What is the integral of-5sin(3x) ?

The integral of-5sin(3x) is 5/3 cos(3x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of-5sin(3x)

\int - 5 sin (3 x) d x

\frac{5}{3} cos (3 x) + C

Solution steps

\int - 5 sin (3 x) d x

Take the constant out:

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

= - 5 \cdot \int sin (3 x) d x

Apply u-substitution

= - 5 \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

= - 5 \cdot \frac{1}{3} \cdot \int sin (u) d u

Use the common integral:

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

= - 5 \cdot \frac{1}{3} (- cos (u))

Substitute back

u = 3 x

= - 5 \cdot \frac{1}{3} (- cos (3 x))

Simplify

- 5 \cdot \frac{1}{3} (- cos (3 x)) : \frac{5}{3} cos (3 x)

= \frac{5}{3} cos (3 x)

Add a constant to the solution

= \frac{5}{3} cos (3 x) + C