My Math Forum pls explain the solution of e^x^2 dx

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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 : $e^x^2 dx$ 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 $e^x^2 dx$ 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: $\int e^{x^2}\,dx$ or $\int $$e^x$$^2\,dx$ 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 : $x+x^3/3+x^5/10+x^7/42+x^9/216+x^11/1320+O(x^1^2)$ what is the $O(x^1^2)$for ? also I don't have any description for these: $e^(x^2) F(x)+constant$ $x+x^3/3+x^5/10+x^7/42+x^9/216+x^11/1320+O(x^12)$ $1/2 (e^(x^2) (1/x+1/(2 x^3)+3/(4 x^5)+15/(8 x^7)+105/(16 x^9)+945/(32 x^11)+O((1/x)^12))-i sqrt(pi))$ 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 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.
 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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