# 4 ∫cos(\\frac{x}{2})dx

Explanation:

Step1: Use substitution method

Let (u = \frac{x}{2}), then (du=\frac{1}{2}dx), and (dx = 2du).

Step2: Substitute into the integral

(\int\cos(\frac{x}{2})dx=\int\cos(u)\cdot2du).

Step3: Integrate (\cos(u))

Since (\int\cos(u)du=\sin(u)+C), then (2\int\cos(u)du = 2\sin(u)+C).

Step4: Substitute back (u=\frac{x}{2})

(2\sin(\frac{x}{2})+C).

Answer:

(2\sin(\frac{x}{2})+C)