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

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

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

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

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

Solution steps

\int \frac{1}{2} (1 - cos (2 x)) 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{d y}{d x} = x + 5 y

ln (x^{2} + y^{2})

\int \frac{( 2 - x ^{2} )}{x ^{3} + 3 x ^{2} + 2 x} d x

x \to + 4 lim (3 e^{1.7 x} + 1)

x^{3} + y^{3} = 12 x y - 8, (6, 4)

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