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