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

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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

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

\frac{\partial}{\partial x} (3 e^{x y + 9})

f (x) = \frac{3 - 2 x}{3 + 2 x}

x \frac{d y}{d x} = y + x^{2} - y^{2}

x \to - 6 lim (2 x + 3)

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