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Trouble with the integral Help

  1. Nov 11, 2011 #1
    Trouble with the integral!! Help

    While I was working some examples of integrals from book, I found this example:

    [itex]\int {{x^3-1}\over{4x^3+x}}[/itex]
    and I can not solve it, because I get always incorrect result.

    Result is: (from book)

    [itex]{x \over 4}+{{x \over 16}*{ln ({{x^{16}}\over{(2x-1)^7(2x+1)^9}}})}[/itex]

    Can you help me solve it!!

    Thanks.
     
  2. jcsd
  3. Nov 11, 2011 #2

    gb7nash

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    Homework Helper

    Re: Trouble with the integral!! Help

    Before you do anything with the integral, take polynomial long division, since the degree of the numerator >= degree of the denominator.
     
  4. Nov 11, 2011 #3
    Re: Trouble with the integral!! Help

    You can notice x^3 - 1 is of the form "a^3-b^3". You can factorize ;) !

    And you can factorize: 4x^3 + x.

    It is a partial fraction.

    Good luck ;) !
     
  5. Nov 12, 2011 #4
    Re: Trouble with the integral!! Help

    Thank you!!
     
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