Question

求证limx->+∞ f(x)=0

Answer 1

f(x)=∫{0,1/2}lnt*t^x/(t-1)*dt+∫{1/2,1}lnt*t^x/(t-1)*dt=∫{0,1/2}[t/(t-1)*lnt]*t^(x-1)dt+∫{1/2,1}[lnt/(t-1)]*t^xdt=A(x)+B(x).

在(0,1/2)内,|t/(t-1)*lnt|