Quick integration question

  1. Doing a friction fluid denisty question and have to figure out why it cant be done.

    d(1-v) / (1-v) = dt would integrate to ln |1-v| = t + c



    now im faced with the same integration but the function has changed and now im staring a

    d(1-v) / (1 - v^4) = dt is it possible to integrate that?
     
  2. jcsd
  3. Tide

    Tide 3,137
    Science Advisor
    Homework Helper

    Yes. First, write [itex]1-v^4[/itex] as [itex](1-v^2)((1+v^2)[/itex] then do a partial fraction decomposition. Also, rewrite d(1-v) as -dv and you should end up with something like

    [itex]-\frac {1}{2} \tan^{-1}v - \frac {1}{4}\frac{\ln v -1}{\ln v + 1}[/itex]
     
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