How to integrate a/1-a?

Integrate a / (1-a)

Let U=1-a

then a=1-U

da = - dU

a / (1-a) = (1-U) / U = (1/U) - 1

The integral of [ (1/U) - 1 ] dU = (1 - 1/U) (-dU) = U - ln (U) = (1-a) - ln (1-a) + C

A / (1-a) = [1-a-1]/1-a

so=[1-a]/[1-a]-1/[1-a]=1-{1/[1-a]}

so 1ntegration of this

so

integration of 1. da - integration of 1/[1-a]. da

now suposse

1-a=t

so

by diff

-da=dt

so

a

integration of a-integration of - 1/tdt

a+ln (t) + c

substituting the value of t

a+ln (1-a) + c