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Math Help - [SOLVED] integrating

  1. #1
    goldgophermn
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    [SOLVED] integrating

    How do you integrate

    1) (1/30) e^(-x/30)

    2) 1 - (25/x^2)

    Thanks!!
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by goldgophermn View Post
    How do you integrate

    1) (1/30) e^(-x/30)

    2) 1 - (25/x^2)

    Thanks!!
    1)
    \int \frac{1}{30}e^{-x/30} dx

    Let y = -x/30, then dy = -dx/30.
    \int \frac{1}{30}e^{-x/30} dx = \frac{1}{30} \int e^y (-30dy)= -e^y + C = -e^{-x/30} + C

    2)
    \int \left ( 1 - \frac{25}{x^2} \right ) dx = \int \, dx - \frac{1}{25} \int \frac{dx}{x^2}

     = x - \frac{1}{25} \cdot \frac{-1}{x} + C = x + \frac{1}{25x} + C

    -Dan
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