Is it possible to integrate this new function?

[dowjonez]

Doing a friction fluid denisty question and have to figure out why it can't be done.

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



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

d(1-v) / (1 - v^4) = dt is it possible to integrate that?

 

[Tide]

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

-\frac {1}{2} \tan^{-1}v - \frac {1}{4}\frac{\ln v -1}{\ln v + 1}