What is the integral of (cos(x)-sec^2(x)) ?

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

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integral of (cos(x)-sec^2(x))

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

sin (x) - tan (x) + C

Solution steps

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

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

\int sec^{2} (x) d x = tan (x)

= sin (x) - tan (x)

Add a constant to the solution

= sin (x) - tan (x) + C

\int f (y) d y

\int (- \frac{8}{e ^{- x}} + 2 ln (x)) d x

\int \frac{x ^{4}}{2 ( 1 + x ^{5} )} d x

\int 10 x^{4} - 4 x^{2} - 14 x + 12 d x

\int (x^{7} - sec^{2} (x)) d x

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