∫e^x^2dx=?

圖片參考：http://i212.photobucket.com/albums/cc82/doraemonpaul/yahoo_knowledge/indefiniteintegral/integrateexpxsquare.jpg

參考資料：
my wisdom of maths

The definite integral of it can be computed.

http://i187.photobucket.com/albums/x22/cshung/7008072400640.png

This integral has no closed form. It is called the error function.
Simon YAU, MSc Math

There is no simple function for this. This seems to be the ERF function. I have found the following: http://mathworld.wolfram.com/Erf.html

chu:
1/2x..x都唔係constant都比你放到出去
虧你話去考dse~幫人拉curve?

You can use substitution.
Let u = x^2
du/dx = 2x
du = 2xdx
dx = du/2x

(Integrate) e^(x^2) dx
=(Integrate) e^u du/2x
=(1/2x) (Integrate) e^u du
=(1/2x) (e^u +c) where c is a constant
=(1/2x) (e^(x^2) + c)

Really??!!

2012-02-15 06:59:52 補充：
This kind of unproper integration problem is really interesting!!!

此積分無法以初等函數表示