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Math Help - how to handle fraction + integral?

  1. #1
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    how to handle fraction + integral?

    The equation from my book: (25.4)

    integral u^n du = u^(n+1) / (n + 1) + c

    says in the book its a confusing equation to boot. Can I get an explanation on this quiz question?

    Integrate:

    x / sqrt(6x^2 + 1)

    steps, per answer key:
    u = 6x^2 + 1
    du = 12x dx

    Ok, so u is the denominator, and du is the derivative of the denominator... do I have the wrong equation for this question?? I'll stop there, but the answer key proceeds.

    1/12 (int symbol) u ^ -1/2
    1/12 2u^1/2
    1/6 u^1/2
    1/6 (6x^2 + 1)^1/2 + C

    Thanks.
    Last edited by togo; March 6th 2013 at 09:33 AM.
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  2. #2
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    Re: how to handle fraction + integral?

    Quote Originally Posted by togo View Post
    The equation from my book: (25.4)
    integral u^n du = u^(n+1) / (n + 1) + c
    says in the book its a confusing equation to boot. Can I get an explanation on this quiz question?
    Integrate: x / sqrt(6x^2 + 1)
    I think that almost always students who are confused by u-substitution are so because they fail to consider the derivative.

    For example: if y=\frac{\sqrt{6x^2+2}}{6} what is y'=~?.
    Do all of the steps, carefully and one at a time.
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