# How do you find the antiderivative of #sinx/(1-cosx)#?

You can simply do a u-substitution.

Let:

Therefore, the antiderivative/integral is:

We know this works because:

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To find the antiderivative of sin(x)/(1 - cos(x)), you can use a trigonometric substitution. Let u = cos(x), then du = -sin(x) dx. Substituting these into the integral, you get ∫(1/ (1 - u)) du. This integral can be evaluated using a straightforward u-substitution. After integrating, substitute back u = cos(x) to get the final antiderivative.

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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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