What is the integral of cot^2(z) ?

The integral of cot^2(z) is -z-cot(z)+C

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integral of cot^2(z)

\int cot^{2} (z) d z

- z - cot (z) + C

Solution steps

\int cot^{2} (z) d z

Rewrite using trig identities

= \int - 1 + csc^{2} (z) d z

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 z + \int csc^{2} (z) d z

\int 1 d z = z

\int csc^{2} (z) d z = - cot (z)

= - z - cot (z)

Add a constant to the solution

= - z - cot (z) + C