To integrate the function cot²x with respect to x, we can use a standard trigonometric identity and a basic integral rule.
First, recall the identity:
cot²x = csc²x – 1
This identity allows us to rewrite our integral as follows:
∫cot²x dx = ∫(csc²x – 1) dx
Now we can split the integral into two separate parts:
∫cot²x dx = ∫csc²x dx – ∫1 dx
Next, we can integrate each part individually:
- ∫csc²x dx = -cot x + C
- ∫1 dx = x + C
Putting it all together, we have:
∫cot²x dx = (-cot x + C) – (x + C) = -cot x – x + C
So, the final answer for the integral of cot²x with respect to x is:
∫cot²x dx = -cot x – x + C