Hello everyone! In this article, we will go over how to take the integral of $\dfrac{x-1}{x+1}$. The technique shown in this article can also be used for integrating many fractions of rational equations, so it’s definitely a handy tool to know.

Taking the Integral of x-1 over x+1

We will start expressing $\dfrac{x-1}{x+1}$ in a different way. This is the most important part of this integral:

$\dfrac{x-1}{x+1} = \dfrac{x+1-2}{x+1} = 1 + \dfrac{-2}{x+1}$.

Now, we can integrate:

$\displaystyle \int 1 + \dfrac{-2}{x+1} dx = x + -2 \cdot \ln|x+1| + C$.

And that’s it! We have successfully taken the integral.

Conclusion

The technique of splitting the integrand into two fractions is very important when integrating rational functions, whether you have to use integration by partial fractions or the technique outlined above. It is definitely a good idea to try this if you’re confused on how to solve a difficult integral. Good luck on your future math adventures!