# Integral problem

1. Feb 16, 2007

### Ami

1. The problem statement, all variables and given/known data

2. Relevant equations
Can any body help me with this integral problem???Please.

3. The attempt at a solution

Is the only solution by the "douple integration" method ???

Last edited: Feb 16, 2007
2. Feb 16, 2007

### NateTG

What have you tried?

3. Feb 16, 2007

### drpizza

Calc I or Calc II? Are you sure you wrote that problem down correctly?

(edit: have you heard of the imaginary error function? Either that, or I'm completely blanking out on this one.)

Last edited: Feb 16, 2007
4. Feb 16, 2007

### Ami

I'm really sorry. I've written the problem down uncorrectly

This is the right one:_

5. Feb 16, 2007

### Hootenanny

Staff Emeritus
Try rewriting the problem;

$$\int e^{-x^2}\cdot e^{-\frac{1}{x^2}} dx$$

6. Feb 16, 2007

### Ami

I tried this step,but I couldn't continue.

7. Feb 16, 2007

### Ami

Maybe we need "douple integration" here.

8. Feb 16, 2007

### lalbatros

cheat with this site:

http://integrals.wolfram.com/index.jsp

enter your function as follows: Exp[-x^2-1/x^2]

You will see that it is not an easy one.

However, I guess that for a definite integral {-Inf,+Inf} it could be easier.
Are you sure you want the indefinite integral?

If yes, you can still try to figure out out to get by hand the result mathematica will show you.

The result is:

Integrate[Exp[-x^2 - 1/x^2], x] ==
(Sqrt[Pi]*((1 + Erf[-x^(-1) + x])/E^2 + E^2*(-1 + Erf[x^(-1) + x])))/4

9. Feb 16, 2007

### Ami

Thank you very much for the wonderful site,and for replying.

I've tried it,and I saw the result. But as you said,I want to figure out how to get by hand the result.

I still need help.

Last edited: Feb 16, 2007
10. Feb 16, 2007

### lalbatros

That's where cheating becomes really an art.
Try calculating the derivate of the result and write the calculation in reverse order.

In this process you may have some good idea.

Another method is to look in the Mathematica package how it does that.
It is very difficult to read, but it is easy to guess the ingredients.
Probably a standard form we be used and some integral table results (not many since erf is an easy function).
But you need Mathematica ... and that's very expensive

11. Feb 16, 2007

### Ami

Great ideas,especially that one about cheating:rofl:

I will try this one,because I can't use Mathematica package right now.
And we will see