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

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

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

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

- 2 tan (x) + C

Solution steps

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

\int 2 d x = 2 x

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

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

Simplify

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

= - 2 tan (x)

Add a constant to the solution

= - 2 tan (x) + C

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