integral u/(u+1) du =……

[tex]\int \frac{u}{u+1}$ du$ \\ \int 1-\frac{1}{u+1}$ du$ \\ u-\ln(u+1)+C[/tex]

[tex]\int \frac{u}{u+1}du \\ \\ = \int \frac{u+1-1}{u+1}du \\ \\ = \int \frac{u+1}{u+1}du - \int \frac{1}{u+1}du \\ \\ = \int du - \int \frac{1}{u+1}du \\ \\ = u - ln(u+1) + C[/tex]