How do you integrate?

Question

v/(1-v)?

Answer 1

Here is my little trick again.

Write v/(1-v) = (v-1+1)/(1-v) = (v-1)/(1-v) + 1/(1-v)
= -1 + 1/(1-v)

Integrate that to get
v - ln(1-v) + constant

Answer 2

Here it goes:

v/(1-v)

Let u=1-v, then v=1-u, du=-dv

Then,

(u-1) du

=((u^2)/2) - (u) +c

=(((1-v)^2)/2) - (1-v) +c

which is the required answer!!!

Answer 3

-v - ln(1-v) +C

Doug