$\int \frac{x}{x-1}dx$ integral | What is the integrate of x/x-1 ?

Hello everyone. This lesson we will tell the integrate of $\int \frac{x}{x-1}dx$.

What is the integral of x/x-1?

integral of x/x-1

First we separate the expression.

So;

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

So our answer;

$\int \frac{x}{x-1}dx=\int 1 dx+ \int \frac{1}{x-1}dx=x+ln|x-1|+C$