What is the integral of ycos(yz) ?

The integral of ycos(yz) is sin(yz)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of ycos(yz)

\int y cos (yz) d z

sin (yz) + C

Solution steps

\int y cos (yz) d z

Take the constant out:

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

= y \cdot \int cos (yz) d z

Apply u-substitution

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

Take the constant out:

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

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

Use the common integral:

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

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

Substitute back

u = yz

= y \frac{1}{y} sin (yz)

Simplify

y \frac{1}{y} sin (yz) : sin (yz)

= sin (yz)

Add a constant to the solution

= sin (yz) + C