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Rational Integral

  1. Mar 14, 2013 #1
    1. The problem statement, all variables and given/known data
    evaluate the integral.


    2. Relevant equations
    [itex]\displaystyle\int_2^∞ {\frac{2}{v^2 -v} dv}[/itex]


    3. The attempt at a solution
    how does this integrate into:

    2 ln| [itex]\frac{v-1}{v}| [/itex]

    i tried and got 2ln|v^2-v| but not above.
     
  2. jcsd
  3. Mar 14, 2013 #2

    LCKurtz

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    Science Advisor
    Homework Helper
    Gold Member

    Did you try factoring and partial fractions?
     
  4. Mar 14, 2013 #3
    Try simplifying the denominator and using the method of partial fractions. Ahhh beaten to the punch!
     
  5. Mar 14, 2013 #4

    epenguin

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    Also since you know (knew?) the answer, differentiate it and you see what is right and may get some helpful insight and reinforcement.
     
  6. Mar 14, 2013 #5

    Mark44

    Staff: Mentor

    Others have shown you the right way - I'll explain what you did that was wrong.

    These are correct:
    $$\int \frac{dx}{x} = ln|x| + C$$
    $$\int \frac{du}{u} = ln|u| + C~$$

    BUT, this is NOT correct:
    $$\int \frac{dx}{f(x)} = ln|f(x)| + C$$

    This is a very common error among students who are learning calculus.
     
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