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

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

Popular >

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

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

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

Solution steps

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

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

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

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

Simplify

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

Add a constant to the solution

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

\frac{( 2 s + 3 )}{s ^{2} - 2 s + 5}

y^{^{''}} - 6 y^{^{'}} - 27 y = - 3 e^{- 3 t}

\int (\frac{1}{x} - \frac{1}{e ^{2 x}}) d x

\int y^{2} e^{y^{2}} d y

n = 1 \sum \infty (\frac{1}{10})^{n}

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