What is the integral of 56cos(8z-5) ?

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

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integral of 56cos(8z-5)

\int 56 cos (8 z - 5) d z

7 sin (8 z - 5) + C

Solution steps

\int 56 cos (8 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 (8 z - 5) d z

Apply u-substitution

: \int cos (u) \frac{1}{8} d u

= 56 \cdot \int cos (u) \frac{1}{8} d u

Take the constant out:

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

= 56 \cdot \frac{1}{8} \cdot \int cos (u) d u

Use the common integral:

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

= 56 \cdot \frac{1}{8} sin (u)

Substitute back

u = 8 z - 5

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

Simplify

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

= 7 sin (8 z - 5)

Add a constant to the solution

= 7 sin (8 z - 5) + C

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