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

The integral of 1/2+(cos(2x))/2 is 1/2 x+1/4 sin(2x)+C

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integral of 1/2+(cos(2x))/2

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

\frac{1}{2} x + \frac{1}{4} sin (2 x) + C

Solution steps

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

\int \frac{1}{2} d x = \frac{1}{2} x

\int \frac{cos ( 2 x )}{2} d x = \frac{1}{4} sin (2 x)

= \frac{1}{2} x + \frac{1}{4} sin (2 x)

Add a constant to the solution

= \frac{1}{2} x + \frac{1}{4} sin (2 x) + C

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What is the integral of 1/2+(cos(2x))/2 ?
The integral of 1/2+(cos(2x))/2 is 1/2 x+1/4 sin(2x)+C