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  • What is an integral number? - Mathematics Stack Exchange
    In normal use, integral length would be equal to some integer, while unit length would be of length $1$ (see "unit number" here) Presumably the author meant, "in the unit ( with a different meaning! ) we use to measure lengths, these lengths are integer-valued"
  • calculus - Finding $\int x^xdx$ - Mathematics Stack Exchange
    Thus, it cannot be integrated in finite elementary symbols, which is why any answer to the integral requires infinitely many symbols, or a new notation However, I obviously used some heavy results If you want to see the proof of these results, I recommend researching differential algebra
  • Integral of an absolute value function - Mathematics Stack Exchange
    The absolute value equals "the inside" when "the inside" is non-negative, and equals " (-) the inside" when "the inside is negative So you need to find where "the inside" is zero (i e find the roots of $-2x^3 + 24x = 0$ and possibly split the integral into two or more $\endgroup$ –
  • What is an Integral Domain? - Mathematics Stack Exchange
    An integral domain is a ring with no zero divisors, i e $\rm\ xy = 0\ \Rightarrow\ x=0\ \ or\ \ y=0\: \:$ Additionally it is a widespread convention to disallow as a domain the trivial one-element ring (or, equivalently, the ring with $\: 1 = 0\:$) It is the nonexistence of zero-divisors that is the important hypothesis in the definition
  • integration - Integral of a complex gaussian function - Mathematics . . .
    I am having difficulties to compute this integral $$ \int_{-\infty}^\infty e^{\pm ix^2} \, dx $$ I tried to use complex integration and Cauchy's theorem but it didn't work




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