What is the integral of cos(θ)(tan(θ)+sec(θ)) ?

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

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integral of cos(θ)(tan(θ)+sec(θ))

\int cos (θ) (tan (θ) + sec (θ)) d θ

- cos (θ) + θ + C

Solution steps

\int cos (θ) (tan (θ) + sec (θ)) d θ

Rewrite using trig identities

= \int sin (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 sin (θ) d θ + \int 1 d θ

\int sin (θ) d θ = - cos (θ)

\int 1 d θ = θ

= - cos (θ) + θ

Add a constant to the solution

= - cos (θ) + θ + C

\frac{\partial}{\partial x} (x^{5} e^{x y})

- sec (10 x)

\frac{d}{d y} (x^{2} (y - x))

\frac{d}{d y} (y sin (x))

(x^{5} - x^{3} + 3)^{4}

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