Explain the solution of integral e^x^2 dx

Explain the solution of integral e^x^2 dx

hi

for this integral :$\int_{}^{ } e^{x^{2}}dx$
I've found the solution :
Alternate form of the integral:
$e^{x^{2}} F(x)+constant$

Series expansion of the integral at $x=0$:
$x+x^3/3+x^5/10+x^7/42+x^9/216+x^11/1320+O(x^1^2)$

Series expansion of the integral at $x=\infty$ :
$1/2 (e^(x^2) (1/x+1/(2 x^3)+3/(4 x^5)+15/(8 x^7)+105/(16 x^9)+945/(32 x^11)+O((1/x)^12))-i sqrt(pi))$

i'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.

ps . : whats $O(x^1^2)$ for (on part two)?

please help me.
Thanks

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Re: Explain the solution of integral e^x^2 dx

Yes
$\int_{}^{ } e^{x^{2}}dx = e^{x^{2}} F(x)$
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