What is the integral of 1/6 sin(6x) ?

The integral of 1/6 sin(6x) is -1/36 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 1/6 sin(6x)

\int \frac{1}{6} sin (6 x) d x

- \frac{1}{36} cos (6 x) + C

Solution steps

\int \frac{1}{6} sin (6 x) d x

Take the constant out:

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

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

Apply u-substitution

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

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

Use the common integral:

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

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

Substitute back

u = 6 x

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

Simplify

\frac{1}{6} \cdot \frac{1}{6} (- cos (6 x)) : - \frac{1}{36} cos (6 x)

= - \frac{1}{36} cos (6 x)

Add a constant to the solution

= - \frac{1}{36} cos (6 x) + C

y^{^{''}} + a y^{^{'}} + b y = 0

\int x a^{2} - x^{2} d x

f (x) = (x^{2} \cdot 7^{x})^{7}

x \to \infty lim (\frac{sin ( 2 x )}{x})

x = 4 y - 8, x = 4 y + 1

What is the integral of 1/6 sin(6x) ?
The integral of 1/6 sin(6x) is -1/36 cos(6x)+C