What is the integal of e^(x^2)x^4 from negative infinity to infinity?

Thank you!

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- Mar 19th 2008, 10:58 PMromtikintegration
What is the integal of e^(x^2)x^4 from negative infinity to infinity?

Thank you! - Mar 19th 2008, 11:54 PMMoo
Hello,

The function is an even function ie

--------->

Now, let's integrate.

At first sight, you have to use the integration by parts, this must be almost a reflex when you see an exponential. The exponential will very often take the place of the v' function in :

So you must make appear the derivate of , 2x, so as to be able to integrate :

the integrate of will simply be

------ integration by parts ------

the derivate of is

(the two limits tend to 0)

In the same way, make appear the derivate of so as to integrate once again by parts.

And there, i can't help anymore because of the last integral : i don't remember how to do (Surprised) - Mar 20th 2008, 12:17 AMMoo
Ay ! I found ^^

This integrate is not defined, because though the limit in exists (0), the limit in doesn't.

, so the integrate diverges.

Are you sure it's the correct text ? :D - Mar 20th 2008, 07:42 AMromtik
Hi,

Yea that is the question..ahhhhh I needed the answer to be zero! Ah well, thanks anyways! - Mar 20th 2008, 08:27 AMThePerfectHacker
Note, .

Thus, which clearly diverges since RHS diverges.

Maybe the poster wanted, ? (Note the negative).

In that case,

- Mar 20th 2008, 10:17 AMwingless