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Math Help - Route cubed

  1. #1
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    Route cubed

    Hello there,

    Doing a bit of integration using substitution and when i come to sub back in i have come across an interesting case:
    Lets say that:

    u^2 = x+1

    then what would u^3 be?

    I have come up with:

    (x+1)\sqrt{x+1}

    Is that correct?

    What i have is:

    u^3(\frac{2}{5}u^2 - \frac{2}{3})

    is there an easy way to take the fraction out?

    ...okay well ive got it like this:

    \frac{1}{15}u^3(6u^2-10)

    is that right?
    Last edited by darksupernova; April 21st 2010 at 02:52 AM.
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  2. #2
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    Quote Originally Posted by darksupernova View Post
    Hello there,

    Doing a bit of integration using substitution and when i come to sub back in i have come across an interesting case:
    Lets say that:

    u^2 = x+1

    then what would u^3 be?

    I have come up with:

    (x+1)\sqrt{x+1}

    Is that correct?

    What i have is:

    u^3(\frac{2}{5}u^2 - \frac{2}{3})

    is there an easy way to take the fraction out?
    I would think there are two possibilities for u^3, the one you gave, and the additive inverse.

    Edit: You added the last three lines afterwards so I didn't see them.

    Are you saying that

    u^3(\frac{2}{5}u^2 - \frac{2}{3}) + C

    is the result of your integration on u du?

    Any rate, it's probably easiest to write, for example, (x+1)^(3/2) and avoid the trouble of all the radical signs.

    Did I answer your question?
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  3. #3
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    whats an additive inverse?

    would that be:

    (x+1)^\frac{3}{2}
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  4. #4
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    Quote Originally Posted by darksupernova View Post
    whats an additive inverse?
    Just the value times negative one.

    I edited my first post to reflect your updated post.

    Edit: Ah, there's more now..

    Quote Originally Posted by darksupernova View Post
    ...okay well ive got it like this:

    \frac{1}{15}u^3(6u^2-10)

    is that right?
    I'm not sure what kind of simplification you're going for, but what you did was valid.
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  5. #5
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    ah yes sorry, i realised more info might help!

    Thanks for your help, your right, the answer leaves it in the form to the power 3/2...

    Nice job
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