Mathematics

$$\int { \log { \left( \log { x }  \right) +\dfrac { 1 }{ \log { x }  }  }  } dx$$


ANSWER

$$x\log { \left( \log { x } \right) +c }$$


SOLUTION
$$\int {\left[ {\log x\left( {\log x} \right) + \dfrac{1}{{\log x}}} \right]} dx$$
$$ = \int {1.\log \left( {\log x} \right)dx + \int {\dfrac{1}{{\log x}}} } $$
$$ = \log \left( {\log x} \right).x-\int {\dfrac{1}{{\log x}} \times \dfrac{1}{x} \times xdx + \int {\dfrac{{dx}}{{\log x}}} } $$
$$ = x\log \left( {\log x} \right) - \int {\dfrac{{dx}}{{\log x}} + \int {\dfrac{{dx}}{{\log x}}} } $$
$$ = x\log \left( {\log x} \right) + c$$
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Single Correct Medium Published on 17th 09, 2020
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