I have a homework problem that I can't get started on, below is the first bit. I feel like I should just be able to integrate to find $C$ but I get a divergent integral. Can someone give me a hint as to where to go here?
A particle of mass m is in a one-dimensional inﬁnite square well, with $U = 0$ for $0 < x < a$ and $U = ∞$ otherwise. Its energy eigenstates have energies $E_n = (\hbar πn)^ 2/2ma^2$ for positive integer $n.$ Consider a normalized wavefunction of the particle at time $t = 0$ $$ψ(x,0) = Cx(a − x).$$ Determine the real constant $C$.