>>9
To clarify: 1^(X+1) is always 1, obviously.
I'm guessing your reasoning went like this:
1. Given (X*X)^(X-1)
2. Can be simplified to X^X
3. Can be simplified to 1^(X+1), as per step 2.
The problem is that step 2 is false. 1 can be rewritten as (X^2)^(X-1), or X^((X-1)*2), not X^((X-1)+1). Rewriting X^X in the same way gives X^(X*1), not 1^(X+1).
This is middle school material.
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Anonymous2007-11-07 14:19
let F(x) = f(x)x^x
F'(x) = x^x
gives us a first order ODE to find f(x).
=> f'(x) + (1 + ln x ) f(x) = 1
couldn't be fucked to do anything actually interesting with it like fourier transform, trying to solve by an integrating factor led to the rather annoying integrating factor x^-x
Fuck yeah.
Might give it some more though later, have a degree to do though
The function is Riemann-Stieltjes integrable since it is monotone, so an integral does exist. However, the antiderivative can't be expressed as a finite composition of the traditional elementary functions as a result of differential Galois theory.
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Anonymous2007-11-08 2:17
i do all this numerically, since i have a computer.
lol at all you losers who dont have computers
>>23
e^(0.5x^2*ln(x) - x^2/4 + c) = e^(0.5x^2*ln(x) - x^2/4) * e^c. In other words, the derivative of the "integral" you gave depends on c, which means (until you at least specify a value of c) it cannot be the integral of x^x.
>>1
Maxima doesn't know how to do it. Probably not possible.
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Anonymous2007-11-10 0:49
there is no analytical solution you asstards.
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Anonymous2007-11-10 2:18
LOL I GOT YOU STUPID NIGGERS.
YOU FUCKERS ALL THINK YOU KNOW SO MUCH SHIT ABOUT EVERYTHING BUT FAIL TO RECOGNIZE ONE OF THE MOST BASIC NONINTEGRABLE FUNCTIONS.
FUCKING RETARDED LOSERS LOL
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Anonymous2007-11-10 2:45
>>30
It is integrable, you just can't express it as a closed form solution. gb2elementary analysis
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Anonymous2007-11-10 5:39
>>30
What the fuck, is your caps lock key stuck down? Turn it fucking off!