What is the integral of-cos(2y)+cos(y) ?

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

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integral of-cos(2y)+cos(y)

\int - cos (2 y) + cos (y) d y

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

Solution steps

\int - cos (2 y) + cos (y) d y

Apply the Sum Rule:

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

= - \int cos (2 y) d y + \int cos (y) d y

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

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

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

Add a constant to the solution

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

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