Learn How Do You Integrate Cot2xdx

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# How do you integrate cot^{2}(x)dx?

We will use the identity cosec^{2}x = 1 + cot^{2}x to integrate cot^{2}(x)dx.

## Answer: ∫ cot^{2}(x)dx = -cot x-x+C .

Let's integrate cot^{2}(x)dx.

**Explanation:**

We know that,

cosec^{2}x = 1 + cot^{2}x

Hence,

cot^{2}x = cosec^{2}x - 1

Now,

∫cot^{2}(x)dx = ∫(cosec^{2}x−1)dx

=∫cosec^{2}(x)dx − ∫1.dx

=−cotx −x +C

### Thus, ∫cot^{2}(x)dx = - cot x - x + C

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