Question

How do you evaluate the integral `int (x-1)/(x+1)dx`?

Answer 1

`int (x-1) / (x+1) dx = x -2lnabs(x+1) +C`

Explanation:

Split the integrand function:

`int (x-1) / (x+1) dx = int (x+1-2) / (x+1) dx = int (1-2/(x+1))dx`

Using the linearity of the integral:

`int (x-1) / (x+1) dx = int dx -2 int dx/(x+1)`

These are standard integrals that we can solve directly:

`int (x-1) / (x+1) dx = x -2lnabs(x+1) +C`