Mathematics

Solve $\displaystyle\int\dfrac{{{{\left( {\log \,x} \right)}^2}}}{x}$

SOLUTION

Consider the given integral.

$I=\int{\dfrac{{{\left( \log x \right)}^{2}}}{x}}dx$

Let $t=\log x$

$dt=\dfrac{dx}{x}$

Therefore,

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

$I=\dfrac{{{t}^{3}}}{3}+C$

On putting the value of $t$, we get

$I=\dfrac{{{\left( \log x \right)}^{3}}}{3}+C$

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 111

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