Mathematics

Prove that:
$$\displaystyle \int \dfrac {(\log x)^{2}}{x}dx$$


SOLUTION
$$I = \int \frac{(logx)^{2}}{x}dx  $$ let logx=t
                             $$\Rightarrow \frac{1}{x}dx=dt$$
$$\Rightarrow I=\int t^{2}dt=\frac{t^{3}}{3}+c=\frac{(logx)^{3}}{3}+c$$
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Subjective Medium Published on 17th 09, 2020
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