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

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

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

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

3 tan (x) + 2 cot (x) + C

Solution steps

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

\int 3 sec^{2} (x) d x = 3 tan (x)

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

= 3 tan (x) - (- 2 cot (x))

Simplify

= 3 tan (x) + 2 cot (x)

Add a constant to the solution

= 3 tan (x) + 2 cot (x) + C

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