I want to ask something about: 

"Since $i \log\_e i$ is concave upwards, it is easy to show that $$\sum\_{i=2}^{n-1} i \log\_e i \leq \int\_2^n x \log\_e x \,dx \leq \frac{n^2 \log\_e n}{2}-\frac{n^2}{4}$$" 

$i \log\_e i$ is concave upwards because the second derivative of $i \log\_e i$ is positive. Correct? 

Can you explain the inquality? I don't understand how we show it?