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