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Solve the integral 1/(1+x^3) dx

  1. Jul 29, 2010 #1
    I try to solve the integral 1/(1+x^3) dx , but I got stuck

    Now I got as solution:

    (1/3) ln(x+1) - (1/6) ln(x^2 -x+1) + (1/2) integral (1/(x^2 -x+1))

    Can someone help me to solve the last integral? I have absolutely no idea how I can solve that one..

    So integral: 1/(x^2 -x+1) dx
     
  2. jcsd
  3. Jul 29, 2010 #2

    arildno

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    Re: Integral

    Write:
    [tex]\frac{1}{x^{2}-x+1}=\frac{1}{(x-\frac{1}{2})^{2}+\frac{3}{4}}=\frac{4}{3}\frac{1}{(\frac{2x-1}{\sqrt{3}})^{2}+1}[/tex]
     
  4. Jul 29, 2010 #3
    Re: Integral

    Thank you very much!
     
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