format long;

f = @(x) cos(x.^(-1).*log(x))./x;

q = zeros(1,1);
I = zeros(1,1);
count = 1;
for n=200:200:2000
    a = zeros(n,1);
    a(1) = 0;
    for j=2:n+1
      b = fzero(@(x) x*exp(x)-(i-1/2)*pi,0);
      a(j) = exp(-b);
    end
    q = q + integral(f,a(2),1);
    for u=1:n
        q = q + integral(f, a(n+1),a(n));
    end
    I(count) = q;
    count = count +1;
end