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

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

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integral of sin(2x-y)

integral

sin (2 x - y)

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

Solution steps

\int sin (2 x - y) d x

Rewrite using trig identities

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

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

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

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

Simplify

- sin (y) \frac{1}{2} sin (2 x) - \frac{1}{2} cos (y) cos (2 x) : - \frac{1}{2} cos (y - 2 x)

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

Add a constant to the solution

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

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