Mathematics

# Integrate $_{ }\displaystyle \int { \dfrac { 1 }{ y\ln y } } . dy$

##### SOLUTION
Given : $\displaystyle \int { \dfrac { 1 }{ y \ln{y} } dy }$

Let   $I=\displaystyle \int { \dfrac { 1 }{ y \ln{y} } dy }$

let  $\ln{y}=t \Rightarrow \dfrac { 1 }{ y } dy=dt$

$I=\displaystyle \int { \dfrac { 1 }{ t } dt }$

$I=\ln{t}+C$

Where $t=\ln{y}$ and $C$  is an arbitrary constant.

$\therefore I=\ln{\left( \ln{y} \right)} +C$

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

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