If anyone wishes to tackle it, go ahead and integrate and see what a cool result you get. I thought it was anyway.

$\displaystyle \int_{0}^{1}\frac{x^{4}(1-x)^{4}}{1+x^{2}}dx$

It shouldn't be too bad. Some division and term by term integration.

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- Jul 10th 2007, 09:00 AMgalactusintegral with nice result
If anyone wishes to tackle it, go ahead and integrate and see what a cool result you get. I thought it was anyway.

$\displaystyle \int_{0}^{1}\frac{x^{4}(1-x)^{4}}{1+x^{2}}dx$

It shouldn't be too bad. Some division and term by term integration. - Jul 10th 2007, 09:47 AMThePerfectHacker
- Jul 10th 2007, 10:00 AMgalactus
OK, sorry, I didn't know. I didn't realize it was a Putnam problem. Rather cliche then.

- Jul 10th 2007, 10:04 AMJhevon
yes. in fact, it was mentioned on this forum already, see page 2 here. it was used to prove that 22/7 exceeds pi

but thanks for reminding me about that impressive result. i dont get to see it as often as TPH does :D - Jul 10th 2007, 10:06 AMThePerfectHacker
Read about it here.

Here is a much more nastier one I found on AoPs:

$\displaystyle \frac{355}{113}-\pi = \int_0^1\frac{(25+816x^2)[x(1-x)]^8}{3164(1+x^2)} dx$ - Jul 10th 2007, 10:18 AMgalactus
I seen it in "Gamma, exploring Euler's constant" by Julian Havil.

A nice book. - Jul 10th 2007, 03:14 PMThePerfectHacker