# Integration by substitution?

1. Jan 11, 2008

### cabellos6

1. The problem statement, all variables and given/known data
I want to integrate (1+x)/(1-x)

2. Relevant equations

3. The attempt at a solution
I have looked at many examples of substitution method - this one appears simple but Im not finishing the last step.....

- I know you must first take u=(1-x)
- Then du = -dx

what happens with the numerator (1+x) as this would be the integral of -(1+x)du/u

id be very grateful if you could run me through the steps for this please.

thanks

2. Jan 11, 2008

### HallsofIvy

Staff Emeritus
You need to simplify the fraction first: dividing 1+ x by 1- x gives -1+ 2/(1-x)= -1- 2/(x-1). It's easy to integrate "-1" and to integrate -2/(x-1), let u= x-1.