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

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

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integral of 2tan^2(x)-cot^2(x)

integral

2 tan^{2} (x) - cot^{2} (x)

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

Solution steps

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

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

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

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

Simplify

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

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

Add a constant to the solution

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

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