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

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

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

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

2 csc (2 x) + C

Solution steps

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

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

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

= tan (x) - (- cot (x))

Simplify

tan (x) - (- cot (x)) : 2 csc (2 x)

= 2 csc (2 x)

Add a constant to the solution

= 2 csc (2 x) + C

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