What is the integral of 2sin(x)-sin(2x) ?

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

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integral of 2sin(x)-sin(2x)

\int 2 sin (x) - sin (2 x) d x

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

Solution steps

\int 2 sin (x) - sin (2 x) 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 2 sin (x) d x - \int sin (2 x) d x

\int 2 sin (x) d x = - 2 cos (x)

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

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

Simplify

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

Add a constant to the solution

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

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