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Math Help - Indefinate Integral Help

  1. #1
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    Indefinate Integral Help

    Evaluate: \int x^2 \sqrt{2 + x^3} dx

    I can't figure out how to do these and my book provides no help. If anyone can give me an example I would appreciate it.
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  2. #2
    MHF Contributor chisigma's Avatar
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    Is...

    \frac{d}{dx} (2 + x^{3}) = 3\cdot x^{2} (1 )

    ... so that...

    Kind regards

    \chi \sigma
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  3. #3
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    SO the Answer

    is 3x^2?
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  4. #4
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    use the substitusion method,

    let u=2 + x^{3}
    then
    \frac{du}{dx}=3x^{2}

    and solve it . . .

    cheers
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  5. #5
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    And, just in case a picture helps...



    ... where



    ... is the chain rule. Straight continuous lines differentiate downwards (integrate up) with respect to x, and the straight dashed line similarly but with respect to the dashed balloon expression (the inner function of the composite which is subject to the chain rule).

    Spoiler:

    Spoiler:


    __________________________________________

    Don't integrate - balloontegrate!

    Balloon Calculus; standard integrals, derivatives and methods

    Balloon Calculus Drawing with LaTeX and Asymptote!
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