Mathematics

Evaluate :
$$\displaystyle\int{\dfrac { \left( logx \right) ^{ 2 } }{ x }dx} $$


SOLUTION
$$\displaystyle\int{\dfrac{{\left(\log{x}\right)}^{2}}{x}dx}$$

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

$$=\displaystyle\int{{t}^{2}dt}$$

$$=\dfrac{{t}^{3}}{3}+c$$ where $$c$$ is the constant of integration.

$$=\dfrac{{\left(\log{x}\right)}^{3}}{3}+c$$
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Subjective Medium Published on 17th 09, 2020
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