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Integral of fraction - is this correct?

  1. Apr 11, 2009 #1
    I am trying to find the integral of the following:

    [tex]\int\left({\frac{3 + 5x - 6x^2 - 7x^3}{2x^2}}\right)dx[/tex]

    What I did was to split up the fraction like so:

    [tex]\int\left({\frac{3}{2x^2}}\right)dx + \int\left({\frac{5x}{2x^2}}\right)dx + \int\left({\frac{6x^2}{2x^2}}\right)dx + \int\left({\frac{7x^2}{2x^2}}\right)dx [/tex]

    Simplified the fractions, worked out each integral then added them to get:

    [tex]-\frac{3}{2x} + \frac{5}{2}\ln x - 3x - \frac{7}{4}x^2 + c[/tex]

    The text I am using has no answers and when I tried to use the integral calculator at http://www.numberempire.com/integralcalculator.php I get an answer that is a fraction.

    Am I correct and is the process I used to solve this correct?

    Thanks.
     
    Last edited: Apr 11, 2009
  2. jcsd
  3. Apr 11, 2009 #2

    tiny-tim

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    (use "\left(" and "\right)" for big brackets :wink:)

    ?? :confused:

    I used that calculator and got

    (10*x*log(x)-7*x^3-12*x^2-6)/(4*x)
     
  4. Apr 11, 2009 #3
    I got that too but I don't know where I went wrong with my calculation...
     
  5. Apr 11, 2009 #4

    arildno

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    Yes, your answer is correct.

    It is also equivalent to that fraction, as far as I can see.
     
  6. Apr 11, 2009 #5
    Great.

    And thanks for the tip on the brackets.
     
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