Question
Evaluate the following integrals:$\int(\log\text{x})^2\cdot\text{x dx}$

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Question is modified

Show that $\frac{9 \pi}{8}-\frac{9}{4} \sin ^{-1}\left(\frac{1}{3}\right)=\frac{9}{4} \sin ^{-1}\left(\frac{2 \sqrt{2}}{3}\right)$.

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