What is the integral of 1/(tan^2(θ)) ?

The integral of 1/(tan^2(θ)) is -θ-cot(θ)+C

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integral of 1/(tan^2(θ))

\int \frac{1}{tan ^{2} ( θ )} d θ

- θ - cot (θ) + C

Solution steps

\int \frac{1}{tan ^{2} ( θ )} d θ

Rewrite using trig identities

= \int - 1 + csc^{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 csc^{2} (θ) d θ

\int 1 d θ = θ

\int csc^{2} (θ) d θ = - cot (θ)

= - θ - cot (θ)

Add a constant to the solution

= - θ - cot (θ) + C

What is the integral of 1/(tan^2(θ)) ?
The integral of 1/(tan^2(θ)) is -θ-cot(θ)+C