# How do you use substitution to integrate #cos x/sin x dx#?

The procedure is outlined below.

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To integrate (\frac{\cos(x)}{\sin(x)} , dx) using substitution, let (u = \sin(x)). Then, (du = \cos(x) , dx). Substituting these into the integral gives (\int \frac{1}{u} , du), which integrates to (\ln|u| + C). Finally, replace (u) with (\sin(x)) to obtain the final answer: (\ln|\sin(x)| + C).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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