Integrate the following :
`intcos{(x)/(2)}dx`

Explanation

To solve the integral \( \int \cos\left(\frac{x}{2}\right) \, dx \), we will follow these steps:

### Step 1: Identify the integral
We start with the integral:
\[ I = \int \cos\left(\frac{x}{2}\right) \, dx \]

### Step 2: Use substitution
To solve this integral, we can use a substitution. Let:
\[ u = \frac{x}{2} \]
Then, the differential \( dx \) can be expressed in terms of \( du \):
\[ dx = 2 \, du \]

### Step 3: Change the limits of integration
Now, substituting \( u \) into the integral, we have:
\[ I = \int \cos(u) \cdot 2 \, du \]
This simplifies to:
\[ I = 2 \int \cos(u) \, du \]

### Step 4: Integrate
We know that the integral of \( \cos(u) \) is \( \sin(u) \):
\[ I = 2 \sin(u) + C \]

### Step 5: Substitute back
Now, we substitute back \( u = \frac{x}{2} \):
\[ I = 2 \sin\left(\frac{x}{2}\right) + C \]

### Final Result
Thus, the final result of the integral is:
\[ \int \cos\left(\frac{x}{2}\right) \, dx = 2 \sin\left(\frac{x}{2}\right) + C \]

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