What is the integral of sec^2(θ)-sin(θ) ?

The integral of sec^2(θ)-sin(θ) is tan(θ)+cos(θ)+C

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integral of sec^2(θ)-sin(θ)

\int sec^{2} (θ) - sin (θ) d θ

tan (θ) + cos (θ) + C

Solution steps

\int sec^{2} (θ) - sin (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 sec^{2} (θ) d θ - \int sin (θ) d θ

\int sec^{2} (θ) d θ = tan (θ)

\int sin (θ) d θ = - cos (θ)

= tan (θ) - (- cos (θ))

Simplify

= tan (θ) + cos (θ)

Add a constant to the solution

= tan (θ) + cos (θ) + C

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