determine whether the integral diverges or converges

if it converges then evaluate the integral

integral from 0 to infinity: xe^-(x^2) dx

integral from 0 to 1: xln(x) dx

integral from 1 to infinity: (ln t) / (t^2) dt

integral from 0 to 2: 1 / (t-1) dt

i have solved the first integral and i got the answer as 1/2 but how do i show if it is diverging or converging?