If so, how can you integrate it?

Also, what about

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- Feb 7th 2010, 12:51 PMpaupsersIs this function integrable?

If so, how can you integrate it?

Also, what about - Feb 7th 2010, 12:54 PMpickslides
- Feb 7th 2010, 12:58 PMfelper
A function is integrable is possible to find it's primitve o it's exact numerical value (using elemental functions).

- Feb 7th 2010, 02:24 PMpaupsers
- Feb 7th 2010, 02:27 PMpickslides
- Feb 7th 2010, 02:37 PMpaupsers
- Feb 7th 2010, 02:43 PMpickslides
Parts won't work this time, my apologies

Wolfram Mathematica Online Integrator - Feb 7th 2010, 02:48 PMfelper
You can do this integral using doble integrals, or some know values of the gamma function.

- Feb 7th 2010, 03:08 PMvince
this can be done.

Choose

Notice that then v=

You will then notice that the**uv**term of the integration by parts is 0 (remember that for definite integrals, this term gets evaluated at the main integral's bounds, i.e., and 0.) What you're left with is

A rather cool method for that one will use polar coordinates. here's a link:

Gaussian integral - Wikipedia, the free encyclopedia

(note the limits of integration for the Gaussian integral: You will need to divide by 2 (justified as the integrand is an even function)). - Feb 7th 2010, 03:30 PMpaupsers
- Feb 7th 2010, 03:31 PMpaupsers
Oops, I just saw that you edited your post to explain that part. Thanks!!

- Feb 7th 2010, 03:33 PMvince
- Feb 7th 2010, 04:02 PMRandom Variable
Use the fact that

Make the substitution

which implies that

so

then

and

notice that

now swtich the order of integration and differentiation (which in this case is allowed)

so

letting a=1

- Feb 7th 2010, 04:44 PMfelper

Set then