The integration of e^(x^2)

[Redbelly98]

I don't know how many times we have to say this- it's given in any good calculus book. The anti-derivative of $e^{x^2}$ is not an "elementary" function.

My best guess, this number is aleph-naught: infinite, but countable.

I have assumed an infinite lifetime for the forum.

 

[vitruvianman]

I have assumed an infinite lifetime for the forum.

lol

a nice point of view

 

[LTA85]

No.


If u = x^2. du = 2xdx, not 2dx.

You're right. What a stupid error I made.

u = x^2, du = 2x
multiply du * e^u = 2x e^x^2.

 

[thepatient]

You're right. What a stupid error I made.

u = x^2, du = 2x
multiply du * e^u = 2x e^x^2.

$$\int$$e^x2dx If:

u = x²
du = 2xdx

You can't substitute dx by du, since dx = du/(2x), not just du. You would have dx in terms of two variables, you can't integrate x in terms of u. The anti-derivative of apples can't be oranges.In no nice way is this function integrable.