What is the integral of (cos(3θ)-1) ?

The integral of (cos(3θ)-1) is 1/3 sin(3θ)-θ+C

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integral of (cos(3θ)-1)

\int (cos (3 θ) - 1) d θ

\frac{1}{3} sin (3 θ) - θ + C

Solution steps

\int cos (3 θ) - 1 d θ

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int cos (3 θ) d θ - \int 1 d θ

\int cos (3 θ) d θ = \frac{1}{3} sin (3 θ)

\int 1 d θ = θ

= \frac{1}{3} sin (3 θ) - θ

Add a constant to the solution

= \frac{1}{3} sin (3 θ) - θ + C

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What is the integral of (cos(3θ)-1) ?
The integral of (cos(3θ)-1) is 1/3 sin(3θ)-θ+C