1$ /* describe(substitute) */$

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

g(u):=substitute(u/2,x,f(x))$ g(u);

h(u):=substitute(1-cos(u)^2,sin(u)^2,g(u))$ h(u);

w(v):= substitute(v,cos(u),h(u))$ w(v);

xi(v):=substitute(acos(v),u,w(v))$ xi(v);

integrate(xi(v),v);