Compute for

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- March 5th 2010, 02:05 PMKrizalidIntegral with logarithm
Compute for

- March 5th 2010, 06:35 PMTheEmptySet
First integrate by parts to get with

and

This Formally gives

Now justifying the limits

Both of the above limits only exsist when

This gives

Now let

This turns the right hand side into a form of the Beta function!

Now using Euler reflection formula the product of the two Gamma functions can be written as

- March 5th 2010, 10:13 PMsimplependulum
Are you expecting a beautiful solution ?

Intuitively , I think there must be another method which doesn't require any knowledges of Gamma function . - March 6th 2010, 11:11 AMKrizalid
no, i'm not looking for a beautiful solution, i just wanted to share this problem.

here's my solution:

thus the integral equals

hence