Answer
$\dfrac{1}{2} x+\dfrac{1}{2} \sin x+C$
Work Step by Step
Calculate the anti-derivative.
Since, we know $\cos^2 x=\dfrac{1+\cos x}{2}$ and $\int \cos x dx=\sin x$
Then $\int \cos^2 (x/2) dx= \int \dfrac{1+\cos x}{2} dx$
or, $=\dfrac{1}{2} x+ \dfrac{1}{2} \int \cos x dx$
Thus, $\int \cos^2 (x/2) dx=\dfrac{1}{2} x+\dfrac{1}{2} \sin x+C$
