Find

Printable View

- Sep 20th 2009, 01:43 PMKrizalidCompute an integral
Find

- Sep 20th 2009, 02:21 PMNonCommAlg
- Sep 20th 2009, 02:56 PMKrizalid
yes, but can you find another way to solve it?

- Sep 21st 2009, 01:14 AMhalbard
Another way? What does (s)he want? Hmm ...

Let and let .

The substitution shows that .

The substituion shows that and so .

Thus by symmetry.

Now put so that , for and , and .

Thus .

Thus .

Wait a moment, this is merely a disguised version of the method. It's no better than NonCommAlg's rejected solution.

(Thinks: Perhaps I should have used an infinite series, or some kind of limit, or introduced a parameter, or ... (Mind boggles at this point))

An answer that is not really an answer? This is trickier than it looks.

Hmm ... - Sep 21st 2009, 07:00 AMKrizalid
- Sep 22nd 2009, 04:32 AMsimplependulum
What about this ?

From the Lengre's Identity

I think it is the best method by substituting ..