative of \( \cos(2x) \) is \( -2\sin(2x) \). This means that if we want to find an antiderivative for \( \sin(2x) \), we need to consider a function whose derivative gives us \( \sin(2x) \).

2. **Adjust for the Coefficient**: Since the derivative of \( \cos(2x) \) gives us \( -2\sin(2x) \), we need to adjust for the factor of \( -2 \). To find \( \sin(2x) \), we can take the negative of half the derivative of \( \cos(2x) \).

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