Derive the seven stress resultants integrating

Question

Response to the following problem:

Given the following stresses

σ_x = A^k z sin (αx) sin (βy)

σ_y = B^k z sin (αx) sin (βy)

σ_xy = 0

σ_yz = Q^k sin (αx) cos (βy)

σ_xz = R^k cos (αx) sin (βy)

Where k = 1 . . . N, N is the number of laminae, and A_k, B_k, Q_k, and R are constants, derive the seven stress resultants integrating over the thickness of a laminated plate with N = 3, t₁ = t₂ = t₃.