Integrate the following :
`intsin2xdx`

Explanation

To solve the integral \(\int \sin(2x) \, dx\), we will follow these steps:

### Step-by-Step Solution:

1. **Identify the integral**: We need to integrate the function \(\sin(2x)\).

\[ \int \sin(2x) \, dx \]

2. **Use the integration formula for sine**: The integral of \(\sin(kx)\) is given by:

\[ \int \sin(kx) \, dx = -\frac{1}{k} \cos(kx) + C \]

where \(k\) is a constant and \(C\) is the integration constant.

3. **Apply the formula**: Here, \(k = 2\). Thus, we can substitute \(k\) into the formula:

\[ \int \sin(2x) \, dx = -\frac{1}{2} \cos(2x) + C \]

4. **Write the final answer**: Therefore, the integral of \(\sin(2x)\) is:

\[ -\frac{1}{2} \cos(2x) + C \]

### Final Result:
\[ \int \sin(2x) \, dx = -\frac{1}{2} \cos(2x) + C \]

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