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Integral of (log x)^n / x: substitute t = log x

This type of question, asked 2 times: May 2021 S1, 2 May 2023 S2. All 2 questions below, oldest first.

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  1. Question 1

    May 2021 S1

    136
    ∫(log⁡x)2x dx\int\frac{(\log x)^2}{x}\,dx

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  2. Question 2

    2 May 2023 S2

    141
    ∫log⁡x3x dx\displaystyle\int \dfrac{\log\sqrt{x}}{3x}\,dx is equal to

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