What is the integral of cos^2(w/2) ?

The integral of cos^2(w/2) is 1/2 (w+sin(w))+C

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integral of cos^2(w/2)

\int cos^{2} (\frac{w}{2}) d w

\frac{1}{2} (w + sin (w)) + C

Solution steps

\int cos^{2} (\frac{w}{2}) d w

Rewrite using trig identities

= \int \frac{1}{2} (1 + cos (w)) d w

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int 1 + cos (w) d w

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \frac{1}{2} (\int 1 d w + \int cos (w) d w)

\int 1 d w = w

\int cos (w) d w = sin (w)

= \frac{1}{2} (w + sin (w))

Add a constant to the solution

= \frac{1}{2} (w + sin (w)) + C

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What is the integral of cos^2(w/2) ?
The integral of cos^2(w/2) is 1/2 (w+sin(w))+C