- #1

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1. Int{x=0 to infinity}(exp(-x)*Ln(x)*Ln(x)dx)

2. Int{x=0 to Infinity}(exp(-x*x)*Ln(x)dx)

Any idea guys?

- Thread starter mathslover
- Start date

- #1

- 17

- 0

1. Int{x=0 to infinity}(exp(-x)*Ln(x)*Ln(x)dx)

2. Int{x=0 to Infinity}(exp(-x*x)*Ln(x)dx)

Any idea guys?

- #2

CompuChip

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I suppose you will want to somehow use

[tex]\int_0^\infty e^{-t} \ln(t) \, \mathrm dt = -\gamma[/tex]

(the Euler gamma). The second one will also involve a Gaussian integral.

Will think a bit more...

- #3

HallsofIvy

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This has nothing to do with "number theory". I am moving it to Calculus and Analysis.

- #4

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it can be shown to be = Gamma''(1) and

- Euler's Constant = Gamma'(1)

where Gamma(x)=Gamma Integral

I just don't know how to use the above facts.

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