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Weird Exponential Integral

  1. Nov 2, 2006 #1
    Ok, this isn't a particularly hard integral, but for some reason I don't understand why the answer is what it is. Here's the integral (BTW, it's part of a double integral):

    [tex]\int e^{x/y} dx[/tex]

    The answer is: [tex]ye^{x/y} dy[/tex] but I don't understand why.

    Wouldn't it be in the form e^u, with u being x/y, and du being 1/y dy? If so, then the answer should be [tex]e^{x/y}/y dy[/tex], right? That's wrong I guess, because the rest of the integral is pretty much impossible to do if that's the answer. So basically, my question is, why is the answer the answer? :redface: Thanks!
    Last edited: Nov 2, 2006
  2. jcsd
  3. Nov 2, 2006 #2


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    You're integrating wrt x, so just consider y constant.
    The derivative of yexp(x/y) wrt x is exp(x/y) by the chain rule, so that's the correct answer.

    If you use substitution u=x/y, then you should replace dx with ydu (not use dy, since you're integrating wrt x).
  4. Nov 2, 2006 #3
    Ah! That makes sense, especially since there's already a dy in the problem. No use having two of them. Thanks for the help!
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