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

We have to integrate $\int \frac{x-1}{x+1}$

### Solution

$\int \frac{x-1}{x+1}$

We will split the integrand function

$\int \frac{x+1-2}{x+1} dx$ $\int 1 -\frac{2}{x + 1} dx$

Using the linearity of the integral

$\int \frac{x-1}{x+1} =\int dx – 2\int \frac{dx}{x+1}$

These are standard integrals that we can solve directly

$\int \frac{x-1}{x+1} = x – 2\ln \left | x+1 \right | + C$

$\int \frac{x-1}{x+1} = x – 2\ln \left | x+1 \right | + C$