What is the integral of csc^2(θ)-1 ?

The integral of csc^2(θ)-1 is -cot(θ)-θ+C

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integral of csc^2(θ)-1

\int csc^{2} (θ) - 1 d θ

- cot (θ) - θ + C

Solution steps

\int csc^{2} (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 csc^{2} (θ) d θ - \int 1 d θ

\int csc^{2} (θ) d θ = - cot (θ)

\int 1 d θ = θ

= - cot (θ) - θ

Add a constant to the solution

= - cot (θ) - θ + C

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