kill(all);

van=facebook.com/LearningCalculus$

f(x):=(1-cos(x)^2)/(5-4*cos(x));

'integrate(f(x),x) = changevar('integrate(f(x),x),u-cos(x), u, x);

g(u):=(sqrt(1-u)*sqrt(u+1))/(4*u-5);

G(u):=''(integrate(g(u),u));

F(x):=''(subst(cos(x),u,G(u)));

F(%pi)-F(0);