What is the integral of cos(3xy) ?

The integral of cos(3xy) is 1/(3y)sin(3yx)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of cos(3xy)

\int cos (3 x y) d x

\frac{1}{3 y} sin (3 y x) + C

Solution steps

\int cos (3 x y) d x

Apply u-substitution

= \int \frac{cos ( u )}{3 y} d u

Take the constant out:

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

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

Use the common integral:

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

= \frac{1}{3 y} sin (u)

Substitute back

u = 3 y x

= \frac{1}{3 y} sin (3 y x)

Add a constant to the solution

= \frac{1}{3 y} sin (3 y x) + C