How do you integrate #ln(b/x)dx#?
Please see the explanation
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To integrate ln(b/x)dx, where b is a constant:

Use the substitution method: Let u = ln(b/x), then du = (1/x)dx.

Rewrite the integral in terms of u: ∫ln(b/x)dx = ∫u du

Integrate with respect to u: ∫u du = (u^2 / 2) + C

Substitute back for u: = (ln(b/x))^2 / 2 + C

Simplify the result if needed.
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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