What is the integral of [1-cos^2(θ)sec(θ)] ?

The integral of [1-cos^2(θ)sec(θ)] is θ-sin(θ)+C

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integral of [1-cos^2(θ)sec(θ)]

\int [1 - cos^{2} (θ) sec (θ)] d θ

θ - sin (θ) + C

Solution steps

\int 1 - cos^{2} (θ) sec (θ) d θ

Simplify

1 - cos^{2} (θ) sec (θ) : 1 - cos (θ)

= \int 1 - cos (θ) 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 1 d θ - \int cos (θ) d θ

\int 1 d θ = θ

\int cos (θ) d θ = sin (θ)

= θ - sin (θ)

Add a constant to the solution

= θ - sin (θ) + C

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What is the integral of [1-cos^2(θ)sec(θ)] ?
The integral of [1-cos^2(θ)sec(θ)] is θ-sin(θ)+C