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send me the full solution to solve this!!!!!!!!

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- Sep 20th 2007, 07:20 PMkamaksh_iceimproper arctangent integral
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send me the full solution to solve this!!!!!!!! - Sep 20th 2007, 07:23 PMThePerfectHacker
- Sep 20th 2007, 07:25 PMJhevon
- Sep 20th 2007, 08:42 PMThePerfectHacker
Amazingly this integral appears in my Advanced Calculus book so the credit is

**not mine**(though I wish it was).

First you must say . Confirm it is uniformly continous and do the following double integral trick.

.

Change order,

- Sep 20th 2007, 09:19 PMKrizalid
More generally

If is continuous and the integral converges,

This beautiful result is called Frullani's Integral.

Nice, isn't it? - Sep 21st 2007, 07:01 AMThePerfectHacker
- Dec 7th 2007, 07:28 PMKrizalid
I found (not mine) a proof of Frullani's Integral, and I'd like to share it :)

Let

So

And

Now let

&

The conclusion follows.