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by The Music Roob Ninja on November 11th, 2010

The Music Roob Ninja

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What is the integral of 1/(e^x+1)? Please give all steps. Thanks!

I have got to ln(e^x+1) + INT((1-e^x)/(e^x+1)) and I have been told the latter integral should resolve to x, but I have no idea how. Please help urgently!

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  • by WarHorseLeBron on November 11th, 2010

    WarHorseLeBron

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    Selected by the asker, The Music Roob Ninja. (What's this?)

    y = 1/(e^x+1)

    y = e^(-x)/(1+e^(-x))........just multiplying top and bottom by e^(-x)

    u = 1+e^(-x)
    du = -e^(-x)dx

    int(-du/u) = -ln(u) = ln(1/u) = ln(1/(1+e^(-x)))

    multiply top and bottom by e^(x)

    = ln(e^x/(e^(x)+1) = ln(e^x)-ln(e^(x)+1)

    = x-ln(e^(x)+1)

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