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

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

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integral of 2tan^2(x)

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

2 (- x + tan (x)) + C

Solution steps

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

Rewrite using trig identities

= 2 \cdot \int - 1 + sec^{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

= 2 (- \int 1 d x + \int sec^{2} (x) d x)

\int 1 d x = x

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

= 2 (- x + tan (x))

Add a constant to the solution

= 2 (- x + tan (x)) + C

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