Solving an indefinite integral of the form ∫xcos(αx+β)dx by the method of integration by parts, where α takes the values 1,2,3,4,5,…n; β takes the values ±1,±2,±3,±4,±5,…m.
An example of solving integrals for α=1, β=4 is considered; α=2, β=−4; α=3, β=−2; α=4, β=2
∫xcos(αx+β)dx, ∫xcos(x+4)dx, ∫xcos(2x−3)dx, ∫xcos(3x−2)dx, ∫xcos(4x+2)dx

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