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

\int - 3 t^{2} cos (t) d t

n = 1 \sum \infty \frac{- 3}{2 ^{n}}

x, x^{2}, - x + 1

\frac{d}{d x} (ln (\frac{x - 1}{x + 1}))

\frac{\partial}{\partial x} (\frac{m}{x ^{a} y ^{b} z ^{c}})

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