Question

How to integrate (1+2z)/(1-z^2) dz.

Answer 1

hint : 1-z^2 = (1+z)(1-z)

Answer 2

So partial fractions?

Answer 3

You could use partial fractions
or you could write
\[\frac{1+z+z}{1-z^2}=\frac{1+z+z}{(1-z)(1+z)}=\frac{1+z}{(1-z)(1+z)}+\frac{z}{1-z^2}\]
but partial fractions works too