Question

Integration of 2v/(1-v)

Answer 1

v^2/1-v is the answer

Answer 2

Integration of 2v / (1-v) is 2( 1 – v ) – 2 ln ( 1 -v )

• We have to calculate∫▒〖2v dv/(1-v)〗                    ……..(i)

• let (1-v) = t

differentiating both sides ,

-dv = dt            ……………..(ii)

• putting value from (ii) to (i) and after manipulation,

∫▒〖2(t-1)dt/t〗 =  ∫▒〖2 dt〗 - ∫▒〖2 dt/t〗

                        = 2t – 2 ln t

• putting t = 1-v  we get,

2(1-v) – 2 ln (1-v)