# e^x integration problem

• Feb 14th 2007, 10:11 AM
Nerd
e^x integration problem
I'm a bit rusty on my e's so:

The integral of e^x is e^x +C

So what the integral of (e^(-x^3))^2 be? -e^(-2x^3) + C?
• Feb 14th 2007, 11:15 AM
ThePerfectHacker
Quote:

Originally Posted by Nerd
I'm a bit rusty on my e's so:

The integral of e^x is e^x +C

So what the integral of (e^(-x^3))^2 be? -e^(-2x^3) + C?

No
• Feb 14th 2007, 12:34 PM
CaptainBlack
Quote:

Originally Posted by Nerd
I'm a bit rusty on my e's so:

The integral of e^x is e^x +C

So what the integral of (e^(-x^3))^2 be? -e^(-2x^3) + C?

I doubt that this is expressible in closed form in terms of elementary functions.

RonL
• Feb 14th 2007, 02:19 PM
Nerd
Ugh (I'm a horrible proofreader). The actual problem I was having trouble with is:

integral of (e^(-x^2))^2
• Feb 14th 2007, 04:47 PM
ThePerfectHacker
CaptainBlank said that it is not an elemetary function.
Look The Integrator--Integrals from Mathematica.

The probability function is not elementary.
• Feb 15th 2007, 02:04 PM
Nerd
Ahhh. Okay....

So...what does that mean again?
• Feb 15th 2007, 10:32 PM
Jameson
If it's elementary, then it can't be explicitly be expressed using standard mathematical arguments (powers, logarithms, trig functions, etc).

The simple integral of 2x^2 dx is obviously elementary. The answer uses numbers and powers.

The more complex and nasty integral of sqrt{1+x^2} dx is elementary as well. It has some inverse trig which makes it not fun to do for most, but it can still be expressed explicitly.

The integrals of e^(x^2), e^(-x^2), e^[(x^2)^2], and many others like these are NOT elementary because we cannot explicity state them with our normal mathematical lanuage, so to speak.

This is not a rigourous definition of elementary at all, but I hope it helps you understand the concept more.

To check this yourself, type in some of the integrals I gave you on the site ThePerfectHacker gave you a link to. The site won't be able to do some of the problems and on others it will give you an answer with something like, erf(x). All I'll say about the erf(x) is that it's NOT elementary. :D

Jameson
• Feb 16th 2007, 03:22 AM
CaptainBlack
Quote:

Originally Posted by Jameson
If it's elementary, then it can't be explicitly be expressed using standard mathematical arguments (powers, logarithms, trig functions, etc).

The simple integral of 2x^2 dx is obviously elementary. The answer uses numbers and powers.

The more complex and nasty integral of sqrt{1+x^2} dx is elementary as well. It has some inverse trig which makes it not fun to do for most, but it can still be expressed explicitly.

The integrals of e^(x^2), e^(-x^2), e^[(x^2)^2], and many others like these are NOT elementary because we cannot explicity state them with our normal mathematical lanuage, so to speak.

This is not a rigourous definition of elementary at all, but I hope it helps you understand the concept more.

To check this yourself, type in some of the integrals I gave you on the site ThePerfectHacker gave you a link to. The site won't be able to do some of the problems and on others it will give you an answer with something like, erf(x). All I'll say about the erf(x) is that it's NOT elementary. :D

Jameson

I might observe that I have had some trouble with "the integrator" recently
not integrating what I know is an elementary integral. But then Mathematica
is not the only CAS that has had problems with that integral.

RonL
• Feb 16th 2007, 06:59 AM
ThePerfectHacker
Quote:

Originally Posted by Jameson
I

This is not a rigourous definition of elementary at all, but I hope it helps you understand the concept more.

No it is not. I asked several times for a better definition but nobody gave me. It is anagolus to the meaning to "solution by radicals", the simple meaning: can be expressed as a finite combination of radicals and standard arithmetical operations. See it is similar sounding by elementray. But there happens to be a nice way of stating solution by radicals. However, nobody seems to write what it means in a nice way to what it means solutions by elementaries.