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Math Help - figuring out a rule..

  1. #1
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    figuring out a rule..

    ∫1/(x^(3/2)) = -2/sqrt(x) ???

    im trying to figure out the rule here. its poping up a few times. these 2 questions especially:

    Wolfram|Alpha

    (click on "show steps" and look at step 3)

    or here

    Wolfram|Alpha

    (sort of the same question really).

    whats going on there? can someone show the working out to me for how we end up with the answer?
    Last edited by mr fantastic; September 28th 2009 at 11:37 PM. Reason: Added url tags.
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  2. #2
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    Quote Originally Posted by Prodigga View Post
    ∫1/(x^(3/2)) = -2/sqrt(x) ???

    [snip]
    You're expected to know the rule \int x^n \, dx = \frac{1}{n+1} x^{n+1} + C where n \neq -1. In the above integral n = - \frac{3}{2}.

    (You are also expected to be fluent enough with basic index laws to know that x^{-1/2} = \frac{1}{x^{1/2}} = \frac{1}{\sqrt{x}}).
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