kill(all)$

van=facebook.com/LearningCalculus;

f(x):=log(tan(x))/(%pi+cos(2*x));

integrate(f(x),x)=(-%i*li[2](-(%i*(-1+%pi)*tan(x))/sqrt(-1+%pi^2))+
                    %i*li[2]( (%i*(-1+%pi)*tan(x))/sqrt(-1+%pi^2))+
                      2*atan( (   (-1+%pi)*tan(x))/sqrt(-1+%pi^2))*log(tan(x)))/(2*sqrt(-1+%pi^2));