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Quick Integration Question w/ e

  1. May 16, 2005 #1
    Quick Integration Question w/ "e"

    Hey folks,

    On my calc homework tonight, I have to solve the integral [tex]\int (1/e^z) dz[/tex] as part of my differential equation. Anywho, I thought the answer to that was [tex]ln (e^z) = z[/tex] but my TI-89 claims that it's really [tex]-e^-z[/tex].

    Could someone please tell me which of us is correct, and more importantly, why? I was under the impression that the antiderivative of e was simply itself if there was no inner function (and since z is just a variable, I don't think there is).

    Thank you!
  2. jcsd
  3. May 16, 2005 #2


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    I'm a little confused by your question but:

    [tex]\int \frac{1}{e^z}dz = \int e^{-z} dz = -e^{-z} + \mathcal{C}[/tex]
  4. May 16, 2005 #3
    Oh, wow. I didn't even think of it like that, thank's a lot! Yeah, the question does seem odd now that I know the answer.
  5. May 16, 2005 #4
    Your calc. was right this time, your answer was incorrect. You should remember that you can differentiate to check and [tex]D_x(ln(e^z))[/tex] is just [tex]1[/tex].
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