∫cot²(x)dx
-cot(x)-x +C
Let’s use the trigonometric identity: cot²(x) = 1 + tan²(x)
So, we can rewrite the integral as:
∫cot²(x)dx = ∫(1 + tan²(x))dx
Integrating both terms separately, we get:
∫cot²(x)dx = x + ∫tan²(x)dx
Now, we need to find the integral of tan²(x). We can use the trigonometric identity: tan²(x) = sec²(x) – 1
So, we can rewrite the integral as:
∫tan²(x)dx = ∫(sec²(x) – 1)dx
Integrating both terms separately, we get:
∫tan²(x)dx = tan(x) – x
Therefore, the final solution to the given integral is:
∫cot²(x)dx = x + tan(x) – x + C
where C is the constant of integration.
Simplifying the expression, we get:
∫cot²(x)dx = tan(x) + C
Thus, the solution to the integral of cot²(x) is tan(x) + C.
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