∫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.
More Answers:
Mastering the Integration of sin(x): Unveiling the Antiderivative and Fundamental Rule of CalculusThe Integral of Cos(x): A Step-by-Step Guide for Finding the Antiderivative
Solving the Integral of Tan(x) Using Integration by Parts
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