Evaluate

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- Mar 12th 2010, 12:18 PMKrizalidAn arctan integral
Evaluate

- Mar 14th 2010, 02:28 PMKrizalid
okay the problem at first glance it's hard, but i don't want to give any hint yet, so i'll wait a couple of days and i'll post a solution.

- Mar 15th 2010, 07:26 AMDeadstar
Posting in thread so I remember about it. I think it has to do with...

.

Then find an expression for arctan(x)/x maybe and use integration by parts. I'll look at it later. - Mar 16th 2010, 07:15 AMDeadstar
Will just post any working as I go along...

__Spoiler__: - Mar 18th 2010, 12:34 AMsimplependulum
I make use of (again) 'magic differentiation' to solve this problem .

Consider

Sub. , it becomes

sub .... After a few steps , we can obtain

The integral

Consider

Magic Differentiation !

So

The answer to the problem is

- Mar 18th 2010, 05:44 PMKrizalid
okay, my solution uses the fact that

- Apr 17th 2010, 09:21 AMRandom Variable
- Apr 17th 2010, 11:18 AMKrizalid
as a double one.

- Apr 17th 2010, 11:43 AMRandom Variable
- Apr 23rd 2010, 11:08 AMKrizalid
sorry for the late answer, actually, it holds for a better way.

try to find it, my time is bounded by now.