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

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

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integral of cot^2(u)

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

- u - cot (u) + C

Solution steps

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

Rewrite using trig identities

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

\int 1 d u = u

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

= - u - cot (u)

Add a constant to the solution

= - u - cot (u) + C