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Math Help - Exponential Integral Problem help

  1. #1
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    Exponential Integral Problem help

    Hi everyone, I'm currently really really stumped on this question...I've even tried working backwards but can't seem to get it...well heres the question, hopefully someone can help me out!

    find the integral of:

    e^(2x)*dx/(e^x +1)

    I'm assuming we use substitution or integration by parts? does the equation need to be manipulated first?

    Thanks!
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  2. #2
    MHF Contributor red_dog's Avatar
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    \int\frac{e^{2x}}{e^x+1}dx=\int\frac{e^x}{e^x+1}\c  dot e^xdx

    The substitution is e^x=u
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  3. #3
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     \int \frac{e^{2x} dx}{e^x+1}

     = \int \frac{ e^{2x} + e^x - e^x  }{e^x+1}~dx

     = \int (e^x - \frac{e^x}{e^x+1} )~dx

     = e^x - \int \frac{d(e^x)}{e^x+1}
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  4. #4
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    Quote Originally Posted by simplependulum View Post
     \int \frac{e^{2x} dx}{e^x+1}

     = \int \frac{ e^{2x} + e^x - e^x  }{e^x+1}~dx

     = \int (e^x - \frac{e^x}{e^x+1} )~dx

     = e^x - \int \frac{d(e^x)}{e^x+1}
    Thank you very much, I finally understand it! I had a feeling I was suppose to manipulate the question somehow, thanks!!!
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