`int2sin(x)dx` is equal to:

Options

A. `-2cosx+C`
B. `2cosx+C`
C. `-2cosx`
D. `2cosx`

Explanation

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

### Step 1: Identify the integral
We need to evaluate the integral:
\[ \int 2 \sin(x) \, dx \]

### Step 2: Factor out the constant
Since 2 is a constant, we can factor it out of the integral:
\[ = 2 \int \sin(x) \, dx \]

### Step 3: Find the integral of \(\sin(x)\)
The integral of \(\sin(x)\) is known to be:
\[ \int \sin(x) \, dx = -\cos(x) + C \]
where \(C\) is the constant of integration.

### Step 4: Substitute back into the equation
Now we substitute the result from Step 3 back into our equation:
\[ = 2 \left(-\cos(x) + C\right) \]

### Step 5: Distribute the constant
Distributing the 2 gives us:
\[ = -2 \cos(x) + 2C \]

### Step 6: Simplify the constant
Since \(2C\) is still a constant, we can denote it simply as \(C\) (where \(C\) is any constant):
\[ = -2 \cos(x) + C \]

### Final Answer
Thus, the integral \(\int 2 \sin(x) \, dx\) is:
\[ -2 \cos(x) + C \]

---