# How do you find the integral of #sin(lnx) dx#?

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To find the integral of (\sin(\ln(x)) , dx), use the substitution method. Let (u = \ln(x)), then (du = \frac{1}{x} , dx). After substitution, the integral becomes:

[ \int \sin(u) , du ]

This is a standard integral, which equals (-\cos(u) + C), where (C) is the constant of integration. Substitute (u) back in terms of (x), and you will have your final answer.

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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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