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

x^{- \frac{1}{2}}

\int x ln (1 + x^{2} + x) d x

\int x^{1.3} + 7 x^{2.5} d x

\int 5 cos (x) - 2 sec^{2} (x) d x

\int \frac{8 x + 1}{4 x - 3} d x

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