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Math Help - Integration - Algebraic substitution

  1. #1
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    Integration - Algebraic substitution

    \int \frac{dx}{2x^{\frac{1}{3}} + \sqrt{x}}

    let x = z^3
    dx = 3z^2dz

    \int \frac{dx}{2z + z^{\frac{3}{2}}}
    \int \frac{3z^2dz}{2z + z^{\frac{3}{2}}}
    \int \frac{3z}{2+z^\frac{1}{2}}dz
    im stuck here
    .... divide numerator by denominator

    \int 3z^{\frac{1}{2}} - 6 + \frac{12}{2+z^{\frac{1}{2}}}dz
    im stuck at the integral of 12 / (2 + z^(1/2))
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  2. #2
    Newbie
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    Jul 2007
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    Try taking

    x=z^6

    then dx=6(z^5),

    substituting and then Simplyfying u will get

    6z^3/(1+z)

    You can then divide and integrate as usual
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  3. #3
    Senior Member
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    thanks
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