What is the integral of 40sin(5y+4) ?

The integral of 40sin(5y+4) is -8cos(5y+4)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of 40sin(5y+4)

\int 40 sin (5 y + 4) d y

- 8 cos (5 y + 4) + C

Solution steps

\int 40 sin (5 y + 4) d y

Take the constant out:

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

= 40 \cdot \int sin (5 y + 4) d y

Apply u-substitution

= 40 \cdot \int sin (u) \frac{1}{5} d u

Take the constant out:

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

= 40 \cdot \frac{1}{5} \cdot \int sin (u) d u

Use the common integral:

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

= 40 \cdot \frac{1}{5} (- cos (u))

Substitute back

u = 5 y + 4

= 40 \cdot \frac{1}{5} (- cos (5 y + 4))

Simplify

40 \cdot \frac{1}{5} (- cos (5 y + 4)) : - 8 cos (5 y + 4)

= - 8 cos (5 y + 4)

Add a constant to the solution

= - 8 cos (5 y + 4) + C

What is the integral of 40sin(5y+4) ?
The integral of 40sin(5y+4) is -8cos(5y+4)+C