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

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

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integral of-40cos(5y+4)

\int - 40 cos (5 y + 4) d y

- 8 sin (5 y + 4) + C

Solution steps

\int - 40 cos (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 cos (5 y + 4) d y

Apply u-substitution

: \int cos (u) \frac{1}{5} d u

= - 40 \cdot \int cos (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 cos (u) d u

Use the common integral:

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

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

Substitute back

u = 5 y + 4

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

Simplify

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

= - 8 sin (5 y + 4)

Add a constant to the solution

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

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