General methods of calculating indefinite integrals of the type ∫xnA(p)B(q)dx are pre-sented, where A and B are solutions of the Airy equition y" = (λ + x)y with the para-meterλ, p, q are the order of differential, n is a non-negative integer. General formulae of this type of integrals is given for corresponding p, q ≤1 and functions A, B with dif-ferent parameters. For A=B a method of integration is also obtained, which is quite dif-ferent from that of Albright. As an application, these formulae of integrals are applied to the problem of the orthonormalization of the wave functions of an electron in a triangular potential well, and the transition probabilities between the energy-levels are obtained.