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

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

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

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

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

Solution steps

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

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

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

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

Add a constant to the solution

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

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