Expert: Paul Klarreich - 5/6/2009

Question
Hello Mr. Paul,
I have a question on integration, but I could not solve it, not my maths school teacher, no friend and not even my coaching teacher.
Please tell me how to do that, I have tried every thing from substitution to by parts, but I failed.
Here's the question.
Integrate e^4x² ( it is e to the power 4 x square ).
Thanks in advance for your help.

Answer
Questioner:   MOHIT
Country:  India
Category:  Calculus
Private:  No
 
Subject:  A typical Integral
Question:  Hello Mr. Paul,
I have a question on integration, but I could not solve it, not my maths school teacher, no friend and not even my coaching teacher.
Please tell me how to do that, I have tried every thing from substitution to by parts, but I failed.
Here's the question.
Integrate e^4x² ( it is e to the power 4 x square ).
Thanks in advance for your help.
.................................................
Hi, Mohit,

I assume you mean:

{
| e^(4x^2) dx
}

Now you certainly tried substituting  u = 2x, right?
And you got:
 
1 {
- | e^(u^2) du
2 }

and you did not find this in that huge table of integrals in the standard sources, whatever they are.

Sorry.  There is no simple closed form integral for this.  A shame, too, because it comes up in the study of statistics.

(I think your teacher knew that, too.)