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

Explanation

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

### Step 1: Rewrite the Integral
We can factor out the constant \(\frac{1}{2}\) from the integral:
\[ \int \frac{\cos x}{2} \, dx = \frac{1}{2} \int \cos x \, dx \]

### Step 2: Integrate \(\cos x\)
The integral of \(\cos x\) is a standard result:
\[ \int \cos x \, dx = \sin x + C \]
where \(C\) is the constant of integration.

### Step 3: Substitute Back
Now, we substitute the result of the integral back into our expression:
\[ \frac{1}{2} \int \cos x \, dx = \frac{1}{2} (\sin x + C) \]

### Step 4: Simplify
Distributing \(\frac{1}{2}\):
\[ \frac{1}{2} \sin x + \frac{1}{2} C \]
Since \(\frac{1}{2} C\) is still a constant, we can denote it as \(C'\) (where \(C' = \frac{1}{2} C\)):
\[ \frac{1}{2} \sin x + C' \]

### Final Answer
Thus, the integral \(\int \frac{\cos x}{2} \, dx\) evaluates to:
\[ \frac{1}{2} \sin x + C \]