What is the integral of sin(6x) ?

The integral of sin(6x) is -1/6 cos(6x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of sin(6x)

\int sin (6 x) d x

- \frac{1}{6} cos (6 x) + C

Solution steps

\int sin (6 x) d x

Apply u-substitution

: \int sin (u) \frac{1}{6} d u

= \int sin (u) \frac{1}{6} d u

Take the constant out:

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

= \frac{1}{6} \cdot \int sin (u) d u

Use the common integral:

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

= \frac{1}{6} (- cos (u))

Substitute back

u = 6 x

= \frac{1}{6} (- cos (6 x))

Simplify

= - \frac{1}{6} cos (6 x)

Add a constant to the solution

= - \frac{1}{6} cos (6 x) + C

(- 72 sin (t))^{^{'}}

y = 2 x^{3}

\frac{d}{d x} (f (x) (x)^{n})

\int \frac{x ^{5} - x ^{3} + 6 x}{x ^{4}} d x

\frac{d}{d x} (sin (3 x^{3} + 2))