P panky Jul 2011 408 16 Jan 27, 2020 #1 If $\displaystyle I=\int^{2}_{0.5}\frac{\ln(t)}{1+t^n}dt.$ Then the sign of integral for different values of $n\in \mathbb{N}\cup0.$

If $\displaystyle I=\int^{2}_{0.5}\frac{\ln(t)}{1+t^n}dt.$ Then the sign of integral for different values of $n\in \mathbb{N}\cup0.$