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
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

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