Mathematics

# Integrate the following function: $\dfrac {(\log x)^{2}}{x}$

##### ANSWER

$\dfrac {(\log x)^{3}}{3}+c$

##### SOLUTION
$\displaystyle\int \dfrac{log^2x}{x}dx$.

put $logx=t$      ....... (1)

Therefore, $\dfrac{1}{x}.dx=dt$
=> $\int t^2dt$.
=> $\dfrac{t^3}{3}+C$

Put value of $t$ from eq. (1).
we get,

=> $\dfrac{(logx)^3}{3}+C$

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Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
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