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

The integral of 3sin(3x) is -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 3sin(3x)

\int 3 sin (3 x) d x

- cos (3 x) + C

Solution steps

\int 3 sin (3 x) d x

Take the constant out:

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

= 3 \cdot \int sin (3 x) d x

Apply u-substitution

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

= 3 \cdot \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

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

Use the common integral:

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

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

Substitute back

u = 3 x

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

Simplify

3 \cdot \frac{1}{3} (- cos (3 x)) : - cos (3 x)

= - cos (3 x)

Add a constant to the solution

= - cos (3 x) + C

\frac{d}{d x} (3 cos (x) - 5 cot (x))

(x y^{2}) d x + (1 + x^{2} y) d y = 0

\frac{d}{d x} (4 + \frac{8}{x})^{2} + (2 + x)^{2}

y = x^{2} - 1, x = 1, x = 3

\int 3 x ln (4 x) d x