`int3sin(x)dx` is equal to:

Options

A. `-3cos x + C`
B. `3 cosx +C`
C. `-3 cos x`
D. `3 cosx`

Explanation

To solve the integral \( \int 3 \sin(x) \, dx \), we can follow these steps:

### Step 1: Set up the integral
We start with the integral:
\[ I = \int 3 \sin(x) \, dx \]

### Step 2: Factor out the constant
Since 3 is a constant, we can factor it out of the integral:
\[ I = 3 \int \sin(x) \, dx \]

### Step 3: Integrate \( \sin(x) \)
We know that the integral of \( \sin(x) \) is:
\[ \int \sin(x) \, dx = -\cos(x) \]
So, substituting this into our equation gives:
\[ I = 3 \cdot (-\cos(x)) \]

### Step 4: Simplify the expression
Now, we can simplify the expression:
\[ I = -3 \cos(x) \]

### Step 5: Add the constant of integration
Since this is an indefinite integral, we need to add the constant of integration \( C \):
\[ I = -3 \cos(x) + C \]

### Final Answer
Thus, the final result of the integral \( \int 3 \sin(x) \, dx \) is:
\[ I = -3 \cos(x) + C \]

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