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?
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]