Answer
$$\int\cot xdx=\ln|\sin x|+C$$
Work Step by Step
$$A=\int\cot xdx$$ $$A=\int\frac{\cos x}{\sin x}dx$$
Let $u=\sin x$
Then we have $du=\cos xdx$.
Substitute into $A$: $$A=\int\frac{1}{u}du$$ $$A=\ln|u|+C$$ $$A=\ln|\sin x|+C$$
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