I need help proving this inequality.
$\int_{1}^{2} \left(\frac{x+1}{2} \right)^{x+1} \ dx < \int_{1}^{2} x^x \ dx$
Normally I would define $f(x) = \left(\displaystyle\frac{x+1}{2} \right)^{x+1}$ and $g(x) = x^x$ and try to compare those two.
Any suggestions?