# Complete the square doesn't work here.

In this substitution, I tried the method of complete the square, but at the end the answer is not correct. I'm totally sure that the answer is: $\frac{2\sqrt{7}}{7}\arctan(\frac{\sqrt{7}(2x-1)}{7})+C$, and I try different techniques, but I can´t get this result.

This is the Integral:

$\int\frac{dx}{x^2-x+2}$

• Look at my generalised answer here and check – Oussama Boussif Aug 26 '15 at 15:23

Since $$\int\frac{du}{u^2+a^2}=\frac{1}{a}\arctan\left(\frac{u}{a}\right)+C$$