What is the integral of (cos(3x))/3 ?

The integral of (cos(3x))/3 is 1/9 sin(3x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of (cos(3x))/3

\int \frac{cos ( 3 x )}{3} d x

\frac{1}{9} sin (3 x) + C

Solution steps

\int \frac{cos ( 3 x )}{3} d x

Take the constant out:

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

= \frac{1}{3} \cdot \int cos (3 x) d x

Apply u-substitution

= \frac{1}{3} \cdot \int cos (u) \frac{1}{3} d u

Take the constant out:

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

= \frac{1}{3} \cdot \frac{1}{3} \cdot \int cos (u) d u

Use the common integral:

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

= \frac{1}{3} \cdot \frac{1}{3} sin (u)

Substitute back

u = 3 x

= \frac{1}{3} \cdot \frac{1}{3} sin (3 x)

Simplify

\frac{1}{3} \cdot \frac{1}{3} sin (3 x) : \frac{1}{9} sin (3 x)

= \frac{1}{9} sin (3 x)

Add a constant to the solution

= \frac{1}{9} sin (3 x) + C

What is the integral of (cos(3x))/3 ?
The integral of (cos(3x))/3 is 1/9 sin(3x)+C