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Root integral question

  1. Feb 18, 2009 #1
    [tex]
    \int \frac{dx}{x(1+2\sqrt{x}+\sqrt[3]{x})}=\int \frac{dx}{x(\sqrt{x}+1+\sqrt{x}+\sqrt[3]{x})}=
    \int \frac{dx}{x(\sqrt{x}+\frac{(1-x)}{1-\sqrt[3]{x}})}
    [/tex]
    i got read of one root but instead i got another one
    ??
     
    Last edited: Feb 18, 2009
  2. jcsd
  3. Feb 18, 2009 #2

    Tom Mattson

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    Staff Emeritus
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    Notice that the denominator can be written as follows:

    [tex]x\left(1+2x^{1/2}+x^{1/3}\right)[/tex]

    [tex]x\left(1+2x^{3/6}+x^{2/6}\right)[/tex]

    Let [itex]u=x^{1/6}[/itex].
     
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