Answer
$$\int\cot xdx=\ln|\sin x|+c$$
Work Step by Step
To evaluate the integral
$$\int\cot xdx=\int\frac{\cos x}{\sin x}dx$$
we will use substitution $\sin x=t$ which gives us $\cos xdx=dt$. Putting this into the integral we get:
$$\int\frac{\cos x}{\sin x}dx=\int\frac{1}{t}dt=\ln|t|+c$$
where $c$ is arbitrary constant. Now we have to express solution in terms of $x$:
$$\int\cot xdx=\ln|t|+c=\ln|\sin x|+c$$