Integrate e^(x^2)

  • Thread starter newton1
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  • #1
newton1
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does the integrate e^(x^2) can solve??
i think is no...
but why??
 
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  • #2
HallsofIvy
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That depends upon exactly what you mean.

Since e^(x^2) is a continuous function, yes, it HAS an integral (anti-derivative). Every continuous function (and many non-continuous functions) is the derivative of some function and therefore has an anti-derivative.

Is that anti-derivative any "elementary function" (defined as polynomials, rational functions, exponentials, logarithms, trig functions and combinations of them)? No, if fact for most functions the anti-derivative is not an elementary function. (There are more functions in heaven and Earth than are dreamed of in your philosophy, Horatio!)

Of course one can always DEFINE a new function to do the job. I don't know specifically about e^(x^2) but the ERROR FUNCTION, Erf(x) is defined as an anti-derivative of e^(-x^2).
 
  • #3
newton1
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eh...

may i ask what is Error Function??
 

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