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Math Help - Antidifferentiation Help

  1. #1
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    Antidifferentiation Help

    Hello, please assist with the following:

    Find An Antiderivative of the following:

    1.) X/(X+1)

    2.) 1/(X+1)^2

    Please show working, thanks!
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  2. #2
    Junior Member enjam's Avatar
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    Ok, for the first one:

    x / (x + 1) = 1 - (1 / (x+1))
    ∫ 1 dx - ∫ (1 / (x+1) dx
    = x - log (x+1) + C


    For the second one:

    ∫ (x+1)^-2 . dx
    = (-1)(x+1)^(-2+1)
    = -1/(x+1) + C
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  3. #3
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    Quote Originally Posted by enjam View Post
    Ok, for the first one:

    x / (x + 1) = 1 - (1 / (x+1))
    ∫ 1 dx - ∫ (1 / (x+1) dx
    = x - log |x+1| + C
    [snip]
    Correction in red.
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  4. #4
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    Hi enjam and mr fantastic

    A little correction : "log" should be "ln"
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  5. #5
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    Thanks

    Thanks for the assistance but could you please explain how you got 1 - (1/(x+1))?
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  6. #6
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    Hi andrew2322

    Use long division to divide x by (x+1)
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  7. #7
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    Quote Originally Posted by songoku View Post
    Hi andrew2322

    Use long division to divide x by (x+1)
    Alternatively .... \frac{x}{x + 1} = \frac{(x + 1) - 1}{x + 1} = \frac{x + 1}{x + 1} - \frac{1}{x + 1} = 1 - \frac{1}{x + 1}.
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