What is the integral of-4+tan^2(x) ?

The integral of-4+tan^2(x) is -5x+tan(x)+C

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integral of-4+tan^2(x)

\int - 4 + tan^{2} (x) d x

- 5 x + tan (x) + C

Solution steps

\int - 4 + 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 4 d x + \int tan^{2} (x) d x

\int 4 d x = 4 x

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

= - 4 x - x + tan (x)

Simplify

= - 5 x + tan (x)

Add a constant to the solution

= - 5 x + tan (x) + C

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