I say that Fernando Revilla wins out on this puzzle although I'd say we all win out from our knowledge gained.
I've been promoting what I refer to as the A-S method (the addition-subtraction method) for use in helping to solve certain integration problems (this method was inspired by what I read on LaPlace transforms from Rainville-Bedient's Elementary Differential Equations) as it simplifies those problems' solutions. I tried the A-S method on the puzzle which failed to work so Fernando Revilla referred to another method that, while it works and is listed in Schaum's outline, isn't simple to apply (as Schaum demonstrates).
I will continue my integration and differential equations studies to see what else may be learned.
January 30th 2011, 12:47 PM
here's my approach:
first we calculate some integrals separately:
now we're ready to solve your integral, so by using (1), (2) and (3) we get