What is the integral of cos(5-7θ) ?

The integral of cos(5-7θ) is -1/7 sin(5-7θ)+C

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integral of cos(5-7θ)

\int cos (5 - 7 θ) d θ

- \frac{1}{7} sin (5 - 7 θ) + C

Solution steps

\int cos (5 - 7 θ) d θ

Apply u-substitution

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

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

Take the constant out:

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

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

Use the common integral:

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

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

Substitute back

u = 5 - 7 θ

= - \frac{1}{7} sin (5 - 7 θ)

Add a constant to the solution

= - \frac{1}{7} sin (5 - 7 θ) + C

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What is the integral of cos(5-7θ) ?
The integral of cos(5-7θ) is -1/7 sin(5-7θ)+C