First rule of integrating non-analytic functions: If they're analytic everywhere in the interval in question except a finite number of points, split the integra

First rule of integrating non-analytic functions: If they're analytic everywhere in the interval in question except a finite number of points, split the integral and compute it one analytic segment at a time! (Second rule: If the function is non-analytic at an infinite number of points, you probably still want to compute it one segment at a time, but adding them back together afterwards may get messy.)