What is the integral of-56cos(7z-5) ?

The integral of-56cos(7z-5) is -8sin(7z-5)+C

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integral of-56cos(7z-5)

\int - 56 cos (7 z - 5) d z

- 8 sin (7 z - 5) + C

Solution steps

\int - 56 cos (7 z - 5) d z

Take the constant out:

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

= - 56 \cdot \int cos (7 z - 5) d z

Apply u-substitution

: \int cos (u) \frac{1}{7} d u

= - 56 \cdot \int cos (u) \frac{1}{7} d u

Take the constant out:

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

= - 56 \cdot \frac{1}{7} \cdot \int cos (u) d u

Use the common integral:

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

= - 56 \cdot \frac{1}{7} sin (u)

Substitute back

u = 7 z - 5

= - 56 \cdot \frac{1}{7} sin (7 z - 5)

Simplify

- 56 \cdot \frac{1}{7} sin (7 z - 5) : - 8 sin (7 z - 5)

= - 8 sin (7 z - 5)

Add a constant to the solution

= - 8 sin (7 z - 5) + C

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What is the integral of-56cos(7z-5) ?
The integral of-56cos(7z-5) is -8sin(7z-5)+C