Mathematics

# $\displaystyle\int \dfrac{1}{x+x log x}dx$.

##### SOLUTION
$\quad \int _{ }^{ }{ \cfrac { 1 }{ x+x\log { x } } } dx=\int { \cfrac { 1 }{ x\left( 1+\log { x } \right) } } dx$
Let $\log { x } =t\Rightarrow \cfrac { 1 }{ x } dx=dt$
So, $\int _{ }^{ }{ \cfrac { 1 }{ x+x\log { x } } } dx=\int { \cfrac { dt }{ 1+t } } =\ln { \left| 1+t \right| } +C=\ln { \left| 1+\log { x } \right| } +C$

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

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