What is the integral of 1-cos(x/2) ?

The integral of 1-cos(x/2) is x-2sin(x/2)+C

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integral of 1-cos(x/2)

\int 1 - cos (\frac{x}{2}) d x

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

Solution steps

\int 1 - cos (\frac{x}{2}) d x

Apply the Sum Rule:

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

= \int 1 d x - \int cos (\frac{x}{2}) d x

\int 1 d x = x

\int cos (\frac{x}{2}) d x = 2 sin (\frac{x}{2})

= x - 2 sin (\frac{x}{2})

Add a constant to the solution

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

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