Mathematics

Evaluate the following integral
$$\int { \cfrac { 1 }{ x\log { x }  }  } dx$$


SOLUTION
Let 
$$t=\log{x}\Rightarrow\,dt=\dfrac{1}{x}dx$$

$$\displaystyle\int{\dfrac{dx}{x\log{x}}}$$

$$=\displaystyle\int{\dfrac{dt}{t}}$$

$$=\log{\left|t\right|}+c$$

$$=\log{\left|\log{x}\right|}+c$$ where $$t=\log{x}$$
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Subjective Medium Published on 17th 09, 2020
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