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
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