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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (cos(3x))

\int (cos (3 x)) d x

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

Solution steps

\int cos (3 x) d x

Apply u-substitution

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

= \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 \int cos (u) d u

Use the common integral:

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

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

Substitute back

u = 3 x

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

Add a constant to the solution

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

\frac{\partial}{\partial x} (2 x - x^{2} y + x y^{2})

\int 5 cos^{2} (x) sin (2 x) d x

\frac{d}{d x} (sin (9))

x \to 0 lim (e^{x s i n (\frac{1}{x})})

y = 3