What is the integral of 12sin(2x) ?

The integral of 12sin(2x) is -6cos(2x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 12sin(2x)

\int 12 sin (2 x) d x

- 6 cos (2 x) + C

Solution steps

\int 12 sin (2 x) d x

Take the constant out:

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

= 12 \cdot \int sin (2 x) d x

Apply u-substitution

: \int sin (u) \frac{1}{2} d u

= 12 \cdot \int sin (u) \frac{1}{2} d u

Take the constant out:

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

= 12 \cdot \frac{1}{2} \cdot \int sin (u) d u

Use the common integral:

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

= 12 \cdot \frac{1}{2} (- cos (u))

Substitute back

u = 2 x

= 12 \cdot \frac{1}{2} (- cos (2 x))

Simplify

12 \cdot \frac{1}{2} (- cos (2 x)) : - 6 cos (2 x)

= - 6 cos (2 x)

Add a constant to the solution

= - 6 cos (2 x) + C

\int \frac{1}{x ( 1 - 2 ln ( x ) )} d x

\int (p^{- 1} + \frac{4}{x}) d x

\int x \cdot x + 2 + 2 \cdot x + 2 d x

\int (2 - s) s d s

\int x 64 - x^{2} d x