What is the integral of f(x)=cos(2x) ?

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

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Find the Antiderivative f(x)=cos(2x)

integral

f (x) = cos (2 x)

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

Solution steps

\int cos (2 x) d x

Apply u-substitution

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

= \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 \int cos (u) d u

Use the common integral:

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

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

Substitute back

u = 2 x

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

Add a constant to the solution

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

\frac{- d}{d θ sin ( θ ) cos ( θ )}

(4, 5), (9, 11)

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

- \frac{d}{d t} (e^{t})

\int \frac{1}{( y ^{2} )} d y

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