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Math Help - antiderivative help

  1. #1
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    antiderivative help

    hey guys, a little confused on the order of this one. any step by step help is appreciated.

    find the antiderivative:
    <br />
f(x) = (x^2 + 1)\sqrt[4]{x^3 + 3x + 2}
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  2. #2
    Super Member Failure's Avatar
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    Quote Originally Posted by JGaraffa View Post
    hey guys, a little confused on the order of this one. any step by step help is appreciated.

    find the antiderivative:
    <br />
f(x) = (x^2 + 1)\sqrt[4]{x^3 + 3x + 2}
    Use the substitution rule: let  z := x^3+3x+2. It follows that dz = 3x^2+3=3(x^2+1)\,dx, thus you have that

    \int (x^2 + 1)\sqrt[4]{x^3 + 3x + 2}\, dx = \tfrac{1}{3}\cdot \int \sqrt[4]{x^3 + 3x + 2}\cdot 3 (x^2 + 1)\, dx =\tfrac{1}{3}\cdot \int \sqrt[4]{z}\, dz=\ldots
    Last edited by Failure; May 4th 2010 at 11:08 AM.
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  3. #3
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    Thanks!!
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  4. #4
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    Quote Originally Posted by JGaraffa View Post
    hey guys, a little confused on the order of this one. any step by step help is appreciated.

    find the antiderivative:
    <br />
f(x) = (x^2 + 1)\sqrt[4]{x^3 + 3x + 2}
    Observe that 3(x^2+1) is the derivative of x^3+3x+2, so:

    \frac{d}{dx}(x^3+3x+2)^{5/4}=3(x^2+1)\times \frac{5}{4}\times (x^3+3x+2)^{1/4}

    etc...

    CB
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