# How do you find the indefinite integral of #int 1/(x-5)#?

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To find the indefinite integral of (\int \frac{1}{x-5} , dx), you can use a simple substitution method. Let (u = x - 5). Then (du = dx). Substitute these into the integral:

(\int \frac{1}{x-5} , dx = \int \frac{1}{u} , du).

This simplifies to (\ln|u| + C), where (C) is the constant of integration.

Finally, substitute back (u = x - 5):

(\int \frac{1}{x-5} , dx = \ln|x-5| + 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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