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Evaluate the integral: ∫log(log x)/x dx

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Evaluate the integral: ∫log(log x)/x dx

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Best answer

Take log x = t

So we get

1/x dx = dt

Here

Again by integrating the second term we get

= t log t – t + c

Replace t with log x

= log x. log (log x) – log x + c

By taking log x as common

= log x(log(log x) – 1) + c

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