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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


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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


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    Homework Helper
    Gold Member

    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


    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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