Impossible integral?

FrederikDan

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Apr 25, 2022
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I'm trying to determine the "doubling time" of the following function as a function of T. I have tried converting the function to the integral of an infinite sum, but that didn't seem to clarify things. I am aware, that there most likely is no analytical solution to the integral itself, however, I was wondering if there might be a way to determine an analytical solution for its doubling time as a function of T.

problem fordoblingstid.png
 
I think that the symbolimg.pngused within the OP's image means x3\sqrt{x^3} (please correct me if I'm wrong)

The following step in your work looks dubious to me...

img2.png

It appears like you're trying to raise all the individual elements of a sum to the same power. Here's an analogy...
32+42=52+023^2+4^2 = 5^2 + 0^232+4252+02\sqrt{3^2}+\sqrt{4^2} \ne \sqrt{5^2} + \sqrt{0^2}3+453+4 \ne 5
 
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