How can I integrate a fraction of polynomials using polynomial division?

[Mikael Lindberg]

Hi Everyone,
I ended up here when I was searching the web to find out how to integrate x/(x-1). The explanations and the attitude towards learning and instructing made me feel like this is the place to be! Looking forward to explore the universe with you all!

 

[micromass]

$x = (x-1) + 1$

 

[Mikael Lindberg]

There is actually a thread about that integral that I would suggest: https://www.physicsforums.com/threads/how-do-you-integrate-x-x-1.525399/

 

[micromass]

More generally, if you have a fraction of polynomials which you want to integrate, then the first thing you want to do is polynomial division to ensure that the degree of the denominator is strictly smaller than the degree of the numerator.