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Simple integration

  1. Sep 13, 2009 #1
    Cannot figure out the integral of : v/(v-1)^2


    I tried partial fractions then integrating but didn't get me anywhere! HELP!
     
  2. jcsd
  3. Sep 13, 2009 #2

    gabbagabbahey

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    Partial fractions should work...why not post what you've got?
     
  4. Sep 13, 2009 #3
    Try to solve for A and B: v/(v-1)^2 = A/(v-1) + B/(v-1)^2
     
  5. Sep 13, 2009 #4
    simplest solution:

    let t=v-1
    dt =dv
    function now becomes Integrate[(t+1)^2/t dt]

    no partial fractions needed
     
  6. Sep 13, 2009 #5
    If the original integral is:


    [tex]\int{\frac{v}{(v-1)^2}}[/tex]

    [tex]t=v-1 ; v=t+1[/tex]

    [tex]dv=dt[/tex]

    [tex]\int{\frac{t+1}{t^2}[/tex]

    Now separate on two fractions and solve two integrals.
     
  7. Sep 13, 2009 #6
    yeah.. sorry for tht mistake :P
     
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