integral of cot(x) dx

The integral of cot(x) can be found using integration by substitution. Let’s start by using the substitution

u = sin(x),

which means that du/dx = cos(x) and dx = du/cos(x).

Using this substitution, we can rewrite the integral of cot(x) as follows:

∫cot(x)dx = ∫cos(x)/sin(x) dx
= ∫(1/u)du
= ln|u| + C
= ln|sin(x)| + C

Therefore, the integral of cot(x) is ln|sin(x)| + C, where C is the constant of integration.