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 Self-root function and reciprocal self-power function have same integrals Ztolk Junior Fellow Posts: 21 Threads: 4 Joined: Mar 2010 04/03/2010, 04:25 AM I was playing around with Maple and I noticed that. $\int_{0}^{\infty}x^{\frac{1}{x}-2}dx=\int_{0}^{\infty}x^{-x}dx$=1.995455958 I then added some parameters and came up with the following: $\int_{0}^{\infty}x^{a/x^{b}-c}dx=\int_{0}^{\infty}x^{-ax^{b}+(c-2)}dx$ For positive a and b, and c>2. I do not know why this is, but I find it very interesting. The self-root function is the inverse of an infinite order tetration. « Next Oldest | Next Newest »

 Messages In This Thread Self-root function and reciprocal self-power function have same integrals - by Ztolk - 04/03/2010, 04:25 AM RE: Self-root function and reciprocal self-power function have same integrals - by tommy1729 - 04/07/2010, 03:44 PM RE: Self-root function and reciprocal self-power function have same integrals - by Ztolk - 04/07/2010, 04:04 PM RE: Self-root function and reciprocal self-power function have same integrals - by tommy1729 - 04/07/2010, 04:17 PM RE: Self-root function and reciprocal self-power function have same integrals - by tommy1729 - 04/10/2010, 10:18 PM RE: Self-root function and reciprocal self-power function have same integrals - by Ztolk - 04/11/2010, 12:52 AM

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