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Interesting Integral

From	"apovolot@gmail.com" <apovolot@gmail.com>
Newsgroups	sci.math.research
Subject	Interesting Integral
Date	2017-04-18 16:11 -0600
Organization	World Wide Maths
Message-ID	<180420171611144575%edgar@math.ohio-state.edu.invalid> (permalink)

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Per
https://math.stackexchange.com/questions/2230651/a-conjectured-continued-
fraction-for-phi-phi
integrating from 0 to infinity of the function:

e^(-x*(2+(1+sqrt(5))/2))*(cosh(x)+sqrt(5)*sinh(x))^((1+sqrt(5))/2)

is supposed to be:
(phi^phi - 1/phi)/2
where phi =(sqrt(5)+1)/2

Maxima can't find this result symbolically, but numerical integration
gives the expected result.

What about other computer algebra systems?

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Interesting Integral "apovolot@gmail.com" <apovolot@gmail.com> - 2017-04-18 16:11 -0600

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