Mathematics

Solve :
$$\displaystyle \int \frac{1}{x+x\log x}dx.$$


ANSWER

$$\displaystyle \log \left ( 1+\log x \right ).$$


SOLUTION
Let $$ \displaystyle I=\int  \frac { 1 }{ x+x\log  x } dx=\int  \frac { 1 }{ x\left( 1+\log  x \right)  } dx$$

Put $$ \displaystyle 1+\log  x=t\Rightarrow \frac { 1 }{ x } dx=dt$$

Therefore 

$$ \displaystyle I=\int { \frac { dt }{ t }  } =\log { t } =\log  \left( 1+\log  x \right) $$
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Single Correct Medium Published on 17th 09, 2020
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