Mathematics

# Evaluate the following integral$\int { \cfrac { 1 }{ x\log { x } \log { \left( \log { x } \right) } } } dx\quad$

##### SOLUTION
Let $t=\log{x}\Rightarrow\,dt=\dfrac{1}{x}dx$

$\displaystyle\int{\dfrac{dx}{x\log{x}\log{\left(\log{x}\right)}}}$

$=\displaystyle\int{\dfrac{dt}{t\log{t}}}$

Let
$u=\log{t}\Rightarrow\,du=\dfrac{1}{t}dt$

$=\displaystyle\int{\dfrac{du}{u}}$

$=\log{u}+c$

$=\log{\log{t}}+c$ where $u=\log{t}$

$=\log { \left[ \log { \left( \log { x } \right) } \right] } +C$ where $t=\log{x}$

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86

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