integral of cotx
The integral of cot(x), denoted as ∫cot(x) dx, can be evaluated using integration techniques
The integral of cot(x), denoted as ∫cot(x) dx, can be evaluated using integration techniques. Let’s proceed with finding its antiderivative step by step.
First, let’s rewrite cot(x) as cos(x)/sin(x). The integral becomes:
∫cos(x)/sin(x) dx
To simplify it further, we can use a technique called u-substitution. We let u = sin(x) and du = cos(x) dx. This implies that dx = du / cos(x).
Substituting these values, our integral becomes:
∫1/u du
Now, we can integrate 1/u with respect to u. The integral of 1/u is ln|u| + C, where C is the constant of integration.
Therefore, the antiderivative of cot(x) is:
∫cot(x) dx = ln|sin(x)| + C
where C is the constant of integration.
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