What is the integral of (4(sec(θ))^2-sin(θ)) ?

The integral of (4(sec(θ))^2-sin(θ)) is 4tan(θ)+cos(θ)+C

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integral of (4(sec(θ))^2-sin(θ))

\int (4 (sec (θ))^{2} - sin (θ)) d θ

4 tan (θ) + cos (θ) + C

Solution steps

\int 4 (sec (θ))^{2} - 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 4 (sec (θ))^{2} d θ - \int sin (θ) d θ

\int 4 (sec (θ))^{2} d θ = 4 tan (θ)

\int sin (θ) d θ = - cos (θ)

= 4 tan (θ) - (- cos (θ))

Simplify

= 4 tan (θ) + cos (θ)

Add a constant to the solution

= 4 tan (θ) + cos (θ) + C

x \to 3 lim (\frac{x + 4}{x + 7})

\int_{0}^{1} (x^{2} + 3 x + 4) d x

x \to - 3 lim (\frac{3 - x}{3 + x})

2 (ln (x) + 1)

\int \frac{1}{x ^{e}} d x

What is the integral of (4(sec(θ))^2-sin(θ)) ?
The integral of (4(sec(θ))^2-sin(θ)) is 4tan(θ)+cos(θ)+C