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

The integral of 4+tan^2(x) is 3x+tan(x)+C

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integral of 4+tan^2(x)

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

3 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

= 3 x + tan (x)

Add a constant to the solution

= 3 x + tan (x) + C