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Find the integral of the cotangent

by RoRi

Evaluate the following integral:

    \[ \int \cot x \, dx. \]

Since cotangent is cosine divided by sine, we first write,

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

Then, we let u = \sin x and so du = \cos x \, dx. Therefore, we have

    \begin{align*} \int \cot x \, dx &= \int \frac{\cos x}{\sin x} \, dx \\ &= \int \frac{1}{u} \, du \\ &= \log |u| + C \\ &= \log |\sin x| + C. \end{align*}

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