Two Integrals

  • Thread starter mathslover
  • Start date
  • #1
17
0
I have tried many hours on the following integrals and would appreciate any help from you.


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?
 

Answers and Replies

  • #2
CompuChip
Science Advisor
Homework Helper
4,302
47
Quickly checked it with Mathematica... the indefinite integrals are no fun (they involve hypergeometric functions and error functions) but the definite integrals come out relatively nicely.

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
Science Advisor
Homework Helper
41,833
961
This has nothing to do with "number theory". I am moving it to Calculus and Analysis.
 
  • #4
17
0
For the first integral ,

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.
 

Related Threads on Two Integrals

  • Last Post
Replies
5
Views
648
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
4
Views
1K
Replies
2
Views
989
  • Last Post
Replies
4
Views
2K
Replies
1
Views
2K
  • Last Post
Replies
6
Views
2K
  • Last Post
Replies
4
Views
582
Replies
2
Views
814
Top