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

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

Popular >

integral of ((1-cos(2x)))/2

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

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

Solution steps

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int 1 - cos (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

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

\int 1 d x = x

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

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

Add a constant to the solution

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

\frac{sin ( θ )}{7} + \frac{c}{θ}

x \to 3 lim (\frac{π x}{4})

x y d x + (1 + x^{2}) d y = 0

\frac{d}{d θ} (4 + 3 sin (θ))

3 x^{2} e^{x} + e^{x} (x^{3} + 2)

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