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

∫(αx+β)cos(x/γ)dx, ∫(x−2)cos(x/3)dx, ∫(2x−2)cos(x/4)dx, ∫(3x+1)cos( x/5)dx, ∫(4x+3)cos(x/2)dx

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