What is the integral of sec^2(x)-3csc^2(x) ?

The integral of sec^2(x)-3csc^2(x) is tan(x)+3cot(x)+C

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integral of sec^2(x)-3csc^2(x)

\int sec^{2} (x) - 3 csc^{2} (x) d x

tan (x) + 3 cot (x) + C

Solution steps

\int sec^{2} (x) - 3 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 3 csc^{2} (x) d x

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

\int 3 csc^{2} (x) d x = - 3 cot (x)

= tan (x) - (- 3 cot (x))

Simplify

= tan (x) + 3 cot (x)

Add a constant to the solution

= tan (x) + 3 cot (x) + C

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What is the integral of sec^2(x)-3csc^2(x) ?
The integral of sec^2(x)-3csc^2(x) is tan(x)+3cot(x)+C