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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.
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.
Will just post any working as I go along... Spoiler:
Then for limits we have and
So our new integral is
I make use of (again) 'magic differentiation' to solve this problem .
Sub. , it becomes
sub .... After a few steps , we can obtain
Magic Differentiation !
The answer to the problem is
okay, my solution uses the fact that
Originally Posted by Krizalid okay, my solution uses the fact that Did you write the original integral as a triple integral and then change the order of integration?
as a double one.
Originally Posted by Krizalid as a double one. ?
sorry for the late answer, actually, it holds for a better way.
try to find it, my time is bounded by now.
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