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Integration: 1/((x^(1/2)-x^(1/3))

  1. Oct 4, 2009 #1
    I have no idea where to start with this. Sorry about the format, I don't know where to make it into an easier to read style.

    1/((x^(1/2)-x^(1/3))
     
  2. jcsd
  3. Oct 5, 2009 #2
    The problem is: [itex]\int \dfrac{1}{\sqrt{x} - \sqrt[3]{x}} dx[/itex]

    Here, http://www.wolframalpha.com/input/?i=integrate+1%2F((x^(1%2F2)-x^(1%2F3))
    Click on show steps and that's it.

    See LaTeX for formatting your equations here.
     
  4. Oct 5, 2009 #3
    Thank you!
     
  5. Oct 5, 2009 #4

    arildno

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    Or, you could do as follows:
    Introduce:
    [tex]x=u^{6}\to\frac{dx}{du}=6u^{5}\to{dx}=6u^{5}du[/tex]
    Then,
    [tex]\int\frac{dx}{\sqrt{x}-\sqrt[3]{x}}=\int\frac{6u^{5}}{u^{3}-u^{2}}du=\int\frac{6u^{3}}{u-1}du=6\int({u}^{2}+u+1+\frac{1}{u-1})du[/tex]
    which is easily integrated.
     
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