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What is the antiderivative of #[ln(ln x)]/x#?

Answer 1

Ezekiel Alexander

#ln(x)ln(ln(x))-ln(x)+C#

#d/(dx)(ln(x)ln(ln(x)))=ln(ln(x))/x+1/x# so

#int ln(ln(x))/x dx = ln(x)ln(ln(x))-ln(x)+C#

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Answer 2

William Abdalla

The antiderivative of (\frac{{\ln(\ln x)}}{x}) is (\frac{1}{2} \left(\ln(\ln x)\right)^2 + C), where (C) is the constant of integration.

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Answer from HIX Tutor

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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