Homework Help: Integral problem

What have you tried?

 

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.)

 

Try rewriting the problem;

[tex]\int e^{-x^2}\cdot e^{-\frac{1}{x^2}} dx[/tex]

 

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

 

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