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.
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.
Read about it here.
Here is a much more nastier one I found on AoPs:
$\displaystyle \frac{355}{113}-\pi = \int_0^1\frac{(25+816x^2)[x(1-x)]^8}{3164(1+x^2)} dx$