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

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

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integral of tan^2(u)

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

- u + tan (u) + C

Solution steps

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

Rewrite using trig identities

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

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 u + \int sec^{2} (u) d u

\int 1 d u = u

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

= - u + tan (u)

Add a constant to the solution

= - u + tan (u) + C