Question

How do you integrate `(1+x) /(1+ x)^2 dx`?

Answer 1

This is quite easy, as you can simplify the fraction as follows:
`(1+x)/(1+x)^2=1/(1+x)`
To do this, you have to point out that the domain of the function is `D=(-infty,-1) cup (-1,+infty)`.

Now you can integrate
`int (1+x)/(1+x)^2 dx=int 1/(1+x) dx = ln|1+x|+C`