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Integrate e^(x^2)by newton1
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#1
Apr203, 10:32 AM

P: 152

does the integrate e^(x^2) can solve??
i think is no..... but why?? 


#2
Apr203, 12:39 PM

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P: 39,338

That depends upon exactly what you mean.
Since e^(x^2) is a continuous function, yes, it HAS an integral (antiderivative). Every continuous function (and many noncontinuous functions) is the derivative of some function and therefore has an antiderivative. Is that antiderivative any "elementary function" (defined as polynomials, rational functions, exponentials, logarithms, trig functions and combinations of them)? No, if fact for most functions the antiderivative 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 antiderivative of e^(x^2). 


#3
Apr703, 11:18 AM

P: 152

may i ask what is Error Function??



#4
Apr703, 11:55 AM

P: 24

Integrate e^(x^2)



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