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Math Help - Integral problem

  1. #1
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    Integral problem

    d(x) = *IntegralSign(b^(-x/c) / (f + ax))dx

    a, b, c, f are constants

    I'm stumped. A little help
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  2. #2
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    Mmm... I dunno, I think it doesn't have an elementary primitive.
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  3. #3
    Eater of Worlds
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    I concur with K. It appears it's not doable by elementary means.
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  4. #4
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    I was thinking that if you use u = f+ax and dx = du/a

    you might find the solution. I end up with this answer after my math:

    ln |ax + f| + C
    ---------------
    ab^(x/c)

    I'm not sure if its correct.
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  5. #5
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by cetaamoxclob View Post
    d(x) = *IntegralSign(b^(-x/c) / (f + ax))dx

    a, b, c, f are constants

    I'm stumped. A little help
    Quote Originally Posted by cetaamoxclob View Post
    I was thinking that if you use u = f+ax and dx = du/a

    you might find the solution. I end up with this answer after my math:

    ln |ax + f| + C
    ---------------
    ab^(x/c)

    I'm not sure if its correct.
    The Mathematic site gives the answer in terms of the error function, which can only be approximated. But let's see what your substitution does.

    \int \frac{b^{-x/c}}{f + ax}~dx

    Let u = f + ax \implies dx = \frac{1}{a}~du

    So
    \int \frac{b^{-x/c}}{f + ax}~dx = \int \frac{b^{-(f - u)/(ac)}}{u}~\frac{du}{a}

    = \int \frac{b^{-f/(ac)}b^{u/(ac)}}{u}
    (which is pretty much the same form as you started with.)

    I can see no way to integrate this (barring some kind of approximation.)

    -Dan
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  6. #6
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    A friend of mine thinks the answer has something to do with some sort of infinite series.
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