Integration by Substitution

First of all, let's have a look at the substitution method:

圖片參考：http://i388.photobucket.com/albums/oo325/loyitak1990/Feb09/Crazyint2.jpg

So it is found that such integration does NOT have a closed form.
Instead, if the expression to be ingrated is changed to Taylor's series form, then the integration can be done easily:

圖片參考：http://i388.photobucket.com/albums/oo325/loyitak1990/Feb09/Crazyint3.jpg


2009-02-23 02:56:33 補充：
If we differentiate 2/3 e^(開方三次)x, it will give:
(2/9) e^(開方三次)x / x^(2/3)
which is not the original form provided.

你係問∫ e^(3x) / √x dx ?