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

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

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integral of tan^2(w)

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

- w + tan (w) + C

Solution steps

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

Rewrite using trig identities

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

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

\int 1 d w = w

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

= - w + tan (w)

Add a constant to the solution

= - w + tan (w) + C

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