Boundary Values & Fourier Series · Superchallenge problem

A rod $0 \le x \le \pi$ obeys $u_t = u_{xx}$ with $u(0,t) = u(\pi,t) = 0$ and $u(x, 0) = x(\pi - x)$. Find $\displaystyle\int_0^\infty\!\!\int_0^\pi u_x(x,t)^2\,dx\,dt$.