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

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

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

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

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

Solution steps

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

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

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

\int C d x = C x

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

Add a constant to the solution

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

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