Integration by substitution for (1+x)/(1-x)

[cabellos6]

Homework Statement

I want to integrate (1+x)/(1-x)

Homework Equations

The Attempt at a Solution

I have looked at many examples of substitution method - this one appears simple but I am 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

 

[HallsofIvy]

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.