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Charlie Drinnan
May 13, 2020

Difficult Integral

in Math Problems

An idea for a video: Integrate ln(x)*x^(ln(x)-1)

19 comments
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Ian Fowler
May 13, 2020  ·  Edited: May 13, 2020

I started with integration by parts since int[ln(x)]dx = x[ln(x)-1] but didn't get very far. Nice problem. Thanks.



Charlie Drinnan
May 14, 2020

Yeah. Seems like integration by parts would work.

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Ian Fowler
May 14, 2020



Charlie Drinnan
May 14, 2020

Ultimately did it this way, but was after many attempts to make it work by integration by parts

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Ian Fowler
May 14, 2020  ·  Edited: May 14, 2020

@Charlie Drinnan I nearly **** (am I allowed to do that here?) my pants when I saw

e^(x^2+2x+1) * (x+1). :)

And when you move x^-1 in the denom and you see ln(x)/x with ln^2(x) in the exponent - same thing,


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Charlie Drinnan
May 14, 2020

Ha. Yeah, same boat. But, that eureka moment when you figure out the ln^2(x) insight is really nice.

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awang23
May 14, 2020


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Mason William
Sep 13, 2021

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