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

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

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

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

sec (x) + cot (x) + C

Solution steps

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

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

\int (csc (x))^{2} d x = - cot (x)

= sec (x) - (- cot (x))

Simplify

= sec (x) + cot (x)

Add a constant to the solution

= sec (x) + cot (x) + C

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