# How do you calculate #int\ ln(x)^ln(x)(1/x+ln(ln(x))/x)\ dx# ?

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To calculate the integral ∫ln(x)^(ln(x))(1/x + ln(ln(x))/x) dx, you can use integration by parts. Let u = ln(x)^(ln(x)) and dv = (1/x + ln(ln(x))/x) dx. Then, differentiate u to find du and integrate dv to find v. After that, you can apply the integration by parts formula:

∫u dv = uv - ∫v du

Substitute the values of u, dv, v, and du into the formula and perform the integration to find the result.

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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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