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Please check this for me.

  1. Nov 19, 2004 #1
    I just got out of a differential equations exam. In that exam, i had to integrate e^x/x (e power x over x)

    I worked it out on scratch, and i came up with this:

    e^x = Sum(i=0->infinity){X^n/n!}

    So dividing by x we get Sum(i=0->infinity){x^(n-1)/n!}.
    By integrating we get e^x.Sum(i=0->infinity){1/n}.
    The latter series diverges, so i concluded that we can't find a solution to that integeral. I re-checked the work that lead to that equation like four times, and it was all correct.

    So could it be that the there was a fault in the exam?

    (sorry didn't use latex or whatever it is called to represent my calculations)
  2. jcsd
  3. Nov 19, 2004 #2

    matt grime

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    well, you should check again cos your logic is wrong - the term by term integral doesn't equal what you said it is, and omits to integrate the 1/x term at the beginning as well.
  4. Nov 19, 2004 #3
    did't understand.
    Integral of x^(n-1)/n!=X^n/n.n! right?

    sumation(x^n/n!) is e^x no? so you are left with the harmonic series which diverges.

    I can't find that logical error i might have made, can you clarify please?
  5. Nov 19, 2004 #4


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    Well, for starters you should recogonize that
    [tex]\frac{x}{n} < \frac{x}{n!}[/tex]
    so it's not the harmonic series.

    I assume you wanted to do something like:
    [tex]\frac{1}{x}e^x=\frac{1}{x} \sum \frac{x^n}{n!}=\sum \frac{x^{n-1}}{n!}=\sum \frac{x^{n-1}}{n(n-1)!}[/tex]
    but it's not at all clear to me what that last sum is going to be equal to.

    Mathematica/Wolfram indicate that the result is pretty ugly.
    Last edited: Nov 19, 2004
  6. Nov 19, 2004 #5
    Hmm, can you clarify those? didn't get what you're typing...can't see it
  7. Nov 19, 2004 #6
    OH, and you'd get 1/n, not x/n.

    the series 1/n diverges....
  8. Nov 19, 2004 #7

    [tex]\frac{e^x}{x}=\frac{e^n-1}{n!}[/tex], This should be e^(n-1)/n!, dunn why it isn't working with Latex


    But [tex]\frac{x^n}{n!}=e^x[/tex],

    Thus[tex]\int \frac{e^x}{x}dx=e^x.\sum \frac{1}{n}[/tex],

    But [tex]\sum \frac{1}{n} [/tex] would diverge, thus the integral can't be found.

    Edit: Hmmm, i read the Latex help file, and i doesn't seem to work :/
    Last edited: Nov 19, 2004
  9. Nov 19, 2004 #8
    You need to end things with [ /tex] (no space). You have reversed the /-sign (to \).
  10. Nov 19, 2004 #9
    yep sorted it out now :) thx

    Come to think of it, i do have a hole in my logic lol....how can i integrate with respect to n, can I? dun think so :P

    *kareem is the newb*
  11. Nov 19, 2004 #10


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    To group in Latex use {}'s - for example e^{n-1}.
    As in
    [tex]\frac{e^x}{x} = \sum_{n=0}^{\infty} \frac{x^{n-1}}{n!}[/tex]
  12. Nov 20, 2004 #11
    Yes, i was aware of that, but i just didn't bother, that was unproffesional :(
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