wave equation neumann bvp

[akoaysigod]

u_tt = c^2 u_xx
u_x(0,t) = u_x(pi, t) = 0 0 < x < pi
u(x, 0) = 0
u_t(x, 0) = (cosx)^2

then using separation of variables, etc., the general solution is

u(x,t) = 1/2 A0 + 1/2B0t + sum[AN cos(n*pi*c*t/l) + BN sin(n*pi*c*t/l)]cos(n*pi*x/l)

Then using the conditions I've decided that AN must be 0. Leaving only

u = 1/2B0t + sum[BN sin(n*c*t)cos(nx)] then
u_t(x, 0) = .5B0 + sum[BN n*c cos(nx)] = (cosx)^2

But when I try to find the coeffecients

2/pi int(0, pi) [(cosx)^2cos(nx) dx]

I get just 0. Where did I go wrong? I uploaded a picture of some of this because I know what I'm trying to say but I always have a hard time reading text versions of math.


Oh no, I feel stupid. I figured it out after much frustration.