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How would you integrate this equation?

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- Thread starter shansalman
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- #1

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How would you integrate this equation?

- #2

ranger

Gold Member

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You could use integration by parts. If it helps, rewrite it as:

x^{-1}*e^{4x}

x

- #3

Tom Mattson

Staff Emeritus

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- #4

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By definition, it is -Ei(1,-4x). Where Ei is the exponential integral.

Hope this helps.

;0

Hope this helps.

;0

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- #5

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Using a substitution, this integral can be simplified to [tex] \int \frac{e^u}{u} du [/tex]

No matter how hard you try, you can never succeed in integrating this integral. It cannot be defined by any known functions, much like [tex] \int \sin(x^2) dx [/tex] and [tex] \int \frac{sinx}{x} dx [/tex].

No matter how hard you try, you can never succeed in integrating this integral. It cannot be defined by any known functions, much like [tex] \int \sin(x^2) dx [/tex] and [tex] \int \frac{sinx}{x} dx [/tex].

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- #6

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Simply put, im sure your familiar with the chain rule, power rule, Lhoptials rule, etc... The method to solve this is similar to those... it just hasnt been discovered yet. In theory there is a number formula (like Log, sine, tan, cos, etc) that hasnt been figured out and that will be used in the new formula. Cool huh?

Well go get yourself a nobel prize and invent the shansalman's rule for integrating this!

- #7

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Integrate: square root(1+x^3) dx

integrate: e^x^2 dx

How do you guys do that latex stuff?

- #8

- #9

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Im sure your right. It would be amazing nevertheless.

Just think, there is something that exists out there that will probably be taught at the high school level once its discovered. Its something simple yet nobody has figured it out yet. (This whole paragraph is obviously a maybe).

Just its really exciting isnt it ?!?!?!

Maybe this new function will relate some of the major theories out there (e = mc^2 and some others) and we can finally prove the grand unified field theory (the everything theory). Then im sure it will get a nobel and maybe we could travel to the stars! OMG im so excited now! Its like wondering "what if" if you won the lottery.

Just think, there is something that exists out there that will probably be taught at the high school level once its discovered. Its something simple yet nobody has figured it out yet. (This whole paragraph is obviously a maybe).

Just its really exciting isnt it ?!?!?!

Maybe this new function will relate some of the major theories out there (e = mc^2 and some others) and we can finally prove the grand unified field theory (the everything theory). Then im sure it will get a nobel and maybe we could travel to the stars! OMG im so excited now! Its like wondering "what if" if you won the lottery.

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- #10

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Found another one:

Integrate sin(x^2)

Integrate sin(x^2)

- #11

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Im sure your right. It would be amazing nevertheless.

Just think, there is something that exists out there that will probably be taught at the high school level once its discovered. Its something simple yet nobody has figured it out yet. (This whole paragraph is obviously a maybe).

Just its really exciting isnt it ?!?!?!

Maybe this new function will relate some of the major theories out there (e = mc^2 and some others) and we can finally prove the grand unified field theory (the everything theory). Then im sure it will get a nobel and maybe we could travel to the stars! OMG im so excited now! Its like wondering "what if" if you won the lottery.

The function has been discovered already. ZioX mentions it in the third reply to this thread. It is the Exponential Integral function, one of a family of functions which has been studied by many a mathematician.

- #12

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EUREKA!!! we are all going to be rich! :-) that is too cool. im behind in my reading it looks like!

- #13

Gib Z

Homework Helper

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[tex]\int f(x) dx = F(x) + C, \frac{dF(x)}{dx} = f(x)[/tex].

Now if i wanted, I could study the properties of a particular F(x), as they did for the Exponential Integral Function.

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