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Math Help - How To Solve Integral of e? And solve velocity?

  1. #1
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    How To Solve Integral of e? And solve velocity?

    1) int(1/(1-e^(-x)))
    My attempt:
    ln |1-e^(-x)| + c

    Answer:
    ln |e^x - 1| + c

    2) Solve the differential equation:
    (e^(x-y))dy=-dx

    My Attempt:
    -1/(e^(x-y))=dy/dx

    Answer:
    0 = e^(-y) + e^(-x) + c

    3) a(t) = -32 ft/s as the acceleration due to gravity. An object is vertically thrown downward from the top of the 480 foot building with an initial velocity of 64 ft/s. With what velocity does the object hit the ground?

    My Attempt:
    int(-32) = -32x + c
    v = -32x + 480?

    Answer:
    v = -186.56 ft/sec
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  2. #2
    Super Member Random Variable's Avatar
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    May 2009
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    1)  \int \frac {1}{1-e^{-x}} \ dx = \int \frac {1}{1-e^{-x}} \frac {e^{x}}{e^{x}} \ dx =  \int \frac {e^{x}}{e^{x}-1} \ dx


    2) hint:  e^{x-y} = \frac {e^{x}}{e^{y}}
    Last edited by mr fantastic; June 10th 2009 at 05:35 AM. Reason: Merged posts
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