\lim_{x\to + \infty}\frac{x \cdot \ln (x^2) }{x^2 + x + 1} = [ \frac{: x^2}{: x^2}] = \lim_{x\to + \infty}\frac{\frac{x \cdot \ln (x^2) }{x^2} }{\frac {x^2 + x + 1}{x^2}}