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Rational function integral

  1. Jun 5, 2006 #1
    how to calculate the calculus of this rational function:

    [tex] \int \frac{dx}{{x+x^6}} [/tex]

    could anyone get me through the solution?!
     
    Last edited: Jun 5, 2006
  2. jcsd
  3. Jun 5, 2006 #2

    TD

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    Hint:

    [tex]\frac{1}{{x + x^6 }} = \frac{1}{{x\left( {1 + x^5 } \right)}} = \frac{{\frac{1}{{x^6 }}}}{{\frac{{1 + x^5 }}{{x^5 }}}} = \frac{{\frac{1}{{x^6 }}}}{{\frac{1}{{x^5 }} + 1}}[/tex]
     
  4. Jun 5, 2006 #3
    so final result:

    -0.2* ln(1+x^-5)


    is that right?
     
    Last edited: Jun 5, 2006
  5. Jun 5, 2006 #4

    benorin

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  6. Jun 6, 2006 #5

    TD

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    Indeed, if you don't forget the constant of integration :wink:
     
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