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Math Help - exponential integral

  1. #1
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    exponential integral

    What do I do when the power in the numerator is larger than the denomenator

    e^16x / 4+e^8x
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  2. #2
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    Quote Originally Posted by gammaman View Post
    What do I do when the power in the numerator is larger than the denomenator

    e^16x / 4+e^8x
    What do you mean by evaluate? What are you trying to do? Differentiate? Partial fractions? Integrate? Simplify?
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  3. #3
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    Oh, sorry I am trying to integrate.
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  4. #4
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    Quote Originally Posted by gammaman View Post
    Oh, sorry I am trying to integrate.
    You can write it:

    \int \frac{(e^{8x})^2}{e^{8x}+4} dx
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  5. #5
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    Ok, and then from there I would do my normal substitution?
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  6. #6
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    Quote Originally Posted by gammaman View Post
    Ok, and then from there I would do my normal substitution?
    I think so, yes.

     u = e^{8x}

     \frac{du}{dx} = 8e^{8x}

     dx = \frac{du}{8e^{8x}} = \frac{du}{8u}

     \int \frac{u^2}{u+4}\frac{du}{8u}

     = \frac{1}{8} \int\frac{u}{u+4} du

     = \frac{1}{8} \int\frac{u+4}{u+4} - \frac{4}{u+4} du

     = \frac{1}{8} \int 1  - \frac{4}{u+4} du
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