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

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

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

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

tan (x) - sec (x) + C

Solution steps

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

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

\int sec (x) tan (x) d x = sec (x)

= tan (x) - sec (x)

Add a constant to the solution

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

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