Integral without using Euler substitution Help me please with integral:
$$\int \frac{2x-\sqrt{4x^{2}-x+1}}{x-1}\;dx$$
I must solve it without using  Euler substitution.
Thanks!

Hint: writing 
$$\frac{2x-\sqrt{4x^2-x+1}}{x-1}=\frac{2x-\sqrt{4x^2-x+1}}{x-1}\frac{2x+\sqrt{4x^2-x+1}}{2x+\sqrt{4x^2-x+1}},$$
we find $$\frac{2x-\sqrt{4x^2-x+1}}{x-1}=\frac{4x^2-(4x^2-x+1)}{(x-1)(2x+\sqrt{4x^2-x+1})}=\frac 1{2x+\sqrt{4x^2-x+1}}.$$
