I'm not sure I understand your statement. I know that a wave function can be either classified as sines and cosines or as exponentials, I haven't yet seen a wave function that includes a integral before.
Homework Statement
5) A free particle moving in one dimension is in the state
Ψ(x) = ∫ isin(ak)e(−(ak)2/2)e(ikx) dk
a) What values of momentum will not be found?
b) If the momentum of the particle in this state is measured, in which momentum
state is the particle most likely to be found?
c)...