What is the integral of (6+tan^2(x)) ?

The integral of (6+tan^2(x)) is 5x+tan(x)+C

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integral of (6+tan^2(x))

\int (6 + tan^{2} (x)) d x

5 x + tan (x) + C

Solution steps

\int 6 + 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 6 d x + \int tan^{2} (x) d x

\int 6 d x = 6 x

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

= 6 x - x + tan (x)

Simplify

= 5 x + tan (x)

Add a constant to the solution

= 5 x + tan (x) + C

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What is the integral of (6+tan^2(x)) ?
The integral of (6+tan^2(x)) is 5x+tan(x)+C