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

The integral of (cos(2x))/2 is 1/4 sin(2x)+C

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integral of (cos(2x))/2

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

\frac{1}{4} sin (2 x) + C

Solution steps

\int \frac{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 cos (2 x) d x

Apply u-substitution

: \int cos (u) \frac{1}{2} d u

= \frac{1}{2} \cdot \int cos (u) \frac{1}{2} d u

Take the constant out:

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

= \frac{1}{2} \cdot \frac{1}{2} \cdot \int cos (u) d u

Use the common integral:

\int cos (u) d u = sin (u)

= \frac{1}{2} \cdot \frac{1}{2} sin (u)

Substitute back

u = 2 x

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

Simplify

\frac{1}{2} \cdot \frac{1}{2} sin (2 x) : \frac{1}{4} sin (2 x)

= \frac{1}{4} sin (2 x)

Add a constant to the solution

= \frac{1}{4} sin (2 x) + C

x \to - 2 lim (\frac{x ^{2} + 6}{x + 2})

\int (\frac{ln ^{2} ( x )}{x}) d x

f (x) = 6 - x^{2}

\int \frac{7 + x}{x} d x

\frac{d}{d x} (x - cos (x))

What is the integral of (cos(2x))/2 ?
The integral of (cos(2x))/2 is 1/4 sin(2x)+C