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

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

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integral of cot^2(t)

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

- t - cot (t) + C

Solution steps

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

Rewrite using trig identities

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

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

\int 1 d t = t

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

= - t - cot (t)

Add a constant to the solution

= - t - cot (t) + C

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