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

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

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integral of-56sin(7z-5)

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

8 cos (7 z - 5) + C

Solution steps

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

Apply u-substitution

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

= - 56 \cdot \int sin (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 sin (u) d u

Use the common integral:

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

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

Substitute back

u = 7 z - 5

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

Simplify

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

= 8 cos (7 z - 5)

Add a constant to the solution

= 8 cos (7 z - 5) + C

\frac{d}{d x} (3 2 x^{2})

\int \frac{1}{x ^{5} \cdot x ^{2} - 1} d x

\frac{\partial}{\partial x} (4 x y)

3 t^{2} + 2 t - 2

\frac{6 x ^{2} + 6 x + 4}{x}

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