∫cot(x)dx
To find the integral of cot(x) with respect to x, we will use the technique of integration by substitution
To find the integral of cot(x) with respect to x, we will use the technique of integration by substitution.
Step 1: Let’s start by using a trigonometric identity to rewrite cot(x) in terms of sine and cosine:
cot(x) = cos(x)/sin(x)
Step 2: Now let u = sin(x). We will differentiate both sides of this equation to find du:
du/dx = cos(x)
du = cos(x)dx
Step 3: Substitute the value of cot(x) and du into the integral:
∫cot(x)dx = ∫(cos(x)/sin(x))dx
= ∫(1/u)du
Step 4: Simplify the integral:
∫(1/u)du = ln|u| + C
Step 5: Replace u with sin(x):
ln|sin(x)| + C
Therefore, the integral of cot(x) with respect to x is ln|sin(x)| + C, where C is the constant of integration.
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