What is the integral of cos(2kx) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of cos(2kx)

\int cos (2 k x) d x

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

Solution steps

\int cos (2 k x) d x

Apply u-substitution

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

Take the constant out:

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

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

Use the common integral:

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

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

Substitute back

u = 2 k x

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

Add a constant to the solution

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