** Tip:** See my list of the Most Common Mistakes in English. It will teach you how to avoid mistakes with commas, prepositions, irregular verbs, and much more (PDF Version).

To integrate $\cot(x)$, recall that

$$
\cot(x) = \frac{\cos(x)}{\sin(x)}\,,
$$
so

$$
∫ \cot(x)\,dx = ∫ \frac{\cos(x)}{\sin(x)}\,dx\,.
$$
By choosing $u = \sin(x)$, that is, “$du = \cos(x)\,dx$” (in quotation marks because this expression does not make sense mathematically, but it does work formally), we get
$$
∫ \frac{\cos(x)}{\sin(x)}\,dx = ∫ \frac{1}{u}\,du = \log(u)+C = \log(\sin(x))+C
$$
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**Where to go next?** *Check out my other* articles about Mathematics