What is the integral of tan^2(θ) ?

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

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integral of tan^2(θ)

\int tan^{2} (θ) d θ

- θ + tan (θ) + C

Solution steps

\int tan^{2} (θ) d θ

Rewrite using trig identities

= \int - 1 + sec^{2} (θ) d θ

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 θ + \int sec^{2} (θ) d θ

\int 1 d θ = θ

\int sec^{2} (θ) d θ = tan (θ)

= - θ + tan (θ)

Add a constant to the solution

= - θ + tan (θ) + C