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Integrate e^(x^2)

by newton1
Tags: integrate
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Apr2-03, 10:32 AM
P: 152
does the integrate e^(x^2) can solve??
i think is no.....
but why??
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Apr2-03, 12:39 PM
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PF Gold
P: 39,552
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).
Apr7-03, 11:18 AM
P: 152
may i ask what is Error Function??

Apr7-03, 11:55 AM
ottjes's Avatar
P: 24
Integrate e^(x^2)

google: erf(x) error function

first result:

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