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!
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 $\frac{2x-\sqrt{4x^2-x+1}}{x-1}=\frac{4x^2-(4x^2-x+1)}{(x-1)(2x+\sqrt{4x^2-x+1})}=\frac 1{2x+\sqrt{4x^2-x+1}}.$