# How do you find the antiderivative of #int (cscx) dx#?

One way is by trickery.

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To find the antiderivative of (\int \csc(x) , dx), you can use the method of substitution. Let (u = \csc(x) - \cot(x)), then (du = -\csc(x)\cot(x) - \csc^2(x) , dx). This simplifies to (du = -\csc(x)(\cot(x) + \csc(x)) , dx). Integrating (\int -\csc(x)(\cot(x) + \csc(x)) , dx), we get (-\ln|\csc(x) + \cot(x)| + C), where (C) is the constant of integration. Therefore, the antiderivative of (\int \csc(x) , dx) is (-\ln|\csc(x) + \cot(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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