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Math Help - Exponential Integration

  1. #1
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    Exponential Integration

    Our book does a really lousy job of explaining the intricacies of exponential integration. I came upon this problem that I don't know how to solve:



    I'm sure that there is a chain rule here, so this is what I did:

    using the rule I came up with:



    If this doesn't make sense, my exponent comes from the idea that the integral of -2u du is -u^2 (I think).

    I know that my answer is wrong, but I don't know what I am doing wrong.

    Thanks.
    Last edited by mr fantastic; April 21st 2011 at 01:51 PM. Reason: 'Fixed' latex.
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    Quote Originally Posted by joatmon View Post
    Our book does a really lousy job of explaining the intricacies of exponential integration. I came upon this problem that I don't know how to solve:



    I'm sure that there is a chain rule here, so this is what I did:

    using the rule I came up with:



    If this doesn't make sense, my exponent comes from the idea that the integral of -2u du is -u^2 (I think).

    Sorry, latex doesn't seem to be working for me, so hopefully this is readable and I have written it correctly.

    I know that my answer is wrong, but I don't know what I am doing wrong.

    Thanks.
    Yes it's wrong. Substitute x = -2u. Then use your formula.
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    But that's what I am asking. How do I handle the -2u in the exponent? Do I just leave it as -2u? Or is there a chain rule or some other process that I need to apply? Since the integral of -2u is -u^2, does that somehow enter in?

    Unfortunately, as I mentioned, our book is silent on this, so I really have no idea how to handle this exponent. I wish that I could show more work, but I'm truly stuck.

    Thanks again.
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    Quote Originally Posted by joatmon View Post
    But that's what I am asking. How do I handle the -2u in the exponent? Do I just leave it as -2u? Or is there a chain rule or some other process that I need to apply? Since the integral of -2u is -u^2, does that somehow enter in?

    Unfortunately, as I mentioned, our book is silent on this, so I really have no idea how to handle this exponent. I wish that I could show more work, but I'm truly stuck.

    Thanks again.
    Haven't you learned how to change an integral using substitution?

    Do what I said. The integral becomes . Do it. Then substitute back x = -2u.

    Surely you have learned this technique? (If not, then you should not be attempting the posted question until you have).
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    Yes. I do know the technique. We just haven't applied it to a situation where the substitution occurred solely in the exponent. I didn't see that the coefficient 2 would fall out as a constant of 1/2. When you said that x=2u, I didn't realize that you were suggesting a substitution. I just looked at that and saw what I had already done, which was to replace the x in the differentiation rule with the term -2u. Now I see what to do with it. Thanks for your help!
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    BTW, if you didn't know the rule (or if you're like me and only choose to remember a small number of rules), you can convert it to a funtion of e...

    .

    Which would mean



    and you would then make the substitution .
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