How does doing a U- Substitution come out with this outcome?

Question

I saw this on a website. I am working on Integrals and the U-Substitution didn't make sense.

The original problem was $\int$x/x+1$dx$

The U-Sub did u = x+1 , du = dx

then it gave me a $\int$u-1/u du...

How did the u-1 become on the numerator is my question?

Answer 1

By the way it becomes easier to do this integral by writing it as $$\int \frac{x+1-1}{x+1}dx=\int 1-\frac1{x+1} dx$$ The latter integral can easily be performed as $$\frac{d}{dx}\ln{(x+1)}=\frac1{x+1}$$