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

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

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integral of (1+cos(2x))

\int (1 + cos (2 x)) d x

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

Solution steps

\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

= \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)

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

Add a constant to the solution

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

x \to 1 lim (2 - \frac{1}{x})

\int \frac{x ^{2} - 36}{x} d x

\frac{( 1 - 3 x )}{2 + x}

\frac{d}{d x} (8 sin (x) - x)

\frac{d}{d x} (\frac{f ( x ) g ( x )}{f ( x ) - g ( x )})

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