How do you integrate cot²(x)dx?

We will use the identity cosec²x = 1 + cot²x to integrate cot²(x)dx.

Answer: ∫ cot²(x)dx = -cot x-x+C .

Let's integrate cot²(x)dx.

Explanation:

We know that,

cosec²x = 1 + cot²x

Hence,

cot²x = cosec²x - 1

Now,

∫cot²(x)dx = ∫(cosec²x−1)dx

=∫cosec²(x)dx − ∫1.dx

=−cotx −x +C

Thus, ∫cot²(x)dx = - cot x - x + C