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Homework Help: Please confirm the answer for this integral

  1. Sep 22, 2007 #1
    Can anyone confirm that the answer
    for int (1/x(x-1))dx


    - ln|x|+ ln |x-1| + c using partial fractions?

    Thank you.
  2. jcsd
  3. Sep 22, 2007 #2


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    Staff Emeritus
    Science Advisor

    How about expanding [tex]\frac{1}{x (x-1)}[/tex] into

    [tex] \frac{A}{x}\,+\,\frac{B}{x-1}[/tex] and solve for A and B

    then solve the integral
  4. Sep 22, 2007 #3


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    Science Advisor

    Can't you "confirm" it yourself by differentiating? The derivative of -ln |x|+ ln|x-1|+ c
    (assuming for the moment that x> 1 so both x and x-1 are positive) is -1/x+ 1/(x-1)= -(x-1)/(x(x-1))+ x/(x(x-1))= 1(x(x-1)). (You might want to combine those two logarithms.)

    I suspect that is exactly what he did! Doing it again is not a "check".
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