(%i1) integrate(cos(%pi*s)/((1-m*cos(%pi*s))^2,s,0,x);
Is x positive, negative, or zero? positive;
Is m^2-1.0 positive or negative? negative;
Is x-1 positive, negative, or zero? zero;
(%o1) -m*sqrt(1-m^2)/(m^4-2*m^2+1)
But the right answer should be m*sqrt(1-m^2)/(m^4-2*m^2+1)
My maxima verion is 5.21.1
Lisp: GNU Common Lisp(GCL) GCL 2.6.7