$\underset{n\rightarrow +\infty }{\overset{}{\lim }} \ \frac{10^{\sqrt{(\ln n)^{2} +\ln( n^{2}})}}{n^{2} +1} =+\infty$

Prove that:

$ $ \underset{n\rightarrow +\infty }{\overset{}{\lim }} \ \frac{10^{\sqrt{(\ln n)^{2} +\ln( n^{2}})}}{n^{2} +1} =+\infty$ $

It is an exercise on first chapters of calculus textbook. I think it is possible to solve without integral or others advanced methods.