What is the integral of (cos(x)-sec(x)) ?

The integral of (cos(x)-sec(x)) is sin(x)-ln|tan(x)+sec(x)|+C

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integral of (cos(x)-sec(x))

\int (cos (x) - sec (x)) d x

sin (x) - ln ∣ tan (x) + sec (x) ∣ + C

Solution steps

\int cos (x) - sec (x) d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int cos (x) d x - \int sec (x) d x

\int cos (x) d x = sin (x)

\int sec (x) d x = ln ∣ tan (x) + sec (x) ∣

= sin (x) - ln ∣ tan (x) + sec (x) ∣

Add a constant to the solution

= sin (x) - ln ∣ tan (x) + sec (x) ∣ + C

(t + 5)^{\frac{2}{3}} (3 t^{2} - 2)^{3}

\frac{d y}{d x} + 5 y = 70, y (1) = 110

x \to 10 lim (\frac{7 x ^{2} - 70 x}{x ^{2} - 100})

\int cos (0.5 x) d x

e^{- \frac{x}{2}}

What is the integral of (cos(x)-sec(x)) ?
The integral of (cos(x)-sec(x)) is sin(x)-ln|tan(x)+sec(x)|+C