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