What is the integral of tan^2(x)-1 ?

The integral of tan^2(x)-1 is -2x+tan(x)+C

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integral of tan^2(x)-1

\int tan^{2} (x) - 1 d x

- 2 x + tan (x) + C

Solution steps

\int tan^{2} (x) - 1 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 tan^{2} (x) d x - \int 1 d x

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

\int 1 d x = x

= - x + tan (x) - x

Simplify

= - 2 x + tan (x)

Add a constant to the solution

= - 2 x + tan (x) + C

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