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

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

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integral of cot^2(y)

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

- y - cot (y) + C

Solution steps

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

Rewrite using trig identities

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

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

\int 1 d y = y

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

= - y - cot (y)

Add a constant to the solution

= - y - cot (y) + C