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

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

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

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

- 2 cot (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 cot (2 x)

= - 2 cot (2 x)

Add a constant to the solution

= - 2 cot (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 -2cot(2x)+C