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

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

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

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

tan (x) + cos (x) + C

Solution steps

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

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

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

= tan (x) - (- cos (x))

Simplify

= tan (x) + cos (x)

Add a constant to the solution

= tan (x) + cos (x) + C

x, x = 4

\int \frac{3 x + 1}{( x - 2 ) ( x + 3 )} d x

\int x - ln (x) d x

\int_{0}^{\frac{π}{8}} cos^{2} (2 x) d x

x^{5} cos (x^{2})

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