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\int \cot x\,dx\,

The first step here is not a substitution. First, we must change the integral by using trigonometric identities.

\int \cot x\,dx=\int {\frac  {\cos x}{\sin x}}\,dx\,

Now, we are ready to do our substitution.

u=\sin x\,

du=\cos x\,


\int {\frac  {\cos x}{\sin x}}\,dx=\int {\frac  {du}{u}}=\ln |u|+C=\ln |\sin x|+C\,

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