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

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

 

Hence, this is the answer.
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Subjective Medium Published on 17th 09, 2020
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