1. The problem statement, all variables and given/known data http://img4.imageshack.us/img4/4224/landau.png [Broken] http://g.imageshack.us/img4/landau.png/1/ [Broken] Note: do = 2*pi*sin(x) dx Well, as you can see this is an extremely painful integral. 2. Relevant equations 3. The attempt at a solution I have tried u = cos(1/2x) resulting in: du = -sin(1/2 x) (1/2) dx sin(x) = 2*sin(x/2)*cos(x/2) (n^2 u - nu^2 - n + u)/(n^4 + 2n^2 - 4n^3 u + 4n^2 u^2 - 4nu) (by expanding both the top and bottom, but as you can see it's messy and useless, I'm also dropping the constant because I don't care about them right now). I have no idea what kind of substitution to use for these beast... It evaluates to pi*a^2 with the integration limits 0 to X_max.. Anyone have any idea how to do this by hand? I am tempted to use Matlab, but I really am supposed to do it manually.