What is the integral of sin(3x) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of sin(3x)

\int sin (3 x) d x

- \frac{1}{3} cos (3 x) + C

Solution steps

\int sin (3 x) d x

Apply u-substitution

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

= \int sin (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 sin (u) d u

Use the common integral:

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

= \frac{1}{3} (- cos (u))

Substitute back

u = 3 x

= \frac{1}{3} (- cos (3 x))

Simplify

= - \frac{1}{3} cos (3 x)

Add a constant to the solution

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

\frac{d}{d x} (\frac{6}{1 + 6 x})

\int (5 x^{14} - 11 x^{32}) d x

x d y = y d x

\frac{d}{d x} (3 x^{4} ln (x))

\int 8 e^{2 x} + 6 x d x