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December 1st, 2011, 08:19 AM   #1
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pls explain the solution of e^x^2 dx

hi

for this integral :
I've found the solution :
http://www.wolframalpha.com/input/?i=integrate+e^x^2

and also this one:
Example 4:
http://faculty.eicc.edu/bwood/ma155supp ... ntal28.htm

i'm newbie in the integral . I need to explain the integral of for next session.
can any body explain the solution of the integral? just say a brief description for each part.

please help me.
Thanks
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December 1st, 2011, 08:29 AM   #2
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Re: pls explain the solution of e^x^2 dx

the integral in images:

Indefinite integral:


Alternate form of the integral:

Series expansion of the integral at x=0:

Series expansion of the integral at x = ?:
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December 1st, 2011, 10:10 AM   #3
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Re: pls explain the solution of e^x^2 dx

The images do not display for me. Do you mean:

or

I assume it is the first integral you are interested in, but wanted to ask for clarification.
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December 1st, 2011, 10:25 AM   #4
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Re: pls explain the solution of e^x^2 dx

Hi thanks for your reply I mean the first one.
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December 1st, 2011, 10:32 AM   #5
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Re: pls explain the solution of e^x^2 dx

About all I can tell you about it, is that it is not expressible in elementary terms.
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December 1st, 2011, 10:55 AM   #6
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Re: pls explain the solution of e^x^2 dx

no problem man, but , please tell it step by step.
thanks
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December 1st, 2011, 11:13 AM   #7
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Re: pls explain the solution of e^x^2 dx

for example the teacher asked in the following sentence :

what is the for ?

also I don't have any description for these:







I just guess It's related with this formula
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December 1st, 2011, 11:14 AM   #8
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Re: pls explain the solution of e^x^2 dx

What I mean is that the integrand in question does not have an anti-derivative that is expressible as a function built from a finite number of exponentials, logarithms, constants, and nth roots through addition, subtraction, multiplication and division.
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December 1st, 2011, 11:21 AM   #9
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Re: pls explain the solution of e^x^2 dx

I'm sure someone more knowledgeable than myself will explain the big O notation and the series expansions.

In the meantime, you may want to look at these articles:

Dawson function

Error function
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December 1st, 2011, 11:48 AM   #10
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Re: pls explain the solution of e^x^2 dx

Thank you for your description. umm could you please say what's the sing of big O in English?
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