How to Find the Integral of cot(x) Using Substitution Technique: Step-by-Step Guide

∫cot(x)dx

To find the integral of cot(x), we need to use a substitution technique

To find the integral of cot(x), we need to use a substitution technique. Let’s assume u = sin(x), which means du = cos(x)dx.

Now, let’s rewrite the integral using this substitution:
∫cot(x)dx = ∫cot(x) * (cos(x)dx)/(cos(x)) = ∫(cos(x)/sin(x)) * (cos(x)dx)

Substituting u = sin(x) and du = cos(x)dx, we get:
∫(cos(x)/sin(x)) * (cos(x)dx) = ∫(1/u) * du

Now, the integral becomes:
∫(1/u) * du = ln|u| + C

Remember that u = sin(x), so we have:
∫cot(x)dx = 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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