In[2]:= NIntegrate[Sin[Pi x]/Log[x], {x, 2, Infinity}]

NIntegrate::ploss:
   Numerical integration stopping due to loss of precision. Achieved neither
    the requested PrecisionGoal nor AccuracyGoal; suspect one of the
    following: highly oscillatory integrand or the true value of the integral
    is 0. If your integrand is oscillatory on a (semi-)infinite interval try
    using the option Method->Oscillatory in NIntegrate.

                   73
Out[2]= -5.68811 10