P versus NP is considered as one of the most important open problems in computer science. This consists knowing answer following question: Is equal to NP? It was essentially mentioned 1955 from a letter written by John Nash United States National Security Agency. However, precise statement problem introduced independently Stephen Cook and Leonid Levin. Since that date, all efforts find proof fo...

We establish some inequalities involving $\log(1+x)$ using elementary techniques. Using these inequalities, we show an alternate approach to evaluate the integral $\int\limits_1^\infty \frac{\log t}{t^2}\,dt$. This is later used asymptotic value of a logarithmic sum.