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

x \to 0 + lim (\frac{sin ( 2 π )}{x})

y^{^{'}} = - 4 y, y (0) = 8

x \to 1 lim (\frac{1}{x} - \frac{1}{e ^{x} - 1})

ln (x + x^{2} - 1)

\frac{\partial}{\partial x} (e^{x + y} (x^{2} - y^{2}))

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