Mathematics

Evaluate the given integral.
$$\displaystyle\int { \cfrac { \log { x }  }{ x }  } dx$$


SOLUTION
$$I=\displaystyle\int{\dfrac{\log{x}}{x}dx}$$

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

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

$$=\dfrac{{t}^{2}}{2}+c$$    .........where $$c$$ is the constant of integration.

$$=\dfrac{{\left(\log{x}\right)}^{2}}{2}+c$$      ..........where $$t=\log{x}$$
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Subjective Medium Published on 17th 09, 2020
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