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Math Help - Integration

  1. #1
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    Integration

    I did this integral:

    integral(e^x / (1+e^x)^2, x,0,1)

    I approached it by expanding denominator and then simplifying. How comes that gives erroneous error.

    Ive got e^x / (1+e^x)^2 = e^x + 1/2x - e^-x

    then upon integration, taking limits, ive got

    e-1/e+1/2
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  2. #2
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    You can solve this with a u substitution.

    Let u = 1 + e^x so that \frac{du}{dx} = e^x.


    Then \int{\frac{e^x}{(1 + e^x)^2}\,dx} = \int{\frac{1}{u^2}\,\frac{du}{dx}\,dx}

     = \int{u^{-2}\,du}

     = \frac{u^{-1}}{-1} + C

     = -\frac{1}{u} + C

     = -\frac{1}{1 + e^x} + C.


    Now substitute your terminals.
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  3. #3
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    Ok nvm. Figured it out. Very silly mistake
    Last edited by Lukybear; September 30th 2010 at 04:44 AM.
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