Re: TI-M: Integral of x^x
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Re: TI-M: Integral of x^x
I was doing some research today about Euler's identity and I came across the
x^x integral. In fact, it can be solved, according to the book An Imaginary
Tale The Story of sqrt(-1) by Paul J. Nahim. On p. 145-146, the author
describes the process involved to solve it, I think as done by de Moivre (but
I'm not sure). I didn't have enough time to really check it out so, but I did
write down the answer: the indefinite integral = the Sum of
[(-1)^n]/[(n+1)^(n+1)] from zero to infinity. The first few terms are
1-1/2^2+1/3^3-1/4^4+1/5^5........ you get the idea. Just in case anyone
cares, the definite integral from zero to one = 0.78343....... Hope this
helps!
God Bless,
Will Landry
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