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
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