Integrate cot x dx

To integrate the function cot(x) with respect to x, we can use a known identity and substitution method. The integral of cot(x) can be expressed as:

Integral of Cotangent

The integral is given by:

∫ cot(x) dx = ln|sin(x)| + C

Steps to Derive the Integral

• Recall that cot(x) can be rewritten as cos(x)/sin(x).
• Use the substitution method: let u = sin(x), then du = cos(x) dx.
• This transforms the integral into ∫ (1/u) du, which is a standard integral.
• The result of ∫ (1/u) du is ln|u| + C.
• Substituting back gives ln|sin(x)| + C.

Thus, the final answer for the integral of cot(x) is:

ln|sin(x)| + C