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
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