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Answered question

2021-10-23

Evaluate the following integrals. Include absolute values only when needed.

\int \frac{d x}{x \ln x (\ln x)}

Obiajulu

Skilled2021-10-24Added 98 answers

Given integral,

I = \int \frac{d x}{x \ln x \ln (\ln x)}

Let,

\ln x = t

Differentiation,

\frac{1}{x} d x = d t

The integral becomes,

I = \int \frac{d t}{t \ln (t)}

Let,

\ln (t) = u

Differentiation,

\frac{1}{t} d t = d u

I = \int \frac{d u}{u}

I = \ln u + C

Substitution back,

u = \ln t

I = \ln (\ln t) + C

Substitution back,

t = \ln x

I = \ln (\ln (\ln x)) + C

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