Integrate the following :
`intsin2xdx`

Explanation

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

### Step 1: Identify the integral
We start with the integral:
\[ I = \int \sin(2x) \, dx \]

### Step 2: Use the integration formula for sine
We know that 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 constant of integration.

### Step 3: Apply the formula
In our case, \( k = 2 \). Therefore, we apply the formula:
\[ I = -\frac{1}{2} \cos(2x) + C \]

### Step 4: Write the final answer
Thus, the integral of \( \sin(2x) \) is:
\[ \int \sin(2x) \, dx = -\frac{1}{2} \cos(2x) + C \]

### Summary
The final result of the integration is:
\[ -\frac{1}{2} \cos(2x) + C \]