Evaluate the integral of cot(x) dx.

The integral of cot(x) dx is ln|sin(x)| + C.

To evaluate the integral of cot(x) dx, we can use the substitution u = sin(x) and du = cos(x) dx. Then, cot(x) dx = cos(x)/sin(x) dx = du/u. Substituting these into the integral, we get:

∫cot(x) dx = ∫cos(x)/sin(x) dx
= ∫du/u
= ln|u| + C
= ln|sin(x)| + C

Therefore, the integral of cot(x) dx is ln|sin(x)| + C. It is important to note that this integral is undefined at x = kπ, where k is an integer, since cot(x) is undefined at these points.