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December 1st, 2011, 08:19 AM  #1 
Newbie Joined: Dec 2011 Posts: 6 Thanks: 0  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 
December 1st, 2011, 08:29 AM  #2 
Newbie Joined: Dec 2011 Posts: 6 Thanks: 0  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 = ?: 
December 1st, 2011, 10:10 AM  #3 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  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. 
December 1st, 2011, 10:25 AM  #4 
Newbie Joined: Dec 2011 Posts: 6 Thanks: 0  Re: pls explain the solution of e^x^2 dx
Hi thanks for your reply I mean the first one.

December 1st, 2011, 10:32 AM  #5 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  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. 
December 1st, 2011, 10:55 AM  #6 
Newbie Joined: Dec 2011 Posts: 6 Thanks: 0  Re: pls explain the solution of e^x^2 dx
no problem man, but , please tell it step by step. thanks 
December 1st, 2011, 11:13 AM  #7 
Newbie Joined: Dec 2011 Posts: 6 Thanks: 0  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 
December 1st, 2011, 11:14 AM  #8 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  Re: pls explain the solution of e^x^2 dx
What I mean is that the integrand in question does not have an antiderivative that is expressible as a function built from a finite number of exponentials, logarithms, constants, and nth roots through addition, subtraction, multiplication and division.

December 1st, 2011, 11:21 AM  #9 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  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 
December 1st, 2011, 11:48 AM  #10 
Newbie Joined: Dec 2011 Posts: 6 Thanks: 0  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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