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Please show me the detailed solution to the question:

Compute the value of $$\int_{0}^{\infty }\frac{\left( \ln x\right) ^{40021}}{x}dx$$

Thank you a million!

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    Hint: Let $u = \log x$, then $du = \frac 1x\, dx$.2012-03-25
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    this integral is undefined .2012-03-25
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    OK but this leads to the expression minus infinity plus infinity and then what?2012-03-25
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    I want to clearly see why this integral diverges2012-03-25
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    Because (for example) $\int_e^\infty \frac 1x \, dx$ diverges and you integrand is larger.2012-03-25
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    @martini, but in the interval $(0,e)$, the integrand takes large negative values though. How do you account for that?2012-03-25
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    @FortuonPaendrag If we are not considering the PV, AFAIK such an integral diverges if it does "on one side".2012-03-25
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    @martini Ah, thank you. Like an alternating sum whose terms are only getting bigger in absolute value?.It makes sense now. I should have given it a little more thought.2012-03-25

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