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Integrate the function
$\frac{(\log x)^2}{x}$
$\frac{(\log x)^2}{x}$
Solution:
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Verified Answer
Let $\log x=t \Rightarrow \frac{1}{x} d x=d t$
$\therefore \int \frac{(\log x)^2}{x} d x=\int t^2 d t=\frac{t^3}{3}+\mathrm{C}=\frac{1}{3}(\log x)^3+\mathrm{C}$
$\therefore \int \frac{(\log x)^2}{x} d x=\int t^2 d t=\frac{t^3}{3}+\mathrm{C}=\frac{1}{3}(\log x)^3+\mathrm{C}$
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